Breaking Dense Integration Limits: Inverse-Designed Lithium Niobate Multimode Photonic Circuits

Breaking Dense Integration Limits: Inverse-Designed Lithium Niobate Multimode Photonic Circuits | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Article Breaking Dense Integration Limits: Inverse-Designed Lithium Niobate Multimode Photonic Circuits Haojie Xia, Xu Han, Hu Jiang, Jie He, Zixu Zhu, Jiahui Su, Mei Xian Low, and 11 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7481144/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 21 Dec, 2025 Read the published version in Nature Communications → Version 1 posted You are reading this latest preprint version Abstract Despite the growing interest in thin film lithium niobate (TFLN) as a material platform for photonic integrated circuits (PIC), its moderate refractive index, CMOS-incompatible fabrication processes and inherent material anisotropy still raise questions about achieving dense integration comparable to mature platforms like silicon photonics while preserving the superior properties of lithium niobate. In this paper, we employ photonic inverse design method to enable miniaturization and dense integration of lithium niobate PIC components. As proofs-of-concept, we design, fabricate, and experimentally demonstrate mode-division (de)multiplexer (19×25 µm²), multimode waveguide crossing (15×15 µm²), and waveguide bends (30 µm bending radius) in TFLN, achieving a device footprint reduction by an order of magnitude compared to conventional counterparts. The fabricated components are used to construct ultra-compact multimode photonic circuits for large-capacity data communications, demonstrating dense integration of over 10 waveguide elements within a 0.06 mm² chip area. By integrating electro-optic modulators on the same chip, high-speed data modulation is demonstrated with 120 Gbps data rate per channel alongside multimode signal transmission. This work is expected to advance more than 10-fold higher area density of passive components and optical path design in TFLN, paving the way for scalable on-chip multimode photonic systems. Physical sciences/Optics and photonics/Applied optics/Integrated optics Physical sciences/Optics and photonics/Applied optics/Optoelectronic devices and components Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Introduction Modern photonic integrated circuits (PICs) are undergoing a paradigm shift toward dense integration, which is essential for scaling bandwidth, minimizing energy per bit, and supporting on-chip convergence of diverse optical functionalities 1 . Achieving such advancements requires photonic platforms that offer not only high index contrast but also wide spectral transparency, strong nonlinear and electro-optic properties 2 . Conventional silicon, silicon nitride and III–V platforms, while mature in CMOS-compatible processes, face inherent limitations in nonlinear performance, electro-optic response, or material transparency. In this context, thin-film lithium niobate on insulator (TFLNOI) has emerged as a promising alternative that combines wide optical transparency window, strong nonlinear optical performance and high-speed electro-optic modulation 3,4 . Recent advances in TFLNOI-based electro-optic modulators have demonstrated unprecedented 100 GHz bandwidths and near-1 V driving voltages at different wavelength ranges 5,6 , enabling more than a tenfold footprint reduction compared to bulk lithium niobate counterparts. These breakthroughs, driven by applications such as terabit per second optical communications 7 , precision optical metrology 8 and quantum photonic processors 9 , position TFLNOI as a versatile platform for multifunctional photonic systems. However, the relatively modest refractive index contrast in TFLNOI waveguides, especially those fabricated with partial etching, inherently limits the mode confinement 10 . Thus, device dimensions such as waveguide bending radius face limitations, which constrain the achievable chip integration density and challenge the scalability demands of large-scale PICs. To bridge the gap between TFLNOI's exceptional material properties and dense chip integration, advanced photonic design methods are emerging as powerful tools toward compact footprints while maintaining compatibility with fabrication processes. Inverse design, which leverages intelligent optimization algorithms to explore vast parameter space, can significantly improve multistage efficiency in device design, simulation and fabrication by enabling fast creation of complex optical structures, e.g. metasurface, with ultra-compact size, unprecedented precision and functionality 11,12 . Significant breakthroughs have been achieved in silicon photonics during the last few years, with the device footprint scaled-down to micron level, paving the way to densely integrated on-chip optical systems 13-16 . However, to obtain inverse-designed PIC components and complex optical systems in TFLNOI, the inherent barriers of material, method and fabrication process are particularly intractable. First, an X-cut TFLNOI platform experiences refractive index anisotropy in the y / z plane, and the traditional scalar-based inverse design methods are inappropriate to address the scenarios of anisotropic material. Although a Z-cut TFLNOI platform can avoid the material anisotropy in the plane of lithium niobate thin film 17 , the access to strong electro-optic coefficient of lithium niobate ( r 33 ) requires to lay out electrodes vertically, which is inconvenient for chip integration. Second, a tensor-based inverse design method can be extended to the X-cut TFLNOI platform by considering the impact of material anisotropy of lithium niobate 18 . However, a computational complexity increase is inevitable compared to that of traditional scalar-based inverse design methods, which brings higher requirements for computing resources and simulation time. Third, the generally used physical direct etching method for TFLNOI can induce a slanted waveguide sidewall which limits the device feature size 19 , resulting in significant degradation and variability in device performance. Thus, the inverse designed lithium niobate photonics requires an overall optimization to overcome the material anisotropy and limited device feature size, while reserving the access to excellent material properties of lithium niobate. As shown in Figure 1a, we demonstrate inverse-designed high density multimode photonic circuits for high-speed and large-capacity data communications in a silicon nitride-TFLNOI (X-cut) hybrid platform. Integrated multimode photonics can enable large-scale signal parallelism and enhance the information capacity of PICs by introducing higher-order waveguide modes as data carriers 20 , which has also attracted attention in optical computing 21 , sensing 22 and spectroscopy 23 . Unfortunately, the arbitrary routing of multimode signals is usually built in a large chip area even in high-indexed material platform, due to the radiation leakage and inter-mode coupling 14 . As shown in Figures 1b-d, we design, fabricate and experimentally demonstrate an optical mode-division (de)multiplexer (19×25 μm 2 ), a multimode waveguide crossing (15×15 μm 2 ) and a multimode waveguide bend (30 μm bending radius) for the first three quasi-transverse electrical modes (TE 0 , TE 1 and TE 2 ). The measured insertion losses are lower than 2.5 dB at the wavelength of 1550 nm, while the mode crosstalk stays below -15 dB at a wavelength range from 1530 nm to 1570 nm. These components are used to construct ultra-compact photonic circuits, enabling arbitrary routing of multimode signals through dense integration of more than 10 waveguide elements within a 0.06 mm 2 (200 × 300 μm²) chip area. To demonstrate the advancement in combination of high integration density with excellent material properties, a high-speed data modulation and transmission system is implemented through the monolithically integration of electro-optical modulators and multimode photonic circuits. The single-channel data modulation and transmission rate for on–off key signal reaches up to 120 Gbps. Results Waveguide platform. Silicon nitride is selected as an isotropic optical loading material. Thus, the optical structures in the loading layer can be optimized using scalar-based inverse design method and fabricated by mature silicon nitride etching processes, enabling improved design efficiency and well controlled device feature size. Though there are also other available loading materials, such as silicon, polymers and chalcogenide glasses, silicon nitride can offer similar but slightly lower refractive index than lithium niobate, enabling high mode confinement in the lithium niobate thin film, similar optical transparency window and mature fabrication process compared with lithium niobate 24 . The silicon nitride-TFLNOI (X-cut) hybrid platform is designed to avoid the direct etching of lithium niobate thin film, while providing a high mode confinement factor (~60%) in lithium niobate. The layers from top to bottom are air cladding, silicon nitride loading layer, lithium niobate slab, buried oxide layer and silicon substrate, respectively. The thicknesses of the silicon nitride and lithium niobate layers are both 300 nm, which avoids the mode lateral leakage at second-harmonic wavelengths 25 . The thickness of the buried oxide layer is selected as 4.7 μm to ensure index match and a relatively low radio-frequency loss for electro-optic modulation. Mode (de)multiplexer. Mode (de)multiplexers serve as critical PIC components to enable parallel propagating of multimode signals in a single waveguide. Previous works in TFLNOI platform are generally based on directional coupler structures by forward design 26-29 . In this case, the low-loss and low-crosstalk mode coupling relies on strict control of phase and mode field distribution, requiring a large device footprint. In contrast, in this contribution we employ the inverse design method to implement a three-mode (de)multiplexer with an ultra-compact effective size of only 19×25 μm 2 . Figures 2a and 2b show an illustration and a scanning electron microscope (SEM) image of the device structure which is designed and fabricated by patterning the silicon nitride layer. By considering the anisotropy of lithium niobate, the device is designed along the crystallographic Z direction to avoid the mode hybridization between TE 1 and TM 0 modes 30 . The widths of the input single-mode waveguides and output multimode waveguide are designed as 1 μm and 4.3 μm, while the gaps between the adjacent input waveguides are 2 μm. A near vertical waveguide sidewall is available when etching silicon nitride. To achieve fabrication reproducibility, we set the minimum feature size as 100 nm in this work. The achievable smaller feature size enables creation of refined waveguide structure, which is demonstrated to significantly improve the device performance including insertion losses and mode crosstalk (see Supporting Information S1 for details). We use two cascaded devices with the same structural parameters for signal multiplexing and demultiplexing in the experiment, as shown in Figure 2c. Grating couplers are used as optical interfaces, which are designed with a period of 920 nm (940 nm for Y propagating) and a filling factor of 0.4 31 . The simulated electric field profiles of single device are monitored by using the three-dimensional finite-difference time-domain (3D-FDTD) method 32 , at a wavelength of 1550 nm. As shown in Figure 2d, the input TE 0 modes in the middle (I 0 ), upper (I 1 ) and lower (I 2 ) waveguides are coupled to TE 0 , TE 1 and TE 2 modes in the output waveguide, respectively. The corresponding transmission spectra at a wavelength range from 1530 nm to 1570 nm are depicted in Figures 2e-g. The simulated insertion losses of the TE 0 , TE 1 and TE 2 modes are 0.52 dB, 0.63 dB, and 0.87 dB at the wavelength of 1550 nm, while the mode crosstalk stays below -20.1 dB across the whole wavelength range. To further characterize the device performance, the transmission spectra of different modes are measured by using the device shown in Figure 2c. As shown in Figures 2h-j, the measured insertion losses of TE 0 , TE 1 , and TE 2 mode channels are 1.05 dB, 1.42 dB, and 2.5 dB at the wavelength of 1550 nm, with the mode crosstalk lower than -15.9 dB across the whole wavelength range, which are in good agreement with the simulation results. The demonstrated mode (de)multiplexer exhibits comparable performance with the conventional counterparts based on directional couplers (see Supporting Information S2 for details), while representing a more than tenfold footprint reduction. Multimode waveguide crossing. Waveguide crossing is another important PIC component for dealing with the cross connect in waveguide routing 33 . The discontinuities at the intersection can induce mode coupling and interference, presenting inherent challenges for device design. As shown in Figure 3a, an ultra-compact three-mode waveguide crossing is designed with a device footprint of only 15×15 μm 2 . The widths of input and output multimode waveguides are 4.3 μm, which are consistent with that of the mode (de)multiplexer. As aforementioned, the minimum feature size is set to 100 nm by considering the trade-off between device performance and fabrication reproducibility. Figure 3b shows a SEM image of the fabricated device. To ensure the device performance, the electric field profiles of different modes are simulated at a wavelength of 1550 nm by using the 3D-FDTD method. As shown in Figure 3c, the multimode signals pass through the waveguide crossing with negligible inter-modal coupling and radiation loss. We characterize the waveguide crossing by using a pair of auxiliary mode (de)multiplexers based on directional couplers. The microscope image of fabricated devices is shown in Figure 3d. The input TE 0 modes are coupled to different mode channels at the input ports, and then pass through the device. The multimode signals are demultiplexed at the output ports for transmission spectra measurements. The insertion losses of the fabricated waveguide crossing are measured through the cut-back method. As shown in Figure 3e, the measured and fitted insertion losses of TE 0 , TE 1 , and TE 2 modes at the wavelength of 1550 nm are 0.16 dB, 0.33 dB, and 0.55 dB, respectively. In addition to the ultra-low insertion losses, the fabricated waveguide crossing is also demonstrated to have low inter-modal crosstalk at a wide wavelength range from 1530 nm to 1570 nm. As shown in Figures 3f-h, the simulated transmission spectra predict that the inter-modal crosstalk for TE 0 , TE 1 , and TE 2 mode channels stays below -19.4 dB, -46.2 dB and -18.9 dB. The corresponding measured results are shown in Figures 3i-k, where the inter-modal crosstalk is lower than -17.7 dB, -15.0 dB and -16.1 dB for TE 0 , TE 1 , and TE 2 mode channels, respectively. We have noted that the crosstalk for TE 1 mode channel is limited, due to the unexpected mode coupling in the auxiliary mode (de)multiplexers (see Supporting Information S2 for details). It should also be noted that the anisotropy of lithium niobate has been included into the device optimization. Thus, the designed and fabricated device has similar performance when light propagates along the crystallographic Z direction of lithium niobate (see Supporting Information S3 for details). Multimode waveguide bend. The waveguide bending radius is strongly limited in TFLNOI platform due to the relatively low refractive index. The single-mode waveguide bending radius in a micro-ring resonator typically reaches up to 80~100 μm, for reducing the mode mismatch and radiation losses 34,35 . The multimode waveguide bends requires larger size inevitably due to the weaker confinement for high-order modes. Though shape optimization like Euler bends 28 , B-spline 36 or air grooves 37 can significantly reduce the multimode waveguide bending radius to 100~160 μm, there is still a gap between the size required for dense integration. Here, we demonstrate an ultra-compact multimode waveguide bend with an effective bending radius of only 30 μm, which is equivalent to that of the sharpest single-mode waveguide bend with a partial-etched waveguide cross-section in X-cut TFLNOI platforms 38,39 , to the best of our knowledge. The schematic diagram and SEM image of the multimode waveguide bend are shown in Figure 4a and Figure 4b. The widths of the input and output multimode waveguides are 4.3 μm. Figure 4c shows the electric field profiles of different modes, simulated by using the 3D-FDTD method at a wavelength of 1550 nm. After passing through the topology optimization area, the propagation directions of multimode signals are turned by 90° with negligible inter-modal coupling. Similarly, we characterize the device by using the directional coupler-based auxiliary mode (de)multiplexers. The microscope image of fabricated devices is shown in Figure 4d. The insertion losses of the fabricated waveguide bends are measured through the cut-back method. As shown in Figure 4e, the measured and fitted insertion losses for TE 0 , TE 1 , and TE 2 modes at a wavelength of 1550 nm are 1.02 dB, 1.96 dB, and 2.17 dB, respectively. The waveguide bend has low inter-modal crosstalk over a wide wavelength range. As shown in Figures 4f-h, the simulation transmission spectra predict that the inter-modal crosstalk for TE 0 , TE 1 , and TE 2 mode channels can stay below -20.4 dB, -16.2 dB and -19.8 dB at a wavelength range from 1530 nm to 1570 nm. For the convenience of measurement, the propagation directions of the multimode signals are actually turned by 180° in the experiment (two 90° bends). The corresponding measured results are shown in Figures 4i-k, where the inter-modal crosstalk for TE 0 , TE 1 , and TE 2 mode channels is lower than -16.2 dB, -15.1 dB and -15.9 dB, agreeing well with the simulated results. Multimode photonic circuits. To further demonstrate the device performance in dense integration, we design and fabricate two types of multimode photonic circuits. The first PIC shown in Figure 5a consists of two independent circuits with path crossing of the two circuits, while the second one shown in Figure 5b is a single circuit with multipath crossings of the same circuit. The input fundamental modes are first coupled into different mode channels by the mode multiplexer. The multiplexed multimode signals are then routed in the chip plane by using the waveguide crossings and bends, which are finally demultiplexed by another mode demultiplexer. An only a chip area of 200 × 300 μm² is occupied to implement these operations. The measured transmission spectra of the first PIC are shown in Figures 5c-e. The insertion losses for TE 0 , TE 1 and TE 2 mode channels are 4.2 dB, 7.8 dB and 7.1 dB, while the inter-modal crosstalk stays below -20.3 dB at the wavelength of 1550 nm. Similarly, the measured transmission spectra of the second PIC are shown in Figures 5f-h. It can be seen that the insertion losses for TE 0 , TE 1 and TE 2 mode channels are 6.5 dB, 11.5 dB and 11.9 dB, while the inter-modal crosstalk still stays below -12.5 dB at the wavelength of 1550 nm. Despite a significant increase in the number of waveguide elements, the measured results still indicate good performance, presenting the good system scalability and dense integration capability of the inverse designed devices. To demonstrate the advancement in combination of dense integration capability and excellent material properties, an on-chip data modulation and transmission system is implemented. We design and fabricate three electro-optical modulators based on the micro-ring resonator structure, corresponding to the employed three mode channels. Light emitted by the lasers can be modulated by high-speed radio-frequency signals, then routed in the chip plane by the multimode photonic circuits, finally detected by photodetectors. A microscope image of the fabricated electro-optical modulator is shown in Figure 6a. The designed waveguide width and the coupling gap are 1 μm and 750 nm, respectively. The radius of ring waveguide is 300 μm, while the length of straight track is 1.5 mm. The measured transmission spectrum of the micro-ring resonator is shown in Figure 6b. The insertion loss at a non-resonant wavelength is lower than 0.54 dB, while the extinction ratio is larger than 12.4 dB. A ground-signal-ground (G-S-G) travelling-wave electrode is employed. The width of the signal electrode is designed as 23 μm, and the gap between signal and ground electrodes is 6 μm. Figure 6c shows the measured eye diagrams for different mode channels with the modulated and transmitted on-off key signal rates of 100 Gbps and 120 Gbps. The measured signal-to-noise ratios are larger than 5.4 dB. The clear and open eyes indicate the good system performance. Discussion. We compare the overall device performance including effective size, insertion loss, mode crosstalk and data modulation rate with previously reported works, as shown in Table 1. It can be seen that the measured insertion losses and inter-modal crosstalk is comparable with that of the forward-designed counterparts, while the device footprint is significantly reduced by an order of magnitude. Even compared with the previous single- or dual-mode devices, the demonstrated multimode devices exhibit relatively compact size, low insertion loss and low mode crosstalk. Moreover, the demonstrated PICs achieve similar high performance in electro-optical modulation when compared with the directly etched platforms, due to the high mode confinement in lithium niobate thin film. Table 1. Performance comparison of some previously reported TFLN components Refs Device Mode Effective Size Loss Crosstalk Modulation 26 MUX TE 0 ~TE 2 18×347 μm 2 <2.1 dB <-17 dB / 27 MUX TE 0 ~TE 2 22×500 μm 2 <4.69 dB <-10.6 dB / 28 MUX TE 0 ~TE 2 17×450 μm 2 ≈0.2 dB <-19 dB / 29 MUX TE 0 ~TE 2 17×450 μm 2 <2.0 dB <-12 dB 60 Gbps This Work MUX TE 0 ~TE 2 19 × 25 μm 2 <2.5 dB <-15.9 dB 120 Gbps 17 Crossing TE 0 12×12 μm 2 0.48 dB <-36 dB / 33 Crossing TE 0 17.5×16 μm 2 0.07 dB <-50 dB / This Work Crossing TE 0 ~TE 2 15×15 μm 2 < 0.55 dB < -15 dB 120 Gbps 38 Bend TE 0 30 μm <0.05 dB / / 28 Bend TE 0 ~TE 2 160 μm 0.026 dB <-25 dB / 37 Bend TE 0 ~TE 2 120 μm < 2.5 dB <-12.2 dB / This Work Bend TE 0 ~TE 2 30 μm < 2.17 dB < -15.1 dB 120 Gbps This Work System TE 0 ~TE 2 200×300 μm 2 < 11.9 dB < -12.5 dB 120 Gbps In summary, we have demonstrated ultra-compact multimode components and photonic circuits based on a silicon nitride-lithium niobate hybrid platform, by using photonic inverse design method. This hybrid platform shows a good combination of the excellent material properties of silicon nitride and lithium niobate. The optical structures in the isotropic silicon nitride loading layer are optimized by using a scalar-based inverse design method with improved design efficiency when compared with that using a tensor-based method for anisotropic materials. Moreover, the silicon nitride loading material owns mature fabrication processes, enabling improved device performance by means of small and well controlled device feature size. The reduction in device footprint supports complex optical path design within an ultra-compact chip area, while more chip space reserved for other important active functions such as data modulation, wavelength conversion, and spectral control. Our approach is scalable, which can be extended to a wide range of passive components which is expected to be important building blocks for realizing densely integrated and large-scale PICs in the TFLNOI platform. Methods Inverse Design method. Gradient optimization based on the adjoin method is used to implement topology optimization through iterative material distribution updates. The dielectric permittivity of design area is initially projected onto a [0,1] space for parametric normalization (Eq. 1). The material distribution is subsequently smoothed via a convolutional filtering (Eq. 2) to eliminate subwavelength defects. Finally, an adaptive binarization projection function (Eq. 3) is used to increase filter sharpness β and obtain a binary distribution of dielectric constants. We only need to optimize the distribution of isotropic silicon nitride loading material. Thus, the scalar-based inverse design method is applicable. Fabrication processes. We use an X-cut TFLNOI wafer from NanoLN, China. The silicon nitride thin film is deposited onto the chip by using reactive sputtering process 40 . The grating coupler and waveguide structures are patterned by using electron-beam lithography, and then formed by using single-step inductively coupled plasma etching. Finally, the electrodes (500-nm-thick Au) are fabricated by using laser direct writing, e-beam evaporation deposition and lift-off processes. The propagation losses of the fabricated waveguides are measured to be about 0.25 dB/cm, by using the cut-back method. The coupling losses of the fabricated grating couplers are measured to be 6 dB/facet, at a peak coupling wavelength of 1560 nm. Experimental setup. Light is emitted by a tunable laser, followed by a polarization controller used to maintain TE polarization before coupling light into the chip. For static measurements, signals coupled out of the chip are directed to an optical spectrum analyzer for spectral analysis. For high-speed data modulation and transmission experiment, the laser light is modulated by the on-chip electro-optical modulator using a 2 10 −1 pseudo-random binary sequence generated by an arbitrary waveform generator. After coupling into and out of the chip, the signals are amplified by an erbium-doped fiber amplifier, following by an optical tunable filter for reducing background noise. Finally, the signals are received by a digital communication analyzer for eye diagram measurements (see Supporting Information S5 for details). Declarations Data Availability The data that support the findings of this study are available from the corresponding author upon reasonable request. Acknowledgements This work is supported by the National Natural Science Foundation of China (62405082, T2325022), Natural Science Foundation of Anhui Province (2408085QF217) and Fundamental Research Funds for the Central Universities (JZ2023HGQA0479, JZ2024HGTA0185). The authors acknowledge the facilities, and the scientific and technical assistance, of the Micro Nano Research Facility (MNRF) and the Australian Microscopy & Microanalysis Research Facility at RMIT University. This work was performed in part at the Melbourne Centre for Nanofabrication (MCN) in the Victorian Node of the Australian National Fabrication Facility (ANFF). This work was performed in part at the OptoFab node of the Australian National Fabrication Facility, utilizing NCRIS and VIC state government funding. A.B. is supported by an ARC DECRA fellowship (DE230100964). Competing interests The authors declare no competing interests. Author contributions X.H. conceived the project. H.J. performed the numerical simulations. M.X.L. and G.R. fabricated the chips. X.H. and H.J. established the static measurement setup and performed the transmission spectra analysis. 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Sharp bend and large FSR ring resonator based on the free-form curves on a thin-film lithium niobate platform. Opt. Express 32 , 9433-9441 (2024). Wang, J. et al. Large free spectral range, high Q-factor microring resonator in thin-film lithium niobate photonics. Opt. Lett. 50 , 3094-3097 (2025). Frigg, A. et al. Low loss CMOS-compatible silicon nitride photonics utilizing reactive sputtered thin films. Opt. Express 27, 37795-37805 (2019). Additional Declarations There is NO Competing Interest. Supplementary Files SupportingInformation.docx Supporting Information Cite Share Download PDF Status: Published Journal Publication published 21 Dec, 2025 Read the published version in Nature Communications → Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-7481144","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":507683042,"identity":"aae4c528-28ea-4501-80b8-20e567627b19","order_by":0,"name":"Haojie 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University","correspondingAuthor":false,"prefix":"","firstName":"Andreas","middleName":"","lastName":"Boes","suffix":""},{"id":507683054,"identity":"d6b6d3cd-58f6-40e8-8b59-8235220bb21b","order_by":12,"name":"Chengliang Pan","email":"","orcid":"","institution":"Hefei University of Technology","correspondingAuthor":false,"prefix":"","firstName":"Chengliang","middleName":"","lastName":"Pan","suffix":""},{"id":507683055,"identity":"72701d94-4bf2-4059-b92c-8805c4c9878e","order_by":13,"name":"Guanghui Ren","email":"","orcid":"https://orcid.org/0000-0002-9867-8279","institution":"","correspondingAuthor":false,"prefix":"","firstName":"Guanghui","middleName":"","lastName":"Ren","suffix":""},{"id":507683056,"identity":"e994eb7a-3645-4f06-8465-8fcdfa826a92","order_by":14,"name":"Yong Zhang","email":"","orcid":"","institution":"Shanghai Jiao Tong University","correspondingAuthor":false,"prefix":"","firstName":"Yong","middleName":"","lastName":"Zhang","suffix":""},{"id":507683057,"identity":"6827da6b-dd60-4da9-a82b-53f0d15811e0","order_by":15,"name":"Xi-Feng Ren","email":"","orcid":"https://orcid.org/0000-0001-6559-8101","institution":"University of science and technology of China","correspondingAuthor":false,"prefix":"","firstName":"Xi-Feng","middleName":"","lastName":"Ren","suffix":""},{"id":507683058,"identity":"e6c9027c-1c39-4561-ab0e-f140fe5eff8a","order_by":16,"name":"Yonghui Tian","email":"","orcid":"","institution":"Lanzhou University","correspondingAuthor":false,"prefix":"","firstName":"Yonghui","middleName":"","lastName":"Tian","suffix":""},{"id":507683059,"identity":"29ae67e3-722a-438e-913a-0d42fac8aeac","order_by":17,"name":"Arnan Mitchell","email":"","orcid":"https://orcid.org/0000-0002-2463-2956","institution":"RMIT University","correspondingAuthor":false,"prefix":"","firstName":"Arnan","middleName":"","lastName":"Mitchell","suffix":""}],"badges":[],"createdAt":"2025-08-28 14:16:05","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-7481144/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-7481144/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1038/s41467-025-67927-7","type":"published","date":"2025-12-21T05:00:00+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":90477129,"identity":"a9eac0cd-05cd-4357-a47d-6df4cb0138ad","added_by":"auto","created_at":"2025-09-03 07:19:11","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":280773,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eInverse-designed lithium niobate multimode photonic circuits. a \u003c/strong\u003eSchematic diagram of an on-chip data modulation and multimode transmission system, where the chip consists of an array of micro-ring-based electro-optical modulators and the inverse-designed multimode photonic circuit (PC, polarization controller). \u003cstrong\u003eb \u003c/strong\u003eSchematic diagram of the inverse-designed mode (de)multiplexer. \u003cstrong\u003ec\u003c/strong\u003e Schematic diagram of the inverse designed multimode waveguide crossing. \u003cstrong\u003ed \u003c/strong\u003eSchematic diagram of the inverse designed multimode waveguide bend.\u003c/p\u003e","description":"","filename":"1.png","url":"https://assets-eu.researchsquare.com/files/rs-7481144/v1/dc7dc344f59c456a015c122c.png"},{"id":90477137,"identity":"6ceccc5f-b5b0-41c1-b2cb-ba0ad84b4bc2","added_by":"auto","created_at":"2025-09-03 07:19:12","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":249185,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eDesign and experimental demonstration of mode (de)multiplexer. a \u003c/strong\u003eIllustration of the designed mode (de)multiplexer with an effective size of 19×25 μm\u003csup\u003e2\u003c/sup\u003e.\u003cstrong\u003e b \u003c/strong\u003eSEM image of the fabricated mode (de)multiplexer\u003cstrong\u003e \u003c/strong\u003ewith a minimum feature size of 100 nm. \u003cstrong\u003ec\u003c/strong\u003e Microscope image of the cascaded devices for signal multiplexing and demultiplexing in the experiment. \u003cstrong\u003ed \u003c/strong\u003eSimulated electric field profiles for the TE\u003csub\u003e0\u003c/sub\u003e mode input at different ports of the mode (de)multiplexer. \u003cstrong\u003ee-g \u003c/strong\u003eSimulated transmission spectra of different mode channels at a wavelength range from 1530 nm to 1570 nm. \u003cstrong\u003eh-j \u003c/strong\u003eMeasured transmission spectra of different mode channels at a wavelength range from 1530 nm to 1570 nm.\u003c/p\u003e","description":"","filename":"2.png","url":"https://assets-eu.researchsquare.com/files/rs-7481144/v1/1ae4d24152e74f77ad495685.png"},{"id":90477134,"identity":"58727b98-e5d6-4d26-8553-faffbcf67fe0","added_by":"auto","created_at":"2025-09-03 07:19:12","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":318110,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eDesign and experimental demonstration of multimode waveguide crossing. a \u003c/strong\u003eIllustration of the designed waveguide crossing with an effective size of 15×15 μm\u003csup\u003e2\u003c/sup\u003e. \u003cstrong\u003eb\u003c/strong\u003e SEM image of the fabricated device. \u003cstrong\u003ec \u003c/strong\u003eSimulated electric field profiles for different input modes: TE\u003csub\u003e0\u003c/sub\u003e, TE\u003csub\u003e1\u003c/sub\u003e and TE\u003csub\u003e2\u003c/sub\u003e. \u003cstrong\u003ed \u003c/strong\u003eMicroscope image of the cascaded devices connected to auxiliary mode (de)multiplexers for insertion loss measurement. \u003cstrong\u003ee \u003c/strong\u003eMeasured and fitted insertion losses of TE\u003csub\u003e0\u003c/sub\u003e, TE\u003csub\u003e1\u003c/sub\u003e, and TE\u003csub\u003e2\u003c/sub\u003e modes at the wavelength of 1550 nm.\u003cstrong\u003e f-h \u003c/strong\u003eSimulated transmission spectra of different mode channels at a wavelength range from 1530 nm to 1570 nm. \u003cstrong\u003ei-k \u003c/strong\u003eMeasured transmission spectra of different mode channels at a wavelength range from 1530 nm to 1570 nm.\u003c/p\u003e","description":"","filename":"3.png","url":"https://assets-eu.researchsquare.com/files/rs-7481144/v1/ac33c1f1adcdf1a89b7c5731.png"},{"id":90478347,"identity":"61e052a0-8032-4616-86b0-b18142fee22d","added_by":"auto","created_at":"2025-09-03 07:27:12","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":345913,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eDesign and experimental demonstration of multimode waveguide bend. a \u003c/strong\u003eIllustration of the designed waveguide bend with an effective bending radius of 30 μm.\u003cstrong\u003e b\u003c/strong\u003e SEM image of the designed and fabricated device. \u003cstrong\u003ec \u003c/strong\u003eSimulated electric field profiles of different input modes. \u003cstrong\u003ed\u003c/strong\u003e Microscope image of the cascaded devices connected to auxiliary mode (de)multiplexers for insertion loss measurement. \u003cstrong\u003ee \u003c/strong\u003eMeasured and fitted insertion losses of TE\u003csub\u003e0\u003c/sub\u003e, TE\u003csub\u003e1\u003c/sub\u003e, and TE\u003csub\u003e2\u003c/sub\u003e modes at the wavelength of 1550 nm.\u003cstrong\u003e f-h \u003c/strong\u003eSimulated transmission spectra of different mode channels at a wavelength range from 1530 nm to 1570 nm. \u003cstrong\u003ei-k \u003c/strong\u003eMeasured transmission spectra of different mode channels at a wavelength range from 1530 nm to 1570 nm.\u003c/p\u003e","description":"","filename":"4.png","url":"https://assets-eu.researchsquare.com/files/rs-7481144/v1/d958856c3edff0cb469831ed.png"},{"id":90478344,"identity":"22dd4667-0525-419d-811e-2dbb36faba11","added_by":"auto","created_at":"2025-09-03 07:27:11","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":312100,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eExperimental demonstration of multimode arbitrary routing system. a-b \u003c/strong\u003eMicroscope images of the fabricated multimode photonic circuits. \u003cstrong\u003ec-e \u003c/strong\u003eMeasured transmission spectra of different mode channels for the first PIC shown in Fig. 5a. \u003cstrong\u003ef-h \u003c/strong\u003eMeasured transmission spectra of different mode channels for the second PIC shown in Fig. 5b.\u003c/p\u003e","description":"","filename":"5.png","url":"https://assets-eu.researchsquare.com/files/rs-7481144/v1/bb62e4fe254b42ee610d0ea2.png"},{"id":90477131,"identity":"56f0ea30-791e-453f-9271-b16dcbf302eb","added_by":"auto","created_at":"2025-09-03 07:19:11","extension":"png","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":251160,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eExperimental demonstration of on-chip data modulation and multimode signal transmission. a \u003c/strong\u003eMicroscope image of the fabricated micro-ring-based electro-optical modulator. \u003cstrong\u003eb \u003c/strong\u003eMeasured transmission spectra of the micro-ring resonator. \u003cstrong\u003ec \u003c/strong\u003emeasured eye diagrams for different mode channels with the modulated and transmitted on-off key signal rates of 100 Gbps and 120 Gbps.\u003c/p\u003e","description":"","filename":"6.png","url":"https://assets-eu.researchsquare.com/files/rs-7481144/v1/a9f90f83e87a1aec8b1e4fa7.png"},{"id":101551998,"identity":"c57de1ae-8a21-490b-b34d-9cbcb7a513c2","added_by":"auto","created_at":"2026-01-31 08:06:48","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":2783446,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-7481144/v1/e091093e-7d63-425d-b12a-519221062cd6.pdf"},{"id":90477120,"identity":"c683fee0-9d4b-4990-bad9-b01294e836f6","added_by":"auto","created_at":"2025-09-03 07:19:11","extension":"docx","order_by":1,"title":"","display":"","copyAsset":false,"role":"supplement","size":9788879,"visible":true,"origin":"","legend":"Supporting Information","description":"","filename":"SupportingInformation.docx","url":"https://assets-eu.researchsquare.com/files/rs-7481144/v1/91b1adc3185f2a5014d4a527.docx"}],"financialInterests":"There is \u003cb\u003eNO\u003c/b\u003e Competing Interest.","formattedTitle":"Breaking Dense Integration Limits: Inverse-Designed Lithium Niobate Multimode Photonic Circuits","fulltext":[{"header":"Introduction","content":"\u003cp\u003eModern photonic integrated circuits (PICs) are undergoing a paradigm shift toward dense integration, which is essential for scaling bandwidth, minimizing energy per bit, and supporting on-chip convergence of diverse optical functionalities\u003csup\u003e1\u003c/sup\u003e. Achieving such advancements requires photonic platforms that offer not only high index contrast but also wide spectral transparency, strong nonlinear and electro-optic properties\u003csup\u003e2\u003c/sup\u003e. Conventional silicon, silicon nitride and III\u0026ndash;V platforms, while mature in CMOS-compatible processes, face inherent limitations in nonlinear performance, electro-optic response, or material transparency. In this context, thin-film lithium niobate on insulator (TFLNOI) has emerged as a promising alternative that combines wide optical transparency window, strong nonlinear optical performance and high-speed electro-optic modulation\u003csup\u003e3,4\u003c/sup\u003e.\u003cstrong\u003e\u0026nbsp;\u003c/strong\u003eRecent advances in TFLNOI-based electro-optic modulators have demonstrated unprecedented 100 GHz bandwidths and near-1 V driving voltages\u0026nbsp;at different wavelength ranges\u003csup\u003e5,6\u003c/sup\u003e, enabling more than a tenfold footprint reduction compared to bulk lithium niobate counterparts. These breakthroughs, driven by applications such as terabit per second optical communications\u003csup\u003e7\u003c/sup\u003e, precision optical metrology\u003csup\u003e8\u003c/sup\u003e and quantum photonic processors\u003csup\u003e9\u003c/sup\u003e, position TFLNOI as a versatile platform for multifunctional photonic systems.\u003cstrong\u003e\u0026nbsp;\u003c/strong\u003eHowever, the relatively modest refractive index contrast in TFLNOI waveguides, especially those fabricated with partial etching, inherently limits the mode confinement\u003csup\u003e10\u003c/sup\u003e.\u0026nbsp;Thus, device dimensions such as waveguide bending radius\u0026nbsp;face limitations, which constrain the achievable chip integration density and challenge the scalability demands of large-scale PICs. To bridge the gap between TFLNOI\u0026apos;s exceptional material properties and dense chip integration, advanced photonic design methods are emerging as powerful tools toward compact footprints while maintaining compatibility with fabrication processes.\u003c/p\u003e\n\u003cp\u003eInverse design, which leverages intelligent optimization algorithms to explore vast parameter space, can significantly improve multistage efficiency in device design, simulation and fabrication by enabling fast creation of complex optical structures, e.g. metasurface, with ultra-compact size, unprecedented precision and functionality\u003csup\u003e11,12\u003c/sup\u003e. Significant breakthroughs have been achieved in silicon photonics during the last few years, with the device footprint scaled-down to \u003cem\u003emicron\u003c/em\u003e level, paving the way to densely integrated on-chip optical systems\u003csup\u003e13-16\u003c/sup\u003e. However, to obtain inverse-designed PIC components and complex optical systems in TFLNOI, the inherent barriers of material, method and fabrication process are particularly intractable. First, an X-cut TFLNOI platform experiences refractive index anisotropy in the \u003cem\u003ey\u003c/em\u003e/\u003cem\u003ez\u003c/em\u003e plane, and the traditional scalar-based inverse design methods are inappropriate to address the scenarios of anisotropic material. Although a Z-cut TFLNOI platform can avoid the material anisotropy in the plane of lithium niobate thin film\u003csup\u003e17\u003c/sup\u003e, the access to strong electro-optic coefficient of lithium niobate (\u003cem\u003er\u003csub\u003e33\u003c/sub\u003e\u003c/em\u003e) requires to lay out electrodes vertically, which is inconvenient for chip integration. Second, a tensor-based inverse design method can be extended to the X-cut TFLNOI platform by considering the impact of material anisotropy of lithium niobate\u003csup\u003e18\u003c/sup\u003e. However, a computational complexity increase is inevitable compared to that of traditional scalar-based inverse design methods, which brings higher requirements for computing resources and simulation time. Third, the generally used physical direct etching method for TFLNOI can induce a slanted waveguide sidewall which limits the device feature size\u003csup\u003e19\u003c/sup\u003e, resulting in significant degradation and variability in device performance. Thus, the inverse designed lithium niobate photonics requires an overall optimization to overcome the material anisotropy and limited device feature size, while reserving the access to excellent material properties of lithium niobate.\u003c/p\u003e\n\u003cp\u003eAs shown in Figure 1a, we demonstrate inverse-designed high density multimode photonic circuits for high-speed and large-capacity data communications in a silicon nitride-TFLNOI (X-cut) hybrid platform. Integrated multimode photonics can enable large-scale signal parallelism and enhance the information capacity of PICs by introducing higher-order waveguide modes as data carriers\u003csup\u003e20\u003c/sup\u003e, which has also attracted attention in optical computing\u003csup\u003e21\u003c/sup\u003e, sensing\u003csup\u003e22\u003c/sup\u003e and spectroscopy\u003csup\u003e23\u003c/sup\u003e. Unfortunately, the arbitrary routing of multimode signals is usually built in a large chip area even in high-indexed material platform, due to the radiation leakage and inter-mode coupling\u003csup\u003e14\u003c/sup\u003e. As shown in Figures 1b-d, we design, fabricate and experimentally demonstrate an optical mode-division (de)multiplexer (19\u0026times;25 \u0026mu;m\u003csup\u003e2\u003c/sup\u003e), a multimode waveguide crossing (15\u0026times;15 \u0026mu;m\u003csup\u003e2\u003c/sup\u003e) and a multimode waveguide bend (30 \u0026mu;m bending radius) for the first three quasi-transverse electrical modes (TE\u003csub\u003e0\u003c/sub\u003e, TE\u003csub\u003e1\u003c/sub\u003e and TE\u003csub\u003e2\u003c/sub\u003e). The measured insertion losses are lower than 2.5 dB at the wavelength of 1550 nm, while the mode crosstalk stays below -15 dB at a wavelength range from 1530 nm to 1570 nm. These components are used to construct ultra-compact photonic circuits, enabling arbitrary routing of multimode signals through dense integration of more than 10 waveguide elements within a 0.06 mm\u003csup\u003e2\u0026nbsp;\u003c/sup\u003e(200 \u0026times; 300 \u0026mu;m\u0026sup2;) chip area. To demonstrate the advancement in combination of high integration density with excellent material properties, a high-speed data modulation and transmission system is implemented through the monolithically integration of electro-optical modulators and multimode photonic circuits. The single-channel data modulation and transmission rate for on\u0026ndash;off key signal reaches up to 120 Gbps.\u003c/p\u003e"},{"header":"Results","content":"\u003cp\u003e\u003cstrong\u003e\u003cem\u003eWaveguide platform.\u003c/em\u003e\u003c/strong\u003e Silicon nitride is selected as an isotropic optical loading material. Thus, the optical structures in the loading layer can be optimized using scalar-based inverse design method and fabricated by mature silicon nitride etching processes, enabling improved design efficiency and well controlled device feature size. Though there are also other available loading materials, such as silicon, polymers and chalcogenide glasses, silicon nitride can offer similar but slightly lower refractive index than lithium niobate, enabling high mode confinement in the lithium niobate thin film, similar optical transparency window and mature fabrication process compared with lithium niobate\u003csup\u003e24\u003c/sup\u003e. The silicon nitride-TFLNOI (X-cut) hybrid platform is designed to avoid the direct etching of lithium niobate thin film, while providing a high mode confinement factor (~60%) in lithium niobate. The layers from top to bottom are air cladding, silicon nitride loading layer, lithium niobate slab, buried oxide layer and silicon substrate, respectively. The thicknesses of the silicon nitride and lithium niobate layers are both 300 nm,\u0026nbsp;which\u0026nbsp;avoids the mode lateral leakage at second-harmonic wavelengths\u003csup\u003e25\u003c/sup\u003e. The thickness of the buried oxide layer is selected as 4.7 \u0026mu;m to ensure index match and a relatively low radio-frequency loss for electro-optic modulation.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003e\u003cem\u003eMode (de)multiplexer.\u003c/em\u003e\u003c/strong\u003e Mode (de)multiplexers serve as critical PIC components to enable parallel propagating of multimode signals in a single waveguide. Previous works in TFLNOI platform are generally based on directional coupler structures by forward design\u003csup\u003e26-29\u003c/sup\u003e. In this case, the low-loss and low-crosstalk mode coupling relies on strict control of phase and mode field distribution, requiring a large device footprint. In contrast, in this contribution we employ the inverse design method to implement a three-mode (de)multiplexer with an ultra-compact effective size of only 19\u0026times;25 \u0026mu;m\u003csup\u003e2\u003c/sup\u003e.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eFigures 2a and 2b show an illustration and a scanning electron microscope (SEM) image of the device structure which is designed and fabricated by patterning the silicon nitride layer. By considering the anisotropy of lithium niobate, the device is designed along the crystallographic Z direction to avoid the mode hybridization between TE\u003csub\u003e1\u003c/sub\u003e and TM\u003csub\u003e0\u003c/sub\u003e modes\u003csup\u003e30\u003c/sup\u003e. The widths of the input single-mode waveguides and output multimode waveguide are designed as 1 \u0026mu;m and 4.3 \u0026mu;m, while the gaps between the adjacent input waveguides are 2 \u0026mu;m. A near vertical waveguide sidewall is available when etching silicon nitride. To achieve fabrication reproducibility, we set the minimum feature size as 100 nm in this work. The achievable smaller feature size enables creation of refined waveguide structure, which is demonstrated to significantly improve the device performance including insertion losses and mode crosstalk (see Supporting Information S1 for details).\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eWe use two cascaded devices with the same structural parameters for signal multiplexing and demultiplexing in the experiment, as shown in Figure 2c. Grating couplers are used as optical interfaces, which are designed with a period of 920 nm (940 nm for Y propagating) and a filling factor of 0.4\u003csup\u003e31\u003c/sup\u003e. The simulated electric field profiles of single device are monitored by using the three-dimensional finite-difference time-domain (3D-FDTD) method\u003csup\u003e32\u003c/sup\u003e, at a wavelength of 1550 nm. As shown in Figure 2d, the input TE\u003csub\u003e0\u003c/sub\u003e modes in the middle (I\u003csub\u003e0\u003c/sub\u003e), upper (I\u003csub\u003e1\u003c/sub\u003e) and lower (I\u003csub\u003e2\u003c/sub\u003e) waveguides are coupled to TE\u003csub\u003e0\u003c/sub\u003e, TE\u003csub\u003e1\u003c/sub\u003e and TE\u003csub\u003e2\u003c/sub\u003e modes in the output waveguide, respectively. The corresponding transmission spectra at a wavelength range from 1530 nm to 1570 nm are depicted in Figures 2e-g.\u0026nbsp;The simulated insertion losses of the TE\u003csub\u003e0\u003c/sub\u003e, TE\u003csub\u003e1\u003c/sub\u003e and TE\u003csub\u003e2\u003c/sub\u003e modes are 0.52 dB, 0.63 dB, and 0.87 dB at the wavelength of 1550 nm, while the mode crosstalk stays below -20.1 dB across the whole wavelength range. To further characterize the device performance, the transmission spectra of different modes are measured by using the device shown in Figure 2c. As shown in Figures 2h-j, the measured insertion losses of TE\u003csub\u003e0\u003c/sub\u003e, TE\u003csub\u003e1\u003c/sub\u003e, and TE\u003csub\u003e2\u003c/sub\u003e mode channels are 1.05 dB, 1.42 dB, and 2.5 dB at the wavelength of 1550 nm,\u0026nbsp;with the mode crosstalk lower than -15.9 dB across the whole wavelength range, which are in good agreement with the simulation results. The demonstrated mode (de)multiplexer exhibits comparable performance with the conventional counterparts based on directional couplers (see Supporting Information S2 for details), while representing a more than tenfold footprint reduction.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003e\u003cem\u003eMultimode waveguide crossing.\u003c/em\u003e\u003c/strong\u003e Waveguide crossing is another important PIC component for dealing with the cross connect in waveguide routing\u003csup\u003e33\u003c/sup\u003e.\u0026nbsp;The discontinuities at the intersection can induce mode coupling and interference, presenting inherent challenges for device design. As shown in Figure 3a, an ultra-compact three-mode waveguide crossing is designed with a device footprint of only 15\u0026times;15 \u0026mu;m\u003csup\u003e2\u003c/sup\u003e. The widths of input and output multimode waveguides are 4.3 \u0026mu;m, which are consistent with that of the mode (de)multiplexer. As aforementioned, the minimum feature size is set to 100 nm by considering the trade-off between device performance and fabrication reproducibility. Figure 3b shows a SEM image of the fabricated device. To ensure the device performance, the electric field profiles of different modes are simulated at a wavelength of 1550 nm by using the 3D-FDTD method. As shown in Figure 3c, the multimode signals pass through the waveguide crossing with negligible inter-modal coupling and radiation loss. We characterize the waveguide crossing by using a pair of auxiliary mode (de)multiplexers based on directional couplers. The microscope image of fabricated devices is shown in Figure 3d. The input TE\u003csub\u003e0\u003c/sub\u003e modes are coupled to different mode channels at the input ports, and then pass through the device. The multimode signals are demultiplexed at the output ports for transmission spectra measurements. The insertion losses of the fabricated waveguide crossing are measured through the cut-back method. As shown in Figure 3e, the measured and fitted insertion losses of TE\u003csub\u003e0\u003c/sub\u003e, TE\u003csub\u003e1\u003c/sub\u003e, and TE\u003csub\u003e2\u003c/sub\u003e modes at the wavelength of 1550 nm are 0.16 dB, 0.33 dB, and 0.55 dB, respectively.\u003c/p\u003e\n\u003cp\u003eIn addition to the ultra-low insertion losses, the fabricated waveguide crossing is also demonstrated to have low inter-modal crosstalk at a wide wavelength range from 1530 nm to 1570 nm. As shown in Figures 3f-h, the simulated transmission spectra predict that the inter-modal crosstalk for TE\u003csub\u003e0\u003c/sub\u003e, TE\u003csub\u003e1\u003c/sub\u003e, and TE\u003csub\u003e2\u003c/sub\u003e mode channels stays below -19.4 dB, -46.2 dB and -18.9 dB. The corresponding measured results are shown in Figures 3i-k, where the inter-modal crosstalk is lower than -17.7 dB, -15.0 dB and -16.1 dB for TE\u003csub\u003e0\u003c/sub\u003e, TE\u003csub\u003e1\u003c/sub\u003e, and TE\u003csub\u003e2\u003c/sub\u003e mode channels, respectively. We have noted that the crosstalk for TE\u003csub\u003e1\u003c/sub\u003e mode channel is limited, due to the unexpected mode coupling in the auxiliary mode (de)multiplexers (see Supporting Information S2 for details).\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eIt should also be noted that the anisotropy of lithium niobate has been included into the device optimization. Thus, the designed and fabricated device has similar performance when light propagates along the crystallographic Z direction of lithium niobate (see Supporting Information S3 for details).\u0026nbsp;\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003e\u003cem\u003eMultimode waveguide bend.\u003c/em\u003e\u003c/strong\u003e The waveguide bending radius is strongly limited in TFLNOI platform due to the relatively low refractive index. The single-mode waveguide bending radius in a micro-ring resonator typically reaches up to 80~100 \u0026mu;m, for reducing the mode mismatch and radiation losses\u003csup\u003e34,35\u003c/sup\u003e. The multimode waveguide bends requires larger size inevitably due to the weaker confinement for high-order modes. Though shape optimization like Euler bends\u003csup\u003e28\u003c/sup\u003e, B-spline\u003csup\u003e36\u003c/sup\u003e or air grooves\u003csup\u003e37\u003c/sup\u003e\u003cstrong\u003e\u0026nbsp;\u003c/strong\u003ecan significantly reduce the multimode waveguide bending radius to 100~160 \u0026mu;m, there is still a gap between the size required for dense integration. Here, we demonstrate an ultra-compact multimode waveguide bend with an effective bending radius of only 30 \u0026mu;m, which is equivalent to that of the sharpest single-mode waveguide bend with a partial-etched waveguide cross-section in X-cut TFLNOI platforms\u003csup\u003e38,39\u003c/sup\u003e, to the best of our knowledge.\u003c/p\u003e\n\u003cp\u003eThe schematic diagram and SEM image of the multimode waveguide bend are shown in Figure 4a and Figure 4b. The widths of the input and output multimode waveguides are 4.3 \u0026mu;m. Figure 4c shows the electric field profiles of different modes, simulated by using the 3D-FDTD method at a wavelength of 1550 nm. After passing through the topology optimization area, the propagation directions of multimode signals are turned by 90\u0026deg; with negligible inter-modal coupling. Similarly, we characterize the device by using the directional coupler-based auxiliary mode (de)multiplexers. The microscope image of fabricated devices is shown in Figure 4d. The insertion losses of the fabricated waveguide bends are measured through the cut-back method. As shown in Figure 4e, the measured and fitted insertion losses for TE\u003csub\u003e0\u003c/sub\u003e, TE\u003csub\u003e1\u003c/sub\u003e, and TE\u003csub\u003e2\u003c/sub\u003e modes at a wavelength of 1550 nm are 1.02 dB, 1.96 dB, and 2.17 dB, respectively.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eThe waveguide bend has low inter-modal crosstalk over a wide wavelength range. As shown in Figures 4f-h, the simulation transmission spectra predict that the inter-modal crosstalk for TE\u003csub\u003e0\u003c/sub\u003e, TE\u003csub\u003e1\u003c/sub\u003e, and TE\u003csub\u003e2\u003c/sub\u003e mode channels can stay below -20.4 dB, -16.2 dB and -19.8 dB at a wavelength range from 1530 nm to 1570 nm. For the convenience of measurement, the propagation directions of the multimode signals are actually turned by 180\u0026deg; in the experiment (two 90\u0026deg; bends). The corresponding measured results are shown in Figures 4i-k, where the inter-modal crosstalk for TE\u003csub\u003e0\u003c/sub\u003e, TE\u003csub\u003e1\u003c/sub\u003e, and TE\u003csub\u003e2\u003c/sub\u003e mode channels is lower than -16.2 dB, -15.1 dB and -15.9 dB, agreeing well with the simulated results.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003e\u003cem\u003eMultimode photonic circuits.\u003c/em\u003e\u003c/strong\u003e\u003cstrong\u003e\u0026nbsp;\u003c/strong\u003eTo further demonstrate the device performance in dense integration, we design and fabricate two types of multimode photonic circuits. The first PIC shown in Figure 5a consists of two independent circuits with path crossing of the two circuits, while the second one shown in Figure 5b is a single circuit with multipath crossings of the same circuit. The input fundamental modes are first coupled into different mode channels by the mode multiplexer. The multiplexed multimode signals are then routed in the chip plane by using the waveguide crossings and bends, which are finally demultiplexed by another mode demultiplexer. An only a chip area of 200 \u0026times; 300 \u0026mu;m\u0026sup2; is occupied to implement these operations.\u003c/p\u003e\n\u003cp\u003eThe measured transmission spectra of the first PIC are shown in Figures 5c-e. The insertion losses for TE\u003csub\u003e0\u003c/sub\u003e, TE\u003csub\u003e1\u003c/sub\u003e and TE\u003csub\u003e2\u003c/sub\u003e mode channels are 4.2 dB, 7.8 dB and 7.1 dB, while the inter-modal crosstalk stays below -20.3 dB at the wavelength of 1550 nm. Similarly, the measured transmission spectra of the second PIC are shown in Figures 5f-h. It can be seen that the insertion losses for TE\u003csub\u003e0\u003c/sub\u003e, TE\u003csub\u003e1\u003c/sub\u003e and TE\u003csub\u003e2\u003c/sub\u003e mode channels are 6.5 dB, 11.5 dB and 11.9 dB, while the inter-modal crosstalk still stays below -12.5 dB at the wavelength of 1550 nm. Despite a significant increase in the number of waveguide elements, the measured results still indicate good performance, presenting the good system scalability and dense integration capability of the inverse designed devices.\u003c/p\u003e\n\u003cp\u003eTo demonstrate the advancement in combination of dense integration capability and excellent material properties, an on-chip data modulation and transmission system is implemented. We design and fabricate three electro-optical modulators based on the micro-ring resonator structure, corresponding to the employed three mode channels. Light emitted by the lasers can be modulated by high-speed radio-frequency signals, then routed in the chip plane by the multimode photonic circuits, finally detected by photodetectors. A microscope image of the fabricated electro-optical modulator is shown in Figure 6a. The designed waveguide width and the coupling gap are 1 \u0026mu;m and 750 nm, respectively. The radius of ring waveguide is 300 \u0026mu;m, while the length of straight track is 1.5 mm. The measured transmission spectrum of the micro-ring resonator is shown in Figure 6b.\u0026nbsp;The insertion loss at a non-resonant wavelength is lower than 0.54 dB, while the extinction ratio is larger than 12.4 dB.\u0026nbsp;A ground-signal-ground (G-S-G) travelling-wave electrode is employed. The width of the signal electrode is designed as 23 \u0026mu;m, and the gap between signal and ground electrodes is 6 \u0026mu;m. Figure 6c shows the measured eye diagrams for different mode channels with the modulated and transmitted on-off key signal rates of 100 Gbps and 120 Gbps. The measured signal-to-noise ratios are larger than 5.4 dB. The clear and open eyes indicate the good system performance.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003e\u003cem\u003eDiscussion.\u0026nbsp;\u003c/em\u003e\u003c/strong\u003eWe compare the overall device performance including effective size, insertion loss, mode crosstalk and data modulation rate with previously reported works, as shown in Table 1. It can be seen that the measured insertion losses and inter-modal crosstalk is comparable with that of the forward-designed counterparts, while the device footprint is significantly reduced by an order of magnitude. Even compared with the previous single- or dual-mode devices, the demonstrated multimode devices exhibit relatively compact size, low insertion loss and low mode crosstalk. Moreover, the demonstrated PICs achieve similar high performance in electro-optical modulation when compared with the directly etched platforms, due to the high mode confinement in lithium niobate thin film.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eTable 1. Performance comparison of some previously reported TFLN components\u003c/strong\u003e\u003c/p\u003e\n\u003cdiv align=\"center\"\u003e\n \u003ctable border=\"1\" cellspacing=\"0\" cellpadding=\"0\" width=\"682\"\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd style=\"width: 95px;\"\u003e\n \u003cp\u003e\u003cstrong\u003eRefs\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 85px;\"\u003e\n \u003cp\u003e\u003cstrong\u003eDevice\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 85px;\"\u003e\n \u003cp\u003e\u003cstrong\u003eMode\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 123px;\"\u003e\n \u003cp\u003e\u003cstrong\u003eEffective Size\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 94px;\"\u003e\n \u003cp\u003e\u003cstrong\u003eLoss\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 95px;\"\u003e\n \u003cp\u003e\u003cstrong\u003eCrosstalk\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 106px;\"\u003e\n \u003cp\u003e\u003cstrong\u003eModulation\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 95px;\"\u003e\n \u003cp\u003e26\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 85px;\"\u003e\n \u003cp\u003eMUX\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 85px;\"\u003e\n \u003cp\u003eTE\u003csub\u003e0\u003c/sub\u003e~TE\u003csub\u003e2\u003c/sub\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 123px;\"\u003e\n \u003cp\u003e18\u0026times;347 \u0026mu;m\u003csup\u003e2\u003c/sup\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 94px;\"\u003e\n \u003cp\u003e\u0026lt;2.1 dB\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 95px;\"\u003e\n \u003cp\u003e\u0026lt;-17 dB\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 106px;\"\u003e\n \u003cp\u003e/\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 95px;\"\u003e\n \u003cp\u003e27\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 85px;\"\u003e\n \u003cp\u003eMUX\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 85px;\"\u003e\n \u003cp\u003eTE\u003csub\u003e0\u003c/sub\u003e~TE\u003csub\u003e2\u003c/sub\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 123px;\"\u003e\n \u003cp\u003e22\u0026times;500\u003cstrong\u003e\u0026nbsp;\u003c/strong\u003e\u0026mu;m\u003csup\u003e2\u003c/sup\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 94px;\"\u003e\n \u003cp\u003e\u0026lt;4.69 dB\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 95px;\"\u003e\n \u003cp\u003e\u0026lt;-10.6 dB\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 106px;\"\u003e\n \u003cp\u003e/\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 95px;\"\u003e\n \u003cp\u003e28\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 85px;\"\u003e\n \u003cp\u003eMUX\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 85px;\"\u003e\n \u003cp\u003eTE\u003csub\u003e0\u003c/sub\u003e~TE\u003csub\u003e2\u003c/sub\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 123px;\"\u003e\n \u003cp\u003e17\u0026times;450 \u0026mu;m\u003csup\u003e2\u003c/sup\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 94px;\"\u003e\n \u003cp\u003e\u0026asymp;0.2 dB\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 95px;\"\u003e\n \u003cp\u003e\u0026lt;-19 dB\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 106px;\"\u003e\n \u003cp\u003e/\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 95px;\"\u003e\n \u003cp\u003e29\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 85px;\"\u003e\n \u003cp\u003eMUX\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 85px;\"\u003e\n \u003cp\u003eTE\u003csub\u003e0\u003c/sub\u003e~TE\u003csub\u003e2\u003c/sub\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 123px;\"\u003e\n \u003cp\u003e17\u0026times;450 \u0026mu;m\u003csup\u003e2\u003c/sup\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 94px;\"\u003e\n \u003cp\u003e\u0026lt;2.0 dB\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 95px;\"\u003e\n \u003cp\u003e\u0026lt;-12 dB\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 106px;\"\u003e\n \u003cp\u003e60 Gbps\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd style=\"width: 95px;\"\u003e\n \u003cp\u003e\u003cstrong\u003eThis Work\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 85px;\"\u003e\n \u003cp\u003e\u003cstrong\u003eMUX\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 85px;\"\u003e\n \u003cp\u003e\u003cstrong\u003eTE\u003csub\u003e0\u003c/sub\u003e~TE\u003csub\u003e2\u003c/sub\u003e\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 123px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e19\u003c/strong\u003e\u003cstrong\u003e\u0026times;\u003c/strong\u003e\u003cstrong\u003e25 \u0026mu;m\u003csup\u003e2\u003c/sup\u003e\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 94px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e\u0026lt;2.5 dB\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 95px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e\u0026lt;-15.9 dB\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 106px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e120 Gbps\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 95px;\"\u003e\n \u003cp\u003e17\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 85px;\"\u003e\n \u003cp\u003eCrossing\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 85px;\"\u003e\n \u003cp\u003eTE\u003csub\u003e0\u003c/sub\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 123px;\"\u003e\n \u003cp\u003e12\u0026times;12 \u0026mu;m\u003csup\u003e2\u003c/sup\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 94px;\"\u003e\n \u003cp\u003e0.48 dB\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 95px;\"\u003e\n \u003cp\u003e\u0026lt;-36 dB\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 106px;\"\u003e\n \u003cp\u003e/\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 95px;\"\u003e\n \u003cp\u003e33\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 85px;\"\u003e\n \u003cp\u003eCrossing\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 85px;\"\u003e\n \u003cp\u003eTE\u003csub\u003e0\u003c/sub\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 123px;\"\u003e\n \u003cp\u003e17.5\u0026times;16 \u0026mu;m\u003csup\u003e2\u003c/sup\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 94px;\"\u003e\n \u003cp\u003e0.07 dB\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 95px;\"\u003e\n \u003cp\u003e\u0026lt;-50 dB\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 106px;\"\u003e\n \u003cp\u003e/\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd style=\"width: 95px;\"\u003e\n \u003cp\u003e\u003cstrong\u003eThis Work\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 85px;\"\u003e\n \u003cp\u003e\u003cstrong\u003eCrossing\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 85px;\"\u003e\n \u003cp\u003e\u003cstrong\u003eTE\u003csub\u003e0\u003c/sub\u003e~TE\u003csub\u003e2\u003c/sub\u003e\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 123px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e15\u0026times;15 \u0026mu;m\u003csup\u003e2\u003c/sup\u003e\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 94px;\"\u003e\n \u003cp\u003e\u0026lt;\u003cstrong\u003e0.55 dB\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 95px;\"\u003e\n \u003cp\u003e\u0026lt;\u003cstrong\u003e-15 dB\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 106px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e120 Gbps\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 95px;\"\u003e\n \u003cp\u003e38\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 85px;\"\u003e\n \u003cp\u003eBend\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 85px;\"\u003e\n \u003cp\u003eTE\u003csub\u003e0\u003c/sub\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 123px;\"\u003e\n \u003cp\u003e30 \u0026mu;m\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 94px;\"\u003e\n \u003cp\u003e\u0026lt;0.05 dB\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 95px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e/\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 106px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e/\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 95px;\"\u003e\n \u003cp\u003e28\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 85px;\"\u003e\n \u003cp\u003eBend\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 85px;\"\u003e\n \u003cp\u003eTE\u003csub\u003e0\u003c/sub\u003e~TE\u003csub\u003e2\u003c/sub\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 123px;\"\u003e\n \u003cp\u003e160\u003cstrong\u003e\u0026nbsp;\u003c/strong\u003e\u0026mu;m\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 94px;\"\u003e\n \u003cp\u003e0.026 dB\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 95px;\"\u003e\n \u003cp\u003e\u0026lt;-25 dB\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 106px;\"\u003e\n \u003cp\u003e/\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 95px;\"\u003e\n \u003cp\u003e37\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 85px;\"\u003e\n \u003cp\u003eBend\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 85px;\"\u003e\n \u003cp\u003eTE\u003csub\u003e0\u003c/sub\u003e~TE\u003csub\u003e2\u003c/sub\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 123px;\"\u003e\n \u003cp\u003e120 \u0026mu;m\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 94px;\"\u003e\n \u003cp\u003e\u0026lt; 2.5 dB\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 95px;\"\u003e\n \u003cp\u003e\u0026lt;-12.2 dB\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 106px;\"\u003e\n \u003cp\u003e/\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd style=\"width: 95px;\"\u003e\n \u003cp\u003e\u003cstrong\u003eThis Work\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 85px;\"\u003e\n \u003cp\u003e\u003cstrong\u003eBend\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 85px;\"\u003e\n \u003cp\u003e\u003cstrong\u003eTE\u003csub\u003e0\u003c/sub\u003e~TE\u003csub\u003e2\u003c/sub\u003e\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 123px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e30 \u0026mu;m\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 94px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e\u0026lt; 2.17 dB\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 95px;\"\u003e\n \u003cp\u003e\u0026lt;\u003cstrong\u003e-15.1 dB\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 106px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e120 Gbps\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd style=\"width: 95px;\"\u003e\n \u003cp\u003e\u003cstrong\u003eThis Work\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 85px;\"\u003e\n \u003cp\u003e\u003cstrong\u003eSystem\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 85px;\"\u003e\n \u003cp\u003e\u003cstrong\u003eTE\u003csub\u003e0\u003c/sub\u003e~TE\u003csub\u003e2\u003c/sub\u003e\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 123px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e200\u0026times;300 \u0026mu;m\u003csup\u003e2\u003c/sup\u003e\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 94px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e\u0026lt; 11.9 dB\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 95px;\"\u003e\n \u003cp\u003e\u0026lt;\u003cstrong\u003e-12.5 dB\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 106px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e120 Gbps\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n \u003c/table\u003e\n\u003c/div\u003e\n\u003cp\u003eIn summary, we have demonstrated ultra-compact multimode components and photonic circuits based on a silicon nitride-lithium niobate hybrid platform, by using photonic inverse design method. This hybrid platform shows a good combination of the excellent material properties of silicon nitride and lithium niobate. The optical structures in the isotropic silicon nitride loading layer are optimized by using a scalar-based inverse design method with improved design efficiency when compared with that using a tensor-based method for anisotropic materials. Moreover, the silicon nitride loading material owns mature fabrication processes, enabling improved device performance by means of small and well controlled device feature size. The reduction in device footprint supports complex optical path design within an ultra-compact chip area, while more chip space reserved for other important active functions such as data modulation, wavelength conversion, and spectral control. Our approach is scalable, which can be extended to a wide range of passive components which is expected to be important building blocks for realizing densely integrated and large-scale PICs in the TFLNOI platform.\u003c/p\u003e"},{"header":"Methods","content":"\u003cp\u003e\u003cstrong\u003e\u003cem\u003eInverse Design method.\u003c/em\u003e\u003c/strong\u003e Gradient optimization based on the adjoin method is used to implement topology optimization through iterative material distribution updates. The dielectric permittivity of design area is initially projected onto a [0,1] space for parametric normalization (Eq. 1). The material distribution is subsequently smoothed via a convolutional filtering (Eq. 2) to eliminate subwavelength defects. Finally, an adaptive binarization projection function (Eq. 3) is used to increase filter sharpness \u003cem\u003e\u0026beta;\u003c/em\u003e and obtain a binary distribution of dielectric constants. We only need to optimize the distribution of isotropic silicon nitride loading material. Thus, the scalar-based inverse design method is applicable.\u003c/p\u003e\n\u003cp\u003e\u003cimg 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BwKBQCDQVgS6iCy1tbiIFwgEAr0BgZdeeiltvvnmaamllio/cHnooYemJ598skuatsoqqySfSfDRuVq30047DVaGLThnlGzDsXQtt9xy6d133x0sTjwEAoFAINBZBIIsdRbBSB8IDIcI3HjjjckbeixATz/9dLL95rMFQxMK1q0rr7wyjT322MmvjV988cVpjz32SD7I2Vw9HD5XXwfTm4sT/oFACggCgRoEgizVABKPgUAg0DoCK620UvLV8MUWW6w8r7TpppumLbfcsvWEXRijKIpy+49VyXbgRRddlHxTpaW3X3x2YaqppkrjjjtuF9YksgoEAoHejkCQpd7ew9G+QKAbEPAJA2/B+WHfu+++O/mWiTNLPojp3hfG55577nTWWWclW2evvPJK8s0T54t8YXeRRRYpt/H8bIs4Xv/vQDXT+uuvX27/Pffcc+mKK65I8vW7Ue7nmGOO5IzT7rvvnrbddtuSSN1///1p6623TpdccknyOQZlb7TRRkn6jpQfaQKBQGD4QCDI0vDRz9HKQGCoIOB32nCoAAAAEABJREFUm1ZdddU09dRTJ1/U9Wr/AgssUP5ekx/rPeaYY8oD4Ycffniadtppy0PcrFIITldWcMkll0wrrLBC+b2pscYaK/kei4Pf6ue7LIsuumhCksYff/y02mqrxQ/ldiX4kVcg0AsRGKEXtima1NMQiPoMNwh8+eWXybkgxMSZItadkUceOd13331p3XXXLb+F5HX/CSecsNzGQ6a6AxyHvWeYYYaEKE0//fTps88+SwiSn0YYY4wx0gcffFB+4mCmmWYqvwvFrzvqEXkGAoFA70AgyFLv6MdoRSDQIxBASnw51wcil1lmmeQgNadyvoHkLTc/2/L3v/89rbjiiumWW25J3fG1bYe4WbiU7fMDPlKJyCFL6qgeLEvetnv55ZdLgqeO4QKBQCAQqIdAlSzVCw+/QCAQCATajIBvL62xxhqJW2+99cqrN+W8peY3nLbbbrt01VVXpVNPPTUtuOCC6a9//Wvq06dPm/Nva0REyDbfxhtvnPr27ZucofL7UL/97W/L7TfnqvwYp08f9O/fP9mea2veES8QCASGPwSCLA1/fR4tDgQCgUBgOEAgmhgIdB0CQZa6DsvIKRAIBAKBQCAQCAR6IQJBlnphp0aTAoFGQiDqGggEAoFAT0cgyFJP76GoXyAQCAQCgUAgEAgMUwSCLA1T+Bup8KhrIBAIBAKBQCAwfCIQZGn47PdodSAQCAQCgUAgMPwi0M6WB1lqJ2ARPRAIBAKBQCAQCASGLwSCLA1f/R2tDQQCgUCgkRCIugYCPQKBIEs9ohuiEoFAIBAIBAKBQCDQUxEIstRTeybqFQg0EgJR10AgEAgEejECQZZ6cedG0wKBQCAQCAQCgUCg8wgEWeo8ho2UQ9Q1EAgEAoFAIBAIBNqJQJCldgIW0QOBQCAQCAQCgUCgJyAw9OoQZGnoYR0lBQKBQCAQCAQCgUADIhBkqQE7LaocCAQCgUAjIRB1DQQaHYEgS43eg1H/QCAQCAQCgUAgEOhWBIIsdSu8kXkg0EgIRF0DgUAgEAgE6iEQZKkeKuEXCAQCgUAgEAgEAoHALwgEWfoFiEa6RF0DgUAgEAgEAoFAYOghEGRp6GEdJQUCgUAgEAgEAoHA4Ag0xFOQpYbopqhkIBAIBAKBQCAQCAwrBIIsDSvko9xAIBAIBBoJgahrIDAcIxBkaTju/Gh6IBAIBAKBQCAQCLSOQJCl1jGKGIFAIyEQdQ0EAoFAIBDoYgSCLHUxoJFdIBAIBAKBQCAQCPQuBIIsDav+jHIDgUAgEAgEAoFAoCEQCLLUEN0UlQwEAoFAIBAIBHouAr29ZkGWensPR/sCgUAgEAgEAoFAoFMIBFnqFHyROBAIBAKBRkIg6hoIBAIdQSDIUkdQizSBQCAQCAQCgUAgMNwgEGRpuOnqaGgjITC81PX1119Pjz/+ePrxxx9bbPI333yTLrvssuTaYsQIDAQCgUCgGxAIstQNoEaWgUAg0DICP/30U3rppZfSddddl2aZZZY0wggtq6Jf/epXacUVV0ynnHJK+vDDD1vOPEIDgUAgEOhiBFrWUF1cWO/LLloUCAQCHUHg5ZdfTgcddFDaYIMN0iijjNKmLMYcc8w066yzpgsvvDB98cUXbUoTkQKBQCAQ6AoEgix1BYqRRyAQCLQZAVtpLERzzDFHGmussdqcTsSZZ545Pfvss+nJJ5/0GC4QCAS6EoHIq1kEgiw1C00EBAKBQHcg8Oabb6bHHnssrbHGGu3Ofvzxx099+vRJ11xzTbvTRoJAIBDoXQjcc8896Yorrkjff/99Ovjgg9Oqq66attlmm3Kr/quvvkoXXHBBeuKJJ7qk0UGWugTGyCQQ6JkI/PDDD+mzzz5LH3zwQalAvvvuuy6vKEuRc0Qff/xxchZJAcr98ssv3SZKq7pt9vDDD6eiKNLEE09chlf/iKuurvy//fbb9Omnn5bK0LMtuymnnDI99dRTrR4KF7/q1E091JWTdzW8ge6jqoHAcI/ALbfckgYMGJAWW2yxdO6556Z55503XXTRRWn00UdPW265ZRpttNHSfPPNl4455pjyfGRnAQuy1FkEI30g0EMRsNq66aab0uGHH54222yzZNvr9NNPH0Q8mqv2W2+9VVpuLr300lTrrr/++pJ45bTeYrvrrrvK/Oeaa6709ttvl0H8fv/735dvr1nd7b333iWR+vrrr8u330YaaaQ0xhhjlHGrf6699tq02mqrpX322Se9//776YYbbkiHHXZYcsZJvBFHHDGNN9545VbcK6+8wqtNDnm744470j//+c+01VZbpQUXXDAdeOCBKQhTm+CLSIFAj0LA2D/55JPTvvvumyaaaKJSt6288srJuca11lorvfrqq8m/mWaaKe24444lYbJA4tdRF2Spo8hFukCgNQSGcfg555yTnn766bTLLruUK69VVlmlJD8sQC1VDaF55513ku2yWvfuu+8ORjC8xbbccsulo48+uswSWWIJsk02cODA0vqz5JJLluSkKIqSqLF0IS9lgpo/66yzTjriiCMS8/qVV15ZpkNqZpxxxkExnXNiJaptx0MPPZT+8Y9/lJaoQZF/uUG6ELFNNtkknX322WnTTTdNZ5xxRtLOX6LEJRAIBBoEgRNOOCHRK5NPPnlZ4/nnn7+8+sOyNNVUU7kt3dxzz51GHnnkcgFYenTwT5ClDgIXyQKBnoyAbxchGcsuu2x5xmecccYpV19ewac4Wqr7tNNOm7bYYou00047DeGQjEknnXSI5M4RyfvFF18sLUJTTDFFeuONN8q31j755JPSVF5NJLwoiqpXeV8URZptttmSs0ljjz12mmSSSUr/6h/K0NYf4lb1f+6558rzC3n7L4chbccee2x5RsrWH4uWg+K29NQ5x4trIBAI9HwEWIjuv//+NM8889StrBdAtt1228HCFllkkcTKPphnOx9GaGf83hg92hQI9CoEWF1YdlhjmKE17vPPP08sK7bjRh111ITA2EITVut8+ygTFqSl6pwBuO+++2qTlOcEpplmmvTee++V1iQkx/kohIYVabLJJhssjY9Rqudgnr88sFYhNFdccUWqF0e9hTO//5KkvGy44Ybp5ptvTsouPX7588ADD5QrS2caeLGc3XnnnWnXXXctTfi24j7++OPEX3i4QCAQ6LkI2J43VrNVqVpTizXjedFFF616p1GbdF7eyh8soB0PQZbaAVZEDQQaAQEHpJ0ZYppmPbEt9q9//SsxTa+wwgoJUUAsbLHVa4/tOgeo5VPrHM5eeOGFh0jmLJEDla+99lp5cFtZDlP78CRLlXpIhAi5L4ohrUrCWYx8FsAHKJEyCg7hQpCEcwiZeBSg55acOiBLrGGsSNI5u6QeG220Ubml6EyVN2iOPPLIhFS2lF+EBQI9H4HeXUOW8aIoyvOQ1ZayKLM4Lb300olVuhrmvi36QrzmXJCl5pAJ/0CgQRF45plnyu0vZGjnnXcuDzUjG94KsR231FJLJdtzRVGfsHSk2QgQS9ZKK61UfjuJ5Yc1abrppksTTjjhoCwRlmztQlwGBTTdeLvFYfSiKMqvdU8wwQTl2y3M7tnCpB0IEDLGNSVr8T9ihXB99NFHyYHzQw89tDyEvttuu6Vxxx233DJEkI466qjy4PiDDz7YYn4RGAgEAsMWAZZj1m4Ls2pN6Dc6aIYZZijf/K1uu3lpxQsu1fjtvQ+y1F7EIn4g0IMRsPVlwreN1r9///KbI+uvv35ad911yzdFurPqCMgSSyxRFoEQXX755clPmZQev/xhgfImmnraCvzFu7zMOeecSV1tlyFa5513Xtp4440TBSidSN7ws4Unf4SMX0vu+eefL39KZffdd0/OMbCowcKZKelY3ZA2VjF+yBX/oeGijEAgEGg/AsYqy7PFldQWU44XDBgwIHk7ztu09Eh1keaFkdVXX130DrsgSx2GLhIGAj0PAZO/fXsKg+UFAXGWiEWnu2vr8HQmNcpTvu2u2nJty1kZ3n333YMFUW5Whczl0rFK+aZSzlNkZxUQLa8He27JsUY9+uij5bdWfNaAQ7yQrKL42armvk+fPuU5K/n6pEFLeUZYIBAIDHsEvHzCYvzII4+UL7CceeaZ5edEnNXkWJXmmWee5LykbXdv0HprtzM1D7LUGfQi7XCAQGM10RkhBxz9hlpzNfe6PIsLCxRl0ly87vL3LRRWHpYnW2DtKcenCWzPIT6tpXNoG1ly2NM2Yb34tiVt66mLTw94a6ZevPALBAKBnoWAzwc4b4gw2Z6vrR3dZkF26623pv322682uN3PQZbaDVkkCAR6LgImf6/321JqrpYsKAsttFBpTWF9aS5ed/ojMMziFBml1paybJf5JMLiiy9eflqgtTTa6RD3Agss0GxUB0EdaC+KotyqdBC82cgREAgEAj0GAWcO//CHP9Q9zK2SdBursYWZuPw643oNWeoMCJE2EOgtCDjLg0w0Z0nRTttbfg5g7bXXTsNq20m5zg7ZqvPbTfVWhuqaHaLkjb7ZZ589cUXx8zZaDq939WkB25G+y1QvPPtNP/305Ve9nZXKfnENBAKBno+As4221m3b19aWjmGBdjygNqwjz0GWOoJapAkEAoFOI0CZ+bouV0/ZVQtwBgq5sr1YPcNUjRP3gUAvQiCa0sMQCLLUwzokqhMIBAKBQCAQCAQCPQuBIEs9qz+iNoFAINBICERdA4FAYLhAIMjScNHN0chAIBAIBAKBQCAQ6CgCQZY6ilykayQEoq6BQCAQCAQCgUCHEQiy1GHoImEgEAgEAoFAIBAIDA8I9CyyNDwgHm0MBAKBQCAQCAQCgYZCIMhSQ3VXVDYQCAQCgUCgURCIevYeBIIs9Z6+jJYEAoFAIBAIBAKBQDcgEGSpG0CNLAOBQKCREIi6BgKBQCDQMgJBllrGJ0IDgUAgEAgEAoFAYDhHIMjScC4AjdT8qGsgEAgEAoFAIDAsEAiyNCxQjzIDgUAgEAgEAoFAoGEQ6Aay1DBtj4oGAoFAIBAIBAKBQCDQKgJBllqFKCIEAoFAIBAIDLcIRMMDgSYEgiw1gRD/A4FAIBAIBAKBQCAQaA6BIEvNIRP+gUAg0EgIRF0DgUAgEOg2BIIsdRu0kXEgEAgEAoFAIBAI9AYEgiz1hl5spDZEXQOBQCAQCAQCgQZDIMhSg3VYVDcQCAQCgUAgEAgEhi4CzZGloVuLKC0QCAQCgUAgEAgEAoEeikCQpR7aMVGtQCAQCAQCga5CIPIJBDqHQJClzuEXqQOBQCAQCAQCgUCglyMQZKmXd3A0LxBoJASiroFAIBAI9EQEgiz1xF6JOgUCgUAgEAgEAoFAj0EgyFKP6YpGqkjUNRAIBAKBQCAQGH4QCLI0/PR1tDQQCAQCgUAgEAgEahFow3OQpTaAFFECgUAgEAgEAoFAYPhFIMjS8Nv30fJAIBAIBBoJgahrIDDMEAiyNMygj4IDgUAgEAgEAo1+S7wAABAASURBVIFAoBEQCLLUCL0UdQwEGgmBqGsgEAgEAr0MgSBLvaxDozmBQCAQCAQCgUAg0LUIBFnqWjwbKbeoawMi8OOPP6Yvv/wyffXVV83W/vvvv0/fffdd3XD+n3/+efrss8/S119/XTdOezzlp7z2pOnOuHD54osvEpzqlcP/22+/TT/99NMQwdohLWzkUy/OEImaPKSDQ9PtMP+vztqnnbky7r/55pv8GNdAIBDoAAJBljoAWiQJBIYVAm+//Xbafvvt01ZbbZV++OGHIarx8ccfpwEDBqTrrrtuCELw0ksvpb///e/pd7/7XVprrbXSb37zm/Tyyy8PkUd7PG644YZ02mmnpY8++qg9ybolLqKw7777pvXXXz9pa20hSM1VV12Vzj777IQwVsPffPPNdNxxx6Udd9wxrbvuuqV7+umnq1Hq3n/44Yfp1FNPTTfeeGPd8KHt+emnn6YzzjgjXXvttYPkQ9sOOeSQdN999w3yG9r1ivICge5HoHtLCLLUvfhG7oHAYAg89dRT6d133x3Mrz0Pk0wySdpggw3S8ssvn4qiGCLpeeedV1pV+vbtO1j4+++/n/baa680xRRTlJM7wvD444+XE+gQmbTDY+mll04jjTRSOvfccxOyUi/pe++9l7S7XljVT5xXXnml6tWu+6IoUr9+/dIKK6yQxh133CHSwubJJ59Mq666ahprrLEGhSMYxxxzTEKmEKYLLrigbAsiOChSnRsWG+0eZZRREhzqRBnqXuOMM05abbXV0kMPPZS0QwX0+XrrrVf20W233cYrXCAQCLQTgSBL7QQsogcCHUXgP//5TzrnnHPSiCOO2NEsku2UV199Nc0444xphBEGH7533XVXSUpYjMYee+zByrj88stLMmDSHG200ZKtmtFHHz3NMsssg8Vr7wPSwRLzwgsvpDvvvLNuclanepaeauQnnngisX6MPPLIVe923w8cODCNN954qbb9iOGFF16YttxyyzTppJMOlq9+eeONN9IOO+yQxhxzzHILEwFaYIEFBotX+6C9LHPrrLNOma42fFg9I0dbb7110l64qsess85aWs3Iweuvv85rmLkoOBBoRAQG17aN2IKocyDQwxFwnuWoo45Kffv2Ta677LJLsp1mkp5vvvlKS8B2222XVl555cRvjjnmKLfanClCIGafffZyW4XlxrYP4oEMmAxnmGGGcmvN9tv++++fllxyySGsKs7g3HzzzaXVpSiKcsvszDPPTEcccUSaZ555WkTvtddeS2ussUZaccUVk/s99tgjTTbZZOWWlfpI3KdPn7TEEkuk/v37J2d++LXV2Uq87LLL0iqrrJIuuuiihHg8++yz6b///W+Z51xzzZX+9Kc/pdVXXz298847pZ/7V5osUCxFSCNMkT/1eeCBB0qixIIy9dRTJ6Thgw8+SKecckppcZqkyTJXrRvyee+996aFF164tJCxMl1//fXlNhwsq3Gr986NHXDAAWnxxRdP2l8Nc68uLIgbb7xxQk6RVJYrYZ1x8kXS9Pvmm2+eHn744STviSeeON1+++2DstZHSy21VBowYEBJjAVMN910pUXt3//+d2zHASRcINAOBIIstQOsiBoIdAQB1pJ+/fqlxRZbLF166aXpn//8Z7klctBBByUTvi0glg8WIZP2wQcfXBIrZIh1Y+eddy6tHcpmpWH9ePHFF9Ooo45akgCWKoSAxWn66acXbTDH6oMUyNv226677lpaqNRnsIiDPfz8gDwgSiZ8Z3hs5Tnz5BzMzzF+/msiRnBYdvgo81//+le6+uqr06233pruv//+8t4zcuIAtXjqLn9bYyeddFK644470qOPPloSr6OPPrpMawsRqUMIYIdYyWOMMcZIJ5xwQmmpQ0SQS2RSvkjbbbfdlsThx3I055xzChrMyVtb5p577nTNNdeU1hfWmAUXXHCweLUPn3zySUkep5122tqgchsUcTn88MOTNlxyySXpnnvu6ZJzTdrFcrbSSislfWMr8Pjjj09I9/PPPz9YXWabbbaSdNoGFcASOf7445d+GX/+4QKBQKB1BIIstY5RxAgEOo0Aqwzrh0mN9QixOPHEE5NtMFs+E044YUmmWCxYVmyVLLTQQmneeectJ+WJJpqoPIMkjIVlggkmSGuuuWa57eaciokTWWBxqlaW5cb5FeWYKB0MP/LIIxMy09qZHPlMNdVUCQljQXEWiGUDYZNfUfzvzFQuF4mQDkF57rnnEjdw4MCEkLjnEBfkRjwOYVH/ZZddtjxwzvKB0CGKyBRyMP/884tatheWLCv/93//l5555pmk/b/61a9KEiAv5FRdWZkQSnWWv3zKTCp/WOk8Iplrr712QtgQQ0SPf3OOZRABze2uxtM/SByrkn6Vt/6rFzenu+mmm0oLGita1bEWOsuV4yHK2stv8ybLEoxYDpEf8pLjuWovqya58MypAxmr4s8/XCAQCLSMQJCllvHp8aFRwcZAgGVhueWWK61Bt9xyS7klZKuEZcCkboK3beQtLWTA1htCgnwgU9NMM03ZUCTLBIxEFUWRbEchYCZ48cpIlT/yQyiQjaL4mdyYKE2wRfHzs+jKQRa82eY5O1YJbplllinJGgsW4mF7LMepdzVxIzx//OMfk0nd23fuOWecnHXK6dSPZWryyScvLUvOFLEkCXcmCLlCODyzbk055ZTJViUShFTCAqlivYIBAsGixKIFc2ezkCbpq056eCoXkRSGXLLe6BfPHHKBwOy3334eS4ecceVD5Y/0+lfeLDuCbJHCSz95rue0Z8MNN0y1Dm7qV03zyCOPJORL2/g7tA4z55I8hwsEAoGuRyDIUtdjGjkGAoMhgLDYXkJYkBSTp0O4IiECXvU2mZroTf6sB+IWRVFalRAL1gRpkYcNNtigPFAsrbynbdoKQqBsszgnI9/sWEBYOmaeeeaS7CAByAlysPLKK+dopXXG4V8HoAd5Nt2Ii3ggM02PJZlRDouT5+yUy98knv3acmVtY/mSDtHQPtggIqwiXsv3th1iiaSxctmCEq79LCpIJoLjswDOfskLwWM1QrpYU5Al2FbrBAsk1vac/BAceMnT24Y5LrJlS81nCbKfLUH3ynHNTj1YDhdddNGEACNazhghPdrDeubzDdqd07giO/q81pELfS8Ox0qEXHv7DkFGcp2xsqWqPHGyg4845Ief9rG8eVOQrPELFwj0MAR6bHWCLPXYromK9RYETGgmZtYPVgH3tsB898bZG0SgKIpkonYWyQRvC0X7nWUyIdt2EZ/1IBOXu+++u/w4pTM2RVGkvn37JvHlLy3H6sBSxdpha8k5KN9g2nnnncuD0OK05B588MFkywvhYJFCBFi9POd0ylMH24K1JEocZCuTC89VZ/JH+BAih9CRGgQGuUR+JplkkvLcEQy0n7UmW9m8/YeMKBvhggvs5M9iBG9X+TuDBC+ETDhnS5OlCmZXXnllUp4zXc5QOcMkTnMOAUFYlK39Od5bb71Vbj3yz3irL2KK9CBKyF2O394rsqOM3E7bm8gwklXNSztZ2pC+LEvImvSIHJyr8eM+EAgEWkYgyFLL+ERoINBpBJAFW1xW/qwiDkizJCBRDis72G0Cs91iu4mVgJVGwawe3jRDUFgEWCgQC2HiOpuDQJgQd9ttt4QcsagI55AxZc8000wJOTBhsr7UTq7i1nNIhrfP1J1lxiFiW2yec3xERt677757qmex0C755PjVq/hIHmuSiX2zzTYr30yDDfKFZPhukHDt92Zebj8SJ432I2POY8lP/spUb+QSGd1kk03Kc1oOjwvnWNKcxbKdxWLFErPRRhuVb//lMsSr55Tz5z//OSFFtkLFYblBaln5bFvCBFFS564iJyxg3hjU5lwe+WJdVIfsyIB6bdBkhcxtIRvqQZ6yfOX47b5GgkCgByDgDCRLq8XBWWedlbwcY8FjEcV6a+FlsdgVVQ2y1BUoRh6BQAsIeLXcV6URJZOdMzY77bRT8mzLDeExYRdFkZy3MdHn7BAJhMF2CoLjHFMO82xyR5T4sayYmE8//fTE+sCKYDJnAfG2mfNCm266aXLmpyj+d15J2uYcMuf1fOEsPyZmBMQzZ/vNG2rqj7zwa48zecPBYW0EjNVl2223TQieZyRLGEsObGwn5vw9IwNIFH/POcyzL50jpfwQJmeOfEKAtQkZ85YavJCH3//+9+XnGqRjkZKmNae92g1vhBF5eeyxxxLiq7/hjTRpY2t5tTUcEdMnZIpFy0Shf2CQ82C99BaebcPcflt1xx57bIKttDluXAOBRkXAOPYiBSs3gsRya5vbtjcrsUUC521jurCz7Qyy1FkEI31DI2DCcUbFVo23mxq6MU2VR6wQDSuq0047rfx4JStEU1Cn/sPIFh5LTCZnMvQzHw4uI2Oee7Jjndt7773LrUqrUFt8LX1LqbW2FEVRvpGo7bYEnUVzxssnGlie6qW32iVn5K5eeHv8ED5kGP6ZkCFt3iZ0ID2TWhYun1E488wzU71t0vaUGXEDgZ6AAAu5sWxBZIGDJFlUGXsWkazErKes4ManM4esT52pe5ClzqAXaRsaAYdxTSy+HWRQ+bifV94bulFNlWeNce7GVow3z5qbuJuitvm/80q2eiikaqLf/va3JWGo+vXke9t5trEcFrcdmklGZ+rMkoSg2qJEXGyd1suPsvabbc5j2dKsF6c9fvpEX7NU5nQsT4iSvsp+JhMfN83PcQ0EGh0BllOkyPECbcmLAPrbgqRfv368S4dI+dwJ62rp0cE/QZY6CFyXJovMhjoCVia+c2TS8iVmzmBy5qS1yjgULL4zK7XO93JaSz80wm1b+WaQrzh3RXnyO/nkk1O2VnRFnsMqD1uaf/nLX5LzX11ZB6ta58aaI2C298iNrUBbeJ0t21t/1a22zuYX6QOBRkDALoAXVmqtws7o/fWvfy1/F5GOrrbFgsaLLVW/9t4HWWovYhG/VyBgu8Q+t/NCzg05x9OnT58hfiqkXmOdf2FhcS6l1tnqqaaxTWL1H27BFBj0HAwc9q7KadwHAl2JQHfm5e1PW96sxNVyfA7FyzLI1GGHHVYNSj7i25aF8GCJah6CLNUAEo+9HwFmWkTJ9kUecN6G8vYVssPqZIvOtR4ayBXLACtLrbMNUk3jY4MO4YZ7IAUGPQcDcl6V07gPBBoFgXzez+Htap3pZS+zsO5W/fO9bet835FrkKWOoBZpGhoBb4qZuL2pZOB5/dQr5d5ecpDZ4V/nl7wKjzTVNtbbRl6/r7UqefaGVW38eA4EeiYCUatAoPEQsCBFjJr7JIBvt80zzzyDNcwHffP5psEC2vEQZKkdYEXUxkfA6922IBy2vf3225M3KuxlI0cOwhZFkbyafdFFFyVvFjnTVNtqr6h7s8hHB2udn6uojR/PgUAgEAgEAl2DQJ8+fcrf0bTgzTk6f+olBu7hhx9Ofpcxh7n6mK6oX8vdAAAQAElEQVRPlLjvqAuy1FHkIl1DImDV4avUvq3jraFf//rXiUXIdllRFOVvtzmThEz5fo3v/gzrhkb5gUAgEAgEAv9DwHfqECCHuvn27ds3+UQA59tzVSuSxbEdAmHidtQFWeoocpGuIRFwMNABQd8jct7Iq96+t+ObHLlBtuZstfmdNB9GzP498ernUbzpoT0IXm0dtcWXqgcMGJBY1WrDfVRyzz33TD5e6DfQDjzwwIRQ1sZr67MtzIsvvjgpt61puiue9vropIPlvjVUW45w269HHHFE8mpxbbizbT7k6HwabLbeeuvk8GhtvNpnZyPg6CdtlAHP5s6/1aZtzzOM/a6gn2pxLy1r6KGHHppq3wYSFi4Q6C0IOLD9j3/8Izkq8cILLyQf6/U7ipy3RIvi54/uesHmyCOPTMajD+p2pv1BljqD3mBp46EREPAWXFEU5e+d1auvz+TbYnMA3BerbdXVi9dVfshKWybg5srz1W6f+Pd2XlH8rCCqcU2kvnRrVVUUg4f71tD+++9ffg5g4MCB5Su3V1xxRXmt5tGee+U4A3bZZZe1mAw50faWIgkXr6U4LYUVRZGOOuqoZKXJdF8b10/BIJF+TqX6BWzxrER9FkLfIM7epLnmmmuSz0sIb875UORxxx2X/PyK77vAYZFFFkm+C9Ncmo76I/jwRvh8sVg+znNoz/HHH5/8Nhy/cIFAb0RgkkkmST4V4AxqvYWij7+yPO2xxx7lYrCzGARZ6iyCkb6hEDAp+okMk1m9irMAeMvC+SWTtWu9eF3hx9qBlDl82NH8WD9efvnlxOxcFIOTIcQQ4fN7a1ZbtWWwAvHzkUY/w6Ldvs7N8e+Is+Lzkyo+vIhgNJeHurU0mXs7EcH44IMPmsuiTf6UpZ9BqCVL/P2ord+Tsyqtzcw5Nv3jC8G+MeUbSa62aGvj5mdWJO1m5bG166r+DqNKn+N15ZUc+wCfL6nDVN62lLfZZpukfXDkFy4QaDcCDZDArxP43lK98UWnWTg4TtEVTQmy1BUoRh4Ng4C3JJxXqje4NMLEuskmmyRWBa76O23Cu8LZpkFUfBTR90BYP7IFxcfWVl999XTQQQel/fbbL5kI87PJd0DTdhpy4+dM1MW2oi91syj4GjnlgICxiMhDe/PXbcXPjgXEb5rJ22RuFeY33nzV2rZTjld7RSD/8Ic/JGcG/N6SuvtWla23HNfnGHyW4W9/+1uSb/Zvy1UbfdjTAU2/+2SLME/4yIvvqPgdN1tNsMnP6mXbS3vOP//8hPQiLw57IsiPP/54Uk/meG23feVL25Rtbb1YF1nYfJ0cyZKXtxx32WWX5KvBtfHzM8xZeMRBrChrB/5hwQqU47XnatWMsO28887lCwcIkHawGOZ89K9+drg1440wIYHnnntuIm85blwDgUCgYwgEWeoYbpEqEOgwAiw4DpY7PO5HHhEmJM1E2L9//2SPHaFDdpxFMlHaix/QRJT8dAmS5dwVMmArzXkalhKWBV+mZs1AZO67777kezpFMbjFScUdekQKEBsTui99zz333AkRa+mcljNSznqxGnkTcIsttkg+wWBLS33kXRRFubXH2qFe/DhWMGVyJnXOPSdMHKRCXZwlgwUS5oOhJn0/WusbKqwmCCGCACNxb7311uTnRoRrv7zVB07aY6vK9iqihFghT764rTzlVp06i6M8n5Nw5omZX7kIUDVu9R7h9ZtUMC2KITGvxm3LPeKoLvD2A722AJ2bckYtk+WUUiqKouxneOfXqbULLixd8GhLeREnEAgEmkcgyFLz2ERIINBtCJgEEZrFFlusPAx99dVXJwexWUVsqbEUTT/99AlJcljXOSDPLEfOF7F4FEWRHG40GRZFkXbYYYckHnKARJlsbYvVNoKlwfkb55xYIJTpUwksEw899FBt9MGeEZQ333wz+UFd23tFUZQWD9aoovgfQcjlqlvOwIFMliDO7/Epzz3nJ0ByPIeUleE8DsKD9PkRX+fHEBfE0lktv3+HIHK+3lttv58cYYlCerQXOUUQM4nyPa16W2owsz3IKuPQu8PfSMidd96ZELJcx3pXFjBklqWuXnjVT7/5nbhax7KozuIiPKxfCBDixuLJn9yQEffZkRdY+W2s7Kf+2svilf3iGggEAh1DIMhSx3CLVIFA+xCoic1S4OCvCdvkd+mllyaWFNt+rBh33313cu8NDsSKdYXFhfXChD7ttNOWObKQsFTJqyiKkiyxEBVF0ez2CzKCOPi2VJlJ0x/bkg41q0vTY2LtYfEyeXvOTrhvT6lLURTJNqDJGInKcZq77rrrrglJ45AQv2vmnkN0cjpnsLR3mmmmSeqErHirDVnUdnVHJGw/uUfMWFuklxbBhIlXixEIhMNWnG065xtYhxAo8WudtniDJucnXFlIBwLn2b1tVFYvz9nZrlO//NzSVR8op9YhftUzbCxjnFej5YcMKd/WnudwgUAgMHQQCLI0dHCOUgKBQQiwajhfZKvNpI588LNtIhJL0qmnnppsj9k2MllnMvT2228nViUHtqVhSVprrbUSyworDouSbRsHf5ECZEaeVWeCtnVniy77I10Iig9u8mMhsQXIwuI5OxYRYTmtD8Mhd5m85Xi5XHXNfm25IhzyRBSVo/3O7eSzRawutiMRIrg4r2UbUHsQOeTKoXyEgtUGIUS65IOIsOSpE+sPwlJbJ8REPixuOYwlz4/vLr/88qWXPkOmMlalZ9Mf26rIEqLZ9Njif+ltGdY655OQQokRPf3r/JM2ebbdqXx9JU52SHRRFInVLftpBwxhk/3iGggEAh1DIMjS4LjFUyDQ7QggNEgBUmP7DelBdGzjmBzvuuuuctJDgFiYWEZYoFQMkRLfVhGriq0WJKsoisSSYgvO+RyTtq0x53iky87ZIB/l5O+VeJYUZ2FOPvnkZCuOlUZcEzJCksvlx8nbmRx186x+JvfaN+iQKmQCURGv1rFkcbX+vknEsoJ8IUWIB6IDG1YVr+Kb/JUPO6QKPkXxc/vlqV0sd4gCgsMPQWRdghkSoV7i1JYPX+nFU7Z731pyqB3W4svPGzbq6Dk7dRp77LETwpX9kDZWLLi7z/5tuSJHSKy6InhIKbJkC85zNQ/9CW+ELftrMwtU7tPsH9dAIBBoPwJBltqPWaQIBDqFACLjGyG33XZbcu7G21Nrr712+c0Qk7OzOiY5kywLETJkglYoP+dx+LFIeTMKKchhrC2sQfK3zYVAscYI51ggEA9v+tlG8g0ilhzniRAPcVpyJnCWHGUiBSbkhRZaKHnO6ZAbZK5///6JRSb7V6/S+FmZqp97+SMCDpB7/R4hcabJNqVD3ixFthnlixj6llEuGzZwQkKRLunEky+iIRyZQO4c1nYGyhancE7Z3p5TBmuS9AibD9/ZdhSnJYco+TFm574QLf3sbUF4K8ubeEhTS3lUw9QHaVW2trIqIkXkxXOOy4rnXJdvzpAN/uIiVv369UvVuMLCDU8IRFu7CoEgS12FZOQTCLQRARYKh5tZK2yVmeC8iu/tMgTBWRzh6667bvl2Wt7ykr23obzCbmK2/bb00kvzLp1nZ4Ey6XEYGqm64IILBn2hGglAGrwJ5q07r7rvs88+ibWozKSVP84dOdwtmkPPyFl1ywpR8po9QoMQidcep11w8Zt9iA6ygEjKE0asJMKRHW/uOYOU8/fsnBVrGIIhXQ7z7CC77Sx+CNXmm2+eTjvttITM8FN3H/BEwHzIzlkqbyvCXzvFackVRZGktRXoO03S+HyCfLgDDjhgMFLZUl7CED94ZxzhjRiqu3AO+WURFIdliZ9zW0ieNxVze/mHCwQCgY4jEGSp49hFykCgxyOAfHlzzKvmLBWsWc7/sDx1pvK2lLyhxsrh/FTOy1kskzyiVxT/ezsuh/ekq7cB/bgm65utUW8jakuV/LW3vt5KQ8IQL1uUbU3fWjx4I4zwVob4LFe+SWVbElHkhzwh3c64+eYUv3CBQCDQeQSCLHUew8ghEOixCHibzqTpkwO2zbwRZiJl0epMpVlPnO/xlhpylPMyadv6cYA6+/XUq3qzkiGUrG2scrY1O1P3oigSwsWqI++uaruzZc6B2bpksZKvqy1DH8/Uz/ycy2KB69u3bxLOL1wgEAh0HoEgS53HMHIYbhBo7IayJvkUgDexOtsSB7qdV0K8OptXT0if24Ps9YT61NbB4XEH0m2t1obFcyAQCHQ/AkGWuh/jKCEQCAQCgUAgEAgEGhiBXkmWGrg/ouqBQCAQCAQCgUAg0MMQCLLUwzokqhMIBAKBQCAQCFQQiNsegECQpR7QCVGFQCAQCAQCgUAgEOi5CARZ6rl9EzULBAKBRkIg6hoIBAK9FoEgS722a6NhgUAgEAgEAoFAINAVCARZ6goUI49GQiDqGggEAoFAIBAItAuBIEvtgisiBwKBQCAQCAQCgcDwhkDPJUvDW09EewOBQCAQCAQCgUCgRyIQZKlHdktUKhAIBAKBQKA3IRBtaWwEgiw1dv9F7QOBQCAQCAQCgUCgmxEIstTNAEf2gUAg0EgIRF0DgUAgEBgSgSBLQ2ISPoFAIBAIBAKBQCAQCAxCIMjSICjippEQiLoGAoFAIBAIBAJDC4EgS0ML6SgnEAgEAoFAIBAIBBoSgW4mSw2JSVQ6EAgEAoFAIBAIBAKBQQgEWRoERdwEAoFAIBAIBAItIBBBwy0CQZaG266PhgcCgUAgEAgEAoFAWxAIstQWlCJOIBAINBICUddAIBAIBLoUgSBLXQpnZBYIBAKBQCAQCAQCvQ2BIEu9rUcbqT1R10AgEAgEAoFAoAEQCLLUAJ0UVQwEAoFAIBAIBAKBYYdAW8jSsKtdlBwIBAKBQCAQCAQCgcAwRiDI0jDugCg+EAgEAoFAYGgiEGUFAu1HIMhS+zGLFIFAIBAIBAKBQCAwHCEQZGk46uxoaiDQSAhEXQOBQCAQ6CkIBFnqKT0R9QgEAoFAIBAIBAKBHolAkKUe2S2NVKmoayAQCAQCgUAg0LsRCLLUu/s3WhcIBAKBQCAQCAQCbUWgmXhBlpoBJrwDgUAgEAgEAoFAIBCAQLeSpZ9++ilddNFFaYcddkifffaZ8sLVQQBOTzzxRJpnnnnSgw8+WCdG57xy/nPPPXd66KGHOpdZF6dWt1NOOSXtu+++6bvvvuvi3IdOdtrw2GOPpVlmmSU98sgjZaFnnHFGWmGFFcr7jv758ccf0yGHHJL22muv9OWXX7aYzQ8//JBmnnnmcry1GLEm8NNPP0177LFHOvnkk5N21ATHYxcg8NJLL6VVV1217J8//vGPzeKsD//xj3+kv/3tb+nrr7/uUMkfffRR2nnnndNZZ53VanryOWDAgLrxfv3rX6d//vOfdcN4ks1DDz00bb311h7b5D755JM000wzpRlnnDEdccQRiT568sknk7zWWGONdMIJJ7Qpn18itftiDtpoo43S9ddf3IFWFwAAEABJREFU3+60LSUwbu6///6yPU899dQQUbVv5ZVXTpdffvkQYS+88EKCtesQgUPJQ/0OO+ywtPbaa7e7xH/9619p2223TR9//HG70zZaghG6s8LPPvtsOv3007uziF6R94cffpjOO++89NVXX3VLe+R/7rnndkv+lPpbb73V7nq/8soryeTw6quvpgsvvLDd6XtSgvfffz+dffbZZXtyvTbffPN000035ccOXe+888503XXXtSntkUceOVj5bUrUFGnsscdOCNk222yTiqJo8um9/xGJd999d6g2EEGwGDj44IPTzTffnEYZZZRE5nMljIG33367JEePP/54uuyyy3JQh67jjjtuOvroo9Omm27aanry2a9fvzIeIvHaa6+V9/5ccsklabvttnNb191+++3p2muvrRtWz1P+a665ZrrxxhtLogQHC4zZZ589XXDBBYNhQg++/vrr9bLplN9RRx2V3njjjU7lUS8x/aeP64Xxo3ubK3eGGWZIsHYVd1i4e+65J916660dKnr11VdPJ554YurTp0/q7f+6lSzN0rTS3mqrrXo7hp1u3/jjj5822WSTNNpoo3U6r3oZdGf+t9xySznY65XbnB9y8fe//72cIKaeeupktddc3Ebwn3DCCZNJZ6SRRurS6i699NJptdVWa1Oef/7zn9OII47YprhDNVIPKsxkiYAOzSp98MEH6Ysvvkijjz56mnLKKRPSROZzHUy0rJDvvPNOaZlgZchhQ/NqsXbllVe2uchlllkmmSjbmgAxQlanmWaahDTttNNOg5Ia/1VMEDEEalCELrr505/+lKaYYoouyu1/2Uw22WSldeV/PoPf0e3dUe7gpXT8aYkllkjLLbdcxzMYTlJ2mCwx826wwQbl6gMzJfzrrbdeuuaaa9LTTz+dPFNOGcczzzwzid+/f//sle66664kDZeV2KOPPpp23333RLD5iyx/KyXPra1mLr300jLPXXfdtdz6++abb9KAAQNKP4NVfm1xVmfK23HHHUsTI+vMlltumQ444IBmkzMpS8Mpn5Lkjj322PSf//ynNFkbONU2XHzxxWXd1Nsqs9nMmwLefPPNMq7877333iaflKxoPMuTObX0rPyxDSqcCbia/913351++9vflkRFHSS5vWm1CHd5SfPXv/6Vd+msetWdP6JjxSzPgw46qLSK7b///gnWAwcOHFRH+ZSJK3+Ya2F72223latf9cvBp556apn2+OOPL4kUf+1UJsfUza/WsWCq68svv1ymt9WhHuLptwMPPLD0l0e2LJC33//+98lWgvi2J+GhXmTX9sK3335bWl2k0z/wlR8Z4MexFiin1llN7rfffkkexoq42fXr1y9lc/0eTVtg/NUx908eP/xtk9XmXX3OY+i4444bbHvnxRdfLMebPGyx6RvpjC1bnuRGe/SH/kR6hZu8xZEuO5a/hx9+OK2//vrl2Oa/2267DVaetNlZKWuz9ot72mmnlbIhXDp+nLHOj5yoIz+kj7+rZxY6cikeWbFdID9hnvOYYxkTh4NZxlU+iIg2q5etHuQEHuRMPsY4a4/tFHpKvbfffvtyrNtCc4xAupa2pWyfy4uTr3GvP//whz8kY40+sAJXv+yEw1q9yKIxlsNsU8FbXtnvhhtuGCTHzz//fPYe7IqcGZN0pv7VViTIVq78yGVOsOGGGybj4Jxzzim3YfUznFh1jIlsbWCB2myzzcqy5ZPHUM6ntStrkn5jhTbG/v3vfydjmT5R32p6ONqGhAmdL5w86F/1P+mkk8ro9913X9p4441LKxrsWOdsZcGfg1UZsemPvBAyY73psdn/VV2z5557lvG0lW5jCZevxb+yBTo2YBzxv+OOO3i16D7//PMkvfjZimec7rPPPsm4Y1EzZ9Kr5A8++lGm1br95S9/SeayLMN0B50i3+xYsljzlGf+IY/yqTr1IZfmNfhVw7RZXuRAHYUZ0/SiPiB/5Peqq65KdI9jAvAgX9JlR17UxTiw/Um+hOlTedY69aDLxdH+rF/piJ2btpelh5f5h1yLxxnj8tI35Ibf7373u0Rf8+8K12GypEL2nKeaaqq02GKLlYILVHvzk08+ebIq1lEqSXB/9atflXvx7p977rmSPADAimaXXXZJhOSBBx4oB6QBbP+UMjRwEbBjjjkmUQL9+/cvB5p8ax2Fa8KUbsEFF0xXXHFFaXY1iExwtipq09Q+m9yUZV9dPiuuuGJpGh9vvPHS3nvvndS9Nk1+1pH23pWD2FA2lBVhomxsd7AUGAzvvfdema9tSuWMM844LZ7ZMSkQVHEpE5MbPytW9bJdQ2BzXVxN8ARcmrHGGmtQ/s7VECrKW16XX355OvrooxOlAzPhcHaPRCAj+seEwZnM1Vtb11133dL6QcBHHnnkZOLRp+pkYpReXbJjrjUIrDAziRUmzRhjjJEMfBMz/MgTZSTMlgCFYFITPzvKDK7ibLHFFqVJmBIxQZks1Hf66acvz/LMOuusST+QQcqA/M0///zJ4NM+hNbKXz4UiS2CBRZYoCR1tke+//77RGmxjJk4rcjkn+uSr+QVns8880x5HmOSSSZJCInVsn6YY445Uq4LS4K6Uz7qQGmSF+NLv+nnnG/tVRr9ZyJitTDZi/NK0xYnhWbiP/zwwxOyYWzJb9555y37y4QlPnzFNSl5Vgf1FXfUUUdNE088cZpzzjnLc1MmMv0jTzJQb4IQx0RjvLE+UOy2KMmqPLUPDvKECYsD/N0Ld+XHyirewgsvnChF8iYvbSJnlKFyTIDk2Hgy2RsD2iOc4jau9BXyNNFEEyWTEAKGcNmygj09RrdIr31wJb8cXURepTVu4Vvr1Bcm6u+KwJ5//vmlpQ/poYvoBGc7qmlZAtVroYUWSia0ueaaqww2LtQJaUM0yLwrIq++ZMPko7/KBL/8MXlpK6xMEuqgXRZAiAbCYWFkov7Nb36TjDP9jsCoozjImzxgLiz3lzzosoEDByay9EuRbbrQofQCeULMWLrpBnqGvq1mYrxZVDvjQ3ch88YALMgqWdamnN72FezkQ3/BB0E2vukPMsrR6eaplvQ3nQdbMoCkwBtZVQ9tkDedYHwjH2RR3+t38ldtR717dZA3vQFzOkaZdDedRb6VB3/3s802W7kQlZd0yKGxjsDDjo7h9DUM9DfcpCPbxsnyyy9fjne6VT7ZkR06Vb/Tn1U9TWbN39rtjJk6OVNL99E34tLP5AeZIhNkz7M5hw41xuBv7BifMDOeVllllaRMMprrUr0i0bCwcNZfxqRxZ34xFvELukWf/ve//y3xMQcpBznMxFhfwQnRr+bfmfsOkyWF9u3bt9y3xvJMJAYBxWiAIVEmcvFWWmmlcpVr0hLPADDgdABWC0yTyJhjjpmA5KAqsiItxaOTdt5553KlR9kDU1jVEV6DirDzR87USxk6R55W81Y3wptzVqUGnglNHPkQavetORMnooi0IWjiqw9zNaGGD6XLnzP4WTHcE2rKxH09h3jluAaBVQjTtQFEycoXOaimNWlYFfOr5m8yMFmaOAxW+RnAyB6cDFSDrSgKSZNVgL6DxQQTTFBao5Ct2n4g2LDSpwYcIqIPykxa+WPlZ6XrLIPtLP1k1UKxy88Eoh9rlZJ2w0VZyI+2OIejOBjBzYTrmcKVv7wpbzIKFwTOJA1/ioOMCTO5CSeXwuSx7LLLJopAWyk5frUOITYZjTDCCEk6ilbfm9z5UZQmQIoWMdI+eZA7ikf7TQL81lprLZe6jlIlW4inePIWEbklf8g1IiI/K1FYwdEkaDIxWffr1y9po3QcfBAMym+ppZYqD5ZTviZR+SMg8BBP/FpnsjNpwWjJJZdM0047bYI/EoXA6CtySfFJixToCxO1Z47y+7//+7+E0CDs2Y8sO5RsTNEPRVGU21oWMnAWj3xoPxJlsUbW9W9VVq2AyQXSDHs6RnvUAR6LLLJIsrUiPzJkglcG3cSv1iHZCA9/cqPvO6Ok1UGfTDfddKVFzphSX4RTfREeW79W4crMTn8Khzs/pMMkgujAGQnmz8nDtdbR2awN8BU26aSTJuPGRMQ/r+CFddR5kYXFoS3pTcqIInJEdoxvY116fUb+5UP3G9fa75C88WPRgFyRY3jBxeQvfj1nAoch+TRG5G8MkQfksSiKRA5yWnJBZ3kms64tOXpVH9iGLIoimey1Sz9LhwQgE8ieecR45c+ZK4zL6twCD+Ne++g8dafHyQWjgT4zZulueVQdmTU21B82dJZwaZEcuoVlBmk0F8DCAsl45A8TelL9peOMMWONflh88cVLyzM/7TJX0UXSyY9OkqbW2Q5UJ3qG/hfOj46AE13Cj5WKTtHf9D45tVCCnfJ33nnncvtb3K5ynSJLiy66aNL5TsSbFCmbq6++Oll5j9q0KtV5zVUUadLR2Hl2Vtu18SltZCvHIciEvjYeE7YBQsAIicmcokZ+gJfjtzbYET3KFPjSUKht2W+m0LBuk4ABjMBI35IzIHVwS3GEaY9JFN6eTQauGV91dj4MmeGfXXP5w9QKhHLIuJrkcrraqwnDIMpkTN8ahLXx9Kk65jxdkYvaeG191g9WEvLJjqJsa3q4yIMM5DQUjvbn5/ZeKWWTOMsIQtCW9PCzKmdpouSNGVhR/FaEuW3CjB2kSXhreetfi4TaeNo333zzJcQo580K2LdpcWMCtcpDfpDg2rQUEwXJQkIxtrWNtfnkZ3LCmYQpOKtUq3NkKMepXvUXfWIiouRZQ6rhrd1bMcPX6ja33UKLEs9pYSseEpDj6Iccnq9FUST1NLlbCMHMajWH56s+IGv5WVvzfVdd1RnxyfV1zTqqq8qolw/yaYJGOkx6+q5evO7yo3PoFJO3NnPmg9ryyI0JWnh2ni0STNi18WufzV+sFwipxQwZqo1T+2ysGtu1/q09Z72NWLcWV7hxTp7NacYxeeRfz1k4mQtYeFhpmiOHDBawNW9V8+GHyLBgZRyRHPlY7JkHPMu/ms498oRMsk5bjCH8mXQLb82RccSYRQsXsFhtLo3+tgOQ6+jK4GJOQ55YH/GB5tJ3xL9TZEmBJjPKzcC1pYCMmFCspIU356x0mNmxVXEIQj1FZHJkhcLCxSPUzKPuq056QgRwhM0gsdrDuLNAEO7WBoGJAsnCpFlHKEETSLWsevfKsPXDdGjrojpB14vPT1xmQ4KLABEAlgZbj8KzswLAxk2uVlpMjBQBciQN0zIlps45jatVBqGuzV88ZkwrCPEQzXrYC+MIvJVKXi2rH8ubfIRz2m7V72qlzk9dCb/75lxL4XA3weZJnQxQAM3lVevPOmB7ihlXf6gP+UEkauO29Zl1EuFi5WK9aUs6VgGTDXkiW8zVJmvK0io452EhYAWGGHP89Q0rIFyl4Zcd+SGv+pFZXjiLAQIOq7zfr++MIfkokyKzSstjL+fnCh+WMIoOmSBD/NvrWHSloQ9gb/EAB5ZJK25hh7EAABAASURBVGEyJLzWGb/qpe8QbRa42jgtPVPWwm2buhqXMDIG8rOxRhmzrPLjyIhr1cGT7MHZBABX1opqHPfGgnj0nmd4W0G7b6tDSnL6emnkh7DlcaovnQWpF7ejfrm9trZzHiZqZa6zzjqJLm1vf+R8mru25A9TmNN/rLDiwjbfe85OH9Elxgk/fUwPmTDJHd3PSo0M0Z/kUrzsyKgdDPJOr7WFYFlgsi6TMXVFnEzWysr5Vq9ZX6gPHcR6VA1v7t5cJn9j0tySZblefHVHqMi8cswL9eIhoEi+uVI4vQpbczmDQ1Uv0V0WenQKy41dAPWRruqMXfMUyyrrkC3m2u2/avzae4s8c5nyyTu9VhsnP9smZG3L8oggqb/+ZZ0jq/LK8bvi2mmypAMJidWUSURFWR4Igo6wWjbJYsYmGMoY6xNulWvlhrVikyYIpnMCb9tKvlgy8z0zp3g6wgq52nh5IjUUni0DK2f7o8yLlDRBAKJ0BgULGJM+YanmQ1kQMitqZZlg7ANrl3hYtziunqsOCWMpky8zpX1kZmvmTfWxujWQsGXCZyVrq4CAIHVIjRW4LYxaSxYFzTFBMuFSXCxDRVGUh+RNvuqYJ4hcL3vkrBTyh40VjfxhCXdX7TSJ6yNbchSTcz32s+HvPJm+NbEwI4uPaGkj8mYw6jv72CZCuGP84hlUJt5cn3w14JFpRBj5sPUFZ/W1ejbIreL1pVWe/pefeNqS83E1YbDoIQsIuK0SBNREry9hbOKm2PQ/y4YBps0mbBi4Mmkjnvbg3cMLefHsvACLoRUtqyFrI7mixOTNFEwx6EurL4pGHciPLSPnVZAeCwvtIBcmAX1O2fLjKAD5SiNPfrCHIXJcFIUmD3L6wKRvzCHZ5AdW2qS/nGuRhyvLCpmEM0Wk7sYB65NJWt/qe+Z5fUjZcSYh7eeKokjqIi7FaYtC2kEVqtwg8sauMpBe7WIlohPUyYTMjK5ddINzHzB0VonlOI9B+FLgdAeyQCkaQ8z/2gsnOJA/lgEEUb0sqJTj3JSytF+79Y2xxEpCBsXh4EH+rFCNzbwFQL7USxvIuvwqzSxvyYW2qZe85K9eJg/yAiN6AJEtE1T+GLcmP/pBPek9dVBPJAxRIcNwMgka98pAlujQSlblpyNYPelPMmY8s9CRdc45UOON1QARpcuMB9ixlMJXux2lMFFJTycj2Mo2wcORv/FlsqLLlElfyEN/VevknswZz7bJyDhZ1ed0k36Er8lY+eSDdUQ/eybb5JAe0m44GVcIvzFEV8FP3+hTllDxzDv6jPyRRXJMN5NDOoUOUrfsLKr0o7GnfepKj5lvzB/0LlzoGot8bdZHSBlcYGgHQ7/TgznffDXO4aVuiIYjD+YffeGZ3jP30S3Gl/Gm3xHALP9wEMdOA1mjT2wPwjATMeWxyJqXGS/oaH61Dqkx9tVDncyViCU5Nv7pK/6cuZUeQjbpWP1HR9K5ji/oM9jQH/JUT854k585R1oyg2yROW2il6r10k/GvjD9ZByRL4twOCHJ0kvj+AnCp53qCH/1N2b0AT/zpbHMSq4uteXJpz2u02SJkFFsFKOCTRa5QQYYdschSITcfY5PGD1zADSA3XPiU5zyJLD8OMLDr+oMbPUgjOLY7zTAxcFShRE8A45yIow6gLIVJzsDnVA4jyIfgyKHUaYUDiJYrw7iETLpWEMoSPcmWVeu2l4Dm3BQoMIImwkIgZBXdgYGi4jBIdwEg+gItwK3vUNo4W6w8686k7b8ERrpDWzhFIb2CqOcTTgGSH7WR+4RI+ZVyj6HU2ImGvmYPMUzIJhv8zM/E5Y4tY7CVaY4lJ8r52xFxssA1P/qKYzTr7V5mTCQDuGcPnblDCTEsxrumWVDu8QRxi/jpN8oA2GcPjcBu0fiyHmWY4qCP8VpgLvX9/bXKVjPcM/pPXNwoQy0xeqXHydvfkhmxtoWCFkhl8JqnUlHWkTchGOsiGNSIh/CTICsg8LyGBGf/Bur4nDGCYsTwuSZU/+ll146mZw9k31bIu45Y1Z5tU556kNekXvhlLg0HMxMNCZ2zxwyLJ5+y/7Ir7Cqc8bRpMIP3kite/kpi3Uu94e+soiRr/w95/FjzEnHGZtVWTQ5FkVRvr0EP3HoJPnUc7AVh1OOla3x4Dk7cWrT0lPIBDnQ7zmusZDvjRWLMQQo+9Wri8VQ1kHikRtXDul35cg3OXdvkUTnIBLkBeGUtzD6ATnLz4iWyRCGJllxOJOT8S8eAlbbRhMnHSWuyc9Eayx51gfwcq88cwZdY/yQfXnlZ3GQA4Qhywds6BPxqrrHuOZHT5lbpDUOybN4wmqdsS4enayN5Lc6Fvr161e+4COO9iJHWc7oRItWi5fafPOzdJzFk3mI1UX7+dF75MC9tlf7kVzmuuk3Mi8ePeLKIQq5HCSSLCAI2a/e1QJEWg5GdGCOl8sQxqhBThF5z3Zx6IpqeoszZSIn4nDmG4s3ZNgzfOjMLAsWJ7m8fEVqjQXxhbsqj+y5lz7HRYj5cbYGzadIuWdOenKCsKmXBXNO25Frp8lSRwrtyjRWAMyntgGBVZu3SQbRMEgMKqs9DJhCrcZnSjWBWI3U5uEZEzcgKG8KhN/QcISEid62RG15LC/alZ3BWxsnngOBtiJgLJmwkBEKnTOZIqRtzYO8suhZ6bm2NV3Ea2wEbIHQoaxLjd2Sxq09kmTMWsxY4A7tliAoyKM6cAgYa329uWto1o1c0mssTZ0pt+HJktUb8oLkYLatgYE82aYgTFbWOb69XiZdeWW/nnC10mcaZiZtrT4RHgh0BgELAiszFkrWN849GWxrvrY3WDFYOp3Pamu6iNfYCNgSYkFq7FY0du3NYXnMstAM7dbY9rMNqg4cq3Pfvn2HdjWGKA9ZYzm2NTdEYDs8egVZosxZjdrR7iGiEjQHxHuadQZJ0r62EMEhGhUegUA7EbAlyVydHdlrTxa2PXJaSqo9aSNuIBAIdBwBhgNjz7kd81nHc+pYSuejlJ+d+dRRio7lVqbqUX8aniz1KDSjMoFAIBAIBAKBQCDQ6xAIstTrujQaFAgEAoHAUEQgigoEhgMEgiwNB50cTQwEAoFAIBAIBAKBjiMQZKnj2EXKQKCREIi6BgKBQCAQCHQQgSBLHQQukgUCgUAgEAgEAoHA8IFAkKWe1s9Rn0AgEAgEAoFAIBDoUQgEWepR3RGVCQQCgUAgEAgEeg8CvaUlQZZ6S09GOwKBQCAQCAQCgUCgWxAIstQtsEamgUAgEAg0EgJR10AgEGgJgSBLLaETYYFAIBAIBAKBQCAw3CMQZGm4F4EAoJEQiLoGAoFAIBAIDH0Eup0s/fTTT4mr1zT+XA778ccf822XXav512YqjKv1b5RneDVy/XsKzjDkekp92lIP9eVaiiucaymOsGoc9xz/5pxwrrnwzvjLl+tMHr05rTHPtdRG+HEtxWlrWEfzkY5razmNEE97uM7UVXqurXmIy9XG51eVA89cbbxh8dyeeojL5Xq656rP+X5YX7uVLH366afpsMMOSzvuuGP67LPPhmjrP/7xj3TiiSemr776Kl100UXJD++98sorQ8TriMe3336bHnzwwfTnP/85ffzxx3WzuPbaa9MJJ5yQ3nrrrbrhHffs3pTff/99uvvuu0u8rr/++u4trJfn/uSTT6aNNtoo3XbbbQ3T0nfffTfts88+6dFHH222zi+88EJaYokl0j//+c9m4wi477770pprrlnKk+d77rknHXHEEemjjz7yOIT7+uuv05lnnplWWWWVVFXWQ0TsoMddd92VjjzyyGbHbAez7RXJ6Mj1118/9e3bN91www1DtMkk8/TTT6eNN944XXPNNUOEt9fj3nvvTauttlq6/fbb25X0k08+SXvuuWe6884725Wup0c2Vw0YMKDD1XzggQfSOuusk2666aY25WEu3GabbdLRRx+dzGc5kbnUuF5wwQXT22+/XXrvscceXdLnZWYd/GNeOvfcc9N66603qF6tZfWf//ynHO+ff/55euSRR8q05mXpnnrqqdS/f//05ptvehzmrlvJkk4dOHBgs43caaed0nbbbZco4Ndffz0Bu9nI7QwgkJTLrrvumvr06VM3NUUw2WSTpQsuuCC9//77deP0RM8ffvghwbUr8eqJ7exsna644oq6WSDxBqbJ/p133mmWGNRN3MWeH374YXriiSfaletEE02UDjzwwDTvvPM2m+7ll18ux1WzEX4JoIiM018e0+KLL57+9Kc/pXHHHTd7DXY1VqX57rvvBvNv68N7772XKMHm4i+55JLpj3/8Y7Njtrl03eWPmCIgHckfefnvf/+btLkj6atpXnzxxZLEnn766emQQw5JI4000qDgL7/8chDZVVZzRHdQgjbekMuO9PM444xT1nGppZZqY0mNEc1ctfnmm3e4ss8//3xpGGhrBvqSq42PWLz22muDeR966KFp9dVXH8yvSx/akJn5SL3aIzOLLbZYOd7HHHPMhBxWddFss82W9ttvv2SObkPx3R6lW8nS5JNPnpZbbrlWG0ExA23UUUdtNW5bIrz00kvplltuSTvssEOrQBMwg/vWW29NSEhb8h/WcX71q1+VuLoO67r01PJZKE455ZS61RN29dVXl/3Nmjn99NPXjTc0PE899dTEutXVZa2wwgqpuUVCtayFF144GadVv5bu5SnN6KOP3lK0ZsMQ2PZaKprNrJsDkOnTTjstPfvssx0qiT45/PDDu4QssSKOPfbYaayxxkp0ZVWvsuBcddVVqSiKNMccc6QZZpihQ/WtTfTb3/42dbSfa/OK55TWWGONNP7447cZijnnnLPsz9oEk046abKoqPUf1s/mbwR5jDHG6FBVlllmmVbn6w5l3EWJOkyWDj744DTzzDOXpn5mM4PXpMNMydy47LLLpt///vdlNa2w/va3v6VZZpklbbjhhoP8fv3rXyeMuPSo+cM8N//886cZZ5yxNOnKoxrluuuuSyY64bXbfCafPn36JCvwnEZ6ilp8q2fbDcJGHnnkNM0006THH3+81ZW4OlFE8vjLX/7SYnz1O+aYYxTRrEPqcn4LLbRQufXwxRdfpH333TdZQRpcs846azrqqKMG5XHeeeeVmMCzaprNEWwprrvuumUceWt3DuvMVT5//etfSxP/8ssvn/7whz+U7d97773LskygVgVWPfzOPPPMNPfccyf1t90qPZKyyCKLJKszV23VV/BUV7KjjnfccUepDFgFmaD5Sb/VVluVZdkCYp3gBytY2HqQB8yltw3wzDPPlJYSk4k8OCt9cnnWWWclKxcrIf7ymmuuuco6n3/++bwSP/mon/raLi4DKn+QLvIn3kwzzZS23XbbhHjbAjMeWLBEv/zyy0v5lxczNcsgHE4++eRElliKTK76XRxt0UZlCoOF8SYtzFZaaaWkffK2lSy+dML5teS0S7nqu8EGGwwWFXnbeeeUgrwXAAAQAElEQVSdS1kU4Fm+8s/l8a86bctj1faAMGXsvvvuZX/NN9986eGHH076xni3zbfFFluU23iUq21QZdg6POmkk5K25q1z9RSm/Ntvv13WQzgyIg53ySWXlOHKJxP8lI9sCGAt0Ue5XSuuuOIgsmr7Tzt22223dP/996dNNtkkIUssbY4TWDmTA3mqj/rKEyHSLlv+/A844IAkjOyTeduc2n/OOeeUk5/8b775ZkkHc8jZ8ccfX2ImnwsvvLAMR/ptu9IXCyywQCJzZUDTH/Xco2kL5tJLLyXPg6yU2r/00kuX5dEZTVFLy/3+++8/KH9x+FcdP23RRuO4Gmbs8Fe3PFZZ3VZdddVkuyjHZwUzHzgqIL3xiOBJa0xITz/aStT3xq+xaFyLX+vgRpdIb86wC6Ge8DWW+cuLPrFb4Fl9xLFjwCLEz/yjj2vzr33Wf+oozfbbb18Gy4s8kTX3MN9ll10Svedq67GM+Msfc6L08lFmPV1NtoRzZPKXpOVCX776umolZEGka+RrizTHZ/1ENMxvdDBM6DBbtvK2NSYuqzBdIz1/faFN5gzh2akXoiae/hGuzXSOuWittdYqCbn5UBphiLU+JL/86jljWz+aRxgzjCd+xpd5ozYNvSLfvNXoWZ3U/eKLLy6jK5vu5U9/2yUSYCwZ9+pjvtLWgQMHCuqw6zBZUkGWG4PAYCHwCApLzXTTTZcIEHOxmiFPlMy///3vZHvAJGAAG/zCa51wSs+gNdFS0v/617/KyUtc4FlJnX322eU+56KLLppspwgjlMyd2O2II47Iq3TAVZ4wAm8SMxEJnHDCCcttOGk9N+cof4JHUCeeeOLUkrnRwEcomsuLvzaYCAmB1T2Fh8RRpMqhhCl1Z69M6pdddlkyCD2vvPLK5UpSPlUnLxOQdlKw8qqGd/TetqbJilAjGia+v//974l1yzNyYGBRkAaCvjGY1P/GG29MBjLclY8kwNDgtxUrPQWlv53BQgaQ8f/7v/8r+8Wg2q/JHGvbSVxKRF5kRPuUuddee5WkUnqD1gCcpokEC6uuwigBmFO65GzKKadUpXKLg5zqYxObdiqTeViZ5LeWiNiOMhhNWCZZJEmbYXXllVcm1h3tpsBM0mQeiaS0Xn311XTGGWeUpnNjx0RDxuWlvN/97ndJ+2GuTR988EG5fWXilOcbb7xR1pvck1tpYa5OZKgMrPOHEiEj5MO4Un84iGoyVEf3nHiwUB+Tj7ENF2HZCUdGjXXx1EGfeLYQUQ451C7jYcstt0z6HCncbLPNyrOMyL145CETBPlT+MapMihp7eZfdcYDDPQdxasNti4Ql5yvfrS1Jx55fOihh8pzECxGCKhneN52222lnJIbY1tbTL7GIYKjfHUm386LmFT0q3EMf3Ft/SNKtskQCYpdOMXtzIu+VKb8q+1wr70UOizgcOyxxyY6Yeutt04mGHrV2LeIEp+zyCKz+kY/sizx16/6EjmCockcqTaW9JOzM84+ffPNN6KXzsRDbpEOmJhkpBOonfS9tP379y/PwukXTv30K71si9u4dC8dYqOvDzrooJKU0lvGprbQITCaeuqpy3M8r7zyyhDnnJAdecBQ2RYU+th4cS8tvBBDEysnnj6gn0z09AEyhfgYn/pa3eo5+Js79DG85PPoo4+WpJm8SGN8O+sHE6SPbNqdEMZJS87Ui1wY7xlH4dmpiz6n9/SrufGxxx5L5iq6nu5CPHN8bdYW+ea5y9VcgTDBgwyrG8wtJI877rjyzJntfmPFPEL3InB2dJTNUpXLkA/M6Gzyre76yHiGGxnTXroQiRVOnyJr6q4fqgQv5+tKtpylm2CCCZK5+bnnnkvkXFito5uM5+wPR+ORHlEv41171cHcac6AAzzxDOOdHMNPOvOT8ZDz68i1w2RJYQTfyokwG3TYmwoZKJNMMklilhPPgLbS0CgNpHAxWvGF1zr55QkGoKxU0hrM4prADGSgUD4mFQINeCtRnc1cPcIIPzdPXjocI5ZeHUwwOT9+BrmJxH1zTp0JOGG0EtCBOogSNUFwJjODisBTJFaBlAdcKNJq3pS5ukpH6IWxeplkDXqKtmodozixewPT5Gwykqbq+GsXAWHFg5V0yidkhIcSoJgIHNJhYGsXBas9JknpYZTztgKnXA3WvIdMaRRFUR6kN8GIo/76a9NNNy3732rOYNQfLAa2EuQhX4pGGEVBKVJm2qvfDHYK2yRgoKsvGRNXHHVZe+21S0Iizuyzz57GG2882XbIUeCIH8KvL7SdgpWZMsmq9nnODg5WelaB2kxGp5122mTxwNzOiavtJlKkgjL7pjJBCc8OnsaM8lytEOGHeCNrcNH32q0s6ZSBRFJC+pOi59+c0zZyaUwWRVFuC+T+QCTJeE6rPjBRn9FGG620JlJAOdyV4qYcKTfx+vXrVypCChmxEEd9jRf3VUfG1B954G9lWLV0kVl6A34IAiUtXtXBFHHRb/oAMVIflmKEQFy6wsRgvJrYkW1Wo6IoEnkURxnGDasX7HOdhGUnPzJofJAP/sgJ/UMG+/btm0YZZZRmt66mmmqq8qyZtMap9FVHP1h88hNO3ug4z+115JKMwFefIUn0jDbqJ4sEWKtLzlsceoBswEV7yJtwOg8xkRa+9BPZoF/oN6SevpHuN7/5TaL/pYMHbOlW8mvMFEWRjKedmyyYZA926ip+rTOx6lcTrbkmh1tg0H/qyg/JsVCgR9SRzMlbnZUpPbIsbktOXLqE/jb5521IVu0sE/rFeKTr6ukc4xB5UI7xayFnQe656owPhAj5MyfByNxhIU5e4UtWpUG2LMZyvvlqXOoLOhEB4a9u6qv98hBHHvItiqJcZNO7RVGUOlpYdvKBt/ZXF12MI/rIGKDj1E8aBIpuhon+MB5ymPCqM0aRLjJBZ9WzbOf4cGMRzM/IMh0qb4SMpZdc6yNlypN1Sb64gHLIJlKnrfX6Kefd1uvPbKKtsWviaSxTKLKAbBh82KtVMCEzOGqStOlRp08xxRSJYrMK5azM5GdAm8R0JIWSgQKcCcPERUEgSIRPgTrUJEJgKTuKnADpXOGcQS5/9/Ucs7PJmzIzaNSRYCEY8kcyTBjqh5ghjFYeBMRKR1msZNW8rVZ1MiWDGFXD6t1r08cff1wvqPRTHjZOOAiNOhIYpkntNlEjk9qJiVMM2kPBqK+4CCdlSFilLzNu5o+BSHD1T3a1USlnbdfO2jB+lGFO66qfKVv3iLIVqXbB1YTJn2PFsnqvzbMrn9vSvraUR5mY6E3qBq+Jol465SEM2pddnnTqxecnb5MVBW+CJOf8m3OUMlmgfJuLk/3Vh9k818WVws3hrmSEkmJ5Eu5qTJIxciVOR53yW6sn+WKRqpahfdpJkfLPY528ea7njH+WDsQKqbIir41nBY24s0rCpTa8tWcK3oLNODTZ18bXViv/7I9ktFTnHK+tVzhYYesnzmSkjGp6dajFU7gxbKKSLjsyh8zSY3Q+i1OV0EhHF4tD9yHiFmsm1raOXSSI/mKJMh8gefKtdXCi7+mFXD+LFljT9+pAr9Smq32mF80jSApZhlltnNaetc182FI8pIg1nZ5G7PQDWTaPMSbQd9X0+kX7zAFV//bcO7aiD22Bs1Ihq/RvNQ+WNKTd3M5aiCBVw2vv1dN8YbzVhtU+IzAW+xbJxlJteEvP+tfYq8aBBwKc58Si+Jn8wb8oimrULrnvFFlSAwKJvJjssU4rVyuvaicQguyk4Ty7Zuc5O8yVorOy5WeytHLRMfK3amTVMvARNWSEEjfRmpAMYkKXO9Dqd9RRRy1XfUhWZugUgPKZ7REpHaI8LqUkqHQE1QoWW5c30x+LlgGc220QW60SLsKDyZow+KsX6wCTZZnhL38oDoNEu/LEouzsRKveY9YYv/ZYPTHlG3BInLhWKQicCZn1wGpAu6y+TAIIrDD4arO48GANE2alY1WB/MHRRCjf5pz+Vr681JPZN8fN9SPMFAeCII7wfEWuKVfWN37wQOasIvSF8y+sHYTfQKcsxeMGDBhQnpnK+fHLjl92ytd3+bl6VTacqn7yyM+UK7Kmb/hTMDms3lWc7F+9N/nIA3Emc/Cthrs3ZpxtYW0h+/woLask99nl/F35GQ/yJovwY0bnz+U4rtkhBQiZcowPaZF7fU8Oq+n0r3jGG39EOtct54cYmYxMMuLY6rbtQ36MB34cEu8qnSuC5+q5OYeUmCitvMVlBYVdNb5y1EvbxaEzjDvjVHp+0kujPq7ZCcuONZv8GmOsjLDJ8Vz1hQmOHrEYye2VXnh2tc/84acfWd1MFiwNFL2wqiPf5MBWg3yQNhNpNQ7/6nP13uKCnqz6VeNbbBhTCBl/hJBlO8c33vWnci2ejBu6F+4Isa0Z+lZa4wYmJj6TlYnQwgtpyvmJJ0xethT1Jes2K7Q4wqsu+7lmZ+ywGJm86QFtFCada3bkXx1tLwnj9KfykWd6WB/wl8aVc191iIo08kIctEc8TjzX7DzXcxbxdBjdKi7MYOA+x1eOsUo/IwHGMbllDWLdE1+96VFE06LIAtZ4lM9tt92W1JMsmZ/ky5/L965c9jNv0MNkzPyFWAqvOvOmMaYeRVGUZ++k58Rz5dxzFtyc7Tz6w7igD2zZCq86R3NYEZ2bynUWLr/s8nPt1fxpiw024jrCQHfhAAwW9DwMYUkO6Vl5cOK7dtZ1miw5D2JCM9mqjAFvckZeCIuOAYyB4hwGoWcSdSaF4tGBwnSeDrICRzTswxu0TIxAMsEbLMgFoiSNMBO1LR/CReFh3gY8QQIggkIhWKFYKSAbVnisQ+qrgwki5ao+Vpe2iyhG4RxTNOsPRSMPbWWCNZgIvQGsLHvO2qM8AueZU0cTkrIodXlyziEgmhQNc7EBoN3yZX4XZluhKIoER8p2rbXWSv37908mLasfiszglB98KUK4ECrKwoCkbExiMNEuz/BQvvibb755OSgoMpMEQTNAtU2+nMlNW6S1n87PypTyt0JRprNj/LMjC7b87B8TYtt9lAOyiUCJ5xxH7ksK1YTGmmJylScl6AyWPFgN+XEsj6x58CZnzgLJ30qWP3mx7UF5IgfKyo41lFJAluAAF2lNBrZ+kF2yZ+sIeXTWRpnqkfNwNQmTTW0Tv1+/follx71zLs4lkS39aasG8dLXxgtSKAxmyCIlxkqnD8mn8ihqdSE7iLCzEMYSubAYsTojs8YbOdFn8lA+YmdSN9nZFlDf7GBsDCFI8KeIrrjiivJMlIUEeYUNRWSBQBGqj7og2OIgXcYJBU4x6jtxKDHbAJS4FSw/DuZFUZQvhKiPiUA96AllKxOpMNkbS8pHpskmzORhwrMYye1wpXxtZ5Nlcci7saw+iA8/pABWlCZ5JHv6O/eBficHxrT4iLi6F0WRkDE6gyXJOSiTgTjGHn2j7YiDuotHR8jfAsTkZ6GkD/QF8iat/rXFqv5VR8cor8x2DgAAEABJREFUlw4ST5tyf9KPsDcOjOFqOvrOuNWX9B95JJeIo3qQGWNW/rb4HU6WPzzVK+elvuLATzm23jzTN+TUuNJGaeWnPepkN4EfmVxmmWXKA+jGMH1CN8IWARWHI+PqZ5FbFEVCAIwxVhYkw5jOdTL+5Um+YW0M0h/ysYAyl+T4tu61XRhnW198Y4TV1ZhnrVR3epNs0bm5LFfyzOlr9dJ/dK8+Ew57sk3H06mOOPCvur59+5bbrSZx9SAn5i1limf80k0WIyyM6qDt5kS4IRX8yYgxSP61A57mEHnqNwtgi1WygbDAjvwhEXQKC5k09Aj9+MEHH5Tf55KeM/6Mk+pWrPlZWRbaMDAm9DldoX/JFJ3q7BI5N3bNWeZmeNJ1ZJjcaWvVwUW55Ft/6jfj3dxtviMP9AL9Zfwr15i1fayt0tBx8iCrDBXaYJzTRRxdxh92+pF8wA8GZBFG1Tq1536E9kSuF9dgMQmY7IVriAHmHsMzwDgkg3JyTxAIHGGktChFQAgDZJ8+fZIJQBg/8QmXPDkDlxAIc8ZAZ1Pe4lAWJkqTE8GhyEyGTLMEhrLMREleOkYaSsnKCtAUo/yEZ6ezTATKJETqaGAiC1lB63REg+CatJEsZZscDSxmTYQj50nRy48yNyHBgzDw41jtXDmdb6ATCM/YOaUOp5yfqzBO203c2DY8CItBgADxZ44lvPrNICB8lAk/pMTKV1x5chQjYYahQc6Po1SVx5mA+XEmE/WjMOAJg4wfZZDxNRlJy+l7Zm/5GMT8YCY/Dkb8OP0hzD3Xr1+/pDz3FC+CpDxp9IP02akPzB08Rgak4WwPuHIIOHmg5D1zwnMertrEnxMfNu4NTjKiP9XJih7xouT1i4lbPNh7Y8W9+srTWPDMIaMGv3tOm7UFfp458pqfKWNjhdJ1zeXBWN5VRxlKbzyIa8JVB36cOhdFUb696pnTBkpafM/Kk6cxoJ38KO/ct8Y4P47siWtx5dmWjPq5R+yQ6Gr5xob4Vr/icEgRv6ozJvo19b1wTr45XP340TvIaFEUiTzy0wbtcc+ZlPKz+CbpoigSfSaczjA5u+f0r/rDzzPHEpmf5W9M6Qv9jRTm/MVlucj1zFfxKX/hXN+mSVcYLDK+Jip14Z+dviPPwsihtBxi5MpZuJBnhMMzZ+GV88hXesvkJ1y/qLvxItyijD/HX33pTWOMH0z0vfHn2fjzbALOupw/XYIcuOfotjzeLTKq2CA6yJV4xldVpvhV44trfPHnyOo000xTfhjZc267ucDYpaPoam3LjhzmMizcjWWH5DMmCKk+VRf6sJ5MyquKPaJG5yK/6mHOUk5+NveROQSDToCP/PW5PiBX5hXHJHL7jHkLSosH+csX3rZE3XNIhCsnPkKf28ZPehiZP9WZo3/hI1x+ytdmbeUHEzpfGP1GXi1cyZ9nsmBuYvCQX9XlfOWDFFpAuefIIjlwrzzj0T2nDOOcTvLMIW/yZriwWOeHLCPW5jb14aev6Dr1hyfrvXQdcZ0mSx0ptKvTECITOLCz8FPOJh6da+LP/tWyESUWIFtTOk8YRaSjkEDPLTkTnYFMmJVtknelvE3k7pnRKUlxDVYTXkt5dnUY4qMe8FE+0qq9/ExyrupnYnZPIRI49xmT9tQJplYJBJMJuT1pI24gEAik1JswYFF59NFHE2uDRTRH5yIxw7KdyLNFNyI3LOsxNMtGapB4fcDR8QiL+XNo1qNRy+oVZKk58K1emPKYnTHz2nhWbAhElRRY1VitW4XVxo/n1hFAUG0B2jKqtXq1njpiBAKBQG9CgLWf1cj5JltvnO0aVqBh2U7WdgvDYVmHoV22Rb2tOX3A2Z1hlRza9WjU8no1WWrUTol6NwICUcdAIBAIBAKB4QWBIEvDS09HOwOBQCAQCAQCgUCgQwj0erLUIVQiUSAQCAQCgUAgEAgEAr8gEGTpFyDiEggEAoFAIBAI9HAEonrDCIEgS8MI+Cg2EAgEAoFAIBAIBBoDgSBLjdFPUctAIBBoJASiroFAINCrEAiy1Ku6MxoTCAQCgUAgEAgEAl2NQJClrkY08mskBKKugUAgEAgEAoFAqwgEWWoVoogQCAQCgUAgEAgEAsMzAo1BlobnHoq2BwKBQCAQCAQCgcAwRSDI0jCFPwoPBAKBQCAQGN4QiPY2HgJBlhqvz6LGgUAgEAgEAoFAIDAUEegWsvTtt9+mZ555Jr3//vttasp7772Xnn/++fTDDz8MEf+hhx5KH3300RD+zXkMHDgwvfzyy80Ft9n/yy+/TMr+7LPPmk3z9ddfp/vvv3+Q++CDD5qN25EAmLz00ktDJIXH008/XeL1/fffpxdffDG9/fbb6aeffhoi7sAmPF555ZUh/Iemh7qpc70yhbWE23fffVfK0scff1wveat+zz77bGop/1YzGEYRjKEHHnigXbKvqtqqzdJ77oz76quv0n//+99EzjuTT3vSvvXWW6U8k+u2pKNj8hisF9/48Sv39cJa83vsscfarMPq5WU80oPqpx6PPfZY0j5x33zzzfT444+77Tb3zjvvJLLQbQVExsMEATqd62jhxoxx3ZH09Iv5pt5c3d785NORucn83pF07a1fbfxuI0tPPfVUmxVNHtS1HXD66aenrbfeuiQttRWv9/zwww+nXXfdNZ166qn1gtvs9/nnn6ezzz47bbrppi0qG5PJzTffnPbZZ5908cUXd+mkfN9996WddtopnXTSSYPV+9NPP01HH310+stf/pIQOpPKc889N0gJp5p/lDThqvEeao8mhLPOOivp43qFvvDCCyXWr732Wr3gZNJHDD/88MO64S15XnXVVWmXXXZJ9957b0vRelwYcnLuueemjTfeuM2ynxth4WGChlv268jVIuHvf/972m233Uoi3pE82puGAtxjjz3S8ccfn4zB1tKTiX/84x/plltuSccdd1wyFmvTWHC8/vrrtd6tPl933XVpiy22SHfccUercZuLQO7040UXXZT23nvvRD8hSWS+f//+pa5qLm1n/Y17OuLQQw/tbFaRvgchQJ7pNHNjR6tFRzz66KPtTv7FF1+kfffdtxyf5p52Z1BJcPfdd6ff//73pe6veLfpFskaFnPaCG2qXTsjjTnmmGmdddZJs8wyS5mS8jb515KhMrDpzxxzzJFWX331NMooozQ9/e//PPPM87+HNtxNMskkaaKJJmpDzJajqMdUU02VRhxxxBYjjjvuuGmrrbZKM8wwQ1p33XXTTDPN1GL89gROPvnkqU+fPkMk+dWvfpWmnHLKNNJII5Vho446alpllVXSvPPOm4qiSO+++2664YYbyjB/ll122dS3b1+3w8Qdfvjhafnll08zzjhj3fIXXnjhMuzSSy8tiVFtpDHGGCOtvfbaabrppqsNGvRcvaEITJoIh/6QvhreCPf6dvrppy/7s7X6WukhC8iNuMbc//3f/yVj0HNHnTFgXHY0fUfSjTPOOKVstzXtNddckyaccML0xz/+Ma266qrp/PPPHyLpSiutlMjYEAF1PFiCkBtB8IeB+466I488Mi222GLlYupPf/pT2nzzzdP888+fxhtvvDTxxBMPlu2AAQMGe+7sA90x9dRTdzabSF8HARO9BVydoG73IjudneNmnXXWtMkmm7S5rtdee21pCDAejIs2J2whojlMW1qI0myQ+WRYzGndQpaqrTRpmQgxWcqoGtba/XzzzddalMHCJ5tssoQwDebZgQdCMc000wwiJB3IotNJpphiioSM1WaELCFyI488cm1Q+WzCsKItH4bxH6sQfcg1Rzy1Y7XVVitJ3u23397pGrMI3HTTTeUWJeLQqGQJAS+KolU8KO4rr7wysTC2GrkdEcjZXHPN1Y4UnY9qgifbbc3ptNNOS2uttVYiQ1abna3vBRdckK6//vqyeEQbBuVDB//YdhtttNESEmgM5GxMElU9lfswh3fFVRl0WFfkFXn8DwFbWHYdOmKt/F8uHb8bf/zxu2SOa2sNXn311dL688knn5TjjF5qa9qW4hnn2tJSnJ4W1mGyxJyMnW633XZp//33L60HBx54YDlJ3XXXXWnllVdO//nPfxJWyp1//vllPKt+Cm7LLbdMG264YaIomN45pj0r5YMPPjj9+te/TocddtggvIRdccUVZRor54MOOijZBhsUoc6N8wG2yJSz3HLLJdtByJttK6u89ddfP5mojzrqqORsjIHQv8k8Lj4zZ0e2Mi6//PLSSgYL+CiX2b1aPfkee+yxpfVNO3/7298mdRLHRL/eeuulHXbYYbCttYEDB5arAVuDzPrqKz6FzKqFJNh2QkxZlpTvvIKtnGOOOUbUpM+Y5rWPxem8884rtzus0Fn2pP3Nb35TWnIQrubILVOwLUITCnP/N998k6yi9bPttj//+c+JDOgv7Ve4frWtweJ45513pjPPPDNpt/Mcwueee+4EO/dVd88995Q4ufK33aL+ZAQx5Jfd7U1kywrdFVGDMxJBDtV30UUXLbdLxVfv7bffPm2wwQblir9ee+HXr1+/BJM111wzUZDyNKHaHlYPVq9HH320JHt77rlnaWG0fcXSQcYoG1tZ88wzT9pvv/3KrVN9L099+sgjj6Q//OEPpVwvssgi6dZbby1lUR05pm9bTfBhQSInMGWpUK4w7VOGbSntlp8zYsaHbVxlqb80+ueJJ55IxqcwpvCll146IVzKq+dguNdee5V1VM4rr7xSbnlttNFGZXv1N4uevoQx2YWNLSxjgMwpZ6mllkr//Oc/yyLgIp144pCXMqCNf6zsJ5hgglLfkHft0u5qcgRK/mSNPxlV1u67757+9a9/8RrkbrvttnL7Hjb60Vk6gbbO4MZClDEiB/zkbXzpFxiJz5GtnXfeOf3444+lDjvxxBOT82fGS62My8vkq67GA9lVB3jJn9+DDz6Y+EnvmAH/PB6UxxkL+gMG7rOl0SSn3WussUbZV+TX+KUz5MMqrX7k5YQTTkjLLLNMUndjQ3+SY1uIxu6CCy5Ykkl6xLghC/2b9CV5dDRAPT7++OPEmixvZaqLLdWTTz653FbW55dddlmiM4wT/UH301/SZycN2ZYHmaY36Cz9TJd4Vob6099kX3x1gR0Z1Ifwo0/Jnu1duNiapEfJovzpBrpQmzzTY/pOPyo7l+NoCR2pP4444ojEwZdOUg5MTznllORIARlba6210o477piUJ15um3nGHCZf41B67SUH5iO6W/1YIbWLrjcvCJMfnZ/zql71a78mfSUfOl0ZdE41jmMcf/vb38qxzJ+OIzN2SLTHuOLPmStZWvmx3po/+cNff9Mr5MJuhriXXHJJma+5hMzxEz87Y0Tf63PlaVsOUwY/ffW73/2unA/la5yRRXJj6804gRtZNT/pE7pYur59+5Y7LOY7+pzO1FYcZZ4m/Uuec3kduXaYLDk0aYABn5AQOJOgrTZhhFKFDDZOA//61yQub0AAABAASURBVL+Wg96A0qkG0qSTTloKl7gcZQIECo65jR+noZQ7ZTznnHOWyh1QwppzhM72jXJ0rpWoyUj+BgYlwIJDEWmLDlB/8QFfFK2v7GvLNoHBZLbZZktnnHFGaR2qPUxHUbCCGdywMdFQQLYrDTaDixIiXPInVOoPM21YpGlSzWGUrbqLZ0LUF7YetA1ZzGHC5cnaon0UDOVhEBrc6kw45W/LzCCCk3S1TjiyYitBXxukJjvtsIpWPqUGSysI6a0iEFDKaMCAAYm/Pl5ooYUEJ3iYmMqHyh8DhCLJXsg1BTD77LMn5uTs72rSh5GrOCyEcBphhBES2aO8EAttVX91skWDkMBEXPlwsCDTBhrlQ3lRErC68cYbyzNj0lAM5PLJJ58syZS8TDiwVpay1YU8mVhHH330kqCTtWmarJeulI68yGutwmIZk27mmWdWrXKrFwnTNuOA8jQmLCyMOUSmjNj0ByEgU5QcuTJ5UMxkRlxhSBDlZfI1QTQlG+y/yfW2224rt7dNKMohj84FkkMWE2NTv2ivPtfH2kPOTQzysGiBIQKFxMlHeeruSu4GK7iVB6QCbtqrfDJXm4RipWuy/znnnJMoXXHJW/Z31T8WcLYeyQbLD/lXd2dETM76nSwaN7ZK1Z3F1HnFajl0jvGq7xGKbbfdNpFj5dQ6+gf+tjfUj1zD1jiCL6zkD1tpyTxskTfP2SEbSI4Jx9Yk+RBm/CMKCAx9SX5NYiYY8qZ8+on+MeZZwtSXXNJl5IScajO5o9NM1tpLnuhRk5mxqx8tkOhT2MBBm8SnH8iaxaFtJLiZOJEKJKi2P5RrYWCs6i/lSkeOyRTMYGxcyF+71N/4MibUV1/pNxPutNNOWy7c5aut8qAL9TXirj3GOVzhRBfQw8a8trBeqiv9isQgD7vsskuCO/LED5nVV8YC/YfkIFvS6U/9wSmbnkIopLFgom/gpr0spMaDPtTv+oeuRGrpEnpXPrXOeDbv0MfaqV9YGKvx5K/9+oq/BRsZIAt0jQUIf27UUUdNCDiZo5eMX/70vPGCAMuHPnHMxpwCK2NIf5Ef8bPTvn//+9/pkEMOKQk1bIW5wtOcYD5QJ7rG2C6Kojzbp59hCFfxpYOv+ct2M3z69++f9Kk+R770IXlmWEH0GWqk66jrMFlSuMFAYRvggC2Kojx3JAwJqlcpDBAouVPsXQI4xwU6AdJxFHH2N3DEA6YJCnsEUg6vvVIShFjHCVNP+SJ0Y401VmnRwoSd9RHO6UgKyr22GSDu2+MIFOFbYIEFym087ahNr3yK1Aq2KIpB5xcMDJ1rYFN4sJGWcBtg8lQn+IknTH0pM/e1jkBrB38TnNWtweQZ60Z6DFR5OCNlUqbE2rL94EyMvAklZUORUTgcBW+QmmwIuPKyQ04mmWSSpB7Kyv6uBrJr1WmD+NmPGdjK8cILL0wGRvZv7koulQlPdUZmDDiT3YorrpjIlNW6CaJaH9ZA7ZJWHpQ8zEx6JtCxxx67LNJEZNVInsXVF/qJ0i6Kn8m2vrLipVxYSClG/a9fKQTYy8zigLxQdp7b64yHJZdcclAyk7s+Vj4FaxVLYVF+xqeV5yRNfaG/q20flEHTDcKNDOrfpsfyP+UoX+Ncu0wqxqUVKtnO7VlhhRVKcke+Mv4yIIswg6l0SKk+ENYWR06QU5Oo9iqHdac2LX+YZH+TsonTdlufPn2yd7PXoiiSumuP/jQBkW99x1/dTUjqr93NZtQUQO81XVr9L3/yJn/yhNwhcSbXoihKPOtloi8QMxNwURRJn4qX5ZFceTY2yaqJA/EwyfMnB0guuSYr/OgyJIaOJEOIEQzoJ7iqnzGovjBBlMm0MQUbC2Qre/ImDdJpEqXDjD/xTJKsNRYuysyOfLKk0KV0BT2i/5AidaUrTfDmHnVTT/OCfs2yKi0ira3qK2/xjE+Tr0WNtMomS0VRJM/iceYPi1ltQfQQH/7ZmYyND/lpi/FkLLB2ITzKJ/c5fr6qP/KIqOX6ax8ZIWvyg1GWKeRNn5gP1FX6nFf1SmboDvODhSEioY+qcdRJn8Ofv3zNucauvqtXX/GqTp+z1BRFUc5xSIt5RP/AStlki66upkOeyKU26ic6RDg968gJfbzEEkuUFngkTTxh5Fq/m1PM4zmdNmgPnaovEDf9Z6wi9uQS+ZU33a+szrgROpO4O9JqOIVRmzfBsVIgENkZ9LXx8rMJzWRN0LKfjqI0kCTgGQA6PodLg5Tk5+66ekOMgsDEWYMIjrKUbyJ3X3WUEDZPGKr+7bmXt/jIjSsHD4LkviOOAkLAYIqIElgkhtKisIqiGMxqqAxKwsoWafFcdQZH9bne/QEHHJAMREqfgqsXpzU/AwrOlFKWJQqdws9pTRpFUZTWouznyloirQnbszRk0yrQc3PORMTSw7KiPyk9bYADJZXTGehcfu7MVV2r8q+OnPq2NV99jGAgeln+1E/eGTtXk1Bb84S/dlPM0nKUYFvTU6DS5nFDpumNZtIP8rbtw8qmHSbuQQHtuDGJ6TeWIPXmTObGUjuyaTaq/I0j40nenHv+zSZqCmBNQQqQIwSFVa3Ju+5/FhSTpMm6qv/qRq54klMTEN1Z8R50WxRF+VKMflFvzqRqkrPqv/rqq0sSh1CwSLNWsKDAE+FMrfxDsI0b1ioyaDvbuG2O6LPcC7MoRY5ayX6IYGXRA9rB0RfVSEVRJHMMoiOcQyw9V+PV3rOCiGPBD391rI1TfSYPrHhVv3r3Fl7mSARPPzEMIC/14mY//cMahhi7ssjlsPZc9TkDBQyyq52fzUHIdtadOX/zh0VoTudK5ukUCxvWfbqTvOY0rnQvcoWwMqxYWGyzzTZJvwnvatdhskRhAccqGZvF/Ag9hqnyOo1ZEECUo3ADA7sElo4lBO6tVJEUeWGlVokGFqGiVJEbrNpqn4BZLfAzUVcBIVAmMsQC66RA7Lky9zrXwHxnhWayUH/psWrkzOC1V0qRWJFTPCYE2xbMu1bk0lfLM+lrDxy0VflMptqkvfle+whJTks4KHema6sXdWE5I+QmM6tDVi7praDga+VIwXtGOEyCtjLUmxKhHOFJicCA4MtT3dRLH7DIwIOp3Lkb7c5bGeqnPvpOP6iTtNqnfKuHXP98LYqifHvJthdlLk8rrKIokhUThazP1As+TNYGsRWHbR/KLucFXyuT/Jyv5CS3zyTnLII6WuVSlDlevlLkZMkg0x59oS3woey1iYJDtORBljhmX/XM+bBI6o899thj0He0WFj0AyJohUx2yKpVpMlSX8CUvDjvoL76gJzI1/6+eukjzyZc9TCB62/9QulQcOqrnupODpFa+/C2xBAu5RoD8ISPCUTbyB3LjTGA5Hg2aWijtLZf+Bmf6uYexuJTWOrFGXf6xJi2yrcKp5iMb6QWrszp8qXI1N+9tspTnfW5umgD0zpHzjiLBBYTaThbtNohrXGmD+GpPO1Sp+zIlAlGOnKufCvRHJ6v2iOtfLRHmerCgqcfc7x8pRe0i+6BlTaoD/k3htRPPlbmiJfybbnoN/XN+YhjQaT/YEzuEDrP6qIOxiisyIkxj0CTJ5gjqFnP2W50NMF4kV5fwS+Xla8mCvJOdlj7xBFXneGlL8ij8mAHG/WnS8RhqdNOckFfqY+8tUsccW3NsX6oB1y1i5xqD9y0UdnOdjkzIw0s1d25NdtlsKcjtJllUR7GAEyVV+uMdbIuL3rZmNVPZIkfzMguOVF/9cj1z/qHnqfH6FzfzhNOxmAiH+2na/WJ/lEnedrqs0hwdENZ+pyeM9aVZa7QXnMLGRRHHY0FedEF8q9tEwKmH8RXf/oW/vDTb+qnvsYe+aNLyYp5gbWI7nd1RrWaN/0AHySDbtBX1XD38CHLruSCLrG9Z/GBMBnr4mWnvRx8LFL1N+zUkazCThvhQA7Ml9plziU3OR9XW5jaahtZHHKhb8kYq7edDf4c/apP6RjEkqzQO9LTKcqXDn4IqnnNGTQESv/Bjz5XJ/pYGmnJk7p0xHWYLAEI07YVo/MMQIddNdSA03hAGqAGA5ZpQFAetlYIhcaIy6xoctJ4K3AdrlOkQRAoAora3qOBCmRXk1S10QTdCsJKT146H0EAGEEk7ABnnsdEERVxmfIJgEN69vy1R50wWmWawHScPKvlEWZxKSgDQ/lwoRAoE2kQCUQFFjmtSVI5hM2g0V4DWXutCnU4QWYadfaIoLhXjoGPdVM+wtRJ/WHJIRzCtdNAMykgmurDNKlN6khR2PMniNqhzgSMkkBCKCQCZgAamPDJ9c9XbVMvz+pgpaiOnjl1ZEEzMCkDQqxPmIbVOw9meb/88svlwXLpqk48E7U6UuD2o/W/vOzfV+O6X3zxxRMrBbk0Ydkmo5gNGMqTWVb7EWNmX3lxFDiCLY/stEcbhXMmd0SJPMIUcdW3cIUVmbEqIhP6G9b6QN3liZjC2WrSMwc/ZVBG6qVNyJRBLX1R/LyVZ8WEZGuH8WQLAn5WhvBkmlYmWTXO3MPB1gG5UH/yDQ/K0vgkc8pEMClkMqdOnHFpsrV4ITvkyAsR5A9OzmFou3yVRabdayOyQLnrc3VB6IxnV+13TzFuttlmSRoObsaQVSHl5964pUz1ozpx8tX3mXAbc/pDu4RXnfboV0STvmG9UJb267NqXPdkg6yRF/2mvfrCWNG3wugvMgg/eRnjtpiMXXlwsDMpI/YwVkdt8KwPjXnj07g26WqLe4pfO/STcSR/eou1SBpbfsaA8aScqoO7+Fk+6GP9alyqPyzJk76if2FsbCtbu6VDDvUPfMiM/MkTf3nrI7qKzEhjPEkHL/WmP2xVW5BqlzT6nIxaeHgmU7apTM6IOz86h3wrr9bBn34Qj26k8+lv7VJ/+Xg25tRZHyEqcDI+9L+04tsmM2bpPPqffJIzYdpkMtUvtrGUqa0INpInD9uC0up/RgB5a692kDVx+JNhecBIv9W2yfilp9QfOYE5uaLrtEXZxhlyAVuy58yleYFcstzDQt2qedNJyuRn3OR7z9mRHZghN+TCXAFjdVdvbctxXck1HJBrmPEjO2RE32uHMWmMWbzDXV5wMGeLn504zi7Sh+LQdfSTemofHcOfwyVgQz49q7NxQRfRd/Sw/oKPuojDIbYIoHtjXD30Mz1ERyFZuT7tvXaYLBkcFD3rDSFUMQcMTUKEwT1nsFHE7pErV87gNpCsojxzwvkRAs+E01kSjdQwkwx/TnoMn392ABHGIU38CZZnzv4mP1erfH7ImSuBNQkQDM/y1zaDh1Kwysh5yoPT+eJmVy1fuYiBMMRImdJkp23CKLBcpsnHBMcfjupgQpeGsFCWyB+hoVy1HzkSn4MdrNwTQAPCvXQUrnwytvwJI1KUy+dHAbhyJmDK2mDSVumrTtmUBz8KkSJzn51wyoRFkRJANoQZdPKnBCgrKxb1NXCFV12uL2VqhaOfpOX0SzWue37CKE1Tq08fAAAQAElEQVRK271yKWvYeaYcxTV5eeZMePxqHUUonCMfwmGpT/npC/hok/HAz0AnL+4RgowdWc/x5cPBj1VEXM6qkxxQ9J6NKziRLfmTC0oUDkVRlAevyZDJW72k4SieoiiSennmYExmquMTFsI4/urEwVF5/I1v+LnXDxQYvDxziE+1bHKrXeopXP2yLHomF/oyj0F+Fi3wcc/RBUgRomGlrE4cBWlSpH/E40ziwmqdsSNc+TDMz/yM69r4JgthcMj9p//pCGNIGJz1T+4zOoKMV/OCnX4Tn9MXiJd7/siKfvSsLPJBV5BP4zE/C6f/TE7kxrP09epuAhHOwS7rEc90UcZau8iSdulfY1/bPIvLGavkRJvIfO47deSXZUZ9yYXxJZ289WsVZ3kZHyZOceBlYSwfWPLjTH78ah05Ik/iIJDC6S1lqr865bEoDqe+JlFt8MxlPaJ87eVHPjn3HJxdObpMW+hZzxwZVb7+82xRWX3mB2u6kG5RP7IuTtWRZ3gLh5n6c9JzyKRw9/oNCSJj+ZlOqZevcWqeMGYQBO2pluvePJTzVlfjQn7yNrbFqTo46mPh5MaVo1/1gXvpEfPq/Eyuqvm4R/bIpjScdlooCuP4ZdenT5+kbrnv4VObXlsQWfonpzOepMvjy7hBAMmqxZKxqKyOuPaSpY6UEWkaGAHnqgwGiqcjzSDkJkGWk3rpbTEg0ywYBkO9OOE3fCJAybHuIe0ZAVu97k2YruG6DwGEi/WdFbMzK/KO1NB2FsLB+uJNPta6juQzPKZhzUSaRh111F7dfAtLC2wkkY7gbFUibSyrXd34IEtdjWgvyw+BKYqft4I60rSiKBIrCXNtvfRWylbu9cLCb/hGoCiKIb5ibvVrlTh8IzN0Wm8rzZapBY1V/NAp9edSWKdsbSkfWWO5+Dmkq//2vvyQBmeWel/LhmwRKz45Iauc858sS0PG7LxPkKXOYxg5BAKBQCAQCAQCgUAvRiDIUi/u3GhaINBbEIh2BAKBQCAwLBEIsjQs0Y+yA4FAIBAIBAKBQKDHIxBkqcd3USNVMOoaCAQCgUAgEAj0PgSCLPW+Po0WBQKBQCAQCAQCgUBnEaikD7JUASNuA4FAIBAIBAKBQCAQqEUgyFItIvEcCAQCgUAg0EgIRF0DgW5HIMhSt0McBQQCgUAgEAgEAoFAIyMQZKmRey/qHgg0EgJR10AgEAgEGhSBIEsN2nFR7UAgEAgEAoFAIBAYOggEWRo6ODdSKVHXQCAQCAQCgUAgEKggEGSpAkbcBgKBQCAQCAQCgUBvQqBr2hJkqWtwjFwCgUAgEAgEAoFAoJci0GVk6bXXXks77LBDeuedd7oUqhNPPDFde+21bc7zm2++Seecc0668MIL03fffTdYurfffjvttNNO6dlnnx3MPx4CgUAgEAgEhi0CUXog0JMR6BKyhCDtvffe6frrr09ff/11l7X34IMPTv/4xz/SG2+80eY8r7766tS/f//0yiuvpJ9++mlQOnVca6210v33358+/fTTQf5xEwgEAoFAIBAIBAKBQEsIdIos3XPPPemQQw5JE088cdprr73S+OOP31JZ7Q7bc88904orrtiudKuttlrabLPNhkijjhdccMEQ/uERCAQC7UEg4gYCgUAgMPwh0GGydPfdd6e//e1v6ZFHHklXXXVV+uKLL0r0Pvvss3Taaael008/vfT7/vvv01133ZWuu+66dMopp6TLL7882SqztXb88cenAQMGpA8//LBMK544//73v5Mts9Kz6Y+8r7jiiiT+448/3uTz83/x+XHPPffcz541f5V/5513lmmfeOKJmtB4DAQCgUAgEAgEAoFAoGUEOkyWJp988tSnT5800UQTpemnnz6NPPLIZUlHHHFEGm+88dLNN99cbnkhNCxE5557bppuuunStNNOW4YhSPPMM0968cUXSxLlHJE0M8wwQ7md9+ijj5b5ffvttwl5QrDeeuutMq6AW2+9tTzLJA/P++yzT/r444/dDuYQJURr5plnTjnPwSL00odoViAQCAQCgUAgEAh0DQIdJkvTTDNNue2GNM0+++xplFFGKWuEtKy11lppsskmS6w9Cy20ULmVtsQSS6Sll166JEssUfvtt1/afPPNk62xhx9+OA0cOLAkP2OOOWY69NBD00orrVTmJ9811lgjrbfeemnBBRdMTz31VHnm6Pzzz0/8F1988bT99tuX5Z1wwgllmuofJG3llVdOyy+/fNpoo42qQXEfCAQCgUAgEAgEAj0fgWFeww6TpeZqPuKII6aiKAYFjzDCCIkrip/9fvjhhzTJJJOkyy67rCRTzz//fPnmGnK04YYbpoMOOiituuqqpXVJXBkVRTFYnl9++WXivvrqK8FlmPNS9SxLb775Zvrxxx/LeOpR3sSfQCAQCAQCgUAgEAgE2ohAp8kSIuJttXpEpV4dRh111MQ582SLzZkiW3EvvfRSmn/++RNLkEPdt912W8pkqDafMcYYI7FonXfeeemTTz5Jn3/+eXr//ffTMsssUxs1IWa235Crl19+uczzvvvuK9MNETk8AoFAIBAIBDqOQKQMBHopAp0iS84q3XjjjenUU09NiItX8vfff//yXBEydNFFFyVnmHxSwP29996bRhtttNJy5N423DbbbJO8VSetM0vbbbddcoh7ySWXLA+KC3Pm6KSTTkpnnnlm+R0n1y233LK0Lm299dZpq622SrPNNltabrnlknzV6ZprrkkPPPBA2nHHHcuzSuLfdNNNaaSRRioJFIK27bbblueqUvwLBAKBQCAQCAQCgUCgGQQ6RZZ84BHB8Y2lI488MnnbDKnZYostkoPVN9xwQ9pjjz2Sw9juF1tssXLLbO655y6JENJz8sknp4033jjx23fffUt/5MsnABAdB8SvvPLKkhAhXKxECNVMM82Uzj777JKk+QglwuR8k3NRynMofNFFF03zzTdf+ZFKcQ844ICSHK277rpp3nnnLb/h5BxUM9iEdyDQWxGIdgUCgUAgEAi0A4FOkSVngFhqnFPi3HPN3Yuf61aNw78oilT1K4rBn6th7lPTP1flcfJo8irPR3nmsl+Ol69F8fMZKHGKopAsXCAQCAQCgUAgEAgEAnUR6BRZqptjeHYdApFTIBAIBAKBQCAQCAxzBIIsDfMuiAoEAoFAIBAIBAK9H4FGbmGQpUbuvah7IBAIBAKBQCAQCHQ7AkGWuh3iKCAQCAQCgUZCIOoaCAQCtQgEWapFJJ4DgUAgEAgEAoFAIBCoIBBkqQJG3AYCjYRA1DUQCAQCgUBg6CAQZGno4BylBAKBQCAQCAQCgUCDIhBkqds7LgoIBAKBQCAQCAQCgUZGIMhSI/de1D0QCAQCgUAgEBiaCAynZQVZGk47PpodCAQCgUAgEAgEAm1DIMhS23CKWIFAIBAINBICUddAIBDoQgSCLHUhmJFVIBAIBAKBQCAQCPQ+BIIs9b4+jRY1EgJR10AgEAgEAoEej0CQpR7fRVHBQCAQCAQCgUAgEBiWCPR4stS3b98066yzDuH+9a9/dQq3Cy64IK266qptzaPb4x1wwAFp9tlnT8stt1x68cUXu7287irgpptuSltssUV64403uquITuX77LPPpk022SS55owuuuiiNO+885YydvTRR6ett946vfXWWzm4xevjjz+eNtpoo/TKK6+0GG/AgAGpX79+LcbpjkDl7rvvvumrr77qVPb//e9/S/ns7n596aWX0mabbZYee+yxsr7bbLNN+ve//13ed9Wfe++9Ny277LLNZpfDZ5tttrTjjjuW/dZa/zabWTcE6IsVVlih7I8jjjiiG0r4OctvvvmmbPt11133s0crf7/99tu0//77l+Ohns5ec801B8vBOMzxtt9++0Fh559/flpggQXS3HPPnerp+ffffz+tttpq5XjdcMMNm9U1hx9+eBknl5GviyyySCJngwrs4M3111+f/vCHP5SpjznmmHTllVeW9/GndyLQ48mSwWJg7LLLLomS4AzIv/3tb6Wgfv755x3qmQ022CBde+21HUrblYl++umncpCNM8446ZFHHklLLrlkeuaZZ7qyiKGaFyV++umnp8knn3yolttcYT/88EP64IMPEsUvzswzz5zOPvvs5Or5ySefLOXqhhtuSL/97W/T6KOPnk455ZQ06aSTCm7V7bHHHun7779P+rE28ttvv52++OKL9PDDD6crrrgimUxq43TnM8KhL2BQr35tLVs7/vnPf6avv/66rUk6HO+MM85Izz//fIln//79y/sff/yxw/nVJnz33XfThRde2CwZfv3110u9cPLJJ6ejjz46jT322OnYY49NU089dW1Ww+RZ/S30jjvuuHTmmWcmz++880631OVXv/pVQrZXWWWVMn+EW3nlQ80fMrLxxhunZZZZJp133nlpu+22KzF7+umnU3arr756mcqYs1Cl63LYlFNOmeaff/705ptvJgQI/iOPPHK6+OKLyzFUJvzlDzL76aefpiWWWCIhVs3pmj/96U9l3y288MLpjjvuGFQPiwfj/JfsOnRB2E444YRy7MsAaTLOTzzxxKEyTpTZORep24tAjydLtQ0aaaSR0m9+85v0xz/+sVxxYve1cRrp2SROYYw11lhpxBFHTCYI5LCR2tCT60q5n3rqqaUSrldP2H/33XdpjDHGSH/5y18SS0a9eM35HXzwwXWDkPi99tqrnOznm2++tMYaa6QRRhi6w83KnJWmbgXb4TnJJJOkbbfddqjUv1+/fmmaaaYpa2csTDvttOV9V/2ZaKKJ0nrrrZcmmGCCulki1iZik+mKK66YDjrooJIw1Y08DDxN0gi4+rG+HHrooWniiSceKjVBgixeawv7+OOPk8UrnYwA1YYjWQiwsSXuSSedlOacc87Bxtqee+6Z5plnnsQa9Nlnn5VZ0IOffPJJSXRKj6Y/wuSFXDU9tvv/Rx99lIxHMt3uxL8k+PLLL9M111yTll9++V98fr5og/oicz/7xN/ehMDQ1d5diJzVzphjjpluvvnmMleTHlMuZTugacvjtddeG2RCtwIwYG11Mas/+uij6aqrrkoUTZm46Y/nrbbaqhzArAxNXuV/Kzh5mkgpqdKz8ocCYYkwaYp3ySWXDAo999xzEz9WsWwtYqrdb7/9yomZgrESMfDkY/tK4qeeeipZFUmrXH7cOeecU9aZNeP4449Pt956a9p7771L0iiuvGwfaaNnE7Z01fx23XXX9MILL/BOTMesLKwG4t94442lvz9nNq1a1WeHHXZI1cGvLeLCFMkQt+puueWWBDMTDn/x//73v5crwHqWFds6ub4vv/xy0nfw79c0aVpVWjXvvvvuaZ999iktMyYL+AnnHnrooeQfCwrsWSb4w5lF4ve//33iD7OBAwcmZRx44IHJSlgbrWCtOpEBxNU2ImwpZfl6lh/3yi9bbXA1ifK77bbbRBvMvffeMgUMFwAAEABJREFUe+Uke+eddyZyUbVgwlg6EwaLDzIHL7K4+eabp9tvvz1J379//1J2dtttt3LLwHbflltumayKrb7JjnxYIxV+9913l9uf/LIzBoRx2il/bfNc6/RRTnfZZZfVBg96fuCBB8p6/fWvfy2tP8YE+efkTy5EJovyMybvuusuXqU78sgjy/TCqtixEPCTroxY+WPFbuUuf/0nCLbic4ccckgiF6xnZPnyyy8vx4X41bKRZvGNdXnUOhjv1zQ277nnnnIxpi+MHX2DRIlPVuSRnf7JskDmyJixq5/Ef+6558rxYNzpP/V/8MEHE7lUP1Yu8WqdspXBwcbYefXVV8tx8J///Ccpt7YdwtXfuGHZMXmzlNER8mHRyeWcddZZZT+ol3bzh4+2Ij3GkTLJoXC6Qt+qizD6VBqOPqULbG95rnUwEYe/8WwLbLHFFvM4mKPT4Z3H2fjjj19am/S1MScyPEcbbbSE9Hpur4ORMnI6dbOogY/t3pZkP6cht3PNNVcy/2Q/V5Y4CxTyY1zwC9d7EBihUZvCEsD8alIz+K6++uqEDFFcFI1BRTEz5VpJGGAmTKbiDz/8sJzE8kSLdCBdFIVVJ0ViopGXla2JRj5ZAWbMTjvttNISZNJdaqmlEjPzUUcdVW67UComa2mZi9UFIfrzn/9cbrepB4WHkPTt27dc7ZooKBPlOwcjrYGtXdKaFEy8BraVGUXHJG9C4GeioIANfu31bNA6k2O/3jNCwBpnglYeJWiVtfTSSycTpraZbJQrjAlbfUwWa6+9dtppp53KeBS2NoqfHT9KWlrKEyGw+lpwwQVLQme7KsfNV/mts846SVtZDK0apbFapjQpxZVXXrk8lwBPdac44az/TdLI0NFHH520m8JST36UvT6DFQxtpVDItqcoe32wQdN27OKLL15OaOQBOUS81Z/Sg626sQxZ6cLPpMESCD+kK7clX1ktkC9WUBPnSiutVAYhGvL83e9+l5BKZAkJtM1DnvUPZattZEK54403XimrE044YblNiDhoI9lBYvWL+iJPiClyzY88TDHFFGW5JmR9LA3LAFzLgF/+kH95KF+9Tbbk/5fgwS7qbZyYeOEt78MOOyxpFzxYD5B6faT/YYxYyR+WJj5yvNBCC5XnW2R+xRVXpPvuu6+UAf55YSEMCXKGT91h4epZf2+66aZJ3vqTDlAf44xs61dnAGEoH1d6wVX/WFTwr7o55pgjIebOryG5iy66aCJLyIJ+11/IiDNtCL42sz4Z08YbXMnYMk1bUSZl8r755puXW0HqA19yhdgiMoirMaRe1XoYR8a1usrbogtpZ03Rxnnmmae05JDHnM6iQ10sfsiIcagfXddff/1EFsiV+PpMfeVvOwxmxol+JVPa5jyRsUIvssYYF7PMMkupp4RJLy9O3xqv7qvOoozegWGWJ1YZ1qVRRhmlGrW8N6ZgZtzyMH7UAf7GmTC6Zaqppiq3y8Vpi4M3i5e6kG99KR0dQI6Mf1ggi9orrDlH9swFzrPVximKojx+oH3mpdrweG5sBBqWLBF0K2zmaIqSwqHETL6sGpS1bS2DzWCm6Kz8KECHOylxQm/wWik4a2MlY6KmnEwu4ltF2UN3Vqp2AFgpUhwmewPu17/+dZpxxhmTSdfEYMKWFtEx0E24FJEJ0WBTPoWgnq4UCEuBsyEzzTRT8ozA8LOfj0xYvVFayJmJQnkUHT/bPCbNySabLJlcrbRNwiZRpMdZLxML0gEnecCBMhOfKFOMFCbiR3mZkJADypjCorwpHLghndJkB1uTf36WJwXdp0+fZIVaVbDimBBMgPpDW00C/OHB/T979wEnaVG0AbwbEyYEI4riEYwYwE8JxkNRMQAnGFAMh4oCJlRUMAFiQhQTSM5Zcs5w5BwEJAocOeecv/330cd7w8zu7Ozu3e5t8aNv3rdDdfXT1VXV1T2znnPOCTY5Z6/lCJYBMi8Mr3mFO8PBUHMy9YeeBjCGi8+cc+I4ypfQ1Y+k3G6Xs6FMYsQp2jqH7jmJLHBoGaY555wzMYLqNlPOT/OMLvrKOY1wwJ9wvfnRH5kzF+iJNJFtTroxmB/vjA1+0ZHQ9SmRLfPMIHIEyI41oExiLF2uZSwYimaZcobERgKenAF4yW+XOBMMI7lgjFdaaaW0wgorlAu3nDiOGmNtTr1zVB0XcbJsGjhKIoc2N+aOvFl/MDZeGxuyXPs2HnLPMXZEQ+ZE3sjkPPPMUxyR6lzZ3DD+ZJvjow1ZV5+TaJ3owzy3u5Nm3DDOOZe1p66IZeVFlMbdQnItsuCTYTcX2qqXcy7H6anvP7QYY/PL0UEPDbjRA3SHNWG991Uv/+OXLuM0qs/hsz5FkXLOqfbls8qVhsYqKmLconn441TQUeaAPoM3vSjKY/3AnANHdqydSZMmJdiQPbyLeNOJ6HvPOZexeU6N/zgH7nY1ssrjwgsvXO4J4YtsyjReGJJp781Ep6BtbDWffrPubEjpX3NtHeU8TR/Uev190s1kmx0w3kqfTidPymFN/1iTnWhZZxdeeGEis2jRicbOgVJW28njFNf3+Jw9EJhjrA6DwrXwGQFKgLHh5Oyzzz5JosApE06CnYmFkfMzFxjlRLBFYDxXPCgwC2fTTTct9NC0U67lnT4pA/3iSTRDO4nS5Xx0alfzLURKQ//yKA80m7zJ7zZRSnCx45w8eXLiFPbX1pi1aS5+9RkFSs5YalprrbUUdUycSFEVO30RFkqlWdlYm+/dPJt39DiNooDdtOm1jjlwNFvH63PBBRcsyrIVn177aG1HFjljnBpl5p/TQZ68t0uMEuebI2J3bA4Zy5yfKe/t2nPGOSI2HaJEjGe7es08xoVT3szzDBfGQvLOMNnQkB+RNUegDDAnULnxWnsMofeBkjVEPkV+RAE4gpyx/tpZT/iiL/qrN1AZh4czJ5rJCeKMeB+oXbOcTHHsbaDIk8iSNVLrKOfMcjprnuOeXtd/pVE/0ck5l+M8/UsiXJytWmewn+TT/HZqJ9rGYVMuUswZ47x4byZrm2ME15pP53DmOZAcJuuPk1rLB/tpDm0a0Gti3C2dnHP55qtIn9MLmxvrpzl+m57qPHdLN+qNfgSGwVmauYOk9OyyhI5FP+za7FocC9jR4mbq1KnlG04MjMVm12MnxXFS3kwcEbs3UaSqsO1e7EYZZMq91qfg6nP91IeQu0iB3Ya+7aApBzvZWs/OmpKv750+7QztPoX4KTY0jY/C6dSmv3yGyGKGE0XkqKC/+rBifEVgKG7GDK5w9AzH2p4DVp/bfdrNizCIdlH4jHGzHqUJL46sfFEmnzXZ9ekTBhxeX5M+44wzEoVpB9xKr7Zr99nsp115uzy8O5Ks/VDwHBkOjGfzAxtHh6JQZKGVjjGQzdb8Tu+iJYyPyAv6ZBJ2NRJC/hn/Kh+ic/BjhERRybijF0ahUx+t+eRdn6ILjqfQb61T30W48OQ4WP2aXz85QuaVQ8FpU5fjJ1IiSseIWLeO17QRZZswYUK5V+ado+BnHTjE3vFS6zr2FmmAhx0+h4vDBmN1OyXYqMcpUMd61Y+oi/fBJHMiQkw3cE5FbGp7fBir+TYnHNBaVj85AiI77i7JE50Q7fUsmQc6gCOIDnrq0inKh5o4wvCGZaXFiaXv6nt/n/ixFs1rrWdM8KzvrZ/65KDIt8ZFtIzN8b48ifPpLpcoOF0jrybrkDNH/9qA1fxePsknfWIObDDIAvlHiyz67JSse5tz0XVp6b7jVlFckW0bAu3gQj7ZFe+RZh8ERr2zRDFxjhhKu2WJE+LMnyNDKAm9Habwu2cXFO1oRXgIriMsgs4QmTphf9EWhtflR4uXIyEcq73dHoXPIWM85Eload9M+mAs7RaFy/FGoTuqoqS1kzgsO+ywQxKpQt8uiXF1rEEJULy+uURRGoeds2f1ORucFHcNGFF5fvvEkYm+RYzcKaCw3GMSxWFERRmM07jQxAdctKd8p0yZUr5+rC18KWUL3ztDZ9ds184wc6D0iS90JEaviYXjO9E0it6Y0MMDZUdh2iE26zvKch/JMQt6HI5abrdtrPp3pwYWLsWqyxCrj0dj8GyH7N4BJQYvx2X4068dpONAYxCNoigZTkdgjm4cEzC8aHm3w4W19mTH0Y4+yCEjycg6YsUTbBZaaKHybTeyUPnn3FDw5sgciEq6l6N/0Rv3OdyNgTW8HJ1wDLUzh/LQV25+Ocvm0fzBDc/6Ml/GyDFFg9yJqsLJGPTF8XUvCj3Gwd0UTo/2Ej7skpXDiQHHN8dAucT5Nwa8cHzIjyNPmMMFlhxIu2r3ajhFNiEwJEecWzIIL1gyuPpxdM7p4oTKV4cBMg79olvnm6yTPzLB+PpNMj/3wIA7FoQLJ84crr/++uXoF+bWsXGRI31Yf5wSR3n6qInMkAMXfdGGibmmJ6wZ8maDgDeJcwoDEVKYk3nyQb6M3dw5ajOX6/fxox/5jrvk44VMV72knAw52iVzjjjNDQfZfDLq5Ac96wOW2kgcLvU5kY7uYWGujd2Rn8g2Z9UxuTHpR/+S8cLHhtH4yAua5o5Tw3G1gaN7HWNxNpq6EI8cHW04t+YMXmScToSjsprIAnnFk/4ld5Hwx5EzP+TCnUkY2sDBSyKTMHOUab3S3ZxSMtHUH/qi08gTuk4e9CNZJzaPNqHkhkzLh5V2qe8fOLlW0PfY9f/0ORllSziFdLz1CYeuiUTFUYvAqHeWKDiLzW7TgpI4HhSVBQ/ZnHO5M2GXr5zhbN57sBuwcBgV9SdOnJhcoiTYlC/FTplRNNozFDnncleGUZInoaN9a6JY3VGizCjLnHM522dctJM4cHb8xiJxjPBPEXk3Phdjc87J2PCnnXsDHD1Kw7tE+alDKVuInDBjdswlvEx5oCn5FhFlgDdt8SQfv/pEg+MAZ7QoHHy5rKs+Jay/nHO5x6GtfKmp5FPff8aOJlwpKYlyVZfi49j2VZv+P9w5dpU3Cq0WunBud65/ypOz6AjGfa/KAwWvL/TlSQyFb5zJZ1QoRNEhBl3/+lIGI04VfrUzbnLhXbm5grsLxdroA208i96gLY8h5zhxmCrvPnPOSajefDDeDC66DJGxwFp7DqF888ERyjmXr1VzTJWjwRjlnMtX942DscI/vjmblLR5Zti0kdzrouyNRz13ksi3fslZM/LESeIgaqdfssDJNdb01H855/JDjrDQv82Jcs4p+vqpzjD54SCiZ9wMfc65rAljlc9Q4oVBcaxijuTDwXy7l5L6/uOkicoq4+SZk5xzuZCPDw4aw4svWKEvUmI948k740129IeOucYXh6mvi+n/kz90tEGb01bfzSEHk8ygIcGbfMjnnMCBbuJwGFdT3qw7HeWcy+8I4REN61ZkRllNcOUQ6FsdGzqRCzpNXuWP01HbWBd4NkaOsTXgmQPIcaEb8Wcc5gc/aEtkQ75yTiyHDF0yjgb5to6MVbm5zzCewUgAABAASURBVPnpI16yz7kxPyLZMEJLW/MKR/RqynmaLuHs6F/idNf54AC592n+6CbtOI/0iciQ8aEPB7JCv5EnjpS6NdG5Tbz0I6HLaYWDL9ioI99zbWvTRwfX93af6lf+lMPfBqDOCx0PO5s05ZHGNgJzjG32Zy33diwMOkXEUZm13Izt3hkvRoeCZYTG9mhmLvcu3osOMICcXMmxMAM3czmZqb3N9M7IJecDvhK8GUiR5JnOzCjrkIPF6eOIiuTOTPboDQ71UI7ozK2No2g4nT5Y/jm/HEObl5CHwaI3NuqHszSEeXJfQdTFMYJQ8RBIjfumjiztoO2oWyNW4x6cAQAQEbEbd5RQk2NhEYoBmkbxIBAQ3XDsVzEWnXAcJoI0CDKzbVXHh/BwFDszBynyutZaaw2pSzpHNNkRsiO0wRITHWUHHDkPtm3UHxsIhLM0hHkSfmaoJItlCKRm36ZdjsxdBcc47uW4jNtls6jWhwDjREmTw5oo/76i+H8YEcg5J0fNFWPy2othHUaWRhWpnHMSXarXHUYVcwMwQ+fUeXXXcIDqzyimv/ykxjMKImO2QSCcpdlmKmMggUAgEAgEAoFAIDASCFRnaSRoB81AIBAIBAKBQCAQCATGPALhLI35KYwBBAKBQCAQCMyIQLwFAsOLQDhLw4tnUAsEAoFAIBAIBAKB2QyBcJZmswmN4QQCYwmB4DUQCAQCgbGAQDhLY2GWgsdAIBAIBAKBQCAQmGUIhLM0y6AfSx0Hr4FAIBAIBAKBwPhFIJyl8Tv3MfJAIBAIBAKBQGD8IdDDiMNZ6gG0aBIIBAKBQCAQCAQC4weBcJbGz1zHSAOBQCAQGEsIBK+BwKhBIJylUTMVwUggEAgEAoFAIBAIjEYEwlkajbMSPAUCYwmB4DUQCAQCgdkcgXCWZvMJjuEFAoFAIBAIBAKBwNAQCGdpaPiNpdbBayAQCAQCgUAgEAj0gEA4Sz2AFk0CgUAgEAgEAoFAYFYiMHP7Dmdp5uIdvQUCgUAgEAgEAoHAGEMgnKUxNmHBbiAQCAQCYwmB4DUQmB0QCGdpdpjFGEMgEAgEAoFAIBAIjBgC4SyNGLRBOBAYSwgEr4FAIBAIBAKdEAhnqRMykR8IBAKBQCAQCAQCgUAfAuEs9YEwlv4PXgOBQCAQCAQCgUBg5iIQztLMxTt6CwQCgUAgEAgEAoFpCIyZf8NZGjNTFYwGAoFAIBAIBAKBwKxAIJylWYF69BkIBAKBwFhCIHgNBMY5AuEsjXMBiOEHAiOFwBNPPJEuueSSdOONN6Ynn3yydPPAAw9Mfy4Z8U8gMJsg8OijjxZ5v+WWW4qMk/kHH3ywPM8mQxzXwwhnaVxPfwx+NkNgVA2H8dh9993TPvvskzxLl112WeJEjSpGg5lAYBgQ4BjtuOOO6dBDD02PP/548n7llVeGvA8DtqOBRDhLo2EWgodAYDZE4HnPe15accUV00tf+tIyuosuuijNOeec6VnPela6995702qrrZY222yz9Lvf/S7ddtttpU78EwiMVQRe/OIXp+WWWy7NPffcZQg2BtYAeb/77rvTmmuumTbZZJO08cYbp3vuuafUiX/GDgLhLM2KuYo+A4FxiIDjuDe+8Y1l5C960YvSC1/4wpLe+ta3pvvuu6/kxz+BwOyCwO23354WXHDBMpy55pqrbBRe/epXp9e97nXpoYceKvnxz9hBIJylsTNXsw2ndlWnnXZaOumkk2abMY3ngVx77bXpgAMOSHbSnY7Ybr755vTa1742zTHHNJXDcRJxev/731+OKzhOvWLoboh7IkcddVS68MILeyUT7QKBrhBwtLbffvulK664ouMRG/l+zWteM13er7vuujTvvPOmd7zjHeUOk4hTV52NkUrjgc1pmms8jDTGOCoQEEE47rjjEmXx3ve+d1TwFEwMDQE75YkTJ6YzzjgjnXrqqeW+RqV4wgknpOOPPz5xjueff/6anU4++eR09dVXp4MPPjgxKhyn6YWDfEDn6KOPTiJUb3vb2wbZOqoHAoNDQLSIvJP1s88+e7rD5E7eiSeemOg3a8HmoFI+9thj0//+97905JFHpgUWWCA5sqtl8Tk2EAhnaWzM02zD5bnnnpte+cpXpre//e3Td10p/hvzCLzkJS9Jn/nMZ9Lll19evhFUB7T44ounz33uc2W+HUXId/FVJEj9D33oQ2mppZYq95iUDTaJUvrGHRrzzTffYJuPs/ox3OFCYJ555kmf/OQn08UXX5xEmtAVNf3gBz+Yll9++SLv1SHyDVDyPmnSpLTMMsukd73rXaH7ADbGUjhLY2zCxjK7FIYow2KLLZae/exnj+WhBO9tEHCUtuiii6bzzz8/PfLII6XGEkssUQzEm9/85vIuf9NNN00bbbRRubtBFkQZS2EP/7g0zhiJbvXQPJoEAj0jwGFaaKGFEhl87LHHik7jtH/kIx9J9W6eu0m+wPD3v/89vf71ry9O1HOf+9ye+4yGsw6BcJZmHfbjrmdHLx//+MfLRcfhGvw111yTvvOd76Stt956ejh8uGjPKjpjud8JEyaUKNFNN93UdhgMxU9+8pNk3t75zne2rTOYTHdDOFzD5XwzemeeeWb68Ic/nM4777zBsBJ1xxkCOefiFLlacOedd7Yd/Zxzzlm+7enO0iKLLNK2TmSODQTCWRob8zTmubTDcvm27riGa0BC4NJw0euWDqO67777ljB8t23GQz1HD9Idd9wx4sNlpFwcf9WrXjVsfT388MPpggsuSL7qPWxEuyRkjRxyyCGpk6PZJZmoNhMREF0SGe3kLM1EVqKrEUYgnKWeAY6Gg0Hg1ltvTY5LfGV8MO0Gqvu+972v3BEQsRiobi/lfg/on//8Z/rud7+bHCNWGjnn9LKXvSx+H6gC8tSn35R5+ctfnu6///6nckbuQ3TKt+/s3oerF0eJ7liN5EXxqVOnph/96Efppz/9afm9qco77BheMlfz4nN0IyCi+YpXvGKWONejG5nZj7twlma/OR2VI/JNkYUXXrgc0YxKBjswdfjhh6df/epXaZdddklXXXXV9FoMmyjEcDt/0zsY5gc7XxdLf/jDH6aVV145+br/MHcxnZzL3nfddVf5ivT0zBF4gL9v2LlYOwLkR4QkR+gf//hH+te//lVkqumAk6nhdv5GZBBjgKjfOHr3u9+dVl999bTqqquO6KbGNzmb85jG6n/Bd78IhLPULzxROFwIUF7DeVwyXHwNRIeTd+CBBybG32Vl9f2uj2/17bXXXuXSJqPtF6gZQuU1Pf/5z6+PPX2i20qzP0IwdjzYrON3jLw7GvNNHN/WWWWVVWb4er/y4Uw55xF3lPB7/fXXl+ie57GSRFf9xIGj4xtuuCG5IIx3TtIxxxyTfBWd8RWZY4B9c1C55JjuE5/4hMdBJTLR7bGiC/iON8n4oDoZhsrGp+9uSFmP1mazrjH6hqU8Drt7Z5/+9KfTpz71qRGVd/3NCrz0G2nmIRDO0szDOnoagwj4anAr21dffXU655xz0kc/+tF0+umnlxC8+1hSa91e3xkOP7I4mPsrDLDLyQxea7949o0x0T2Gpn6Nv7VevI8sAn7qwKX01l7OOuuscv/Nb/j4sUOOEsfJkV1L3UG9+htl//3vf9Oll17aVTvOnH7dBeuqwTBV4hT6rSzH9d2QdGHab3hZJ+3qw3CBBRZINmicKser7epF3thGwPog3zYbdSR+68pPmJh3X9IYjA6tNNp9hrPUDpXIG3YEXPgVCRh2wiNMEM+OsJrdOHrzrT5hfj88546OT8q5WW8ozwyBO1FveMMbuibznve8p/wZhXZO25QpU9Kuu+5ajn78inD9+1WdiDPoX/nKV9Lvf//78gvbneq1yxcNg1u7suHM04eI3nDSHGlaooWOQH02+3Lv5Qtf+EL5hWeXhn2r0C8+S816g31mKDgWolndtCUX5Ji8dFN/uOrYGHBs9N0NTXfKRG59w7Zd/SOOOCLtvPPOSVR40UUXLX9Wp129mgejL3/5y8lX/Ds5YLVu66eIFllszY/3kUXA76ttueWWJWqYcy6dcZL/9re/lZ8vcTxPF22++eaJ/SkVhvBPOEtDAG80NBXKF24WKWgmv/dBUVYePbtQqo4fhVxvvfWm/xaOOqINLkv7thpDLa+Ztthii8QpmDRp0gyXUpt1+numgBwt9Fenl7KDDjoo/fKXvyx3EyjGXmj018bOHO/NOnDgHIkC+HFNv8xrB/Of//zn6WpPPdndUMAMAeyb6Zvf/OZTtWb8EFXg8HDGZiyZ9ubbWn7LhVKYlvP0vxMmTCjf5qIkai7cHRMwIBtssEExyBRJLW/3iV9zbfzNC9S/+c1vBrzzJLKlz3Z0hzNPH61zM1T6joE23HDD5IjVkaVI3VBptrbnKMG1mc9JgPlb3vKW8vtT1iDFL1rYrOfZ3HKsmrLkmZPlywjqSHbbfvOKU8HBl9dM22yzTVp66aVLlLSZLwJJX5CzZn43z8YGP84fnprpBz/4QVsSdFgneedYfvGLXyz3Blsb+8kI7VqjUfDJOSfy/otf/CL5ja+cpxnTVhr13a/IO66DmUv28o1lnXXWGfDO08ySdzxFehoBep9s0ME552S+yINPtdwBZNNcn6CD5Q0lzTGUxtF21iNgkXOCnM1TrhSPuw92SXaJ7it49+0bgsMQC/kTquZvE6m7++67l5/hd5GZcTU6ysPfcOOdE87999+/1FE2mIRPjthg2nRTd8UVV0zu6gjjM+7dtOm2jrE7lhC9aDVuTRrG9dnPfjaJNjXzPTO+DIYf4zz00EPLDzRyrvwwo4vW6jQT3OFtPiz2ZplnDoKd7I477pjcy5DXTAymIxR9yOesMfx77rlnsvvl+OTcv+HQztgZSwYk52n13dNy9EiW2vGmnSQiBhPPI5n0wWkdzj44FX/605/KNzcdmYnWDSd9ciRSaXPSH12/bE6m/u///u8Z1URBrGXRP7yuu+66yZxzRjh4tYE14WiLI1bz6qdjOT+SuNVWW5UfU6z5PnPOackll0wbb7xx2bXL6zYZlz8Wy8ncZ599kvVJn+DTcysd8u5PgHDyc54mZ7UOrMgsB59jVPPr53Oe85z0ghe8oPwpHXRS338M5Q477FD+ViGHbzDybs2415fzND7oSHPggnh/mwuOIVns6z7+n0kI+JLEm970prLxy3nafPl2LJn3pY/KhnnzS+ucbmuh5vfyOd6dpV4wG1VtGEMOkugSRb/ffvslO0k7RsrEgmeYeeDLLbdc+UFIwuRvGx1wwAHl2KYO6LLLLkuUEmWMrnxK2L0c0SiKRN54SdVR8sl56GXcdqnmYkJfxIfxYPxc4HXxup0hpuynTp2aOFg5T1MCzX7dvdCWcZCaZZ71l3NOaCgnA5MnT06OOQY6ijHnhx12WNpuu+3K33MTlaCQ0JXIhh+S5Kx5jzR4BEQ9HAkMJSLGkbaec87dK9ZLAAAQAElEQVTluMHOmlPgcnPz2NY9NQ5fO6favIpOtkZl6ohsbjg5Nlc1r5tPusemgcNEv5AZ/NJPvo3ZSsPaIquita1lHHJOm/aiN63lDCGdp30tJ//f+973EsPYxKK1rXeG1d8m3H777ZMNimMdd/qUSdYqnGx4vEcaHQiQGQ42vVo54hib8+ZmoZb59HdI/YaZ515TOEu9IjdK2ok0nHLKKcnZrV2QP1jqGzYMI2VjlyW8z8BSLtgWbbIDZEy9S5QNxTlx4sQSqWG05U+ZMiVRVu652InKG08JVgxOr86SnS9HCZ41MuO3WRzhtTNi6nFQ+/vdKHP35z//OTEUrXNhznPOJYrUWtbfu/m3g/cHQDlznCZGj3PWbOfypEilMTTz47l7BBhpqfsWM9bkiIhmiFAx5O7v5JwTR5a81dqcJfPaSZZsjrbddtuygapt6ic65J4s1rxuPjn5jvEYNBs1ETIyKfLiG5mtNODAIePstZZ5R4cz085BzzknmwGG0jjV7zZZZ46UbQhEY/3A7Mc+9rGy0aw0rHlG2Zowhpo/uj9nf+7IpA0HOauj5QjZLLSTMXXmnXfecj3Bc68pnKVekRsl7ThLBISz5JiMQ2N3hz1KiLPj/hKFIE9ibBluDlStKzplN8mIU65C4HvssUe5p0RpcL4oUO1r0rcdI6PfTIsvvnhyh6fWi8+UGCaLvN2RSBMfWIs6NB3ZZrnoD+NBWXSiZe4Yg2a7gZ797g/ny5GOsDUnyc662Q7/7qMwfFVumuXD8Yx3R4zkuClTnv1mznD0MbvQ8K01eLWLyhgjOeLse25Njq7de3KfB7at5d45IJJnTo2jfnWbyR0rUUt1msm3SPUhit3Mb33Gvz7aybs8945Etm0AW9t6V4esWzfeu02OBW0i/ekdP8fA6XIRvNnetYbNNtssiVDRic2yeJ51CNCB5l0UEReOTwUFbO4cT9vM/frXvy4/+qq8JnJSn3v5DGepF9RGURuCwokRPmbEPvCBD0znjrKiLJseOOVEmOwav/a1r6Wcp/0mjl0oGjnnZKcmQsUgumTsD0W6h1IjU7UD5e4yHXfccamZCC5ear3+Pt2dYJRHS+qP117LKHKRGjtXEYFKhzNr9y06UPMG+hRqdo/D5fCBDNFAtGq5u0kMg18pFzHi6HKeGdJax32Ar3/968mPWpKxqqhq+XB92sGTS/IomtBMvmTQTT/qjRZ58ncL2/E81DzreqeddkrmgpM7GHrk7uc//3kxJhxjm62B2lvrjqya8+GZU+QeW7M9HeM6ACdElLKW0St0iWhRzevvkxy658dJbspif226KXNn01WDb3/724lOEzmiK5s6y8V6jpR7YI4COVPd0I46I4+AzQF5pAf1xm6JePuCjW9HOl4WNeQQK5c4+wIBnntN4Sz1itwoaMfDZjwpEgqTQyOKVFlz+dWZu7N4XrX6FJ5vja222mrlWzfqihCJVFCaBJHx9jsVFKlPx3N2kDnPeIeGwvYL176S3ky+oYYe2gMl/Nkhj5bUyi/jLcqS84xjb63X37vLhRwSO/laT3TPBXsGj6Npd61Mf44kRAW8N5M7JI4LvvSlL5WLtxwbzqb5a9aTj+dmXn/P6FI42jiWMH8iO+RFO8c9dtj+DAjjbG7dE2F0lY+2xLiOFnmCWys+HE2pNX8w7wyDjZLIbqd2dAJHvc6jehwVl/1Fiskjp9g8VsOjTk0MklTfu/0kTzYB6Nc2ZEj0W9SQQaM7lJFVURvGzHtN+PnjH/+Y3M2ik9T3ezoctFrHJ2fHZtG68d5NsmYcWeqXQ+ZuFTzqGuQ4bbLJJuVbn+5Z2VjC2hc9uqEfdUYWAQ64b7g5Hem2J5v/Vqe+27a1XjhLFYkx9mnxMpq+/su4iQy0DoHzY2d06qmnJobO7+b4lood1fLLL1/+9IiIgTp+T8e5r/tJ7hlwlNC2M3aUR6E0la6+KBtt//KXv6Rm+tnPfpY4auqM7ZTKN4XgOBhl3Bwzo7bmmmuWC6TuGTECyu1u55tvvmT3yvmoiphxssPNeUbnzDef1l9//eSytuMC9X3j0Y9jNnljVCRHqvrpJumPjKDHCeI0oWE3zWnzDUhOrXIGReTQn38x/93QjzozIsC4SzPmdvdmDe62227JuuSEcz443u1a20T5YoY5U+7owg7cxslceneE9te//nWGL3qo6yI6OdDeezcJPfcnyTu55HCIJmnLQeKQi15y0KrTw6Ejf6JR6kmcFV/1Fsmki4xv7bXXTn5OgUyqI+mPfDpOG4wsuuNlkyc6ixdrTv8cNxsP1w9sOulMThyHd++9906D6QN/kUYOATLmUn7Vp7Unc2mz5EJ3zXMFgo71zd6a18vnHL00ijazHgH3VXxryS7JZ6cQo3tJvh7MuIlk+DtnogOEyig4NRSTozlf7bWLW2ONNRJ6vjIrX+jcN0yaikrb2T0xFvAYyjgXWWSRRPmaJ4bN5Vz0OCOUNqPpaE4EQD6MGSjGijGQJzEI7hVRAnbTLjOKELjULxKljsQQKicfOc/ocClvlzhCZMjxlXspfhrA3SWGTASEU/7Vr361OI6cMI6xYxyOdTt6kdcZAfd94Nq5Rv8lDPpKK62UXDwWwfE7Qmi2a0VmyIZIsfKccxKJ+v73v1/+TAxZc6n/D3/4Q1nv6tTEiSAXZLHmDfSZc06+4elbnyLSIkm1PSfPWnAB3P3JKtvkSx2Rp0pf5ABfjq1tBDhMHPRvfOMb5acCaj1rhnNDVw3GkfHtQT+T4jepHBW660nmrXfrkRO18sorl80kB49+5KzhvfYdn7MWAVdLyK2fzbHBq9xYH76MVPUsves4zh0mclfr9fI5WzhLvQx8rLehREQ8LGDK13u7MTGcHCP11Keccn7aiCrXXnktI3A55/ItGfkSGu3od5tHWTLkA9XnRLivYtdcFepAbQZTLkIjCld32/21zXkaBs06dpqicd201w6WcIehT3jLp+gZFDtjx5zyauIQMXAMQc3TjjLPedrcMXRo+qx1fNqVc2gYEO/dpJxzMUL4wy/DQxa0zTknz/K944NBYYS9t0vmsJu5btd2MHn6IFcDtXH0RGk6bhqo7mDL9c9pad3hdqJjnTbnjIyLEpLLTm2a+TlPmw9zL5mLnKfJRLOeZ/04enD/hrzVPPPrWbKuW2mIsoh8MkQ5t6etbbukT3KEN3qFvKhnnKLh5NouX15NfpIEftaWvJxz+VZaztP6hhlaTb7VU986dKfIe7cJT9YSmuSafEva5zwNX316r3VHg7zjJ9LTCNgQiszTo3TO0yXTnuhWkX33LNWdltv7v3P03jRaBgLdI8Ah4AQN1ILg25mKxjBEA9UfTLndsvtadpWeu2k7YcKEGRQ3w+YbOj67ad+pjm8MOvryzTaGpRnBcvfMxXrHn53ad8qHn2M6xqBTnZHOd8TSzVwPlQ99+IZef3Q4VAw/efLjnP3VHWwZB8AFZ0c06HfT3rz4GnM1zpWGSFE37QdTJ+ecRFE4i+ak27Y2E+6sOR7rts1A9US4ybO7jSJezWiYyJKIlPKB6DTLHfm5yD/UiEGTZi/PomJksZe2HdpEdpcI0HU2BJze1iYc3M9//vNJRLO1rJf3cJZ6QS3aDBoBoXURj4Eachoc+VDyOU/bWQ7Upttyi2eFFVZIyy67bAmxd9OO0XBUaYepPsXsMiha3ntNxulOhoumfkitlR7jAS93zLrtw5GpIz3HJ922GYl6Igt4HwnaTZr6gGMzr/XZvMHD3TpRlNbyobznnJNwv3l0XNMNLU6Sr6LXI0z8kbFOX43vhmZ/dcgDGXORub96tcwmwDfFODc1bzg+OUSO9W0C3AcSgWrS1Z+57JZPPycgIoZek86seOb4kcVZ0Xf0OfMQCGdp5mE9rnviDAh7DwQC5S5UT2kPVHew5Rw2BtOxSX9tHX+5C+IivEvYvglY67tk6lsYFHXN6/Wz7opEklppOHLwTRx1Wss6vbuLpk27XVanNiORj/du5nqofeuDXPVHh1EWyXAMJ4rTX91Bl/U1IK+OPgeK3Dh6mjRpUnLvjPPC6e5rntxNG+6IF7o1VWeMM1Lz+vu0RjjvHJf+6vVSJgrkzlR1FJs0yIxy9/ia+Z2eybnf1DG/nerMrHy8k8WZ1V/0M2sQCGdp1uA+7nplwNudK7cCwUnyd398iybn/iNL7mEwgpyXZnI04j5DK23Hei5Z+6p+f0bW7t9O2NfP3d9wmRAtxxNoc2AcK/rbWe36UVfqr0z5QCnnab9QPFC9Wk5pM4713advjPicHRNDaX76GxsHydfYXfCs89hffY6yr6g35cmzuW/XznGub31p16685nGuOW1+QoJzzLjiTSSF48SJJ/O+6eYeTm3X/CSzfq+rmdfNc87dyxH5sVa7oTvcdQbTt7lXv8mDCI/fd2rmxXMgMFwIhLM0XEgGnX4RoMic7fdXiTPjW3s552TX2KoMW9tyvhiPnXfeOTWTe0l28k/VLx/qulfC8DmKY7xKQZt/GAvHNu66+LZMrcJRchnVPRkGTVShlsXn0wjAhuP2dM7IPHFoB4roOFIiU+bN/bOBOOEEM7hNefLsiLO1rftQaHN2HJu2ljffOTq+HYZ2jZ5wllxC9c6JskakZrt4Hv0IkHfzO/o5DQ6HgkA4S0NBL9p2jYCdtJ0zA9Opka+uuyg5efLk8jtNOefy44ucHz9w5yJtsy2DvNZaayU7+2byO0+Oz5p1/RaVXwNW5psR2jJUviLv0ilHrVm/3bOv1TtC8dXtkbpj0q7fsZbHgWH0c+4/MjjUcTnO8Q03jnA7WpwRvxVmrvzRTc6VeiJ+vnbs5xf8/o+8mjhUvkrelCfP3/rWt2qV6Z++em6svmZe76xwqH0NnVM+vWKHB5sBl1Nd9ifzZLJD1cgexQjYmI3EseUoHvK4ZG30OEvjEv7xM2hRmJxzuaPRbtR+xM63zByX+PaOr1L71pp8RtHfJOPUuB/Srn1/eX6HA23HZoy4XzT3Y3wMmx+eszN0pNcfjXZlfn8odpQzIgNLDkx/kbsZW/T+5mI0R4nT246KOefMrLLKKslcc5L8Arpf8/Wjqxwm7wMdobWj7YKxaJOv14uYikiJQOWc02KLLZb62xS0oyfP19X9fatwmqAxNhLZM/e+1DA2OA4ue0UgnKVekYt2g0Ig55x8C8bfYbLjbza2M/NnWESWHGlQPBtttFHiNDnecOHU15gZIcav2XagZ8rMV5L92QTRJoaIkfMtM9+4c1fEDn8gOu3K0cp5ZKMn7fodzXnmh8Pkfs5I82nefFPR7wi1ypTfwuJc+3FDjpuokl/wJVuiTCKEZGrChAlFzgbDK+PoV805R5xvyY905pzLH1115y3n3uTCEfBgeIm6sxYBdyw5ue0iS7OWs+h9uBEIZ2m4EQ16HRHwDRbHbIxNs5Jv4IgoMXzyfTXfby35JV3vkntC/nxDN5d01a9JBUA33QAAEABJREFU5McRh18BzjmXXy72i7zrrbde+UXqWi8+hwcBUTxRRHM6PBT7p8LZ4SyJGjVrzj///OUeG0dGvoiNKKVjL+8SXsnaYHk1PlGpaiA58f5UkD8hgm6k8YGAaDQZopM44eNj1ON3lOEsjd+5n+kjp1Ds6h1hiBp1ywBHyZ/2EJnyLZhu20W9mYuAo1NzK2I3syIk7iO5D+cbbIMZraPYbbfdNi222GJd/+bWYOhH3dkfARs/cmQTJ8o5+494fI8wnKXxPf8zffR+vM8xxfHHH18ubw/EgCiUb6a5G8II+9XrgdoMptzfyhMlcCw3mHZRd0YEfIXeHxwVXakRlxlrjMybo1B/HsY3F88///yuOuHQuavmDxv7ZmSnnwXoilhLJX+0E11/hqGXu1At5OJ1lCLgW5aOef1CtKsDo5TNYGsYEQhnaRjBDFIDIyDi4A9kupzbjePjyMNX/t09uuuuu8q9p4F76b6Gb9jZHXb7o33dUx4/Nd0P8u0v93Zcxp/ZI3cnaY011kj33HNP8hX8gfpfYoklSj2XsE888cQkOjVQm27L/YCpe3l+vNSfNum2XdQbOwg49iXvP/7xj5M/VTR2OA9Oh4JAOEtDQS/a9oyAuyLhoPQM36hq6H6Qy9OcllnJGHkSfZyVPETfsz8C/kj1csstV/5m5Ow/2hhhRWCYnaVKNj4DgUAgEAgEAoFAIBCYPRAIZ2n2mMcYRSAQCAQCgcBwIxD0AoGnEAhn6Skg4iMQCAQCgUAgEAgEAoF2CISz1A6VyAsEAoGxhEDwGggEAoHAiCIQztKIwhvEA4FAIBAIBAKBQGCsIxDO0lifwbHEf/AaCAQCgUAgEAiMQQTCWRqDkxYsBwKBQCAQCAQCgcDMQ6CdszTzeo+eAoFAIBAIBAKBQCAQGOUIhLM0yico2AsEAoFAIBAYCgLRNhAYOgLhLA0dw6AQCAQCgUAgEAgEArMxAuEszcaTG0MLBMYSAsFrIBAIBAKjFYFwlkbrzARfgUAgEAgEAoFAIDAqEAhnaVRMw1hiIngNBAKBQCAQCATGFwLhLI2v+Y7RBgKBQCAQCAQCgUBFoMvPcJa6BCqqBQKBQCAQCAQCgcD4RCCcpfE57zHqQCAQCATGEgLBayAwSxEIZ2mWwh+dBwKBQCAQCAQCgcBoRyCcpdE+Q8FfIDCWEAheA4FAIBCYDREIZ2k2nNQYUiAQCAQCgUAgEAgMHwLhLA0flmOJUvAaCAQCgUAgEAgEAl0iEM5Sl0BFtUAgEAgEAoFAIBAYjQiMPE/hLI08xtFDIBAIBAKBQCAQCIxhBMJZGsOTF6wHAoFAIDCWEAheA4GxikA4S2N15oLvQCAQCAQCgUAgEJgpCISzNFNgjk4CgbGEQPAaCAQCgUAg0EQgnKUmGvEcCAQCgUAgEAgEAoFACwLhLLUAMpZeg9dAIBAIBAKBQCAQGHkEwlkaeYyjh0AgEAgEAoFAIBDoH4FRXRrO0qienmAuEAgEAoFAIBAIBGY1AuEszeoZiP4DgUAgEBhLCASvgcA4RGBEnaUHH3wwbbbZZuk73/lOuvfee0cE3ltvvTV95StfSR/96EfTRz7ykfTGN74xTZw4MX3iE59IiyyySHr00Ufb9oufAw88MG288cbpmGOOSZMmTSqfzco/+MEP0kknnZSMo5nf+nzeeeelz3/+82nZZZctPOj3wx/+cOEBHzfddFNpcsstt6Qtt9wyHXLIIemXv/xl6RMfpbDvn+uvvz5997vfTTfeeGN64okn+nKe+f/vf//7tMsuuzyzoJ+cRx55JO2///4Fj36qzZZFF110UfrsZz+bjj322Fk2vrvuuiutvvrqae21127Lg3JrhKx8+tOfTtddd13bejMj87HHHksnnHBCWUOXXXbZzOiy5z4mT56c9tprr0G1/89//pN+9rOfJWtxUA1ns8p33313+vnPf56+8Y1vjNjI6LB99tknrbHGGkPCmxx+6UtfSh//+MfTqquumh566KHC81ZbbZW+/OUvpzPPPLO8D/WfJ598Ml1wwQVppZVWSpdccskzyN1///2JTTj33HOTNUuOrNtnVBxChrH++Mc/TmzBYMjgZ5111kkbbLDBYJqNqrqPP/542m+//dIXvvCFdPPNNyfv1vef//zn9MADD/TM62233VZsLdvZM5G+hnP0pRH734BPO+20EaNfCX/wgx9M++67b9p2223TPPPMUxygww47LK2wwgrphhtuqNWmfxL6XXfdNV1++eVpzTXXLJPCaeIYTa/U9/D3v/89HXnkkcmC7+R09VVLDAyH7aCDDkoW8Bve8Ia0xRZbJDxY4Pfdd19xgP70pz+lV73qVel1r3td+sxnPpPWX3/9xGFDQ5pvvvnK4udgTp06VdYzEgVHQTyjoE0GJ+3SSy8tC5tDh8821QbMevjhh4sS6bX9gB08VeGee+5JjNlTr8PyQfnBYajEyMypp57aE5n//e9/6ZprrmnbliO74447Js71oYcemj71qU8lOLStPLjMnmozRBdeeGFHHq6++uo0HHj2xFxLox122CF97nOfa8nt//Wd73xn2mijjdIrX/nK/isOodR8M15DIDHiTfH43//+d0T6mTp1apERxu6UU07puGHtpnPrzvr43ve+V3Tl//3f/yUbZG3vuOOO9Otf/7q801HyhpI4dzZXneT7hS98YWITFltssWI7Lr744qF017atzf5f/vKXxBa0rdDIxO9VV12VOAOcrJHgp9HdiD+aw7PPPnt6cOJZz3pWWd82mS94wQt67p9zC6OeCTzVcESdpQkTJhSH5am+RuRj7rnnLn28+MUvfgZ9UZpXvOIVz8gHnt37t7/97fS85z0vLbroommBBRYo6YorrpihvkVKsXCsZihovHCOll566fSc5zynkTvtkWMz77zzpp133jmpN2nSpPT6178+velNbyr9ti7M97znPWmJJZZIRx99dGJIp1Hp7V+Lzq6LYRB5e+5zn9sTofPPPz/tscceQ1J63XTM0ZwyZUo3VbuuM3HixLTQQgt1Xb9TxYMPPrhE5zqV95f/7ne/u2NUjzEgc+Yo51x24W9961v7IzeiZS960YvShz70ofTyl7+8bT//+Mc/EgXdtjAyEydpu+22S5zK0QwHp+MDH/jAsLNoY0jXcbjpQ1GaOeecs+d+OEYMHXmkq+l0m00EOcoTJkwom124yxtKYpzf9773pQUXXHBAMvT0e9/73gHrjWQFusOmXEBg8cUXT7Oan6GOlUMkut7Olg+FNttXZWYodHp2lv76178Wo24nfNRRR6VJfU4Ao7Dbbrslzoh3YcHKXK3/rW99q2alww8/PGkjicIosHvnYKy88sqlTJ7ojoWtHqMtryYLkqGp783P17zmNckEHHHEEUn7nXbaqXitjhkoCzuFZz/72WWX6RPf+m/SeMlLXpLm7nPIzjjjjLIom2X1WR1Gpr43Py1yIX8RnhVXXLEUNesf2hdNaBofC5Yjxclpd/y3et9xTsXAjsu4fvWrXyURPDuN0kHfPz/96U/TAQccUHbRyi2svuyyI4KjUGfNo9gcVcn//ve/r9r0hLcf/ehHJXKnL5Ef/asrCY+rLIrIyAp1yuf0MBiem0mUTn2hZvmOnUR/fvvb35bI4NZbb53wfuedd6pWEmf1i1/8YpGHZZZZpkT7FPzhD39Iv/jFL9Lvfve7UrbpppvKLmn33XdPSy65ZPrqV79a3tv9Y6x4kLbZZpvpR5/kRJ4kLCxqKSooCmiMZFuZnZB+PItqwp+sepeWW265dt3OkEf5a+Oz1t97770TpY2GfmsD8vOb3/ymjNUaoSDxgkfHwOqLkJI1hmT55ZdPHDERVmWSuUaPTFC08mDoWIaz6p2T3c5R58RzGh2rwMKRsvlfZZVVkk2FY4xl+46i0ZD0rS9z+re//a0cEcgX2RHBUqatTYu59I4/soG2ul/72teSNWnsDJTorXpS8x3P3v/5z3+m448/XnGJ7orYbdB3NHHOOeeUPO3Rv/3228u7daYfCbYls++fb37zm0XmzYuyqp/6iqb/bwOlTDJu8+/IgLzge8MNN5xe14PotLo1yWsmulEZPjgcnhkPEW9zbL6Nz7NNgHIRbUc2q666apEL61qUgTzX+vqYPHny9HJ8y2tNItpowkwd40FHNAUO8MVbbWe9qV/TUkstlcwjGwBjR1a1rnWvHj4Y95pfP23IlEvsBufH0Yt5MJ/k+4c//GGtXj5tgszjlClTurrmgbZEf9E3nskfOfVuzVmLhXjfP8oZ2uOOO67vLZVoKz1JRktGyz/WkTZk1Zy0FJdTDLJPNtRzHaO1jsgKHQ8ja8RRH3rmoDU6PbFvI+h6BXonnnhiIcVZdfqAPlksmX3/1Ln92Mc+Vo7Z+7Ke8b82zWRNqfSvf/2r6FInOK6syDP35oM8atPUU66JvP/970+StaA+zDnOZNzRr6igdjVde+21qs2Q6CCbs0022aQcvZKLWt8nOT3rrLOKjrP+5JG7erVFIEKe/pr2ZIZOBvHSs7MEKAtTSJJAGQhlSeHz9i1eChkvFrvwovNHi0K4kIA7dmBsTC7wOSSEQ9THoAFh0VJwJsXkm0ChXXS7SRwVBn7PPfcsd5LsVBh2DlDOeToJC4ZSbj2rFo2x02D4Td70BoN4cAeJE2Rn1Gy2/fbbFwM9derUZnY5qqNYW3mh9GHCSBMETiphFLny3iRCeDld8KS0OYbKCR48PQs5w4JxZgDNBewZfuWSiBslwEmxIDmg5kQdmMKNAWWkLfA55pgj4dFCYaTJBaWAF30w7haf4xD9EXhzy2BSVquttlrCu+NU/UtkBj3ywgESdXOMymiQI7TWX3/9RIbIICfcXFKyjHQ1lGjVhEeO4Mknn1zu1KEJc+/kkHHk+FGeeOS8c+zQZBBELPXlOJUyo9jQ5ojjn7GHkzmS3ylRBkv3RSXxbl70jTeOrk9jISd//OMfk3VDDuVTSNYXPvBlnJQEDBdeeOFynFfxwaM5si4ZLY6OcZlDtDib6sLAOwPdTrmcfvrpJUK2+eabp+c///nFuWXUYG8OzQmFivaiiy5a7udxhDlL+GVsRV0YG8aEAjV2c08OYWRM+KBM8cJAkBc4MQraqPeTn/wkqWMtoGfu6BkGHk/ow57hFtkwHtiZOwZFPbqA3MKdjMLa+oC3zQddw9l2L0Ud/TYTRwIfxoaedcSpMAewNZZmfWMwVnL86le/OsGsWQ5Xc/XmN7+5HMeTI5s9EWlzoowcMqgcXevHhop84xltBpSuhZWxWHPWP0NlftynJJuc42bf+BXBQdO6pTdgwIHmuHG+tZdHL1kfxu+TbFr31ga9bb3AmYHXB/44PubH5pYzJ78m80fHmG/Y2MTBxtj1D89///vfyYa7tvFp/dlI2eTSQ/L6S9Ymh44+d2eUA+a4a/755y93TelXzgQacDNW9oxDTc44So7I211HgKAIPxYAABAASURBVPFrX/vaBL+3v/3tab311kNmejIX9Ke5Y+9sLoyZDqqVjBtm7AF5sulhp8iBdmxIrevTOrHpr5tmbdhGuprughlerQH44408W091vaEj2Yyy5zAyf+TNJpneMGbrdq211irHkBwvttx4BAOsIX2ZD46ldUaW2WtyKpEvtsVa8szJI8/WKJ2OPj6aCX0bV7yjbd7ICHkUnEDLOqJf6CDyaFz0G91AZtHFN93YpN3L8xy9NKptOEnAwSBHQqjLguIcMKoUqroMnQgUoXSOjXECTjgoGs4MD5Di5+Ez0I6qtCWoHAHKXF8ArnSVD5QIuYWMH3xYjASIAm22BTDHjzKhgJplnvFMGD0PNqHHUcJHbUt5G7udYc1r/aS8mnkWIKdDHkWCrkVIYCiBJn112iVCrC1+0LcQKDMXoPFjocOqXVt5L33pSxPjTGjVR0vYlJL0XJUNATefcLbgX/ayl6Wcc2LILKbantK2A845I982iWhVRUQ5qjRp0qRy4ZOxxc9cc81V6MOEwyEKQjHj913vepcmMyTyZpdj4XGsyKUKlD/ljHdjgRf+lXWTRHwoO9HMXuSFjFMKlJD+OI/GY4dNseNJvmTO7awZG2uQM8LoczCsRfIAJ/NC6ZBh7UScjFFUyLs1wsFxf8+7Y0B36zx3Sta+XTnHjDFXz9itcXJhzcojT/I5lJ/85CfLUXV13LWjZK1xhkt9Mk551nXxjne8IxmD+SdD6kgUtE/JHJNhRkD/2uvDeOVZM2SATmEAtJEY4kX7nDrrx3g5CBQ0PukBkUeySTHbNGnTTMrJG0fKOmqWtXv++te/ntAxFxy21jrmC690I3rmVn2bBXIBI3LJsBkvnKuTjhYdy2mgW9xRNC7zYJ3bVDCa5BymOc+43jg61iaaDI15s4bMA0cLpuZAPxIdDBcGHHbmAM/KWhPs0ck5FyebbmjWId9wlueUwHo2Xu/9JXpcPcbdPPRXVxl9YAzw5VzL41TTKe5vcTLkSdZ9zjk5BTBX+iKrylqTvjmCsIaf8re85S0+pidyR9Y4X+aYM2tubVhrJTLLAahyDl9OEttkzq3/WrfdJ/mhH+BhPugftph9tZHFmw0cOweLJg06gq72Sf+bVzadYwwfG2N00CZn5oh84Auf6sOIg8cZtnGgS+kJbegK2NvY6pcjY61aC6JKOc8oj+qw1+p5luhr42Hz6ARyaf7oPhjxEUQb4UevGydZJ8v6QmMoaUjOEiYwZxdsodj1UNYWucVk8joxp4xy583XxElqrZ9zToSs1uGVA6G1XrfvBNvEMhC1DePCYNqZ4aHp7dc6BBnP9X0wnxwTgsc7ru0YJ4IpfCi/qfRqnbn7jv/qc+sn58BuBhZ2DBZ3c0yt9Tu955zThAkTEsVfMbar6FSfYNrJmF87I45Su7r4E320Q0Tb+C3knHMxGAxo7Y8jUJ2DVlpwsfBEKFyWZ8ha6zTfGQNtKDi4Nsuaz5SshUpx2THiVzkF06rM5Xeb6i6b4+Fot9t2tR7nUcSjziVFlHMujmCtUz9hxrHheMJHhIhylSimnHP55iSFR6mRldq2+Wm85oeRbOYP9tlc65v8dHN/wq5Y5JECJAuieoPtU33KnV4wl6ImdpPWqp0th2yHHXYoX7xQt5k4B5RtzWMYPeecfQyYbBDMF0PQjTK2EaRrGADz1tpBzjnRqeZBFJGBEyniTGpH18pjCBh764tjXelwNMgxXcZpUj/nXO5l0m0wlkQX5pprrtqsfMKLEVReUyno8A9DyfCt1RdtIHeMJ3nsUL3fbDrZBqpWoltajXkta34yspwcOsHGu1nW7tl6ZHOshylTppQ7pGQHXnRxuzbd5MEu55zIQcWObAzUln5iVzrV49yLXNJp9Ao92Klup/ycc8KfNVl5syngTKXGf64+iNqKjHLObahqcVMuzDd7UctaP3POSXRZVFV/+BfpbK0nkq4fNoFTxCa31ml9p6dEtTjnbIbynHOi6/SjP4lNJVPWtzrDleYYKiGCyoMEIE+P08RhGmjhUJSMLi8fDyIbFITnZrJ7Fv63+5BPkdjJeR5sYoR45zxPxrS2R9+xj10yZ4ln7LhCHUqJotKumwVcaTY/TS46hF6+HYjw5uTJkxNeGGhKm3JXbidIwIXjvbdLjheFHRl6C5NXX+k36xMwyoAD28yvzwyEcTqLxgdnyHFELW9+UmjmFv8cWDzDtFmn+cxIceSE5I0NhnBmWIROOQSMNMWFtrbyzDUD6t24hG85jgyfXY78TolzISpg/tBmzMiVnR0sajsOsR24qJVFpZ4yRoB82YF5F5YWufEsUc6SZxEkc2WXz1m1u9QOn/iHp3qDSZSUzUftwyfHo1W5VZqMlDmBLVwla4nBUcdOT5lIU11r8psJtgwfRSP/yiuvTOTF5sc45DWT+SBTlH0z3zqy7o1fv63lzbqeheLJ3rrrrptEFhg/+YNN5tfY6CJ3asiQuRH+Z8A463V+m7RFO8iaaLN8xxp+fkT0xvtAiWPIoJFRUazW+mS8mac+48yhgWGzrD6bK3PNIbKThgsejUkd/dBHjD4D31wPnAGywmnlOKkvuoQe4+SdERH1pD+812T3bx6sbXl0i89OSb90l+Nf0Tu8ttbltLbmtXs3FuvGUaJy82lj5Lm/5DiH3SG76pFbuoSj6L015ZyLg0QXk1VrZ+LEiclYXWVord/tu82wCLcocG1D9upz/aSPyIB3x1jmSITXe7tkDXEoOCjkuBmFatY3buuxmVefyYTI3vrrr1+zyk/X0FvTM/oe6GmOiPVjTul34+K8c6LYhb5qiS6sY/DeTOyjiBr9WevbxNGPzXqe0WEL6CVrwRqS318S2bOu4UzPiybZGLNDrqNoa23Qf2SK7rQpJg/y1aFz1OslDdlZImwUgIULLJNKWRI+jBJEzPq0o7LAOEna+EqgBcoTZGgoNGetFLTjPEBYDHbpviKqHg9SKLN1sBSeC4UmAA3nzeoAldcqzEz4hLIpFLtxxpNzZ0J5uAyMZHK1zzknyhxfnDuCZ3z4rsKgj5osAGFUfFPQjLAynrXx4tE7Qw0vIUoCaXchSmOXyMAQCEIqX/2aGDNGzDkvQVCfgXCm7Z4BmrWuT7sJfTL4nDOKWESHcqMsnY/DxPk5BwktjhcDoH1N5sCY4MqAUk6cD7sHQomOS4kUs3sFlJ22HClHPRKnDj8cUTTIAZ452OZbn8LgjkHIC1pomD/zbgx2ODnnRIFoZ8ctNEw2yBQa+FCPk+3I1t0ERwgiDk18yBB80ba4hKAtQjxqDxNl+nrb296WzL9x2d0ZC17t7EVGyLv5s0NSJuLnfop+8eXduCkIRyHGVRMlRh7szh0taWMOREr0L3JnztAnf0LN1kptDycRFUon55y04WRTxOpYc+RSPnkj93ikeBlNijDnnMylMapn84Mm5YI+OjVxRMkSo6S9cTHsyuFh/tCw2zNec19lUCQPFuRbKJ3scwTIAbknF/DkODM2dsDkkyKHJyzJP/m1vuBOMRsL+dQvRc/Q2qCIrJBp9R17oEsP+eSQCtHDHW1tyaQdK8fCmtcf2YaRaARdZZw1kS18kj/jtTmAr/VhvhipWtcnvWEuyJm1C2dOvbKayLt29CddZF7JH/2kDhnnQFl/jiIYNXxaM8qNeckll0w2ft5tuqwJDoIxwtimCp+cQ4YGT6JNZMUGTj2yxgmX6E5z4CjVBkB/1gIZML8SJ5/+5QjiCaYcZ8aXY8UQw4S8cIrIAP4k46FbHPXomyE3Dxw76wCP1qN5UF/i1Fmb1iv9zsllJ+gJjhA6ntVtJjzB0KaCvSLnsGXkOTNklN7ioDDGxk1GrQXYwZMOIPPGD3f1yKqjff1K5q3Zr2fHbsaknKMHWzwok0THOJhknC5QnxNJVxkLOVOvJuuH3FkDytlbTpNL5NaXsbp3x0bTl/qVOA7krNLxyZ5Ze+aSjbRujM9a4tBZP9pa+9YPHURvGTd5YHfhQz9YzyKZ6pMt9WFkfHjTH+caz3Sbtc/mGjNaxm+DLdJsTPqCt/knG5U2H8H46R0nNfpzjE/3kQe86U9Ujk7UzprRfy9pyM6SRW0hWPwYAILb555524ywZECA81zrm0DvEkGwyD1L6jNg6ABBnkTI5LUmk0sBqsOgoKWOSRQWZBDxJs/itNsCvsVtQePFoqvvJo4xtTAInUWlLQNMeAiy92aibPRfkx17LXdfgVMmgsOQM976Uu4dL5QRpUxIYFfHr45EENB29qxcyNS7hcxpUaeZKA+eNKFxP0NdbSl9zxID73iGkvCunOJo0iFodsnqMN61vXdKUf8Ve0KtvXE05w1tODtGQIMAy7PQHRHpz2JrvsuTRH/sKtTnMPqsSX10yYU8uMK91tMOjyJGaNUkelB5ZvCM23jMK2OGlgRjbey8KQpz4J1Dw9hpZ2EbA0VKbrUTaWI8lXNEal+UkfY1iQKoL9kIyHfR0rvE+ZbHmHgnJ+ZMnkTxUwgccu9kiCNRZYecaCcx1vAi094lmGsnUdTyOBecOk6y/Gbi7FBoZMD41RehUYez5V3ihChHx7vEINd3OoChczSlzCcaniXvxuUZv8bkWSLX5tQzXqxdF3K9o289cZbMkTztrV9YeZcYY/0xlN4lcwc3htk7J48DwKHxbp61qYkBkW+erQ/1RSsqr/CodX0qUx8/NhXq411ZM9EjZEYe3QMLa9A7/hhydLQnF+hxkpSLjJNRzoB3yXogj9qQQ7pS8i7pTz1HMd4lThMHyLPk3acEBxtBn95r4iAwiHX9NNtbj6LL6rIDrbJFpyqTOFV0I2eRvMuTmrLK7pBljgDevavDjthoMvhoKGsmNK0zsiifU2nDYlNg7XPO0JHoep8SGfcpmY/mu3GixTFRLtlwyWtN1q5yqbWMvaG/lHHSbQZshL3TI631bf6U0310vHqSZ+vAMztG19W1IM9aIUeVnsgOeVFWk02HUxx1qjwr41DRMeSI/FmjNhfKzJUNhy930ZXy6GY4shHe8YambxV7Z5+sZfTMS7VT+qdz1ZHYbp/NxLkm7+bbszKOuM2FPsiAPGsTRuRSfq9pyM5Srx3PzHaUlsVqQerX0ZMIEc+ccZfXLhE0Cw7o1ROnvHjPnLCn2wz8xJk0WXZZdirtWoj2ULwWX53wdvXGQp7F6JIpZ6MmkaBWp2UsjCV4DAQCgRkRYNgZybq2fXJc6NYZa878Nw4RfSvCNfN7b9+jzYEoqQ2EiFj7WrMml5MoUmcOa+KIcmhmDUejs9dx4Sy1g54HbKfCS25XLk/Yzq6r6RhRCHUXr85gkgXM6xamb9cOT0L7FrkweLs6YyXPzlHExs6iJhFHu6GxMobgMxAIBNojIPrJAahr26djqPa1Z26uaBE9PXN77b83kSxRDpjVKGH/LWZeqWMrEUpzWNOaa65Z7tPOPC5Gf0/j1lkyNY7d7JA8t0uiSo5W2pX1msdq0pKXAAAQAElEQVSLF9Fq1x4/jqjalY3FPLtMx501iTaNxXEEz4FAIDAjAjZzdV3XzxlrxFsTAXodTjbebECzbDQ8s4P4q8n7aOBrNPEwrp2l0TQRwUsgEAgEAoNEIKoHAoHATEIgnKWZBHR0EwgEAoFAIBAIBAJjE4FwlsbmvAXXYwmB4DUQCAQCgUBgTCMQztKYnr5gPhAIBAKBQCAQCARGGoFwlp5GOJ4CgUAgEAgEAoFAIBB4BgLhLD0DksgIBAKBQCAQCATGOgLB/3AiEM7ScKIZtAKBQCAQCAQCgUBgtkMgnKXZbkpjQIFAIDCWEAheA4FAYPQjEM7S6J+j4DAQCAQCgUAgEAgEZiEC4SzNQvCj67GEQPAaCAQCgUAgMF4RCGdpvM58jDsQCAQCgUAgEAgEukJgtnOWuhn1fffdl2688cb0xBNPdFN9WOvo8+abb054aEf42muvTffee2+7opL36KOPFt4feeSR8h7/zIjA1KlT0wMPPDBj5gBv99xzT7rlllvSk08+OUDNkS/Gw2233ZakwfT28MMPpyuuuCI99NBDg2n2jLq99v8MQiOccf3115fxXnfddenxxx8f4d56J//YY4+V9TrUeemdg9mvJd139dVXpwcffHBQg7v77rvTDTfcMOrkhb6itwYaDDkn78Y/UN3BlN91110Fl8G0gWM7HWVOlJH7Vnq33377oPVak4Y5b77P7Odx5yxxUv70pz+lddZZJ91///0zG+901llnpdVXXz2dcMIJbfs+4IAD0pVXXtm2TOYOO+yQ1l577TSrBQcvoy39+9//Tl/84hfT2Wef3TVrFMXvf//7tPHGG6d2C7xrQsNUEQ9nnnlmOuOMMwblvFFcO+2005CUkSHoX9/klOMkb7SlSy65JP3jH/9I1sJ3v/vd9L///W+0sVj4gd+JJ56YVl111XTRRReVvPhn6AjY3Oy3337FCR0MNXNw5JFHpuF2NgbDQ2tdDtw222yTll9++dai+j79c9ttt03k/ZprrpmeN9QHG/ff/e536Yc//OGgSB1xxBGJnmo2smHbeuutC4/0UbPs0ksvTT/60Y/SFlts0czu6pmONt/bbbddV/VHqtIcI0V4tNKdY4450vOf//yUc54lLD7vec9Lz3nOczr2bTG8853v7Fj+ohe9aJbx3pGpYS64+OKL04UXXjgoZwELc801l4+u0pQpU5LoBHmYc845u2ozUpVEhM4555wyXrLxiU98In3yk58c1DzPN998aYMNNkivfe1rB80mZ6PZv76XXXbZQfU/6E57bGAXvueee6aPfvSjacMNN0w//vGP09xzz90jtZFvNtB6b8fBeeedlxiXdmWzMq8XQzcS/L785S9Pa621VlpwwQUHRX6ppZZKkydPLvp/UA1HsPKznvWsRP/kPLA9Gox+65blZz/72YmM5jxw/02aNgD0VDMv51ywzXkaLRsvDpXTkuc+97mln2b9bp9tgunqn/70p902GZF6485ZesELXpAWWWSRREhHBNEBiC6wwAKJYRugWsfiJZdcsl9nq2PDMVIg2rfXXnul888/vzgPg2Gbge+mvjAxxX/nnXcmCujNb37zLJMHu7F999237NJEIrrhfzjrOB7aZ599SsRzOOmOFC2RYYrTvOnjAx/4QHrVq17lcdamNr3nnItBf8UrXtGmtH2WXfSuu+6aLr/88vYVZlGuzcWWW245i3qffbu1+X3DG96QOBMDjdIGYaA6gy1/2cteVmR0OOyhMbCtnD98iADSs6Jn7J4kfzDpggsuKJHjz33uc+mFL3zhYJoOe905eqVoUX/zm98sHv6vfvWrxIg7ykDP7u+f//xn4nma4F//+tflyEvIz6C//vWvp09/+tNJWNHuUDTll7/8ZeL5r7vuusnOUfmb3vSmBGg0O6Xddtstvfe9703vec97yhEEL3bixInpz3/+c4kcLLroouljH/tYEq257LLLnkHm85//fNnF281tvvnmafHFF09/+ctfSj1KGb8f+chH0hprrNFv2FfY8bOf/Wx6xzveUUKNm266aXr3u99d+nZkBpsPfvCD6fjjjy+0YbHSSislvFJC7jI5tzaO4447rhwJnXTSSYkx0M7Rm/NgjRlYYclPfepTaZlllkn//e9/ZXdMPHzHfpyJD3/4w+lb3/pWOaM2h/qHz2KLLZYoRCFq47dzW2+99Qp/P/jBD5K6HTvoK8CbcaBlPmDpjP2mm25K5EO++WUIGDw4WFgco+WWWy69//3vT+qae2P7+9//Xo4bTz/99PTlL385feUrXylYGodjoq9+9avlHQaOjPTVx8aA/5MnC5gz9p3vfKcc52iEJ3M2sU92yOOtt94qOx1zzDGlnw996EPpb3/724B3gu64447029/+tsyLMcEBbfLFKfO+wgorpLe//e1p6tSp6eCDD0677757Eoo3JjK35pprpn/961/JPMu3XqyPpZdeOk2ePDntv//+iVy+7W1vS2REPQ4PpetOw7HHHpvIVsUcztYjmXvXu95VxqOtMR500EFlvQmf6197x8Qw4rx5tybRssbt8owHLgsvvHCy/qxVY4VtAa3DP5zT73//+8kO0c4UPeuCbOn/fe97X1prrbXKWhPtOvDAAwuv1gBdgZ9f/OIX6dRTTy0RJfxy9mAkGjaxb+7UMwd//OMf04orrliOwKwd9P76178WetaMNcYxdwQrOqVf7ckEPJU56qvj3nnnncuo4PHzn/+80FliiSXSf/7zn5I/0D/miS60Bsm3NUlnmFd94Mnc77LLLslRkaMRfH/mM59JdNhRRx2VNtpoo2T+rF9zR3daO9ZExYqcGqd1bJ7MO/qwtuboZvOpXwm266+/ftHPncbgWHuTTTYpdym/9KUvFf6sR+3R1t/2229fbAAZJXuipeSNLMP4a1/7WtHTm222WbkzREa1/cY3vlHkzx1Sx8jaqo+OvoybjrZezj333KIXyZ7xuK5ApvABv7333juRZ2P83ve+l+gGcwgfhtu4ybZxeocfHqpegplIyMorr5zopTpfRx99dCJ72rVLdI9xwZIMGauxX3311cnade0DTXqRfkODjFoL+t9jjz0KJvIHSmSTniJH5I8MWQN0Flp4sEbce+VoWAPkhhzBjK7UB7zho9xcGB8stWcL8I4/sgdf64HcmfeTTz45kTNrFi1jMU723lqEh3z2kP62puAqT78/+9nPiiyYD3mdEp6cMsw999zpJS95SanmCBJfxgrL0047rehk8yWPrXRcZ33hC/by2XV6oxDp8Z85emxXdv4Y55xMmjQpAYBQAYrAMv6UggFRMJSscrv6hRZaKBFsjoHwPyeG8qc4tTVpyueff/6ERn88WlB/+MMfijHlpdvFEVzCQ5FRbIy/kC1AW2kxyvXogkNUz47xQOgJxSqrrJKm9hk2i7m1fX0XGsYz4dKX/tESRXrlK19ZHCcGCD1tOCboOSsm1ITbolEmMa4mmvJkkGBBeJRZIISH0YTlQM6SOx6cFIYanhYt4ecwEHIKlWPqvhQBI+DaUBaUoDxzqO9OCV1KiaK3iIR2yYIxTpgwoShYDoA5MMcEl0DbQRNuhtc5OMXI8FF2HF4KnoxxmJSrR5Z+8pOfFJqUEFwH4u8pvsuis+g5LuTEwlN21VVXpbe+9a3JPRh8ufBNGf/mN79JkydPTowS/PCtfqfEaRH1OPTQQxNaFDtsjAMe6JpPMrXaaquliX0GnoFYddVVE6wYdZigz/nQjuxRAtaSexfKOQXyrCnzQxlV+SBzeDUXjAg51B/eOcDWy2te85rEATAu65fR0j/aeNC/pA5DhRYlTUYPO+ywdMoppyguTjcZQc+YS2aHfxg7x0ucIwYRPTJDHsi7NWAN4h32DN3kyZMTw0B2ONOciCX7oqvWNH7hY1xf+MIXknHgFz04MVgcV3KEN+sEvUUXXTShwznhCKjLCBhbHT8HllNu3OTEFyvga+7MIzqcUFhySjoMeXq2MaPFeaAnyDRjzUCjRUfYfJonOoLewjcnxTy//vWvL5sHRs/zi1/84mQTx+DgS3QSHRhwwGGtH+OTb83Dlq6RrH2GEn16nAxNZ7bl4f/+7//KPRQRA+P3CTtyYkx0GINtPq1LeJhnPMCT40SXqUduzDN8zQHHWXdkndFmTMkb+WbY1d9qq63KOrGO0EaX/tKOnDgtoFfoANhYC6IQ9KOoo+gJfeZoXxvJuLXDv03ejjvumOgXcmhsbAeZ4Tx4Nv/atUs2isrx/O1vf7vYCvPNqaBXrHkyTbe5wwarDfqOzOkb/cNXXjvarXl0P3kwx9YB+dYH+0DubcQ4GDDmQFszdDE7AldrhaNtLsiOccOMzptnnnnK5pH8uapCtif26Sc2Bg3OFb5d1OZs4k0/NpEcJf2rz1lVRk8LUlg/bD05hS1djm82EHbqtkscQ/NmDl1PUMe7TaGxkStlNj7mmpyzHfQC2dQ/+ZDPsbQpMi/o9JJ6dpZMGIMDBJNN8HLOxcuzEE2eRcUrXLpvR0zATSRj98Y3vrGc04rCUObaA5XTQgmIfmjLIehmUOhZ8BYQgE2m9niz2OxOCIL7Kd3QU8dEMHoTJkxIFBnvmPOgrL9EgC0Swo9/wkp4CSihrG0pdwvaePFMabp0XsspCg6MNnBh1GGsnDGEEQGS15/AqU9gXvrSl6ZXv/rVxVkgPATOHFKmFp5y+Mw777wl0sYTl4Rn9YFOf4mDVfFhRDhhwrLGYc61tWMxVwwFI41/RoqDq646rYmCIWeve93ryh0awi5RgOpanPCDs/deE0UCU+OFA+VHeZNRcoAHBpri6K8PeBqv8fhkmMkSh8X9AGvAvMMKDpzyJj0YiR7I44AbvygQWSaH5p7hwxP5Us+8cijw7Z3cqMvBsBFhoM2vHTTFQmFaDzlPu1ugTU36xkN9Z1gX6Ds69i5Saj1wQoxDngv1/c2fOjXB1zjwgWf0jId80RF4wrv6DBT5M066gZKGn7Jmgi0a5AHedtWw0Ae+lalvUyYPPTKz1lprJWvAPMhnuIxDXYkTR0Y900/kmbLnuKKLDmeDXqi4q9spib7lnEtEkWzQVYwFuUPLps8GobU9nMyz9aUMBuSGAaZnzJX1bX2gY0wMoXfl1qJ82HO+yDEHwNo319YgXYl2t0lb/aBT21gnNmScJPItnzMHOzt7Rs045Ev0pA02GSWr+CJLsEXXhtNY8c2GGIN2ntGttMyZ8XPSbMTZnbe85S3lSx4icyIkZJ8siX6iwcBbA+bdO97hZOOhP2Ozeck5J7KpTn/JJl0bmzbOHkdDfY6rtWv8ZLuOwfoh3x//+MdVK3JYMSsZ/fxDnvELGwEGeg8WeCD7mtb5tO7haUzoq6ecPSJ/8GB/6DRyoIytoU+te++cJE4mzDi+5oUuo5uUGwsHyHziyRpEU1lryjmXoAGZV0dApTpdrXW9K+d4qUsvy7MezJ31i0/jI3P0BnzhZ/xC/AAAEABJREFUbd7pAz5HzYe1CGqlg9ZgU8/OUqeOKBSGn2fnkyIxeZLnTu1myB/kCwNPOditUBAmDAkLiBDz9oGa8zONg3rtkkVip0LJ1US5tKvbzLMwKDMeOw+dcbDrs6irQDbrd3rWP4XYqXww+QTe4iB8zXbwoajgw4nJuXt8mnQ8W4ycVM/NxBmgxGqecVVlUvMG82kM6NVFRqYoisFg221/Fil5rvPvkzLur70dOuVR68DeeBnImufTfKBt8Xsf7sRw2emLjFkb6DuCoGhFkShdeQMlc8oA1Hrmz1qu70P95JTCuZWOOc05l+N6uEvWUGs9yo8hVi5xfry31kOPwVKnptY6zXf1bXCaeZ7JOQVcaTDsMFHWTbKDp8jRZ/jppUrLrriVBqwZes6bSBd9RtZFycgU2VIHD5WOT5E+xtH69i6hL6+1j6G+c0gce4oY2AR2I9PqilKp65oGh6cXPhh3USKOJj0rYmHMogqcRnki19Zbpc/I0iMiijUPhoxtfR/Mp+CAjZRoIAepOhKdaJB5/Q9Vv3NgyJKNAGdapIgjSbY69S1f/5wcz60J7xxwES9RcQ6V9U/ebJRa64uy0hE+W8uG+m5tk1fRNDyjZ1PDwRaNF2l3MmQNtMo/XUGv0H1kX2Kb5aHTS+rZWQIQAWS0eLfeDYixsCMTFuPZ8UoJpZ0ow8lTVEc0RITAs0mnmBgZoAPHs+hMLe9vcDnnxDERBuT9UhTq55zLvSULUdI/IcErPvTJ2OLbDlWyuPBuXJQUAyNfclyFbn+J8FIABIxSNUEiWyaecjMeoWR8GL96eMGbcKrxe+ZkqeM+gL5Ff5zPiqCpDyNt0UJTXie+8AFjQoaWHRTv3ILleOhHeFMonOKDj/Gjax7MM6zU79QHIwU7c6APZ9fmz24RnnbR8jmSDAx6nIXaP/6NyXjg5NlOTXntX33Ycuwc/Yia4BvmdjxN/MxpJ17tgMw7Z9ixDV7g4xMW+iPTojp41pdP904OOeSQTmRLPmMhfA9jbfAPm5ynOaIUkHyYiCTihfEz5+QLHxLsyQd+YKKcDFP05sfcqydRuvLgI9+GAf7uiqFP8eE751yOzeBGjtDUR+2f4kFP0r85cezjaBFNfJsXIW19GrDxwcp6hp+28jslGyjRNwaGsjMPdoP640igp63dMKwYVP06ghGlND58qac/UQ5HG9aYetaI8RoXniqflKVjL3KvnqOBKuPkHhbwxR8sORbC+Y4c1ed45pzL3UfHdXixIXTUhSc8t0vwF9k4/vjjy0VV68NOnhyL8JpzelIfG/QdzcDDfJh3RzdoMl7WjT7dAxGtcWWBIVNuE8dYOopCh65wnCTy5Wi9YmM8sIeNBHNzR971h1anxOknX/oRcdUGZrDDszLrT0ITPTIGY/NU+zInnm3U0KAf6W5zqg2dob62aJI3+JIrtMyn9mSFbuIo2CTjD5awgzVdRJdaYwyu9sasT3U4a9YIWYGruXcsrm+8wNvYjFHSdyds6Ha6kUOBDh7pFjT0h6ZxSNYyeRAd5iSaLzIrX6SoUx/y9ZNzLvfktKOX6CgyBnPjI5OeYSMKCm/9VgzV4XBzfERg8OzYUqTLxirnnKxvNls7tpyD4t5SjcQZj3UCFxsQGzBt2V5jadLCNyefToSnBB9zbQ49+1SvNZlTtPFR9bm5pcvoe3Nr7Pgyj3QEXMy96BnZoru0kW8DST5b++n2vWdnCQC8egNiGAyeAFAeFBhwAWQBG4zLmwYp3Aowk2migA5whohBFS4zURY8JUFwTcJAA3LcwauWal2hOgLGMBEAHqg+CJPoEyHRNwVEubhjYmfiXoewIgXJQ5UvCc1W2p0+7TzreBl9hsARmsnVRnhTJMyiMn7GXplP58rOhQkQB4BzQzHoWx6lCGvOAmE4/PDDE1oWpMWJfrtkYZgPCwctgmP8jhAsXHkcQ9EGBsyC4oETeobI7hevVWDb9eEYxRk3uUDP7p5ScqeI0mb45Ds3ZijQk4++OdGHfilJzgWDZf7JhTK4WVRw8XsdaHB05Jtnu3T4kR/zS8ba8SkPZpx3DoBn2MLBkS2ZED0ydsrWXQtzhXeGwvyg0Skpd/HYAtXGHRTzVuuTR/mUgHrWj2MhY3MUwFk1Rk4RHrybF/IhWslQwogBxLPdsL6sJ1jDSxuG1DrSF4zNp50vutYWRcIYCWGbO+uQrGpL5skKmowKx4GsoQVr/Jk/jjAMzS2FSokOtFatCcaV02AjZa2ZK4qXg6QfWHHwrT9yrl/GzrGd/qwXRt+4HLm4gybyop76dseMF55gg56jOc4jnaQe+ec0GqddKTniTHDkGRz4uVdFJtRnYHLO5fdwlHFC1Cc/ZFEf7RJeRDiUmT/YuTtk3t2JhC3lrg8OHcOOV/NgTWpHz3JaHV94xyMjSRa8w8r65oCiYx5gRIeJIlZsyApcGJicc+JokDHyTu7R6pTIq/XKsbNerEn6gBzYvZsDtOBFnq0Zetd42QZ9kQ0yDmuOAV4ZOPYCX8rNmboiQ/QyHOg8sg4bY+GE0BH0Bv1t/jiwxkDX2izDHX3trXVrxrjpQusC9nQRGTKX5NA8KjPXZNrasEZyzv3+9p0xOabFJwzMI97IuLWLB7qDDMPK+NgZ84tHY7PO2MpO+Mun4zj81VZZzxxNtpXMoAUbNlD/5Apv5JkzIeJmPNYaZ5s95EyYWzqV86YfskMnVPmi0zj2xqLchsOc0SVkzf1c65A+pvPRYgvYQmvauNlxZXPOOWeCubVP9s0Z+4Vuu4Q35XSRcvJBXxgruXKNQx0bDbjKt6bNMzm0TsyLfLJIbtHpJfXsLLnQhUFCZqIpBBMJKIzUcnUoZnkWlDou9VFWJtm7RBk4c/XsoqOjIc+UQNPYoNMpoUvh13J3HdCgJEWInFna+QtXyvdMeRMG75IJdI+q0pBX00DhTW3Qs1gsZoaRgDOYFJ5ynnql1xy/c2B8KsMrwSa03iWLEW3PknfOm2cYcaDQ75TsZit92DKIrfThA0M0JY5HfbcgKPhO9OVbQNpJxmn8FBmc5UmEnSPFUfNud9Msp0A43co4nc3+LTb9UO6Mtjo+KUb5dXzkrObJb5csMu3Nk0+JcmbIPLtPQbkyUN4lyrUdrWYeZUCW1ZcY+Ga5BSyf8oGPMmO2jshdHbs6FJZPiVxaS57NBUfLbk47hoeRUGYduv/iuZnMDV7kWWcw8kzZMqro6L8pk2SKzJNfdSWbHcbINyS9w79Z3s1a5QTjQXvrgqKFt3dyDROp8ivfeOW5h+FdYrzlUcjeJWsCD5U+bNSR1FdHItuit54l7xtuuGH57SY8WLfwUCYpR4PDUWUH/hwn+f0lRsa8oMNI17qcRu/ypWqcqkzWd/WtWbLj2VqmIzzX1MQKBvhEv6nbHBE1x2x8FXdyX2m1++SU4FG/nHLP5JG8qk9/yRMxciTm2XrxKenLp8R54fB5ltgHBs+zRB/QC57JF7zpJv1Zo9aOMusdFrWcsefwcHb0oQ455aBYY94legXPZMO7RC/RL+beu2RsPiXttemUyKd6xlzXYh0Dp6Y5D7CgW9SXzC157US7mc++aSMJECizEaryxf4as3lQR7LWq5zBiF10F1aZd3Nv3GhJ6KGjnnfrFeaepTrX8OeMsVX6sx7MPVocW7qQs44f86Y/yRGaqJDnWhfddsncsacukXP6bE6qDiC75Fw7c4qeRB9xBNnLpi7mUKrba+rZWeq1w2gXCIw3BBwZUQ524pST3et4w8B4KTKRBIpPZEhepEAgEAgE+kOgbuBE4/qrN9Jl4SyNNMJBf9gRGGsERWIc2dgZ+cqrXexYG8Nw8Gsn6tjGUUUzajIctINGIBAIzJ4IiJA6qnSUNitHGM7SrEQ/+g4EAoFAIBAIBAKBUY/ACDpLo37swWAgEAgEAoFAIBAIBAIDIhDO0oAQRYVAIBAIBAKBcY9AADCuEQhnaVxPfww+EAgEAoFAIBAIBAZCIJylgRCK8kAgEBhLCASvgUAgEAgMOwLhLA07pEEwEAgEAoFAIBAIBGYnBMJZmp1mcyyNJXgNBAKBQCAQCATGCALhLI2RiQo2A4FAIBAIBAKBQGDWIDCQszRruIpeA4FAIBAIBAKBQCAQGCUIhLM0SiYi2AgEAoFAIBAYaQSCfiDQGwLhLPWGW7QKBAKBQCAQCAQCgXGCQDhL42SiY5iBwFhCIHgNBAKBQGA0ITBkZ+moo45Ke+yxRzrxxBPT9ddfn6655prRNL50yimnpPPPP3/IPF177bVp7733LmP1ecMNNwxI8+abby7199lnn9RN/QEJ9lDBH281Nw899FAPrZ/Z5IILLihj2n///dOjjz6avDdrPf7448kfSr388svTk08+2Sya/nz33Xenww8/vNA588wzp+f3+nDFFVekE044Iem7Vxq1Hb6qDPujr+S7ljU/77jjjjRlypRmVsfnq6++Ou27775lvPvtt18iSx0r91Nw0003pSOOOCK1m8vzzjsvHXvssf20frro4YcfTkcffXQiG0/njt2nSy+9NA2HHLUiQH7NMf12+umnl+KLLrqozCP5Lxmz4B/zT07xdfzxx0/n4Iknnih6uM7rnXfemQ477LB01113Ta9TH84666y2mJGNk08+OV122WW16kz5vO6664p+feCBBzr2Z32bhyuvvLJjnaEWWGPGD+NWWuSMPDzyyCOtRQO+a2e+jjnmmNQ6xgsvvDDpc0Ais1mFU089NZ1zzjk9jeq+++4rOvWWW27pqX0vjYbkLB1wwAFpm222SS94wQvK4vrlL385LI5JLwPp1OZ5z3tees5zntOpuOv8Zz3rWWWcf/zjH5MF5b2/xhyCX//61+m5z31uMaocJs5Ff21GouzZz352gkHOecjkKdCNNtooEVRKdd11102Mf5Pw7bffnjbeeONkITA2zTLPlNDBBx9cnGoKUt2hCPyNN96Y1ltvvbTddtsNi7M055xzJpgxJuuuu27afPPNsf2MNMcccyQOyl//+tdnlLVmoAcX8vDggw+mgWSntb13DtZPf/rTtOmmm6b7779f1gyJnOF9hswOLznnpC6+OlQZM9lTp04t8299DTfTHA2bLZtA696Gh77jlJCL0047bbi77IreIYccki6++OKiW/785z+n6jzsuuuu6Ve/+lU644wzCh0y+vznPz/5LBlP/WNM1sz+fRuep7Kmf+Sci74YDp05nWgXD9YEO5JzZz1Fbxjf2Wef3QXFwVehm9Zff/20ww47FB3XSgEmvehSGzmYm4dtt902cY6atCvdZt7s/nzQQQcl+vXQQw/taag552KPYdoTgR4azdFDm+lN/vnPf6aVVlopLb/88unLX/5yWmaZZaaXzaoHhnf33Xef3v3//d//pbe85S3T33t9eM1rXpM++clPFiOz5JJLple96lX9kqKwOBWf+cxnEkU7efLkYoT7bTQMhSIeohg+kZswYXQNijMAABAASURBVEJafPHFiwL0PpQkombcxvLZz342/exnP3tGlGPKlCkp584Kz25XNOq9731v+v73v1+ckZe97GU9s/WKV7wiLb300gM6xHaFFNVAHU2cODGZ67e97W3pfe97X8fqc889d/r2t79dxmrT0LFiX8F8882XyIyF/cEPfrDQ78vu6n8Rk+OOOy7NO++86fOf/3zHNm9961sTTDtWaBRwrN7//vcnstHI7uqR02e8t956a1f1R6rS3/72t0IatsbC2JaMYfyHfrN2vve976Wtt946Gfc888yTVl555UTHvPOd7+y6N1FKDn3XDTpUpN8Y3o985COJbmHYX/e615Xan/rUp2aY05e85CWJPM8111ylnPxfcsklabHFFkuLLLJIyWv9h2y8+93vTgsssEBr0Yi+v/rVry76lXPXqaMPfOADg9blThWsn040m/kcoeWWW66jrlxwwQXTUkstNaCuadIUReLksUOf+9zn0mabbZZa5eZNb3pTgnmz3ez+TGcPxS6/8IUvTMsuu2x6+ctfPrxQ9UNtSM7S61//+qI07LhyzmmVVVZJn/70p4tXPrVvx8dgC53amUmeH3vsseR4itJ1PGHHXCMuogSMqU/tmztotORpc88990wfkr4pEGUiFXZaQuXy7ABFgWp9NOT7VN9nJeRZXk341b6Wt/vkDKl37733Ju3wrZ53Oz/hWuMTYXnxi1+c8KeeNiIz6hq7dvKU2d3gUWTKcZA2ohHGoRw+2kloy5MsSm3thkV7tMP/XXfdlRg2z9rgTX2p4mJO8IAnNPWrT/WbiQIVBrejNjaOyu9///vpVfAtkYvpmY0HY7ULNlbjMb+MDx7xIxmHJuiba3KCH2OT30zyzX/OTztnsIYRWpIxGSfD5119fOjfuz5gXekav7HP2RdhsiBrPozUxbt5R4Nit1Gw04V3rdvNJ57w4BMf5qi1nb7+8pe/lGM7uDB+6phDvDT7vO2225KkXF3j8N4cmzLJWOBgnORCPWNCD108qSdV3mBqzAz1v//976SecvTVkYxHnrkiT+rL15dnZT69y9efPEn/8tBt9q+smfBup07G1TdW85RzLsdN8ozHuLTDizwJbvJaU1P+YEJmYO84i/zhRx4nn8wap/WMDrqSfO/kTxt5EnqwE0E1Xrighb6x4p+sa9tM6mgvWVN0J9rWj/7lSTYaIhPacoo4O54ltPWHBzKKB3IBQ/KtTtV7ePSujH42HuPWvzLz5tnc4Rd/+Ddv1qF+8KdcPe3RaybleIc3PrRHSx1zg45nyTs6kv61Nc/41jcsta/9yFNXgq1xwGf77bcvRz2e0YWJOhLe5dWUc04wzDmXtaQOLKos4aPSwZ9+jMfY9YcXbST94BmPMCETeBY9s2a0U6aNOVCOD3NFF8AIHfXQVtaUZWW1vTK8yMOLuZKnLZ59KmuOt+bhCV31yZh5UbfyI7+Z1K119FXLrDltJO3xX8uan7W9cs5pswwv2sIY5uh794k3uHk3jkqnyg8clUnqwV4yfnlSxaXZ52Ceh+QsiQwwdna8//rXv0poWOd28WuuuWaJGhgEb1pdAO22227pq1/9anJ8Ybe26qqrlnsY5557bnG2fvGLXyQ7oLXWWitVQ2wRobHFFlukv//972nDDTcsDpd7F7x171tttVUShqbQ0HLXxHm+KMhee+2V3Gv58Y9/nFZfffVkAQnn/uQnP8FuuU/0u9/9rnj9jNOkSZPSlltumSzAUqHNPxaRIymRtZ133jn96U9/SpMnTy6OCWftpJNOKne4dthhh+T+DiOjD2NwHLPnnnuWOz/eReX+8Y9/JGNQ/+tf/3raZJNNyrtnYxf+//nPf5422GCDEs1BE3baGMcuu+xSjraOPPLIYshEgcyDsj/84Q/lnBzPcNcGZuv3hZyvuuqqNGXKlII9Hhwv/OhHPyq7aALbHPoXv/jF9K53vSvBEU7NOzIWH1xh0GzTfDb/xn311VcnxyYcL1jpF0/Csp7Nt/P9j3/844lcwYQyaNJyDwseZMh5v8WkXFt8VHo77rhjOZaAhWMzsuBOlb5g7zhClIJyw9MXvvCFxLCg1Uzmz5jJhT4rP5SrBWtBN+v390x5/va3v01f+cpXEv7Ixdprr52qUqxtYUUxkWUyLd/ihw2eRRYoJ0b9O9/5TiKPeFEfbtaRzYN2NdVy44S/nfcaa6xR5MrYyKajPkpbdFRUVEREf5T6gQceWOTMWqOMyKmxqGc8+FX2pS99Ke20007JfFrLlX/OPBzNj3VG/ihH2MtTpg1ZqTw3PxkpR7wUovrmUjllSE5gQLYpb/zhRT38WTvGoH5N1oQ5UOc3v/lNiSChBWPt3Q2yPqwnx9DwErnFt/Fppz84oEnOYG7N/uAHP0h0g+ig+uQKfscff3xZ2/C23syftjUZY+WJvnO9wVyRce3JOB76O8IgF3SSuRVNgrv2jj9s5PRFJ1ordCGejde6+trXvpbw6LjIGKwTeJKpb37zm+X4WTvrU5m28mFmbfzwhz9M9JE+mgnPNtTmmD4jL3SItWN+RHXU9w4b2BrDBn06j85QZgynnHJKmSeRbTiTBetavzZFIoGwdpROv5AXd/0YS3yhy7bQi9YTus1El7FTxosWm2KO0F+/T2fiT3u2xxpznIm/Kg/4NW/6c0dJmf7VtdGg05VbV3DWh3drk+yvttpqxf4Ymz7JFP6817mCFd3FeTZWtM2FvvVJJ7KzZEfZd7/73aJL0TEea1Z9elDki+4hW3DHg3x8q18T/uAMYxh+4xvfSNY1/ugfsmJM2sKntquf7KmILBukH7qilon+yTNGOshdJhsiNKs+ksfhtxbUXXHFFZN1xbkkU3iyhj3zO5SRU/n0K11Q++vlc0jOknAiIWcgAe1OhckXchQad+zAmFDqL33pSwt/vEn5wpkEj9IGCoGX73jDAjfJFjhBJ4wLL7xwYlQIC8+SolBfWrLvWMzkWDyOTiZOnFiM/4te9KLp5/XC9O5o2JlQ0ha3xYQpRpSnapJM9Nvf/vZEGEUOlLdL+rWj82ms66yzTtmNELAlllgirbDCCmmhhRZKaNr9ERIThk9KQkjfZMIDTxSUMsctaApRwke4nGGGCZ4JOmVqLASDUbIoKfH555+/HIdqyzk1fjxW/hkTtPVj3hgkCwkt+Xgx/o9+9KOJkrGAatv6ScFoDztjphyVWZwUoedOSSSKI4Y/i1cYFS7wRpOhMz4KFN855+S4AYawrHQZM8qMLEiOFWoZWdHefMKFAocLmfzQhz6ULD4hf4ub3HIKzAMszEOl0/ppgWpnDh13GYs6MPNpjhgbzwOlKos+8URZUsCtzims3vjGNyZzTKbRNU+OI8w9OTBP6EjKjRuGjo8cFzFo8mvKOZfj4JynReO0k0QkONYUICMqqsC4vfnNby79Ww+vfOUr07e+9a3k2MDc5zxtfsylqBfFbXdo7vDpeMg6JtMUI8eEA0iOzbd51beNBWcJ75Qcg45W5bn5aXPmuEn4HQ3HmsrRIU+MC6VsPukOihJdeWSD3KovmS992WDUOvSYujYEOeeysXPkTG5sFGBvvJw0ilg7RsS4OCHWtTWLN2uMbH/sYx9LjnVdU3B0S0fQcwwW2XWUiJ+ayBpHBQ2J7HIurFP4mxM82CzVNq2f8Den8mE1efK0awDakw355okuZLxtvuTpA5ae6TE8e6a/6SPPaGubcy7HYjXf+OFE9zl2VLeZrC9trX965h3veEdST3/6rXUZ75xz2SzTN6Ix9EQtF+Emf/o1n3TfG97whlIfVpxv48G7MZAXOldEkkNT54w8mMdKt37ikSNkfsybemSi8qjcs/HAk24WbeeIVdqcZPNsDRqv/q0FuGmPPsdm0UUXLeux9m3O4EHOOEPsp80V5xfv9DpM6IWll166HOmTcetL33Qj20j3oWPNkjkRcBs+dPBGpsmWDaf1TAdy+pWjY+1YG5Uvn5wVeGujrXnmyGijL/bSuDhp5FebZtJeEhAxf9oo55yiRz/om0zQPQIbaFlPaLPz9NN73vOecl9PW8l4+QRoWHN0nvmh+5u2gHNIz2rTSxqSs8TDNBkWop2XwVMg/TFCCBga578GxBga6IQJExIFQgg4FxQTgChNAmDBoy8US1lYDBwuwuQeTbs+gUq5KkPf8ZD7KAwvocx5msFgBBkeAmbngq8aZte2XTIGi51D4rNJr7U+YScEsLJQLGx9MEof/vCHy7hrf86uGRd3UNTBP75hAo9KGw4Wm90PhWfh1rL6yVhZCPXdAoCDd/xTLJQFfihDc4OP6gCo10wWK6fWnHG8LAxGgkASTO8cLcrFTptBb7Zv98zYw0UZp0Yi0DA138agrJkoBnMFF7gbi7rqUJQUGMfZLsVOjnJVVpM5sHDsiCm6mk+p1ufWT4qJwmaQjReNZh1OV/O9v2fySgbJtHGa51Z6ndpzSsi/eVKHEjc+cu2dPFpD8BcJJGPya6KsyQQ68uAN40UXXTShyTDJlzhpnGEbGoZQXmtiqOz+OS0553LpEn1yu8wyy5TL7PrUzu5cBM/4vVPg+udo2iWaMwqPw8JIqdNtMga4VBw5nhS7qDe6lCiHnow3aVL0nA51YEaO0WnWafdsN83p044c2c2TR3rJXBgzI0lHtbbnIFHwNlnGWuei1qPv4OfdmqcL0PXebdK+OkWd2sCeHOKVw5dzTjal1lOnNvLJGP1szfmkO9Agy3S4NalM3WayhtSFL31lbMqtfzLjmXyQE3neYQNHesI7uhP6bIW2PtVjP6w/ToH5tIlXtzXZRHBezJmNmXXMALfWQ5NNMA42RDSSQwsbdckvfungihUDLyKENjkSKSEP6tdknTP89Ls+5JMV69ez/siGvtDPOU93CuBKDjg15ooeZkPxhhYnlQMqIskuWI/0C559wlsf6ovEaGutwJZDT0/omwPKSXNqYwOvTU3GmHMu9kqe9UtXs8HwMl5zYhw5T7Ot6tWkPTlhy2Bn7MpssF772teWEyMOJV9C4AV/ZAVvxmu+YKc/tktbyVrUr2dYCJgYL6xsis0Jh5LzV+dL3cGmOQbboFlfyJZXSAgsAsbSRNQ6IhN2bxwFi4AhUyZf8ixEDDyK2rt6PnnlwAICB4ZRJyToSUCzcNRtl9ChMNuVteYRGIJIsVpwjKZJaq3X6zsBMXGMAhrGQ6AsCu+9JB69qASHoGngKi07dDjVd58E1JEAxeLdvNSF6n2ghKbIIUfF4uWUmBNzITzLGXMExHkTFRE5GIimOWKI0VQ355wIvOdOibw5FhBC1x4PxiSPkSCT5JFSg406lZZ6Ipmw5zDBpJb198moML6imxwwR1TqV9oWe87PVBDqDDXpA/bd0qkOHQfEbteOstu2zXqUmZ2gI3XORtNgw9Ha9c0smDACzbbtnmFkrijYWk4JmitHSz7NGV2Qc3dYMpSVVusng8Dwoocu+tZesx7DTy8pU8cKXysEAAAQAElEQVQ7vJt12j2THzqJ4tZOH9Yb+bM5qvoNf/VZOdysObgxqtZj6/EA3cCwi47pW3vOoOehJuuMgz0YOvDAu7kyf/hqxXEw9Pqrm3MuF6wdLdFP+sYzx047fHj3Kfrp0xrmZIsEMfDwU7eZbIZhaPNd58xctRsHvPXrkx2y+aBHmvRan9EWTam0yQMarfV6fWfrOPWOn9gpkV6OP3k1HzAhh5wB9gYu7fqClTHXNYhHMsrZ4ZDaKKMjodmkAQM2DIbyzQ9n1pi9D5Q4uHS09aYunWZe5HOI2Hv9SpV/9p+et9HhW9BJ2jaT+jbQ+JFvPMZoTPita1s/xqtOL2mOXhrVNpSfnafogiSc7UhBuUERHjs15/6UoXJlvH9HbNrw9uyAOUzKKA/56MrnJQphMtIiG8qA4ptp6BIUSgtN7U0e42vnxrs3MTxPzxQnPtBiBAiDkK9jAJNGGC02QOPDJ5qSyahHBcK5QuWMpwXL40WDEmKYhGQtdmFFYXnGn+FyRIB/u0mCDiM44NEYLE47VMqWMdYHA8Uj1xfnFJ+e7Ra0ga96+NOG4BIqzotxmwMLnrPmaEGZc1982MFOnjy5/NwDIbabUN85NKwobGNvJjQpd+2FUjnIHM1mnU7PeDcvBJgs2FFwuGBHCaBpwdgRGws8zBWMmzQ5snaPjuCMH+bGaF5E6uBhJ4GeOYMv545xF/XibMGD00OG7LZESGDGmMFAgju5grMy8od3zrQFiCe84dmC9S58bOF7rglvxmGhciYtfIqJfHh3DMwQ6YMCqe18WuDmHd9oUBzGR27QI2fomX/zCTd0RP4ocJGNyht6jJ1xWTfwIku1Hb7JH0UKD444Z4vyhSvZYoiM2e4PPe+cT/Pp3XisB7jB1ziNH1/q4seRkrmR8C4PD5xXeY4J8KCN9Wn+0K6J0saTutYXecU7XKw9cwQr82QNi3ypi657R5VOzrl8g1c/VV7MH3w4MxQ27I0BLmSGDJFXUaHmWkJbvyKrdI3jbbJJv8GLYSZTxkMm3e0wZkcG5qny5BPWdul2xPg2Jkfc5hu29IM7MPhUvybjUGburF98km38w95um7ybFwZPIgPwU4/cGJ/NhjXF6NgIoYUPsqCeOTZG61N7WMsnS3iwXsy5ssqbT+OmZ+hebeBJn+jLWOhjNBwR4cHdE32qJ7rJYRApwa9jeBtGkSHRLc6UObNO6BXrAg/sgfp0LptBB3FSjQcNcoO3mow351x+EkUdc2yO2A3YoG38dKM1RH61RRv2lTZdoX8bSPnmAmZk1Dt50s66peNhTA/ATF9wgJFymOKbM0hfSvi07ug1slhlXPSbHjfP9AuZwyN+zRGZc88WLeOr9eHqy1lV5pThHY81iSSxZVVXi2KRSzjg2RisF+OQB/Pa1qf16NM9PfTVh6k16rhNZE6+VPHh3BmfPkW+tKcr8cbemlvl5sW9Sm1hDy8OJdnSVr71CAM0eklDcpaEuERiLELJObpdLUYA73iO5ytPqNoZpDKG3mRr43Izx0G+JPwuXxjRWbo8R1PCg7xmRspiMrnqCdc5QmCw1HWOalLl8e7x5NiIsiAkHC/PDLzdCE8aHfTw6lmiYEwGmpKFKl+IU4iUsqbkhT7RIEQEsJaJ+sBHGxNuLEKl3vVtd+DZIscjg5ZzTrxhQiOSoQ9jhaVnu3fnvTDgfBEwPBMKjp5+1NF+4sSJ5WcOtFVPGWET7eFo6NvFW3jDFW92UBwJyppyYqiNvSZ3ANxrody1N6/VOa515HOgzGnOM0YHcs7Jjhx/dv0wZVz0XWnCjKGw+xYqJyd1bmsfDI96IliUodA6+YKpowA8ceTx4h1tZWQD9jDlFMMETo7iYKA+OYMhHChAETLYe8YTmULHPOOHnGirD+9oaOu5Ju/mk5NqftGDpXknO3ZPHE9zmfOMmFGM1gKDYN7gb/61Q8+cokeurSX8GRO5wou50HflJeecYOruFXrw047CwSdH1Jq2eSED1sWcc85ZfiZBOxjgySZGXfKPvlA+Q+FIF8Zki/xwsPDmnpf5ducClmhKeCUL6FSerV3rybg4j4x65d+nuVUffXdSrG8yYF0rczwG05xzEtaHkb7QhyMaNRmfOdYOPfNqPOoz1jCCC7zhZN3pBy3RNuXq+rR+jEckDlacOsc45ssatBZh4w6nMevP0RSDX/nxiRdGq+JkfORFmfUDf+3xJa8mfFhbdI8y47ZBolusGQYVP/iEl82osdAB6mlPN1sP6pkv/TqOZZTxDxNjMUfWp3lCQ3sy4Vn/1pfnyptPsmD+9a+MXNDV5pmMu4sj35qlZ/FFPvHp2Zjwoo21Ajs0PJNnMmZ94d88mDPzBT9lxue+DVqeyYi+8FYT+aWPbGT1TW+TEViYN3dm0EVfn/jVls5y56fSJmfkyNybE3Ohrjzv+NQOXbrJWoMDOaLLzRe8PKOVcy4/+YDvmuhFjil9hC/55om91J6ONBf6hZU58qy+jXuzPl1oPFXmlFXnBp+SOjao5ko5O0Em8E0m2Ff0yQa7DCftaoIn+6NcezpbVNocWLPGKl/6xCc+UZslY6ArYSMz55zoHnhbh9YUeXFCpO1SSy2VyATM2QK6uebPO++8SPSUhuQsmXiLBfiSBVa5sOgMmCFnOCm1Ch4BUVcbC6y28UlJy2eIDVCe5IxSvskhvPJcnJRnMRAOecCTp44IhWc7A/3gReLkEB5lnnnDjIB3yaRQZIQRTcniITzKfRJgn97RJkCe9VV5re8WjLHAQx4hm3vuucuEepfgAZc6JvzpQ5mEp9ofLClU78Zj4cJLv4REPxYMZaCtRLnmPE3IvEvmj3Cr610ihD4lQmjsNVEkFgy8lUu1rH5SaHiFZ84zGn68aVMThdHavzxKwpjUo6y1q/TrJ7kjCzCwmGBivvRvMWor4UUb44eVd/NRx0A24QU75drIg0N9hwO8axtzhW9RArsYxou86IeyoTg918TA6QNt80Qu6zu5ociVSQxsbefTWNCkCCo/jCsZUp+8oAcL7xw980oOvXNi0KmJYqNElEnNuW/KC9mDAWzVYwTQMDfmxLrxjhfl3hkxz82En/puzrTnINe8Ol6yVfPMpfUiCmmHbO70VRPs4aY/67y2M64qN8avftUH6uBbXjNZc5S1cvTIgbVZ51o+486Z9CzBmy5r4gUHdPGGhnro4U8+Gt7hwbk2b+qQNW3UaSZKXblU+yPfxiVP4tg125gz+WSryRsZMu9whwF8yQt+8E3XaEe+yItnybqjV7XzTgbVJd81z7u5V669vsird7Sb/MmTzF1tgw/rqY4Lb9oYm7qS9Wfs8vEEM/n6lieRVXn4qmvD3NND8n3mnMvvR3mXyIq2rUnfxoI3a1e59tpI+IexZ7wrl6w7eZI5o4vYBu+SZzx7Nv/asCveJbLhU9K+ypy+RPPJjbKaREnxZ62YV/n0IV1VdQp9g8c6J9a7fitGtb48Mo1GTfJaE7nURh04KCcX8JLMX1075lR5TTlPuxOnrWSdVL2ijrya2Bl5Ep/AODxLdAja6hon3UtHeJfoAdhLnuVJ8NW+1zQkZ6mXTu3OhMyE3IXKKg1RHiEy4X0KsuaP9KfFRxgd+xEgyQU3SoMQjnT/QX9sIkBRCZNTYs2FPTZHMzq5FkX1hRFO1ujkMLgaCgLRtnsERHsdqbFPNXFMRU26pxI1h4LATHeWnLlLflfCkUFlXnhUvt1604us5SP5SegYPf1LzmJ5yyPZZ9Ae2wiIFDgGG9ujCO4DgUBgrCDgzg37VJMo2ljhfXbgc6Y7S7MDaDGGQGD8IBAjDQQCgUAgEAhnKWQgEAgEAoFAIBAIBAKBfhAIZ6kfcMZSUfAaCAQCgUAgEAgEAiODQDhLI4NrUA0EAoFAIBAIBAKB3hAYda3CWRp1UxIMBQKBQCAQCAQCgcBoQiCcpdE0G8FLIBAIBAJjCYHgNRAYJwiEszROJjqGGQgEAoFAIBAIBAK9IRDOUm+4RatAYCwhELwGAoFAIBAIDAGBcJaGAF40DQQCgUAgEAgEAoHZH4FwlkbTHAcvgUAgEAgEAoFAIDDqEAhnadRNSTAUCAQCgUAgEAiMfQRmpxGEszQ7zWaMJRAIBAKBQCAQCASGHYFwloYd0iAYCAQCgcBYQiB4DQQCgYEQmOXO0kMPPZT+8Y9/pPe///1pxRVXHIjfcVO+ySabpN/85jc9jfeiiy5Kq6yySrr77ru7bn/55Zenj33sY+mCCy7oqs0tt9xS6h9//PHPqD9lypT0/e9/Pz344IPPKBtMxjXXXJNWWmml9N///ncwzTrWPfTQQ9NXv/rVdOedd3as01qw1157pV/96lfprrvuai2K90AgEAgEAoFxgsAsd5ZOOOGEdNttt6X999+/QH7ssceWz/H+z49+9KP061//etAwcAS22mqrdPbZZ6cnn3yyq/Y333xz+vOf/5yuvPLK9MgjjwzY5p577km/+93v0lVXXdXWIZo4cWJxgJ///OcPSKu/CvPPP3/aZ5990iKLLNJfta7KzjjjjMLzrbfemh5//PGObZTdd9996Yknnih1Pve5z6UNN9wwzT333OV9Vv4TfQcCgUAgEAjMGgRmubN0yimnpNe97nXp5S9/edp3333Thz/84VmDxGzS6zzzzJMmT56cOBrdDulVr3pV+sEPfpBe8IIXdNVkrrnmSuuss07X9bsiOsKVFl988fTDH/5wwF4uueSStO2220YkaUCkokIgEAgEAuMHgSE5S7vssktyTLH99tuntddeOzWjQgcddFD66U9/WqIj9RhF3hZbbJH+9Kc/pR122CH98pe/TFP6jmwOPvjg9K9//Ss98MADJcqElrTzzjtPn4nddtstHXjggaWfnXbaqbTbcsstk4iBuv/+97/TDTfcUModXzlW0lgkQXlN8hwPMYjnnntuiYAo86xMZEWUS54keiLfkdZ6661X6Gt77733yp4hHXDAAWnttdcudfbee+/06KOPliMf+DhqhMd//vOf9L///S/9/ve/L/X23HPPGWjUF2OHl3dRoj322CMdccQRpQ16tf+bbrqp5OEVjuo3k8iMMsdr+vXcbF9pmrsaTdH+vPPOS+uuu2762c9+lo466ihZJXFu0cCbKEzJbPnnzDPPTNttt10Zv6jVNttsU3jnYP3hD39IjvBamqQTTzyx9AUPfSs3h3/84x9L/bvuuiv9/Oc/T2eddVaSt8EGG5QomH7wc+SRR5ZokLkXJSMLxr5On1N3zDHHIPeMhJ620sUXX5wuu+yy9Nvf/rZEs9Awf4cddlgiWw8//HBpf9JJJ03H++STTy55d9xxR/r73/+err/++nJ0Sq6vuOKKUhb/BAKBQCAQCIx9BHp2ljhK7tX89a9/TS996UvTG97whvSLX/wiXXfddem4444rTs/3vve99O53vzv95S9/Kc4QQ7TrrrumD33oQ2n55ZdP3/3ud9Nb3vKWWzgz2QAACWZJREFU9MEPfjB9/vOfT3POOWdaddVV02c+85lyt2TrrbdOm2++eWKYORf//Oc/k+MpkaiNN964GKj99tuvRKM4MKuvvnpac801k3tQ7qdwfDbddNP0mte8prRjkHfffffE8cL7aqutVo54Fl544WQ8nDXOAwfu29/+dnr2s5+d9MMxYQy/+MUvpm9961vlXg+ems4CR4QT+IUvfCFN7DuG4kTef//9xbAyvM961rPKPR5Y4e0Tn/hE4Um/+kyN/0TYNtpoo3ThhRema6+9Nv3kJz8pR0gcOjww/hwJTYzhox/9aMEQvpwE+TWJqDg2Y8jh9p73vCeddtppifE//PDDkyM7mMKMc6Ad55ZTAAPHUDA7//zzy9GeMU6ePDnlnNNjjz2m+gxp6tSpxUkmA/D55je/mWBtjGussUbiLLbec+LwcYKUu6fEOeO4fOMb30icILyTLU6LIzFjwKMoJDwXW2yxhEf8w1V0iHO7zDLLlCO3Sy+9dAYevaDFoTH2V7/61YkDPt9886VPf/rT6Y1vfGP62te+Nt3BO+eccwodTiB51OZ973tfiVRxpuRJ7ld9/OMfR744XE3ns2TGP4FAIBAIjDUEgt+CQM/O0pe//OVyKZvTs8IKKySG9XnPe16J/px66qlJ1OcrX/lKMZScFg6SegzdEkssURyseeedN7nX4ljHMRzniNPFEL3jHe8okQaOjTYuHzPcHJ+ll1466Z8jJlLxpje9Kb3whS9MIhgcAnQ5A0YoOvLJT36yRLM4DXhBZ8kllyxRr4985CPFmco5J3d8RCOWW2654vyJYIh4ucvDUTFGzpLIB6ek6SxwuESWOFiiHZwc9EQ6jOcDH/hAeu1rX5s4UBw7R0Jf+tKXyp0ftPBak4vuE/scLu/Gw+lcdtlly1EZg/6Sl7ykOCp4e+tb35oYaPPACYKPdjXBFsbezQ/nwrPEAeRsaQMj5fJdEOd8cIpEXYyf87HZZpsl2L3tbW8rTkWtr01NEyZMSN/5zneK4yuPo7TUUkuVvNe//vWJY1LnRnlNnCVRK5hoz2Ext8qNV7SGMy26Z84WWmihNGnSpJJgNMccc5T5e9nLXpY4prUdufDcmjg2nHjRIVE7zuJzn/vc5BhTP694xSvKGMlwbctZJxvw4tCbE866S+NvfvOby/Ed2cYPeua/to3PQCAQCAQCgbGLQM/OUrshv+hFL0oMDsMlyiFCI4medHNJ10VvRxqVNgfK7pzhqXmD/eRAMYqcHI7FQO1FkUQomvW8cxAOOeSQZDwSJ6LpLIiorbXWWkm0RoRkgQUWaJKY/szp4Piph87RRx9domnTKwziwUVkR4qDaDJDVcdh7bDlUHJG8YZHibOn/lD6m6HzxgvnlsPhqPDrX/96cbTNQ6PKsD+KfIlsGs+Pf/zj1JzLTp05Uryr7ziwlr/yla8szm99j89AYBYiEF0HAoHACCIwZGeJgcOfT4bXkZAIiuMJxlyZyITjGc/9pfe+973liItxVs9Ry7ve9a7EmHrvJXFwRF1EZG6//fYBSbz97W8vDlGt68joxS9+cWIoHSUhwGA6muFEeZccUzk6EskSyaljV9ZM+HCs5DhKvmiXO0meB5tErBzV4UVbR4H48NyaOGkcT0dJcBVREb0zTxwTd7Mcm4kocRxEeUTH0DEuzuCiiy6a4MFpqvXdI7v66qtV6zn5Bh/eROFcNHcU565ZrwTJYZ0b4+QYwaZJjyNorh1r6qvWr3VgCo/67lN0tB4RelfHUaDnSIFAIBAIBAKzLwJDdpYcc4g6iAj87W9/S45aHHEwNI6HlIksuWfjLo6LxC55g1Q9d1IcJznyctzmN20cUWnH8LvI65hEPfdC3AVyzOcoy9HN5MmTy30oF3QnTZqU3IlyDObTJWvGbP3110+MokiVo6SVV1653NthnHfYYYdyKVekxz0hR22iDe6u4GHq1KnJkY+7N+5nyRMFUceRm3FIjgZ9KlePc4KGKBOD7c4Vp8QxlKMsx0rquhvT+i00OE2ZMiUZt6iYKB3+YOTujjI4iZS5oyVqhpZyY3SBmwPzqU99KnH0HA05cmPsOXHGw/HBp/tC5slxEofFnR9HchxXR1DoqqfMZennPOc5yXEq3BxDTuw7LjQmY5fgBWPOFjxhZb7QEHnjbDii5bSpLzmadPTH0Tbed77zneXeGceTY2lcZIITtH7fXPpJBZfZXYInH2g7ghQNcwzn232OF/FunOTqxhtvLHfnOO76dwyLhigfPLV37OdbhJxX8qZcHxxu7xw5vOkHbffBYGW87km5Y4U2+SZ7ZNS7KCQH01hT/BMIBAKBQCAw5hCYY6gcL7jgguWbTIyfoyr0RFY4TpwEl6oZN4aEc+O+z+qrr65auQQrMuI+EEPsGI/D4107NNyxmTx5crnsLJ+j4Q6MyAADy2gzsJwlBlpdfYjcuP/icjTj51I1A+bbc55FV/Cjvk98cJ4Yfo4FA48HzgyniGF06VmeaIqoTs65jMM/xoy2cveeGGDjV1dfHB+Oi/s07rtwGtTlpLjkjkZN7izhxxgcEeFf5I5jwACjJ8rlfs1nP/vZ8g0xtBw5uk+Df5ea9e9IFA6wUYfTtuOOOxandu65507uWSnTFobuA3HeOHl1vJxUToT54YjCxsVwDoKL+Y5eK+8TJkxIIjl4dL9IXfPkor35NC58cGBqG5FI44QZp9qccAT9Bpdx6At+okPwNE/wgI8+YKg/8+t+k0vop59+epFLF/R9C5Fzgxf0OJxVzvBqvmBFTsmwemhwCvWhL/VtDNSp80yOyQtnDhYcLs42OeXoc2K9u+DvyK6ONz4DgUAgEAgExhYCPTtLjIFdv28UMUBja9gDchsVAoFAIBAIBAKBQCAQKAj07CzlnMs30hw15fx0hKVQjX8CgUAgEAgEAoFAYJQgEGwMFYGenSWXYx0nOarwNe+hMhLtA4FAIBAIBAKBQCAQGI0I9OwsjcbBBE+BQCAQCIxlBIL3QCAQGJ0IhLM0OucluAoEAoFAIBAIBAKBUYJAOEujZCKCjbGEQPAaCAQCgUAgMJ4QCGdpPM12jDUQCAQCgUAgEAgEBo3AbO0sDRqNaBAIBAKBQCAQCAQCgUALAuEstQASr4FAIBAIBAKBwChEIFiahQiEszQLwY+uA4FAIBAIBAKBQGD0IxDO0uifo+AwEAgExhICwWsgEAjMdgj8PwAAAP//ugWWPwAAAAZJREFUAwA1IzY1lDPOEgAAAABJRU5ErkJggg==\"\u003e\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003e\u003cem\u003eFabrication processes.\u0026nbsp;\u003c/em\u003e\u003c/strong\u003eWe use an X-cut TFLNOI wafer from NanoLN, China. The silicon nitride thin film is deposited onto the chip by using reactive sputtering process\u003csup\u003e40\u003c/sup\u003e. The grating coupler and waveguide structures are patterned by using electron-beam lithography, and then formed by using single-step inductively coupled plasma etching. Finally, the electrodes (500-nm-thick Au) are fabricated by using laser direct writing, e-beam evaporation deposition and lift-off processes. The propagation losses of the fabricated waveguides are measured to be about 0.25 dB/cm, by using the cut-back method. The coupling losses of the fabricated grating couplers are measured to be 6 dB/facet, at a peak coupling wavelength of 1560 nm.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003e\u003cem\u003eExperimental setup.\u003c/em\u003e\u003c/strong\u003e\u003cstrong\u003e\u0026nbsp;\u003c/strong\u003eLight is emitted by a tunable laser, followed by a polarization controller used to maintain TE polarization before coupling light into the chip. For static measurements, signals coupled out of the chip are directed to an optical spectrum analyzer for spectral analysis.\u003c/p\u003e\n\u003cp\u003eFor high-speed data modulation and transmission experiment, the laser light is modulated by the on-chip electro-optical modulator using a 2\u003csup\u003e10\u003c/sup\u003e\u0026minus;1 pseudo-random binary sequence generated by an arbitrary waveform generator. After coupling into and out of the chip, the signals are amplified by an erbium-doped fiber amplifier, following by an optical tunable filter for reducing background noise. Finally, the signals are received by a digital communication analyzer for eye diagram measurements (see Supporting Information S5 for details).\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003e\u003cstrong\u003e\u003cem\u003eData Availability\u003c/em\u003e\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe data that support the findings of this study are available from the corresponding author upon reasonable request.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003e\u003cem\u003eAcknowledgements\u003c/em\u003e\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThis work is supported by the National Natural Science Foundation of China (62405082, T2325022), Natural Science Foundation of Anhui Province (2408085QF217) and Fundamental Research Funds for the Central Universities (JZ2023HGQA0479, JZ2024HGTA0185). The authors acknowledge the facilities, and the scientific and technical assistance, of the Micro Nano Research Facility (MNRF) and the Australian Microscopy \u0026amp; Microanalysis Research Facility at RMIT University. This work was performed in part at the Melbourne Centre for Nanofabrication (MCN) in the Victorian Node of the Australian National Fabrication Facility (ANFF). This work was performed in part at the OptoFab node of the Australian National Fabrication Facility, utilizing NCRIS and VIC state government funding. A.B. is supported by an ARC DECRA fellowship (DE230100964).\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003e\u003cem\u003eCompeting interests\u003c/em\u003e\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe authors declare no competing interests.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003e\u003cem\u003eAuthor contributions\u003c/em\u003e\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eX.H. conceived the project. H.J. performed the numerical simulations. M.X.L. and G.R. fabricated the chips. X.H. and H.J. established the static measurement setup and performed the transmission spectra analysis. Y.J. and Y.T. established the\u0026nbsp;dynamic measurement setup and performed\u0026nbsp;the high-speed data modulation and transmission experiment. X.H., H.J., J.H., Z.Z., J.S, Y.J., and G.R. discussed and analyzed the measured results. Y.H., L.F., T.G.N., A.B., C.P., Y.Z., X.R., Y.T., A.M. and H.X. participated in preparing the manuscript and contributed to the discussions. X.H. and H.J. wrote the paper draft and revised it based on the comments from all authors. The project was performed under the supervision of G.R., Y.T., and H.X.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003e\u003cem\u003eAdditional information\u003c/em\u003e\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eSupplementary information\u0026nbsp;\u003c/strong\u003eThe online version contains supplementary material is available.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eCorrespondence\u003c/strong\u003e and requests for materials should be addressed to Guanghui Ren, Yonghui Tian or Haojie Xia.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\n \u003cli\u003eSu, Y. et al. Scalability of Large-Scale Photonic Integrated Circuits. \u003cem\u003eACS Photon.\u003c/em\u003e\u003cstrong\u003e10\u003c/strong\u003e, 2020-2030 (2023).\u003c/li\u003e\n \u003cli\u003eZhu, D. et al. Integrated photonics on thin-film lithium niobate. \u003cem\u003eAdv. Opt. 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Express\u003c/em\u003e 27, 37795-37805 (2019).\u003c/li\u003e\n\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":true,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"nature-portfolio","isNatureJournal":true,"hasQc":false,"allowDirectSubmit":false,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"","title":"Nature Portfolio","twitterHandle":"","acdcEnabled":false,"dfaEnabled":false,"editorialSystem":"ejp","reportingPortfolio":"","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"","lastPublishedDoi":"10.21203/rs.3.rs-7481144/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-7481144/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eDespite the growing interest in thin film lithium niobate (TFLN) as a material platform for photonic integrated circuits (PIC), its moderate refractive index, CMOS-incompatible fabrication processes and inherent material anisotropy still raise questions about achieving dense integration comparable to mature platforms like silicon photonics while preserving the superior properties of lithium niobate. In this paper, we employ photonic inverse design method to enable miniaturization and dense integration of lithium niobate PIC components. As proofs-of-concept, we design, fabricate, and experimentally demonstrate mode-division (de)multiplexer (19\u0026times;25 \u0026micro;m\u0026sup2;), multimode waveguide crossing (15\u0026times;15 \u0026micro;m\u0026sup2;), and waveguide bends (30 \u0026micro;m bending radius) in TFLN, achieving a device footprint reduction by an order of magnitude compared to conventional counterparts. The fabricated components are used to construct ultra-compact multimode photonic circuits for large-capacity data communications, demonstrating dense integration of over 10 waveguide elements within a 0.06 mm\u0026sup2; chip area. By integrating electro-optic modulators on the same chip, high-speed data modulation is demonstrated with 120 Gbps data rate per channel alongside multimode signal transmission. This work is expected to advance more than 10-fold higher area density of passive components and optical path design in TFLN, paving the way for scalable on-chip multimode photonic systems.\u003c/p\u003e","manuscriptTitle":"Breaking Dense Integration Limits: Inverse-Designed Lithium Niobate Multimode Photonic Circuits","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-09-03 07:19:05","doi":"10.21203/rs.3.rs-7481144/v1","editorialEvents":[],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"nature-communications","isNatureJournal":true,"hasQc":false,"allowDirectSubmit":false,"externalIdentity":"NCOMMS","sideBox":"Learn more about [Nature Communications](http://www.nature.com/ncomms/)","snPcode":"","submissionUrl":"https://mts-ncomms.nature.com/","title":"Nature Communications","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"ejp","reportingPortfolio":"Nature Communications","inReviewEnabled":true,"inReviewRevisionsEnabled":false}}],"origin":"","ownerIdentity":"d15de6d5-10ee-4225-9bd5-6abe8b972073","owner":[],"postedDate":"September 3rd, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"published-in-journal","subjectAreas":[{"id":53928515,"name":"Physical sciences/Optics and photonics/Applied optics/Integrated optics"},{"id":53928516,"name":"Physical sciences/Optics and photonics/Applied optics/Optoelectronic devices and components"}],"tags":[],"updatedAt":"2026-01-31T08:06:38+00:00","versionOfRecord":{"articleIdentity":"rs-7481144","link":"https://doi.org/10.1038/s41467-025-67927-7","journal":{"identity":"nature-communications","isVorOnly":false,"title":"Nature Communications"},"publishedOn":"2025-12-21 05:00:00","publishedOnDateReadable":"December 21st, 2025"},"versionCreatedAt":"2025-09-03 07:19:05","video":"","vorDoi":"10.1038/s41467-025-67927-7","vorDoiUrl":"https://doi.org/10.1038/s41467-025-67927-7","workflowStages":[]},"version":"v1","identity":"rs-7481144","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-7481144","identity":"rs-7481144","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}