Introduction
Mantle convection is a key driver of the long-term thermal evolution of terrestrial planets. Caused by the buoyancy-driven creeping flow of silicate rocks, mantle convection can be quantified through equations of conservation of mass, momentum and energy. These non-linear partial differential equations are solved through fluid dynamics codes such as GAIA [1]. However, the key parameters to these equations are poorly constrained. While the input parameters to the simulations are unknown, the outputs can sometimes be observed directly or indirectly using geophysical and geochemical data obtained via planetary space missions. Hence, the “observables” can be used to constrain parameters governing mantle convection.
Given the computational cost of running each forward model in 2D or 3D (on the scale of hours to days), it is often impractical to run several thousands of simulations to determine which parameters can satisfy a set of given observational constraints. Traditionally, scaling laws have been used as a low-fidelity alternative to overcome this computational bottleneck. However, they are limited in the amount of physics they can capture and only predict mean quantities such as surface heat flux and mantle temperature instead of spatio-temporally resolved flows. Using a dataset of 2D mantle convection simulations for a Mars-like planet, [2] showed that feedforward neural networks are capable of taking five key input parameters and predicting the entire 1D temperature profile of the mantle at any given time during the 4.5-Gyr-long evolution of the planet. Using the same dataset of forward models run on a quarter-cylindrical grid, we show that deep learning can be used to reliably predict the entire 2D temperature field at any point in the evolution.
![](https://www.epsc2021.eu/_protected/abstractImages/274101-1-1.jpg)
Fig. 1: Machine learning methods have been shown to work well for these low-dimensional observables such as the 1D temperature profile or components derived from it such as surface heat flux or elastic lithospheric thickness, both - (f) in a forward study ([2]) and (g) an inverse study ([3]). In this work, we demonstrate that (h) a surrogate can model 2D mantle convection using deep learning.
Setup of mantle convection simulations
The mantle is modeled as a viscous fluid with infinite Prandtl number and Newtonian rheology under the extended Boussinesq approximation. The thermal expansivity and thermal conductivity are pressure- and temperature-dependent. Same applies to the viscosity, which is calculated using the Arrhenius law for diffusion creep. The bulk abundances of radiogenic elements are modified via a crustal enrichment factor, assuming that a crust of a fixed thickness formed very early in the evolution. Partial melting depletes heat-producing elements in the mantle and affects the energy balance. Finally, we add two phase-transitions in the olivine system. For a detailed description of the methods used, we refer to [2] and the references therein.
Compression of temperature fields
Each temperature field is of the size 302 x 394 grid points, making it a difficult task to predict such a high dimensional field from a limited amount of data. Hence, we first use convolutional autoencoders to compress each temperature field by a factor of 140 to a latent space representation, which is easier to predict (Fig. 2).
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gklRllWG2l6FvaZwfICFSTttVsrYD+Vq+EHmRWOY3O+5f25Sb/oQ6M1YllVoVJ6YO6KtpxO+ybCtm/V29fJHjWpA+msdIur7MB7rdtO6auBbNuGesSZxgCoEXcv8W36tXQY4FDgmCUuyhJB1JQrkpxAijSXZMXSRxAqiJTDxr5j+UZbZ1noW5cwbQ6A6kXiTk0rkXC0LA7acqR0goJUkpNl+DJU+MLkKiBlFXLO74+XcouUyELMvU1fNbxCb+HRcK7eY7JPh6btjxdpbnO6p8bersG23N8JKCUhiVxjkaKl46lubAquVMrJw9nKMxmhMQzEqhhKkPmyPCc/j1MhtGuIlBZntdzFQNbLx9RMv+dRkD9/IrAcj9L+ZcZUTXmKkurMkhb3HdruDxv8ArVEE8PgE/wA6FAR5BIr7DfIHKPSYB+wQ4HgQ7gP2dh4HjVZ7rwo9qttrdpqWWIOw5DhZjIm56zV8zC43jFE1XMb7vL4rk/N2319YcP22lS94wjcLxITMnMUG5OZSuy7d2wayUU4Wh2r0+jPtZ+UueLf4d9jRxh4hmILPuMxzXZwanMPcsQbnHmaoNyzMAOGUJmaLiVqrd37ZsKz8G14i7HJzJQbiS2M2qybzW8H4dHjEbFvE8rJXm2/KqCWRmEcm/tmBsgJtalmmok6eXKzqoqvXaVlhWgiQq1qo0jZq0kZVJJ3JMnRxak1RkZCQwII/f/zx/o+aj0gg6I0R8g+DXfJnwqPD+nfjS7/bVSyTVmUzh86rhHPrPD5Bt7HcdV7nS8wwVxyJFTrS8W2r2ir3yfhmlVsU/JV2qNU6+anxsC4qVYWieIv/AIVez2yQ12kKNjCBxXmu1N8+umG4yuM15PMsRatx1BvmOchWSVtk1IrSeQGg1/Is6WCo+QH9goFecM6wrB1uOGo1v4bZEA89w7gPcBD69NfWldOx5RK3i6hUrGtOZmjqlj6o1qj1ePOqZczGuVKEY16DZmWOAGVM1io1ogZUwAZQxBOIcmHXcdNNKU0000pTTTTSlNNNNKU0000pTTTTSlNNNNKU0000pTTTTSlNNNNKU0000pTTTTSlNNNNKU0000pTTTTSlNNNNKU0000pTTTTSlNNNNKU0000pTTTTSlVz+KR4itL8LvarKbqb7ju1ZPr0VeaTR1qvTpaChZk7m6vHrNs/K9sQhHFbMjsjGXTMPmqeYQCCUoHOXWuZ/LadpJ3KBX+zPca1ZGOAOV2d4xG+dJJfWdFmvIx6bhQO3CZ3rYB7/lQ44G7T5QHLRVe8Oi4WWVq1MuJa9lHEUkwg73Xoi0QK0qNlVYRrhSGm2rxg6XauXwLE6kQVTQI4OksibhQuqdbmOXMSGAr6hbTapX3kUnMV2YvuLcNxDK0swhKrMOGEU3UxinHLTrctsZNj1sJN46cKtX7lqsrGoJvHG0Yji8+WsvvUu7eFWnmgSOT3O7NCsLMR1QjWp115J8HY8VIPE/TjM8us/vrK9xVnAbqa0j/AIhcyxPLLbx28kojSKCZmCrcxfA35J1obq04/wApM8D3eVkHA9zzbObgsFSuI5HJbA0dlvCDW24+t9QzZi+fxPknGuQk8cPMuNpWh2OLl4eZfJ+gjFBmKpCHXWUihkmD21DbFinwL92sBRI3bRMba88NMeyS81VapBZqtFytVdYG+Zrs1PmqNZcgr3YMXpKUKjvEMPW2DXxa0dVSBctqYi5im6ielrcZTahlSQdVHcPtR2uTE2dUrd3Y6Fi+e272Zq6OVNRuqhdcTp1NNwYSLJLIvpti7h1yOEXJG7xooBzwdy/4X+KDXVwvtRz3LYmyTBuWMozxjnGearnQWeNWkxESGOtwGPGbVtLMVWbxA0W9eVlAUzD5byfTcIK8/recKzlqodbZrhShkAt9vI0YKguIWVZWXyNmNX12G9D5/bkPpVzLjvZ5seuQgCtJ9xi3a6UxKQGl9opHce2Cygv7PVS6gkdhv6jVp8OjZTeqrb6Ra9vtInarfKhkWh26EfKWMW81VMt5scbj8hRDsSTyblIllze7WyU4dNlm8izsZyqxjtizTSZk5h/sC2cSc2vZnu3jGatnXyHTsp/OgsIdG0Nbtj+o1mgU2SjbO3dpWCJjq9R6dXajH1eLkmdRLXWBolWBVZvZBN184XAfjN+PH4Uy0ZF5s+dG5DAcSKLZSMz4V1l+phFpGFumFY3G1J+/t1bcGaCmES0nrdLxbIqaZlaksUh0R3EfDK+UubAfEKdV/HFmnFdqu4yZ9O0bYnzJNxaVatkwqAgZhi/LRQjqtbVlVhSbR8FOt6dcpJwp5MbXJESGVHVpYZYXaOWN43U6ZXVkZT+zKwDA/wCwKjpkZGKOrIynTKwKsD+xBAIP+xVnOLvDo25YTueBLDimNttRq23BllIMY4zVvVzuNOhJzKFKo+MlZxkpkSfuNihUadjSmuaRR6lW5uFo8FE2+0Lkriki6aum08teCmAwchz9wgICHbngQHgQHgQ7CHOvOvzr600000pTTTTSlNNNNKVpK/KS3iEpvXxPSJGSZx6Mrtdo7yCPItnSzD4wGbsmNHaCwsGL92U8gydgmgoLZVums0KgoZuVyZUdeWOlZA0qV5YF3kweMAYJ+RRcHDlSCRZuoF9Gtlx4KcUox08TYnOP03PlqqqHMc6ptiH5SGykT768Dza6IGgqhtYGeaLufStowlkRyBkl5Hou3ixiKn9TIxUGQjJMVjKqETRRQA7xZXWufV0Vna5ECAZwq6WTRIXkoqLruTlTIBh56QUVWOXkxhAOtQRMIByOp1w8qQcVxMsbDulnG8i+Ne4txL43oHbqFZifg/4Pnor6G23v8E47DIgMTY64A156Ce4vFduygFSVVWZd+N78nxXQJ2Dd12TWZmVK6S6EnLF8iA+mlot0QVI+XaCYPpN37cvmCACCjRyVywXAjpm4RT4sFU3ICRUiavICUSLppqgJPrL+UKYDFHv1FHsICICAhrPdjgloM3zdtrI7iIA67mNfxazd86iTLODpO5Osv0lRZTEYu7QVCXgzuCsnj1Bfy1oWfTVeaxDNwK0Q/VZrGRX6SIOWj1qJxayMe8RK4j5Niqcqah2j5sYqyIKppronFVq6TTdt3CSe9Y/KW9/BG4I79RpvBGtKTr51v+4H4P8Ag+N2uLSezlMTMrBgTG4P4zx7ADoQN7AO2U/HnWxsia23yx7hMmIK0nHMvRbokpWSRl8xZmP5u2OjZPp9ZI7r0fULbTLIzl1rkq7jpGnxEK5Bkk5gGKJJMbRW4mHkJWMrozns9Sj7c23KeHLJ3DD+ZsdXpePuO2WuXp8bJeHMmQ7h8gpN7bchMZMlgudOePY2UbxdeXk3V3hXTReEYyt0ZrNADtSJnbJ22fsnjtjIMFiOWD5muozfsXKRupJyyfNTIvGjhM3Jk3DZZJZMe6ahR554JJNONcC6aIAyekcNnaTpuCiIpvGDgHse9ICB00/VMHxSvGqhimJ5wCVym4bKLt1cPn+J2vITtltoZFiQQzRRGK5V1GmEjjcdxE41+Eke0P8AQ4/ug7nPpRa8iiunthjrS77PPY3CWptp0lkkaWeG5mgd47q3kLnoJbdJImA6SaJ7bKPgqfKrC26cru03xUpONpd7Sct6jUN2DtgjWoGYmkVwjkq9uIg0W7NhSLEZ2AMhyVGMo6sKujAleYarqovLK93pGjts+bIPGa6Lpq6RScN3DdVNZBdBZMqqKyKyRjpLIrJHIqiskc6SqRyKJnOmcph+Qpl7bvWt7MXJ2VezxVR3SxDIHJ7RNorNK/maGYNjNkUbg+RcrIsrdHdTZu9t7hgdVWNBJ1NGdRbZdSFtP8B35QVkHw9Lij4eniPr3D8BdfmS0vHt7sqS0lcts02kum2QpVl9Q5FxM4OceaRSHeIu3iuOiLIO4ZSRx8+IhAQNnePZHAXJgvYGQMSYpRtopkGvyjfyDrf5ISHT5I0d1UTkfGstxbJSYzLW5hmX8opV/KC5hP8ATNBIPDo36/3K21YAivpSaaw1jvcJhfKxyNqHkasTskchFBggkU4+yJpqJFWTUVrkqDGbBJRI5VElyMDt1kzFURWUSOQ5syAYBHgB7+/HsIB+kB7h+sNYGsBXnTTQRAPcePr7/YHuP6tKU016eYn/AAhP5xf69PMT/hCfzi/16Ur3016eYn/CE/nF/r08xP8AhCfzi/16Ur3016gcg+xyj9xgH3HgPr+se339te2lKaaaaUpppppSmmmmlKaaaaUpppppSmmvAGAeQAQEQHgeBAeB+wfsH79dNmci0Gu22mUGfulWhrxkULINBp8pPRjGz3UtOjUJi2qVWBcuU5OfSq8U6ayFhWi2zlKGaO2i0gduV038xSu56aaaUpppppSmmmmlKaaaaUpppppSmmmmlKaaaaUppr1E5S+5ih94gH9I68eYn/CE/nF/r0pXvpr08xP+EJ/OL/Xp5if8IT+cX+vSle+mvTzE/wCEJ/OL/Xr8iumx1lG5HCJ10SpnWRKqmZVIqwGFEyqYG6yFVAphSExQBQCmEgj0jwpVJ3j6ysZAbHK9ZJ9F4rWqxur2t2GzCwZJSDtKuxGTGryXVbtHBDtnDkjRNQGiLootV3h0G7kDoLHIbRvy2Uh5SDTK5dTSEnIZAuUbZ3MnHTnzmrlyuThzW35pyGdjFv5NCMjRY2VoWLhJGt2NKSrL+PbpxjRmx3cvlE6kuv4bVuh4VErlxN5cwyydoG8sFBikbYEg+XICyiRSpoGZoGXXMPlopCc5jFHgwaINztEK0scLDRbs8sjXabTYRNjCuST6UfIowLR3Y2KsgycLwqr81qfTbqSVh3a7EzpyYxDGVIqBJe4bJBFx0SNPHHMt9fgI7qNoIbRgwUnsGLEqND8lU/qBVzPp0kt48Cr3E8Ues1kCEZl7ui2tiPxXZcHtMfHVlkVT8GPTcddEZEoU6eZmUTRbwcfBA/bGMmqzna46ectFl0hKog8Sjjxj6KHrIspD+jVajwxWBt+y+U7LYLQhYMnuXGUHRK4nVWzy5Lpz8rHxjNudvBqx7qaTkG67ytgcfgqU61l2KLcyjA7YEfTKsuwuI3IjWtt7UOPJBGi25w/rYPLCoZlGT76IbJP1kmJiqNXSErBC6QloiVSQclbrkcJoHfMzTbBTFljoz0IiPn2tkXPGSEpLxCsao2IhMQ0hGIsXqaD9SMMzYOUZOOkE3cY7QUIDgWUw3OwRGMMsrveJzNpf28cIt3lljBiDKoTqDrYEpZXUnr51oEAb8ipuyKIkzfa2017E8ssdvciP2ods+5rcyzGMxyK0ZVwoAPQdh2Ghmql5MzKrktjV8DBPun1lXWJW6SLhMnqPQwiklOADUZqPhmEEZtGTM3LRcjJL0+Fik3B3AJNGRnAY2zttQwzuubT8cGP67tL3jwBHSxk2EOtRsP5idJI+tdQ9+oirZJrjK9LEOR8yutYaN6/JouAkZ+Fes1lbFFdCgmz6rSjGer05PQlhjFfPYTkNKuoOUaKimokoZu/hzMZAgLoqKIOEzvVEnLZRZq5Iu2WWRP2C23i3W6zSN0tc9KTVylpBKVkbK5XKnJrP26Lds0cEO0TbIMwZtWrRmybMUGrNizat2TJu3aopol9WSwVpnoltb+ztUjSELDcxFjkI5QQof3iAhjCkbQk71+XcEdY15N6d47lAvhkcZj7NZrRTaX9uH/itrkEbwXlijSCe3ZfEkbhiT4B0QyTR8Lz5RhvS8LfIERtO8Qmv5EzLt7gXTOHO0t6hpDPuFIT6LVjJY6tEo8Fvk7HrdsTrj6jOzTqPcxqbcaDc4dsiETIfSK24blcHbt8P0/PO3bJFbypiq8sAfV+2Vp0Kzc5ydJX0VKMVyoycBYoZwJmM/WZxownoGRTUYyrBq4J0j8uJzO4y3CUpLC+6GGQlq15SrWkZPiWjJne8TSzkxfJkoKQUKDdKJUWBM0rBqAlVpZADIS8a1P5E/FY52Vb495nyezdaiaPeBlfbJlF63krhRUJB22xfnujtV02BrhTl3QLhj/M9VZmK1F4siaWgH4JVy3tLDUHrU7uC+T8RvuOzbf8A6izkbrDdxqQjH9EkU79qXXnqT1cbKE61VQeY8HzPDLxYMjGJbWbZtL+FW+3nXz+JLAe3MAPyib8h5I2PNfXW01GXaDu8wPvmwBQtye3K5trpjPIEcLhmuJSNJyvTLToRnqbcYbzVV69cqtIGPGz8K4OfyVyJvGLh/Dvo2Seya1qFabTTTTSlNNNNKVrJeNFRYO1blsdO5NrHKuUMIRbVJZ2xVcLpJ/Pi5rFAqxIt8BUwMof6BVUzCYTDwUBExqWJzb7XXIA5ZLNzOW5wdNipRkS+VSXamBwRw0YzcKu8VWQFIFypx5TKCKQj6U5AFPV8ni7JipuNoH2fgbig7+3/AKZW/wDr5/Vz9WqqHCarWXjW6iRwMZ23MUhiimY5+kVGoFKcA484/lgmI/ndZBLyUwc89+dfUV6kcV9YeQcTxOVjGKssxDaW9rIrMsUDQWjEDszKCGdnH4hT8ADqa7I+gfEsPe+h/A7+VGF3JgLq5c6i6uYL++2uvaEhXrGoO5P1UnYIBrhlsCSXonjVhLt7nCOl3Ei5jlzkjZyPfOODLzUQ9MVw3ZySvAesCSZRsJMIlK2lQESNHbGLdyx3JVpqZrPRTyZgI0VVmkrHFCLslYQfODKqEdsXhXjc0O6eGOuVu6M/rqsiq4XrttQXevCurhYSAZt2zM7ti2dSTtEr79/EclCPaGAQagkkis2UTeOylM7OuY4qINTtCoFTOsooH42OgwdgQHzESNHYeaKKplRMmQ6xOhUyD9Y5HLU65R8pckisqm9T/IP5r0RjslZ49PfrMtsbmIsLzAQwtI0YkvIhIkas4XzICCsbjt+Q7t1YdCC2wN55N6fi6ie4xwluIFZip6xLITHtDLGLdwzLoMFmSKLvGOzrJD0eqIlIStHEwJ20yHuYAlKnMoeUUA56XK0U5milUIH5xmybtMeOopv8HXUp2MPDyLyIenQ9UyWFFQUVQXRPyQiqSzZbpKKrdwgokuioJCGOiqQTppnExCzuzhtoewiz2WrUcomqiJzu4VuiJEnRAEoKHjG5UyA1ffTLzEpJpMn3mECIbxTtZlXnUL7m1YOlGFmfEllwl6mpHtvhKrFP0l3q6UfCgpLJvkzedDO2KMbIuyNDoPemXKo2Oc7RRufpHwvlOI5baW+QxOQhurS5i7K0bq3WTqrqraPjsoPyRvxvz8wHmbSfFAmSKWcbCFCqlxrqeylVTvtOzHyQeoI8nz0xo5exDxvJMTlTdMlCuG6ol60uooCUyayXIea2XSOo2dtxECuGiy7cw9Cph12nJeDMZ74GFDrUpYRpee2sjG4kxpkaXjnPkT61gavVMSYvy44QLIjZ4ljLs3tAhMptxYzterzmJfWVjIRFdXbuehsVSryMaxlJI0YwcukEXz9JkrIqMGZjgVw5KyRAyzs6SQmFNEgCJj9AGASAYBynC5JUx7NMJejNyC4ilBFgvLs01UWhVFmir13Gslvy57JJpMkGj65S6wPysv7kQkDV4EVYtxteUwlnl8fLY5GJZkcFrcoSrxThSsUkcvQ9GDEdupHZNqVcELUTc94xYcvx32JsXlu4VZ7e5dlgFs2t6Nz0kO2bw0SKzaJ7KQdi8P5NB4nVJ3BJNvCe3/wNatuS8dMpaM2m3vIDJk9tkjAU8rsbBt/cWs5gnkLNj1nHyEtjF81l/UOqdHzFQRdI/NOrt5Hc0/Fut1O4VwfuCyZRWpDEM3p9+VQzpjsiBB6itUo6+OC36Ma/4JUq9kuIImkIlTIH1/KG3bYSt9fnY3xHNoaydRf45t9TuWT08bJN4mUw7kllNsXVRzVFwseHl1+uWOyJx5bEikzax1ZyAoKSjVKEtbEiH08vCF8RCreJvsZxNuVjfh0dflmqlEznUI84eXS81VFszb3SLRbidRRrDTnqGF2qSSyqqwVG0QpF1BdpOikqnlcZdYi+nsbuP25oHKn/ALXX5WRD+sci/kh/Y6+Qaozk8beYi+uMdfwvBdW0hjkR1K70fDr2A7RuPyRgNMpBBqQ5cibpaGIFyBg+t5ZiU/UHVs23u4NmE95KYdRFnOJ8wO62ZDsAmFtX8q296oA9DZosqBSHrd8XLc5ia4bCsu1dGdeU2/fHsNSKWOcsVqexjcHnw7LtKlVCt6rkKMgwt0e19H6h8aAGxwTlmiodddwwFQTXqCACHAhyA+4D3DVS3jdsGL7w4c1N3zJm+b/H8PG9M+aN3rYDFy3TQKcGztJZADlAwgBgT6uBEOeBEBxteCoF1Hwk9qUrT6XMSi+bCyM5S6hNvRHIEA2Kq9mKzFSb1ZFAccFBNFR07WOkmmApppmKmmIkKGuwfuQm0T/KM1/tHr//AA61LDGuE65CY7x6vjqwXjFKy+PqE6UZUmyrOags6Xp0Iqss5xxdUbbQfyqpzKLBEwEIsoYxxK6SMbrDKtca5SjpQrO0zVEtteFs4Ek/GQc5Srck7IBPSJP64SQtNTkEHH5Qrh9GS1bM2MBDowjgigppKVX1+5CbRP8AKM1/tHr/APw60/chNon+UZr/AGj1/wD4datF00pVUk5sIw1tQjlNxmDrZm2p5WxU6hJKozJ8gwL+NL85bTXqNYo6bhD0FBlPQ0zVbNNRbyOfiKZPVJyDJRnKsWD9rsnEOABwIH7GOAfk1PYDmAvH0O4dPHA/WHA8jzzqpbcwADg68AIAIC6xyAgIAICA5hxyAgID2EBARAQHsIDwPbWsbZadM3/OduqlZrU9fMhZH3NbiaxXooMgt6skuvB2mHnkGpHEo3ZM/UOvnPbpiYnbLbhIk2jISBg4tMgkKVSt93zC/Yf/AEan+7ryByj/AIwf5xTFD7uTAAc/o99aQX7n9u5/6Mkz/wB4/G39ttZVwpt58R3bPkaKy9grArqFu8S0XiXcXYM/Yzm6feao9k4Sam6DaYhe+oot2Fnd1qGaEtjIBsdN6V5KBOfz5GPklK3KeQD3ENOQ+0P5daw+9/xGdyvz+xM9wxki57earM4IuFnvFKeU/FV2nIzIONst5ixjdmCIKsLY1nnbq0Y7Y16tumF8iKuEGopZn6nqHBm6cV8c+KfvbqFuqt6ksvZCz1UI5yq7k8bS+BKDX6zkeFkY55HpIschU561cwCjJZ60tMHYo9xJRj11Dto182dwss6VTUrcgEQKHIiAAHuIjwAfrHXgDFN+aYpuPfgQHj+TVYmds42rd74eGRsj7G5K8mydKRdMewteip0mKMt1aXh7PRbnecb2F09kmKlDyClQFZGNmIY8u3eCSVTbRckcJSOfK0Z7M/Etz3gvKsga/wBsz9uawxJS9Sq2YpHIDS0ykniB42Wk4t7dKK3l3tnna+2YySV3kLrjmzPAt1gqOPmEhDRcdPJGZzalbhOuEsdlrtOgpW0W2ehavWoNmtIzVhsUqwhIOHj24AK76UlpNw1j49mgAgKzp24RQTAQE6hQ1xGP8g0vKlNreQseWOLttMt8Own65YIdyVywlImTbJO2TtEwcKJCogsmKrZwmi7aKids8QQcpKok4jL+JKFnfGlyxFlCDNY6DfYVaAtEKSUloVR/GLqormSRl4J7HTEauRdsgsg9jXzV23WSIoisUwd1K7PVLfVb3AR9rpNlgLhV5Yi6kVZKvMxthgJRNs6XYuVI6Zh3T2NfEbvWzlmuZq6VKi6brt1RKskoQvYRARAQAekRAQAQ45ARD3Dnt29+/bWqxXb7njwPM1uanlt+8yHsNuzmPZVObYx10WeNpR20VnLRdWYrQ9sgoPK8MzrmU8jZcoTm/wAb+HdedhrXjuMj7YjMVtfZ3oF/p2UadAX6gWOGttPtDAslBWGAkGsrEyLUTmRUFu+ZLOGyirV0kuxfIlVFVjINnTB0VJ22XRIpVWOYMz538PXN9wy3m652vM2wLMVkJKWC9y6MU4tGx+3TMrHQ7BCRSh46us3O1ZZBxHxEQRlGX/LyeQZghn7ka2motqHm6yW3QbLs3Zd3UYrxMfeZkrdnMQtU26Z1Tj31rndutEjkKItQdl448Qbx1CreH8gX55Z7xYsyNb5haKCoNb/fs1XybyZQsWRFu2LZuEirHEyUFOMGsnEy7F3GyLB4kCzZ2xfN1GrtssmPHUku3VUSOACU3SYekxTcGCh251NPwtI2443yNBDkTwdcqQk5TrDFP27mXdbLQyVMHrMvTZdgzMyWk9otmY2v4DHR8Uxv+W0LzYXS0vII1dNNdNSrKtkm8+m73ccWfIdHqVyr0PT7y8x2pOz8X5NLyPIREFBSr/IWD7R5vGTMHTTqZVa49yogxio6+sY9aaimKbFVIRmbrV4ztt8yf4fmX5PfFhPIUPOUJpHyEfU7dljJNnj9suCds8FiWt1Ov0XcAsxSsuQ5Gh4ySjVa9ttxBtxYz9k3F5tuePbDkCCir1j+dumRLr9om+LGW7NKaprSOmMd7icX0HDFu3I7dLO3kFrpt0smaqeN0rWO73NkiWNdd25owbvPikXGOBlIgyBELJEwEodWKQUqTVJyrjHJS083x3kSi3xerPwi7MjS7fXbUpXZMyjpIkdPEgJKQNDvzqMnhCs5IGzgx2johUxM3WAnftaxe6bbBmLwtM1qb0tnPkpbcHss+sW4LHz1bJ1nXh6zHRjWfmISyiyaZPkpHGLskFegoVsRr0GvgLJWX3kw8eyuPH0sxjLyNn28DEm9DEkblHF0u2Fcii0VdqUvIMHVnx5bGD19FS9bsbZkuoYpUZaKlEYKdKknE2+KZksVfVdxLtBbSlSsEQAORHgA9xHsGvUDkMPBTFMPvwBgEePt4AdYJ3RwmULLtwznXsKPZSNy7OYpvMVjV/CTzSrTLS7P68+bVxeIsr5RFlX5ROTUbiwmnayLaMdeU8WWRTRMoXU527+INu828ZmO/s0zuW3EhBRcfC53wPfpCxTZaYL5JhKSCFMf2SbtL6v3ypWKw1mmRtjsbxlWMlsW1rLFonZuoGxtFK3PtNYtw5mjGWfsfwOUMR26OutIsjcy8XMx5XLcRMkoZFyzkI1+g1lIaUZrkOi+h5dmylGKpRTdNEjcc9lv0q+g6NcpqMVKhIxFVscmwWMmRYqT2PhXzxqqZJUDJqlTcIpnFM5RIcC9JwEoiAqV2zkPtD+UNedaTkP4l+/NzCVBzIbusgGmbTAjLt4qEwhhm0OzItZazV5VY5ka5Ujunzt1TJyeeMIOAdRtciHcU2eSyzhXk1ofh3eKlb5S4o4M3dTdyn3duly/g0z3Y8Wx+OIf4vMy0kk3xlkNCGkFYKHcFOtVYLHFqQZMy3idnFa3ItWkyzYOZpSth8RAA5H+v9QAHcR/QHfXr5hfsP8A6NT/AHdRx3iKHDaLulVRWXbqk25ZwOku2XWaOm6pMY2kSqoOW50nDVwicAMksgomugqUqiRyKFKYNJXF2HbnmKbjKRijG89kS3J43aZFnUwynB01s2i3U00YrrNm8yFVh4+NjlbJWa/ERLaQsM47I0kJqWfAKg6Urf48wv2H/wBGp/u689QCA8cgPA+5TFH9XUAc8fo9taQX7n9u5/6Mkz/3j8bf221K/aLBb/8AYre39/itvsw7wnJpllc+0J5m3FdqVf1OtNWrh5eaGlIZIYBD36kVJjZ1IqHaqpQ+QVpROKsvlOmMJLR6lZAyntexhuo8VLfFWcqK24sXUK1iuyxXzRm4uCeqSj/H+F4A3xB/I1ywuHLBrHecVjGICzZNnLt488pRy5UPrKY+EJtDDuLnNYfpHI9f+v8A/HX1jrnMOT7G1+KZvmtcYVwSMtWGNvlpjCO0youyxllx/guejiu0SqKlRdlYyLcrpEqqpUnAKJkVUKUFDWH2CDQscU5h3MjYItu7MgKzur2CUq8yBEViLCg3nIRw0lWSLkCeQ79C6bLrNjqIFcJAcTaUqruyeFNsipsceYuNpybUIhMonNK2zMVKrEYBQDnkJCeose0P27gBFjCb6gEdYS/Ei8PWVMdHHKe7DNzknJQDDCby4woqewFUvr3FtexigQR7eepeASKH0hMJQ1bvB4Ow9XpEk3H42qTiwkHq+c9hjRutsE/PPmfOy8LWSylU6h6utOVIIG7hxwGsrqKqrFIVZVVYqYAVMqyh1SplD2KmChjAQoB2ApAAoB2AADSlUXfuW1Zs48VnDtyxmzP+ZLZp3LVqwzJC/wCCoNDw3iywNiKFAQEWrzJDcQEOg5ihyITr8Pnabe8Xzec9vH4z2U0cbY/Piy0QcHRYmkU521d5SirtbLJFFvS1cmMjvIMk56l3GNpCxqKxJXKrSHPFxnkR7ecev5drP/OR3X/9n9sX+wt60pUOfFK2g4Jj9pkms7rBrLMOsj49F1Y8iz1iyBMuj/E3Zzcr2hSxokUUEBDhvGoplKJhKZECh060D7a9QTIeXCRtZjOCgBE2kHVyJlHgOkCN3kLHqHKAiPBSdJuADpHsOtvvxXA52ouu/H/KRj/uP/Xn4a1pXZDotPMAAMXp5MHt9HuHIhxwIDwI/YIhxwIc6pP6+/UBzz0t9RrDBcbvYosdcYPHXr2soPWS4uLu/jkPbYG2S3j8aOtfvojqL9G/EsTmvSi9vbpCL08yy9tHMscTERx47COEPZQ7DtK517ij9dA/MC7Hhq4twdwbeXibBEEj4yHVpsvAAxbsY+DeyUpEt40kP6icrTlm+nJd22lYpnHdZpd/6tw9jni7ZWLNhxdMVpaQTSiJCUgJgEiz9RcHSGcUQjlTuCPq3JsyjGTsnA9bpeKmIMTSDRNd21sdaaRT+VRXthkINrISib2QSFVpHw9dai2A3lLO5BeIK6bNCKCU5kCEbFFd26ITqRaIJpNxBdy34/STqcLNsztX8ammRUhOoqqjqTbCKQgKJlhd+slkTICAGRdpuZQGZwBVrF+YUpybxw36xnwd/YW/MIoIxdrEXnhJUps9S0iFOqgOCoYyKxZWYLoebDZf0+gvbJmxyNMOitcIsUUa+8Y45AYykoaWVU9qQNFb+6qtCrTN0YClqiUmmuJgzK0ISdxgJ9ZCsw85S5slenqfapp2RjVZaz16bhpTrgnkm4bR0s1K3ds3nLplXLGaaRaovcX3CsRUSYruEmV56CWk5eIbyD6FUrUoD2IM1MsR/BnlJr0AuWr1m/aEJLPg8tVZs5Mg9ZOUAs0yrt/lI96NwpUrJV6zNCKOmc9FvHLd2oURL1DIvo9RQ0qzVOmRM06go5lG5yJBPlnjJHJE1wW2DkY6kzUO5bLNJatXFg+eNDlL1ox03BrRZHXWQ5klG3r4+MRSXbmVaqpybBZFdRu7bKKdFeA8+wnO7S0ymDyUN1BcCJZEWVX6Fh8kA7TRK766B12I3o1A+Ww11h57hp3mkjAiT2GLaLBiCxXr0XR6Rq8ZRW0WkjBaMtiRVA3qQ8sAEO3bkR7cCA8/q57D2/VzrJib+iZSo34DM3Qy1mpTp2gaMRQfpR9kg5EpBZxdhx7PvCKM4e8w6C3w1COkhThbnDFZQbs67luaJn8OoPHaKRxUDjj2Afft2+znkPq/XxrmKdY39cs7OzpwVbsRmCMikjF2yMWlocF38e6j0ZT0yD2PVLLQ53ISkC9Bx0xky1ZSAt3BmxUhla5xkF7bXFrfww3Nq0bRNHJ/8jAAppvBjOyNMCGXwysD5MccnxON5JiZsbeWTXInYSrEdKY3A8NHKTuJxsfkP+R81ITwt/EGyV4CG+hKiX21yGSNie4dOuTF1ViWzszGSpMuotGVbcDT64dRZWEyRjhVJ7A5FqSIqOpqNiZ6nuPXumFImWH1T6la65eqvXbpUJuKstUtsHE2Ws2ODfIScJP16ej28rCTcPItTqNn8XLRjtrIR7xuc6Llo4SVIYQNr5KWSsAst3mFkcc1Z+olmLGj6atWHmNjkW5nkyWwLkXsuMXk8uRo3eNrO6TZOalZFkmKSFmZRsXYm8SpLuZSQ2QvkjPigz1hrtz8KjcJISbDIuE0bLa9uqVsByynRo0VKHTyfhN63kgSeIzGLJ5day1yGXKtItarJ2mHKkziqI1QJVzlvH34/lri1UO1o7GWynbZ923fRUFtaMkRPtyjwewDf3CqLcq47d8YzV5i7qGaNY5Ga1eZdGa1Y7ikBHhj0ID6+GB8DxW8ZppprV61ymmmmlKqi344tq93yTXJSYalGQa0VmxbvDNm6xUkU56aXIU4qpnUAgLLnMPQCoF6uRRU5EBrHtO32FlAWYSQShlUhMZs/F2k4coeYYygGbuPTIqGbGEQVIkoddt1GA6CROoxhug3Vxpn1tiDFADGLV0A45+l2k5EQ7dxDnkO4cd/f6g1Cp4zUQ/JOESKkKJgKVdMDlDkeowJnDpWb8iPPCRyFMPJgDkR54E/VFn89i/qB9RpLPJXNoLTkSvasqrPb9f4fYExzQOG3H2HZZIx2Qdh7Tkq6dAvRPmmUxvCuP2ttfzatrRo4rcXLRyW2rmdt2pBPQMHYSxsDE4cglNkSVJW3A9pqrlZ8xdDYGZlBMoqoKhZEOvt++BXMYq6pgAoFEVU1FBACIoqCIF1ixRsukqdFVFVFVMwkUSWTOkqmYB4EqiSgFOQwfWUxQEPs1cNY4Jg6ZCuRPygUBwiZI/SsUBKmU6hS+YUQXbKkOUqibgp+ORTUFYhiDqGd7qQx66sjHESWathHzmyzZs9UjOBHoM0WeIOHJI9TnhuBlDFZq/vYwhw3OrHVh6pyXcpj5BboL8RLL91Z7mhu4WCus/tTvHKG6N2lSSQugHboUExjuVwn1Ju8rGlrfpDM4JhhnlC2TCUN0W3na2imt+xZekTxwRxyE9TIZGiV4gS9fbSkZ6OSSS6DJ8NllSmD03UU4EKY3lmEzA4GMUQAigswOougmq1O+j5CsHcnhJnGEkJP0zhlGnfPZB+6YNhXdV+SdFSbSM2MeU/91It4Zo0G1xaKoPUlGaVpg3TlUs8lKW4XV6urKFZKKqK/D2rVuKipzKHVUUSK9WOJj8j0Cu7VIkQPoERImUgAXWGLxAIWCFdIqpEUUSSKiJTJAsVVuqBWrI6iZvoreWoJIVwkYOl22dwjZX97NVwP0a+kT19zfBOR2XHMxfzTYHJzIluk77+0LEbjXsWUKmm6AMQoUjfUqo9vM+KRZzEJlo7dILqRFmljhO1Ik7e1MH6IQXVwX3GdvIpZDudzrvyNKscA8K5ftCuI1yYQYzrAwv4N+TuIGYyyJfTnOYAETNF/SyTcwCk9YtXCZ0ScAsdQ7wxRIoKJVQS87yz+V5xyHVBEVeOgFRRTOqCQm6xSTMcpRIUTBLa2UhzT7tNVNBRVGIuEZMRcQQyyno1Xb9FZOFavAE4JOF46xtWkW3eLlM4KmdhKkOkV4mJopHRKR6J1m5inKYeQMUSqJ8m4OmoUw/RVIPJDEEOSGKYhgAQ413ZwuZjzFul4vtMslrG0bx+FZZACrfsNed/7Hj96w31hJZSfbdz/wCsGLupHZHJ2CNnyrIy77fPnS70M4YUsl6xhY22SKtCsLbGOGNhrtsxxLx0jMwGXceOWAR+RsbWmHbMHDCWrtlrr55Gu4166QlDfl5SvIKSMSioFongLZ5gfDU8aDL3h9sJ+WLte3tV+m2zByVodKGeVy1zuP22YsEMppdcxwCyOKPZrLhOzrkbtXNjuMdV11wKVu3SJUdSch2KkvWC0MMQ5CNlyzcW3noVhNNGEsRLyQkWPqiFfRjtVApEF3MS+YOFkiJgdUVEklE8A+Ib86cZZ521eI9hx9MxUldJGnWn1LiXmrAljrcbt+eQKy0JHyMq9eSLWCeMImsT9ZiHT5QzRsSdjWg/D2CZCRx6p2HvWlhfx2w727tBPchh2McvmJJECAlA4/BmZirOwGwfFW/XzC3nXH5prGzNul1LaLkbZ3FwIJI1kt7W9hMYRgsizNBcCZ/l4tINCvsaAICACHsIAIfcPfVUXjY/+rnzT/8APsQf/tymandtnzjWtzO3nCO4anHTGr5uxTQcqQiZFgXFoxvdYjbGWOWOHs6i1pBaMdpm4Ok5ZqpHADkMAQn8Zmv2OyeHfnRlVq1Y7ZJMlsd2BxEVSCk7JNBCVrI9XnbDKIw8O3dyTlnBwbB/MSqrZsr6KLZO3yxSt2ypywdVaK57HH97fG3/ANN8ef7FQWu5awxjrJeMy45xyQ2TsYgYmOcfEMA5Ho/YxaXBAIf+f/qEBDXcfwm4x/jPxj+0ijf2g0pXdtNYHytmIIPHlplsNzmCsh5OYsUFahS7nnil0Cr2CQNIsknLSYuKT2XUgm6MUpIPUnIRzgF3bVsxN5RHRl0sZtc25jeNWp1g2cwrtRo2O7Qebnm0qi1eHQTM6bpLRDMRdooODKpJL8IGcJJkW8tITimVSsn7l/7x94/63jj37f8AvhxzrX/28uW7rf7i0zZwi5K33ybsWS4oKprA3es2UOR4yX8sxvJeNDmAjpqp0rtzmAqyZDCADaTuRyJmeWwhfmX4QNkyQOwpKCbKEyFcrTOuVlMo0QrRCOZozMYDpyd0KPKKRVVVkirEQICwp8ZP3CeG5uqyDuLxnvBxdkLavX8yUW0rSdmp73H2Y4Ki5Pauq2Sppy9im1MkXtWDtNXjWMeSPcVWjQ/zuRTBncJNwlHxCjRSptk/ML/ml/oDWHcuUPK13cY+WxdneVwkNXtgzVubR+PKZf2mS4EzVNBGmzIW4AXrkcm7KZ6eXraiMwr5p0BOBCJGJ1RnhHxRxIcsnObNgEQEEzQb7IDMUe3Ad5zGVjItwP1nSJyHcQ+rWVoLGe+OPi45rOUPbTZJZsmUr+dDPl+r3xNcFjnFyEJGbWFo+O/JiRIG7VZRL8kCgnE6h9KVUTknw9t025fb1HZPxi7wnbsrVC4bpsfNyTc7fscFvFEd7qc1yViq60ULqcx5A2NexScxNVe8rMlzwKDgYF9HSTF2qshR3IX2wksNljLzh7PTS4xVoxHi0akEg+TXrliDGkhXnEBLRLBg+u7Obdy1Gq8LWYaXiajXYqCNNTaKL71kevJ78W1fGVzxJheKpuQ/mwFvUueXrlMt6dLSk/W2BsmZfveSGcVHTU1X6tJSoRUda2ka7fOa9Eg4fNnR0WhG4pGPBfxBfDdjtwM9Uc/4XQj67nmh3zG9yn4UFkYOuZzhKFYFHydctboFm8TEXVlGysynU8pykVY5eIbGNWHTVzAvw+HKVrf7T9x2Y9pW55/H4nqDaEuazeqOM2YsyflGGq9ayLTXpnjCMZupq/OafGwmQYF3Y2c5HzjJ+eylVgoel2hA9UdKoxtu28LZHjDfNjij769pdfbSctZmtSypkrBkanTY2QzTEPgQXm1X0nXbMxjqbn9KpPpuBm7h875NxZYRNzTWjssmtDzrSf8AJNtzkw4IMzs/ZzbNN+m9TaTO4fFMsiXyXIOEhTbyVPdoJqk/9kchQFI/chy8AbXd9v8AsUxJXsAYPq+TcSUuDypTsbVCFtc/jmQkanOIWWOi0CShWmQMer0qek/Ie+amSWKs3O8EnqfLJ1gUFK1qdgHiDXHY3Kw6d4Ug2m2u7LEdX7EyEPm9pa8VzjnI1tr9tyjUa3amV5a1J06s7DJtqyXjCWtba32auUqFloqGi7OZZjYtyfHeRKTlil1vImOrLE2+lW6IYztcscI6I8jZSLkW5HTRygqQeohjJKFBdsuVJ2zXBRq8QbuklUSUA+Id4QE6swuO5TZhdL+2zkjFuD3Gg2WcjbopliFWnISUm1IC4XZRrYKtksY2PkUnN0eWmRn7bAuH1NM/buJNm+bx08Ka5708B5dncaBAXHOWJMiu7rdC134ZcKqWvptIOOtvz6j08qmbR2KrbdrpcJqKvVFkJ2QC2S8cwlI4Il/FzHxFStm3MOGcb56okrjjKlZa2mqSxmq6jRRw8jn7GQj3KT2MmIKdil2c3XJ6KeoIvIqfgX8fMRjlMq7J4ifnq1radb9xPgnZ4+YmTV8hZ12a5Pl7JYXGSpuwGWZwiy7Ba2zlpiyzcM4bwuXIWOqmUb3lTHKuTHrjPsha4250GLZW9GYrzq/kdzcpG+WS1bbNzEAfq6V147HcbkFknwACY6Z8b2i0P1kwNyUBJFgofjqIiJe+sUZszBspz3Q5rEe4Qko0qNlRQRlIfLONcyYlO1ctjBIs38daLFUaqvXpeJcNCP2dggZ9lIRLhAiqEggb89Spn4/yBTMqUyvZBx5ZoS40y1R6cnAWSuybKYhpRocx0znZyMeu5ZrmbOU12TxNJY52b5s5ZOATct1kic5NwkVY4iTgZxg2k4iZj30VJsHafmNnsdJNVWT9muTkBMi6aLrN1ilMUTJqGADFHgQ1JMZbm5fwdMwSEDOZloOeNhdwFgSvSFEs7adew7g0Uadsl5KkgSWjqzlWAhaleL1laiv7yBM8yt/irhS2TG6JS8CvtbY4yXQsu0yByFjO4Vm+UqzMU5CDtNPnYuywEm2UMdMx2ctCu3zBYUF01mrkhHBjN3aC7ZUCqoqFKpVMjtjM+EXYTR80xeXbwsLXYkXrYzpi2nHuwm1S9rilISPTjSItjL7Xlpt1Hs6hEQFfyBlOJyTNDMS8y1r6BXLfo24yUl/DKxdgqJ2wKs8V7Y2mQJ3KG4neleI/GWcZSZhrVMZjvchjzITJ9MVbLWTL1lPMtvxnXqM9oyF4yzlhxbpqrwsxW70xLZ7DfxNwkRZoeVgJxi1lYaajZCHlo52QFWz6NlGizCRZOCAICZB2zcLtlyAYomSUOXkBHkNe/MGB8deHwuxp+eMWVXPPhKPLBJS1Yj7vUEL1I+Hjeb0hJY98muRiTX1CW3GXgb7K0Okw9IqttytWJ+3zcjMWxtX1ActlKt42wbmMe7y8X2eaZUm4U2XqtqlMT5rwrmCtxzC8YsyKzrlbs01jTIEWze2GqPpRKq3WrS654GbsMA9jp9qmV8o4I+ZtaNt2O2jN3hb5kd73Nn5bvcsFCjXoW9YNJarNI1yh0WvIsJGWrk6yk4XIjk+IPhFdssXjuysDU9Pbld8pv5cVZPH7yUj2fF5H28582FbmdvmR9s1sxWvtWs2aHWOdvGNE7KrivGNVsu4LH9iQnKZuCyVWaPdXgYXdWymyOV5fIs9JZfytuU3T3DBVLjW+LV63NWi33jbTN3GEN8WJhsNIsePLXJNIuLjcrUmq2uOyZXqpY5Js7ay8IxtqMUwr+S6YWdibPXoHJNYZvaJeVq1OhBv3KsXLM2Kldl2o7sMW7usaJXzHUrH/ABOLevK7kGkFnIKasGObnEPn0RN1mxfAZGSaCRKVipMsBOt1jQ9whm6Fkrrh7DvUHAwV8TbwxYLdfCvsq4naxlaz7GljHc6mkwhWzXOkPWo2TYQ9UtUi6UiAbXaIaSB2GLcjTU0Zrj5dQE3TRxCmMVnBTc/tVyz4V2XS7y9mAMY/bci5cSGasW+XerCtD1KMiI6UeVKZKlF5EfucVOG9OkYLHNoRTrQbdLnlOVlQO+x9IyjGPuL20+IptX3K4ZZZegct47q6bVy8grzUrPkCltLJjy4Q79/DzNZsrNOdXMioSTiZE0DJFD0dqg02ljhRXin7dYVK1Z9p28TK+wvJM/aI+pM6fieTul6jcs7W5IMyx9qlZeAj6myNP15rYV8lVutZQgvimM6FGW6wz8BXsp16EsJGSJ49WuWpjuLYmy/h3dXh+MyHiq3xeQ8X5Er65WU1EndtQdRssyO3dM37F0RnMwEsm2cmTfQ0u1j5qLUUKR40bLdIapT8Q3C+DN2Kr3OG0mPuFw3aVqAsEPHyuK8OXOfq+WEpCmTlNjYa2ZIWi6njSIvEE1l0UsYZYt1/XQxsdmRIzReEMok2gz4deXc47ddwmLqnHUbfPZZbPyQzufcPTe3qYkcM0yYjKrcGks7Tym9yXIxFSzDVXVDolPNITAGZXOgJMDLqis4g101K6D4gexO77D5Gx2Worzc5tif45WqlCunn2p7MUCWms3xdxQxflebK/nHj2EXTlXDOFyZapitV+xsyNqLMMvjgtVp+LtE26ZHzq/v9ZxPiC1ZUj8euK7C217KZqqkL1vZZCTNFvHzOzpU6PVkJR/U5qeIyr8U5jqyARTdKSUkESKk3BchXDJmW6fP0Sb2SWC4Uq2Ri0ROwWUcgYYhoCVYuQKIt5GJUl7i7OQihSLJmVhlVGrpFF02L6hFBQtTWCNmu/baFfc5mxNgDEWUcd5nnabaq+a+7uZtpbscM4I+QiOKVOyr7D0tI5Gdx4Wxr8NtjmWjV3kY3RYyAneNTvVlK/jxhnjdPivaXnvbJvIx1KV+Bk9s2eK9ttyW7vGN7a+ViqPgrIMvJ42yS/hby/mH7yqU+Hr5KlkBaIcSF2Vcyre3KoTbFCUnK5PDJzvh+n7iZF1NX+FUK72mx0ezb11GXu0i+fnvuMHKbNlFUeLskm6cHQbLqlIk0MAkSOPUHbm43DWwu2T+5+q50zXtAxFSp+VuGQb5mi2MszSWVoG4yEjjF7RaSzjqDZfiLZnItXcgZxKOWDKBhPSoip8OVcdADk1Dw15Pbxuetm4PZ1CY9b1zKVEsVXu+Hbnd57GlWp9gkLLj6xpWXHMpV8ZZNkjxk+rVZYJ2lP04iuV165Yu6cg1aO5KOSUrmWuc3s8JRpOCtwVoQUDlGUmaJGYlr6gDx0qBJZls9FlDIjzyCjWuPDCUBMVI/KZVP7rg+vEvh3NLi2UmPqBS4nyWEczYXNO8PlCmx5axdfF3EbWoaHjlUeG3kIxsjOkWBVcVXKAIJC5yN+DzebyJvwT7auofcw7lcmCYfvEdqfI/rHUZc37Cc153m1rvccFbeV8issVXrFNWs6G8LcHFM4SEu0fMJLg5rcDt2ioGX8mTljv1HEgwXkTIlMzReJJAgVJSoz7VElT+INuh6EVjcbVNoHPSioYQ4whtwKPIAUR7CHH38B9mrXBRXL+cguX/ORUD+XkoapMxztXxniTxENzdMyi1sFHhW+3jb8nTbFO5PyDjmu31Su0nDlOtU1RLRLW2vhcYtjaoaeZPkI96/NW3INmUg0i1hZo6neGJ9rRP/ACGWZBp7gHot5d7ZdIDx2L6fL5eOOPo8cCXuIdx0pUwRAS/nAIfeAh/Tr0E5A9zlD7zB/XqJaOOdvDYeW2f7o2HkRDyt8WQDgHPHHSVzltyQoFAOCgBQAA+rXIJ1LCiJgMludyMmAc8EDezPKphyPPZN1fHBO3sHUA/R+j7aUqUgGKb80xR+4QH+jX8+1n/nI7r/APs/ti/2FvWsQVeWxVVFl1UM9p2IF24N/IvO4eBuTVEAUIoC7ZKXsBzIPPoeX6kqgnFA6iQgIG5DJe0Ocg5/cRuxeQE7B2BmSE2yIHe1+aip1kRclDvBjoHeRDx62IuQpyGOgZUFiFOQxyFA5RFSsqb4aVGX/BjqvSxUztFLZV3ggqiVYAVaOHB0hKUxTdJgE3ZQodZBERKPOqM7Dt4iGhDMvLSFkqU/kmQaswIBg4AwkcJkYSCS5B6QVIqqYCfR6kFCCTr2EdyTYXeNHCIByYZuFMAdvcqy3cAH34//ALwPsNXkrHnSOqi6blWQObrOmqH0ee5Oshy/lEVOkRAFUxAe4FUKoT6GuNP18ZfLY/1osUsr2S0iHC8JLE6qZI1nGRzDH3oz3DxMAVcKocbV9S9TGbp/TjzDJ4Pi9zY2d9JHF/HLy4NosojLO9tj19+BidJOOi/kfBVem033FUN12/2uKRKeGeoy0e28lUqCzdNGTKgyQVaskVnhU0wdIMWqqrdoLhNBNFE/li4OmRIiWFV20gyUFq+brtHSfAKt1SGIcvI8cgBg7pm9ynIIpn90zmDuNzbyEaPklCtymFZJFRT0qxiHUMVEBOoo0ckBLzFE0wFcyBkkjgRNQUTqCXoCJ+SqE0eHMs1YtF3SHnK+lVQE6TsvAmVO2BA6CzV6QAMqqVoskjIIgoZVBR0l5jirtn6q3l61rBymFJZva6WWStdyQXKw9VMRiZmmSVOwLRhfc2QfZVpYle8nCfU6adhYX8cMsSuGd2SO0uoHkA1JOUAtp0c6BmZYwSNtMYlkkSCqLIy6SoCgCyRhFVRucOkFDgXgFkj9JvTugL9EjkCG5IHlOUnbUyjVSGmfsGs5FBewQTJFwuWPeNHbJUStGc7COXBFpGAfrAfmPAzwqTpi+KoY1UsqbOZTMpEOVFXFi1lMnHQqiYM2DZZaSRQS9KzRbnTI1aqKux88CncKlOZ2yIPmuFC8k6unngwYgetQfpqNDlIYHZigj1mAiRHw/kkiKiP0SN5FI5o12fgQS85o+OU3w1IAuT9NHr1n/Tzk2Puor6STi2TmgVrSZ31GJHCl0RmPRX/Errx+aNpduK3fknHrfleMurn7ZILuAugKMshuI1SJnLMqqC6ktogM245I/wCawiA1xL3SpetP1BKg5Wg13TlONl12pm5HBUFhSWYSRekpI2wxioCznIRfyXLB+kqBElGSjR046u8WFi1STAvSZTgTCAAPA9+3P6Ps+ztx9ljm42nztGmV7ZUX8hGpP0miMy3aLKoN5RsXhOKUmGXUZpIlRMBK9JN5Fu5IkUYMqwKKyDo2oKZGim6FkkSM0iJxL9Ys1B+SXpRNCzQDIRhW4f4JG7dx6Eyfu3XZrtT8KNlAD+hDhnLrPlmJxmRt3iltbm3S4V42JDF1QgMD+3YHz86/T4FVMriZ8XPcx/kZH2iEj4MbIsi6I0rdW2CD+W99QSQOCgFZwJCOVhnoMJNt6p63kTyKEQhGosma7148dyblRJszZIMm6x3ijk4NTNwOguRUivlHzTusyRJbfb3s28W/Aii0LuIw3l6l0LPbddk3hkMm2WMqik7UrhJpwyj6NfI5JocPkPDGTZmKcqRdtawsZLgPxyVnjmwkxWVj1EHiHpVTN03SCrZ8n6hk6ZPGjhi+ZPmvmo+oZPGTldu4TBZA4kU6010VU01U++Zn26yNq2jbhKRSyNDTVS+GZqTqcPKGnmjl3i1wq6uzSOeg3Rk3ElD0myTsg3ZTSS8u2jGrVq1fTkU8ipx95+f4+zyXHrp2J+9su13aIqjbKsi/cDf9QAgZmKjwQNnyq7gX1rw8l9xiW8+yS4fHexPDcxqpuLZQypcl2XbNA0b+VYdA2mBBA39U7bxm+i7lcF4j3AYykCydAzLjupZKqLrrTOuWDuEK0mmbN8VMxwRk4wHRouVamEFWkmydtVikWROUMya1Bvkce8Bxmfw/8i7XbHKme2baHlJZCuN13fnLo4hzX8UutWSKRYRcmSjb7H5OZJ9InbtWKsW1T8spU0w2+dVnI0SKptTTTTXxSuAlqtXZ0eqZhIuUUBLySqvWKDhYiQGMYEyLKFFZNMBMYQIRQoAYwm9xEdR+yBtsrM+0cL1gPgkj0CZJoqootGODB36OT+Y4ZGN9ShDqolHjlAC8iEoNB9vbn9Goz536Pem/qTYXVjy7iOGyTXaOrZL7KC3zMEjAKtxbZaCNL6KePQKn3mjbqFkjdNrWYxPIMzg7iK4xmQubV4mDBFlYwtr+14GJidT+oK/60fNUeX+nzNdcO4aRaLNH8Wouks2VASmFBQ4KmWKP+GUhues5BMU7ZVFwQwpJqGCP76vGN5ixk+DmKYo+YmBiHKoUxTpKEHkiiapBEiiZh6FCCICHcB1c5uax63nq2W2NEvLloE6ZXCyQAVVWPWUBMhjm7cmZOFEzENz2QWXJz09IarOfRyIioi4bFRMPJRVbEEhh+rqUbdXkqlHsJgSBA/HIk+lwQ3Bj6jfRC69G/Um740Lx5rI21tkuN5SZTEb7DylobJppIl6W9/aPbzY+6bqls8tr9wHijlC1fD0n9TWz2AEzxqtykrwZCFCGZJvxaV1jcgyQzB/eUAyOOxj6t1G6ps51c9YmWkk1T6WEin5IAIGP5arUvSkkYw8CJwbFBsBjfSU9AZUw8qDzgZd8mLRy5diVsxMzk2YrdZSncLrMVU00GRFDCou5SdnaLCKRDJNBIVw4VSEpOqxjcFTgdwgR7gpB9U9bjGOi8mIVy4ScelOU3AGBJVy0K0WASlMmDlcVSFMmYoVzu4cokKzkGBHaSHmg2UIuo0dtk1lRcKpEcJAomoiLg6i4IuWrkiSyip0TEBQ5Rk30ozuMusfirzLSPZZPHajfwUVry0eNfdPQM5jYdJR02G7heygM1Xq4PmGzvF4YUcXLwsbeWQFHlkx8gcxNEZnij+4X/wBtqR9x+20vR29uN4AbjaeScRaOGiI+tlEFJWGIgBiqHmoxBL4zFMxIIG9RIRJTGjUU/wAoq8pLJBEBdPCAeAtsg1rADq0RqYKSREjPbbFoEDzk3AAAurSwRIHLmDlDiD6W9MU567KruxeJpwrqPeFtvzlUGpa5FGH1KzGImUbCh1KqtnYNEEXyyrU7tmZFVFZGSO9SO5ZHbLGTQBdsZquYhkKunNg+MSh5lFX00yu/WlCLQpDM1Wsg5UUXUPHpMB8xn0KqqFSTRNyRMwoiJymOB/6A/p65ld5jgGAyA7XsYtUhllBLbKAJsnf9MqqGB32GwR4+Yc5nhrR8ndxwyLbtG7tCZR0HR3IELqdEeIx366MUq9tyBiBH8xgIJQEeBHjp7frAefbj2H39hAfbvrOMPS09xW3Lcdtdcog9sEvQZncDgsoplWcss3bf4OTuryDiyqdk18k4oZX+oiimJfVSR4rnlXoEeRfVVtMAMhPVJzFcj1uLC0fsqCyXEw9RnD5lY49SvGXOP0lVoRCLFc4ib0KyxjGNlnaOnXWG9La0zqTt67a/hjx+hMuHipHDZZu5mFULO2ZOixcMo8h1qws8aOF3MW1B2ZV8RNNZgLddWwuVe2zOGv7UxyAyWdw57p+ETxxmWNixHykiqRoHwP181A3OcJBk+L8ixd+YjG+Lu7iJ0ZJVhuLSFrm2n7gsVKSwqR2RXK9l0Aa2zvkoGe3GavB4xLW374H8nt6yVlnBblZQ5RdljI+fb5HqaC5AETkTZVXJMXFtOr6Ppo4hCfRT4DZKcN0HaCzZ0ik4bOElEF266ZFkVkVSGTVSWSUKZNVJVMxiKJnKYhyGMQxRKIgOlr8izeGJte3zQDJwc1eit2UW7hmgiIpIBIY1ZMlFychyJnLGEiUziI9yNEh7CA87qGqvHwdft/5v/n5rnTWEfxadu/8AERhn7P71dA+r/wC3dPxadu/8RGGf2V0D+zus3aa+KVhH8Wnbv/ERhn9ldA/s7p+LTt3/AIiMM/sroH9ndZu00pWGme3XAUc8ayDDCWIWL5i5QesnrPGNFbO2btqqRds6auUIBNdu5brpprILonIqiqQiiZynKUwZlAOA4D6tNNKU0000pTTTTSlNNNNKU16gUA7/AEvs7nMYP5BEQ/1a9tNKV69JffpLz9waCQB9xN+o5w/oMHP69e2mlKwhnLbZgjcrQbPjDOmLajkij3KPNF2SFno0oKSDIy6Dny05hgZlOxyoOGrdYjuLlGTsiiRBIuAAIDhqk+HttOxbUIGkYkxs+xPC1Zu8bVxXHOQMj1WYiiP5N5MuzBNsrWMk/UWkn7tyKkqu/MXzQRKIN0kkSTU00pUURwPmWtAT8G+6rIaKJFfNLD5hqdKzJCl+ryjSBWVCyAdHj/HvZ1uRERVMPHHGyx91yUPMwF8xhgPOFXl2T2HmE6dc7di2YlYWVarsJJmNKvsDeK44TfMV12zhstlOPTFNcxAXAv0hmBppStchG9S/hiyktj/KGHc2h4W+XXU/By0RZqmzvTbY+4u4IRA0xrL4cnbfGye0+xmlC1GgUys1+byRBXGdfSFml04t41OWZG0zD9U26V6Widkm2i0uD3KLpsLYc6bh5tPGDGzVqgR0jEYuZOI6NgHlvs8fRqxJOImNUh8c1hzZnC0ja7vP2DIdktVznbbRIUwgIh3D2MHYwc9uxg4H/XryBQL7fyiIiI8faI8iP6xHSlRRRwPk6/FUPn3OExYIl6UpXuMMPxA4gxsu2VQMm5jZqUSkrFly1NVAOZu7Tc5GgoSVbmUI8q5U1RQJ0nbD4amxbZotdXW2vbZj/GbzIc82s9ufIFm7S+kpxmD0Gz1u9vMxZ3UOCXxB4JWsGtGs+VhEW4iVMSzl00pXoBCAHHH0f8UeRKHHsAFHkAAPqAAAA+rXnoD9I/oExhDv/wDCIiH+rt9WvbTSlAAA9g4+7TTTSlNNNNKU0000pXQ7hi7GuQlmLi+Y+o90XjE10Y1e21GvWVaPSdHTUcpMlJuNfnaJuFEUjrptxTIsdJM6gGMQoh038Wnbv/ERhn9ldA/s7rN2mlKwj+LTt3/iIwz+yugf2d0/Fp27/wARGGf2V0D+zus3aaUrCP4tO3f+IjDP7K6B/Z3Xfqhj6iY+au2VEplTpjN+4K7fNKnW4SttnjoiQIEcum8IwYIuXBESlRKsuRRUqQAmU4EDp13DTSlcTNQcVYWJ42ZZIv2Kh01Dt1wN0CokbqSOAkMQ5TENyJRKYBDkdYLtu3GkzTdX4SDmCdiU3lCRQ75iY3HIAq3cnMuUojwURRcAJS+xDj21IrTUfc39KfTr1Ghki5nw/B56SS3FqL27s41ycMALssdtlYRHkLYI0kjxiC4QK7swG2beUxuby2HkWXGZC6smV++oZWWNm8eXi2Y331AIdWBAANU+5GxvZsdu5SGfJAinLt0iNn6fJ2jwjV2VwmVs76CiRF2YotnBTAQ6Shm5HZCJ/SGJc1ELvFVBWIcpiKCIgJTJimYhxDsYOBKYgh7iJTkOHHYQHi/TJVFjr9V38G8RTFwKSi0U5MUBO0kCE/ImKYe/lLD+Qck7AoioYBARKTioaehkGL5wzlWLoXCLkyKrhq5Ig6EiImRVQcpuEl0HS6Jg4IuIJLG6ATXOoUQUJxO+rL6cj6OcmxEWLyMsnDsxFey8Xusg0rGyMU4ur7B3k1vG4+4tJ7sXNteCBUu7e7X3mWW2kIuf6Meqc+Xt7tbyBHy9sYPuzD7ayXK9Fhiu41kdOwaKIRTRhyyPGpjUrMQtdWb6Qc0E5l2qXU6ZnB+sUhOPNOmkcq7gSl+j1umRDeo6A4UdMGivZR0oIwnUflXJ6YqZzLriVIhEQMZRRQ49JSIJkKKh1jm7EITkeofo88at+v1ZA0W/KkQHDFYFkm6gkL0iJgFRBNwlyIoLGUIh5zc/HSPmAmJ0BBXVUM3DqV6WnWzdEyzKQR9KUxFPSyCce4Og/aKMHxUljs1TtzIt3nSkom9aHcsnSJ0lRMXXfSHIWt5YDE5+drS4xl2LcXfmT3o3/nW8odO3uq/lffHdW6iX8gQKvr6XckbI4q9tIAt3LC0dzZxu/QJHI0cU0T99e0YCokS3boTt4do5BEaM5xMXY4qxJOSkcJseo8oDUxVDGbP40XdjBkoTqIZZlIMZmVYnKJkVZllDlAx25uDVT2CrmdCtSpFy3ZT1emXzOvSDxTyIl6i8XH1cCs/MAlikX0kCU3W5F3/cki0rIN5BzHIyab9K6GWqbQzVdwz9YCCyRWj9k+BuodIqiqbtq5SVbpopuGyhmSzFVM7VBVuo6SKPqEHIHJUrkVNu3lmMQ+KmLpjVa7Hvljl5O7XRYnFM7gTGEFFEo07CNERKXrbR6QqFMp5ih+730j82mv8Ah5tYJ/vYsZcGGJkZpOsTEFfHjaKG6HYU/ieyqd1qvPsFZtfCNWaGR4omZ5E6OlzHCqsxX8h+bK7MELK8U8bK5UgiJrtmuzXdMXaSrdy2WcNXLdwkZJds6QVOi4bOEVAA6K7dYh0lklAAyShDEMACHGpEYQz1aqFaqcuWFbWt6wnq808s6Ei8m52vIOl493TDNUHYMp5GWhpWSr7VGQjXkimwflhmbwrMrNq24KXWgphIhLOm4kF0Uk029gi12aNmboolIRNCQUeADKxsUkC+Wl8XFKWakBMjWfTap+jN+cbVWNcUomSmK8k6pPzt+ESUpIIw7N41kmKyPqk0I5nNyDp6yUjHqb5N2yK4RRUQesHS6b1NBNW8S39nkrYpJD2Z1crHIpAMgjI6K+viQeCD8jxreqgnL4j+VPY5CGJ7e6iktSpIkgnSeNuyLpt7ZV/EMOwI1pvNWTfJ7UPxDvH9z1tBjXShMX7jcL3N1i1s4K4bJylbTj6/uQw1IF9QcBXfRGOvnbWHPWBlE5AJVuJU1SKE19GXXzLafdlKR44ngQX2OfN3tismMsNYrs8lGPCO28snJ5Nzlgs79N8iY6T5s4rk2LZN0mdRN4xatzkOZIUhD6Z6YCCZAEeRAhQEftEADkf1jqsGSgFrf3duAQIbiWMA/KhXYKp+PIXQP+a5tZqxXGZjKY5G7pY5C8tEf/vS3uJIlb/7KoP/ADXvppprxVjKaaaaUrrtshjWCuTcKQyJFZSLeMkTr9XkprLpCVFRQCFMfoTV6Dm6CifgOwDqF8jtQsrwxjkm60UxgAR6/ivHPfvwDMe3cOAH3AeBEOORnlqMG7+2Zco2DLXbMJhYF7xBFbvWkZUMLmz3bptuXzSDEVrHI5Fxc2fSDp6dh6h++tSTZhEkkuhsLtdq9Ywn6pfT76Z+sl/jsjzvFXuQusVZvY2MlnlL3He3bSTG4dHFpIgkPvMzBm8r2IHya2bj/L89xcTDDXa23vury9oYpuzKOoI9xW1+Pjx/j9hUR8pbDsiXesuIaJt1IYvzeoM1dPvnACKQrtjohydtHKrBwc3mclIIh1KcCJjDzDhXwhM8rAPOTMR8+wdrnwUA78BxAduP9eso468QzcHkeUxTf2TvBRsburnsLw3e6dWYW1za91uG8vEFFvtjyTjq+yVliH8TT8dWPJVfa1KtStNfP7HWadkE1iko+WfRi9Zm3tEylnzJn4w7C9Wig5DrFFyL8y8O5zqONJzH1VyDIx9SYmyU0aU9xfLeFlrOLcqKylASuUDbkmdlew1grZVzTFRkLBKaTj/o79DMZDHBaYHLpHESU7ciyzOCQi+X+42QFjQAH4CgfAqW+O/U76wcWtpbPDZ3HwQTS+9IsuBxNyS/79p7WRgNknQIGySRvzVSeQPBTz/b687hm2VcNNV3Ma/Ygq5LehIQzs8oYqgHQrxjlKQkgUBApQMJimEA7FMMBZr5N3vuev5AYvdLgCMh1HS5YuLbPcyx6EfFlOJGDEjWPrCDdIjZmVFAU0g8sTEE/JjGE42zF3y71j1HJ9eTifT2LFef7FUbrkJ7tKv0pkDH+J/xbm2V8bW6+7WqflSwS8fW8m5iRnqJAZGiLzLwrXGMY2lrKzrVrfPJWF7jhbxUJbNu6PZziZm8xLSoPLmFQkcwUCak1XGWyZ4su3DHm4+MrlDZuJtkuzoFFr1ta1+QmZOBlHV9tE4/iIVeOPjmeUkrN+n9vH6Y4OHj3ElFri4CDHFegZKQa8D+dee7J4Hj5/8AysZmPqH9Us7dG8yWYsZrg9tsmFxcI27d2PSO2VQS3nYHjZA8E1SAy+TB7xHb4ys7uV24FJ0GP6tvGZYmXx1+S8EN66DjulM5eoxlxdqmIYpSg3P1iZPO+EPk324jD2SIfKSm4fC87PUxrPv6nCowV8jo57ZnlbmIqEXmZU8e9dMI2Pkn7d45CPjXztVJNTyfLUTIRXY4jMw5gS34TWCZw1HUw5IbahyzTCRdfn0ruys0Tkuv0ia+c9oezisI+YyCcy4NFwcRW480UmwScvZiVcyCjaPmjreZefcnmilhe7txHNG0biOxtYyVdereRHsbG/I0f2rAX3rFz/IWlzY3OXia2u4JLaaNcdYJ2imQxyqrrbh07oWG0ZSN7BFa+nyfnwis2eEZhzP+N815MxbkyVy5lCt3yHkcXBcfQxzKGpwVx01lhuEDAORfLu/3wiLNBdAUQMdRVNQwIl2C9NNabUYU0000pTTTTSlNNNNKU0000pTTTTSlNNNNKU0000pTTTTSlNNNNKU00H9Hvqvmt7lMttN6txwRlhrEY8xzOTklA7aW7jB+Rl3GcUYLDVLyVY5qN3DIZFfYzSsMLJrZSbLYpeY3g7K6rWP307Fy8ijHSihVKsG01A4cubim2+WHwIjP4ZteKHGKrpma7so3GN/r+RMW1JWZjqRhiOk74tlWw1OzWDJd3b387dunj2toKVnF9wdIA2eIMgc41yjvRu23nNuamuVZfFlswPjHBVhy7YHFHrdnq91xBYpC9UunYAxZfbraLvL0C3XTcmaZuI1Fi3jMcK1ZzTUHskhIVawsJ3SlWd6ahTsA3H2zdNtzZ5NyA5xIrf47KGc8ZXNtg+yqWzHEfK4ozHdaAxQg5txLTDx+V3XIKDl1JFy6RSnSySVkiWLCAmolqnNbSlNNNNKU0000pTTTTSlNNNNKU0000pTTTTSlNNNNKU0000pXgQAQ76hBk3b/AGuw2eblYZlHumUlILvUBF+2aHIDjoUOQ6awF4EqplBASiPIcDzyI6nBr+KR9b6B58NFsWQ9MuDEXpVzMweCkcGvqytjFcC28/y/UAgYq5kusqIgqJB1E3q76McN9a8HY4DmS5IWuNyH8Ss5sVdRWl1FcG3ktnHuTW13G0ckUh7xtEQWSNgQVrPce5Hk+MXrX+KeNJ3iML+6hdGTsr+QrofBXx5+Cf3qsCU2sZWcsnrdCDjDmcNzEKB5+MAoqpGBZt1dZx/NWTJwfn6JTGDsAiGq67Z4bm7aRmXa8fSauuxMVoRsoe/1pA4poNEUhAySixRLwoVTnkB555ATAPOpZ0XfZuiv91V2+RbfEcLmeR3H23GcBecg4MzVjaIa4+pu11hnt3YLRtwtmTGmTIxa0XNd/jvHU4vklrC3OlQ89lOOZmcQR6rIZdwdvGzjl6/7MHrdjil3Qt0+B2uZ7ni+Br92XyhgqrfgjaWIcmT+SVbYvUpmkz+anbHEFOrrzHlZl7Q1myWmCsEqtTrrFsIMxP0L+jOHV1tb3mzdypDS5rHMydSW6oUwkek7MzdSCNkka+Km3iv1P+pXEJribFx8cke5jVJRe427mX8eunUR5KDTkKASSQV8EeARV6r4YW8NQjooUWqlA7ToJ1ZFqwgZUr+OXIXgVhApQIiscxh44AvSHJjFDVcuWfBF8SKRnHUnRsN4hklJR8T1r6fyVjN+6bRUdERzVjHtEbCi9atkHcgrJPXqjZuR8sdlHEUdJtUit1tlvcju83I4U3FSWNqbjuByrA2LA+fL5jCmjjDK9JnrLk/FOJkcgUTGlSzS9mpbHmYb9kqXYWpCQxNSafF22qUmEd3AknJqV+Zj3kOsoeMDf8U4L3AncKYQms+YwvklHUKXyBUMpbaMb3XHlS294u3I5GtclijMlmZZajZiqxOQWmJ4GssbG8f3vINnxvJxxWMVL2VnAWb9IuD4b0Wt7q14m15dQ3h7TJnZor8b2D+It4LEDz+4bx8/rXq5F9Vfqbyd1kyNtxZGXpr7XF3sSn29aDK+VlBBIUnfyUT4A1VCRfBH8X1Fz5yWI8KmIB01k2x7/gQzJNykdNVJ2kxPXRaJuklEwEixUOrkTlMB01FCHSvgB+KjcVvjdwr+LH8mr5yPS6zTAykgxQUcmdHI0alYRsKyZKOF1XJI+MftGiZwEStkhMXjdE3P5tyTjCq4SvGI2uNrPUbpuC2447vElY3VjknC+Pc5ZfoOLiymOCVUU4mQnDkvSUxHzk5MkrzNsxIqSLsaj5JolL4AD34Dnv37f+O+pwX1GziEFLPDRsNfkljIreNa0RdeP38frWqH165zslIsDGxBXsmMftonegXu2/HfnrrROuwOq0NYLwKvEhY+Jr4ZW4BXFtBRwdtDkdu7W9T4Zmoq0ojF0XLdhvtxkI+uEcElpJRoxmgBu0ZNRO/dpmSa8lP5hN8oOeA59+A5+/jXnTWk3l1LfXVxeT9feuZpJ5Og6r3kYs3UbOlBPjZJ18k1D15dTX13c3twwae7nluZmA0GlmdpJCB+gLMdD9PimmmmvNXmpppppSmsV5cwri3O9ab03LdNjbtW20mhONY2RVftvSyzRu7YovmryMdsX7ZYWEnJR6/kOkyOo+QesHRVmjpdE7TSldCLtH2xkudWyIhgrGbK5UOrRGP6ZOR9VjY5Ws0+BhZSr12FhmrBFuwYo1msWKw1uruUWpX1ar09NQkE6j4yVfNV4xym0HbZh/I+1PF2McS12kY3d3y8TjiiwK8w0qaryk4AyNVKo3GC+JmjghYOAuljYMq2VuFeKL5F2eLO+jYpyyaaUrOaexDaCnSFcYfgDoqlCcWVK6SlbXbSDlnY7F8DNVPV29Vw/VeXJqNVRQq5oi1OZiGNWmzWANHjEtkGaf8APvDx/Sne3fKtzWrEOFtxxgvMzXH9kQZptJukoWrHMnW58tVkmoIuoE0jBJpRiikYq2VRaooFbHRFBIxGmlK7fU9o22+l5HreZKziivxeUqnR4rGdevJV5hzYIygwsAyqkZVEnr2TcirDt4ONYthbOCreoctkpRyZaVAXoyT000pTTTTSlNNNNKU0000pTTTTSlNNNNKU0000pTTTTSlNNNNKU0000pTTTTSlNVp75dv+KarhDdLuOg6/JNc0GwflKPi7uvc7xJL1AtzqLeq2qQx3DSdkeVvGdgn6+0Qi5Oz49h6zY3KBBMeU85RRQ7TSlclvOxlSsW7WN0lsx7Er1S25Qx9SKDebdFTM6nbJqpQ68LimGiSWdSTVnYn4NRrFPxkO/hZCOk4qRm5azsHre1SDuaVkJU9pG33Hl6yHk+o0NaMt2U5mZsmRDrXK+S9at9isKEEylp6aoc1aJGiOppwwrUBHJSnzbK+YxsPHxzBdsxbJtwaaUrKuNcYY9xJAv6vjOnwVIr0harhd3sPXmKbBi4teQ7LJ3a5zZ0E/o+rnbPOSko5AvCKJnINWaTZi3bNUcg6aaUpppppSmmmmlKaaaaUpppppSmmmmlKaaaaUpppppSmmmmlKa4+Wi2M3FyENKIA6jZVk6jZBsKiqQOGT9BRo7QFVBRJZMFm6yiYnRUTVIBupM5DgBgaaUqIquwHaS4qbukOsUqvI1/bWt+dTr7IOUX2RVbYwpr/G7KUDLTu6rZTTI2x1MTNARjkriSKJSJqaqYMfgEvJR7rEm47argbDWItzu43E1IWxtl6A2xXpjE2Gk2+81qHaMMWYFtNExpH/ADDibK1x8vH0CrdUbTmDmrLNK4oorJxKLWWWVfHaaUrMtM2c7eERrF9PS5l/biY1YU5hMzOS8pzq0DFyuN4jGstI1VvM3V+yqNymKMxRrszkOsNoi/S7JR6eRsrp1JSLh12hPaFttLi+1YSe4mr1hxxkA9pcXyKuK8zd5m6SF1j04u0zNrutvk5u8WGwTMWzYRTmxS1jdzhIuMiY5CQRZRMag1aaUqLWJ9u2JtzkJuGYZvhJ65sILfJkifg2CWQci1RjCSmK0aDUccLQzOl2yut4pvSYmh1RzW49gm3j4qyRY3Nq1JcZCTnXtm7dBNsgk3RAwJIJppJgdRVY/QkQqZOtVY6iyp+kodSipzqKG5OocxzGMLTSlftppppSmmmmlK//2Q==)
Fig. 2: Convolutional autoencoders are used to compress the temperature fields by a factor of 140 to a so-called “latent space”. When constructed back to the original size, one can compute the difference between the original and the reconstructed field and use it to optimize the network weights.
Prediction of compressed temperature fields
As in [2], we test feedforward neural networks (FNN) to predict the compressed temperature fields from five input parameters plus time. We found that while the mean accuracy of the predictions relative to GAIA temperature fields was high (99.30%), FNN was unable to capture the sharper downwelling structures and their advection. The FNN fails to capture the rich temporal dynamics of convecting plumes and downwellings as the network only sees disconnected snapshots from different simulations (Fig. 3, upper panels).
To address this, we tested long short-term memory networks (LSTM), which have recently been shown to work in a variety of fluid dynamics problems (e.g. [4]). In comparison to the FNN, LSTM achieved a slightly lower mean relative accuracy, but captured the spatio-temporal dynamics much more accurately. The LSTM not only captures the downwellings, but also their advection in time (Fig. 3, lower panels).
![](https://www.epsc2021.eu/_protected/abstractImages/274101-1-3.jpg)
Fig. 3: Predictions from FNN (row 1) vs. LSTM (row 2), when compared with an original GAIA simulation (column 1) in the test-set. Column 3 shows the difference between predicted and original temperature field, while column 4 shows the horizontally-averaged 1D temperature profiles from GAIA (solid blue) and from the machine learning algorithm (dashed red) as well as the difference between the two (grey line).
A proper orthogonal decomposition (POD) analysis (e.g. [5]) of the example simulation in the test-set shows that eigenfrequencies of the FNN predictions decay rapidly after only the first three to five modes. On the contrary, LSTM predictions are more energetic and hence, capture the flow dynamics more accurately (Fig. 4).
![](data:image/jpeg;base64, /9j/4AAQSkZJRgABAQEAYABgAAD/2wBDAAEBAQEBAQEBAQEBAQEBAQEBAQEBAQEBAQEBAQEBAQEBAQEBAQEBAQEBAQEBAQEBAQEBAQEBAQEBAQEBAQEBAQH/2wBDAQEBAQEBAQEBAQEBAQEBAQEBAQEBAQEBAQEBAQEBAQEBAQEBAQEBAQEBAQEBAQEBAQEBAQEBAQEBAQEBAQEBAQH/wAARCADxAfIDASIAAhEBAxEB/8QAHwABAAIBBQEBAQAAAAAAAAAAAAgJBwECBQYKAwQL/8QAZRAAAAYCAQEDBAoOBAkGCQ0AAQMEBQYHAAIIEQkSIRMUMVcVFhcYQVGWl9XWCiI2OFJhcXd4gZGxt9F1krW4JTI1VJWhtsHwGSMkJidlGig0QkZZYobhMzdFR1VydoWHmMbX8f/EABsBAQACAwEBAAAAAAAAAAAAAAAEBgMFBwEC/8QAOxEAAQQCAQMCBAUDAQUJAAAAAwABAgQFBhESEyEHMRQVQVEWIiMyYXGB8CUXJCZCcjQ1UmSRkqGx8f/aAAwDAQACEQMRAD8A9/GMYwiYxmIbwv2meNdfOdq3zZcQqivGhW3N66WzZ3IZmgtyeFHmjS2EnG94xY6OioQTNzaiJULlx4+SSpzTPtcIsvYyPL/yu48RegWrlI/WzEG6gH6MxOXsFoGrjTI7IGKe7tpEFPj4J0xzo+rporeGlvibG0Nq1+kTm5oGtpbFbgrJTb4pkXNiuX7ji68lqCmNL2DX8bfXZmmMks+2HSiobAt40esbJYgnry6VrMpNC5hHH8ttYnCDyiDs74iWupJjpq3E6FgrIpGWnarPVLdHVrmySuRq5XKkMNj7FDGPaQPjm+L2x6etSikYqkJBKZO1R92XK1itYQQSUl7ve3ONJK3x174xX6gOR/zbN31uzGPuolXfA+B1xExt6h5No2HX9hExWR7IjHyPkS/j7bT6Q1OZzcachPVIy1uumylKYJCnQNFJQF6G6l6fXmVztqXhGz185WXHJzJVFlSFfHo20wVuj6pbuc0kNh685WfJJDG2xP39nlrbmtN59uoc3hxRItNCSd1C1Nnq1bF046tQJLFg0ukQRReRCSZnlxGLeXfhnf8AoylUqVzJWg0aFY1y5Zl0V61ccimNNovLoGOLPKcumMn4ZnfhnWSffGK/UByP+bZu+t2PfGK/UByP+bZu+t2ZthsqY55E4xNY7vuoYJfHWOUsZ56fZMcezyJrSPDWccnMADE5pqFcn3MIMDvlb7CXt46jnZu5p+Dr/VD+WYPv/Duz/wBWfh2/s7KM7Ozuz+HZ+H/qyjZ74xX6gOR/zbN31ux74xX6gOR/zbN31uySfc0/B1/qh/LHc0/B1/qh/LC8UbPfGK/UByP+bZu+t2PfGK/UByP+bZu+t2ST7mn4Ov8AVD+WO5p+Dr/VD+WEUbPfGK/UByP+bZu+t2PfGK/UByP+bZu+t2ST7mn4Ov8AVD+WO5p+Dr/VD+WEUbPfGK/UByP+bZu+t2PfGK/UByP+bZu+t2ST7mn4Ov8AVD+WO5p+Dr/VD+WEUbPfGK/UByP+bZu+t2PfGK/UByP+bZu+t2ST7mn4Ov8AVD+WO5p+Dr/VD+WEUbPfGK/UByP+bZu+t2PfGK/UByP+bZu+t2ST7mn4Ov8AVD+WO5p+Dr/VD+WEUbPfGK/UByP+bZu+t2PfGK/UByP+bZu+t2ST7mn4Ov8AVD+WO5p+Dr/VD+WEUbPfGK/UByP+bZu+t2PfGK/UByP+bZu+t2ST7mn4Ov8AVD+WO5p+Dr/VD+WEUbPfGK/UByP+bZu+t2PfGK/UByP+bZu+t2ST7mn4Ov8AVD+WO5p+Dr/VD+WEUbPfGK/UByP+bZu+t2PfGK/UByP+bZu+t2ST7mn4Ov8AVD+WO5p+Dr/VD+WEWFq5u5qsOUv8LGH2HCZJHWBilCpsn8W1jxitikTm/s7evbD07m6pVYauMadU6ojY4hSm8mQbuSJKogzbNeRwagAOWc2AAAA97vV/gHgH/wA6Fw/zH9o5I/CJjGB69B6en4Ovo6/B1wiYys9ou7lDHu1AQcbLAl9PyCgrL4rXnfNcx+I1dJYzYUKVVLbvH+vGxHMbBebMlDbOFD6jtZ8WrwZoNCEKDdE2kpiFQ6HqT+888b7tap0HG2q6KWxZht/lvyXi/HWKTmZx9VL49WDPvX9kW/Ytinw5M7R/WXPDFXdUyRDEY8sfmprVzB4YlD0apZ0a9AqIp75oIiHoDr4gH6hH0/q/46+jKFF/OvliwJpBxGVyCrnLlqi7R6uuA7Lf+1eLk1fm1/ZnG734yG+3GnCJboSdYDFRTZLYqogqWaoYc5WizNr9qYiiroZGiZlcSuT8/wB9+YlU8pJVFnyc8JboZa9kttRCHrokx2LXNg1JW90VpOV8HROUo2jcu0Y7GGJTRnYVaxlUvkaMkLImaG58LZWsizrH+VaCVsbTJY3SXIh4j783pXdkdktZpi0zo1LigPQOCbRXKEyrVOtT7FqSAUp05/kTNBNJL2EdQ5j3xiv1Acj/AJtm763Z+3iSaQr4u8d1RA6mkKqVrRSnMDUQAwhREms8kwNd9dd9QMLM13DXfXXcO9031126gEhu5p+Dr/VD+WEUbPfGK/UByP8Am2bvrdj3xiv1Acj/AJtm763ZJPuafg6/1Q/lm0QLDp1118RAPDUB6dR6B18PAOvwjhFG73xiv1Acj/m2bvrdj3xiv1Acj/m2bvrdnWbI56cKqiUKENj8oaIirokBQKhlXWTFVL4X5ocWmVh7CNTg4uu26VUekRqCtUYmp1ri1IjtC1Tq2lKo4u/bM9nG0HaJxvlY7mmaqdyhjVPXfI055aJW6IlxiZY1VuoRqdESthfkSryB5m5TozK2TbT2bNbm5eRS098Yr9QHI/5tm763Y98Yr9QHI/5tm763ZX67dupwSbzwTN+96SA7bYrQoG6hpq2JzhOKcFJZmrjLS4y2FI/MWd7djnJQsJbEjDGJzIlixOw1vYzlE+sb9vVw/wDLlEI6s5XOWygow1P5rSzUQeoEvclLumJbXKfIHc1x1dlbdHfYrRvF0GWOzNEQR+2V5a2tUT/P8f2VlPvjFfqA5H/Ns3fW7HvjFfqA5H/Ns3fW7Kx9u314j7eW2SVHygUp061M3mrtoBXaVB5wtI0cEe5K5RbIJlSE5jPRSf2TTbnIPam5tMnLPOZnRGqN/Ab9kB8SE47lqab5PpFOh65IKFbEKlRrwWNalYhc0OyVRdBe+rg3ujVI2RSi7wng+QyctZepp0TcdtjeXZm95cNFvrLl+G4b68v48fXx7r6jCc3doQlN4s7y6YvLhmbl3fhn44Zn559uH+zq0f3xiv1Acj/m2bvrdj3xiv1Acj/m2bvrdlQSv7JO4BINDd1sYvBP5LUvYC9kNJCadsc3mOhBZOoXh3e+pQ+xhqbY8wgg3eVQlPsdodKUehHRP/Chuz23K3NTxa5FuhZhhW5zftS7klLElSkRnHmqW63FWpSQgxwJXnb7a+c6MTbInbzTYWYtE4m8jMVvIq84DsEbzAJCPKMIFl7DlN4TaMZOzyeMuGfpfjZAweatEAGth8pYLZHI1YYcfbLOwKHR1lBCAXkUcO4PqmNpRj3Icu3XHm7j3xiv1Acj/m2bvrdj3xiv1Acj/m2bvrdlIWv2UV2f5on6Jq35KK1CTXTdWgSxGtj3FMJqXZaUlMT62h5Ldx210MaNkZCk3UuVa+14xRruIrdftt9lAcC9TCyPcw5LbHm7AGgaQ+vRJ2LE89L52CrayNSPMdtkwOGh+22u4sDzFXnckvV/82QbKGGzBDfDjxWSmf4WN3swo2ZF+DmFrEbTQYTyevKvJjxMzdtxOxGl0+VOHqG2FD8SLWdgJXey9Njjw+QmF7bFcD1mJGu8HOx2cLiZ+tis43br8K7f3xiv1Acj/m2bvrdj3xiv1Acj/m2bvrdlKO/2TpwV00I3Gp+Tn/P9zUC/ajWgHEmmFJDgJVFjaXUk0rRw0LU93ymhKpimqQNjDY0V7MftH7Jm4NabdTKr5KASGombHhF6x7gFaedbGbdBtPX7YNUB+mmu22mm57lGNRN0TPalW0TA6tsx3EwdfzRHPJ4BaOMuO5ZxdoyiP9H88oydmdo8uz+62Dene/P3f+C9pbsw7hucDk2YQ3bqac3eszRi8fzNJ+GePln48q6H3xiv1Acj/m2bvrdj3xiv1Acj/m2bvrdlM5X2SzwlPEvUmpuSRnldwLJNCNVoCYzbbcCdTvKDZgGapPK76GidsQBwINFSkEwqE+qE7cR9ktcHlW3eT1VyVNS+TBSKvWK1l5MEm5KdWWYGvupDtsdskWJQ8iAjoK0VCYtQan0Srl0ltK294GJ+Gc52682Gcj4y20Akd3ZoFm4miObvGTdMnZ+Yy8flfiUL0t9STyBAOibYSdmDkrwjgck8jwi0XeYo/D8zgzTg7yiztxKL88OyuW98Yr9QHI/5tm763Y98Yr9QHI/5tm763ZTkT9km8KzjDyPcl5JFqE+vTcveMVt0MN7ywryZG4WWPlNBPaXnUDh1008kmRmbBqYqWENf2K+ySOFJikEm1V8j0x+5Yblgqi1eF6b98xOnJ17xdjGjqO6pzZSdxHXuk+drdt9uqArRwkNoG7POQ/wrnu5AD2ZQfG2mlGsw2K9h4uNnYMROxJFduiI365SaPlSo+kPqlMbGh6fbdIUrDVGI2CyDje05HE1dp9jp7zlZx9rnr62ePHKuH98Yr9QHI/5tm763Y98Yr9QHI/5tm763ZT9v9kicIiSxOUVvyGTl93YzQN4tAhNOLKIPXHgSXpYO2uxxTahcVPk9zNNNzyUiTU3qu1OJ+o/ZHfCzUvvb1lyD1M8tqRsV7W4FsOu+xgI/KDtpPtgFODl1T9/UNjfNAFcBHgKYPr/Z7vHTXn+Fc50W5yFVn8vP02CQmw5wBLp4LOBHaEowd3jN2i7M7syyy9GvVeM7I5enm3MSnGMrcHwl7qrRmNzRkePa5DGQmcsZEaLONnmz9LO6t898Yr9QHI/5tm763Z8duTSBGtYEz/UV6xVFIJVFYcnfpFXhKVjRPM0kDfFo+DosRyJwPRI1b46t6I1b5ocSkFTqep8mn1MM0qiY/siPhbIHBqQt1fX4bs6mAJY+1mDeUIRaJBeFKw0kZ5oO+ySPGEOpqQkwxQYdquakwHLkXdUW1cgFqRzruEOCLbU1IsvTiysSHa6jqBqdVyBrBQmODXfXQzTyhJuhmupmuhmuu4Bvppt11DSZbBZnBEgLMY23jSk7rQhbFIUpOGbCKzNL/mGR2hOP7oy8O3LOqtsWpbNqRqtbZ8Fk8Ee9Wa5TDlKhahLNV5PBrIIljFyBeTPFiR5g7s7M78OpGAIiACOogIgAiHh4fi9OM3YzUqupjGMImRx5Z27WNHUDY9hW5LWmERBBHXNoGQvOqrZKQ+SduWx6PIy/MkqxUCx1dnFM2I/IEDvueq1L6hruIDI7NBAB9P8AqEQH9QgICGEXlXqq2q8lHZZdirZ7O9GSyteDF58IduZINTG/rt6cGG8apjX7i7z5o2atHVK309aFi1vLpgsBvUo4k3ojZguOTpI2euSz84Wxp75BWX2jl40fb1gVJSF3cwa8kdL2jXDDBFSS19Ku4lVBS1vTuKI7brydRWR19KrJYXFvbJs1MAlSp+rsqQM765MQm6u91PktB6dQEenoEd9x2D8XeHbvdB9Ah16CAiAh0Ec11L00Hrrr0H9fo6dAAA9AAAeAAAAAB0AAAADCKADlRyGhNOB1VVo+HNtP1TYbNAkESd0APsged2umLjJaH1dNz3AhUQrJ7qpS5pSGYUrkrW7iQDal10SFR37dKtoTL+zdvicSuKsskXUSni92x9Q7MSV5VM3tGlseXyfZr8qTuoTaO8SB4aHosjfQhyZlKtC4aKERhpG0/wC9/us4yfpDof4N3TmKO0lXR5v4E8utpU1HvrEvoCxmJc1k6kCCkZIwnx5ECkxZruhRtxDi6o1Tq4Lw1b29sIWLl5hSNMeaX9iFVOUQLoL1qkckQ3KuMtQo5K1UK/RZrY+8URxUrtgMphrWigMMBpwJMRIxeD2vRMndwu7ajlseamC7jtkwtuuXI1p3MdAgchXlH5jSEesS5Qfji7UhZrzs1nKGJhSm02lVXT80yiCwuSsWqbVkkMSjD6z6oi9CUYNbwxt7i3apSitdSi02qNSQCcovXQssnXTTTXXTXXUO8ZVz2PXJHTkvwNpR/Na/Y52rOPs9HyQ8h3SP7U8v1YRaNNSp8ZHpCQmTLUKwhSkKWJfJaqmF7TOsec/8ItanXLRuvT0592AGrWDV7FWxSOIpIFp23g9qrOMnaVey8OISOF/0yvBmi82fhmZazYcWXB5/N4YxQnJictkMdM9dnYB3pWy13MBnmR2CVx9wXM5v25R5lJ+XdjGMwrTpjGMImMYwiYxjCJjGMImMYwiYxjCJjGMImMYwiYxjCKOLX99pNv0d6v8A4n3Bkjsji1/faTb9Her/AOJ9wZI7CJgevQengPwD6eg/k8OuMYRVizThtymkHPSH8x2PlTUrHE4NAZXSrNT67iu8vjwbTFjTmqZ/YTGus3TkU1FnTpye6qbyozNyIGmaI23OalOuhMjPK87N7jeXD22bwjKBS88iUiK26i5bpeU/FKwNKfZ9GWn0zMxr4ky1BOYe3StrU27EV8HldlQuayDWUQiWSFpnIrG9exusea1W1hOMIqiFPZkSdygUikrtf5ZvMd+5nRnnmTyEQVaWlr9luqFQdBTcShaCklE6WOR9GtvH9IqpddF1dqmTd1Z3t+lgzxJLVxSpNLPiTxfeePoXfNbFsFJbN58lbfPua5J60Q8a+im7skhkQrOFQuAQg2RzFwjUCryuoLGo0wpHyYSmQuiop3kb69qnF7PKTzEzQfR+sP3hhFH/AIo/ey8f/wAzldenx/8ARZtyQOR+4ofey8f/AMzldf7LNuSAEQ18R+MA/WPo/wCA8fiwijRyt5MwvixUzzYUpPb1btuWcghkTVOZraqlshEsDfNNDUTa+OiRiY28FconEiRMLwTDoSzvsockmyJtMDfzsyqsO0J7TecSNPpL2Q6pI1LJjEXR1R2OrQ8NzS4pPzz42/0O51agF55QRi0qjliNHKktuNcnCtbhrQ4hyWpG8zeI62G26is7lby2bE9UXFOE0QrKZjXxUr49ufHyR1wyUnPqzIbuSjBbc2eG6wZvFbwOnTU1pYhFEba0KkRMcgT3H288tTOZTHLhoNC47XcOicDiTYQzRaExlgh8YaE5h5pDTHIw0o2NjayDVJhqgwlvbEKZKXucYYbuBflDN9jN999iKgitfsfmAtje2DZvJqz1TukLaFBhNHQquaZj6Z0bY40xctc27vLTZsvLVp2hnb0adxPkvnfkWtlSeTKYmhvjySRTT2GPBBrMLMdEl4yfYnzsB0d75nbYk3BxMI3Wa6tUQPi7UlTKfNkSYW5AiSt2qBihrSUk0aq5rdHEbjVqshCnPVqjyUqVKQcpUKTziyCCCCNNjDjjzjttCiSCStdzTjjd9Sii9NjDNtddRHPMv2iPa1or6gyvit2Y1izqb8vJlZznDm9mgEXJQFvdWxRgWOliWSgtl4VpWevqvQjoekT2YlE17e1bE7tkZREI1BMnK3Gva9m9tzANf1uh8yy9mvbtxBK1VoVqtCgOJshlcnkb5q+PxWHxoJMfJ5bIWAUaIP1DlZ3hGViwGuWc3N7RykxOuUr2NpZ7aT47KXsTgfmppgpTvNiqd63M1qYjNSp165bV2YSRCN4jKQeT+YfFrsaOA1NOd83FSbrKGRllLdBUyBJc1rS98PmoapHVrYNtX64USBmUoNmBlVLVS88ndmUI2x1Vlg4uB6l0puOdYbyFr+RuHHnsi6F45QV71Vt0J5G8qbFmmrK1wVqiOi97ZorUz82r5Lbkid4M9PBzFD4tGz4q4wRxekTWjl6RctTmds4S9m46uEkicrihyXk/a4PKmY++xsRrcJTx8gy4qb117bH3h5UU11a01p2FEgcXGP3gtuMEoyMho1cYi9nOaExm09EFW9lrW2gopJyBf3u45mLK2sy3R7f3Z0Y2/RCyvDOayx0xTqhMSxRmcViGWVVuW2oJpVLiRu0s8tWMg+ZZ1e3qfp3okwPn81Pdcz8uPXyOJpiu1deDkLQjAkTHjE+G2O3Gj1jLQyWXva672wTa5qViu4SG6vKhomm0bdXJ1658hDOgv4fL5Cka5uRMZQs1LNOpd02WVuaTr0L5QGDlaWeJtN8lQ06jioSd3L5RWTs76wnEl1OkVx35eUmWvjcrMb+Ikf3q2DLnRdLpWc1+16eShfKlzzrL5ClKnEBfmplh6Ox3xZJWNdIIfYyNWWolbX3YrxaYtSBVFezniZSc5GiUJHi3JpYUvJWJAZ4E5JzC0MmmMUbVaXUnVWcxNq2NNRD4yGySrpiliM8ruMOUm9ncTreAwwrfWLRCOsQnHuSk7drZ29DvuoenEt5eTeqUgrUr2YeywfHMpPoQnWvOxjscRsuNMUbd2AkrUeoaB18R6j12ER2/xhEdhER6/D8fh19AZVvxzjaNHH4vDapix0sSQ5ca+Uk96xWNaIM1ozEEOpMhTFEMjmsks2IvBmifniTQ8x6xNdvZG9T1bFRPkw1K1wluAK9axXoikGsB8JrtbA4EQBQIWIxDx7cQJNpSlOXXHyhRL7HmbVyUjR8qviJXvkixITIWOAezGqHzLeap0fVQiSIFTqn7y1vJOE9ciWyCGSgxY6GM1rQJvkcgkhCvseXj2yCRu8uUPJKLNLEUkPqtmYe8k0FAjBACspcm2TBuwHPzUcubkaBQTIC4jYDFowvcfFuO9F3ki+oD3Q6h4gI9R8fj9Pj+vNw6aj6QDw/V6fyZAl6h7PHutTPQxsDmY5Y47F0KzzKzu7EkTsELMjO7uxJklPqlKTu7yd3r8vWDfINCNDI08QMMXHXFi8ZRrNWE7QZw1yOCZhC/SH+SJOOYRd+XizqldD2GfEY5vLSSRZMHrfUg/U9QQhhDDqepXNeyNwU6IW+MmIUxZjr0fkLeUR7HNJpiiOIkusI8wjDd3NN2HXZ2Fm+VX07u87CqFVsDm66md4RdZM5CTsYQgTn7EeSk6hpENztjjG1rYNzjjXhpLdzrdgAA9Ga5GLv26G/fs2YbluHYd0oW46ejjgLjZ/y/lfx5bw61hfU71CNy0twz0Iu/U8QZA1aLy5k/U8K7ig8uZSfqdnk7yd+eXdVUpexP7M9MBHe4vw9Xun1T66Gq1r0bvtsnIixGm5oaLiizR3CINO5pe5Yk77mu4eSAp6cylHPldjV2YxQCAcO6qM66eS28sVITe8V5FwT+T2AX0AHQU7mqK2AQEdwBNuZtuakTmF2b4yBLa9nnx1bFm34eTtxlLrcPL93HB246v+b7/Va6e8bmTq69s2R+rnq4zWRj1dXu0umw3LP9Wfwq7knZNdnIh32MS8QabK3231MAfYNfv5PfQ4hQGxIGOuwED5wnKP8A+ZAvqaGxg9dzTdt+eTdl/wBn2k00LI4jUfoUXoWXoV7TSNywJKTeZ6JxLMUb6bJgSBom82HUSBIITFbFjolTAVPPGYJbDn5dTSzmYk0uGl1ZO6/U0X5i0uT+eH8tz7P5byo09t2onmezbBN+HjzLNZKT9Lvy8eXsv4d/Lt7P9VCHTs2+CJZmhunFOkwMLM0OAzaFo9zPK6GieBnf3M2ETBO3UG7mbdd991zlsYOwubgKr9f/ACdHBju93XipR+ofB0gjWHd+07gDqIagOmxeuqbyO2o67EbN7VuSOm7Q1bI5p4zDLM5iTu8srkpPJmZ3e/ad3ZmaLM7uXl2aLNHh/HHj2UeWw5+f785mJfV+rJ3X5f7vyf38e/uoXh2dfBnUN9Q4o0QGhggJhXueMnkjAAzv9wwryXktyx12PI2K302L2Sq16PbQUjguIUabdnVwZ2KEnbipRw6DsO4gMCaeombF6liaO3d74nDtpqp8sO3lfPtQcO/5/wD9JyaOM+PmuUfp/wBSyH5f2/75Z/Lw7v4/U8eXd/H1d/u6+fn2c8/6zlvzfu/1G5+bjnjn9bz7v7/d/uoXp+zq4LpVaJan4nUMWpbVBCpDv7nDAZqmNTKdVRIakGp90+xGm5acoUphW6TdGjQt5hG7egRpSMmcjSwLgsTAB6iN+8YhER9Ij74is/8Ajp6A6+GSEyP/ACR+4eJfn84xf3iKzyMazYsu0rBzHlHloyMWZZMz+7M5JSdm/hn4UGxbtW5QlbtWLUht0wewcpnhF/dodyUuln4bw3HspAYxjMKjpjGMImMYwiYxjCKOl7/dZxk/SHQ/wbunM+r0aVwRHIlqYlajVlbJlaRQSUoTKUp+glKU6lOdruSoTnE77lnEG6blm6bDpvptqI6jgK9/us4yfpDof4N3Tkig9AfkD92E8/R3Z28s7e7f0XjvSNvaYdmNyLl7fStSvTjx3vTk9KLEL4+RqDMMnhc5kMmmEhlE5j/HORRXRyLqn2TpaGFy8ppmCOKbpN9X5K1sMmemR4Ua3J8ce2f4W3m0tqN4sD3Lp4U2aKJHGbGaD4eWhWJmxGrdBalrguXJXdsLdVpUcYjkS9Y6ShyAVDQ1mt+p6kiyS6qRrfkHXMlqu2Iu3SyGylAeiXoFmolqkZxqc8hM9MToSGrhH5I0ioMUschaD0rqzLe4qQqStw2Dfyrc7+x6kMMlDlbMhBntas91yGPJ7I1sSOUg6V2SdBawobjpF7QgjZAmapYLxZpdxSqZjbMxr0Hl+d0ip3fFldINF5y+L359j1/Px423F2/mTyF1bDhz9N8kIR7cnyFW53QZA3SwpQKxgF/TlEsyNOLi6xjdm9PdgFUx++63Zw0qdGNKtsmhV6Va68hNCNexmcNdnGlmJDhHoIWvaxdozu5rFmyTwvW9H5bFpKj0Wx2RsT+k31M21VMTs3vCbbUlapbTB1UtqhSTsBbijWINtg3EAWpVKTr5dOaXpz4KCBEdfK6d4OvUOvQQ6CID1AfEOggIePw+GeL3i7wmpC5dY2TxR5PW/wANrne47JZdWkYNnmptd8jWGFzK0YYfcVCqSZQ3y1wrd2k/mhMY1kcKjMnh0BMPW6RaVPK9yl29iZPHbt0aOVol8Q5NVVyOYCHjREMJk6b2gjpHSH2KnIRSLjEeu7YUtY48rbHQoT9jIyxOS4iNbr5A+rV6PObU9QtyuzwPqFjuxXj11g7Lichgr1t3lGPZDCp86pxLFn7nJ7oBSHHxPuOw1nh6d6dloUX1z1a1Z7Fycxlx21Usvqp6JGgScGsX7daxhnDNoM0TxyLM05wgSAm6px9GXlNPwg//AM6fzD9ubg2AfQP+oc8zLx2mnao8bmdPIeVfAZ2NhyMpK1ucug4tjiX7N7xwssperQxZ1eNkLGvlr03qlioNi06JEhTwlvVbyBS4v2kgKv8Asg/g3K3IppnymeU4t3cdEBu1gx/zdMm0Pe3NuLWOBrUa56oy0bS1+zz4VrupBr3c2iNN58hfz1BSXBL0z3CbAljKVPY2sV5Whw1nJUM7aYUet5d3H4+wbI15whCZCDPUGSEGeUoRZfOR9C/UulSt5Wjgx7RhKJ5VrGc07IUdoxAzxcfI3vYixZHJ37o+mTN0ylJoM7z5i18+MivXvNniraKFOshd71g7GntqdzNbdJmwA6oijkbCrNIXItF5uxCtCMoj6FyT6GHbIHh2RMagdXg4EOSPQSBnde8La4InANRMDbZAtSLdQ8irUIDh7yU80OhK5KqRGj6NFiY9JsIKCTS9abbx9/HkcV6lbpEb3Harmrz9+P2lhB/f6/VcvuY3I44khX6F2kWL8SHaqnrzZ/Ph4lHF254fjx548crmcZ8NVBewiAdeodfAQ+Iegh+UPhD0gI9M3+V18Ovh1/b6Ovj8Q/iEfR45C5b/AD+zf/b+/wBPqoPLf5/H/wC/3+i+mM0AeodQ9A5rnq9TGMYRMYxhExjGETGMYRMYxhFHFr++0m36O9X/AMT7gyR2Rxa/vtJt+jvV/wDE+4MkdhExkI+atz8gOPMVZbiq1Dxmfqxhqd+V3THOQtxq+Oa5W2m+xmkbX15dzu2yGrY26oDvZXRxYbRZW5jkfnDdonm0U2RKjVuMeFfamcdOaihjjMcaLWqSy5GxSWSxqA3ZXrxDy7DjsKXoWqXyqkrLTaulP35DWNwcUWx0lqGeSojVpXtr4pSI2pwTKNyKyrGMYRM0H0frD94Zrmg+j9YfvDCKP/FD72Xj/wDmcrr/AGWbcy/LXSNMsafHOYvLbH4uja1pr+9O7wTH2xsaRI3KXLFz4erQFNCcogzYd3Ddak816gbooKM113DEHFD72Xj/APmcrr/ZZtz9/IOl9L0gBMRLfio26NMxgk/jzovYEsvj+kmruVNsuYCpVDF61tRS2NHOTYTo6shjm0q99PJL2d6ZH1va3dERYf4n8ZItS+gS5hs9ZajetqytKmrd4Lboc0s7VSFbGyNyr1qLVQVKlbZ07D7bHE5fP3HY014IBKLWgZ9D3bZ3mabvrqAddgAeoeHXx8eoB9r6R/F4fkzDlAU+momr2iuyHjV/NSO0xkro6p2VBF2xVIJ7M5BPZGDBEmncxpiMZTvkkXp43GG85UUysxSRIe4Oq7VW6LYpdov2h1R9npWcanVltbpKlcxkwMjZD486oml/NjjakFxncvIVLRBOSiiDHtqbr3zU2zi9uDKzJViRW4FqSPoQi2D1alYRLFu9bqUKVUA5mPbvX7IqdKpXCJpFNYtWjhrgCNnIUxIDgzyky2+CwOW2bKVsLhKZL+RtRsEFXE44cBp1jXrlgpTkCAFanSrWLduzYMGvWrAKc5RiHObVT9rH2nkJsEbn7MygoZNLKvSymlNXbVOotMvapWsNlKFeS9Wsssp+aS1T8VVtKwhMMjuNwSJFTCvTbOEEeDG8sHJwT9c7O/swIXGIW5Vf7HGSyDTLViduQtmPWjg0OHL8dFMoKhl005MtI55zC6arxz82QQ+lyVidLNEJCaQO+5kXPbHy2ot9mBwqdrAlUjsxfFt60mvIEHiYvpS98ncrikGoh/8AYy1654JOb6iNJdRks3jj022zybkTrIwkj0hcYmxNb2oeCJ9Eg9g0OhcegjCjjMTakjFHm01du1sqETvMGwlcuUuBiFuTmmGFoG0hQqN1b2tHqQ2tSTyTe1I0LcnToye8bNfD6U4D/ZvgLVOxs1ntG9RtnxfbeOWzFaxK1Ww1HIC/UNq+qWJPXwg4O4splQWNvN/vBMGLEdL2bP4zA16uN1Emep4hpVcphMRmbUnLStkxNHH2t0v0B2D1qG0bJ8G9wFWu5W1nGmrY6odroLF63+SEQVggrX7HsTaiRbK/Y9S9K0TW2M+z47IGdtYhe3FCyo21p0clbc0oCVGyBvRJA0TlFJ0pCcokjTvHQPiD9ma4zg8pTJKUyTlOcn5lKT8u78M3L/54bhvZmXICEIWcilnIhJu7ynN+ZO7/AHf/ANGZvozM30TGMZ8r4TGMYRMYxhExjGETGMYRMYxhExjGETI/8kfuHiX5/OMX94is8kBkf+SP3DxL8/nGL+8RWeEUgMYxhExkQ+W1scjaSj7FZNL1TVdwQSMkSFfdMZm91IKHmqJgJ0atmZ9rSZTNlXVArVt2wPO0gY7TktcsyxPu3Go501bkqyzsOcL+1R4i84lZEXqyWSKNWeYgkrnrVlnRhVE5K6t0NdSGSWOtfSVKe9VXdkbjjkpSkO8wo2w7JiqTRYgVHu5SZelMNIpsW1ZbbUFfySxXiPTyVt0ZSJ1J0cq+BSiz5+8mrHFG1pEEXgcLb3WSyJecsXEBsnbUJvmqUFDitMTN6NWpJjCw9oVx2fOFyXniYvmjHRq5CsMSJnyBvxFlqX8ixVdRIIGlrZDo4yNbYUitBMTBIzD0RShzeJG4tqAkNd1QiXKG1Z+nq6ASWwVUTn05Iizfo6GRSroi5zyfvheixKVuii8PZg2dH9z6HeXBAi03P2TkqDdddgK21HzaUZXV+zXskILVKLjByNjd28PuWNT8mXan7QrRTWLrc8dg/PN75RuMPqpZLXBCxTGQLarLNFEj1cUyEJzsxxZasSK14GpyK66s+f8AR08jNxvUpb7KpCR8fH+Jx+6KxuaBOLDZVfmz9CkdK+d18fiamcIn2LzttWAqjEohrxJWJYaie2tStRPMdf25s6Zf/NXynEvkByB4iyGvJu+0DGXWaSBJZUTs5LHlTVGY+ulTsxFIiNYM+GPTw1ogTNDinVnNTaoPFU4lq9U/mJ2P+GzVObS5pc1+YzjVlo0/VdqVvxRoeqWa4oc7VjYM42oP3b5ZObIcK4kJaOXRSPnPd2ooNF95Y2NDw+BDnl2TNwR89mXuM/LopOuuQVcyKpbVanZ/r+XpvY+UMDZMZpDRfmrcNtVLM4u8IkEdfD2VwL22Idmf2TBtd0m26RyTKk2+xYkXRLtP84knF04QDXY3kC1mjoAj9qJtL3OZ3fHoPh3hAOoAPQPEMkkHoD8gfuyFlo1m3xGZ8NtWSSzzRlhdvJ4m3Rt2mr3KGx0Rm09cfkHOUr5Wc+SmTSFuKJApC9u8jUrADffZVupMANxmmHoD8gfuwi1z4nkFKSTCDy9DSTdNyzSjdNDCjSzNR0MLML3DbQwszTYddy9wHTfUR13DbURAftjCKjTmh2NETuvWTOfHqRQenD5c9ReXyiv3+uyXiuX+a1+wTFirV/Ic4yrZp7DGuv1k2d5azwSIOaWIbSVZInVkQQ+RTWSylTBiK82uQXZdPyChbAr1nmsc1OMRq6+lkqsuBskSOZ3OJVBDZBSfIi12h8T8gHbkAoYni85pBYxEG8uHPU9YIsxIjZy5SVO5erIfHwH0DnWpLDYjM28xpl8Yj0qajdTdDWySMrY/NxmigsSj9d0LslWJdtTyhEs4BJ6Glj3DO9r4Z5w32ZFTFXfbscRpEhRG2dEropsxXH0Us8/WQj3UIV7W1ILd/bDpOKfWS9tLaiimw5enPc0TcpVI3CLkpE28ilTJHT57IoRwy5pVw7PKaK1fa8NlRB7K+LvaumbH5MbqldSCkL2KlqZJrGHxvTSJxcGlO+ENbu27PGr62klbrUy83ENmdkX2f9mq1zoooJsgb0tUbrtnWmpXN6Z3KdBRJW3R4La64kLBG9nghub2xvTuKhiPUkN7W2NxO2iBAmTF1P2t2VXNfjrYW1gcOLIfpmiFS8q1DnDrNClr9ke8gmkqn0hPto9+X61RfD89Lt69r5oXuZ9bRmvKsYnlqgsUi3k0CFblAY1WbErGLXI3tMJJjm3P2lCTO328P7ePbwpVK/exp4WcdctULAyDKM9OwasaBBSjMc4FDOE4yHOEJwkzs8ZRjJuHZnUvZr9j6cA5BJD5RDirnqJYYBBiVLWNnLW1G0npXFpcUitl3eUD06oD0Z7ToalL3dVKEtad7KGJDXFIhUpojuHYpc56ZdxceKnaCOCplTI1BiVhtcmWsTiceS0ypoQNBjxGFUjSkkChmMiKSPbcmY1jC7vauUNKdO9llK9ccM/al9pnxdcm2J8lq5TTIStGduN1vOpHyo5bJJV5GLMezS23DVCMuiEjXNpe9bFxd33ijktZ2vZ2WEs08a4k9vJdk9Odt7xbn57K3z+H2tUpjo7GMRcycGBLOKnd3DdQ86tLjCpfDF66XSyIvje1J3wqU+5m0pYwzPsdU2Qng5j0iKMvNT1Q32nUq49tjuXsZUKxBYrL9GVxzxeUJEDKrfhYh2StBokHFos8XfpeEuJt1Sj67ep9Y1ouQ2GOztcojx9iG44zF7Z1VwtJgPAudp3bQDh6neFgFkRn6YNOc4xaLUryHtJO1R4sSk6EXzUt4M8gaVoNy81tjCGwK7XOPsglUpwhr37XE7e+xOQGtbTHW0tokG61thbi8J2M9JMXE6Sa5vhXbv2rDly6IW5o0x6csoAhc4byFrWU0fYCFwCLiYk9m46Y2NBGu+6ko6QOJ7aYUlmT2qa4TBErCyIxkb76pIZPq9sxlSSGv5jE53HHFGlcET1DpKyytiWoF4GboVydxYXBxbz0a0CTd0irQ4SVIFGCUZuOm/dw7efDfi1yRET7xoWsbMcfNi0Rb5JYwiOkpSMrQzUlIRKEnmkiJTEBvv5Agp00KI7+wk6afDMJ6i0LdW+2Z9NNHyFs98Z6Z8N8y1b4anIp52Kpm7mxCMTpKAVY9arTiIdbgwLBDSNC2g9T/SfM28MLZvSseIoDxhK+w3tcLQyV7I5Vo0o18njaFkGvDx9fkd8lvGzzFhjzth7FypCq8T1vw7tlGVWgJdJhRj+lZTlopxkENkzZL2UsTX2UN5RBTmhJ2aHU0wiPlszSsanU9BJ5oTLyGrZNX0KU2I7SVgfao8V5rqm0Wvr/AApapMSJ9EcoYFA/9LX6shbcmBW0nL0Yi8rnN0KjpgnAW/MkOmU7RCFfMRknNrc5E9kPyDoKeuNodj5YMA41tM1ira1W9x+kqZNI60n0kYC17ahmaaOWgyWLCC5G9xlyPjMlcy0cVe1qAFem0iUkP70QbiaR23ySo2MRc/tK+yHiNhxnbQFUl5BcOXxmeUiJuVKY0ukek7ptGYuUR1629qkZSSYv2+kQ6URxrLjTO5HRtOojo7S0P0pygMldxL2McDF1qVu9WyWYBr+TDEwqULnwY8+5MFmxV79kgAjxOfLlT0w/MbOFxwI2Rhih1XS9ihgXwOBlkLOz37dLGYrUtwp29oqHrtdMKtl9TzY4XKti1TpvYHOqa9iJnMHH0svctEHA/oxinJKipshJcYxbdeOqRSnTq0xhcqakuxyRYS9K0CvQhepSHilcm6Ovjw2HbF66OLE2qH5EJ7MGi/fLiZ3RLddzESxEsLKM8kZulUlKNCzQ0JNEszcozfXQwClBBo6bdN/JnE79O6bptt5zOOtT9k9z/Kd2/i9e0pbpsyIFW8jrJzWJmm0WgHNrVkLXt6razWM10kDQ9ORxLvIXpsTPkRkXsQ3whUt1r4HuFPMnHDskFqFyLXQXk3PI2SicVS1rTnolyle17GSlRJCBJetJCKhwdQM82XHvcgRvCpRPN1E+WlOPkEcZ00FzXNVrkEM2w5fDzsVwXAjzOvGi5KdoUTVLQiVTEietZFJi17QRzr2AziUM5xeKpd7VtIrXreNsbXnNdyFG5apXsdsmq2oXaFmsRxFqXIUzSIK0AsZCOKdeBITjNpQaTdLXR+cD8IAA9enjrtqHxB6fT128BAPEB8BAB659tDddwDoIeIiAdPh6fFlHJnA3nhDUaVLAeX5iktCUkTJUimRT9mSnaFsMVZgTHlLjZJskaExaNzaU+haxa+NcYZiXhO4vNo2BN5YZ+7bTteq7N2EhXFbNQEHHnd40qGuppxA7T5zUBuiK2jy48dh9i1mjeiUaGJ9BrSpWBVuBNl2kbEjqdE//AGDcdbsydndh2jWcYR+H48Nar9HL8cxZyRf35bzHmL+BsXZ/7r37UbTvy7DunvYgr9P0ZrtNoNKXHMYyJF5M7ezu0Vd5jKRU3Pbm5WqvZBc/FBycSS1CNIDhGG55KOM84eYRG046ihB2QKFKpU4u6Fs3I8ihmdjvaKNMO7HXcLl1kE/tZe2NjmoBtNqGnEZK2IA0pQikbUsQqFG7E6vCVvKcH9riyJNu6bISPYt1ej2dg1j2j3OJI6RaNtOpivx9B2aTPOpUq5ETexcdk8dajP24eLRstN+fP/Ly3D8sz+F4/pduM2eVKlRyoW9j4rMYq8OX/T2rncf+WaHVHz1tF1dbjKu432tHFZ6WKkbwtnkK1SqzyjlsoiZpBCVElcN0yp1cy0SlSraUTW2aFSOTA5JU6iHtTizt8oIa5Y4+1lPKaIcweOM4bCnVluCHJyTCDT/Nn92TxteUYkbY66O6A9A9CjU6u0cTyyMp5Wz6amOEWd35sYH5M3vqj2N11F3Wthx0eu7hMnXg78NOdQrjl/MSRjIcm/6ZPx9eFoMhqG1YpmlkNey9aDv0sSdE7ik/njoNGEgzZ+H/AGTl7P8AZSexnW2iVR59EAZn5md+mnldvYt1bnANShWKm/yggiVHiBfsghWoA3H7Xz1GqSf+UJzyi+ydQH/j4vT+z4fizSu0ou8ZRlCTPw8ZM8ZM/wDLPw7f3VelCcHeJITHJvDxnHpk39Wf291HFr++0m36O9X/AMT7gyR2Rxa/vtJt+jvV/wDE+4Mkdni+VU3zlmfF+E8tOG7jzNi/HVppjSFcilMDvTkm1NaqKwTkS3uVMLYHDmCWTZzIq6tJZLoQXY8jaXyUNwySSGQgWGDvjUqIdkD3l/iPdEN5kyO4bgbm+ubNrGl+Q0tgPEW/I2x6qW6VwY+m6yQ2a/wCVqlLmkkjaist5surD7EhKpNFZk2Rjdvb9VZbWrXLYx9qdyLQVlZPGal7I5i1/wAIqLuuP3k6S205RXFS2k8y6cVvtWh8HrIprvGMTetYdFXJqk8xlDzMX2GPRq16i8dhzW5R5yfEuzrLPs/J1CZ5Szm4V/zZQc8I6zTdyjxFrtcepGMoYrs3sMdMLq9I1UHCIBCSiGBMpTO5Pl2Td610kOhChbuhKb06cindjKmnXtQDW2xXxxDj5JD+I8U5dtPB2U8ogsCOkKWy93OYNVUKHRNThzODsvpRhvN8aqXkNlbTRI9o5gYvdEcBXwprVSUJUcuOU5/GxoqBpilautw3DyGuVkoqlq1QyVphLa+TRfFpdYD25zCdO6N2Sw2Ew2v4BMZVI3xMwyZ3MLak7PH429vToiR7EUvc0H0frD94ZUa69qX7D1G8uCygX8rk1HuZ0R4DPvHc2yokQwM/IWet7JK4esX3koatGNNTkkraSME+ZJ8bC9JGvTu6CIFV77fjwjYSs4f8qHTkw3Xa0y+sFVR2hx1vN8oK1IiRMmqzIiEvaojCrASOcDsplaWBJLY64RKfxw5QDhHIvJo2/ezEZk8aa3Nr38sRZG4ofey8f/zOV1/ss25vtzkzUNIvLQxWDIHFvXObSrkiv2IiUuliWKQ5vcUTOvnlgL4qyu6GvYEidnBKgUzGYns7EWb54Z52KRpeFLfs4ofey8f/AMzldf7LNufC4eL9UXi9Nj7O219MWJGVVE3fSPTCUxFHN4IvcUzwvryxUMadG5LO4Gtdkha0+NSEtUkEFDsh020a5FI0DsRSCMM7mnUegdQHqG3h06dAHqPXoAaiP22wj0APtuvQBHPGXzts+q+1h58cdasouFOki3pl3nKa0nuxpgoZ6tsGOwu0W1DT0YjjLH3F2dPaxadotrg/SuRtbCZJlkLhpey9pUxluUObf6e+bF7U1Q9GPi+9LCkVYw6yD9qbImURR7rpOxvNhtLu2ku7KXogdNUSplbyXF59l1TctQsxaAV6tNuQSPShrsB+IjSbF5FymldQnsyC8l7VY/HywHB11dJsz1XAFKKHVXHVLywuTXvXCtZCUwyKQRUWZXvaqGfSFS/OhcdSExdR1r0nYWBntXqfdjWmDRMWKhrQyOGZyeo+1OWtrtkAp2K5oT1rB1Nj2YVmt3bFTK08GZhMFyTbquqNj9f1HLbHc+fVM1l7EsXgp15EoYnJ6yGpcr7pVIckexnI3rV7XsHkMOKTFhh7+XslZmgN29C3GKm2Sm6vZmRna36PHvSRukkpYHlUh381nbm3pzJq6aN7Wvd2RqcpPIAWP8mKYHNazuciVrn0g4xU5LFSqR3o8AzYWABpr4AHXUPAPR6Pg/F8QfAGb85XZsGt2DWrE3Ic5JEJN3eTvKb8v5k7u/0Znd3fhvdcyt2z37J7tkki2LRJGKScpTlKc35d3lJ5Sd+OG5lJ5OzNy7+6YxjMKjpjGMImMYwiYxjCJjGMImMYwiYxjCJjGMImR/5I/cPEvz+cYv7xFZ5IDI/8kfuHiX5/OMX94is8IpAYxjCKp3nuv4rq+T3CmGczoZR7jTT4zcjXqKzHkW4rPczR3pFyKhPgMFIYZHIm6lHOdSiMr59LIudZ8ekb2Smr14JrT2Kczn5SdlLi5atWcurBtyXx1gqmfV3xLvxxrDi5dleBo5RxchcuPldJbX0iT2kcXCPOK2JSiZTeoZE7ws0IrvqzGR4tKnfmN8EI7dq/bzYzSXjXx1sHkTxW4q0vyAJuRymVtcpa5q+3GF5lNSo4A6wiqo9C7nk7BWKBTKSZRKJM4TOVon4pv9pCCKsyZFIpc1qxk72dq6MG0ovZ4bzHo7mhF4rLFEdYplx+hdJwGAV23JmNnVE1gnjdDPb3C0SpsFXtIO6YajctUshTabotEeqU00in30AQ6CHUPR0Hx6/lzTu69BDu69B8BDoHQQ+IQ+HN2MItAAA9AAHXxHoHTqPx5rjGEUdL3+6zjJ+kOh/g3dOSKD0B+QP3ZHW9/us4yfpDof4N3Tkig9AfkD92EWuMYwiYxjCJjGMIuOc2lteUCxqdUKVxa3FKoQuDauTkLG9ejVl7FKUi1CqLOSK0ygrfcs9OpJNJOL320NL31EQys26OyE4U2mjel0XrcKKsB1ZpHH09mUgcREJI2M0oj7zGnNlIZ1aZ3hRrADW/OiVuZvawQVHCl67aHKIwqWqVe9oeMIvK5N+xr5SccpWfcXGuyYtMF5clROp5VSwvaiLnhzKrmEaepGbW7Ssnj9VdkSAyLRJjrZk91J8QqmGJbu7wpWzpVsEKcuuxLtl+anGxQig/K+qo2/yLVRuhOSWlH3zjlcCp8TxxC/FR9ojrOzyGAy0maO79EazgEsb/AGMib1O10rXNsxmLTFXBuQ+sQQDYBAQAQH0gPiA51yUQ+KzePukUmEeZ5RGXtIYgd2B/b0rs0OKM3Xu7p1beuLPSnlD6QDcoR036GaDqYAbgRQA42dqFx15EO7ZEnIiUUJYD4U77RuDXzvCom8TEyMvCSPyrSGqGeZyJE9AxvTk1oxKWbsrg76OSdYwNzolJct0FjJmxW2ogIhoG4ePe1Evv6/g9dg1DYOg+Oo94B1HxDp6aS+TXYm0rP294XcZFsR43uzuojLu+wTeuGmbUjN3yvzLAd68Pk0T2UtMtYm6LzixnqyAYoBMI7GXewSE8yeY6ulClzeV1cpfZz9rdxsTJzKetCaPLI2aaIW1BUPMKXvcib2UlVGyyU/tL5EMbDXzmnY2RA/GxyNpwXt4uB2rfu1qn6eSCwosT6s/1Z+W/qroeV/ZRcR+VrexuSqCJ6VtWIvLjIYXeVCNkfri1o+5u5xit2D2yszWnUObe7LzBdFqNWZ5T2U/wkgWIVpp5x0NklVduXxEYFRNb2/x657VtFH0xDHoTdTLLY5yMkMKVbk+aKN7YSyBkYzHZm8saClLK1Eocd06Qw9M+PHnCNoS4govtupXWqDSE8mqpkdgLGMxqKdpVV8oib9YUDUS9JIZlHKmt+KyBDWyCUXHWtelwlqtx4rvRDopseT+1dqgShcyyJ51umoznHxj5EFpEMAtKOkTY5SnRLKnmK5DC7gZnBWxt0oRIHesJCsSS5OoXRl4apCi83bladU0OKZaSo30EwC9jUy1+oViOZr8B4ixhalTLx+bY6hUPGbQJj8bfexQpW6ZCTPStVq4ygLKX5pCIQc7nU3nLQxANfy1bFbJghZyvn5Uc3QGW2S0I0CWq8dipSo7RUo5UcPh8pTo5uqC0N2K8YWhBsDiHwY7T3TkJbkx4lck6mU8WeZkDIcXk+oHZ73fWGexNt0RKF79WsnUI27Z+WsCVyQK5JH/N1BxLSsRyZicX5hMXqGq3EBK26dO7t1+IOvxgHXw+Lw8f9+QA52dn/W3OKOV6LzKJTVFpU5LFc7qC7a0PIZbGgUgWMylmXEtshKLKeUrG7EHJN3tvanNsUrN2puMLVlmpC8gVxT7URRx3Uwfhv2pJNhUXyNa3lZAoZftnxJciofkm1I3IpthssZboSAfESpY8JVKRvkIPZrUgVPIJVJ7imd3oxpTTaWGNsBKlLWMPncll6uAJfz4w065akz1shOsQ+IFUsmuzG9Q+NPaqGqjIKyS+Sm5aAWjVl53F4HL4zJbnrZcLggfO69I3p0K9l72YwtU2HJdJl6NrKA5yuv8AxeNyrkeN67fwNaePBlzn7o8hZv22012AQEAH8Q+j0dPR+Tw/J4ejwzrbzEo4/wChpT3H2R4KOSqkJpTo0NrmWahXlklr0Zha5KfpulXFpyC1hG+okqiyCCz9TNCiw17FqYGw9Og+AePXp1AfQIbAA+AgPgPTqH6s+maGMnbyOcoOz/uHJ4u3H8t7f47KhxnODtKE5Qk3s8ZPF29vqzt9mUf5JxgoGXHbKZBT0AXK9jSVPn/tZaUq/RUlcXd5TKS1aMhOeChO9v7w+lGDsI7Py4x7O8o6aEqy4myzspeKMiNPPaGOVQc00UJZXtSfdUaVvTtJTIkYxakSxGsJQucbRNrsMfkOg7PRD1L5TKnVW9SRajcUFmWM3NLYs/jn5o5nJ1vpwO4ZoO3LPw8Hk8JM7s3LSi7Px5W9x+17Nin5x2wZimz8M8A37DDkzcOzTG5HhKPLc8Si7c+fdm4pVdeycc4SWpdOP/IGxIVICy1RyPzxYW1lHLSo/OG9Gq2WMKcNET4pOlRUfSS0ttNUweKKZi+xhnU2lMnSZ7Su4k1Vy6raQvqHkNZTdY8S1RPCaHKWZdql8xUEL2JIUe8MalsFQCFyaEOoQdsQPp4QlvRvJUoNlEklu702z8xk69t2aylQtTJkqX+60W+Ks0Kj3xNF+WYNwYRnG30eLSeMo+JM7O/OyyW97DmaJqOYLRyfejGLXbeMovkgNB2dmr5AQBWRR8dLwabwlB5QeLxlJnjg0/fZzbr4f+LtV38T7h6/7v8A45I/I4tf32k2/R3q/wDifcGSOysKnN48KiHtueVNu8ZYEwOkXv144pQTel+Rk1Q3KyRSGvJk35GV4krxdRnG10l9gw+ZxOuWa0Gx0saTH7GIWuUWKfAioND5SxOByol1nPwav5x5J7cnLGj0sLsXj3745ex8XbISsqNsYJlWLPUlTEy5RCnRA1NRE5gLLeI2owRSwdfZMmSp29Z7GPbyyoGxebjntG7Tq2uk9VpLP7RyQcBUsiGZlIUrPFKBliO3y0IR0Vqd0S3pS1wJdC4f50m3I0YyWUDNpBvs5+yPkkII/wAvZW2vN7XrG81z/wAhJzy0gMY5HSeK0dyVmVbQeqkdpVanr+uXcrWHRyAV3WUfdY5Apm7y+uj5q2R9QyzGQxd5eGBwKajCWZpIofPnCTlsparB4PpK2iR/GayO0fK5sH8oRstjTnsVMu3KNk5qS2olFVbpjJ6puX3VGhwrKOuqQk+vDYO7Ipu4y1vdm0+HqJlcuq5tnkFScsRzHiU9y6a1VyiSSTjukprlYx1VbKaPRQkEkQ5MQO1HJDF2qtrDFDIpWzOlVvbmoQuUWVPMffnl7aJAqaVFn2MIvMug7LjkYycWJsa7Vyy2XJb/AO0IhHMDlJw6mPIJ1nHuwUNFa8bK4R0JMOQ87SatNg2Ue/xiEX9OVj2RH6slk3ZFdVNrg11yQ2rj7Cuz14kymsq95PRK06Rh9HUJdd8OE5pjhiikrDZEdo6vV0JhTXL2twdo7qbDW9Xalrskut1zgEJcHyGQ5dKNyGx4WLFzmBdr2aD6P1h+8MIo88SSCUnFzjwlTl6EpklK1omTk6AGhRCZPEmskgkvUPDQoknTQsvUPDXTTUPgzIbZbVXPs8kFWstiQh3suJIiHSTwBtlLItmUebj/ADMSlr1Gky014bUu2rk27CcrRlal6uTbsaOmrgiE/oHFPXv8YqB169O9Tddh18PDrFm34wEP2gOY8h/EBjiN1GW0E8kzo0NkptyfwmvFTZE0jREp3fBpZ1pvu0obWRHM5MidzfPDGVgkbwsbY+Lqp0D2TIZoYTFSKjz7IxOY7MbuIlEMl2MLNOpLyAikVdKdQoDneY7xe3tVEbX28rTtrto6omWFxNplzayo0zC5rJM/SAttaN9HEssg70F8a6MhnHOp47UteAuKgkY1U6RFA7IkyZ3Z2FWJJ6JmdVRaZIsd17bp1THOz0Vu/KNNCUzuoVKUXnBnnHOptZdP2SPOi7tYWqUQmD8c1chh0eRL218biGuRwdBBoXvLilp7WoZFqZCdYUtJa2sVz8idl8dd28kwosx0QeqpClKRJiEpAbgSmIKTFAYaceZ5IgvQovvnqNzTztw001DY04004zbruaZuYO2+3R9jmTCaDoervULj7OYbL+omdF3GlG9Zzl6WD1mweHnpIHUNcxNuvHl2DDNWejpkc7z6p6h3ZUsVpOoU9gvZrEYjU8JfDGQMcDD1rmw1G2fL1sZOmNrF0mNz+ezWIt5C+QtgpKDVRuOtUENv2YxjOcLlaYxjCJjGMImMYwiYxjCJjGMImMYwiYxjCJjGMImR/wCSP3DxL8/nGL+8RWeSAyP/ACR+4eJfn84xf3iKzwikBjGMIqJO2+5IzagYDD92G0q549s59Q8pLHarnsSrK0skqSXHUEMiMhqfjBHFtxtr3WsMe7zBylj6YqdmZxlEsa6uWxKvySJIu0cUMzeBN2Ml4OXK57rNxr+Wceo5yGQRSirFrFljLdCJi0oKLp9VZaWOP0SSpWOxmuFXOtnsR0sBBu5J1i5vcYvo7r9onvsX1btKZPA2mMVzHrE7Qyk+CcclKqVFqm+7oVxvnDFdQNZTAp1bkbXyL1Mae9CDjil6n2ATnnDs+pd3PXXUpDsPXOyitySWZX1+sC3kPF+WUBqG/wBXWlOcha3qyuapqSa14lq+t5MDHXjZVxBUOfya6lMkkUHlMljyhxYFspaHFO0KkZaU9iZyK1rGY7teYyeBQGRymF1jKrklbWmS7MVZwp2hLDJZYvWOKNvLQt71Y0mh8KatE2qvdycF8gkbakTNiJYYVsqWgmQqYIRntLYQ89n5G+eLlVtgtRMtdS4PGqKSOEQfbMkFvu96LOOUOqpmdEzslha16l1rFIWZE+C8ERtubV27+5uBDS3rFGhFZnjK86j52usp98HCrW46WpXV/wDGhXWKixKRg57VfLs9Q26EqxXWVhVi/QoloLm0UexZJa1PHnLPHnuMP0HlqJyatkCNtdHX8VvXHySuarm5dxVgdvVZL2S3IkkmjZbcPiNOzOS1gEfkTnKSqxVXRFLEhZzxsu0j5Ojm6RdelTaFuabYxAPeXpiKR17/AHWcZP0h0P8ABu6ckUHoD8gfuyvuJXAy39UnAC5I+tkjk02HYUJkqdfL25hbJQpNV0ZchK46QI4mAxEt22cU6vz02I7mxJUeIqoweexKG44ywQPQH5A/dhFrjGMImMYwiYxjCJjGMImMYwiYxjCKOF6cQ+MnJhJulvqjKxtUwWw5lIdZjEWlykiBoUApA9sa5WBBMna0BwLVflUje7pk5gKTg3L2AzbrTJyA7C5LuucZhxusZOpFE8r5MipO505xjHMVC+w1VxOjG88j2FO6Xk0HySytWJW9yl8KsFSti8WjMXORJ1TM2S5s9FWMIvMHRXKDtB+HUkSwPlA2WjO4HA69lFguhNz60JAWwKJqerkLrb01hlxoJK9vk6sFnt1+jsQqerHF6e3VygqV9X2QsiLCtg1kuE7O1Z4DNHaVcc4QEA0irlO2RchdoYvkLhu0MsmrOyEqFosGOqnshK4qW3RSwKkcuYV6VKqObZXGGvdPr5cwzvWA8ouOMR5NViMCkzbC1ShqlkInsYVzuAstkxtBKK/mTDNGrR6iTyeh0eY69nMQR6XNaF4YHF2jDm5t6R8bDzSlRXnJc+JXbMcYJC7kUPLJ9JY6uWyR9cDKTsSojq7kswlcqmEyd35BQ96Fo2qlI7s4vDTGY7Xlbi5I25rNa1TpKG5DF5c+y3JXPZp2qd+jasUchjrtPJY6/TLIFyhkcdZFcoXqh4O0w2adsIbACRfmJBx8O3LPvtY2TJ6jnKWfxDg+MptaDMNsLWaN6jkKh8dlMXkasnaFvG5TG2rePyFWbtGxUsmE7x6+prWux15CT21+MrzSt4vSd65J8J7OlnEq73QtTqq3li6rzwQwCyylOv8AlJHYleCwumz1rubo5vyOQGbb6qC1JJNtefz9ofbPau8CO0NVnsdfPkUeuZEDeprMoLOeNjTJiLYlNTLk509dIXGqAXNrKWrYE8yXWGplSBcyJ4slcpo4y6LrIo1Mmsumy7dsr237U6Lim7iDTUgZkalXukPX8UecUZf1remVJzkxTmx6nOZrY8q27VSUqbUhi1WndQJYU6baUvMdZFe93K+fJZq1sxtcHrodrIbYa2NxjtYxg43bdgV2eKYcISDjGytfIBq1ZCg9AYvgXcvwzmnlt4bCSutV1nYI5LHwoUzd/ODFg7texKuH4zH2hEsHqzLVsyIMBwWyxu1GDceFchSVQezDGeOKSfZHPLypZatYLH4bNUoaEm6Ar2ytMMumr0QmOJ5gmk6KJeokSF3PYW7U1SvXM2u8ceXNIUljz4fEn9hnynKpn2UlDI/F4rJp5xHeGguVNCt31Qxi+mGVq40S3tcVdVmk219zNtCK9EsuaVCMXMSzFrWsZJCYSiZprBT5DVHuVmcjSK0ez5K84zG0G545eU4xi7c/+F3+6wQ1rOFjQkHHkP8AM36aMK5a9gp5drvdDBAYhoz7fMukkIu3DxfiTcL1kYzy/QT7Jqo6ct7M+F0v7BRh7maeBay175A1y2xxjkSpM4L0yeVmuMbRO8eIVtzeChApVM25bjuv3LSCcXCrfUVh6HuP9419yUpuuL2qt42fK+tKKt0tjC8wvQhUCJeX/wA+gcU+hh2qR3Z15axneEYHG6pHRArT6nHaF6m75I2ATIwoGFMkhMZhxJB5uF36WL0dXU43l+VpM3HPjlRLGHy9SrK9axeRr0Y3Z457pqdgVRsgMfeJR+JmOIfi4C5JKt195h/qPDo8rqjX99pNv0d6v/ifcGSOyOLX99pNv0d6v/ifcGSOzMtcqde0quqY1rdvE2KL+dL52dlFzdovRZP76OiFEPUImE7jRdc61vSjnNL7r2bwqr5XIW95m0zjj07qGoiTNkJkMWakD0+q0ilk4LswnW+rnklwWw/dojb3Lyhq/uSd1VVEjUVNxlhVM39FiYZBHkqxIu+VzSkTlr7tWs1fpbV6qXQuaG1jOpFC3J6ZUu6Mw5rbsdduZyKtWhazaD2u6ZnxyqZZS3IqU7WXD4ZHZAlnHJOCpq8XcfuPs5lctgNgsFfw2xW5xsx/2A1vYXSxnqFt8FaJowKFJiF+nbwMvJx5DJ+Sdjx1/cJjxxV8h1bVxPmquNjG2uS1GzVDUzfJz4H3mZkMktXt13p7Va4FMjEykiSNyVUoZXR1jRDIuNIp/wCMYwiZoPo/WH7wzXNB9H6w/eGEUf8Aih97Lx//ADOV1/ss25mSRuKhoZHh0St6p2VtjavckrSgL2NXOilAiOVpm1GVr12NVLziS0acrX7Yw47TTUO9sAZhvih97Lx//M5XX+yzbmFO0wueR8fuC3JW24bIFMVmMTrw32pSJFqn2XM0lfHdqjzM4IgVEqEwqUqx1LOJBQQcV39OphW+nXUcNkzArnO8ZzYISFeAotIsmHB5vEcXduokuOmEeW5m8W+q3+qYKztO061rNJ67XNiz+HwdR7cyDqxs5XI16IJWSCaRB14kPGRpji84CaUos7sypt+x062dpMh5u8i7WjDsbYM65PpWJvcpghLcFLCXW8eed3JuY1zioVuDQ9tMusWbNr4lTEIAb05iRDqcbqeoSp/T7rqGodAyo3sQKVRVJ2b3Gl4XtBBE/t6FLbon0iNT6A/yhxtuZy2z2pS/r+6CpwOb2iaJ0yMVm5u6RPvunJEsofJhbnl59QSUm27LY/FzMTFa98DqeJJYfkpMZqONp6xQMRmnOLFsVMSE5XaT9RCzk79UpLY+oGeltG7bVsMhQrvmc/lMk9UM5Tq1Z3LhTkrUXlGDxoBJOQ6UO2N4VYii8IyZ2TGMZTFT0xjGETGMYRMYxhExjGETGMYRMYxhExjGETGMYRMj/wAkfuHiX5/OMX94is8kBkf+SP3DxL8/nGL+8RWeEUgMYxhFTn2nVoTGMXDw9rVu5aVtwngdk6Xyul11XDUtOWRCpA+wlprpRD6dYXq5jUMWhVmzAp+kkmjhi12TEv8AGYRMkyZpf3REi1bep9mdKOTlv2Dcsjf+0BYeU3H+i7aklNRZfWfHCiYLT9zJ963hEqJe4jYMBOcV+znUcplrrAJxrEXp1hznM4q4pU6pHsDmws3Uu3U5BzOmagZWXS04jQ1Yv9Q8mp2rsqb1VV9oR+cXvUEOi0ioLjMp2u+Kzap4kZcqlznD6Sue40plkpGtt4XXTmyyV4BXvNfgDeTfehfJB1rJ5h0t4uQ272mB8XZnXjHH2avXeEMtIVMfYrNXa6LNzYwzSDw28V1kRxpm7UUvbnBwTvLGhe3ZLHCjtCKZdqSWZQ6v5NJa/rZ0t+YMrfouYa2ZJHFIi6y9aUsS6C0oZJOXRliTQo3T7nqdFL66oEI+bbE7KdDDS+tAVK8Qua7r2YMe44S7jqkqTkDxZ5GVxydp9tmNz1hJ4RekggHMZ65Y6Qn2x1u6S0yDEOjJtpXBr3LG1OQgk7wjfC0i5hbVqkfSBjCKtXiNVN3PnKflvzKvKqjqJOu+GccaSrWnXqYwucTZmr/j0Xa0iWTKfOtbPcqgCR6mk5uuSJmZhj8skm7ZFIw0LnVemc3pQztk4rNp2qbojmkQtyuIRZkVLckzyXHZ3GGeUspTskTqkidyKb3hIrTFLika9ei1VF6amiiXrUe22yZWoKMyRjCKHty1zDWewOHrs0spTSfDLhSQ6LImhSuaI+xxnal7hI0Z0MUa1SOLaJEiZImSNoGMxm7SkK1TNm6QkNdNZgh6A/IH7sjre/3WcZP0h0P8G7pyRQegPyB+7CLXGMYRMYxhExjGETGMYRMYxhExjGETGMYRM0EAHwEAEPx+Oa4wio/7aDUKfTcDudSHTVPtw15wVWsnbiOolao6J5C7GUZbmmx+gCJZe2sjiyk0TNRJHzPUTR1DUN9btyA1218NttgDqGo+V2272oD9ruAht0EN9e7sAh4dB8OgZEPtAeOhPLLhVyf467E6nLrXpecxqOd7TUzVPM9Wk13gi3yewCG+7fNGxiWlgAd4NydR16bdM6L2WvIs3lX2fvFO7HI7ykpkVRsDBP8AQzcRUprNrvy1dWSlWEmf9ITKi5nFngwxMp11PKA3TvAPe6j1TKu+b9HtVyXLTtaLteZ0+9NvPZwu1A/FerC9ueJ5il6hFeUm45m3S/7+IA/0sgaHHEbIBni3huSAl2Dv4589uVX+vH8O6nsejTKijCFJJakk3XuGEqNQUFb69Q27u5RwGF7a97XUR121EBHXURDrqHTErnx7ol7OOOeaZqd2NPM2NPMc60g68w80xQsV7mGmK2A7c0zZS4L1G2+47bbHrVZ2wiapP33zGHj44zlan/08P92+ijW5cPuKC4s0VvGegFRmxIF+WMpWsTT9NSQ02KEvcyK7bBsn3JTnJ/SJJqYjcvoJYAOMezn14/J+ItYN3F1wmjnSLQqn7TEFNhFKCZaJyKxZRrJSnQpUkQm66ESjd4Jb/wDohOnsbok8mGxY6bbTcO69dfHoHj16B1H0h4B8ew+jX8f4sgz2c9NMlA8Y2OrI9a0NuZtYJ/cKwJtBDCTGDZTIbOkshVx4PN3V500dIqoczGB4KFaG+jihUd9Ol26ka6ksJfOaBIAA4mxuTgSzJotYHOVjFOAAneTS7JmgYh4tCTdYa7vKL8NO9ULFWXpztlY+Wyw7/wCL9Gs0cKJzywt6tDE72HI5O+zV512yWMmXG1cXItsBfhsrlohBZi5p1cvNf32k2/R3q/8AifcGSNEQABEfQACI/kDI5Nf32k2/R3q/+J9wZI7NsqKqV7/5DWDZXKCm1vCK2eNJ0/r5HzTpe5qe5VTG6oLEpU11jPKEY5qsZUMBhsrZG+XQGdqIiYwSmWp9VD7Cpi8kxBoeWR5c31hsd4zyHkDIoM4q+RyTjykm5UnXJm0vjVO5xYUD9rJbe17oRcHmexCFu6WTA4GOeq1rTNZ7anbdWo4hbucpPIIqu7QbiZTFkcvKMSV/wL4G2vyXuavL0fH67OYEZVFV+pjNcn00lXRpZHoZDnt2uW6nVO6simHKpCpRONf1pEZ8ua3k1tVODMqsB4H0BKOONQvkIltPcPqQWrp+8yZPEuFMQkcJqlUjXssfRA/PLTJ2poWmzlYc2nJXZeUm2SntCBjL0O2NIO10Ipt4yFi3tBeKrfeo8eVM/dgnBdktVJqX8uvLGPqBDer7HiZYyUU43sRFTKcb7mdo4pSuKGtlk2Jk5pqxAzii1f3BC0qMw35yNqXjPC22c22/uDQ2yGXR6voezR+LSmdzae2FLTVBUXgVfwCDs8gmc2mD7sjWnIWCNsjgt1QN7m7K9EzS2OC5MRZyzQfR+sP3hkOU/Prinvx9k3J1faGrBU8JlS+vZqok0SnEdnUQtBtkaKHqqikVSO0bTWs32+ZLHNrjjXVu0NMnEgdndlIjzK6lvTUcsy3RN+QbkTD1c0gbZZTKgbZE4RZ1Z7Zp+0aQmLa9tidvWqCFUJt2JQ2U+ZmI3NCoRPBDWezL9Tt9ETgeelWFJiLieKX3sdAfmbrv/ZZtysj7IDthXWfZrWyxoU4KVF1vMepEwvVWtSK9G2XkOit5Mb90R6czdZs3MpqTROdsaiN0VmAqTHaAGgWb8UfvY6A+L3G669H/AOFm3Kh+3bNYptHOB3G09i2dpVffPChkTA5bmjomj8ei84jRVhm7EaKNdlCt7jcmFlS6mJVKcpOe4777ozhJPzfamQgtt1MoslRw5B7Pr84ZPI9T1Kko5apJiFjAZZkflukI4jn3DuKDx6Xk7Xv00HWfdcPZuYK5s1LFDyufuYSgwHPeqa7hsjnLDS+JsVQtVAHHztXnkeEmpAsduJSdAp28cWq5eKj490xV76WBbpXlaw+GK9dX9wkxQbxtmTNRXkHZ0bmpcanFOlKFMkNb04NBAlsxIGp28hQdILPiUHQd/Hr123HqA9Q6Dvt0/J0DwD8QZ9s1NuyW7bt3T8d+7aPbN0+3dsFkWfH8dUn4588KkGLI5SmlGEZGJMsoji0YRlOTylGEW8Rizu7Ri3iLeG8MmMYyOsaYxjCJjGMImMYwiYxjCJjGMImMYwiYxjCJjGMImR/5I/cPEvz+cYv7xFZ5IDI/8kfuHiX5/OMX94is8IpAYxjCKnrktc9nWnyApFu4bLKJvBwjKnmDT168cOQNqWdUMJmhVaOdEEy51amxppW1WCRTWnZo6Q0hBIpG0+xaWM2A/Io2U6+2gx6YbAeODnf6+EqyOQ1P0/SkjbHgW2MxGlLXfbcie0PTNjf5itMeX6pacNZVwOAuKEI8ijaxClQo0aop1MMWGI0dRfaJcIuONh8uqQXwfs++Nd9cor0iN5vkinV6T+R0nUm8XrdBTyB7dbDW19XdjSK0bdWFOUPZK4Qkxjd0a4sgmrw5v6VnaAINsH7Pzjq9caank8JeuO/GXjWa6WA4SYiFcWJ5YVgwR2KVsLA3bSV6drIrWsHlLKlJrbu3KUCNkWNmjW2tagtzMUqFKZMRTxxjGETGM0EQD0iAflHphFHW9/us4yfpDof4N3Tkig9AfkD92R1vb7rOMn6Q6D+Dd05mtatcBcE7a2+aaGbozVxx63Q40rQos4lPoUWQnNI3MNNNMHbbfY7XQovT/EM2MANSLsGM4Lycm/zxi/0a4fSuPJyb/PGL/Rrh9K4Rc7jOC8nJv88Yv9GuH0rjycm/zxi/0a4fSuEXO4zgvJyb/PGL/Rzh9K5oGskHoALWHqIdQ/wcv8Q+MP8ACviH4w8MIuexnAhpJREQBawiIeAgDcv6h+X/AAr4frwOskAO8K1hDX4xbl4B+32V6YRc9jOC8nJv88Yv9GuH0rjycm/zxi/0a4fSuEXO4zgRLk3T/wAsYv8ARzgH7nXrn2aVitT56Qu0I1VtywUZ+yUTPNzu8mTLCTytThE4oNyFZYbk77m+TN1MDU0zTu7CRcxjGMImMYwi+R3XuDsAAO2od7UB+HbUQHXr08enUP25SJ2TgBSfIPtTuEJmwJEFJcxDr7rNoMDyZbZT3MSKJLRZEDOWI/btDVL0UtSa7FaakkqTjSQANu91u+2AB1Hr8Q/i/wBeUacgFBnEbtleL/IVb0SVF2gFOLeDc+cNtvJN7HyArp2cLT49uriYIl6mK5yznyavWvUQON8sn6a93UOg9U9OGfMYn1I0n99jYNOJmsJXd2Zp7Bot6vs/UNn/AH2SarV23HVBxbumsZIdcXUQzDJBufpkp2faIbDDK/17VmLh/wDaxnBOTv4i0OX9leYHoD8gfuzXNhYiOoCPUPAPAQ6CH+/9viHoHN+cqZ+WZ/upy+Jo9A1EfAA21ER+INd9dhH/AFdPyCOV5dmNRNncdOO0irq148njUhO5A8h5o2IE7q1O+h8RnVpPcnirmKhnUqkpOzk1OBarZHuZqrSDv5FWSSeG5eth5nT7UB/C16/k72vXqHxfCPXw6BlZ3Zcq7ENqzkQkspVOFjo083eVLYwqJ4ZIjnLaGp54UZGtWg2S9VJkXKRHbEsIoNt2fVHoGjYOqfXu66e0wmzeIlIZpGepl4jLCX6A4yfGyLE0eh3eROgfak04dLwny0ur8vRsE+Rf0y9RBhuY0WMjnvT+zkKRxklk7dgX4tBjzY0sTwGMFRrVxshElc8itZqdEwNCbFlO1/faTb9Her/4n3Bkjsji1/faTb9Her/4n3Bkjs3K5yqAu2+dIQqb69ZXbi9xMvyZ13RfKXlGzvXL6LySYxtmhVEF1QmnkDqSLRV0jrs92rP955HlJjgMpaGuFw6MvUldUMjK0IZzJydn+z0zAXHmNSFB03VFQ13RHK5XA0hNMtu7bFZY6udDUZYLy5PhOypSm1sSNLJnvApmSgM0SJzow2lbJ0isFaQmPHamQ195KWNxs4XR2luFNzm2ZHLwul9Rc0Y9ZLm1xNhpg2s4zu+1IsrVzaZConixdbCdndWdpWoFm0RUujkveEjOkPbnnDvZvcjbVqC3EPBKwKD4bVhAmCxeQVKxAzhU5zhDGItb1JQasb1liWTRWepTj5A3WLXdzNUnXz5G9lySO2egkEDsJmXu6lFJVZFHGTMM1LrW3uzs2ra2N+UdhdsgTyQi0iLqyeHwVTx/e+esO5lpuT59yp2A6skUUh1PNq2DuOhsx0lKCxo2TXBTH7MLWdOssX51Suv7LriK3ihndmULNuCvNbRyg0/lHFS6rhiSuymOEyutJKiklTwZtRTaf0FPIFbckjO1rwd1Y25kdlCWQssxTHsahOrt08iX1Eeg+I9RDv7jqI/H3B27vXwDx6dQ6B0zd5PXoIfbB1+LfcB/IAhsAhr/AOyAhr18emEXj5euN3JmdUZMOVc8e73Kgk87bGnuaMykda0hMqiu3XifEaBbuNMouWu+OqvWd3NXLGS/6opVDWpcikF/MdOxNqt40oiwPNzm65bs6FVp2HFuXbMisnkms4xjfCNt4W3Jd+skPvtXW59WV45WOczPd+RNdOJlXEfu06eMVUzS2Y2/Pj5Hil5adxe46hjzpvbd5Ev8Hx/C67Bt1H4e9173e/8Aa69fx5uDTXX0B4iOvUREdth8QDx22ERHw8PEfR0D0AGEUe+JRYkcXOPJOxxqnYmla1K2UKPJeXU7lxJr02UH+RLJI8sftqJp3kSSSfKb7eSJKL7petOvajNoWB2mPZAVpG9nJ1miSyLUspYyppTtF0bLFoSxJJbrIjF2jA8KCHFwWQ1yaW1Qm7/lfNFKBUU2lqCHtNcfxR+9koD8zddf7LNuVOW8zq5D9kF8SQMWI1ieFcEbtnqZvJ22MVMZZchca8PUOADqGifd5U2GX7HalbGbGpkakw3yXUoN7Jqb3B5lrVPBVc+1DFbDfs1rjSevRBT1/JmhmnjA9ebmw1uNXIVOJzZrgASmEw4zFK/+neRq4fJZ/K2M0TCFqaVtoaBBCEZ8lfy+INgRYMkTVrMGr5cWVPSty6REjVKZw2a5+2WF7xHTuh0AADp1DoHdAA6+ABr1Huh06dNf/N/xfHp1z75tAAAA6B06B0/4+PxzdlbXP2bhuExjGF6mMYwiYxjCJjGMImMYwiYxjCJjGMImMYwiYxjCJkf+SP3DxL8/nGL+8RWeSAyP/JH7h4l+fzjF/eIrPCKQGMYwioT7cLev3WN1o1vHGWpeQliVnUXK3lXFXC7LKtmuorAa/wCPMYrwy2AiBVPrEEql1rTYicxSOxhrKXNLcxMQSmSvz+haURzU+zP7P+N0zVz7y9oOkaqQVjF6T5CxxjU7NU2nU5TSlfN+OdJ2mDk5q569PziwSpmTTQuMP0Zb3A1sTFNDU8F6kqXtSQVgTtW4AbyVlXGvh608auMPI96tFBeForCeSln27TqeuYjUrXAo5IZVB5zSUXkNgeyb6ZbDbBn2OR49uVPzNIBJdvOIoS/mJcQ9nLfU2oW1tOB864k8dqCjpFuXZWDS+cZbssC3Eu96wip6+5Kvx1oKLYr6JzKTqLdpux26etFqrpTJ5bo+MjnBrLY2F2LY1i8iutttztdpgL+spGJQebWdro3ExWPWVN3quoMqUrHdAjXKZJL45CrEfmpA0tJ693DRphr2tcz0JLSQUl2XefpaxYp2mczfezWovmHvUEXVXpyHmVd0pW9MN83dk0Gcbxtq+lFAw5uWT9fGt3xDBELxpvMJK97RU57IirY6Ft7ModhSJ97QLUOtNPApGppVpgL9Z5KNOZEGa0ZJI4hAnBx1cEYnkSWRxKKzaRNKL2N8+3KUtcWejhXapSTEfm5hxxVKtN9nDy+ZuzygnE+y3/jTHbg4v3DUV88W7EgEltKdwd9sGor2WcgG1NcLHJq8gD2wR17dFJ9dOZcQUSleVGXRdJ05vsolSsJhFL+lOXnId7kHJ+iLKoyJTLk3xecaadFzLSE6KZK9tarb9Z3Z4gc+irlcprCtiLi0qopP41L4hIXB1Eh0hvnrFIHVI/okyTH/AC7tm711RwKYWDF5RxZgUfvlpR2+xE8saSp6wLHrBdWU80bCIFd6SwmONxZSy2ifDJNIouZM4jKZZEYjIUTO4rid941JM4cR+O9zw66eUnKXkUprZutrkudTUXTV1UT7JZjBKyqeg41JmqCR8uey+JwJ+m8qe5HP7Al0nfBhEUbEoPDRHWxsUlsp7w6TxXNre5kgncUSReQBpJ4ELUxCskD0xgGpzgKUFmFgaQbrqYSaGvlCt9Q3L212ABwiq04/WJZ0643dmE98hTy26+pk71/Jpmzux6VHJ3Rw2om4/On1a07JWdVuuXotm91fTCGBnKJc16nYxoZx2FuS2abD0khY/wDcJviPoDq6Jw6j8QB6RH4AzAN9R9hMsXizIzWVpNkLffRbagfjm5Ga9oW5dT9zGrkCN2MJ2cEqNaYWWYrTEKCyVO2gCdpuPXrIAQ6yYoP+4Tf9TmQOHblFUC5dsQubnJybv+Sy7XNeDc4uDcC9t4iJVLevBAtPRgub1HuhlipblnkfOm9SOmvnCM4g7ua9/ua/i/5ZRd/6qntgf/2epP8A+xcuoDQQDoHh6f8Azt/h/X8HweHhjubfhD/W2zpwdu9O4CFCXpHUnOMINOf412mHXNoxaU+mNjpi83Z5dMeGi78RZmZuIT17Tu7/ABr+f/Lg8N48cvF+fHLf54pX/wCWUXf+qo7YDp8fvPkoD+rpY3j/AMdfDJz8ReWh/LJimb6fxm5VcaBh743MmjNypqkqqn2U6uDX7JC8RJCU/v3ssyoBAW9xWCaQKdyEEwF7f44zB7m3UPth6f8A3t/5hmupfd2Hbr4iI9fER9IdOviI/EH7M1Gf2HTcnjZ1cL6d19eyEiClDKj2fPZOQoQm0iDapfLOqRix5g8pR6h89cPzNwvsQbEJs87blg3PI+yKHL+OH6oM0vD+fHHPHD+FXP2nNzWfU1JVhHKglqitZvyN5V8YuKSe3Uba0PDjT7Hf9qNMOlVhsTXIUThHlUvbY0Lo1QTZ/QL2VJOHqOrnFucyEot6nEVdLqN4tcyIxRy/kRz+Pm0oqmx3Yhs5HzW3rZ432i2QZgi00mk1Y7PtZrf4szTismpwSGO6GtpZD2hID07tL3GlvmyHRpsaviiau5LVVLKWuWLEzCvJmmQlPDRu4OrMtIWNDqgf48/sMgYVrbIIxKotImprkkTlcec22QRiRNba9srgjcURB+kFXrsoKanCaQBbl4cubsdXCnbZomKyG0r6VPL5WFd3oxt8WthLAFbRFmBORJZrF2tFHXKeStFLZsQ2Fmex76jWHnqzKQpSrz7MXtF3m7eYYjMuTUQtKDdonCrkvTjtSSGx4VKH3ivpx+sxWyxCplMUjLstfImouTilIIFd0hSSdChN0sSMWUk1LTqE5xW+JjOaFmyfsu+zoqF/5qb8eOQXOya2Wxv/AC4sCxI7GpVWlWUnLLQndjT5NMZuvQtO78q0j1Z00yJlO5qhRrYmhaMvqiEwu/yX8KOPUp9wUxBBW+BrONtmQS0qodK4JQQt2YniAR12haBhPcWxt2UucLfYO/vcKlcZWb7JHuNuRyPcwg4tOpIxlSHZpcWqHe4C9xmLvUkGrqNduPsBa7FfdZ2yReCyS2Xm5pYoa2p6bNk5Mol0wc27SRyQeqxexROIsupZCZlDdSRdj7OblKXzL4Y0PyAUqmNRK5TENmGzyI25tzuxNlyV06uFdW+1szg1KViBYyprFi8jMYFyZQanco+e1OaUw1ItTnGTczAVH8b6149OdzraxRuLG3Xjbbndkpi/n+hsVZp4/RiLRiTLIWzaIyNIw3SgYkgkj80JTjkSuXr32QlaJ1T0t13z7hEzg2r/AChJf6YT/wBgsuc5nBtX+UJL/TCf+wWXCLnMYxhExjGETKi+3Gq57sDs274lsMJ2Gx+OO8J5ZVosJT+cKmyWcb5c02WapRl66bngqUxVpkzYApw8uJK80vQftxAbdM6rNoozzqIyiEyFPqsYJlHnuKPSTfXXfRS0SNqVsjmnM03DbTbQ5EvPL213AddgEddvAcs2lbHPT9w1bahw7r69sGIzEgO3MbIqF8Fk1UkX8SFaCOdcsJflmMsoy/K7rDZF365g+3dFMfLeHbqi7M7P54dueWf7rrNK2ew3VUFW3FFzSzo3a9dwqyGA4szUzTdonEbbZKg6b6bb6iOhDloXuHeEdd9NtdvtgHMoZTP2Dkqd1XZ0V9UErP3UzXibZV4cRpgJm+wmkL6KtGRR5iIO02DUSTNISpjAgSAd3QsNNSw7gajly+odAAMkb/rsNR3nb9XFNy18DsmZxdM78u1qhUvnFQtxk7ReQ7dOILI5dMeoZYS6YtJmXlUrnrAM/hyCHOTfaTxZ5s/2eMuWdvPll8zQ690OvQOvQfyCOodev/AeOV/8Cr7sm9NeW6ezXdvdldO80btpmI7N7QhaPMYBEjWM6LNavRCAAvWokjgYB7qpDzxcOwbHeOgZP84emgj8HdHr1/KH4/g6fB1EPT0yCXDG3YbZUw5mxuJU9GKnU1Dy2m1eSpVG90extoyciOxp2W2jI9UjS2BpIpAW4Epl2qgxzVCS3p9jnM/7XQvnVyco5LEN8T2WI94fw3BOLcmrMVmeUW7bdhhSJwSTPx+3qfll0PXgQPpPqJL8PjyJagNWtxzrzpxLrgXzrUjShA8o2yQyxLtaiRqTT6ZdudmLCi0lmRqHryzm3h0/8Xer/D/9T7hyRwj0AR9HQBHqPo8PjyODT99lNf0d6v8A4n3Dkjtg72u2vo72oh+0OmbdUNUac4ohJ+WjH7RZGm7LmzkEC5fSioI6TyCcL2SvkKnD7F4QtqKBxuRwNyZpLGeRT6wyh4CctcWd0La9R16iyNlBUQodU4yn7O2rWCva7fKveIFwsi834z2XMK0IYeH8ZliKLVeZOInX9kSNid1tlJN5ijsabkSRgmE+Wp3FSVLW5wibo9LXJz0N3KhPePZ69oc729ZDzRds8L2+qJBz5gXP+IILbgF8u9hIrAgleV1C0sMkblDJm0RlTEVamB6rTdmptTu+pC0SwcPKB10sL4KUByBpZJyUl3JmWU7KbX5G8jFN3u2tFME5jteMCEqlqbp9sZG5FYjy/SXdX5rVGjqvUHuZ6bdQ6baJdSiy/J6kU88YxhEzQfR+sP3hmuaD6P1h+8MIo4cZHBC1cVKNc3NYkbm5vpCCLl7gvUko0KFEjh6BSrWLFikwpMlSpSC91ClSoNLIIILMON30L022CljiFZEIvrt3OYVkwiaxOescQ4jweIs73EUL4tbN2h+f4UoRbbPJ/VvTqzNo+v1871M2bJQQQLhF9DUI7H5b9TkBj1q8Iq4rKXkHqonYXGyPwmTpUis1ArUMMpr4hkdSkq4kBORqdkK08CFRX26c4dDdQ27ndGuDgTC3SP8AasdqUbI5zI7NkLTAeG0PXzeVt8TanxwbmqGSVcyt5zdB49FYwlJbE6s8S9m9jSGrVSlWvVjuao1LTzsfcxVQlhsjSvWbdijdrYM9MzCHQyRq0xntZCLwn36U8PPK0+z+VntWapOppDi7dJ0SeXFgPVc2NHi51G9Pghzz5B5/ERxNrfNIrifENGEovkmzRMRJ+68YNj435R/VYbxvXD0B+T8v+sfHNcB6AxkFc2TGMYRMYxhExjGETGMYRMYxhExjGETGMYRMYxhExjGETI/8kfuHiX5/OMX94is8kBkf+SP3DxL8/nGL+8RWeEUgMYxhFSjzhh0h5UIS4u8V72eFlKKi5Uu1bRN3snmFyFoywa3k8uhcAGsYyxWLSlTb2FA+QFko5wtQS2r4zJU7a7Q9zgnmTzMfbEoa2nOXZ5UdB65ikggD3S3Dqv7N46WrMmYW3jZYlg3m5Qp/tuDwWbS5zsGyrrr2FWhpb9kMLzH3SYrXnZ+dZHDjIgrcZMuJUFoEUOuQPAXtFnu4rgd6GlHCX3J5vz0ovnpGNreU32TYqSY0tCKWjieDPyeFsCuLBHXdxqEo7ZwbVBrkQhdTBHyikvTQqwDgrQfI6pnPlRZHKN1pFZaHJW/Ge3D2qgTZ+ogUdaY9Q1P0o3NhamyUSGRnuarSrtnldsJe6Mvdy1JS7hoWJehFYDjGMImMYwijpe/3WcZP0h0P8G7pzNPXpJih/wC4TQ/a5kB/vzC17/dZxk/SHQ/wbunM09AGTFAPo9gDv9TkQOEXXFttVk3L1DW4WLAULmkVbIlTcsmcaSrkywvfyZiVQjUOhaklRpv9ruQaVodrv9oJfXP2vdlQCMLdW2SziGx9wMJLVFoXyUsbOtMSHDtqSp0SOS9Mo3IO3021KO1L8kYOuwabiOogEQph2XvZ+2BN5FZMz4oVDI51LZEtlskk7mxKTnV5kjisFwXPC47Vw00MWK1oipP3AvXQw4R3HTqI53G6+z+4Y8jZkRYV48c60syap2JsjJMllLQesdS2BmMWHNbVqoKWEf8AQ0Ji9ZsQWOv2oqTuoj3xDNO88/0H4rYlyxJFqrPfuNAgeqXW9iTYx+0TpaDRiMZovzP88eGeXQRVPSn4rERLnvUONIlE0s8WGp63O1UybDrPXBhwy3QYshRIV7kT2rtjGnEMdeQ6ZJGLAEjF1kQJsbGx6cptDm5netd92Z2XShjSNjvqWAiYLW4KHApGvAsPHcUh54ah47d3x6cyxSdgk6AHOOPbNIG8TTSAcGN0Qu6ATye6BpILG9QpT+ULHYANLA0TCx217+gdQ6xemvAPhtY1Z1nTc548VvJ6vpspcTV0JdWlQcxQgpyLApeWxJ9Vpe6fVVprrqb5Q03qGodOggA5l6kOP9M8boRrW9F11G6xg2jw5v8ArGYslNSNYPLwKfZzcfImnqNxUrRSp/LbiYID5HQA11AMlClknsNE4KManZi/cDasTs/EdEOuHZnUgLstPudJO/1yi0HcUXk7R018Gkxw0iYvJ7WfYfmdiEamQwmJq4b5MxztVsSyNfYLl1snKtGpI9JsW9URyWRwyBoCGU2NOZHKNBxKp3Sw9YY5WbN5ZP61pmnKpZnVEwudo3VcszaoFW0ILkbmSe2RdsXPjsDlJ5W4JliaMRNqfX72OdT0BLWsxpHb35MUwzWHY/PKP8UqqoeEV0+WC82/U9zWTIUkHUR9U2Ari8rjVjVNC174kXNq1cpYpjFVuyt2dGotg9oCVc+tO+3a+dHGB95TU2yR+CTBqgFv1Nb1Q8jKLmMiZlUjijNcVFzZvm8PTzWPoFjc4PEGk4JHGGzJI2L0ruVHZG4L2Y7V1RJNDIv35SXPLmnQlt0bb0T4sce0bhFYU/188wq1rP5Anvl/VLcFb3BX66UpXan6URsFHrnOAbMsuYyiJNO3dsex3SntYtBqZ7nKrrN6TtN+HXubXNaclsaR1pHOPKGCvN1NVwVDcNRz+u4zaDiQ2VzMX2sbDg8esEYTNlJ+wR+XoI6tj6oUL0SYvIVR99TN3JsPaPcTnxtnTmonMqiAVpOKZgU7bLJpy5KxkMXX8iJWkhNGyV3jU+gsef01bWjJVpDZFbS2bvaAcfotBe/oBa3MEcA7v4AcuOX2/Ji17hJoCpLStOmuLXHqtKzgljzqzIM1QujOUZfJGfzSwbKeaqgbk6v0ydlzqzQmMM9c6t8VY25IU6va5xkzsY0SvvfgMfyIujmq7zt2Yiak5WcEqh4qN2ree4GTmKzWAzrkrK1M60SmICWtLqwHW9C36EuCR3UOJcmjiw49EhLSolK0ik3YvL2iauHkWRKpmUQ4cUaUQ8gL2Qpm10O0gtcPLVPnmPLF7zsk0j5j3IG+s5gqbYwndDZB5o3pXBU3J0Du0nra7mPtXZ2f2a/KbmLOOOaSseQvElHLk1r8Y5LYJypLHJGmYYdY1epXSeJI2StKZ5tUNl19NzHQqL7exqh1dmUktcaynqN8Zb9mbyxtTifKKi5D2vWpt380OVda2Z2hNqVU5viMkygqkZ4wwxqs6GVSiDnq1Lg6xym6tja1JLWBtYG/Sb244CW5FnJkDzxXIrsluQT4z87olUXIRxtVi538PSaxsFbyplqJU/IeQ9XSJEkpmS6q62qRoaxrx6qmQTOEz5RqwLJGhNjUCFOgkCATy2gisc4iX3fNwyGZIrXeeCbwzsjKzqmr3o/JWaXrIUrkvcFJJwTRrk1VwBLHmY5GR/ghwSrnA9e4lKku6Qkojy+02Gr/AChJf6YT/wBgsuQP4a1BbdYSmZnTrhnwL4wsrxH2kpM/cRJm7SKTS11b3M3ctqmaBZxhohMUxNqNSrXtisHp/OLclJxGjYlLNNW7zwav8oSX+mE/9gsuEXOYxjCJjGMImfM3UNtNvEQHw6CHTqAh16CHX8Y/Hn0xnjtyzt4/v7f3/j7/AMJ/njx/8qjLh8uHin2qvPfiNJS9W2M8wlzT2hvHJyDbcpA/r3JoaK35KxINd+qb2yMMwY2WVCiSH7HnsC49yPTFaF6773mB6PH0/D+XKYO2SrqZxav6I7QGmo44yG5uzqt9Fd6hlYUwqXya8cpATrE+T9eJyyu4ccmcq4UbSrcsDQ8kMTNOJKMOHu7Ws1HakCvCsoHb1XSZvmNd2RF2eYwyStZ2p6J4jr6jLXNyrXYPtyVAEmgSuRngWqQLyVSFWSUqTGla9Z9RIfiPCad6k12ecsri62nbU0OZRq7dpmPoYsRS+7jbYNVhgM3EpOhruWnsUK7SjjzdECpwElim/jtkkcHPDdVexJyOzffsncovu0GF1eZcv39QGu2ght6O7t6P8b9Q+nx9HT4fQPXIKcSC+PKK3OcDXSp04Mm5fJQXfkKTLQP9iCLWfoFHFfWDDuWUX7WjY5o2GABYm9F/lw23EO5k7FHTyY9fR0HqIdREOvQPx/H8WQW4u05H6y5C87JY0W1EJ47XHdUInsjgjACfV/qBWRVzJHkkemQFvDgcLlIETdrIW409Ay7bth5QFJ1OuvnO3EL7Fa9h5QCCcWtWWMUnR3QQfH2+JVnnKMu5MjDFNhxnJwzJJ4tCM5w6PrJKMdX9Rh2splKVomv4SWNo0viPgczYHuWusapmWFWML4SrSJayNWVo1QTZKpTYZSWJBrmzC1ffZzX9Har/AOJ9wZI7Yemuwh6QAR/YGRxafvs5r+jtV/8AE+4MkcI9AEfiAR/Zm3VHXnYvntoIxxnv64qVtO2KtjUlhPaL0hVZcalcPlernH+FU1o2m5hP7K87Yi9U69UyTOSzfRLMlShYlbNSdG1e0nFoSu/c/wAa+V/Hzl7CXKxOONpRy2YayyRTD3eQRnV10QoZOibGx4Vs5oO7a2KfOiG54bFe/cIMJ8krL6Gjv3tdYHyONcsOZvIPku1wPmlZ/EGieMlhx6i4xHKDr2lHuwLNsv3I66t6dWBYMyu+uLXSpYw2+6qxQuHQaIMjDobrHXmRSR3dTXhA3tMjuClh3XIo5d1T8iZiz2dbfF++n2inq3WaLIYNpbkdMr6t7fr2fu0KaB2YItLF8DtZgZpw1xrYmMnS9hd3aPN7QzuiRoQEU68Z1LaewrSXkwDeWxnSdKGjeQEQ3eQM2ksPYSzhTmPZMa2XA+Gs5Z4CVu6aINkOpgDoKjvB0zlX+QMUVZnGRSZ5ao8wM6Uxc7Pb44omhoa0RIdTlji5uR6VAhSkh4mqFagknQOne3DqHUi5jNB9H6w/eGcQxSBkk7O3yCOuza+sTskJcGp5Zl6N2anRAp176Za2uTceqQr0ijQQ2IUpFBxJoCA6b7Z9Wx4a3tN540OCJySAoUJfOm9YlXJhUolO6VYQChGceT5ZKpKNTqSe/wCVTnlGEnaFm6bagRYM4rCIcYqBEPU1Xn+yrb/v6fjyuTgglKdO097ZWa7bbirVzXiDCTNO/wB5KWlhFMvyJIBBY9RLPN1UmbrBEzbU0wA21L06AA2N8Vx6cYaBDr0EaarzoP8A7qNwfr9OVxdm15Zfzg7ZWSamD7FuPLSrWBuRCAdUW8OpVA0PA98NftvZB88/dQDvbCWC0NB7oh3QnUjXBAy0a2xVsOKxj4hvYozGc+10/mWLLHEU3FXLCJKV4dLYSfEFqCevhTNE0z9mse8ayKpLV/Uc9nXbWXMHX8JDH5gLgavqls+5a608rbYtkJZQv0B3sAJqwbhGPlhymEYYlsgujxjGQVR0xjGETGMYRMYxhExjGETGMYRMYxhExjGETGMYRMYxhEyP/JH7h4l+fzjF/eIrPJAZH/kj9w8S/P5xi/vEVnhFIDGMYRMYzTbqPTuiAeIdevwh1DvB8HiIden4/T1Dwwi1xlYfFy5uTSjm7zY458gLKrSxIxUdT8YLmrldX1QL6qGMNl7SXkk3OkTdfZCxLKcZecwtFQR4dJGpWtOzk5KnQ8phakpxCEiH/G/m7y4kJHZ78qrTnMBfePvaX22/1qy0Gy1qkY3fjs1zaubctjjg+R+zSHo9/sF5VRupC2C5yJggFrWvcy9mISkiCGMA1PZFf5mwDNB6B1HqPwDrsG369RABD9YB6Q+MMidCzOYK+THJrjZONhVTqUMkLdDK2kNyr7A3SGoFurLoiRPsXbGjY47bZPo6gU4aKCi9jxaROU6pw2rEqiP1UPCq6apk1VTaORVm5fchlNNtN6cE+VF7xaLx2YWTPpVUMnGjD2KKTyaRVRX61SUzL0b03oo89uzU1Ojo0yVS3tCsitjvXYNpZxk6D16chkAj8HTrTl0h6B6D6czWH3Tlf0Ad/aROVkU28ucVpPst6rtMiQxK6RGt93aDT6QK5NYOpkV48Wq2vqiRPCkkFKp2TGaEnOxTnto6Np6j2KcQMXoj9t7Nw+6cr+gDv7SJwi7DmwTNAEQHYOoen4egB06iPT0AHUOoj4B1Dr6QzfkAeYlPcjLKkUSWU1JlyNtTxCWMLYU33DMKc1rO2nZ0jyuGXs9Joi3uJV0sMNam94QKqlk+m7G47KxT7tTkVI3JxjxFP7r18Q8QxnxT6m6EE6HGanG6l6AabqX5LUwwNQDczUrvb+S13267gUG+4FhsBYbbBqAj9sIsO3xftRcZKyfbkvScNNc1nGlTAhe5Y9FOShEjXSmQNsWjqEEzOgc3NUsepC8NjO3JkSFSeoXrU5GhfUzqEa2/tOODbjB2KydeQUZbYNJrxh/G5iksjj0+ijcuuufNhjxEYIG0oiLMcQsem8o1QS7KyU8cTal76L3lKdqJWYZ7Z2NSiYcIhjkMcpAxyZy5VcCCmmRxZkRyJ+iijTm5Qpoy5vZnNsemdcbFCy95BsU+NLiw+TbttnxIe1ArL2j1zw4oyicQrgjx/wCRVo2JzBjdidosLbYEmmkCraIuzXWEu4ico4ye0HJaNgEEi7Q2x5yUlOjHL1jKQ9N8ncm5Rs8CckZiU5FaLavMXjhSPu0BadqMMP2471VFbvugtejf1RsBqqbu0uYopMXMlqZ3A1Yge3aBy5AjTM+rk6ecMaoDkBWpiXZR2tFyQpJydqNZW6xo44L+SscfJfRJbearXJ7Ni8bijVOXp8jbikSHNprejiT41Pvl1atJqoRLShSecHeUKL8ldmkck32ve2TrG7opPpFeVDdnxwm4xP1h7xB+WNfIpwrC+OSz9CbthigtEsSSY206jmldTKctLTur3jc+cJnH16NMS3la7TphFVWJx17Wnh1xQ0icqWcfKwc+d188X5ukZ1amFxOkL9q1mMfaBcXokkxMzutIXcllrVBWdeq6b03Naza28NPa6aVuRelzGMYRM4Nq/wAoSX+mE/8AYLLnOZwbV/lCS/0wn/sFlwi5zGMYRMYxhExjGEX41qYpWmPTnpyVRB5JhJ6Y8vQ0hQUZptoanPKMDbQ0g8vbYo4vfUdDCt99Nw202EMo+7JUsjjXdnaGdm6eGjYw8c+Qvu7cemYQ83SJeM3K9DtP42xRonXbyBrLX89KlkaP82KILQq1pKU0sd99TDbzB8QEPxZV5zS7PqeXhdlScsuKvIMniNy1q2PyKtV1r+5g122wWVScqLNUrqysWv3d7j7bIkbDI/IyiGuCxadtH3TdaYUl3OMQKW7pXp/lcPKjt+k7LlhYTCbjjaZaWat179zHYHbdeuwv4HLZCriqt/JTqGpkzmuWC0KF21UBsh70KlpqrgnCtjJ117IBuUtecmkNpQjIoDR6DQjIkoQ6oyYZotOUWdwtHqZ5cqzw/YPJ7fba/wCJt6R/f8QeHj+vr8OV98YaKs6teY3aD2pKGBG3V1f8uoeR1m8J3hsWqH8YdVQxWWGK2tKbs5M2zc6aEJStXYgjZbqPl0nlCde9kOJfw57b9dE5MgY+2CqUXtawO6Nl7nAGvIrsLqpQHkN4BJ0U2f1kc22VGFa6P6Rie1LLvtq5ktDmYl1RHdS7AQu7JvSd53dyNtibTm63S65Nx9sOGP8AOZHNGGvpLxfWq69eDWnaTHrFTU7zZeebJnVAhXq2clGpaNkW5ImmoUOp2b01DUxItpxW56lulHXs3ja+QfWW2+qbGFzuM2EFOxaFtGo66x6s/grFafw859FixU8zaU2hbNb2k2Mxe64Z2+BjtusVsUUVunG3O5DH7bq+wxBVPVvxhj7ED4gVh7VgdoU6wLFRgRNbHYBbg0iI8s5sI+n3u9X/AMT7hyR2wgGuwiHUA1ERD4wAPR+vI4tAdOWU1D0dOO9YfxQuHJIZS1oFR5F+DXBbnNyD5u2rc/E6tHGQQ3kuZTW8qLldpNsynbtX1M1IZIJfPUbLN2aOIVaw99QMkTSNTUUcZCY8yvDmsWKnfQpHJPs54DT9Km8yePtOUxBqaYKU5auTCvIr53lz40TnSYUbSNmRqZPq6Zuz27p52ng8zjsNmDYU5ntqZdE061rLSInEhEm5q7ezhhVq2zJ7ur3kTy14mWLYaNlSWu58Vrea4QyW6fGmpPHo0/T+ETiEWRB1c0Y40kRxlFP2OPMU3Njre0Mji+uDcyM6dBJjjZxrrLitWpVZVgTJFKNXIH6aS+YTyWvtg2VZdhS1Vovl1jWZYEoVrpFNJvJlhZRjk8uikdSUiVvZWlK2MLS1NaIi81knYoJtTd23ke0RXftEGz7IBY4VEJocnbTbuSvJfOCCwGtqxaH00N5eNfOHAQ7TQqGFKBiqymXOQvShs2ZlLqvG23tHYKbyJhdDvFaIan5GR7jXzXh8uurjS/WVAmRiubWIQ2dxxRUTg4yhbtAdbQreUTaG3NGa3s5S1MjtIYI0J3k9iV7s7yknyo42celdxp+Q6qjqkU32kbgaEt0n13EjrVTtmreY0aIiJ8Y07SgogtoOOZyg0c9dymg89qL30bzjE234pnxa40WJDpfXk84+0pMYJYE3Os2dQ6S1fC3mMzGylAo9j7Ek7KuZjm98nh2zeg2MmLiQfIttkSQRcuqcrukXm444XNyAi9Cc441S9Jz+uavujtQZZVdfbcTY46chknD+oXekaxf+TsqrxDTDG8M6ySNtgts9h7OFcJ3us4VyznsiUJnZ6YoY/HuE4OxBfW/Xg3b9e8fa7kFdpqu5k83IzW8cuSA2LAY23sCjlXaTjE2HdU7txb28nxWObJo7OQRbrXuOzZE4MMq1Tv6dxKC7CD1/BayiTBAa4hsWgEGiiApqi8MhLA1RWKRtsJ233JbmGPMSRA0NCEncwzctIgSEEa7mGbhp3zN9tvvFYTDoI3q2qExSNw9rcH6QShc2xdkbWFAtksuelkilUhVI2tMlTqHyTSBxcHyQOppe655eFytzcT1C1ScduRYZ4n+cjxY48ip1J89Gkq1841T+UFP557Umry2qfy3Q0U/l++BPluhold3yvTfvBlc/ZVbHrr/7XR3ArX2PO7ROVM7SrDcNjFyNlrmJaqjdx6+AEu65zSFgOmg+RT67d3YB8rvZFxUDrxk4/enwp2uvAB9P/VZs8PT49crg7Ho3Rat7TFfroaJhXaj8lmA9Xtp0JXnRxDDUu6xGYHiai22P8kSbsADsJW/QB17ojOqBtzq5c48DSyNMFOuO1mrEptZ14h8lRlUJRaJxxcuU7FnHn7grEGqyI3SOU4Ea8YAtMWmb/Aufu467ajq1eng63b+F2MbZidm2O+8qxp9rF/DV7wWCerJ7LClJyxhIb3R4xjIKo6YxjCJjGMImMYwiYxjCJjGMImMYwiYxjCJjGMImMYwiZH/kj9w8S/P5xi/vEVnkgMj/AMkfuHiX5/OMX94is8IpAYxjCJm3br4dPT3g+Dr4dfEPh6dQ8OvwZuxhFWFUfCnktXvNq0+W0l5eRGaxy5I9CYFOKgS8WmqJ7n1xUSu3nCoY+0WMXcz6ubnqNrLgdtpRIzYst0mqdrSptWSOgb5Qjp9GdmC51LMeOjK/chnWe8YeGU7sexuJ1CnVo0MD7B5HNWKZxGKJ7MtkuUup9pR+koVZM7i9QNqCEQJYjSu7a4zh0mTxHGxZltuMItNQDUA1D0agAB+QA6Bjp+X9o/zzXGEUdL28JZxkAPAPfDIA6B4B0CnLpHp09HpAB/KAD6QDM1B905X9AHf2kTmFb3+6zjJ+kOh/g3dOZqD7pyv6AO/tInCLsOM0HwDw9Pwfr8Mi1f8AeE0qZ6g7ZFYConSeWmLCHtcl0fxIrpAndWFHtPJb7DMbr34Ih0dDkboS27HS4XY9pMamdbHi5Q9RnNXrltGiALNIs4zlFpTgNuBxec/zklGLO0Wd2Z35k/5YNKbxi8mpUPdPGtXjGRZxJJmkSAo9IhyJN3mSUINxCMnZnl1TfiEGlOUYvKbGbCxHbXqPx/i6gH4xDwEfj7vXXr17oiHQc35hUZbdh1DoAj4j6OnXr4ePweP5fxdevh1zTbfQB1AdvEfHUA694fD8HXxHw6j06D4B1+DqFbXatzeZ19xUYJDA5ZJIW/ncueAsbOeoo9OLA7Gx2Yc26FissYjF7WoTKt2iTRl4do8/t2xgpHdlcl7WvKPRKjyd+u9ppWXJ2xGKgllJRCcXLVEMtx4fuTPHGqr9O4v2ldtfKYHImWIt8WuIuRQYrRBCbBXM8zkVcrbCgjdYyJvTNa2Q7EId2lyIrRuug9f8fx9IB5QOn6g/xBH8QAI/jwO2geI94On4twD8oh0APD4x9Hh4hnmQvpBRFxdlHzWuemXPn5x/tjgzV3MZhJryx+XXJ+KW3x/vmJV+ltDeJzQ+MX7JmCzmNiBZDpXV651l1mQwqDyNKlibiQxOatqI+PN6prS44x/s92nhnZ/JYixJZbNl8hVsalHJvkDbZl0yvj5wrnN3N1MyM21LDmqtTXtoHwNbFnCCIzUUXVPskTPp7fquSlHlEXp2AzQfAB/F16D06/F16dOv4uvXp4+jN+eb3ihyjmfLLtYK45IQi15+v4gXtxX5YRjjlXGkneklZySGcaprxMZHG8FUE0VAwK5tKrhte5YqglatIe9J4fCGppJVapDDAN9IWETODav8oSX+mE/9gsuc5nBtX+UJL/TCf+wWXCLnMYxhExjGETGMYRMYxhF8jevc27v+N3dunT0gPTqGwfjAQAQ/HlSnZ/03adB8v+1Vhz3ApIw0faPJiDcnqVnKpMXpE5k8XVVTSFzNUdO8v5QVsYnEZI1eiNUxZBR7jptqZudubluAh18BzZ5PQNh2DUO9t6R+EfyjlgxOx3MRh9rwggVrFLbMXQx1v4hiPOoTG57F5yrfp9ucIxtwfHFodRolh8FkbsYwiScCQwkDEhAFd5NIE5yjxxxJpjmOUJcs/wCV+ppeHZ+Yt5Uc2n77Ka/o7Vf/AKrPuEMkfkcWr77Sbfo71f8AxPuDJHZX2/n3WZMYxhExjGETNB9H6w/eGa5oPo/WH7wwijzxV+9m4+eP/wBT1b/l+5lrD0fF4+n8vwZXD2Jhuq2kOWDl5QvdUu7RTl2Uu116iJC9nlTOzLEpmwfa7GJVKM0nbuDuXqOn2u4+nLH+Knd97Lx96h1/7Hq4EPj8Iw2CHh8PiHUPyeGVy9hgSSZw7nb7pprqbLuX/LGVKzQ/+UVODpay7RwVnCHiYpUK0xxqjfb7bY3vdfizyDYp5m+JFlHyzVpkxZq7h+UDrNapDycMl1Dc/wAUTuUXxnaJCLNDIOVpsw+no+CfLD9L/UQlaeLbDl2b06pZUVhrD5adooN1u4uWNeE2rNUG2PvPlO/CcpTnj2A8f1+q58PEAH8Wa4xnq5wmMYwiYxjCJjGMImMYwiYxjCJjGMImMYwiYxjCJjGMImR/5I/cPEvz+cYv7xFZ5IDI/wDJH7h4l+fzjF/eIrPCKQGMYwiYxjCJjGMImMYwijpe/wB1nGT9IdD/AAbunM09QCTldfD/AAAd/aRAf7w/bmAuR74yx1841O0gd2tia03Ihq1UOTy4o2tvJ2UVFcycjU1YuOTpi9jjzNCitdjA2MM31LLDbfbXUe+LLZpBw2INNtau9D0+pgEqElkxtEo0LNDQTy/Lo38kwSTPJF7mFbDsWOxWm4697TXYCLMXUPjD9oZoPdH4Q/b/APH/AF5hP3TqQ+C5Ij88DaH/APJxzT3TqR9ccQ+eFt+s+EWbuofGH7Qx1D4w/aGYR906kfXHEPnhbfrPj3TqR9ccQ+eFt+s+EX5eSXHCq+V9Tu9LXGhkDhB3h9hMnN1ik0lVeyVBI65mbFYMKfGOZQh2Y5QwukemEaZXtAtaHRIo0VICg2M2KHfTaOWvZv00WwbMxNx83QcSZP7bWiZKeenLR2nEfczWQ+POCVnkz3bDmrKjry2n9XmKLS10acXJOiez2oXpAkcCZL+6dSPrjiHzwtv1nx7p1I+uOIfPC2/WfCLEzBwO40x7jbb/ABUTRN/cKo5BI7MKvI2RWHPJPYlsu1xNIsdlSyeWvIJC42K/zOUtQENp8oVSIXRtbkDW2MhrY2tDYkSZakXHuqpTL6GnT0xKFUl41O0heqfXaPjym0jbjKK2eKkejlSNOuLRyDVVBH51aNSX4hwJTHKQc02hTkQnVF6e6dSPj/2xxDwDqP8A2wtvgHgHUf8ArN4B1EA6/jDHunUj644h88Lb9Z8ItocdKeLtiubqSRJK2T2p67seq4GrZlKplZWKD2w/QiTTpoLirUckjSjZ3eq7ia3RcoazFzfu3n6N56YtycdVOcOofGH7QzCPunUj644h88Lb9Z8e6dSPrjiHzwtv1nwizd3tfjD9ucG0iAuEk8f/AKYID9YMDL1/eH7QzFvunUj644h88LZ/vkwhnIobfpFuKElLalba67mmHmbmWHFjzjjzRDyhx6g99NOON36agO5hm23d11016aa66gRZexmLvdvpv1sVp8voj9M4926m/EfdXrToHTqPt+iPh1HoHX/DPh1HwD4xwiyjjMXe7fTfrYrT5fRH6Zx7t9N+titPl9EfpnCLKOMxd7t9N+titPl9EfpnHu30362K0+X0R+mcIso4zF3u30362K0+X0R+mce7fTfrYrT5fRH6ZwiyfsIhqIgHeEA8A9HUfgDr8HUegdR8A9I+GRDrTl0yWPbBlcFwKUsDK9r7maa1nrk4RhW2z9048zRHX9vpRjbQ8LpdDdGKTLdSWNTLWpATIkKY5Vv7DKVjIgeM2jdtNbaiA2tWg6j9rt/1+iPT7YB8B/wz8IAPh8PQfizHbA48R4rNZTZEZcOPUfsGcaFFzKcMrnWjXLZUWTsTsVpIpCiVkuzxprumT7jqvVHhuYnTmGd8wgnbQi+7X99pNv0d6v8A4n3BkjsifCJfFJfysnyqKSaPSZOl491aSqPjz41vZSU0yzrjEstQY1q1WhG5mum2+mpu2o7667dzvDpuGssMImMYwiYxjCJmg+j9YfvDNc27D06fj2AP9eEUYOPDsLDxFph7/wAH91moaGOwg7OerM1j7GQpGu/wk8bp1RbSg6kACtzMTKS0BA7q9052pIlb1wfY/uziPZ8t2jwUgTuR/IflC9qyUjmeuVgMvumUy9P7KJVLY2ntaoEj0QWjTm6KAcmrRE/JzS0rmSmInjxft6okvGuiG9xs6uCFSaoYEjWI1U4ihRpCgiNt5ChKpTnO2uxZpJpe5R5JpYbl767FmahvrtqGdNLkpkowd/dVrLXbboJg+32I+U2HugGve3F4DfYNdQ1DXvCIhqAAHTUADLLT2P4PUdg1X5eIvz7OazmnyUiSY1R9bqbFVHVGJovGYrrbGYhpPKLRnTr+JPw8M0XrMAsZ15TtPODhs/EEjAIuWco5Vm4GZySaDwLN+sPEowZ4EmzZbxmLvdvpv1sVp8voj9M492+m/WxWny+iP0zlaWFZRxmLvdvpv1sVp8voj9M492+m/WxWny+iP0zhFlHGYu92+m/WxWny+iP0zj3b6b9bFafL6I/TOEWUcZi8bupsBEBtetQEPAQGfREBAQ9ICHszmnu30362K0+X0R+mcIso4zF3u30362K0+X0R+mce7fTfrYrT5fRH6ZwiyjjMXe7fTfrYrT5fRH6Zx7t9N+titPl9EfpnCLKOMxd7t1Nj4e6vWnUfAP8Ar9EfER8AD/LPw4926m/WvWnxfd9Efg//ADnCLKOMxd7t9N+titPl9EfpnHu30362K0+X0R+mcIso4zF3u30362K0+X0R+mce7fTfrYrT5fRH6ZwiyjjMXe7fTfrYrT5fRH6ZzULupwRAAtetREfAACfRERH8gezOEWUMj/yR+4eJfn84xf3iKzzt/u30362K0+X0R+mcwjfVrVg/xeENLHYsDeHVbyA4yFI2xrmUacHBWZpyDrc/YtKiRuh6lSZqUUYZ5IkrcwddNtg1HXXcdSKX+M0AeviAD0H8n88YRa4xjCJjGMImMYwi4V+jcflKEWuSsjRIGzY0o/Zue2xC7oNjyNh2IO2RuKdSm2OJ2EdiTBKHcrYREvbURERrA5cWBSsHsaFcdIFwpVcpLmVRTbk44VxVjZTcFVQ6s6cnsaBrmD1JrBdIizLneS2P7GxmvK9QK1a2wHNtkCZ1FoizU8uelrOVQ8h4ZyBpnnei5m09x/lHJ+Ozbh2p4xSeva/mdYwyaxCdQS23e3akk6g62ZdCI6prmYHzeXxOdvLU8L5DDT2+OPRMVf25QtFARSwoA7jByVpWr78qyu4A6V3bsGjlgRBYureKtrkLJJW4pwTJXdrNatzml8bdjDW18aT9tjmt3SLEBu226cdhzB7itP8Aqrrf5BxL6HyPPZ1cc5RxL4TccOPk5c2p3nVcVq2oZ0sYTTT4/wC3l7XOUtmSSPKTyyVCuPtklkLm1sa1QnSnrGtEkVGpE25wkaTUwixj7itP+qut/kHEvofHuK0/6q63+QcS+h8ydjCLGPuK0/6q63+QcS+h86XYsArGDQWWTBm45sdlu0bYXJ4ba/gkBrTaYzNeiTbmpI1GvbUbGI1o8u6gC0aI6QSJkZiDDPLOToiSFmn6SCzGdyyiewqqbDltW1oquWyI5DpC8wSqEUnYIUosaWoGxQfH4ZrMZQcTH4rpIHTVM3nyF223SNCc01buSo2K0IMIqjV3KGgtfd4R8m+Bj/QFx8L6FdueCKsXUug5sFhVIwMFnxXeSweb1JJn+EOTw3ODXLIa/Qmaqmc1ofXFidyNXVpORPhMteJ8gRciWJzk0+4EoeOrCLbGXSGr5k78WrK0nCZ/RqlyrVv1pSVTvZiUMCbVt2ciJODWadu7EFt+qrZKu8hDHidA79UQrldPuW/Am5bG5N31U2nuzLLEm/FEmubhYURDs0MfC7j9Ho9f09R11ScHZ5NJ0sYTWacwJp0vfJLPrQlSqbTBx1Qdp4AcaZVAOYV3XjXfDc3s7uL0roWva397qod6gb1NtXhHZm9PJ16KKp4+zOfVVX3tUginStyH/wBnyppZJTgKp+bSm6MsyhQRWwe4rT/qrrf5BxL6Hx7itP8Aqrrf5BxL6HzJ2MIsY+4rT/qrrf5BxL6Hx7itP+qut/kHEvofMnYwig5y/lVBcQeOVpci5HQEYnDTWDGhdjohFIZW6OQyFQ6SJkjDc1taySkNMfRnqXN+R67K3hyQt6YkDTlKkkvQdsjRJLTqWG0VLuWnKDgY5UbvRz6U01zBk6zjhbUtteQWkYy1ZHWOBpqVmclh69+nE5lLTWjC0TZ6ZRJf1ujkqObmgk1zKndywYm2TUHYUffON3vumF4QNKF+47AfXRI2YyGyJo2dWzUu2n2MV2v2a0Ze8hBnk8gakT0LR7FlKgWKUpZlEaHgBfUrrTnJIaP4stfDSEzG2uCt+cWOE8lm9btLe9XBw7tdruO0pw9sFRSOdUrQx/JhGwRGsErPG5EvTg5Q1tsifEtylerJMIrUOMdmVPes1t6m7D4kNfHq/qNIr96nlUzZhpyX7HQa2EL8triwYjNa83fIrKYw/qYnMI0t2TnpHSPy6IP7M6N2qfVqc3WZXuK0/wCqut/kHEvofIK8VK+uee8x+TvNe2adlHHtksSmeOPHGqKqsCQ1892YojlLPtyWLMLBnCerJfYcJYy32a3SpjEOZ0k3eHU1hh58hdSWnWQIW8uzjCLGPuK0/wCqut/kHEvofHuK0/6q63+QcS+h8ydjCLGPuK0/6q63+QcS+h8w9eMSZq4gimTVZw6YeQkrJc2lGTXMOSURBXpUgXKRKcXjR/thxh8QKTMhAArVJDnrRxWFj5NtTKj/APmhlfmPbZfprFqwsKS1tC9rHsOPwqUvUDr7R0bmTaczRsY162KxEHp4WtzS0ayN+Jb2k10c3BEgbyVZitWqIJJ33AipKT81aSWV9b3IGQ9nPJGGx+PvJiGcAya2Od+LbgbLbWu2ZUy3uLIwzRomp9Og3xSXSmBtcukj/JkxUYdUMlZNVhKxuf02lm/H9iZLYgesqs7hvHuPkgNeHBIlg8rDj9YrgsY05SQxslCeR067TaHmNz35dRqkRg9+yifzE3dckI0PTbGw9hvFHSguzeqOhrg4oj2gMpNeGGyuS1XpQppzOsC+LDmzpdd0WyDfd8qhlfzH2Dul/dHtnZ3WSEuJzWQ0A0Ap2aCEuds7Lnj3YlFtXKB0eKWDihTVv8hjbF468PfbRE5Vvx/gXuaQaMykDtK/e5LXMCUWzZLFKbUPqiuZC9Q2CbyECkq0HZzeEqYisujkJh8Q879qsWjca8/8j56EfYWlk8882Ezzfzr2LRpPOfIAaYBPlu/5IDDO53fKb9e0YxhExjGETGMYRM0EOvw9P+P+PHNcYRQ95OSHjRxYpOxOQdnVbFlcWr5sIdVqCNVnFXyYSd+e3xtjsUiUVbDEKTV1mE4mj8xRWNpFa9CmWSB7RarXBGn2PVFR84dSekptJbH40S3hyTxpuikmaJWC+VTYyWobEOc64u98nTpE7Ch8+gzhKmCTMa6YxyfxN/QFLE66ISyOLmcxIaynx53dct9pJQVhcleH1mVlUmjIptJI+VJa1dtUlchZo/JppQdzV9eUehjw8+RUlMqCbr690iJr2pTnpGXd6KdVZJiVGdqOKOMUEuuzua95c1rcpSVccGF5440ZxfqyrrCklcyOyXhPAp5bFu2TYEs0qmZT+GsTMbKrNboZAm8qXOT07NsXeZQ6N7GleWtKcRTz9xWn/VXW/wAg4l9D49xWn/VXW/yDiX0PmTsYRYx9xWn/AFV1v8g4l9D49xWn/VXW/wAg4l9D5k7GEWL9qWqANdhCqq32EAEQ1CBxLqIgHoDqzgHUfQHUQDr8IenK37n5JQqgrJTpbT7OqYRjjedcVeUbvyoMZuMjlEiJfacrj0Ag0o3q1pma+49ard7AlLJDjJqdEyXNC4LdXVTEgjZZjwFt24iGmw6gIiGoiAB0ARHp4AAj4B+vKNrjT8u7k5zM59zcHbxnPEXjtaMKeOOTXXVl8W9IBY1lIQSm++0vtJLr1is/XIahcXFQZSdLoYUtJYHVlcbakBcmn41y0QciyFVdvQBdf004lUr2dy6VVpxosyIceZzdp0k4qt8diQlVjXE/UvntLmU4R3bKmOMxWxY1o4uLbEXVwdXEFpDeC9SUaOWda0tT4h19yut/h/8AQSJD6B6f/Y+Uk8ueLkmvC/Uh9F9mobSvJRHyvpWyde09MlHHONkN9eVvMYMsm03LkcJsRfyLnaywKijDvTOtFyivkjA8JXwtPL1SSPIAcB9AegDrr0H49hD0B0AdhHXXw8PtdRDXw+LCLGfuK0/6q63+QcS+h8e4rT/qrrf5BxL6HzJ2MIsY+4rT/qrrf5BxL6HwNK08Hj7ldb/IOJfQ+ZOzbuIhr1D4wDr4eACPiPiIegOo/H4eAYRVC1XckI5TWnbdKsXZ5LdaRi9r31xrnnIFXIeLDXHynGr3CR15L3FNX7bN9bzIZnuQIjY+xr00NKWhu5JHXfVO3lmLC+tQ/mPxnUWHDosl4fLm7jTJ+RbvwmrflkujNMLa4k/IWFuj/AgixUVLc1VqpoI7WFCJJUMUtdwjuzDIbKaC2vchGzvbDI3TC024tSmyOZtC2HRfZuHcNbLrfmM5XRfnOUyTcdmLS3qeBRLBsmJJDqcsSSW5dJ3KFGtbEi2K2tDI8xwfZftK3w5BKIw1pz+AhvEflYhi9C8DVtIuCKqKG7SlZy5U8tlE3ro6t5Xx7jHJ2d8w6+j7JFUkrOt8q936YSllqSVxh0r9uibGmaJBOSZ05tipoRLyK9nSlqe3112Cq636bAA+MDiYekOvoFn6h+QfEPQPjm73Faf9Vdb/ACDiX0PmTNevdDvdO8IddunXoAj4iAdfHoAj4dfgzdhFjH3Faf8AVXW/yDiX0Pj3Faf9Vdb/ACDiX0PmTsYRYxGlaf8AVVW4/wDuHEvof4PTlTjtdTDMb7qbhbfnZcyqpieVRVwNcclqqX8SJO1BDKjjhclmsxeE1R2E/TiPR0spdEmhM5CgSqC5LNYuy7eSXru4XdhsPTXYfT0AR6B8PQOvw+H7crvqykrNfefvJnljbMdBlj8Yrat+K/EtIa7NK09XWBQJ7evez90TSuc/YQ20rhdY5Ci0ToKB73jtFMjkrbSkToi75FiTh5yIjXMN01fWHs81UDpBeqshK1XnLXria6tbkvgU4f4JoQorqJzN7thn2lL5GX3dmNeYkjLJSogPc90oHlBtZU31LVzSuSObVXMDbHJAoLVIXBvhsZRLkakoepahIrTNRShMfp1HuHEGFm6CPXXYMo8p/i3IXDnNxiuKj+zV27ORpqN3vN25TWsdJOOrWPIyLWDBpaztdOI41x5sWcrrnSvVuP8AGroPsa3G2N7wI6FgLBru/wAnXoSvQIHXoHXxH4R+P8f6/ThFqHgAB8WMYwiYxjCJjGMImMYwiYEAH0h1/LjGETGMYRMYxhExjGEWnQPiD4vRgAAPAAAA/F4ZrjCKqntROedk8EEHGCSwSvYtYcdsS8HtoutK+7v+r9H6DrWoLAuy4pbXmjIrIJUTqLwOvnyQtiJ8TrWZckaVyQ8gs85OeX05y7TNxTdpK+cZRa61buJcC4427YU/5Auzw6g7prYpyKUpbM4bW1YmX7RIitoVTt+1w8Sh2VJVjrrIHlQkLUI07UoJOl7yZ4snchLb4fzhU6R/WJcerWtWaTyJPzYqctbAilncYrn4+r4slAvbzIkDRtTRa5g6Fmo1bMlXoddAUKSdgg2f2MdYMjNWNRwCeSlroyO8T+0L41T06XvC2b3RLVnO4agSOE3Mni9MnSOLnDGStt2JDu+IjjtWRDDmVP3kLIb5QiklV/ai8ZbF1kCp+Ktij2hroiUcpY8+8halllRtFjcbISWiUTG6a+VPhJ+7zF4ohd2B0krI5EMk/YWiTRp3dYYkbXxApNwhDe1Oj065VRCCLItOaQowng/yL5dWI8ckailtSStJEKxnFGoIVZzKte1xjaTWi2HTafOMmbliMZexrWtpLlTVEVfkmxz6I69mZyL5LMu8V5rXNUChmgnCXkFwvq1x48wmYsTu+K+R0ZgUKm/IKfpp29K0DPIUEaq6JaRqo40Y8RVC8LpMvcZm7o1LU2Nn6JD2c/KblDLZK5c1beo0YrIuz55KcCVrLx3h05ZnNTpyAe6icna8NXSfOSspA9Kda01Ul1xqmXMUWPLRoi5LMUy9wVJyKcXHznjVHIicJq6bIVedWSuQQJTbFctd903LKjNtqqkDmzs7pPq51kZY7ObexrpLFQkkbfNI9P4yllkYcZBD25vekSkybYAAegAD8gBlO3Azs7ZVxmtdLP5/VPCRtd4zWj3AGq06LjV5obRlyx7cIv7LPCpBZcyf4vWLDJUMaTrZRC48qmxy55JZwTS9O2M2pCy4rCIAAHgAdA+IPDGMYRMYxhEx06+A+IYxhFp0AfAQDp8Wa9OngHgGMYRMYxhExjGETGMYRMYxhEzQAAPAAAA/F4ZrjCJjGMImMYwiZp3Q+IPj9AZrjCLToHXr0Dr8fTx/bmK70niyrKWtuzW9GlcF9dVjP54hQLhPBEtWQ6IvMkSo1nmphKkUqo9sLTqQINKO8gYZ5Ews3ub65VzFt4wBba1MW1WDa4JWlwsWsp/BELouJOUIm1ZMYi8xxKvVp0+2ig9KiPcy1KgkjfQ40krfQrYN9tcIvPnNe23uuMdlpFeTyKoKrVc1TnJ2bJ5TKlTNC6njTbX9VIOTtj2KkPIdfbgfBlHF9/gc4iPlXwVW0mtSDMS5asJUmbnWjW72m/HOjp7MoNM0dsLmuoNq9S8iLaiFTymUUrxvcrPbWh4iKG57CQ66po4YqZH9hkz7s0IJGTAog/MkrsE2LR90SOJkQpt2KcEfeMthxFhmGzXyYsbs24RwIeJ6tWPiunyFkWriCwF1tVvrgvTVwQSuWNteRCNyGQkOQvjnAobDowfrqU0mbKe2cguzq5JT5ZzVqerbip+Ocae0XemF/wCQZ8whUudbnq1avqiv6OuMimTWx1LhcmJs2uq1Yva2ZO9mcaulzg9vmhE2at26PIiLk+0D7VmOcb645PpKci84mNmceUkPjclsbeoJjMON9eXFPVsIVRWqrIsBjWNyZPLXSMzRhcViZuNNYYkfKYmmm8mjTi9trerkja/aScfqdsebQJ/abifGCo3yKxu+bnhlRyqVUXx/f5qjZnRhZrastBpqgZlhDJJYzI5cLCik5FbRmRsskss+JMq8tdkL+SXZo8op3GOadB0dcFGRLjtzXsppu6SuNhQ2fv1v1pMzWqp2ixYJFzGR3TxCSQmwwqBmXNkqfdUUmrrZ/kaBOxzDUWNcz9funsezpLyPvyz4zXnDq5YFybstutiYpOUMcu5fMq4kqyJQqETtlYU9azNriNpQKRt0Gb5CyRmVJ4U4RqQOb6iWSKSx9S2o2oivz16CAbd0NdhDoPgACAh4CHX4egh6QEQHp1ARDoOa9A9PQOv5P15sKK0JKLJK1DQsrTUsvTX0all6hppqH4tdAAP1Z9MImMYwiYxjCJmnQPiDNcYRaAAB6AAPyB0zXGMImMYwiYxjCJjGMImMYwiYxjCJjGMImMYwiYxjCJjGMImMYwiYxjCJjGMImMYwiYxjCJjGMImMYwiYxjCJjGMImMYwiYxjCJjGMImMYwiYxjCJjGMImMYwiYxjCJjGMImMYwiYxjCJjGMImMYwiYxjCJjGMIv/2Q==)
Fig. 4: Eigenfrequencies obtained through POD of the example simulation in the test-set.
References
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