Eyler usuli
Ushbu bo’limning yuqori paragraflarida ko’rilgan usullar taqribiy analitik usullar bo’lib, bu hollarda yechimlar analitik (formula) ko’rinishlarida olindi. Bu usullar bilan topilgan yechimni aniqlik darajasi haqida yuritish birmuncha murakkab bo’ladi.
Masalan, ketma-ket differensiallash usulini qo’llaganda qatorning juda ko’p hadlarini hisoblashga to’g’ri keladi va ko’p hollarda shu qatorni umumiy hadini aniqlab bo’lmaydi. Pikar algoritmini qo’llaganimizda esa, juda murakkab integrallarni hisoblashga to’g’ri keladi va ko’p hollarda integral ostidagi funktsiyalar elementar funktsiyalar orqali ifodalanmaydi. Amaliy masalalarni yechganda, yechimlarni formula ko’rinishida emas, balki jadval ko’rinishida olingani qulay bo’ladi.
Differensial tenglamalarni sonli usullar bilan yechganda yechimlar jadval ko’rinishida olinadi. Amaliy masalalarni yechishda ko’p qo’llanadigan Eyler va Runge–Kutta usullarini ko’rib chiqamiz.
Birinchi tartibli differensial tenglamani
y’=f(x,y) (7.4.1)
[a,b] kesmada boshlang’ich shart: x=x0 da u=u0 ni qanoatlantiruvchi yechimi topilsin.
[a,b] kesmani x0, x1, x2, ..., xn nuqtalar bilan “n” ta teng bo’laklarga ajratamiz.
Bu erda xi=x0+ih (i=0,1, ..., n), h= – qadam.
(7.4.1) tenglamani [a,b] kesmaga tegishli bo’lgan biror [xk , xk+1] kesmada integrallasak
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jVCYeXTpm7oAMAAJgIyfEkO+3/okFp39pOwLaN+La6k6D9EsKu6AAAACZCMjzHe3X+X24bPKK+E7BlMb/qOsLAAoLaiUMfMlQLoAMAAJgI6f8Um+pwvJw0ekxtJ2DLvfz3lUcGthychDoAGaoF0AEAAEyE9H6G7e6a/mYn877Umud2S/mvK48MlBFaBtr/HNUC6AAAACZCej/D9U4ze9bwUbV79GWresBnlUc+1P/3w9Xh3tOf/MmxVJAOAABgIqTvE+xt6bvv9jBpeaJPddVh+DDBt9uzn4UGi8vHLqcNBNABAABMhPR8/Hu1Jn+0Na7b1nYCHrRYzL+pPG4ZjfZdm3iZ76wgOgAAgImQno+vFuT50LgV/1MbAmg6ePC/58rDjiM/87M3YZmxTAAdAADAREi/h9fK+jdbA/g3tBMw1pIH3FYeFjl38Kc28apxogboAAAAJkL6Pby24b75fv76TsDV6fV9symE6mPDdQd+ahMd5Gz/6QAAAKZC+j18f7G9yFnTVQD1nYCflidXdy+piYTqycPBwoOv30sTDpumaYYOAABgIqTfw2vj+P87aVhxJ1it58sisLe/qrrPP7TA/+W7/T/KUPynig4AAGAipN/DQxV3gk1yQH0n4D96PeG3yk8eBP7/y3es5LGEbdEBAABMhPR7eHUsXmuSQ7arwIO/6Tv3ql2HQOWh5+/2/yT7KUF0AAAAEyH9Hl5djq80yWH1nYC/9Fv36gPrJYSfvuclzvKfEkgHAAAwEdLv4dudg4C+rJs+uL4T8Eeibv955Udr1QMev5/1fIBTgukAAAAmQrwDdFHde7C/ze/hu/2PlAfohw4AAGAixDtAB9tKi7nYu8//OSf4apBXpgMAAJgI8Q7QQbWCwNHu/7r7/uf1MK9MBwAAMBHiHaCDu0qLuVt58GdNYquTBVugAwAAmAjxDtDBdaXF3KkYdPP9j3oVgR7oAAAAJkK8A3RwWmkxHyv/vv7+txbHCrZEBwAAMBHiHaCDagGhSq3f74GBxWP8kX3RAQAATIR4B2jvvdJgVgoGfB9MuNCLCPZDBwAAMBHiHaC9p0qDefL7r98nBC+DhwPmQgcAADAR4h2gvZtKg/mz3X978d3+v3R/3gvJ6CL9ej/oAAAA7Il3gPaqDfXd1z9tz77/e9nj/D86AACA+RDvAO1VTyD8GvDf/tsX8CfxYAUdAADAfIh3gPaqRwh9FgLeVPYFrrofAUQHAAAwH+IdoLXXSnt5+PEPm5NqE3rX+YnpAAAA5kO8A7R2X2kvz/7/783xTst72PmJ6QAAAOZDvAO0tq60l+u/f9+P9preh65PTAcAADAf4h2gtbNKe/nw9/1wv+k97vrEdAAAAPMh3gFaO6i0l69vtfZfZMBSgIO003QAAAD2xDtAW5tKc7l4++4N3J5X/vV0uBenAwAAmAjxDtDWc6W5XH0fC/Tw96XaivaoBphABwAAMBHiHaCt29qQ/+fxP9WtgOeDvTgdAADARIh3gLau9tv/r/L/j9V/ehvqxekAAAAmQrwDtLVT9ed/q9evf6+uBrwc6sXpAAAAJkK8A7S13G3/D3/u9u8q/7h4H+jF6QAAACZCvAO09Lbb/h/9NvXbVeWfrwd6dToAAICJEO8ALe3M9ctJ5eifP5V/73MqsIYOAABgIsQ7QEvVZl7Oqkf/baqTAzfDvDodAADARIh3gJaqFX8udo/+re4P6HEqsIYOAABgIsQ7QEvVo3/2Cv68V1vS20FenQ4AAGAixDtAO9tqa7l/l189zaf7qcAaOgAAgIkQ7wDtvGht/E494M6nAmvoAAAAJkK8A7RzX2ks6xV/Tyv/t/OpwBo6AACAiRDvAO1cVxrLde3/PlXb0iFOBaYDAACYCPEO0E71Hj8wyF9dIjjEqcB0AAAAEyHeAdqplvsLHPlTnSEY4lRgOgAAgIkQ7wCtbCpt5TLw/7cHlR8Y4FRgOgAAgIkQ7wCtVCf5g6v8bqqtaf5TgekAAAAmQrwDtFJt34Nn/m6r9YCvsr8+HQAAwESId4BWLittZbjWX3WbQP5TgekAAAAmQrwDtHJcaSvD2/zeF5UfWed+fToAAICJEO8ArVRb98iJv9VBguynAtMBAABMhHgHaOOt0lQeRH7mtdqe5j4VmA4AAGAixDtAGw+VpjJa5+es8kO5TwWmAwAAmAjxDtDGutJUXsd+6LnaoN7lDUAHAAAwEeIdoI3qzf199KeqKwUznwpMBwAAMBHiHaCNw0pT+Rr9qepEQeZTgekAAAAmQrwDtLCttJQLZXa/2k/IeypwxnZ6+/Z0f3N9fnJY3dkgi8OT8+ub++e3zIsXAADYJd4BWqjO7h8pP3dbbVJX57fxwYK2+ncA3l8ebtcXp0fVioVBq6PTy/Xt40v2YkYAAPwdVweg2rBrJ/1s91vX5Vmm/YC9OwAXqXa/LrraEQCA7sQ7QAtXlWbxj/aD61orGqsa0JJHByD/iQYAAIyqA3BSaRYftR/cLPZb0bM8CTw6AIwAAAAGIN4BWlhVmkV9avxqoFbUowPACAAAYADiHQAAANgT7wAAAMCeeAcAAAD2xDsAAACwJ94BAACAPfEOAAAA7Il3AAAAYE+8AwAAAHviHQAAANgT7wAAAMCeeAcAAAD2xDsAAACwJ94BAACAPfEOAAAA7Il3AAAAYE+8AwAAAHviHQAAANgT7wAAAMCeeAcAAAD2xDsAAACwJ94BAACAPfEOAAAA7Il3AAAAYE+8AwAAAHviHQAAANgT7wDF277cry9PDg+WC1keHJ2cXVw/vHlnAgCgJ/EOULTt4/XJQupWp+vHrXc4AAC6E+8A5dreny8Djf+P5cWTd0IAALoS7wCler3WWv8vR7cMAwAAxkm8A5Tp+TTZ+n86uPdOCgBAF+IdoEQvDZv/Dyev3mkBAGhPvAOU5/2iefP/v8Wdd2AAAFoT7wDFuU/P/e+5YiUAAGBsxDtAYd5bjP7/OqcHAAAYGfEOUJbnVYf2nx4AAGB0xDtAUW46Nf//W3snBwCgFfEOUJDtZdf2X+TROzwAAG2Id4BybM+7t/9ysPGODwBAC+IdoBibkx7tP5MAAIBxEe8Apdh2Wf5fsXj3fgcAADQn3gEK0Wv8/9Mf77cAAEBz4h2gED3W/3079H4LAAA0J94BynDbu/0X4VAAAMB4iHeAIjxlaP+ZAwAAjIh4ByjBe7f6f3vOvd8GAACNiXeAEoQ2AJ7cvLxvXu5a7A088n4bAAA0Jt4BChBYAHD0/PM/Xxt3ARae7wEAgFbEO4C/t0WtLb+sHu7TeIOA1xsAAKA18Q7gr36Lf737A01LBFENGAAwGuIdwN19rSHfX80XGCJgBAAAMG7iHcDbtrYDYFW7k183av8PPOIDANCJeAfwVm/c72o/sz1s0gE4cUgPAEA34h3A2XtteP848FOPTToAV+bhAQDoSrwDOLuqtePPoR9rshMg+EAAAIok3gF8bRoNAPz/cwfJ9p8lAACAERHvAL7WtXb8JvyDz8kOwNo0OAAAvYh3AFebZa0dj23mv04NAGwjDwQAoEDiHcBVvQhw9ESfbaIk8INlbgAAehLvAK6Oa+34ffRn9WUAl4apAQDoTbwDeHqpN+Tv8Z9+VQoCnjEBAAAYFfEO4Km+uU9dyv9cXzHw7ZT2HwAwLuIdwNG23qBHlwB8eq2VDf6ypv0HAIyMeAdwFKjvd6s/4i20EvDg0SYuAAD5iHcARxf1xvwl9Zjb/VGDg1tu/wEA4yPeAfzUzwEUSTfm27uTf4sBDy4faP4BAGMk3gH8PNXb/1WjB25f7m7W13/uHl4HTggAwFDEO4CfQG2/8EEAAABMjngH8BNY0KdvAgAAYDLEO4CbbWBB/7V3KAAAbIh3ADeBJQCxowABAJga8Q7gZh3oAHCiDwBgJsQ7gJvTQAfgyTsUAAA2xDuAl23oaJ9n71QAANgQ7wBengPtf7oQIAAA0yDeAbzchDoAVPYBAMyEeAfwchbqALx7pwIAwIZ4B/BSPwqYDgAAYD7EO4CT11D73+AsIAAAJkG8Azi5owMAAJgz8Q7g5CrYAdh4xwIAwIZ4B3ASOAmIDgAAYD7EO4CT4BpAFgECAOZCvAP4eA+2//LmnQsAABviHcDHQ7gDQCEgAMBMiHcAH3/CHQBKAQMAZkK8A/g4pwMAAJg18Q7g4zDcAeA0QADATIh3ABfbcPsvT97BAACwId4BXATPAv7fo3cwAABsiHcAF7eRDsCDdzAAAGyIdwAX4ULAIvfewQAAsCHeAVyECwHTAQAAzIZ4B3CxinQA7ryDAQBgQ7wDeNhE2n+59U4GAIAN8Q7gIbYJQP54JwMAwIZ4B/BwH+sAXHsnAwDAhngH8LCOdQCuvJMBAGBDvAN4uIh1AC68kwEAYEO8A3g4jnUAzryTAQBgQ7wDeIjtApQT72QAANgQ7wAOorsA5cg7GgAANsQ7gIPoLkA59I4GAIAN8Q7gILoLUFbe0QAAsCHeARysox2AhXc0AABsiHcAB9FdgCJb72wAAJgQ7wAOorsARd69swEAYEK8AziI7gIUefPOBgCACfEOYC++C1Dk2TscAAAmxDuAvVelA/DkHQ4AABPiHcDeo9IBePAOBwCACfEOYO9W6QDceYcDAMCEeAewt1Y6ADfe4QAAMCHeAewpZQDkj3c4AABMiHcAe6dKB+DaOxwAACbEO4C9Q6UDcOkdDgAAE+IdwN5S6QCce4cDAMCEeAcwp9UBkjPvdAAAmBDvAOa0OkBy4p0OAAAT4h3AnFYHSI690wEAYEK8A5i70zoAh97pAAAwId4BzK21DsDKOx0AACbEO4A5rQ6QLL3TAQBgQrwDmNPqAIl4pwMAwIR4BzCn1QES2XrHAwDAgngHMKfVARJ5944HAIAF8Q5gbau2//LqnQ8AAAviHcDam94BePHOBwCABfEOYO1F7wA8eecDAMCCeAewphYCFHn0zgcAgAXxDmBNLQQocu+dDwAAC+IdwNqN3gG4884HAIAF8Q5g7VrvANx45wMAwIJ4B7CmVgIWWXvnAwDAgngHsHamdwCuvfMBAGBBvANYO9Y7AJfe+QAAsCDeAawd6B2AC+98BXl/vF1fnB4frBaL/38zi+Xy4Ojk7Gp9/0y9ZAAYP/EOYE0/CkDOvfOV4e3+6mQR/y2tTq7uKZoMAKMm3gGMJY4CkDPvgP62D5f6iYnflmc3FE4GgNES7wDGEkcByKl3QGfbh3Plzr/m0Dtv3cuJdwKU6HROvdXzFtdw1cY7OIyJdwBjiaMAZN6tx9v1qt0XxrF34n1v/3/1eWdAiUQu3rwzmDnq1v4feOeGNfEOYCxxFEB5LZqh5/b3DYWtmdxcfQxfeKdAif7/YCyuZ3KHm5rojJn7+OcMiXcAY4mjAOTIO6Cbl0SFhKCiCidub75WeHrnQIk+Pxqr2613DguvHS7lD1RBmR3xDmAscRRAiZPaJt4TFRIjSjo9+fFn6aJ3EJTo+8NxVNJHdij3nS5mjkKbIfEOYCxxFMBMZ8G2N21W/lWUUxHg9d8AhncUlOj343E+/aUAqW+5mDmtk8Qn8Q5g7DJxCay8A3p4TZRHLP+3tb2u9GC8w6BE/z4fiz9TnwfoMpv3Yeq/F9SIdwBjqZHupXdAB7cdb//LWTT0sFPf0TsNSlT9hBxOfB6gY4d+vgug5ku8AxhL9Y0X3gHNbbruGZZSFg297f1RvfOgRLufkYtyJq+GsHm+vT5tVM6rijKo8yPeAYydpC4C74DW3jpuGf50553+f9s/+wMY3olQor0PyfLWO9Dwti/36/Oj5uN7f7wDw5x4BzCWbO5mNg323LLyz64CFg291P+i3pFQotrH5GT6iwG/vD3eXJ40uc4fvZPCnHgHMJY4DHBuxTCforcHq4ubp9f37Xbz9vJ4c3Uc/jn33tI2tN7ZOxRKVP+cTH8xYNX7x6yA/vU3lx4R/hHvAMYShwGWtLHNwEOs/b/YXyW1eQgsFXBfNPQUnOb0ToUShT4pxwUMYdnSFkHPcQH07Il3AGN66y/z6gXH6iKfBX8J77W7bedFQ9urcHzfVChT+LNyM6dBgL/6FOi8z0GZKfEOYCtdJHtG9wSR8f9FdGnf694Iou+ioZfIKme+xxAQWf57PKce/9+ttiLw0jsd7Il3AFup04Dn1AF4CU+HrJTfwN4Aoueioe06/F22opwpgu7D6+AWM9gO8Es9JGBOvwh8E+8AttKnZEy8RMg/7+EFQVr7//fP7s863jy9RWqdXM1rESda2ETKgJ7NZ92PekjAs3c62BPvALae6QB824Zb0IU6ArK7aMBx0dB9ePTiaD7jN+ggsGf0w2ouF/3ftfbVR995hsQ7gK3Ysrf5dQAid0P6APruDIrbZPsmspZ5PbMVXWgruG30f9cz+eRohVDneQ7a3Il3AFvpczJnUgwj8otIrQPaufG+MklaF1n9d8gQJpKewx+emawF1KoDn3mHgwPxDmDrNtkBePCOaOItsoIudSO0M2/gtGjoLpz9aiY3cegnsnl0OYeev7oJqoyDPWBLvAPYuqED8GEb2ROVfPM7Y+8ud9zb8NzFchZ/N+TwEF5AsvbONTx1CRTbZ+ZIvAPYikwBzq0D8Cf83tOT+jsdKI9b7sjZRUfzGMFFFq/hD9Hp5HcD3GnffK/e6eBAvAPYitSOq5hDPzgyAdDglr66iNJj0dBT+ObtkuF/tBAZRjqY+iYS7etvwTU0R+IdwJZWCvtLCSfcDu00/NYbrAJ6b/fjuUWWcFDBBC2F5wIXE+/+Ry78T+4He8CDeAewFTjRZn4dgNhWiCZz+pU78PXQOffFpv/nsHwLmT3OcSGAdibwhXc4eBDvALa0LvBcOgDbyJmgjW4BKtsArFdLbMIrFw+Yu0QH+wdbfDub8Ej4Rvvi8z3YA07EO4CtdAdg+sPJ68g7b9T1qdyEGze8b+E9zEeTX7mFYbxH1pNO9wP1pH3xMY42S+IdwFakgnzFjXfEob1HVgAuG936/Js7XQwddNdLePjymPql6GgT/jaY7pCSugl6uv0eKMQ7gC3tOOyZdABiK4GbzQH+u4k4Hjjnrsdwt+WU9h+dbcIDgsuplpSMlP/+etPe4eBCvAPY0kphzqMDENsC2PAQhH/bAEwXDUXWLU55whbD24Z7AIuJFgPRxj/dDvaAK/EOYCuy/q1i6mthYgMAq4aP/x2Jt+wpRbb/ndD+o5fOJTFHKbzx4YvXwR7wJd4BbGn7YL6svSMOK7YCoPEXwO83puGxiZG5yxPG/9FTZGvJJDcDvYXf6nTfMNLEO4AtrQ88iw5AtBZy00XAv/OIdq1vpHDxEe0/ettElgVNcCrwQfvem+q6B+jEO4CtZPs/8TOxNrEeUMGFQCPt/wHLlpHBe2RacHr7gSMX0pdyr38MSbwDmFKPw5xDByC6Eajcw8AjkZeT3awFWy+RTvHkegBaGVSPgz1QAPEOYEothfVl2othoosgi/22i6z/o24JcnmMfMSmdjCAtge63BsADEq8A5h6Vy6BOXQAYl915Z4FGjvAtNgOC8Yn1smcVg9AHf5ce6eDD/EOYEpdBzuDDkC0EnKpI4CxHgsnlyCjyCGhC8OdLsN70b72prnvEUniHcDUa7oDcOmdcUDxAZBCG9TnyKbFQzYAIKNNpEDY4sU7WUaxQ0A/lToCiIGJdwBTaid4+h2AdfRdl7kL+C2yPGvB1xWyeo30NFdv3snyie4AFvODPVAM8Q5g6nneHYB4HcQiW9TYBq1CuysYsdhak8PpbDY9U771bA/2QDnEO4Ap9TzML4UOhucQ7/40rQNsKlamlRXLyC/WPE6n3LRWBn3C33pQiXcAU2otrC8THgGIHwZWZJMai7tkAQCye49VCZ/KqmB1C/QE6x6iEfEOYKpBB2C6feFtvA5yidd/bG8WC5YxhOh3w0QmnNTpz0ltd0AL4h3AlLoQduodgHgRAClwsXN0tubcOxmmKVoobxpl8qMd6g/TWemAdsQ7gKnYUp9ZdAAim52lyIMAoiOyS76rMIj32AjZahIfudg54J/v0DscvIh3AFNz7gBs40chl7cGOLoAcCoDsihP9B75xDtZDtEr6n+n3uHgRbwDmJpzB0DZAVHeOqf1pL+LUaZoG7n2TpZBvP9f4hcAjIh3AFPqPNiXyU4xK0OAxdU8H9+ZBZiAeKHQ8S+SU49BYVhttsQ7gKkGHYDJjgBEqp2W2KpGFwBwq4IhRTvJ418GoCwBLnIRMGyIdwBTMx4BUI5BWHpn2xetWUYJAAxpE90pW2SljDZutC+98hYBw4h4BzClXgXT7gAob720efX4Sg0OAcag4ldJcdNkLcX3AIkceoeDG/EOYGrGHYDoScAi197ZdsWOAPr/i4o7FQxqG50oW478WKDjGX7nIU28A5j6M9sOwDZy3NmHwm5u4vuVqAGIgcVrhZY2TtaOdv1PYpMDuhHvAKbm2wHQjkEqaw1gfAKgvHIFmJyj6Mdv1EvllSVAdKznTLwDmJpvB2Adf8dlnQUerccm8uidDdMXXy0/6hqUahH0kc9uoAfxDmBKaQZ/jH65b5gyBVjWjXW0IvvIx2AxEvEZqDHvENa++cq6A4Ap8Q5gSrsMvk1zBGCrvOOiDkBWtiuPvxgLRkCZLBvxEFR0Z62UdgcAU+IdwNQ60frLVEcAtCUAJe2t2x7wNQVf8VUAB+PdhaKUASvrDgC2xDuAqeu5dgC0xQ8lnXaq5GSlEkzENwLIH+9sXambAG6808GPeAcwNdsOgFIFoKQyYMoKQIqVwEj8bnm06wDVTQDMrc2YeAcwNdsOQLxhLaplvYzHHPUmLIyJUjB8rKPlyqiGCPW1Z0y8A5hSTsT7MckOgHYDUNCqx5d4ymVB4xSYtq3SXS6rZkZj2hTgyjscHIl3AFNz7QDEi+sUNa85nnLFmDLla+LUO1s3ytDaWN8SshDvAKbm2gHQ3nc5e5uelZTUKoGZN+WDWNKS2ea0kwDoW8+ZeAcw1aADMMn+sHb9l7OuKV6CZZrdMpRK2TU/znJUyqQGq2tmTbwDmJrpCIC2CaicGUCtVkE5wxSYAW3N3BjXzL9r33gv3ungSLwDmJrpCIC2BrCc96sMU6xYAghD21X8szjGglRa37qkbcAwJ94BTM10BEA7CaSYGUDtS+rKOxzmRfuiGOEQgLKxUY68w8GTeAcwNdMRAO1t33uH+6HVKhrp5iuM1TjGzBrTvgAK2gYMe+IdwNRMRwDG0LYqNQBGOeqKUdOWzY5v0lw7CqigbcCwJ94BTM10BECZ0SzmKND4McB8R8GcVjlnfMcCx4/Y4oyNmRPvAKbmOQKgrQEuZVeTtvWaIgCwNqnPo3YY+OjeDLIS7wCm5jkC8Ki83VKKm2t/GWYAYG5KpXO0FQ1L73BwJd4BTM1zBEAbziykCohWfp0ZANjTLpqxHUyh3QHQu5438Q5gap4jABfK2y2ksql2WAGDlLCnzgEU0m1u6kZ5K6UMAcKHeAcwNc8RgPj55sVUAdEGXEs6rxizoV01I7tt1r72br3DwZV4BzA1yxEAbQlQIVVAtD2Ao5txxSRca5/Jce0E1HYBjrCsETIS7wCmZjkCoLWuhVQB0U4r5SsKHtTyuSUMnG9fHm6uL06OD1eLj7M+Fovl6vDo5Oxyffvwutn5ySPlnWwiz455EO8ApmY5AqDNr994h/ukHVY0uhVXmAZ1Xarzh/L9fn2m7e0XWZ1e3b38hFTeyYHr+4A78Q5gapYjANqbLuOUPe2sglIGKTA32sC5YwXtt9tzpbDXjsXx9eNGnwOc3tcdWhHvAKbmNwKwebzWbhXKGADUShWzSgk+tBN0nBrO7dOVfuMfcPJHO9yYBTYzJ94BTM1rBOD19kJbytzQ8JVC1NPKDTcBbpr/UjoXUNT/IIdj2/GoDZPv633qRPLvs8p6sIW6EdCj6/x82ebX3UxqJINrYuLEO4Cp2YwAbB7Xp9rEegvDFwvWtilbTlKqy772dGxq1KKs/zssY0imKb3rtqf3qPlz8iUOs07Nqzfb1qtn3v5k6MzXpT7HXBMTJ94BTM1iBOD1LseN/6/hFzxrRQAsT15ROyJ7rrq9RLING9dBM1qJuZreo83qmHyvP0uYVkDLuBTAgzpL1t0i1WPimpg48Q5gauojAJun9WnuYcLB5+D120jDomvqZsQ9HZeBqxUPPxVSmrEZrV5uTe+hpCZ/n5yTAPof6z3jK+m2t4Pc/H9I1gHhmpg48Q5gasojAK93l9p+384G34av32QYzgCqIxH7unVM0h/AEnaYN6beI+/rvZjkpMGL5Lxb1BcBWC1O3aybLvrvILnFhmti4sQ7gKmpjgA8/zkd7Fti8Bk49Xt9NfSrV7QaO+k2BJweyR1V4eN2Pc6+fbkmf59Fzhtz9ZqyOUh7s860lCcsec4W18TEiXcAU1MdARjwS2LwFlifATCsAqDf8NV0qgab7qYtcr+tAakFnOp6rgJs9vfJeWOuVgKw2AewvR3w7v9Dqg4I18TUiXcAUxMdAWh5mbYy+O9DnwI0XGz93G71RJdxyU2D7/Pcb2tA7+2ap56rAJ8bdTdy9hj1yanhV6c8DDb3/yM1XsI1MXXiHcDUREcAWi3GbinruuoQ/TbLdP3P6+1F8zoryy53gNun1F7u4csu5PR2f3XceBigb19y0+R+OOdwsb4+fehvitcmax76afBh45qYNvEOYGqiIwCtFmO3NPR9jlpy3eG44vf/m7RBfzNbfUuXzdRyTtunm0Rh+m/9Z5O26+SL5Gws9B3qw54HsP2T7Fgtji/+PDy/vm22m/e316e7P1cnLbcANfywcU1Ml3gHMDXREYBWi7FbGvoWXK804nNc8fZx3eCrtHu2F+XrdKS1Wd+atBEZFug9J7sa/V/jH32R45CXhvYR+XR0HXz517vzFp2AFsN7XBPTJN4BTE10BKDVXp2Whr4FV49dd6wBsn2+SR260uNQ+PUQT+rtYyhA/ZU9ZHiR98TOg6wLxvSe9XDtUmqk4+CPsqNi+3TRdFam5YpJronpEe8ApiY6AjDgJoDBK/Hq3+fOJwHpPas+25PPI885+h1PWgOxzvECG/2PknXXil57cLBigG/6Wzx5SPXKN7fN5u27jGFwTUyKeAcwNc0RgCE3AQzdH0pUk3euAabvUFj02Aj2EnnO0Z99qK3pzPNh0vceZG0tElVqByoG+KgOtZ80uyYemtRo6PIB5pqYFPEOYGqiIwAKbYR97R3uf/f6X8P5HJCtPuDZ45spsr7swHzRY25r5feVaThJXTaStQOfOAsvx5RGzVadFDts/prpTYSd/h5cE5Mi3gFMTXMEQKOtrh3k+6sl/S9ieBRg2FqN12OJYmTkw/Dkg4GoW1Iz3TJrowx5J+b1kfQhtsi+a0Psiz9tGsPtbWLVXrebnbX6nFwT4yLeAUzNbwRA+wbLenp6R/pApXtv7F1fXtF9hiLcTvpseshKvWlOFZ5rKDZW/CHveLFepnaAP9eLdsEet71iN/oqxnWniFwTUyLeAUzNbgRA+zouocBmYozVf/+P/g3afZNCeJx3CseeaQPPydLzDSndxrwrxvU9KvlnqNTp/1a3/9/UKbaOtZm5JiZEvAOYmt0IgLaKyfZE87AH/Y/hP/qn3Wz2WfIUvNEbvOqihdha7g+56vTGr+PkAfftJI6qzTSi0ejlVp1aQvUC6zgEyDUxIeIdwNTsRgC0fUx+e+z/SdxhFdD71+uxdj2qIPi9fDiJ1U5aAf1cazrizVrmy1cvU5V7hEq7Go67rZ/QnrLzECDXxHSIdwBTsxsBuBzgQs0pUe58oH1WbejbFLpOUAZXehXQ3clA3TqXacw8fg+6zvMCPxK7VPPWqNUu1suODaG2XrLz7DrXxHSIdwBTsxsB0BrY3OOXHSTOky3hEJCtvhD8qdOTBr9BS+iQZaAW0O/266qJV77I3WDo6+izfkC19n/d9Um1T2/nIUCuiekQ7wCmZjcCoH1/FXB7rc8mFrFKIXHSUqcv0eAJqJP54GkbOzJ9oUc7GVnrAH5IlNPJuJFGW1rX+demLrLt/sfgmpgM8Q5gam4jANoIZgm314k1VjnPdu9so45SLLp0o0Lf9YfONY/y0e5kM/1Fo+1a9nUt2pJG6byOPkBr/7uvhVXXMHQfAuSamAzxDmBqbiMAWlWWEs7Y1NoKKWUFsB6yw21UaLXTooSiDHlovbpMhXqjHdvsta0S3xjZPqHDtP/6YQY9hgAnfU286n/zcq07vFnJ/Msr29xGALQV2SW0roljDMuYAdS/D9o3aW+heZkCFmTkos7r5FnUHfuT9KlEH6ZdQZJvkkpbrN/nKtAa6j7TJZO+JugATNbcRgC0+4oSjthIHGNYQq3iv6lycG2XPG1C08pldHUy0f6qeRbpxXYa5J8zShSqyDSPpt2or/s8sdbD7jUEOOVrgg7AZM1tBEBbwlTABpvUlVbIOeBqefvWjU5oVrnPIarl0bae5PlWj80y5O8xJpapyluOF9F6Gf0+GlpfrNcQ4JSvCToAkzW3EQDt+i9ggU3i9qqEfQqf1GPVWi55Cg32nk2r2ok2np1nld46/OSr/L/HRCGALF2OZ+UyPen1ltSmrF+ZzQlfE3QAJmtmIwDaJ9n9oL2/qXPFRLzz/dAnglsVuA8N9h5Pq/1X68TkOdolsjZ/iKMjEh/RDKcbBOe/vx306wOrFXv6DQFO+JqgAzBZMxsB0O6wS+joJPZYZd/U3dVGLQfTZslT6C9yVMBYTFbxMj25avVHbj+zjMfvCW1Pr+i/6mCr3Esvek6CrbXo/f4SE74m6ABM1sxGANbK+/Q/aC8xjFjSQaD656b5auWnwGBvz5u8EmmNZo6lJ5EyAIP03ROVgPp/RrWFun3LDGiFgPvuyJzuNUEHYLJmNgKg3WH7H7SX3ARQTl9Mu6dtcRf4ErhrOhjittWZ1u7k2HwSWYE2yLJWfbl7/zO1Bz2uSyvZ2/eLbrrXBB2AyZrZCIB2h13ACnv9K6SM4wq/aU1a48WKr4HvutV0CgD9s1Z+VzkWd4eff5jC0Ylpqr7TDtrRSQd9x8HVQsDrnk8+3WuCDsBkzWsEQD2WpYCFZ/pWojJKFX3Tj4VttuTpNTAy7v1dNwztD5ujmQ7vbh+makTqK6Pf8Ubv2j167xEN9VPb+9c12WuCDsBkzWsEQNvDnKkmay9qndKOn+ehqFPBjXZUvAW+65be33XD0O48M6wCDG/NG+gTvU58SPtNaWjjC+ve2dULrP8w+1SvCToAkzWvEQBtE1AJ5+yk/hollcfTjy1qsOQp9F3nfq8zlGHnnsJ/i3zn8uxI1ALut5hWPTahf09JW1/Ye/HCdK8JOgCTNa8RAK0gy9o73N/UJGIZ6xR/bNVdT+leY/C7roB1GMMYdvVp8NmH2jKSOLCy1w2DVgGg59zCJ60QcIapmKleE3QAJmteIwDaAuYSyuwndlgVkfGX1ptKL3l6Dcz1FnCvM5RBD6EKn0U71IclVa2yT8dDu0BzrIDVdtnkeP6JXhN0ACZrXiMA2gKjEi60xC7AEk4r+EevCbvWHxxa6zTF/X8/tLXtvY+hDs5sDbMF4K/+Vj70OA5I6yYtM1TCURuyHPNrE70m6ABM1qxGANSlWN7h/iY2KX0ooZPyj7of7ECdsC33u24g2v6T3h+94H3zYEfHJluDzi31m9YBzlEuQS0EnGGGYarXBB2AyZrVCIB27zLYDVMLyeusrBJ5+q2gNgIdqnVyVNaby02b3enZrwvedg531aZOA+r+drTWM8MKwMQGhiyfv2leE3QAJmtWIwCD1hjLIFUGoIRSBVXakirtY/Mc+K47LuS7biiXyq+q53L9P6HnHG7pmFpM40PXsQf1459lRYO2xCDTORuTvCboAEzWrEYAtDdbwg67VBmAEqYpqtQR1fi26qfAd93J1M7/2aetne93CsU2dNDAkP3Z1EqVjrsattoKnd7rJD5pr5Dpa45rYuzEO4CpWY0AnCjvcrAp0xbWib9EMYcBfgs2Pb/WkUc9BhqQ08LGNvLTalD1a91CTU7L4+fbSRwH2HVD7Vp7zizLX9U1NpnOAuOaGDvxDmBqViMA2i7dEkbbtGHiD41qiVlaa2lX4S+wh8B33fkMvuuU++Ye6+b/hru16zyZw7T76A/dDjdQVwDm+Q5SS/XmqrGx1l6Ea6J84h3A1JxGALTVS/2+gzNJnLNW0GnA397V0eDgtO194CEXc/iu04af+qz1Dg0t9D40R5WqVtHtC0Mr0pdp/6tawzDXogmuiZET7wCm5jQCoC0yyjPH2JO6gKiUkDvUMYvQByc0FV7QEUcD0mrE9FnhFqoeOVAR4G+pj2mnDTXaFEmuryD105qtweWaGDfxDmBqTiMA2g1AjjNZe0uNrZbXFVO/tgM3tqFljpkmX0unrQ7r8SsI/QUG7iimBqo6zVSpVbAzFcDSei75Tk7imhg38Q5gak4jANogY44yI72plcSljPOK9mgD2/WvsVAXrNkpqeP3NswlFto7P3D1eLXYjXSbTlP3z2fq0Gy1wfmM1xbXxKiJdwBTcxoB0G4AspQB6ym5wbqEWgV71MLw+0ueQhvWi+h5mVCWh3ff3hHaoT308LE6W/+hw2i6OqqQ6VQDdTd7xjaXa2LUxDuAqTmNAGg3ACVsudXuET8VODGobt7em4sOzYKXdL7hwLRB7s57UAJ346uhP8vJ74z2axrV9fm5Nr+oW/QzHp3ENTFq4h3A1IxGALT2tYgNdqlTVoqcGVRXVu+M3YY+akUdbziwtfKL6vp7CH1kBm8/9CPvpMsUhDpqnqtGl5o7Z9F9rokxE+8ApmY0AqCNzBXxHpOVgEucGgwfRfujUhY+sDh6UUL1JTPan3fd8TkDDefwh1oESw9Xtf6zquvmchwD+Ekbgsm6DZhrYszEO4CpGY0ArJX3WMS9deqg9SLKFdeon6Df3+s2MHG8KGHhhR2tDl3HayzUpxh4BeDfxA3uh9b3sOqqgmwbdLSR+bzdJq6JERPvAKZmNAKgLV4uYtotdRRAmYuD1KVVy+8lT9vAL3+ZaXPXaBzGf0/dpqC2gWc02M+a/Jy2vZr0xS+5ejRqIeC8vzauiRET7wCmZjQCoHz/Gtw2NZC8syqim1KjLuD+WvK0DfzMqojfuSWtB9ppmDvQEmcbL1do5xp9ajtSpU7OZyt/qS40zNy35poYL/EOYGo+IwDqJrsi6m6uU3+JYQu8daUuXfhc8rQJfNcddD41frS0Dl6Xmd9NoG6ExSCRfuCdtF7REHof/2Sb91L715lH3rkmxku8A5iazwiAttAoXxmwPpJ/i0LXB2tDKx9LnjaBpWoHOVddj4S2y6PL+s7AEjKT0yKSa1VabldVW+Z85xqqCw1yD5xwTYyWeAcwNZ8RAO2+pYw+TrLASqELhNU54au/m0ABpsMSDl+0po1BdShE9xJYa24yhZzcrdJyQl09XCjfpanVAcu+DZhrYrTEO4Cp+YwAaBONa+9wn1IlVosoVxigDuEu3wLf78cl1F2yp7R0HcagAveQNqUi1cn0D+16M3rt/GyjXmoh4Ow3OVwToyXeAUzNZwRAW5dTxth66pAVm/u7DtRFXIFvwpOZftdp58S1/pUEBuKXNveQyYJV7b4x1K+gRbaPiroyP/82YK6JsRLvAKbmMwKg7QIuY/GNWg7tQ6kdgGQN412nc/2u05bPtx3dCdWbNaoTkbcDsFWXAOb78lGXLuZfXss1MVbiHcDUbEYAtF3AC+9wX1LnrBfSTwlITl5UnRWx5cKDdhPatvFe15/iyOgXq95Lf2hVVUffU5CvZVZvyQfYfsc1MVLiHcDUbEYAtNsWk7XTaepiqA/FdgCSs8IVFzP+rlOmoVtO378FnspqiUiyA9DqelInvhb5PixaIeCML/OLa2KkxDuAqdmMAGjLcgs5ZlfdOvSh3G1Cyb7LL4NKdeVSJnlargIM3F+afYqTo9tt3su7+kwZv3u0KcBB7gC4JsZJvAOYms0IgPZGCzlkRz1F9EO5+4SSxeF+FHHoghttGLrVTWBgPCvfhvkUvc2Wdpvq9E9OvlUNaiHgDpsw07gmxkm8A5iazQiAtsKukP31q9RfotwOwDaZ/UshXS0v2nx3qxWegbtLu5Oikh2AVYsn00bmc455qSPyg3wsuSbGSbwDmJrNCIB2NRbSsKrLoQvKGbJu9F1X5HGGhrTB8zZFfAPzWYd208jJDkCLs3X1k3Mz1udRyw0OcwewTv2ePs39miiOeAcwNZcRAO1LK+tZ4D0kOwAFbxVKNgofyjzMyJLSDW0xhb8JPI1hkSh1NP1DiwtK3wPQsqawRi2zOcziGq6JURLvAKbmMgKglS898Q73Tb0Z+lBwByBdx7iUckuulAHvFgvRAhftILPYETk7APpmuYyfGG2P7VB3AFwTYyTeAUzNZQRAGwEsZRHuqDsAekHX/y0KWWnhaq38fhqP4Qe24S0sN4gkOwDN62qo9XlzfuDVFxrqDoBrYozEO4CpuYwAaJ1xiyNUmxh1ByBVxmhR6EEGtrSBqMbFaAI7500XkmXsAOib5TPuzlNrFwx2B8A1MULiHcDUXEYAtEuxlMsw+ZcoulyIPpu7LLWMsS2t7WzaDw0cAmC4AvCvfqrhl8ZPtVafJmPDrH46B7sD4JoYIfEOYGouIwDa3XUpN9bJv0TRHYBQcfp/Shll8aYUe2rY3IV+z7YjyckOQPMRAP34i4wV+tVCwIM1xFwTIyTeAUzNZARA23/VZtfyoJJ/Ce+Auj9a9Fbl4SdMWfTW8FcU+DUbd9HzjQAkJhMybntVCw4PdwfANTE+4h3A1ExGAALDpr+K6eAk/xLeAXXv6hqGAY5bGSNlMWqzVYCB37LpCsAP2T6o2pKIvD1z7VY8Y7WBfVwT4yPeAUzNZARA64kXU4kz+ZcoegpAP+7edJ9awbQzqRqd9RRYzboeOPO+fCMA6sB8zjsPdahhyDscronREe8ApmYyAqBtNy6mFEfyL1F4B0BdaW1Xqr5oWuPZ5IMY6EAcWH8s8nUA9PNy1vkiq7sNMr5ODdfE6Ih3AFMzGQHQDtorZiBu3NsA/yaOM1x7pyuD0uY1qXsX2M1iXksm2zbARBWAjG9MLQScca1hHdfE2Ih3AFPzGAFQv2mKua8eewdAHe6UVTG/Z1fKL6lBPZrACXP2/fNsHQBtPkSyrgFUa/I1mnrpiGtidMQ7gKl5jABoJblaHsQ+oHF3ALZ6VdeCplpcKYfEpivSBg4BWAzZfEVSpD6nTTsAgTONWv06mtPmGpqXYGyNa2KExDuAqXmMAGgFOcp5e2M+DfDvRt1o9YFdTx+0SeFkWx5YNOewhDXbaYB6rfyMnxd1BDBjvcE9XBNjJN4BTM1jBEBbbbz2DvdrzB2AjV7S5ROFzz4obVFqMvq1/tgDh1GhbB0AfQ1gi+MRU9SleBlfZxfXxCiJdwBT8xgBUA5hG3YJUCvKWbFfrPd7N/euf5d/YdfTB6VVSN3NB24oPT69WlWtTw038Cd2E2Q830AtyXuT73V2cE2Mk3gHMDWPEQCtDIj9HGrMeDsAb2rJ0/LzW1JGoxJXWqBsjstJ1rk6AInD8jJuAlDrDQxUR5lrYqTEO4CpWYwAaKuWBlwC1Ja6Y6jkL4vXZNflSzEllzwpd6P60Pk28Plw6b0mOwAN19XqR+XkfG/qXPwwE2tcE2Ml3gFMzWIEQNtuNNwSoNaSQ4blDFbseE4uXvi2LKez5UdrPtUeXqCapU/roc6of2h4Ta31Z8n4YdFuxoc5CoRrYrTEO4CpWYwAKFuvhlsC1F7i9PBSOwBPye2Lvzj/7K8606ONer/Xm5SVz77QZAeg4dp2fRNAxl2A6r7FQWZRuCbGS7wDmJrFCID2JjMuNeoruWi4yA7AQ/PvupKGW/woK1LXysMCzaXT+tXE3H3jNlXv8Gb8rKiFgJvUX2yLa2LExDuAqVmMAGgtq+1R6qrkruFiihZXaKMrdU/ecQuwjv96lL52oNV1WQEYjtL4bVTps+QZ7zvUQsAD1OLhmhgz8Q5gahYjANo3TUEL67TNip8K3DSsfrfWjb8z2Z9yBq4yHx24XfbqDyYq+Db9KycKCl7mC6zONeS/qLgmRk28A5iawwiAVrgkZ73RvlJ1Qwu8Vwjsr1qqN3YF9be8aA1fdEV6YMX8EGPXjagj6h+aratJDCSs8wVWV9dmX4Q3wWsiueqjVOsOb1Yy//LKNocRAO0Lq6RanPrBIVLUdMWXQOLVi3oD5NZqFUTZ7hn7CwcOAXBaAfhXHcL40uzmPfE0+erzqIWAsx8FMsVrgg7AZM1hBEC7+jIONPamliv5YH7wqy501MnB69+N9n27LPpAIxvKSM868pDAR8PvHJmH1Oe02e7ExEx5vhWOavOV+dttmtcEHYDJmsMIgHZnXdImnMBG711lnR22DSxaPPgYzlSnXIcqvDoiSoc00hy91dsPx6Gr5Bq3ZjtrEh/3fL1dteDQOtvLfJjoNUEHYLLmMAKgbTcqaVpdPx1Vyuqt/N0Efq1Hn3PY6iKxck5fdqP8fg7CjwgsD3XcEZLpc5oY8Mq3OE99oayjalO9JugATNYcRgC0olwljb4l76xKulMIHXVy/L2GTd3gXdxCBnPaITjBz2Ngttxz6iq5yr3Z6L1eByhj0Qt1e23O2hqTvSboAEzWDEYAtNqrw9QB7Sg5t1pQ0aLQUScnP62X2pMZfX+yP2VVeqgpCBwCsPQ8GTo5VdXsrjpR9iLf2nhtCf4i26tM+ZqgAzBZMxgB0NrVot5bcnvV2jvhr9BRJ6e/G6q2aiH0IusZmlIWpYT6eIE7btfJoHXqc9ps9D5R+TpbF0etN5BxKcWErwk6AJM1gxEA7YalqB04ycusmJPDQkednFc2VKuzriVtvPCh3A0GzocPHALgWz42uVulWXOWOPwyWwdA7VfnOwpkytcEHYDJmsEIgFZfp6h19YnSaOV0V0JHnVxUC6qoXxiLktZduFB+PYH1YIHxAt+SkMl6Fc3+wIkOQLZPibpkIduymklfE3QAJmsGIwBaHbCyquun/hKFnFwYOupkr2+izu+WtJbRh7IrvNYSBArmOX8Okh2AZk+jHwWQr0Kfutgw1y6gaV8TdAAma/ojANqa6/x1QHtJfCWGxocdhAaw13s/o1Z5Oyjrt+5AOZ2q1iLVf9Z1BeDfdMnqhitrE5/2bHHVQsCZfpUTvyboAEzW9EcAtJLjhW3ATQyKlvGXCI2o1u9fAgui/ymsoqE9ZT54/1cZqGLjfbeYOrSq4QoFdVVcvr65Wgg40y6gqV8TdAAma/ojAFodsCJa1H+0Y4tL+UuE2q7AmnR1q5jXObbFUDam7A3vb+qtxpH3zWLq2OqGf16tYZZ8iwDVxivPFTX5a4IOwGRNfwRAW3279g63KzW2WsDJRaH531DdF7X4eWFLL+wppSn2BqXW9Z9wL16Z2L/XdKYq8Sy5OgBqIeAsy2qnf03QAZis6Y8AaAOW+Q4cySL1x3CfsQgddbIID16qS68KWc3oR5n/3rm/DxwC4L8QJDVT1bBVTTxLrkJA6va7DLuA5nBN0AGYrOmPAGgzb4XV30jVWPWuWxg66mQRuSFVi58vnJexuVN6pc/6zxXwq0utVW24RiExBZDr2lQnLPrfds/imqADMFmTHwHQNgEsvGdT96ijlZK3bmkHoaNOltEt6epAcUFFjV2s47+a6uRxoIaN9wrAv8mWu+m4WmIRYK6ZDrW70vsLYB7XBB2AyZr8CIDW6/YtqFan3iF8cO2whI46WcVvodTi56vCul7WlC1hlaJw2/pv/ND/F6fuq/3QsExRYiAh0/ScWl2r95zaTK4JOgCTNfkRAO2a859O3aUdW/TJc5QwdNTJShmn1YufF7b6wprSLFV6pYEpoQLOjXvP9ClVd8VlO+5A3X3f9wuAa2KCxDuAqcmPAGhvsLRBt+S9leOahdBRJwfqQi31o1XAhgZX8YV0/+alNvXmooQua/J2sOHzJNYSZjr4Ql1Xs+733FwTUyTeAUxNfgRAWwNUwO3UrtTyKr8a8KGjTg71Wz19PMO3nL07Zcfn7whyfXvZIt8Zud2lDq08aPg8aoW+bKvi1ZX3/arvcE1MkngHMDX5EQCtTS3h63RHqhKQW7mw0FEnR6kDTNT11yXcyzpSbkx/tqYFSlgWMWSlHa/9oWlJm0Q9oUz3w2o3o9cXANfENIl3AFNTHwHQJiyX3uFq1NsV8TsGPnTUyUnyADO9pSh415MBZb3nzyrAem+wjILxt4kPadNb98SHPc/VqRYC7vUSXBMTJd4BTE19BEAbryxvzm2d+FOsfWKFFlKeNjjAVF3mtR48dsmU5R7fH8tAU1HGlFXqQ9p0mCL1PFlaQ+0kkF5fAFwTUyXeAUxNfQRAWwN0mX64sVQhgCyVS1sL/Q7PmtyMqsXPC971ZCG+Jfyr2sO2PndVSE889ZXRdDF7quxVlu6OekX1+ALgmpgs8Q5gauojANrZ5QXUVNmTKgTgMkm4DgS5aPRN9a6WjMlQhnXElA/m516P+m99UUjdytSJFU2r66XWEqxzhFULAXf/Aqj/dbgmpkK8A5ia+giAVnvL/VSVGrVqifgcGRZqqZqORKjTvKWVYbKl1Kf4aAUChwCsvSN/S61UbTAO/inV283yYVcX3XX+AuCamDDxDmBq6iMAWuWNpt9UhhL7AO1PAwodddJ8i7b+HV9eB8yQspv+oymp/9rLWAH4N7l/v/GBFane7iLD9amPMnR8Aa6JSRPvAKYmPgKg7bv1PlonJHF3ZX4YQOiokza3ouomrFH3LHuLDwWfBNeuum0B3Zc4CqD5jXuq6kX/RQChnXr/dPwC4JqYNvEOYGriIwDaHUCJHRttycIH40GL0FEnrTajq8XPy6vDYCne11uGDgEo5tOaunFvvlA1UQig/5LXZ72v0u1XyjUxceIdwNTERwC0Nbc+S+p1qT3WtuvAQkedtFs5FahmW5Gp2us4KcvT3gIfg0JWAKYrATevVaEu0JP+a+IT7X+3jx/XxNSJdwBTEx8B0FYsl7jiNlVm1XQneOiok7Yrp9XP17LAVRhmlMGp23oTUU67oJ6uI23q2eq3wtL30/6UOG+40+E7XBOTJ94BTE18BECbbyux8nZqfNWy0xI66qT1zin9fjFrZcP3+6vTw9VCFqujs/VjKUvmopTlKfWWq6AN4qlmu3kDphbp+dDrOAB9/v9D0/2KFWO7JtCeeAcwNe0RALUQaDnfqRWJhVFruyQvoRuo9jun1YnefLsa3m/2+nqLs4ci/8D/pNbAVRV0UuxaT9r0KKC/qcNxP/QoBhiq1Lun/edjXNcEOhHvAKamPQKg9bVbfFMZOtP/FpmOSGsgdNRZl/6HvhEr05TG+1Uo7cFN0V2AxJ+6yqP+Q0yihH+b24Xkb2DdOWVqMY102XM/qmsCHYl3AFPTHgHQCoGW+bbW+t/CrCUIDqB2mYjeqsXP8/wR7mK3kgclf5km/tRVxawA/KuX1pJ26+FTxYC7z3yk1hd+aF1Wc1TXBLoS7wCmpj0CsFbe1to7XFBiiZVV7YLH0Hddt+EH7W+QpWnbaCs9L8sdBEitpvunqP0qiZmLNl2u1IaCrsV6g5V6atqerTymawLdiXcAU9MeAdDGGAuaVq3Qji/+YNOeBb/rTru9tl78vH/bFtyX/c9RsUesphZ8/lqVtDBcOcbwU6usyWUQndbEv6mldn61HB0a0zWBHsQ7gKlpjwBoQ22F9rPV0UGj1MF70+OuzZB6O9Z719Mm9W1/WGwPIFFT91dR+1UTd+3tVtYk1hNIp8Ywuf3vW7uSO2O6JtCHeAcwNekRAPVupdCx4cTopcWkdvBeZ9W5HdWLn/c9kjE92ntQ6vdpo4HqfqfW55eYuGg3sd5gFqTtXr2tet5uxbJd0jFdE+hDvAOYmvQIgHaZlXruVmJhlMF3Q/C7btFh0/QP9R6952aM1JmyH04K7esl18B96fGbH0DWz+c2vRXysN0f7y11VuGvVutpR3VNoBfxDmBq0iMAWs2S1muAjSQOSb0cPkBwfrLPigl9S1avQ24atCBSUhm9HanzcL8UNiOcOK2iZZvY4Oun1Sf+vuHwf8vnHdU1gX7EO4CpSY8AaG+u7RpgK2rtIoN9gC/B1+/V79DfUq+PV4Pt3h/KPGQ1tZ7uU2kTwvoddrtx9WZ9oOaDCu97FXbUOgMtKu6N65pAP+IdwNSkRwC0ilvF7hDXz0hr+w3bVrDWqRz1G0TXP2R9hrgTm9J/tBxHttIkfVErAP+n32K3brmaLIRseD+8vdlrVC/V+aHmlcBHdk2gH/EOYGrSIwDa+HCxx24mFjENu6b9PbwJoef3kb5yvMedlFJPf1eZBdZThz9LaSsAk9tUW4+rNRnCWTQaa3/a70tc6tvtG4+sjOyaQE/iHcDUlEcAtC+roe+ku0scCDjoaHbgHPoPvefQ1VGNRfdB7uR5cj8KOkynokH80k6sSnw6W8dNnwfwId1/e6l9xC71MiCNF9qN7ZpAT+IdwNSURwC0L6vS7qz+SSwCGPReNvyN2X8aWl+r3305Rnof+Y/SRtI/pSvhFXcnqN+xL9v3s9aN/nwX+kfwuf7B/WigtZoajW9rxnZNoCfxDmBqyiMA2o6l4r5Z/9GPSBkyeKSCev8vI32x/kHn2/PGe74K3fWZOrFuWVwRI33WosNXxSZ9at+Hg/hCgO1D4GZ6/TcxXdH0Dn501wR6Eu8ApqY8AqB9WRVca0O/yRqwJYvckywytEL6wobO+6kSZROrilxWlerAlLd0Qa+72CVvg2+gT8fhya/XdehD8Hl5q2WGGn7mxndNoCfxDmBqyiMA2iLrMjeGfdIHhheD3Rq8Re7FcnQA9bVjnfc2Nrt7/FRkLYDEoXU9F5oPILFzscvK2k3jrfsHf/aef/u8DndIviZ81Ba2WU3tEV4T6Em8A5ia8giA9s1S3Nhqhb41aqhlYdtYfynLdKRe9rbr7bn6pLsOc7yL3BJ1DEtbAfj378sAv+OGtRw+HVzePL29b7fvb093VyeRC3zxvcVX+8w160eP8ZpAT+IdwNSERwC0PWJWx+p2ov9NhhoWXsdeMEszpFd86XaoaqsRgHbH1BnRtzF2/a0MSG+suxUt3DY9FKmh5c8HVnveZjNp69jDC74m0JN4BzA14REAbQqw6AE2/YiUgVYBvkYb0zwVE/TJ444DMs0LvxZaXlVbCFbeCsDUGsCO82qJrYUtHf58XtXjlhs1r6O8JtCTeAcwNeERAG0KsLAC67v0vdEDrQKMr0fLMxGt3zuuuz1pi0WAXV9iWNqOjxLXqapNVodNgF+argNs4vS33VRvsBuN4Y/ymkBP4h3A1IRHALQptiK3hf/St7cPMpatjDrkuRPR13p1LNSjl03eVeSQqtJJLbF8sXpT3f03nHES4PLfb009t7BJJfBxXhPoSbwDmJrwCIB2t1Le8qoqfW3YIKcYKBvSMm1I0j9p3XpkbW4diyz9pLQxJe5T0Senuk+yxMfaW6oukFG70U1a8HFeE+hJvAOYmu4IgFpRr+zOtV4McIgNbdrq7kwtp767sduL6A3SriIPWY/fUhd5XLW6bbHPBtU2OwGUP/FOv16drlid3Twl8o70mkBP4h3A1HRHALSLq8jGoELdIDTEAsa19oKZFkwkDpI9ubp7bju70ayS/PcL5HkXmcUGv3NUmslPPb6wV5clURGhkZOd31mipPaH46t7ZTXfWntoudcEehLvAKamOwJwr7yl0vs06hzAEKWA9C+ik2ZVUxISm94/HZyt719bvL8W7cYix3vILtbVK7IWvF4GqN/UVPNjHWL2fmV6yYJfq7M/kaGAsV4T6Ee8A5ia7gjAWnlLa+9wCfqd7QCzw6k76YsMr6kXP69YHF38eWx2B/ze9Dn/1/8dDCCyUq3EFYCJ/Xqd9wB82bZZ0BlwsL+sp/FJkf87uryrDwWM9ZpAP+IdwNR0RwC0HVbFF9pW91uv879e+lOw6v/ts06/SsXyZN3gOZvcQn0pcwQgsldtkIWeval/wL6D4ptePYDL2ki5XrKgbrnfnqcfUug1gV7EO4Cp6Y4AaFuLsgzfDUndwzzA4qD0XHqGiQe9+HnHD55eT7X6BnrnH0J4VL3QS05dVtd7Y822+yzAQaDD1PykyG/7XwrjvSbQh3gHMDXZEQB1vrLIAdYd6s7o/OuC0huxc9QfatxYf2m03WGjLkyrKLT6cyj+Ik+hudzUxirHWQvrdp+PX1ehC6LtzsJaaz7eawJ9iHcAU5MdAdDuocs8HH6HepJZ/hkMbb7kS446Oi1rvjZ7mxu9oOqvQnd+hEaqi1wBqC+rzZP5rk1t5x/HwWNz9B12AbUvhRFfE+hBvAOYmuwIgLYGqMg91rvetRuY/EXt0iumsnzBN2yrvzWcqGk4eVzkcYDB3/xBoQNU2hB9pm2Lb03Hc36tIuVy1N5KSO1LYczXBLoT7wCmJjsCoL2xQu+wdmhDg/lHszfJAdMsy9Ja1XtpPsO6bvJ0hZ7/FLhTLfLYor/6yUW5+tRbdeirZvkn9iFpXVig9qUw7msCXYl3AFOTHQHQbgtL/YatUocG858Vvk59CrLc4aW/UytaTNQ8N7iNKnTYp36nWmqHW91Yn6+29lvzWfHlOr4apvWegnprvk49pOhrAh2JdwBTkx0B0G5XylxjtUdbg7TO/mrbxNhrpjp6bYr3t5no2N4kZ4/LXD5VPwdnUeoor3ZPnXV+5aXZAv6DG20xbIsCEV/qrfnIrwl0I94BTE11BEA7t6zMorD7tKHBQuezPb1fJe6kSjxdN/RXXntHitF6pLfph7fxfJG8LT4rs1QCRk+8A5ia6giANoI+jkM21LNCS71L9JQYOy5y3mdTu1E9KLX2uzYD0LMKYMDmVpvVObmlKB4GIt4BTE11BEC7f770DtfMWnkLa+9wRXoaXfGn+pK3IvspH8w/ju/3FweB1zq4uKf1x3DEO4CpqY4AaIVAyxwMrtF2AjIHELSNz1MXuX76vTbKU+hehb/qDMBwRxe+P91enR4drv7/PS1Xh6cXN9TDx8DEO4CpqXYAtPU7AxymMwitE1Pk/WwBHmMTJ0Wun65ffcX+XbUZgJEMqQENiHcAU1PtAGgT6GO5iXhT3kOZa9oL8Br5y5e4fvqtNsZT7p9V2wMwil01QCPiHcBUgw5AoRuoVVrbWWhR+ACl9NqqxBHtIryEewAlzvvUVi2uSl0BqB5QXWLfCuhIvAOYmmgH4FF5P+VOs+7TujHFLhZzFy4Cm792Um/1UfVIWdsCaJV1GQDAhIh3AFMNOgBj7OBrBUX7HlxuSFkFMMq9GTZC6z9KrP1QK1ZXcNdUKazHCgBMiXgHMNWgZPYYOwDauSXl3mbVaEMA3HfFhLaAFjiMVS9VUeAoxTflg1jo2cVAN+IdwNRERwC0KiL5ypYPT/nzrL2zFSu0YD1zqbocagMVBQ9NreOfw4JTA+2JdwBTDUYARjjEt9UqiRa70CqgvlH8F8sAY0JloMu7Ta3Nqpe7AvDvNl5ZfzmWPTVAI+IdwNQ0OwCBM1Z/HXiHa+Um/kZGNJVha1v/XZVX/Xlbq3JX8N9TqatZ4u4KoDvxDmBqmh0Abc3yuMoa1NuJX1QDjHgfQzNV69kVvAJQqQJ4wDgUpkW8A5hq0AEY4STfWnk75dZaCXqIvxPOQwsLrFgrbpy6ftRTsTUA1c8gu1ExMeIdwNQ0OwBnytu59w7XUvxw9JLvGT3Vi0CU95uqre4suV/KRxDzId4BTDXoAJT81RShnQpX7l6rsNf4gsYx7WcwVF83UVynr/ZHLXgF4N/n6AdwUfCwBdCJeAcwtdYb/w/j6wAEVoH9M7pJy/ifiGJAQbUKu+VNVNfq6pQ8lB4vArT2jgbkJt4BTE1yBCB+y1LoqXCqbXw8YyznGtqqTa8XVwSgNklRcleuXrDox2FxHSugL/EOYGqtN/4f1t4ZW7tT3k2BJeFS4t/ATMEG1H5dy9KG12tbO4quphc/WZv+J6ZHvAOYWidafxljB0Ab1vjjHa6D+JEAbASoq5WBXnsn2lc7qaLkD2X8XK0R7g8GUsQ7gKm13vgX+f2ZpJxcUvRka8wmWgxgfBMag3uvra8rbaD6bT9h0UPp0ara5a2sAPoT7wCmGnQASr49CYsXLi2xJmwD8UUNxa1vd1fbYFfcr6jWPy15N0e8plbJqYGuxDuAqbXe+H8YXQcgVAv+x8I7XDfRSY2St4+5qN1eF1cFuFZWp+Sh9E20Mz2+tcFAA+IdwNQ62f4XWEY1Ib5orsDmoJn4ToARlmkaVK1oTWl1H2rzOUX34aLHUR4xAYBJEu8ApmrrkeqK20SVohxdMsqzjT/EywFRi6WqVgSouBvV8qcoKkInK3+iBBAmSrwDmFqnmv+iTykLiy+aH+Fwxo/o1ka2AlY87/eTirtRrS3nKLkEQLwIcMm9FqAH8Q5gqsEIwOiu9Xjp8jFvXa7tbvsxug7acF73Z6yLu1Hd7i+qL7oEQLTXWfKyBaAP8Q5gqkEHYHQb52qV4CqKOxausegygOV431Nm77XtksVNX9Wut+ISVrzHrqSi9y0CfYh3AFP1g1NqxlZsJnAa7K+Vd7geXmNfx0UPIht6rbX/xd2ovhS/R6EqVk9jWfKoBdCLeAcw1aADMLb9vvHSZSOfMI++sZLvIu0813asnZR2o1qbACh6CWd0Me1459GAFPEOYEpbMf9tbB0AbVZj3JvmYu+suJluD/VP8mFx++vW+xHX3okU0Y0no11IC6SJdwBTDToAY2tdoqvlZPT3yrWDbr8dl3ara+69/qspb6C6NgFQ8lz6NnYI0Fh30gJNiHcAU9rBed+K+x5NiBYvl/GNZuyJfimvvZM5u68XrFuVVgHo76a2jLPkj+M68lErbl4FyEm8A5hq0AEY2SLzbbRkzv+KGxRu6T22FWB0WzVyeg2sViuv/a8PTRVXpKiiVrD4W3nzKkBO4h3AVPysj7E2mq/KWznwDtfbW6Q2+3JsEzX5vIcKP63K+33U+tolTwDEtpysRnY7ALQk3gFMNegAFPw1FRK7dflw5h2uv1qtu29HI+un5fJ+GfqFHJTX/tfX1BU8AVCfrfiyLG9cBchKvAOY0prLb94RW1orb6XkMdemHiM9gHPvYB5ewis+T8q7T603qWvvSIrIatMFGwAxdeIdwFS6AzC2A3TPlPcyuqrGIbE/2eiObe5rexcp+nw54KDVz0u2HWKoLVMo7pSCish+08XYaoIBrYl3AFNa1ZwvYyueFz04V8o7GrabWA9gEt2bxl4uY5URB92n/vOiLVddrmuNaXmTFL9iK4Np/zF94h3A1OQ6AFvtvRR809VG7At6PgO0L9fRft7BoL+F3zrT7cZb6kttCq5IEftOmPVOE8yFeAcw9aS1l58OvSO2Ez3B/H9H3uFyifQAFtMY4Wgg/jc+H3Yx5O/oS6slF0+1dRsFL0d9joys0P5jDsQ7gKl0B2BkraZW2GA66+QimzdWYyva1FXsL7wYehpk/fNKbU7xqe+pOyh3z8ZbuP1n/h/zIN4BTD0r7WX7b7oCXCtvZe0dLp+H8F6Ag/KWvw8i8gc+GbwD9Ls8vsXa2PopxQXvAHyrh/18u/OZXsK8iXcAU+kOwMgO0IsdYfphSoOYkd2Ah/MYAwi+96XBKsh/Sw8a/6ID1RvLPU7nLby2YllujwXISrwDmNKmzL8UPFsZEr6BafmdPQaRqdqDSb3JmNA7vzIYVq8sMW06JL6pn01R7iUVuf8vsK4yMAzxDmAq3QEY1+FfG+WdjK2iQcJr5Mt6Dj2A+ts+N9lWVxkwa3gXv6mf31TuAoDXcKHpo5lMLAFz6wBolfO/XHlHbEVb1Diy1QxJ7+GzAQssg5/d/ns+M7pFrZyefdnoAe/1+/9y92pE2v+TYjssQHbiHcBUugOw9o7Yyq3yTsY1ltHAJlz1cAYTtrtv+NysSb2qNItNfj40SlNsvaancPt/MZHqGUAT4h3A1Fvwmq8aV4XZ0MlwP8pdetVZeM/D4s4719Aqb3Z5ZTjnUak9vGzw4y+BJrXY8yjuwstKJ3jVAHHiHcBUugNQcMmygEh1+E9T3Ml8H/7WLraVyeT3jR7dmY5PVxdepifGQ3+cYhcAhvuSyyleNECceAcwpS2a+1LsiGVQrD58s2/sEXoOj9ueTXve9utNrq6MlzvsdJdTO+O3V4G/S6mnNkdmkw5nsJ4EqBLvAKbSHYBR3QK8K2+kyZjtCEWWAh5N+qv74895+WQ+Ob1zDFNiaOwtNBi1KrQT+lpfq/hh4t1IoE68A5hSz875NKoVZdrZRiOraNRY8E7z/wZyygsBDq7sW/+/e8fk6ttjgjPqpW4AuAsPnI1r+Q+Qg3gHsJXsAIzqTjJykHmDL+wxi9QFHvhcnBnaGSc/VX7wLTiiXmg93c15KKysykwLDEq8A9jSJs0/jaquzIXyRsa1mrGVyAjuwahGb0Zgt05u9AZ5uw5fVWUup3kOF5Qa/lwFoEDiHcBWsgMwql3A4Ybwy5Rbw21k++N6VH+90u3Pl50ER/Q3f8LrMsvsgW7XfHKAf8Q7gC2tdv4n74CthMfCv0x7QPwh3JM7nHK3x1r95KzT+712cvt4EfsMFrmh/il8+M+Kjw1mSrwD2Ep1AEa1dl6ra3jgHW5gwVXn/7uYdsfHUqjM5OL4+u7pdbPZbt9fHtZn8QG1Etv/TWTKjNX/mC3xDmBLGzQfXbv5oLwRbc3WJGwjKyAnvR3AVHi7RTMltv+Rxf/TLyQJRIl3AFupDsCRd8A21sobmXpxvP+9RP6YU90AaU0rM5lQYpsaeTus/sOciXcAW6kvtVE1HuH9TF/KXIKd1zZcz1W8c01EcsFszOLBO3pIOCqb/zFr4h3AVqoDUGzt8pDwiqYvhdZgyew5+CvwTjUN6XMzIgo9njEU9XgelwkQI94BbIVrgP8zpjN01bKGM9nWFBwE8A41DdoKE81RoWPq9aSLm5lcJUCMeAewleoAjKl+3ovyPg69w5l5qR8O4B1pGrQyk4piCzLWkjL7D4h3AFta7bwPY5oSvNO+hr3D2dn+2d+K7p1oGlJ95bASl/9/2Qu6LLJQEWBLvAPYSnUAxvStEFkC92ntHc7Sfil67zzToK0wiTkseE59N+lFoQcVAqbEO4Ct1N7mItcvR5xO5H1k8LBT4Mk7zSSkD86suyp1+P9DNeghJ/8AH8Q7gK1UB6DMBcxhWlXDUR1qmMHOYkDvMJNQLwScUngd5n9BF39Y/Ad8Eu8AttaJL7ERNZwb5W0svMPZq8wDeEeZhFAhYE3xrepv0nMW/wHfxDuArVQHoOQxzD3aLdqxdzgPjz+z1t5BJqFlIeDL4ufUv4MeMfoP/BLvALZuEt9j3vla0G7RxlTOIJ/tzXJsf8RytSoEfDmCm+rPoMvbwscpAFPiHcBWYmBzTGcBXSrvo9zNWMPaXC3oAOTRvBDwal383f+H/5Murkc0wgcYEO8Atu7177IxnQWk3aI9eodz83ZOByCLzePVyX6BhYDlxeNI7qlFLkYwTgGYEu8AthL1Tcd0FpB2izaKW7KBPI/pj1i27cvt1ekq+ilbHK+fRtL6/++k4BoFgBPxDmDrSe8AzKiAHtDM+9Pd+vLs5PBgufwaElisDk/O13cv42n8AQSJdwBbid3NYzoKAACAHsQ7gK1XvQMwpqMAAADoQbwD2Eoccj6mowAAAOhBvAPY0srnyexK6AMA5ku8A9hKHHFClTAAwEyIdwBj+tbmER0FAABAH+IdwJhe4IxCYQCAmRDvAMa0M3TneIgeAGCmxDuAsUOtA3DonQ4AACPiHcDYsdYBoIgsAGAuxDuAsVOtAzDPU3QBAHMk3gGMnWkdgLV3OgAAjIh3AGMXWgeAQoAAgLkQ7wDGLrUOwKN3OgAAjIh3AGPXWgeAE8MBAHMh3gGMrbUOAHWAAABzId4BjN0o7T91gAAAsyHeAYzdKR0A6gABAGZDvAMYu1c6ANQBAgDMhngHMPaodACoAwQAmA3xDmDsWekArL3DAQBgRbwDGHtROgDUAQIAzIZ4BzD2pnQAqAMEAJgN8Q5gbKN0AKgDBACYDfEOYGyrdACoAwQAmA3xDmBtEW3/V97RAAAwI94BrK2iHQDKAAAA5kO8A1g7iHYAKAMAAJgP8Q5g7SjaAfjjHQ0AADPiHcDaSbQD8OAdDQAAM+IdwNpZtAPALkAAwHyIdwBr59EOwNY7GgAAZsQ7gLXLWPvPLkAAwIyIdwBr17EOALsAAQAzIt4BrK1jHQB2AQIAZkS8A1i7iXUA2AUIAJgR8Q5g7S7WAWAXIABgRsQ7gLX7WAeAXYAAgBkR7wDWHmMdAHYBAgBmRLwDWHuKtP8H3sEAADAk3gGsxToAp97BAAAwJN4BrD1HOgBr72AAABgS7wDWXiIdgHvvYAAAGBLvANZeIx2AV+9gAAAYEu8A1iIdgIV3LgAALIl3AGtv4Q7AsXcuAAAsiXcAa+/hDsCldy4AACyJdwBrm3AH4NY7FwAAlsQ7gLVIB+DZOxcAAJbEO4C1bbgDsPHOBQCAJfEOYC7Y/h96pwIAwJR4BzC3CHUAzr1TAQBgSrwDmAt2ANbeqQAAMCXeAcwtQx2AR+9UAACYEu8A5lasAQQAQLwDmAt1AKgDCACYGfEOYC40BXDlHQoAAFviHcBcaBHgg3coAABsiXcAa8FCQO/eqQAAsCXeAayFSgFTBggAMDfiHcBa6DhgjgIEAMyNeAew9hroANx5hwIAwJh4B7D2FOgAvHmHAgDAmHgHsHZXb/8PvDMBAGBNvANksdk2/tHregeAk4AAALMj3gF62jxcHB8sRBaHF7eNNvOd1TsA90OHBACgNOIdoJen02pZn8V5g8n8o3oHgIMAAACzI94Beng+rbXlf5JzAfVCgGcWWQEAKIp4B+hsuw6s55ezRA8gsAvw1iYvAAAFEe8AXW3qt/+fTvQB/Zv6I6gDDACYH/EO0NHmMNz+p8YA6msAmQEAAMyQeAfoZnsSa/9F1trj6ocBcxIgAGCGxDtANxfx9l/kKf6459oPr5qXEAAAYDLEO0Anj1r7LwfxZQD1MkDXhrEBACiFeAfoYhtdAPDlKvrA+gwA5wAAAOZIvAN0EVjKv+sl8sDb2k9emAYHAKAQ4h2gi0A1v10njR/4ahocAIBCiHeADt5S7X+svH/9KGD2AAIA5km8A3TwJ90BOAit7Q8sHXg2Dw8AQAnEO0AH5+kOgPwJPK6+BYAVAACAmRLvAB0cN+gALOsFfl9qP7RgCwAAYKbEO0AHBw06AHK6PwnwXn8YNQAAAHMl3gE6qG/mD9krBvBe3wGw0s8NAgBgusQ7QAerRh0AuaqOAbwEhg0e3d4BAADOxDtAB4k6gL9Ofqf4N/X1f6wABADMmXgH6OC0YQdA5Pz+bbt5vb9YBP4fEwAAgBkT7wAdhG7n26MEAABgxsQ7QAcPOdr/G+93AQCAI/EO0MEmNKLf0rn3mwAAwJN4B+jirHf7f8QCAADArIl3gC4e+7b/h/U6gQAAzIl4B+gkeR6wbkUJYADAzIl3gE76DQGsXr3zAwDgTLwDdNNnFcAB9/8AgNkT7wDdvDcsBxxwxPw/AADiHaCj567t/xnr/wEAGG0H4O99t/af+j8AAPwdcQegUw9g9eSdGgCAIoh3gO4el23b/yuG/wEA+CTeAXp4bVcO4JDjfwAA+CbeAfrYrps3/wd3W++4AAAUQ7wD9PN23rD5v6X5BwDgH/EO0NfLZXopwNkjzT8AAFXiHaC/zf2J1vqf3FD5DwCAPeIdIIu324vDUON/dHHHwn8AAOrEO0A2m6c/F2cnRwdLWSxXB8fn17dPNP4AAISJdwAAAGBPvAMAAAB74h0AAADYE+8AAADAnngHAAAA9sQ7AAAAsCfeAQAAgD3xDgAAAOyJdwAAAGBPvAMAAAB74h0AAADYE+8AAADAnngHAAAA9sQ7AAAAsCfeAQAAgD3xDgAAAOyJdwAAAGBPvAMAAAB74h0AAADYE+8AAADAnngHAAAA9sQ7AAAAsCfeAQAAgD3xDgAAAOyJdwAAAGBPvAMAAAB74h0AAADYE+8AAADAnngHAAAA9sQ7AAAAsCfeAQAAgD3xDgAAAOyJdwAAAGBPvAMAAAB74h0AAADYE+8AAADAnngHAAAA9sQ7AAAAsCfeAQAAgD3xDgAAAOyJdwAAAGBPvAMAAAB74h0AAADYE+8AAADAnngHAAAA9sQ7AAAAsCfeAQAAgD3xDgAAAOyJdwAAAGBPvAMAAAB74h0AAADYE+8AAADAnngHAAAA9sQ7AAAAsCfeAQAAgD3xDgAAAOyJdwAAAGBPvAMAAAB74h0AAADYE+8AAADAnngHAAAA9sQ7AAAAsCfeAQAAgD3xDgAAAOyJdwAAAGBPvAMAAAB74h0AAADYE+8AAADAnngHAAAA9sQ7AAAAsCfeAQAAgD3xDgAAAOyJdwAAAGBPvAMAAAB74h0AAADYE+8AAADAnngHAAAA9sQ7AAAAsCfeAQAAgD3xDgAAAOyJdwAAAGBPvAMAAAB74h0AAADYE+8AAADAnngHAAAA9sQ7AAAAsCfeAQAAgD3xDgAAAOyJdwAAAGBPvAMAAAB74h0AAADYE+8AAADAnngHAAAA9sQ7AAAAsCfeAQAAgD3xDgAAAOyJdwAAAGBPvAMAAAB74h0AAADYE+8AAADAnngHAAAA9sQ7AAAAsCfeAQAAgD3xDgAAAOyJd4CUrcS8pR76Un/MrUVkAACKJ94BUp6jHYDr1EPvAg96tsgMAEDpxDtASqgV/7LcJh56FXjQmUloAAAKJ94BUkKt+Le7xENPQ70Gk9AAABROvAOk3B5HOwDHiYdeLeqPWZiEBgCgcOIdIG3ztD4NNOX/e0k8cnt3sv+QQ5PIAAAUTrwDNLN9uTlf1ToAF+kHPi53H3I1fFYAAMon3gFaqE0GLDbpBz3tPoRdAAAA/B1XB+C+NgRwk37QZucBp8OnBABgBMQ7QAvbg/0OwEH6Qa+tVg0AADAP4h2gjT+1IYDH5GNuqj+erB0EAMA8iHeANja1zQDJuj7bw8pPH6ZKBwEAMBPiHaCVelWg98QjqoUEF68mIQEAKJ94B2jlrdYBSAzqv1d3Ad7bhAQAoHziHaCd8/0OwEof1T9t3lcAAGBGxDtAO/WzAdXb+uvKD55bZQQAoHziHaClWjEg7UCA6gKAExYAAgDwS7wDtFQvBhTf2v9Y+amjBkUDAQCYDfEO0FK9GNBl7EefF7T/AACEiXeAtm72OwDLSNtebf8PU7sFAQCYF/EO0NZmud8DCB8I8Lyk/QcAIEa8A7RWKwZ0GPqpavt/RPsPAMAu8Q7QWr0Y0FP9h54q7f8x7T8AAHvEO0B7tWJA9R3+T5X5/xPW/wEAsE+8A7RXLwa0f4v/UGn/T9n/DwBAjXgH6KBWDGi9+/+rtQLOaf8BAKgT7wAdPOx3AA52Wvnbyv+58soIAEDRxDtAB/ViQNUDAaqFAtZeEQEAKJt4B+iiVgzo5N//W1f+OVwhAAAAiHeALurFgF5//le1SoB6UCAAAHMm3gE6ud7vAHzP9W8v/v3T4sE3IwAABRPvAJ3UigF9HQiwPau0/4HyQAAA4It4B+jmYr8HcPf/P25OKz2C+CnBAABAvAN0UysGdPR/+3/y7z9Xr+nnAABgvsQ7QEcn+z2A5/ejf/9x+OadDwCAool3gI5qxYBODyvDARz/AwCASrwDdHW43wP4h+N/AABIEO8AXdWKAf06o/w/AAAJ4h2gq22tGNC3C9p/AABSxDtAZ7ViQF84/gcAgDTxDtDZe7D9X3vHAgBgDMQ7QHe1YkD/u/UOBQDAKIh3gO5e6u0/x/8AANCIeAfooVYM6No7EQAAIyHeAXqoFQM67P5c2+CKgoN8YQEAKIl4B+ijVgyo+wnAtcMFPp1lDAsAQEHEO0Afl/sN9knnp7oNdgCYUwAATJR4B+hhXW+xOx8C/Prn/Kj+dCwqBABMlHgH6O4qcMt+3ucJty9316er6tNxqDAAYKLEO0BX2/PgoH3vc4CrqwEXVBUGAEyUeAfoaHMabP/7VwKuVhc4ypEUAIACiXeAbjbH4fZfln2PAr6vPNlFlqwAAJRHvAN08lbbAPjrT8+nvs74XAAAlEq8A3TxehBt/+Wg57x9dWrhMU9cAACKI94BOnheVub8a2sB7vo9ebVv8Z4nLwAAxRHvAO09Vtr/67+P+x2Afiv3NpVnWmYKDABAccQ7QGv3i91J+tpygKc+z/5UeaLudQUBACiceAdoq1qz9/bjH272OwCnuZ6+95ZCAABKJd4BWlrXZvs3y70OQK/6fZe15wcAYILEO0A71fK/D4F/+9Rn+361vsBzjsQAAJRIvAO0US3/u/jdo/e63wFY9Fi9Xx1OoBAwAGCyxDtAC9Xyv8vKUr/aTsDup/i+VZ7lMENkAADKJN4BmquW/11Wh+drOwGXne/dHyrPcpYhMwAAZRLvAI1Vy/+udtf51XYC3nR9kXXlSdZ9EwMAUCzxDtBUtfzvwd46/9pOwM6j99Uzhh/SPw4AwEiJd4CGnleV5v1t739uFvs9gK6Nd3Usoc9uQgAAyibeAZp5qjTxR/VF/rWdgMfdXmZbeYpFz8gAABRMvAM0Ui3/e7yp///aTsCOe/if+/chAAAYA/EO0ES1Pu9JoP0P7AQ87/RCd5Vn6FNOCACAwol3gAb+VJrls/AOv9pOQNlfJ9BIdSqh804CAADKJ94B0qqt8nlsh//Bfgeg00k+1YGEXocKAgBQNvEOkFIt/ysX0Qo/tZ2Ai+BUQUJlq4H0qCcMAEDpxDtAQrX8r1wqP1fbCfin/Yu9Vx6+6p4ZAIDiiXcAXbX8r74s73K/A7BqXw+4upLgtHNmAADKJ94BVO9H1fl/9UfrOwHvWr9cdR6h+4FCAACUT7wDaKrl/2Pr/3/VdgIetX69i17dBwAAxkO8Ayjeqkv7Q/V/djzsdwDkse0LVscbXjqGBgBgDMQ7QNxO+3+QXpRf2wnYdhp/W11I2PlEYQAARkC8A0TttP+LBqV9azsB297FV5cRBOYPagcOfKBaAABglMQ7QMx7df5fbhs8or4TsGU13/vKQwMrDk9CHQCqBQAARkm8A0RsqvPxctLoMbWdgC2b5+vKIwNVBJaB9p9qAQCAcRLvAGHb3TX9r40e9FJrn9vt5TurPPKh/r8frg73nv7kD0sFAQDjJN4Bwq53Gtqzho+qDdIvW9UDri46CJ8l9HZ79jPPsLh87FJsGACAIoh3gKC9LX333R4m7Y7021R7DrEfev8uTbhk9R8AYMzEO0DI+2q3GW96tO+2thPwoMVuvufK445jyb5nAZaM/QMARk28A4Rc7DXjjVvxP7UhgKaDB/+7rTwscuzQT2nCVbNFCQAAlEq8AwTUyvo3bm7rOwFjt/IB1U0E4W2HP6UJDmj/AQAjJ94BAmoVd5rv56/vBFydXt83m0KoHjwYrDv0+j0zcdh0SgIAgFKJd4CA/d12ImdNm9z6TsBPy5Oru5fUREJ1n39ogf/Ld/t/RPEfAMDoiXeAgNo4/v9OGra6wXJ9XxaB4j4Vb5UfPQj8/5fvDkLyVCIAAMon3gECQiX3gvfkAfWdgP/o9YSrjwwUHnj+TnXCKUEAgAkQ7wABx4HGO3RPHrJdBR78Td+6X91BUK8g+PQ9LHFG+w8AmALxDhBwG2i8mxYDDOwE/KUPIpxXfrK2efDxu/0/p/0HAEyCeAcI2B7VG+910wfXdwL+SBzcU116uL/N7+H7SSPlAQAAGBvxDlCKbaX9X+zd5/+cE3zlEw0AgOzEO0ApqhsIj3b/113bUQgAAEon3gFKcVfpAOwWHvpZktDmYCEAAMom3gFKUT2AeKdgwM33P+qbCAEAGBXxDlCK00oH4LHy7+vYxgAAAEZMvAOUolo/oFJ18HtgYPEYfyQAAOMj3gEK8R7eL/h9LtFCryEEAMDYiHeAQjxVOgAnv//6fbjgMng4IAAA4yXeAQpxU+kA/Gz33158t/8vrtEAAMhPvAMU4qLSAbj7+qft2fd/Lzn/DwAwNeIdoBDVA4i+Bvy3//YF6OcIAwAwPuIdoBDVEwQ+CwFvKvsCVxwBBACYGPEOUIbXSvt/+PEPm5PKv/xMCgAAMBXiHaAM95XW/uPk4U11SuC7TwAAwHSId4AyrCut/frv3/f9A4kfvAMCAJCVeAcow9lOY/9+uNf+y7F3QAAAshLvAGU4qDT2r2+19l+EUoAAgEkR7wBF2FSa+sXbd2/g9rzyr6feEQEAyEm8AxThudLUr1Y/MwEv1SEAqgECAKZEvAMU4bY25P95/E91K+C5d0YAADIS7wBFuNpv/7/K/z9W/+nNOyQAAPmId4AinOy1/6vXr3+vrga89I0IAEBO4h2gCMvd9v/w527/rjop8O4aEQCAnMQ7QAnedtv/o9+mfruq/PO1Z0QAALIS7wAl2Jnrl5PK0T9/qusCOBUYADAZ4h2gBNVmXs6qR/9tqpMDN24BAQDITLwDlKBa8edi9+jf6v4ATgUGAEyGeAcoQfXon72CP+/VwYFbn3gAAGQn3gEKsK028vt3+RfV3QEu8QAAyE+8AxTgRWvjd+oBcyowAGAixDtAAe4rTXy94u9p5f9yKjAAYCLEO0ABritN/Lr2f5+qQwCcCgwAmAbxDlCA6j1+YJC/ukSQU4EBANMg3gEKUC33FzjypzpDwKnAAIBpEO8A/jaV9n0Z+P/bA3WNAAAAIyTeAfxVJ/mDq/xuqkMAnAoMAJgC8Q7gr9q+B8/83VbrAV9ZxwMAYADiHcDfZaV5D9f6q24T4FRgAMAUiHcAf8fJbX7vi8qPrG3TAQAwBPEO4K/aukdO/K0OEnAqMABgAsQ7gLu3SuN+EPmZ1+oyQE4FBgCMn3gHcPdQadujdX7OKj/EqcAAgPET7wDu1pW2/Tr2Q8/VIYA7y3gAAAxBvAO4q97c30d/qrpSkFOBAQCjJ94B3B1WmvbX6E9VJwo4FRgAMHriHcDbttKwL5TZ/Wo/gVOBAQBjJ94BvFVn94+Un7utDgGszm/jgwUAAJRPvAN4qzbs2kk/O/WAPyzP2A8IABgt8Q7g7arSpv/RfnAt+2JVAwAAKJ54B/B2UmnRH7Uf3Cz2OwBnVhkBAMhNvAN4W1VadP2cn6v9DkC0agAAAKUT7wAAAMCeeAcAAAD2xDsAAACwJ94BAACAPfEOAAAA7Il3AAAAYE+8AwAAAHviHQAAANgT7wAAAMCeeAcAAAD2xDsAAACwJ94BAACAPfEOAAAA7Il3AAAAYE+8AwAAAHviHQAAANgT7wAAAMCeeAcAAAD2xDsAAACwJ94BAACAPfEOAAAA7Il3AAAAYE+8AwAAAHviHQAAANgT7wAAAMCeeAcAAAD2xDsAAACwJ94BAACAPfEOAAAA7Il3AAAAYE+8AwAAAHviHQAAANgT7wAAAMCeeAcAAAD2xDsAAACwJ94BAACAPfEOAAAA7Il3AAAAYE+8AwAAAHviHQAAANgT7wAAAMCeeAcAAAD2xDsAAACwJ94BAACAPfEOAAAA7Il3AAAAYE+8AwAAAHviHQAAANgT7wAAAMCeeAcAAAD2xDsAAACwJ94BAACAPfEOAAAA7Il3AAAAYE+8AwAAAHviHQAAANgT7wAAAMCeeAcAAAD2xDsAAACwJ94BAACAPfEOAAAA7Il3AAAAYE+8AwAAAHviHQAAANgT7wAAAMCeeAcAAAD2xDsAAACw9x+kBEDBzCiXNQAAAABJRU5ErkJggg==) k
Bu erda y(xk)=yk belgilash kiritsak
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