321 lines
120 KiB
Plaintext
321 lines
120 KiB
Plaintext
{
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"cells": [
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{
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"cell_type": "markdown",
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"id": "cb83cb4c",
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"metadata": {
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"slideshow": {
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"slide_type": "slide"
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}
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},
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"source": [
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"# Project"
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]
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},
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{
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"cell_type": "markdown",
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"id": "0f54afd9",
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"metadata": {
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"slideshow": {
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"slide_type": "subslide"
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}
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},
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"source": [
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"```{note}\n",
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"This project draws inspiration from the `noaa_apt` module of [SatDump](https://github.com/SatDump/SatDump), an open source tool that can decode signals from many different satellites.\n",
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"```"
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]
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},
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{
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"cell_type": "markdown",
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"id": "2a4f16b4",
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"metadata": {
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"slideshow": {
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"slide_type": "skip"
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}
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},
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"source": [
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"Here, we apply the theory to decode the signal we received.\n",
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"\n",
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"Let's look again at how the satellite transmits its data:"
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]
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},
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{
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"cell_type": "markdown",
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"id": "adaf6659",
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"metadata": {
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"slideshow": {
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"slide_type": "subslide"
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}
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},
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"source": [
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"```{figure} img/apt_frame_format.webp\n",
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"---\n",
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"name: fig:frame_format2.en\n",
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"---\n",
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"APT frame format ([source](https://en.wikipedia.org/wiki/File:NOAA_APT_Frame_Format.gif))\n",
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"```"
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]
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},
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{
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"cell_type": "markdown",
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"id": "f653ed80",
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"metadata": {
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"slideshow": {
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"slide_type": "subslide"
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}
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},
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"source": [
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"The image is composed of pixels that are modulated onto a carrier using amplitude modulation:"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 1,
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"id": "2a4aa651",
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"metadata": {
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"tags": [
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"remove-input"
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]
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},
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"outputs": [
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{
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"data": {
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"image/png": 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JrKGhobE7Q8ccNQbarTaroMWRhoaGxu4MbTlqELTlaDZBiyMNDQ2N3Ro65qgh0JajWQUtjjQ0NDR2Z2jLUYOgLUezCVocaWhoaOzO0DFHjYE+rTarMO2n1Xp6emBIKuuRkZHprl5DQ0NjdkFbjhoD7bacVZh2cXT55ZdP9yMdPPDAA/jud7+L1atXY/v27bj55ptx6qmnOn83TRMXX3wxfv7zn2NsbAyvf/3r8ZOf/AQrVqxw3jMyMoJPfepTuPXWWxGJRHD66afjiiuuQEdHR914a2hoaNQPOuaoMdButdmEaRdHH/3oR6f7kQ6y2SwOOuggfPzjH8dpp51W9ffvfOc7uPLKK3H99ddj+fLl+PKXv4yTTz4Zzz33HFpaWgAAH/zgB7F9+3bceeedKBaLOOOMM/Af//Ef+PWvf1033hoaGhp1g75brTHQAdmzCnW/+GjdunW49tprsW7dOlxxxRXo7+/H3/72NyxZsgT777+/0rNOOeUUnHLKKYF/M00Tl19+OS666CK8613vAgDccMMNGBgYwC233IL3v//9eP7553H77bfjn//8Jw4//HAAwI9+9CO87W1vw/e+9z0sWLCgtg+roaGh0WhoS0Zjodt7VqCukWX3338/Vq1ahcceewx//OMfMTExAQB46qmncPHFF09rXRs2bMDg4CBOPPFE57Wuri4cddRReOSRRwAAjzzyCLq7ux1hBAAnnngiIpEIHnvsscDn5vN5pNNpz4+GhobGjIGOOWoMnPbV4mg2oK7i6IILLsDXv/513HnnnUgk3Asojz/+eDz66KPTWtfg4CAAYGBgwPP6wMCA87fBwUH09/d7/h6LxdDb2+u8x4/LLrsMXV1dzs/ixYunlbeGhoZGbdAxRw0BaV99Wm1WoK7f8tq1a/Hud7+76vX+/n4MDw/Xs+ppw4UXXojx8XHnZ/Pmzc2mpKGhoeFCW44aBB2QPZtQV3HU3d2N7du3V73+5JNPYuHChdNa17x58wAAQ0NDnteHhoacv82bNw87duzw/L1UKmFkZMR5jx/JZBKdnZ2eHw0NDY0ZAx2Q3RjogOxZhbqKo/e///34whe+gMHBQRiGgUqlgoceegif+9zn8JGPfGRa61q+fDnmzZuHu+++23ktnU7jsccewzHHHAMAOOaYYzA2NobVq1c777nnnntQqVRw1FFHTSsfDQ0NjYbAcfNot1p9oS1Hswl1Pa32zW9+E2eddRYWL16McrmM/fbbD+VyGR/4wAdw0UUXKT9vYmICr7zyivP7hg0bsGbNGvT29mLJkiU455xz8PWvfx0rVqxwjvIvWLDAyYW077774q1vfSs++clP4uqrr0axWMTZZ5+N97///fqkmoaGxm4KbTlqCLTlaFahruIokUjg5z//Ob7yla9g7dq1mJiYwCGHHOJJyqiCJ554Ascdd5zz+3nnnQfAyq103XXX4fOf/zyy2Sz+4z/+A2NjY3jDG96A22+/3clxBAA33ngjzj77bJxwwglOEsgrr7yytg+qoaGh0Sw4MUfaclRX6OtDZhXqKo7uvfdeHHfccVi8eHHVKa+f/vSn+M///E+l5x177LEwOROAYRi49NJLcemllzLf09vbqxM+amhovHagA7IbBO1Wm02oqwR+61vfivPPPx/FYtF5bXh4GP/n//wfXHDBBfWsWkNDQ2N2QF882xhot9qsQl3F0b333oubb74ZRxxxBJ577jn85S9/wQEHHIB0Oo01a9bUs2oNDQ2N2QF9Wq1B0Jaj2YS6iqPXve51WLNmDQ444AAceuihePe7341zzz0X9913H5YuXVrPqjU0NDRmCXQSyIZAW45mFeoeWfbSSy/hiSeewKJFixCLxfDiiy9icnKy3tVqaGhozA7ogOwGgViOmstCozGoqzj61re+hWOOOQZvectb8Mwzz+Dxxx/Hk08+iQMPPNC570xDQ0NDowbomKPGQJ9Wm1Wo67d8xRVX4JZbbsGPfvQjtLS04IADDsDjjz+O0047Dccee2w9q9bQ0NCYHdCn1RoDR3tq09FsQF2P8q9duxZ9fX2e1+LxOL773e/iHe94Rz2r1tDQ0Jgl0DFHjYEOyJ5NqKvlyC+MaLz5zW+uZ9UaGhoaswPactQY6IDsWYVptxyddtppuO6669DZ2YnTTjuN+94//vGP0129hoaGxuyCjjlqELTlaDZh2sVRV1cXDLvzdHZ2Ov/X0NDQ0KgDtOWoMXDaV69pswHTLo6uvfZa5//XXXfddD9eQ0NDQ8MDHXPUEJD21afVZgXq8i1XKhV8+9vfxutf/3occcQRuOCCCzA1NVWPqjQ0NDRmN7TlqEHQbrXZhLqIo2984xv44he/iI6ODixcuBBXXHEFzjrrrHpUpaGhoTG74azV2nJUV+iA7FmFuoijG264AT/+8Y/x97//HbfccgtuvfVW3HjjjahU9M5GQ0NDY1qhLUcNgrYczSbURRxt2rQJb3vb25zfTzzxRBiGgW3bttWjOg0NDY1ZDB1z1BBoy9GsQl3EUalUQktLi+e1eDyOYrFYj+o0NDQ0Zi/03WqNgb4+ZFahLhmyTdPExz72MSSTSee1XC6H//qv/0J7e7vzms5zpKGhoVEjiJtHu9XqDO1Wm02oizj66Ec/WvXahz70oXpUpaGhoTG74VgytOWortCWuVmFuogjOteRhoaGhkYdoQOyGwRtOZpN0M5TDQ0Njd0aOiC7IdAB2bMKWhxpaGho7M7QlqPGQluOZgW0ONLQ0NDYnaEvnm0M9Gm1WQX9LWtoaGjsztCWo8ZAu9VmFbQ40tDQ0HgtQMcc1Rk6IHs2QYsjDQ0Njd0Z2nLUGGjL0axCXY7ya2hoaGg0CMSSsfo64Lk/NZXKaxrZnda/2nI0K6DFkYaGhsbujL59rH8LE9aPRn0xZ69mM9BoALQ40tDQ0NidccgHgcVHAvl0s5m89tE+F+he0mwWGg2AFkcaGhoauzv6VjSbgYbGawo6IFtDQ0NDQ0NDg4K2HCnCtE8spNPahK2hoaGhobG7gKzbpkTaCy2OFJHJZAAAixcvbjITDQ0NDQ0NDVVkMhl0dXVx32OYMhJKw0GlUsG2bduQSqVg6COdGhoaGhoauwVM00Qmk8GCBQsQifCjirQ40tDQ0NDQ0NCgoAOyNTQ0NDQ0NDQoaHGkoaGhoaGhoUFBiyMNDQ0NDQ0NDQpaHGloaGhoaGhoUNDiSENDQ0NDQ0ODghZHGhoaGhoaGhoUtDjS0NDQ0NDQ0KCgxZGGhoaGhoaGBgUtjjQ0NDQ0NDQ0KGhxpKGhoaGhoaFBQYsjDQ0NDQ0NDQ0KWhxpaGhoaGhoaFDQ4khDQ0NDQ0NDg4IWRxoaGhoaGhoaFLQ40tDQ0NDQ0NCgoMWRhoaGhoaGhgYFLY40NDQ0NDQ0NChocaShoaGhoaGhQSHWbAK7GyqVCrZt24ZUKgXDMJpNR0NDQ0NDQ0MCpmkik8lgwYIFiET4tiEtjhSxbds2LF68uNk0NDQ0NDQ0NEJg8+bNWLRoEfc9s04cPfDAA/jud7+L1atXY/v27bj55ptx6qmnSpdPpVIArMbt7OysE0sNDQ0NDQ2N6UQ6ncbixYuddZyHWSeOstksDjroIHz84x/HaaedplyeuNI6Ozu1ONLQ0NDQ0NjNIBMSM+sCsk855RR8/etfx7vf/e5mUxFislBCsVwJVTZfKiNXLIeue/v4FMYmC6HLZ/MllCtmqLK5Yhn5UnjuW8emMD5VDF1+Il9CJST3qUIZhVK47wwANo9MYiJfCl0+nSvCNMNzD9vfAODV4SymCuG+N9M0kc6F/84mCyWUauC+budE6D5XK/dsvjbuLw9lQn9vpmkiUwP3iRrGuWmaeHEwE3qsVSq1cw9bN+EedqxVKmZN4zyTK4bmXq6YeGkoPPfyNHAPW3cjMevEkSry+TzS6bTnpxG46Z+bsP/Ff8f5v3tKuaxpmvj3nz2KAy+5A/e/tFO5/LqdEzj+e/fjHT96EJMF9UHwi3+sx/4X/x1f/fOzymVL5QpOveohHHzJnXji1RHl8s9sHcdx370P//aTh0OJlMvvegkHXPx3fO+OF5XL5oplnHLFAzjsa3fi2W3jyuUfW78Lx37vPnzw54+GWnC+fttzOPCrd+Dq+9crlx2fKuL479+HI79xF9bvnFAuf88LQzju+/fh/97wz1AT3wV/WIsDv3oH/ufRjcpld2RyeOO378XrvnUPto1NKZf/81PbcML378en//dJ5bKmaeKsX/8LB371DvxpzVbl8ptHJnH0ZXfj2O/dh10TeeXyv35sE97ywwdw4R/XKpctV0x89Np/4sBL7sDdzw8pl39pKIMjvn4XTr78gVAi5WcPrMfJlz+Ar/3lOeWyhVIF7/3pIzj40jvxyLpdyuXXbB7DoZfeiXde9WCoTeT373gJJ1/+AH5418vKZacKZbzjRw/i0K/diae3jCmXf/iVYRx86Z14/88eDSWKL731WZz0wwdwzYMblMuOTxXxlh/ejyO/cRdeHsool7/j2UGs+uodOOO6f4YWd42CFkcCXHbZZejq6nJ+GhWM/e3bX4RpAres2aY8aa7dOo5/bRpDoVTBL/6hvlDe8PCrmCqWsWV0Crc9tV2prGma+PpfngcA/OrRjcgq7jAe2zCCFwYzmCqWcd3DryqVBYBrHtyAQrmCl3dMKE/4pXIFl9uT3Y/vW6csru57cQde3TWJTL6EGx/bpFQWAK6+fx3KFRNPbRlXnvCz+RJ+YU92P3tgnfLE8/dnB7F9PIfRySJuemKzUlkAuPLuV2CawEOv7MLTW9SE4fBE3qnzlw+pT9i3PrUdu7IF7MjkcfOT6gLl+7YQ/vuzQ8rCcOOuSfx17SAAhOqvf/jXFmRyJWwZncJf1qqNNQD4hi0sfr96C3akc0pln9uWxgMv7YRpAjc8oi5Kb/rnZkwVy3hlxwTuUhxrpmnisr+9AAC49qFXlS0RT7w6gic2jqJcMXHjY+rcf/3YRhTKFTyzNY0HXx5WKlsoVfD/7n0FAHDl3S8rC5T7X9qJ57anUShV8L+Pq4+1Xz26EeWKicdfHcG/No4qlR2fKuJ6+7v++l+eV97I3PHsINbvzGKyUMbvV29RKgu4/ey+F3fihUF1cdVIaHEkwIUXXojx8XHnZ/Nm9c6sip2ZPEayrktrteIAeHyDa3F5ctOYshXi6a3u4rZ2q9pCt2E4632W4kL5GMX9nyEsR2tr4P7sNq9V8CXFnRHNnf4OZPHcdrd+Ve5Pbhpz/j86WcSWUTULyuM1cK9UTM8uUpX7P6n61u/MYjSr5s59fIMrJB9T5J6zNwEEqtzptnpq85iya44ur8p9NFtAlnJjPqNorXyMard/vjqivFDW0mf8/fP57WoW+VrHmoe74jzz8g7vvLBOUVB7v3N1q1ct7e5v523jaoKaru/REPMEPac/HuKzNxJaHAmQTCad4OtGBWH7zZXrfYJDhHU73fdP5EvYPi6/UJYrJl7Y7tav6h56acg7UawfVps46J37UDqP8Ul5c32uWPaU94sdEfxiSLXd11Ptvn7nhNKOctdEHkNp10Ko3u6+CbuGdn95aEJpodw0MulZpNXbvdY+47a7qqn/5aEJz+ahlj5TMS1Lkgpq4e5f6J7dqsb9ZardJwtlDCpYnkzT9PQZ/3cogr+dn1UUpbRA2ZHJK7n18qUyNlPiTHUT9FwVd8V2p7hv2jWpNE+MTRawi9o8vLRDrd2ruSvOM1R963eqzRNbx6aQp6zxqtwbDS2OZiA2jXgn2HWKnci/k/E/j4edmTymKB+8SlnAiqHwcNkRXtgBwOZR+fo3j0yCNpLVzj18u1dMKMW/vOpbVFW519JnTNOsEtSjCqL01V3e72zTiNp3Xs1dvnypXPHUP5jOKcWQ+Llv3FUrd/l2n8iXPIJk08ik0mLj7zMba+4z8p99KJ33CGLV/upv51q5r98pz33TrkmPIFbnPn3tXqqYVfMOD/75sdZ2r2WOzORKGJ6Qt/L61yWVz90MzDpxNDExgTVr1mDNmjUAgA0bNmDNmjXYtEk9RqReIB22qzUOQE0gAMAWu3xni5WpQaUTbrUX9I6kVXZ4oqC02Ew3d5XB6+e+dWxK2QIChONeKlccMRSG+zYfd9XA4s0+7iputUy+5JzuC8fdWuBd7mqmej93lXYfyuRRLJuIRw20xqMwTbcfyKC63dW419Jnttjv7UjGEDGAXLGCnQrxhbX2mVq4k/eS/rIzk1c6qVgz913Tx33LyJRSjF4t3MsVE1vtsUm4q4y1LaPh53YA2OobqypjZSJfcsI9wnAn1rowc0wzMOvE0RNPPIFDDjkEhxxyCADgvPPOwyGHHIKvfOUrTWbmgnTYw5f2AAB2pOUnzErFxI6M9f4jlvUCUFsoiQtu3/kptCWi9mvyC0Y1d/my2XwJGTsw0+UuP4AIz0OWdMMwrMDJXQrxK7W0+65sARUTiEYMHLLEKh+m3Q+z61YVpX7uQwrtTr6jzpYY9h6wkqOptbuX+zZFUVoLd/Le/lQLlvS2AVBtd6s84a7iggaCuMv3GfLeRT2tmNfZAkCN+zZfu6uM03LFdKxWtbT7ynmdSDkLrYKgrmp3+bozuSLSOWueqKXdD1nSg2jEQKGsKEqr2l3+OxtK51CqWGL+wEVdANTmGdLuZH4cyRaUThT7x+p2hc0AEXXdbXHsObcdgNr8vsPHfduYmihtNGadODr22GNhmmbVz3XXXddsag522uJmlT14VCatkckCShUThgHsv8CKjxoOsRtd0N2K+V0tntdkUM1dvm4i6toTUexhDz4Vsy3huXROG+Z2JD2vyaCWdifvnduRdNptOKPS7lb5fed3ojWuLkpr426VHehswUCnOnciEA5d0gPDAPIKotQ0zdr6jP05BzqT6O9MhuZ+eAhRmiuWkbEX6Vr6zEBnC/pDtPs2H3cVUTqSLaBcMRGh5okwAqOfavedGfWxSnOXBekvqWQMy/rUF2nS7gu6WzGnPeF5pgzIWHW5q49Tep4IM1b37O9w5onhWtpdQdgR7v2ppDNPhOnv+y+0xkqxbNaUj67emHXiaHcA6YQHLLA6UbZQlg44HLQX1L6OJOZ3t3qep1J3fyqJ/pQ9YSuIK2ehswfAzom89Gk5wn2gqwVzU2TCDcO9xZmwdymIKz93lQDVQO4h2o1e5GVTOBTLFYzYCTsJd5WFjnCfVyP3hT2t6GmzFhvZdk9PlVCwA1JJf1eZcKeL+97zUohHray5I5LCjpRNxiLYq78DgOJiQbh31sb9AFuY5UsV6SPxpGxvexIL7HkizEI3XdyJWFMpOzeVdCxuKmN1iBLU08E9zPxIcx/KKPR3SlC73OXKF8sVJ5aQcFeaH+165tLiSGF+HqQspT1tcfuZ6rm9GgUtjmYgSIdZMqfNMVnLLna0uOnrUBcYZLD0dSTR0251YNmj1ZWK6UwU+8xLIWJY5nvZRX5HhrhIwnEfprnbi7TsQpfNl5wA0/3tRTqTK0nHUeyosd1Ju/V1JNGtyH0kW4Bpu/T2mZey+eSkrQg7qAm7r0N9J+32mQS67UlPWmBMuC69Rb3qi/QOShDPDdPfs+HbfSf1nbk7aXVLaX9nyLFq81zU3YqWuDWVj2blNlEu94QjxsO4YsNwN03TaeO95lqismICaUkrAt3u4bi7fUaV+2Sh5BxYIdwzOfmbDGjuc0P0mZ1pep5RG6tkHo9GDCyfY1ncZPs6Xc/c0O1e2/zeaGhxNMNQKFUwZqv7uR1J9Nhm3/EpuU48alsQetsToawvw1m3PBEYsieXxqaKKNm7v/5UixO0NyY56ZHPHZY7Wei83OXajYiT1ngUA51JxCKGzV2uPLlqpbctLHer/Jz2BHptgTEm2e6knjntCcxpt+oulk3PaaL6cif1J9Frt7vs1TO0MCNlx6fkr0YgfbMnLPcJut0Jd7V2n5tyxbjKlTukb4bhXixXPOOlV7G/B3OXd3HU0u7pqZI7T3QmnQ1g47iTOS6uzJ30l2QsggXdrSBXdIXpM05/D8Vdvd3J5rGnLYFeW1hNFeWvmSL19HWE417r/N5oaHE0w0A6fzRioKs17pgfZQcfeV93W8LZWQwr7A52UTsbVYExYi+SXa1xJGIR5YnLy912LWXDWTBIu8lyd8RJRwKGYThWBGXu7XGKu3q7z6GtXsrck2hNRJGMRWxOssLOXujaE8rcTdN0BUZHwrW+SPcZl3uX/Z1VTDiB+SKQTUOPp93lrQCTtoCcQ1u9FLnT/S2dk79rjMRb9LTHMbdDzR1JrAARwxov6u1ePc5V4j/IhqeHHquSFuJhu+5USwzJWBTd7WpjdYQaq7Vw98wzku2+y/nOk84cHZ472TzKzxMud7e/75Tm7loLU8mYswFUnyNdK6vsxtd6ryvOCHcVl2SjocXRDANZqLpa44hEDHSpWm/sjt7dGncGbqFUkd4d0AsdsVrJ1+0OXADOYic7+EYDuI9PyV9S6BEYitzHfdy7lbnb5VsTHu4yKFGxAN52V7Nadbd6ucsKO1JPl6/dZUBbAXrbE+htDynmW+NIxqLOCUlZYUfcSGG4k76eiEXQkYyht13N+uOOVfc7V6nf7e8JdCpyJ1aA3vYEohGjBu5xp79M5EvSV+Y4fa4tfLuTBdKxekm6BOk+ozpOPeVDcSdzjMXZ5a46VhPU/ChXt2maVLu7fU7WHUnP7fQGULbd6TlStd1zxTJyRatvdYVo92ZAi6MZBtJZnIWOuKZkJz1qZ9GRjCFq7w5kOyHZefa0UdYXyYHP4i5reh2fqh58xbLpSUrJQr5UdtxIvW2UW02ZeyIkd3exINxlhR29++qmrIWy3NNUu1nPULR6BbS7an9pT0TREo8qx3qNV3FXFFeUFaBLkbvjomjzLhZhuMeiEcc9pCxQ2uJO3arcSXu7sV7qYy3VEnfcQ7L1jwUslNJ9Jku4EzGvZvUi9XRR33muKLcBrFRcgdHTlqiBu7fdZUWCy536zifl5onJQhnFsmnXX0u7J5xnhOFOi1LZ+ZH0l2jEQCoZU+beDGhxNMNABi7ZSaq61UYp15RhuGZfmfK5YtnZOXa1xUNYMIo+7mrlR6ldUWs86pwekuGenrLcMIZhmevDWl+6Wr0Ttuyuzo3BcHdF5YopdXqIiJtUMoZYNBLaYtflsxypfvaeNq8FQybuh3Andau2+/iUn7ti+Ul3oVXp64DbZ0g5VasXEcQOd8c9pLYT72lTtzb6213ZckSVp91DMuXLFRPpHCVKVbnnpo97itoAynxvE4WSk0Xfa22U3Ijk/H1GPS6TlCdze6Fccdy7MmUT0Qha41Gl78ziHjxWZTcDXu6uW01uA+hat1XXpWZBi6MZBv9i0eV0wnAuFpWJi0y4EQPoSMRCW19c7uECsv0DSIb7OCUwIhGDsr7ILnTWpNfpExiq7d7VmkBLPIqEHfejwr1KVIZs9+6Q7U4vFqZk3E81d0VrI0PYSVswKIsf6fMZybgff7uFtXo53FvlD08UyxWnfbtb466lUvJzs0SlLHe/uHIsdhL1Z3JFmJTAcD93OGEX1urVZc8TLnfxZyf9rSUeQUs82vB2p8u3xqNIRO34QIn6nTmmjcyPau1e3d/VxBVt9aI3gDLzBG0lpTloy5GGNKonXNXdrNdN0dkqPwDIziLVYsU79SpaT8YYi4U694SPu4Swy9VmtRrzWwFqcAnSz5Hj7hVm6ty9n91ZrCTKm6bpcaslY1HnWLjMZ2e3u2yf8Vvs5NstXyo7O+6utrjDAZCLw3C5x3zc1eN2VLnTi0InJUon8nLHwv3trnrC0c/d2YRJlCffbUcyhng0EsJi5+euZjka91l5uxQ+u98dqTLHeLlbfUbV6kVvBgzDoLiLyzsHJ0IKjLRvA9jrWI7E5U3T9HBviavNE2O+dtfiSEMZVTEYIYNr/TEcKhYMv5tA9rhnVeyL4s5kOrnT7h0Zsy+r3WUWSitQ0ldeIVjS5W4v0qruGSZ3cfkpypVKRKmKJcC9k61Gt5ozacqXJ5NyxLAshvFoBO12QHc47uHjRyzu8u3uuKBbLLeQqrDz34Wn6iJhxXrJfHa/C5r8S/clOe5knpmuODV5geHnrmr1crgrWL1M0+Rwl+8zZHy63GVPdvq5y4+1XLHiJGv1b37l+ozrFaCfIRtM3gxocTTDwDL1y7t3vNYXNbca2VlYE67qcU+me0di4Fcq1ROHygDyT1pkNyqb76fa1C+/k57Iuye2wuyMWNzHJgtScT8sU7/KhBuPGo6wCNNn/P1V3iXoL6+wWFCWxojdT1UCm/0WDJd7WDeFvMXOTUFglYlGDKRsoVNTu4eM9SLtLmUFsMsSMZlqiSkFdFfF7Sj0V3qeqJojlfqMd47KS57orYqXUrB6TRbKzjwRjrvrVqO5j0/JbQBZ3FXm9mjEcC6tVZnfHa+CLwhfJRVAo6HF0QxDtbmbxHCIO1GpXHHuegoVc+QbPKoneNhBzXIuPTqOgf5XRhj6J1w634/MQl2Li4S8Jxmz4hi83NXbnbRbxXT/xgMrbkdmwnaP8VsB/F7u8q5Y1zVlC9pcCSUJ95DfRaLEPeuNr7N4qLd7WHcmq91lLEdkPNPcw/SZMNwrVEB1Z4ixSh9HB4BIxHCEvUy8lRun5u0zMqfV/AHVAJSOxPvdO6onev0xdion7cj3Go8azr1oKulOWG412RO9fpegSjZ72v1N5gkV67rfnRkmVUujocXRDAMr5khl4HrKKwS4+s2ugDuQiOiS4+47Di8VbGi9py0RRTIWtbmHsQLEKO5koZb/7G4aAnmLnd+lBkDpWLl/wk3EIo4/X6Xd/WkIZBZZf36nsNxJf6PdQzIn9djtrr4btXjIW1/8VivCfbJQFgo7OhDVvxFR456guIfvMyrjNJMrcTYi8mPV2+7qllJ/u8vcHzkesBGpZawahuG4JsNY7JTmRyovliMwlOZI9zQvYM2VMQVhx253Fe7ud67kfme41coV+Uz+jYYWRzMMLJOxTKAmmdhSLdaRcPo5YQaP9SyFATQN5u4earFQSYwXzF1d2FWdVlMwd/eEXOj8E67FXV3YVbvV5HezPTUudERQx6Pywq5YrjgTY6ig5snqPqMyYbvcbTdyiyusRcKOdvX6rTdysS/eXD+A+9nDuJFJf5ERdqRtWuPuRkTJrTZZ3Wdq2YSFGaf0WAnDvZvuMwqbMD/3Tmd+VBmnbj/rUQjoDhJ2YQ4BVLe7+hxjcVe3rpP4spZ4xDnRq3LlTiOhxdEMA28nLpo0gy0/IQYP7aaoYQCpBGqOU8KOQOUUTNBnVxF2/pN2oXbxVN1Kp9V8i7TFXW7ByJfKjkm9mruCKAzgLrPYBE2assLOf2KLfk6YoGQvd/UYORVhR/pLeyKKuG8jEkbc0OVV+jspQ+JAALGw858QBEJaOsP2d59LL4ywm07uYU7FdjncVYRdQLvXOM/IbiBLARsR8hwZC69/flSp28vdai/VVC3NgBZHMwz+EzDRiOufzub55ses3cmDBEZYCwaZdEUDiD6JQbi3J6NV3OrGPeetG4CTsXgizy/vT34JuJ87X6oILXaEe0cAd5Uj5YHcBZMuaRuS/JLmLmpzEXeV4FpaUKtypxP5tUv2N/o9Hu4KC6V/kQaAjqScoA5apNW4l6u5h2p3q3wiFnFi7EJxT8hzD+ozYRbKIGEnmuPqwV223YtUskbS7oT7ZKEszK0VzF1ubgeAbCH8HJmm+oR/npARdkGW+Y6EwjxTA/dmQYujGQSPwKA7IdmdCBZ5shi1U5NNmJilMBaMqaKb2p5wj1E7cdHENX3c1d1qpCxJfunnIRr8mSDuCkkkuVYvwXdOZ9cmJ7ZIf5kqinfiXO51tnoFWSpJWRVxRHMPZ7FTt5TWzt0q3+HhLu+GrsVSyptjlERpwFgVcc+X3Du2CHda2MlaG2vn7m7cZFMB0PNQyufOBOQ3A17uZJxLcCdjNREwRwrandTdnog6IRekv4a12LnrUn25NwtaHM0g5IoVZ/dBDzrZnXjQpKUycQTtpGVdJIRbxHB3QxYXuQm7Zu6BcTtyizT5ewclMFR24mTX5+GeJCZr9TQCYbjT/cVrsZO0Nnq42zvCgsKOsk1d2E043KvrltmJB3EnzxJxN03T7TNt6u1OuNPipENynFrcq/uMw13Q34MsnRYXOWEX1O4p0l8luPPGqoi7/5ofp35JYRfMXb7dXe7Vi7xorNAbkWjAPCE7R6YC+4xYIARZSjskXWOBlh/qOaLPnuGMVaV2bwk3vzcDWhzNIJDFxDCAtjglMCQ7UdCkpTLpBe2GZQdAhtrFk5MYgPxuOnDCVRh8/uPBVnk1YUZPWmrciRWAFoXykx6v3eW5u587GXOvLxEKlADri2zdtKUzjEgI4k5PnqJ2z9TAnU5q1xliwna+84CyWQlhx+Muu9AZlKVTjXttC1VQn0lJcif9hd6IAPJjLTNt3N2xKut+DxqntXIPYykNnCMl253mTs8TQmHXRO7NghZHMwhEvbcnvBOHbCfKBnRAMglMFSUmbGc3rO4iCarby50/+ILKq8TOkN1yKtCtJlc3PWF6uYsWG2IFqBYIoh2ZaZqBuzLZnXQ2YKEC5Bcr3qQltmBUnKR2qYA+k5YURzT3ZMy9bypcf5fjTvqEYQRvJoTWFzJWA9oNEFuueNyF4ijA0gkoWL0EwkyUeDTIYifLnbRrJ2MjIj9Ww22iXO5BsWLq1hPrd7WxGnYDGGyhJjFLshZmL/fOGub3DsmNd7liOrFaYef3ZkCLoxmEiVx1B6R/D7WTVtiJB5mcZY+qirkLJh4Od5mdeKDVLIRbzcNdcSdOiyvZsvmSKzCCufPbXcRdNPHU4s6krVJ0LIGqiyQ094DysqLQ2cUngi2dQmEXUHcyFkE8aoTmLi/Gq8WJ9bvaWA1yRwLApCChYFB8oCp3/3eu6s5MBfXXQkmYUNDlHmDlrZm7pPUlgLsobqdSMRmiVi5mKSjGzeIu55arZZ6gNwqBVl4tjlwUi0WccMIJePnll5tR/YwFWWyYFgxZde9zsZAJuxZzu1BgMCwY7Yrcg3zaAH8nni+5weBBZl/ZSauKeyI8d/IdZgv8nTj9nXgFRm0WO/Is6fIe7rKWSnc36LF0KloBqrjbbScdpxbEPcTn9nKXm/BpV6phGNL1B461aeIuEnaEe7tP2JE4mqZwT0qO1QDupKxpwrFQBME0Tad8MHd115KXu9wmLIh7Ns8XdrRgDZpnxN8ZOR3ptdhJt3ugMIt6/sYC+c7jUcOJz6KfJWM1awaaIo7i8TiefvrpZlQ9o5FldWBZC0bArgqQM18WShUnyLMjYJGWHQDVJmdSXt3ylIxFnAywPO606yrIglE7d1krAB1Eb/3fNPk7ccdNkIiGisFg7WalrT8C6wtvwma5Iztr5Z6s/26WJYjdPiNrsWMsNk3hHv47Nwz3zizeZzdN14IRaL2RdEGz2l3YbgHcW+NRkKHDq3+yUHYyg6dCBGQzXdiS1h+eW61ignsFCPncsYhXYMgG8bt1e8dqTRY7apzy5gn6Owuy0mq3mg8f+tCHcM011zSr+hkJMimxxI14Jx088cjshukO6glWlHWRiGKOQsRBGIbhTrqc8uRvrfGos/u1uMu223Rxd9utJe7uxHmDP2g3aXFXi33x72ZlT/AEWRHIs0Q7cTZ3xXYPy10Q5CkzYfu5y8ZgiKwIPO6maTK4y+3EWe5I2T4jtt6w688VK87dZnTbyVobiXUm7CIdtJGhhZ3MHBcx4KQYoblLC7NE2LFa/b21JaLOpb3cOY6aH2mBIc3d2YTVKOwCvArliumkZxBxp6GSF6wZiInfUh+USiX88pe/xF133YXDDjsM7e3tnr//4Ac/aBKz5sEVNz63muruwDfptUsk6yIdtCUecfJgAO5Alj3NwBJmopijbIC5m3AfmyxyB1Ct5m4xdzmB4Z+w2xNRpHMlZHIlDHQyytbMnbhiQ3K3vxeaO9mJV0yLn//Zfu7VYj78YkFzl46XCnCRVExrIW9NRAPLOt9ZyI2IaCfO4+6JM/NwjztlTdP0LIJB3KvEkWJ/Z8XO8CwonhO1ieoTX8I5KiAw18s93DyTaokjnStx+3uG+tx028oGBge55Ojy0ik/AoRdJldCJl9CP6tuwQYuzFixysuN1aCwiba4JexM0+oXrLEm3HxqceTFM888g0MPPRQA8NJLL3n+xpoUXusIcs8AYU4eBU/YvPKsCZd2kfAmbHFAdriA7lq4S+/omO5ISfcOx/ojmrDZ3MObu+nnheFOYmdEE3aQ1SkMd1af4e1m6Tgzz4SdkJ2wgzcijltNmru6W43+TuiUHYRLqWIiX6o4F6uyyjPdamEPIEiMVWeBTwRbMGp2Z9bKXcJyFHaRZrnVOqXbnREUbY+1RnBnzq+Slk56nolEDHQkYsjkLe79qfpwbxaaJo7uvffeZlU9Y8HajcpbAYInbJmJi7fAA9Ziky2Uqzp4dd3q4sb6e/COUuZodtAJFEBe2IliCcIk36T5SLnVQpvq+a5UHvd8qezk+gmauDK5khT30MJOZLGTcKUC3rYzDHfCzubLAGPCZm5EnKBmWQuGf6yKF3laFNJxZvTnmMiX2OJI6FaTs3SGcb87dTOCwYtlE/lS2bnQllW+6qSdciA8y1LK/t5E3MPGdMqMVdM0mVazjpYYMM6vPyPgHuZ0JCDnRp4qlgNdqaT+TF5gsRNyFyfKbQaafpT/lVdewd///ndMTU0BgPAo5msZYtOnYGfCmrAldlWsBZ6OneEN/qAEZ/TzZN1DTCtCCO6ES8V0zflhuPMGfrFcQb7EFhgi7kGmdsArKrmxMwHJCAE5a6M3kF29z4gEsbRbjcldbMFoS3jjzOjnyXEP3oiESb5pPU9iI8IYp5GIUVO7d8gKu9x0cPdtBGhhJ8E9jDAzTZMtcBzunKBmVt0290KpgnyJVz58TCd9+0GYeYbZbtMUOsAbq6TN/a7URnFvFpomjnbt2oUTTjgBe++9N972trdh+/btAIBPfOIT+OxnP9ssWk0FK8C1XfHIZIqxG5ZZKP1108GOMtYbluWHV3epXHEC+sKcumItFvQpllq481wk3kB2dauXyOQsOsXixAzVwL01HvXEmQFq7V496dmxM4Wy1Gk3Fnd+/EiwmKbL87KDM9075DuTTOJY/dnFY5Ul5q3nyZRnLNLS3Pnlw2yiohHDWTjDiCuZRZaVE8zLXfydsyy8AN+KUUuyWJYr1XqefLuz3OeiC7KZFjeJa47odvNb36eDuyjkollomjg699xzEY/HsWnTJrS1tTmvv+9978Ptt9/eLFpNBWuxSFGBmizQWUj9g1cuIJu92EhZQARBotJH8Rm7Oplg8iBh114DdxlRSJ5rJQD0DicZUcqy9oU5xRKWe1DAtcyEz7K4kc8S9hSLjBUgKFuwvzxvoWNZrejJnifsMoyFViZOjSWI6df4C22wtVBG3IhcqQCcwOP6cK/dagVUu6FVLBh+7vQF2TLzTC3c/a5U+nlhrI2yF2SzLG6uGFcXlfLc+WI8V6wIL75tBpomju644w58+9vfxqJFizyvr1ixAhs3bmwSq+aC6VaTcRNQExozsZ1EBw692LACJWXiR2zuiVjEuetHjTtn8NZg9ZKJOQo6qeZwV5qwvdY+EjsjKi86eVQr9zBWL3/sjCp3t8/wJuxggUA/j++W49dNgqKD4MkJFqa/M8a5h7uMK5Z5qlUsKsNyZ4lCee72Iu8XNxKxM6ycYHR53jzB5y4OXaiFOysukuYjN1a880Q8KndBtiNQGEf5pTYStYp5hoVYVH+z0DRxlM1mPRYjgpGRESSTySYwaj5YuSjoHR0r2zIZfFYW0mCzr9zgDRgAMsGOIr9yCHFCPy+MuPFyr4+pn9duKoHw/oVOmjvz9I7YgsGbsGXcchPUYkXDEzvDKM9zpcrES7Eme/p5UvEnvvIywo7nSpXjHlw3QC20HOtNRjBPFMrs2BlWTjC6fBhXqjL3EPOElKUzRLwTQImEGriHdaWqCLOgeUKGOzumU2WeYLe7VFylrzy9GeZZK5uFpomjN77xjbjhhhuc3w3DQKVSwXe+8x0cd9xxzaLVVDADVOmkfIz4Eylzt5Rrib1Qyiw2VSZnicBiGcuPDPfQAkXAnRusWKvVqgbu5YrpxCOFuQZDZkfIdzMEZ3S3uPNP6nFdqTWcmqKfF8Z6Q8fOsLiTsi3xaleqykm7QO4S176w85mJY2d4VisZayMrmFuVO8s1RVvlWGV53GU2UYHcJa7hEHEPLY4UuIfp756NCNOtFtLCLMGddVoNkFubmoVqtg3Cd77zHZxwwgl44oknUCgU8PnPfx7PPvssRkZG8NBDDzWLVlPBEjjkGo1SxTqtETTAWLsa+rUwZluAFiji00PVO2nqGo1COZAfy3Lj5S4+RRJGGHpjtdhWAFYqACnuIU4eyXD3xGDUECRaq4sk0OqVjGEIeeZCSYKlA12pNcSPAHILpajdJwtlJneZdpMJhA+7UPJiZ1rjUUwVy5jIldDbnlDkLr7CgxX74uUuduuxDi9Y7ykhEVPlrmBtDFGeN0/4Y2f8hxsAgbBTsTaG4E6f1K3K65WUTz0RZOmUOxXL5z6SLQgPGzUDTbMcHXDAAXjppZfwhje8Ae9617uQzWZx2mmn4cknn8See+7ZLFpNBctF4rnQUmDqD+1a4rpYyCWqwZMefWO0v/6WeER4YowViO7lzjtqKg4mZ5mcPbFajAmbZFsOz11iRxiGu/3cRDTCdaWyLHZyfUYmzqxaUIssT6xTdjJlAX78iNSJL5l2DzHWZNzAUnE7Nbqhw8wTMnm5eJsoUawXb56gY2dY3Pmn/GQspeJ5gi0wxPMEwBaG/P5am5VX9J1PcOYJ8p1PFctOqoHq8sHWaU/dIU6ryXBvJppmOQKArq4ufOlLX2omhRkDz43RjME7PsW+RoM3Yaqoe96OUmbi8JteSSqAdI6dbZknzFTy9YTZVXljtbx7BZlsy7We+JLbEaq7SPyBxUEJBeW4y8SZcawIDGHHDaiWSN7J342KYzi47S7gzrPSyqXNCN9nrGSCfKvZ8ERegjs7dkVunuAEFjPanQ4JYHHPTxQ4faa2DaDMCUcWd/K5/Re/Aq71s1CqYKJQQldbtXCUidUKc4AAEIcesFIQ0HUDVn/vDHCRc0WlRCA8N9ZLu9UsPP300zjggAMQiUTw9NNPc9974IEHNojVzAB9Y3SYeADeQikV1MxbaAX+eDLpRAMmDou7fY2GkHtQ7IrYVC/z2cUTR3UOD/reI1Z6fFYSR0DOAsK6U06GO0+ceO49ygVnW+aZ+qVcW5xFWhR/IhNQbWVbDhZ2vPiRDoEFhJetWIq7hNVJaicd4jvnZSu2XhONVZ7lR8LFIjPWGGOVdfErXX54oiDBPdwGUMZ6I7K4Bc0T5JkjJTZ3VnbtRnDnbQSSsSjiUQPFshWyESSOahGVYu5ia2Wz0FBxdPDBB2NwcBD9/f04+OCDYRhGoMnfMAyUyzPvaF89MUFNHK0Bi4FoJy9jgah5J80cfO7OgjVx0HWw6ubtRuVMzpyTHIy6eQMXoO49kvjsTO4hXSQi7jy3lufeo3wJc1PVJ0Cddgtx4ouXrZh+TcidE9hLOAaKIxLIHmDNE1kReNmKvdxDHH6wy5ITY0HXaPCEoch6w8tWTHMSlecF18qdUORxD56j6OtmQs0TEv0t7Gk1UZ9hXZVDc+fFzsjMr/XizptjyOujk0X2HMlpdzVrYxB3cZxbs9DQmKMNGzZg7ty5zv/Xr1+PDRs2VP2sX7++7lyuuuoqLFu2DC0tLTjqqKPw+OOP171OHujBEzhxCE7wcGNf7Nd4WVRl4ihYHZgXEK3CPeypKd7EIeLOq5vmzrbecCwQErsqnktQFDvDc3HIcZexWgUvdHS24lBBopx2l7lGw10oA6yNgvxQ9Ov+bMVe7vyNiFDYMbnL5GgSfGeJ2jYivHw7vBNjfFFLrADqotLiJOIe3n1Ocw8UhoJkszzriRx3GSutOL4vTE4y2XYXzZE8FzarbjqQneeVmImWo4aKo6VLl8IwDBSLRVxyySWoVCpYunRp4E89cdNNN+G8887DxRdfjH/961846KCDcPLJJ2PHjh11rZcHntkVEA8+mdNqgPh4chiBItqZ1MKdDKipYpmZRVUmwLVW7mxhyOYusvzwshVbr/FjvURWL9E1GnLc+fFOgCjXUFju4YWhcCftWD+qkwl6uQtivQK4y1yjwVtoa3GR0M8Uj3N2QDWfe3grgIi7KPWFjJU2L5EKgDfPsLkX7bLBGxEhdwlXLCtlSKXiuoHDCEPe/EqXF/WZ4IBqqz3SrI0vFT8WNgFms9CU02rxeBx/+MMfmlE1AOAHP/gBPvnJT+KMM87Afvvth6uvvhptbW345S9/2TROvIELiAcfb9LyJNuqQRyF2Y3Wyt1z71HAablimZ2tWI17uImDZ7Fz4qUKwSdBeBe/WnXLxY+IufN38jxro2iRDLr4leZUK3dxfw1KPcHfzfJirWS4y7gp5LgHiFJZcSPgLo6Xqu5v0YjhuPTDuKGlhVlI7jKiklW/6MCLKC6Tl9PLKi8Yq4LDNoBtjQ3YAPJOytGviWK9WO0utNLyNlGCsUaeGXRSzqpbnISyWWjaUf5TTz0Vt9xyS8PrLRQKWL16NU488UTntUgkghNPPBGPPPJI1fvz+TzS6bTnpx5g3VNFIAp2FE3YvKA/OklYqBNfDnfBxBFiV5WMRZGIsoUdL1uxl7v6iS+6vGjw8+oGgMmAEzjkmS3xSGBuFOGJL46pXYY777SaK+yCs7ILrQDC02q1cecJctFCJc2dJa44C52XO7/PhcmNxXPDAlSfYbWbgDvPcmWaZk15uWRd2GGOw4tSAXgOvHBEqdj1z3JhC6y8EmPNqqf6s5PXgk7KWZxIuwdbnhzuARZei3t4MS9KBcA7KUe/PutPq9FYsWIFLr30Ujz00EM47LDD0N7e7vn7pz/96brUOzw8jHK5jIGBAc/rAwMDeOGFF6ref9lll+GSSy6pCxcasn5h8c6GPQB2ZYNPU3izFXMyZItiKJgDoLYdZUeLHewYUD/v4lcvd4ZrKcefOISilMPdk7wzX0LKJx7dIE+GqBSe+Cp53lfNXeDe4ZyU82dl9/dLoRtYwN1ZLITtri6unMm+EJwKQMyd3268hY5+nWnBkOEucO+wuIvu4+OJecAaw8MTwdzpk3KiFAzB3GUtbqyxSlxb7PL5UnAqAFJ3NGIwT8oB4cIOrNdl3cAMy340gkI5OBUAnfaCF48qdGELN97qm1ePsAtIBSCqWyagu1lomji65ppr0N3djdWrV2P16tWevxmGUTdxpIoLL7wQ5513nvN7Op3G4sWLp72eY/fpx+//65jAkzmA+Lin6xPnL1ZB5Z2LXxmmT/FOmh+sKOYuWmyiGMkyLEeCnbAwdoYjEOjnCoNzA4ShYRjoaIlhjHEShHdlC80ptKgUmKz5FrsIohED5YplLfC/h3dliwx3aVO/wILBs9ixsrKLuQvyeklyD4pfyZfck3IiK22gsHMsR4IgfJEbmLMRYXEXn6gVWIilXaks91BZyJ21AaTjzMIIjOmK9eJxZ20AeacbaU4it1rNIRuMDSAvFYBTd8hNUDPRFHFkmibuu+8+9Pf3o7W1taF19/X1IRqNYmhoyPP60NAQ5s2bV/X+ZDLZkItwe9sT6G3vZf5dnIeDnXEY4A9+semTuEjKqFTMqiBWoQVEMn6FyT0ZBzAl4D79uyL6dfEJnODP3pG0xFGQBUV+sahtNxvmBA7J8TQ+ZXEf6PTXLVikZS0/IRYb69SlyeTeGo8iYliZzSfypar2Fbe73CIfxspL+oFh8E/KVUzLUtPmW1Rq7u+C/trOObVFW52CT8q5ojJI2NV+Wk1QnrcBdFzQwZ9btIGr9cRXLRtAWfc5awPnjnP+/B7EXRSrRW5vYG0ApbnPQLdaU2KOTNPEihUrsGXLlobXnUgkcNhhh+Huu+92XqtUKrj77rtxzDHHNJyPLGqNo+AtNiI3AT0ogkzWIn+8fDJD9UVeljsrdkZ60mO5hwTCkieuxC6OaZqwA7jTJ+XC1F+rqBQvFuw+44kzC9iRiq7bEXPnB5mKc96wxyq9kw46KUeysoflLhvQLRS1HPe76IRh2c7KzuIe+sSX9BwXFLcjuQHMB1+3IztWha5UgbALFBg1fG5AYY4MqFsUq0VzD+yvstwZsYnNRFPEUSQSwYoVK7Br165mVI/zzjsPP//5z3H99dfj+eefx5lnnolsNoszzjijKXxkIBvgKlqseBYM1q6KxM7Q7w2sW+BXrpU7z1wu2pmQ2BlV7jz3EJ0PJsWxHFn1VO/qSN2dEkHJQRM2LzmbiDs9kYoFTlC727EvzCB80t8EsV4C7kGuAtFRfIB/LYGoz5AFlBmcK3LFcqy0or5uGIYbNxSKO1/My7h3WNwznKP0gFeoBtWfEcwzPEEsitXycq/uc6LUEaQsycrO5q4+R9ECQ3QIIEyfEecz449VmfmVFatVb+7NRNNOq33rW9/C+eefj2eeeabhdb/vfe/D9773PXzlK1/BwQcfjDVr1uD222+vCtKeSRAmtpPM18PbVbF2NSR2hn6vp26RFcDhXl03fVIujLldxL0lHnGOmofblZFLdwUWDJHJmmNFEE0cxMVSVV4UO8PZlZH+0hoPPopP1x8sqAVxZo4gLgcKO2G8FVeY8T83/TdeeTH3Wscaj3vw5wZoUcsR8ywxzuEuitXycmefmmKVjUQMKhFk+P4eNM5FsVr060HzjPBzU8JuurmTsqys5l7uIeq2uZOs7NXlZUMu+BuRIFcqzT1Mu4nWtWaCPbvUGR/5yEcwOTmJgw46CIlEoir2aGRkpK71n3322Tj77LPrWsd0grerKldMZ/EUnwoIsGAIdvGA1YmZsTMiN4OzO6iu23tSTn1XJbKeGIY1YadzJUbsDF9c8S4xJWVZR/FpXjyXIIu7J3YmV6qKPxGdupKxFnK/c94iL+BOypYrJnLFStWlvbyrT2juXNcShzs3sFiS+0SOFTsT/gACL7O3v/6g5J1CixtnnhDFanm5B1k6iQWC3+7ZQplrRWBbX9ixXqJYLau8WJSy6ibJOydt7nM6vHGmsha7YIubOz+yBIYMd5E70ypffWWNaKy3875zQawWzStIXAmvZ7I5kdsbgk4cNwtNE0eXX355s6reLcE7MUYPSHGALLsD83bivFNfZJcqzlkTVLc1IOlElezy4awI5OJbnnuJPXGwd8KiSQsA92i1iDuJnSF3u/Wz6hdMemG5cxd5gYuFvvh2Il+qEke1HC+WavcaPjt5vVSpvvhWJlZLjjvHcsSLUxOUlykLhDv55MTdMMqS+oeQ5wpDVnlerJfzuRmxWlZ5sbjicW9PxhxxpMqdFy8lsp7Qf+OlK2H1t1g0gtZ4FFPFMrL5EnrbE8Hlhdx5/U2GO1tcicaKVX8J3W2JwPc1A00TRx/96EebVfVuCd6JMTL4WEfx6fJhgjy95TkDQDDh8sQJy/pBl+dZAfjlw0+avEVWatLjmawluHck2RffuiZvdVEqw53XbqJJ03KxxDCRr774lo7VYiamq1WU1iCueBffysRq1SpKeXFq7k6cH7cTdPGtGwzOjtXic+dvJDzcOTFHoo1I0DgXucXov3FdUxzuqWQMOzP5kNynaX7lHXgRWHmnimWGlZhv8ZMR8zw3sLOBDLjBQJQ6giTvzJcqyORmljiaETasXC7XkCzUuzN4J8ZkOjBvZyNlLuftKAWDt4Ma+P74E1F+Jrp8PRZKYd4XjjCTsbjJBGSH4U7HaomP+PK48ywY7Hw/ohNb9N/835tMrBavbhlrIfezC7jzYmfIQse6NgUQWdxUuAcJar7FzjNP+MqL3Lhi7vy66Wfz4tzYLj3rOw+6+FaGe83zhAR38cGL2r5zPnfO/M7gLhPTKefC5rnVahurohi/ZqFp4iibzeLss89Gf38/2tvb0dPT4/nR8II+Meaf9FTiR3hJxkKbTiXdFCQpX/i6ORNHiM9eKlecWC2ZY65+YadiLuearCXiT/zcZWK15II8eZOeRHAtt92DT33JxGrxrFaiIHyrPLvPyO7Eg7hnJMS8TGBweO78RIj0/WjVfaZW64t4rPIyo4s2It7YGXXuUvNECO4yMZ3kubli9f1oonglee68eYL1nYvnCW76BsHBCfpvodudU38z0TRx9PnPfx733HMPfvKTnyCZTOIXv/gFLrnkEixYsAA33HBDs2jNWHhzt3gFiii4FaDdO7VZX/ym03LFdAQPq3xLPIIII3eLSnBtWO6snQn9WUSnzYJOjIkSnNHcuUHRIbiTRZp1bQr93IkAYafCnXuknLsTD44hkZnsaw3IlonRY1kB6GdXL9LybuBAt9g0cZdz5Qa3u5QLmhP7IjNW/dzL1M3yLO6xaMQ5Lh6Oe219RtRuVh38eQKo3gjJubB51kJ5q5mfOz1PMGM67ecG3Y8mYyGWciOH4N5sNE0c3Xrrrfjxj3+M008/HbFYDG984xtx0UUX4Zvf/CZuvPHGZtGa0WCZ20VJGOm/BU8cYnM5aydNL9q8wGLWAFCbONRN9QB7R0iex4vV4iXlUzlSzj0lKMGdtSOUWSSDkvJJHSknJ/U47c7fyQf3Oan+yhUIfGsf/Tc+d3FQdPV3LrYccQ8vSPWZ4HarVEypPsfmXpuLQ8l64//OJeYJOe4SfSaIu+CaIfpvLDHPmyfoAyX+U4ZS7ndeTjIp6w2/3WRiC4PKS33n3DQGEtZGLY68GBkZwR577AEA6OzsdI7uv+ENb8ADDzzQLFozGqzBKzouaf1N7BcOsyMkC008Gnxj9HRwl4nhqIU7ryydlI/pzpTgzneryUw8/rqLnr8HgT7yzJ40xab6wDQENewIZcqSCdNKysf47CFcLJWKKbxPj8ddxg0sE+DKD8IPHqv0oi/jomFb7GqzAogOEAABG5Ea5wkla2OIdCO88jLzBMAe63Lud97mNfxnl+GejEWRsK3PrHaX+c7DxibyErY2E00TR3vssQc2bNgAAFi5ciV++9vfArAsSt3d3c2iNaPBiuGoVd3LBdeKrADsHB6e+mvgzs0VVMNulFdWhnsYF4fFXWGR9+9GJT53JGIwJ00Z6w0rvxSdTDCMm0PFYhbMXSxQWBaQyaKbrZjnVhNxl7F+BAUWS1l+GP2NlI1F+AKDdepLxT0T5i5A+tk8YcabJ1gWPyk3MM81pTRHqotx+tnssAexIK41cShzIyLkHjy/q/SZ2k/0anEEADjjjDPw1FNPAQAuuOACXHXVVWhpacE555yD888/v1m0ZjRYuzqpiSPBnrBF1yEA7N2sjMmY/jszlkCQgBJgBHkKcixZ3MO7GWS4S7nFggRGgR9cSz+7ejcqdi1Zfw+e9GQmTRb3qWIZJDRB5uQTK7iWVzdJyme933fqSoU7QxTyrkOQ4c7vr+zAYrn4PsFGpEWwEWEstCoHCEhSPnXugrEisL6ILEcyrtDpTqEgYy30lmf0V4nDC3xro7qYl/nOaW61hQ54y9IHXnZHtxq/xeqIc8891/n/iSeeiBdeeAGrV6/GihUrsGrVqmbRmtFg7eRFdxYB1SdBEjE3n4RSrqAQ1hP671XcbesJr25WFlXTNKVMzuwTX+LP7Snv456WEKUphhUgV3SvQwgT6+WkX5DiXp2UL5MT9xmmBcP+PWLAORmlxl12N2sl5auK4chJpJ5gjRVqFy9jwfB/dhlhRgKLc8UKJvIl9FBJ+aTanbURkbBAWH8PHqtSopL6mz8pn1S7C62F7M/tKc/sM+JxPlUso1SueE5CkrbrlMj0XOU+l3Sria206u1WKlecAy/ceaaGjTPA3kxMhyAGwm2imo2GW47uuece7LffflW5jJYuXYoTTjgB73//+/GPf/yj0bR2C7B28jLuGdZJEPpCR6kTNP4cS9ITdvAASEtMPP4JmyBfqqBEBEYN3Hm7UYA9eN3TO3ITNn0ShCz4vPuWrGezdtJyliM2d3HMkkycmIwrlW0FkOWunq9n2lypjPgREXe2wBELDKaLo0YrgAx3kpQvmLuE1UxkIa6RO88N7NkAUidRaYEhlb6hirvcRkTGpcgsa/9t0k7y6y8bnrtcn2GdkKwlXQnpLy1x9olamvtMsxw1XBxdfvnl+OQnP4nOzs6qv3V1deE///M/8YMf/KDRtHYLsNxqMpMWEDxh0/ctcU2nop2FaGfCMDnL3N3DmrBpiwTrviU57vzdLNsfL7/Q+cs7ojIhcpGEjwWw6ufv5KVcegWvsFMVxLVyZ+2Ga7ICSHMPjh8RjzV+Ekm+FYCRAkGSey0ubPr5dNvRKTt4Y1VkwRBtRIQu7BCBxfTnCBPILrq+w8+9WqDIu5YA7yZOVmDUi7uKtTFbKHmEnYyVlH52UKxYM9FwcfTUU0/hrW99K/PvJ510ElavXt1ARrsPmG416U5YvdDS/+femVSDT9qqO3ixkdlJe8tXc+9Isu9bkuHO240C7AlbRpTSE3Yg9xCC1vpdNUg0mDtPYLAmbNX4EWa7c/qbVX9wYLGc9cWt27sTF1vMaO6sE4rtHGsfXT/Nnc71I+MCZ7rFpE9NMRZKYbtXj1Wai1T8CJM7f46qnXv1HJe2+4uswAi7AWTGS+XE6R/oJL9BG0BpgTHt3MXzOylrmtaBB5e74twekGC4mWi4OBoaGkI8zv6iY7EYdu7c2UBGuw/YC53cQhkkEuj7lljXIdDPZpm7hSZngek1jMm61ngn2fKiCZsXKMniLh93w3KxyAWJCt1qggk7HiVZ2cNwD28FsJ5fbUGRSSYIeCdkesKWbTehm0JysfK0m6TAcMap77od2f7K4i6TGZx+Pr2TJwKDl0zQwz3kWBMGFou4B9TvxmrJjdPwcxwrkF4cM2QYRuA8IROTOT3cg8WVzAGElnjEWTuyAe0uP7fPcsvRwoUL8cwzzzD//vTTT2P+/PkNZLT7gOlmyBMrgPoAkInfoMtOFvyxM9Nl6pdbbDI1cGefehK51abHTUFzl8+dIsoyLdvuXheJzEk5T/LOQO7hrADSsTMBrin6O+D1Gc9O3MNd1XIUlnvAQieRrRhwv3P/dTvyLj0+d/mNTHW7i8YpnZOMFnaqY6X6OL3cRqQ9weYuPT+G/s5ZVl7JsZqo/uzq7caw2MmKI8pCXJHciBiGexdhkHVcem73cW82Gi6O3va2t+HLX/4ycrlc1d+mpqZw8cUX4x3veEejae0WYCVDVDW91mIFALwuFukAVcbJJ9l4qfYAgRPGgkG7WFzufBdJEPcyla1YnnsNlqOwpwQDuMsGedLcAyc92XavkbtXEMsJDO91O+rcazl5xOYuN07p63bC9Bk2d7kg/qA+47ph5b7zignnwlO6vDx3/3F6ubEadDpU1b2T9Qk72U1Y0Fi1BIbcHBnMPfzcTj9LHFdZXbdsVnOaX5h25yUebSb4rOuAiy66CH/84x+x99574+yzz8Y+++wDAHjhhRdw1VVXoVwu40tf+lKjae0WCLJA0L+HiQGRHTzExVIsWwkAO32DQTQAyGJEH8umBYZsHIUnDiIvN/j8Lhb/4iHNPaTACBK10jtCn4uFBG+rHi/OUIsN+X8ixr4OwV+eFeslxZ0h5mXdasECQzx1dSRjGJ8qel0sDePOE0f8ssRil86VkMmX0F/FPZx7SOaEIs09HdBnRGXJdTumaY31Vp9FQbbd6U0QnXS0lnaXdcmV7Ot2WuJq3INOfHmSjtYwVmvNUxSGOykrymru5e6WT0sKYlYsbbPRcHE0MDCAhx9+GGeeeSYuvPBCR6EbhoGTTz4ZV111FQYGBhpNa7dAZ6s1Kaan3MFTCWHBCF7o+Isk2YmPTRathbmLlJfbjXa22hPuVPDORJ57tZtBFKSZjFk+8XLFyovkX/DF3O12z9HCzCorIzCC4oZkA0w9wY6FctV3WAt3kRWArj8olkA+CN8r7GR30k6fCeAu2kmzuMsEmFplGfEjEvdcWdyD2l1OzBPu6VyJwV39AAGddFS0WLntri7myXU7mXzJEjgpwl3tAAHtYvEkHQ3R3508cAJR6b9uxxFHiqcEae500lGRwOByl5wfyXU7ZE6q5YQj7RXgnai1uIcfqzP1KH/DxRFg5TT661//itHRUbzyyiswTRMrVqxAT09PM+jsNuhyBg81aVECI4ypX3ZnQd4zNln0iSvxSQwvd3pXZAsMzoWO1dzpwSfOXQK4O3G/FaEWgSEbKGnxq7aAyO6EW+NRRAzLTZHNl6omEtEi7bQ7JUplXRw0v3QI7uT5xMXiWBEk6+8K2AzI7qRpfnSfkQkwtZ7vxnoRYUcnHZXu77W0+3hwn5G1dNLCik46Ks/dbTdZKwDhnsmXfO0uN1Z5glaUdJTFXdbqRa7bmciXkMmV0NeRtOpX7O+BG4lEVCgwuH1GJI6oTVYmV0Kyw2f1CuFVkN3Aebmrtzupu1CqeIRds9G060MAoKenB0cccQSOPPJILYwkQNT5+FTRsbjRAqNFMHEQVxjdgd1FVn4nTg+gcXsgk8Ehqns8YPDI7KRd7tXCTFbYVXMv1sBd3r1DLDRB7S4SV3RQdCYUd7fPuNxJu4u/c16fEXEnLhaLu1XeNE1noW1cu4d3CRIXC2BZ7kjS0TDcZTKq+8t7Fpsa3GqERzRiCNMQBNYdqs+ouzODXCyEe2drXGzBqONYrYV7V5tMu4Ufq9GI4YzHMNx5fUbU1y3u7HYXWahTyZgzT9B9ptloqjjSUAPppHRCNtm4Gbo83YFVygftjNKSA4jeWRBh12zusoM/aEcnk7xShrtoVxXEvVIxHStWpyz3AIudSrunAyY9KYudc3rI7q/5kmPBkG73kDFHQe0uy93vYqGfE48a8haMXFB/rW+f8btY6Od0SQgMPveQY1Uyv1SQi0VlkQ60riu0e2cgdzXXVpj50cu9ut1lXOB+7vTtB2ESfyqJoxr6TIQSdnS7NxtaHO1GaI1HnePJpBPJmi4B1mIhb31JBezEpS0Y9t8rpjvZyC5UbO7ypv6Ub0dYrphOeTF3159OTrulFdqN76YQTzwp3048ky85QZ6y7R623aavzxQ9z0nEJCydPGEm0W619JlIwE5cRWC4MXbh2i2Qu2ziz0T1TjzMQhdofZHgXkt50l8KpQpyxWphJ66bY30J0e6maUr3OXqckg3gdLV7mD5DX1kka/XyzFHTxl1irLZVl282tDjajWAYRtXuQmUn3R3QAUcni56/8ctbl1COTRUAAMVyxRE63YIB1BKPOkeviTBIO5OWTN2Ee4Hibv2/h7ocU1R+zP7s9CQg6yIxTTfGK0y7j1F1jjnc5ScO0u7j9nfWGo8K/fPks9FpDGSPB7O5F23u4nbvcvpM0VNW1F9o7sHuHYnFwtdfrfrl+0yX77MT7kpWgBBuhqC6AWAsS9pd7GJx3RwFm3shBHfaYifvVuv29ddyxXTmnG5Bu6eSMSeh4Pg0t3uYsZqhLJ2iOZL06QJ1Gz1p9+5WcX/jbQZU2p20G5nbE9EI9/5Gmh8dsjGmsDYE9Zm0wlh16y8I3tk4aHG0m8FR6HbHVREYQbvRMclJiy5PBg09iEXuHYDyS0+qCzsedxl/fpc9+Ah38pz2RJR7pQBgCTty0qSae23tLsO929fuKrtR0ram6XJWivUK5G5P+ErcrTJKu1ESUE0tUEoCw+HuTthuf1dYbEK0Oz/GTr3PFMsVJ25HZqw6i/y0cQ8/VjO5orSlk94ATj93dXFFvvuWuNjS2ZaIOhnlXe52fw3JXUVg+NvdEcRtYksn6S8l6vSzWrsHWexqm9+bDS2OdjO4vl1vB1ZR93QHHHd2NupWBPIcerfH5+66p6aHu7wVosdvfVEY+BZ3r8VORSAECgyHu3ihI1aO8Sn1xSIZi6IlTix2hHtt7a6yk+9p95YP42YAXGHhikp5MU/qzJfKTqyeSruT7zqMmyFbKKNUrvi4q7e7ZyMiZQEJ3gyouKbo+JEwfSbtLNLuRoSXuNPl7hXUtca+qIzVaoEhP04Nw5imdq8OW1DiTupWmB9b4u484ecuJewC2l3WWhjEfSZAi6PdDP7BO5K13QTtErtJe4BPFsoo2CdwiOmVLGI8OIuFPWmpTPa1cvfvJi3uCp+dTLhZ9UU2iPuozb1Xod0Jd9M0XfeORLsT7qROMtmHbXc17t5Ja6pQdk5vyX1vCbtOdWEWp9wB1dzlrVZkA0A+Q8RQ28263MkiK+EioZ5PFjuHu4Llh3Am47SzJYaYwNIJuJ991CcwVBbZyUIZRVvYEe5KLmyHu3y7eblPzyZqxHFHynD3znEud7mx5reU1iLMLO7h3cDO3C7d7t55qpZNVKHkhlzI9PcgN3KzocXRbgb/UVM3/kPOxUKsq1WmV4mdUS2meou7d0epEjNEBk/eDtSs0HEMMrEIPiuAy128SFrcvcHoKrFahDs5qZeljoTL7Ej9E8d0tbvUjs4Xx0DaLyZxJNyqI9hiJ7Mb9XIn7V4Ld7fdIhKWTpalVKbdY9GI0z5p/2IlIez8i824gjCjuYex2NHup6qxqrCR8be7tMBwLKUhLEc291zRypmjuhHxW3nVuXv7jJob2TtO1TciwWNVdhPFGqtq3K1xStpcdSOi3WoaocG0vkhMmt4jkwWUK27OGZXdwZjPbCu7SDMtGBLcOxIx576p8akiMvmSkzVXZqHt8Qs7hQBV+n3pENxJWRKoSSYO68SWeAj2+Ez1Km4t+n1uuxeVuY/Zwo4O0hTFMVjcvRaQ2rmrt3tVMLikwHDcmcQKQKw3NXKX2gy0ehcqleBYuo4wfSbqO1pdrphOG8pw72TME8oCw+EuP1bpDWB6yrp+hWxElNrdN0/IbGIs7uHb3b8BHCHzBCW0VbirHH6wuIef3/0bwBFq4yuzEdFuNY2a4fftqlhfAHpXVvSodKn4EZ/JWcXcDVT71EcUJs1IxPAsNoRDazwqDJQEqk3GrtVJrt387T6iYMFoT3hTMNCTlozAYAU1y056bO4yrinr85XtG7pHFUUlKV/l3pFud2/8y4hCf++mBG2lYipzd9xqVX1Gvd0LJTegWm6RJsLMa3VS515rjF3JPsFkva4ShO+emlIUGE6f8Vu95DaA9N1wRJDKzxN+7orCjuXOlGj3DjoFA8VddiNC2s31Kqi6BBnzu8xJO5KCoVxBvlRxNu2q7aYtRxqhUbUbnZSPH/GXJ4MglYwJT2wBtbkZ6Pf5B2847vLuRIBjMg4Zt0Pql+FOn8Dxcpf83NPU7uSYrkq7t8QjSNh9Y3yq6CzWYbm7bgY5dybNfapQdm56V3GRVOwUDOPKfcabhiCswBifKjr9LmLIWZ5IHeSknkoKAot7ja5YijuZY1ItcvMEKyBb1XIUxq1Gv8/iLj9O6bLV3GtzZ8p85xEqBUOaavcw82Mt3MOETXQkvZZ9lfkxiPtMgBZHuxn8x7qJi0TGJw14Ta/OblRxZzFZKCNfKiu7GfxWBJWA7GruxJ+uNvBHJ73uIXkLiLsjrFTU4hjY3FVdJF4Xi6qwG7XvxSuW5d0MhmFQbpKC8k66yr2jHEzu9hnSbvGoIZUUz5+CQTUw2HXFhluk6cBiMk672xJSJztJHVYKhqKywGBZeVW5j00WlAL46Toy+RJK5YqyBYO0O2kzZe5t1dyVx2lY60sbOYDgO7SiyH10sqgUMkHXQcaYstWrzbXY5UtlJ1eTDHf6pN7oZKEG7locaYQEmaB2Zb2nKWR3w7RCH1c4SQFYO0dndzBZVJ60CPeRbMHK25KTdzMA3t2sqouDDFwr825FOTCY5p7OFZ14J1W3nGVFCB8LYJqmcrvPIdwnCs4i2xKPOBfBitBFZR12xI10DEZtAmNOh8udFjcybga6Hrrd1RdZ3yItOV6CucuVTcQizhUldLvL9pmuGrn32tx3TdCCWK2vA5Zbzu3vstZG9/CEp7/Lcm9PUtzDLdLkpF7osTpVRK7ongqW5+62u2NhVhR2VUH8qmN1quA8w5AMqKa5W/OMWrsHpTtpNrQ42s0wp4MM/DxyRTdvi6z1hQy0kSw1+CQ7MB33M0aZfWXLk8VimBr4hhFGXOWVJ452OkHbVEFZVJJ2H55wd0WpZEwqb4uXe8EJ8pRtN/K+ki/uR3axcvpMNu9wlwloDuYezp05TuJ+smoL7RxqM6ASSO7nvitEf/cf63Z3w7Ki1G13lUBygiDuqsHkY5PFUG65Pqdumrvc545HI86CSo9VVcvRWJWlU658H9VuqhaMzta4swG05khVa6MbK0bqjlEB7iLQfUaVO5kLc8UKJgsl5dAD+vAEGWuyJzst7vb8ni246RMk1yXS10ezBSeTf7OhxdFuhj7Pjk598M3taAEADE/k3dwpkuIE8JqNd2byAID+VFKSuyvs6OBYGTeDxd0VKKrBtVbcD+FepLi3SJWf47S7y71bUph5uGfyyu5M2j0Upt1pUaoSSO5wT9HcwwVkV0wryFSdO/nO80qB5EHc3VNPcmPFCejOlZDNlxxL51zlPhOu3fs83MO7xUayBVRMayMyR3KxcjdhBaUgeALS7jszBaicNrO4u8KO9JeOZAxtCUmBETBWZQVCNGI4n31nDe0+OumO07mppLSlM2h+l233jmTMOf06nCkoz++0C1t1nFrcq+d3+c2nuwGcKdYjLY52M5CBO1UsY9vYFAA1N0NfyuqEOzN5d/B2qAwAu/yEW75PsrzjZqB2dCo7aXfCnU7ukjtpu56RkBYMh/tEWO7WewfTOWexkm33PqrdVYPgaZ4e7pKTZiIWcU6yrNs5gYKdVDBMn5k+7nLiho4PemEwA8A6Vi2Todri7loB3ABVdUEdpt2JsMoWytg0MmnV3ZaQSiBpcacsdgo5jqaHOxHzeexQHKcA3e6uQGgcd7fs8ITa/Ah4+7sqd8MwHJ7bx6cwklUTOHNT7vxYO3e1PpOMRZ1Nz0677mZDi6PdDO0J14pAJuxQE24mjx3pHABgoFNusQCAfvu9g+M5ZwDJThxkUStVTKzbOQFAcdKixNFQOu/hIwPyOTfsnEDWdkfKcic77tHJIrbb7Raeu1W+v1N+4hmw3/vctjRM0zr1JCsSiKl+ZyaPXRMhFrqAdlfpM+S9z2xNA7BiGGSOVQNAH8V9uFbuGdLf5do9GjGc8fLstnHnedIbkXZ3I0LGSu3c5dq9IxlzcuPQ3GUR1GeURKld1450zhE4stz7OpIwDGueeGkoE4K72+677HYPw33jcNZJvyDbZwZs4T02WcSW0SnP82TgbXfCXX1+f2Ewg4o9T8yRFDjEij6UzmOH3d9q7jMqG0hqbZoJ0OJoN4NhGJjfZXXif20cAwDM62qVLu9MWiEWC8Ad/C8OZpzkanMkd3XJWNSZuFzu8ousyz3nDF61RZosdNYi3RKPSJ16AqzJlcQXrdk0BgDO9yADut1VFwv6vc9stRa6OR1JaXckaeOpYhnPb7cWm/Dcwwg7L3eVCZdw3zmRx2bbAjJfod08/T2UsLPKE+59IbhvH89h+5jVbmG4bxmdcixPSmO1hnaf73CfwvZxa5GfF4L7C/Y8YRjy9cejEWehDce91eaew/bxXGjuz9jzRFsiKj1PdLbGnM2rI0oVrC+k3beNT1Hc1ef3tVS7yc4TZEwXShW8ssPavIbjnnP7TMj5fSZAi6PdEAu6rcGyeuMIAGBht3wHJBPHjkweW0fVJ715XVYHfnLzGABrl5aMyVkBgCDu8gPfmbDHchgMMemRxYJwn9fZIm0FMAwDC+z6CfcFCqKUTBLbxqYcy1Gt3GXREndFqctd5Tu3PuemkUnHeqNSP5l0w3CfY4tS0wSe3DQKwO1DMiDt/vz2tHNySEXYEcvkk7YgnqdQlvCcLJTxwmDa85oMSH9fY7dbMhaRjn0BqHa3uauIQsJzRybvuOVq4T6nPSmVI4lgoCbuZJ6YckIPauGuOk8M+PrMgMJYIzy3UdzV5kjrvWtCjLVkLOrECDn9PQT3V4ezzjyhwp3Udf3DG/HWyx/A9+94UbpsPaDF0W4IMgBe3TXp+V0G/akkErEIyhXTKa8yAEhdZGexZE6bdFmrvFWXy12+7kU9Vl2ZfMmxvtTGvV26LF3e4a4w8Jf0Wty3j+ecE4YqEz5pp9Dt3u1r9xDc1+/MArDiiFSCcxf42n2pAvdIxKjuMwqbAcKd1K0s5u26X3a4y/eZlnjUcecQ7iqLtJ/7/C75RRpw293h3ivf7nPaE0hELVG6eYQIjPDtrjLOrfeH507KZgtlZ5FWaffFPu4qc4xVv6/PqHDvdl1b5F61gS55QV47d2+7LwnBnYjplnhE6fAEqWvN5jG8MJhxLGfNwqwSR9/4xjfwute9Dm1tbeju7m42ndBY2OMd6CrqPBIxsJgqH4sYzoCSwfI+7+KgMniA2ri3xKOe4MJUS0wpULOau3zdQG3c57QnnLw1pKxsniFgGtq9Ozz3Bd0toNfkPfrapY/3AtXcVfobUM11Ubd8+cU93vfuMVdNEE83d5V2r+beoVR3VZ9RFKW0GIoYagvtohrb3f9+Fe6tiajnVF5rPCp9agqovc/Uwr2vPem45QBrM6si5hf75ijlPlMD9wVdrZ55YmF3q5KYr7XdpxuzShwVCgW85z3vwZlnntlsKjVh33kpz+8r56cY7wzGMmr3u3ROm5K5299hVXbSALDvvE7v7/M7Ge8MBs19z7kdSoNvz34v12WK3Ff6232efLsbhuGxmKgO/D37vZPcMkXL0Uqq3aMRA3v1y0+ayVjU40LcU3HCreau2u4u9/ZEFIt65AVGd1vc44qqnbtqu7t9ZKAzqRSQPb+7xbm6BQD2rLHPqI5Vut33mNuhtEj7rYPK7V7jPEPPiSvnp5TmiWV9tXL3t7uaKN1nHs1dcX70CeJauBtGtWDhoTUR9Yxtde61tft0Y1aJo0suuQTnnnsuVq1a1WwqNWG/Bd5Op7LQAcChS3uc/6uKk7ZEzLMjPXRJt1J5mns0YigtdABwyFK3PlXuczuSHkvTIUt6OO+uBs29ryOhtNAB3nbfT5H7kt42T8LJQ2vgvryvXfq0mFOfp8+oiXF//6yF+8r5nUpWK8MwcAjVR1X7zEqfmD9ocXfwGxmguavWHY9GsGpRV+jy/j6m2udq4Z5qiWMF9b2rc3c/d2s8iuWK4oj+rKp1z+ts8Vioa2n3BV0t0rnUgsqrjrU953Z4BLVqebrulfM60S4ZiB5UXrW/7b+gy/O7avnpxqwSR2GQz+eRTqc9P83Gkt42Zzdy7D5zlXZ0AHDcPv3O/085YL5y/accMA+AlfPlsKVqC93KeSlHoLx91XylHR0AnLjvQBUPWRiG4XzeVDKGVQu7BCW8OHRJj+MaC9Nub6G4v1WRezwawdvsMv2ppLIgPmbPOc7/T95/gPPOYJy4r9tnVLl3JGM4YaVVfo+57cpxEG/au8/5fzjuVpmIAZykWH5uKokjl/UCAA5e3O1cDKpaNwC8dX+1dgOAE+x2T0QjOGGlGvdlfe2O5epNe8+VzuZOQLeV6lgDgONt7h3JGN64ok/wbi8OWNjpbJxO3G9ASRAD3j4aZp4g7d7XkcThinPcEct7nViz41b2C95dDZq7ap+JRgy8ZT/re1s6p01ZYLxp7z602e7+41fOVSoLeLkTHrJoiUfxhr2sfrL/gk5lF/a0w5yFuPbaa82uri6p91588cUmgKqf8fHx+pIU4OWhtHnxn54xh8anQpX/x0s7zRsf3WhWKhXlspP5kvmz+9eZz24N1wZrt4yZX/3zM+bIRD5U+bufHzR/+89NobiPTxXMn97/ivnyUCZU3U+8usv8+m3PmumpQqjyf1u73bzlyS2hyu6ayJtX3/eKuXE4G6r8gy/vNC/76/PmZL6kXLZSqZh/WrPV/NvabaHq3j42ZV593yvmtrHJUOXvem7Q/P7fXzDzxbJy2XK5Yv7+ic3mXc8Nhqp743DW/Nn968wd6Vyo8n95ept55V0vmaWyen8tlsrmTY9vMh94aUeoul8eSpu/+Md6czQbbqz9YfVm8+r7Xgk11nLFkvk/j75qPrpuOFTdz2wdM699cH3osXbjoxvNax9cH6psNl80b3h4g/nkptFQ5VdvHDFveHhD6LF2zT/Wm//72MZQdY9PFcxrH1wfen5+ZN2weeOjG81cUZ17uVwxf3LfK+Yf/7U5VN0jE3nz5w+sCz0/izA+Pi69fhumac6Mi0xC4oILLsC3v/1t7nuef/55rFy50vn9uuuuwznnnIOxsTHh8/P5PPJ5NylVOp3G4sWLMT4+js7O5pr9NDQ0NDQ0NOSQTqfR1dUltX6rORRnID772c/iYx/7GPc9e+yxR+jnJ5NJJJPyRyk1NDQ0NDQ0dm/s9uJo7ty5mDtX3TeqoaGhoaGhoRGE3V4cqWDTpk0YGRnBpk2bUC6XsWbNGgDAXnvthY4OuQBX4oWcCYHZGhoaGhoaGnIg67ZMNNFuH3Okgo997GO4/vrrq16/9957ceyxx0o9Y8uWLVi8ePE0M9PQ0NDQ0NBoBDZv3oxFixZx3zOrxNF0oFKpYNu2bUil1BKLaWhoaGhoaDQPpmkik8lgwYIFiET4qS20ONLQ0NDQ0NDQoKCTQGpoaGhoaGhoUNDiSENDQ0NDQ0ODghZHGhoaGhoaGhoUtDjS0NDQ0NDQ0KCgxZGGhoaGhoaGBgUtjjQ0NDQ0NDQ0KGhxpKGhoaGhoaFBQYsjDQ0NDQ0NDQ0KWhxpaGhoaGhoaFDQ4khDQ0NDQ0NDg4IWRxoaGhoaGhoaFLQ40tDQ0NDQ0NCgoMWRhoaGhoaGhgYFLY40NDQ0NDQ0NChocaShoaGhoaGhQUGLIw0NDQ0NDQ0NClocaWhoaGhoaGhQiDWbwO6GSqWCbdu2IZVKwTCMZtPR0NDQ0NDQkIBpmshkMliwYAEiEb5tSIsjRWzbtg2LFy9uNg0NDQ0NDQ2NENi8eTMWLVrEfY8WR4pIpVIArMbt7OxsMhsNDQ0NDQ0NGaTTaSxevNhZx3nQ4kgRxJXW2dmpxZGGhoaGhsZuBpmQGB2QraGhoaGhoaFBQVuOZgpeuQu46xLn10LZxPBEHqmWGFJJ9a9pdLKIXKmM/lQSUcXA8QqAbWNTSEQj6E8llevOlysYzhTQ1RZHRyKqXH5ksoBCqYL+VAsiijHvFRPYOjaF1ngUfR2J4Dcl2oG3fgtYcLAyNw0NjVmKYg744/8FRjdisljGjnQeA51JtMbV57jRySKmimXM61Sf48oVE4OZPDqSMXS1qK8NE4UyhjN5zOtqQUtM3T4yMllAvlTBQGeLsnWlWDGxI51DqiWOThH3vU4ETrxYmd90QYujmYKpMWDwaefXBIAFADAV7nE95D+T6mUjAJxQtax6+SSAhQCQUy8LAL3kPyG5LwaAPIAJzhuf/q0WRxoaGvLY8k/g+VsBAG0AlgHArnCP6rF/wszvUdjza8i1ocP+wXC48rXMz3EorA19e6tXMI3Q4mimYNkbgA/9AQBQLJv4jxueQNk0AQBffsd+WNHfIf2oh9YN46f3rwcAzOtswXf+7UAlKj+88yU8uXkMAHDqwQtx2qELpctOFsr4r/9Z7fx+2btXYWFPq3T5u54fwg2PbAQA7NHXjq++c3/psgDwjb8+jxcHMwCAfz9yCU45YJ73DU/dBKz9LVDOKz1XQ0NjlqNSBACUOpfg48P/7rx85b8fgu7WuPRj/rp2O37zz80AgH3mpfClt+2rROPCP67F1jFLGX3iDXvgzXv3SZfdOjqFC29e6/z+s48crmQ9+v3qLfjzU9sAAIcs7sa5b1ETMOfctAYj2QIA4NPH74XDl/Wy39wxoPTs6YYWRzMFqXnWD4AXt47j3nLB+dMTsVVYsdcS6Uf94+UX8EDFjsYfA7608M3oUhi8v/udgW0VS9oncwM4ba/DpcuuWTeMByol5/cnk4dg4V4LpMvfu3YtHqh0AwAeGjbwpeXHIx6VG7ymaeI3u8rI2PX3FRbilL0O9r5p65PWv+WiNCcNDQ0NVCoAgKloBx6oHOS8vCZxGI7dq1/6MX957F94oGKJgqdG4/jinidI58wrliv43VgBpYq1cV6UX4I377VKuu4n1mzFAxV3Pn229QgctrSHU8KLP93/GP5RmQsA2JBpxbl7HS9dNp0r4paMuyndt7gHDt9LTRg2EjogewZi4y6vvXL9Tp5/qBr+928ekbd/TuRL2Dbu2jxfGsoo1b2piruaX45+f7liYtuYvO14MJ1DJu8Ks0DuUXs/UCkr8dLQ0JjlMG1xVPK+rDpHbhxx57jxqaJjSZHBppFJRxgBanM7UM1VeX6n6tsyOoVcUX4e9a8FqtwbDS2OZiA2+TrNhmE1gfHqLu/7/c/jwS9Gto/lUKEGowgzifu2sQDHdoSII2050tDQUIBpCYGCTw8EzjMc+DeQKnPkq8Ph50egmut2hc1nuWJi66j7ftOs3sjzUCv3RkOLoxmIzaNWpzlgoZVHaTCtNvi225YfUl6lExJf9t4DHTAMoFCuYJfCzmazPXgc7uPy3MsVE0PpWrhbZVfOs1yKI9lC9c4mYrsXtVtNQ0NDBbblKGdPKWSeUbFuj08Vkc5Zpqf9F6jP7/65fevoFMoKm1cyvxPuWxWE3fbxKZQqJhLRiBMDWwt3v0icadDiaAZiyO5EBy/uBgAMjssHD08WSsjYg4+UH1LpwPZgWdLbhoFUCwC1we/nrlL38EQeFROIRgysWthll5f/7Nupgd9upxCo4u641Xy2cQ0NDQ0ebFc88dwfvsyK1dmusAEk82FXaxzL+trt1+TnOFJ+1cJuRAygVDGxK6swR45b86HLXWFut+vu70xifner5zWV8mRtSOdKmPKb4WYQdhtxdNlll+GII45AKpVCf38/Tj31VLz44oue9+RyOZx11lmYM2cOOjo6cPrpp2NoaMjznk2bNuHtb3872tra0N/fj/PPPx+l0sxaKIcnrM5OBMKubB7FckWqLBlo7YkolvdZ6n5nRn7wDNqDZV5XC+Z1WeJIZfD7uYcZPHM7khjotOpW4U54zu9udbhXWa4iWhxpaGiEgM9ydMhidXE0bM9n/akk5tlz3I4Qc+SCrhb0tls56GTnSNM0MWRvtAl3Fcv+zozlQZibSmJep1V3GO57zu1A0j4hR9aLmYjdRhzdf//9OOuss/Doo4/izjvvRLFYxEknnYRs1vVjnnvuubj11lvxu9/9Dvfffz+2bduG0047zfl7uVzG29/+dhQKBTz88MO4/vrrcd111+ErX/lKMz4SE6Sz7z2QQjxqwDTlBwDpgAOdLZhrJ3BU6YDDtgutryOJOe1WEsWxSXm3GuG5/wJLHGULZWRyci4sIuwGOpOhuO/ycLfKj0766tZuNQ0NjTCwY47y9j51H9s1NTZZgGnKubZ22vPZ3FQSA7bAUHFNuXOkO7/Lrg3pXAkFe5O994DFfVRlbifcqc2rGnfrvfMo7jsUNr+Nxm5zlP/222/3/H7dddehv78fq1evxpve9CaMj4/jmmuuwa9//Wscf7x1vPDaa6/Fvvvui0cffRRHH3007rjjDjz33HO46667MDAwgIMPPhhf+9rX8IUvfAFf/epXkUgwMio3EKZpOp1woLMFve0JDKXzGMkWsKBbnC9o14TV2ed0JDC3Q23wWOXzdvkkutus9qgSGAxMFcrOabGlc9rQlohislDGSLaAVIs4lQBddy3c+zoS6G6L29x9gz9q89AB2fWHaQKjG5wj0MK3w4QBxXTB01AWsGJBUi0xRBSzyU9H/bVyH5sqomtgCYxEe+hnaEjAFkAV04BhAMttt1ipYmIiX5Ka48h8NjeVRJ89x6mcViMutL5UAnNTSTy/XX6OJPWkkjEMdFl1j00VUa6YiEqk6a6du715TVmb3y2jU0rze6Ox24gjP8bHxwEAvb1WvojVq1ejWCzixBNPdN6zcuVKLFmyBI888giOPvpoPPLII1i1ahUGBtzkUieffDLOPPNMPPvsszjkkEOq6snn88jn3S8wnU7X6yNZz58qoVi2BuGcjgS6Wy1xNCYpUMamrA7Y3ZbA3JQlbtQEht2B2xPobWcIDAaIlScZi6AjGUN3axyThTLGJotYOkeGe9HmHkef4q6I5j6nPYle2+o16h+8EX2Uv2H489nAk/8j/fbw8qC2sgDQVWP5ZnLvBpCO96HzC88BMfXrfjQkYc8ZFUTQ25ZAezKG1ngUU8UyRrNFOXHkbOCSzgZOdm6n39vdlnCuR9opaV13N58J9NgbX9ME0lNF9LSLDQPD08S9py3uiCtZ7s3AbimOKpUKzjnnHLz+9a/HAQccAAAYHBxEIpFAd3e3570DAwMYHBx03kMLI/J38rcgXHbZZbjkkksC/1YPECHSkYwhGYuyLSAM0B2QDIB0riS9OyDqvrc94VqOJHcHpO7e9gQMw0B3WwLbxnPS3Mn7etoS6LXrHp+SH3xkV+XhXuVWs7u8dqvVHyThZrzdDYQPQMWE43o1DAOplpiSYMiVKsjbpxKTsSha4mrRAplcCRXbKtCRjEMy5ygAoFwBJvIW90jEUL4HcapYQaFkcW+JR51YDBmYsLh3IovO4jDGh7eha95ypfo1FGDHHFUQcTZfPW1xTI2XMTpZwJI5bcJHjGXdOdKdo+StL+NEHLXG3TlSUqAMT7hzezwaQSoZQyZfwshkQUockfAK7vzKQLliIm2P8a5Wan5X+OyNxm4pjs466yw888wzePDBB+te14UXXojzzjvP+T2dTmPx4sV1q49YT0hGa0ehS4oE0oG72xLopLJiy+4O6N2FY32RFWa21crPXVbg0AOfPGMiX0KxXBFmya5UTMfEa3HXbrWmo2THI3z4j8CSo5lv+81jm/BF6kqDBz51nNRCQ/Dxnz+Kh9dZl1wdOLcLfz77DdJld2RyOPIbdzu/f/Wk/fCx18sLjF/cvw6X/e0F5/d/fe4tzriRwXt/9CDWbrWs4K9fPAc3/l92O/mxYecEjv/+/Xg++TG0GgVM5Qs1W8A0OLBjjsq0OGq3NoAjinNkZ2vcuXJEVtwUyxUnbKG7LeHMkbLWmxFn45t0uGfyJemYUlJPl4e7XNn0VJF4JdHVGkdXCMtTo7HbBGQTnH322bjttttw7733YtEi53pUzJs3D4VCAWNjY573Dw0NYd68ec57/KfXyO/kPX4kk0l0dnZ6fuoJIiSIsOluVVPYdAeORyPOkXYZgWKpe3fw9ThWK0lx4+euOABck3G8StiJkMmXUKEGH3NXRgKy9Wm1+oOII4Gr54VBr6uaiAUZmKaJZ6j3vziYUcr78vRmb11r7DsFZfHCoDfD8DMK3AulinMPIAC8sF0tW/FTW8YAWIs1AJhl3afrCsdyZDhWefKvrMAYpza/ZI7K2BtA2bKkfJfi5pMIMzKvk39Hsmrzu8VdcdNuv68jGUMiFnGEnYpnoNHYbcSRaZo4++yzcfPNN+Oee+7B8uXe3d1hhx2GeDyOu+92d4EvvvgiNm3ahGOOOQYAcMwxx2Dt2rXYsWOH854777wTnZ2d2G+//RrzQQRwO6Bl1OtuVxMoo45bLWE/R74TTuTcybWzxXXLybrVxqusXmqWp1HK6hWlXBQy3ImASsYiaIlHHbNtdcyRJRahF5L6wxFH/IME5AqDhG0dfFHhSoPBdA7pXAmGYeXHypcqStcSkOzExOW8QTExXRX3QXnur+7KolCuIGbXvStbUDqducG+joGIo7Lu0/UFFXPUac/PxBovLzCs76iLso5br4vLk81jZ0sM0YihLDDSdt1k49mj6Blw5vc2V9hNFsrIl8Txm0Q8Es5aHE0jzjrrLPzP//wPfv3rXyOVSmFwcBCDg4OYmrLy8nR1deETn/gEzjvvPNx7771YvXo1zjjjDBxzzDE4+mjLVH3SSSdhv/32w4c//GE89dRT+Pvf/46LLroIZ511FpLJmRHISCxExGJE/pW1vow7Adl2JyQ7G4lOSDpqazyKRCyiPHjGKLcY/a88d9dyZHGX3534hVkPS1Rqt1rjULIXeoHliNy5dPxK6/LOLQriZvOINf4X97Q5x5PXKdxFuMG+rua4fay6N+yckD6WbZpmFXeS3V4GRMTtMy+FRT2WgFS5i5AIOVcc6UMGdYVJxJErTHoc67ikwHDm9ziiEQOdLTG7vIw4cjePgLrAqJojVTe/lFcilYyBhLDKuAVpr0AY7s3AbiOOfvKTn2B8fBzHHnss5s+f7/zcdNNNznt++MMf4h3veAdOP/10vOlNb8K8efPwxz/+0fl7NBrFbbfdhmg0imOOOQYf+tCH8JGPfASXXnppMz5SIKqtL2qDb9QnUIgFSsr6kiNuMXtXRAkrGVdFumbuXmGoMoBc7oKBr91qjUPRzr4ba2G+JV8qO7lOXreXdaRR5coY8t7Fva2OwFDJ6L7RFkfH7mPdNJ7OlaQn7NHJIqbsQPCj97BOzapYrRzuPW01cSfiqKItR/WFLZrLiKCzxTvPyB5pZ1nXZeZI+rAN/Qxpy1HOtTx5uEvUXa6YTrxTV2scEcpyJePVcF164YRdM7DbBGTL7OZaWlpw1VVX4aqrrmK+Z+nSpfjrX/86ndSmFbTpEqB2JtIB2e5RT0CtE7KEmexxT+bAV+buHfwyMUd+Ydbj8+c7Ad3OaTW9kNQV5ZKz0+ZZjkiG3pZ4BAct6gagZn3ZMuoKjJa45TJVuy/Keu8ec9vR1RrH+FQRQ+m803d5IEJmbiqJvfotq5WKsNti30O4uLcV7dkYgBHn7isV7mVYn1vHHNUZtlvNhFE9P0sIhGK5gqx9XQZtedo0Imk5ctYG26ugeKKXzJGdfquXhEuQnoPpOXZ0sqgk7Ei7qR7WaQZ2G8vRbAEdUG39K7+zME2zyq2mEtDtDB57VxSPRpCydxkyuwu/uFFxq+WKZeRLFW95hYnH8afbfDtb447Z1+MWdO5Wm7mD8jWBEiVQ4uyYIyIGFlBXvgxPFFCRDKomGYPndbVgYbea9cU0TUecze9qRb9ibi0vd/WMv07G4K5WLOxWu8ewUKo48UkVYjnS1tD6wg7I9liO2uUtR7QQIAJFJeyBrAF+y9GEZEB31QayXd5yRPi1J6LORlMl7GG0RqtXM6DF0QwD260m7kTZQtlJIOmP21FxTdGBgir1V59Wkxd2RMBEIwY67EDsMG41UiYaMRweHp+4vj6kMaDFUZRtOaKvFLDyY1kmfNXEo30dSfZ9egykcyVM2jv5eZ0t6Cf3RWXkyrvck5jbYdWdyZWQK8rF/gxTGd3ndbUqcd+RycE07UBww7IcVXTMUX1hVgdkq1jHyTyWsgOqAXoDqbD5tMuQjSAgZ11nnSaWiRly40Fdi6oKd1Ys7WShjEJJLoN+o6HF0QwDL8+RyLVIOmkiGkGr7WJQyYXhHzwAkEq6u5NauAvLUgPfsK9w6KyVuz15ZGjuTkC23mXXFUQcRRNAhD3NOBnZO5KIRyOOO1Q2cy59pcEcO2Ow7C3l9A3prYko+lP2RaCS1p9hintna8w5sSZ74iyYu5wopG9Irxg65qghoJJAkjmOzDEkESgPfq8AoLb5dPLI2WMkZidyBMKFTZCM3hmZuX3Szc/kcpc/LETffmDVHQO5qWemWo+0OJphqApqthV22b6/hwfar+sXGHLH4d2AO4IOIjAkLo+t5u7WLXKT+H3S9HNUjvJ7uNvCLkOlKHCO8mtxVF84J9XYwdiAKzCIOCBXIgxn1C1H5EoCWYFBW24AOG61HWnV6xiSMAzD+QzkM4nrt28570g6HGSFHS3MKiTmSPfp+sKOOSqbrluNiBPPHMNA0BzlWF+m1C1HgPz8bppuDjvCvSMpP7f7U8xY/1ff/JIyEcVULc2AFkczDP7j7C3xiJMHRSSOyN9TlLm1W0FgONYXqnxni/zg95teyc7ENIFJgavB5U5PHPIBhy73AMsRPfi1W60xkDipBtCXBVvCxLlpfELsXjJN07W+dCQxp93dycrEYDgZ1du9dcu61VyrV8JTfljC8pQvlZ0+29eRdDjskhRWLvcEZTnSbrV6wqSSQFZZX3IloWXfP7fT5Sck5tfA+V3SOp8tlJ0Tx10+t5yMV4AIOzIne8orca+2PI1LCMNmYLc5rTZb4FfYhmGgoyWGscmi1Qk59wOQTtqRrFb3YY7DA/KDt1iuOAOA1NkSjyAaMSyrV67k4VXF3TZLdySjAdwlgslz1VavwMFL5zna9mTVc0zTvuW8Jc7zBjExVSzDNIG2RFT85gCMThbR0RJDXOIePD8Id8s1qV73lB1/0xqS+8hkAZ0tcUvM77Cv1BCJo6xXYBCRJGM5msiXnCD+vlQCLbEoIoZ1V9totoD+Tn7dI9Q9ggAw0KnmVnNuSLc5O9wl3GpEBMWj1kIbt+9UmyyUMVkooS3Bn5pp7tpy1BgUikUkQWKOvG61csVErljhjh1/IkTAtczLCBTe/C6KOSJ/j0cN5+5Bv7AzOJNGkEtwurjPVMuRFkczCMVyxcmbQivsjqQljkS+4WyhugN2Sg4eIDhuR9b0SgsQMmEYhhVcPT5VtMUPe7GayJcDuMds7vJWq07K7NsRZPImliOzAvzs2KrnGAB6hLWxwc8FLUYtdTebe2/Qi4IEkI5rilhvFAQGcS21J6KOmOhtT2J4Io/hCbE4IgKl1+dWkz2tRsoTixXhLlN+mPrckYiB9oR16Wy+VMGuiQLaevlTM829Yuij/I1AvlhCEgAiESdtRFvCFeSZXJErjsg8ROI4AcYcxQARIR0ey77c/E5b1okI6qCE3VSxzBXkmQCrVWDYggp3hfm9GdDiaAYhS4kfWiSQ/4usN6STtgeVVTCddrVWu6bSgrrJ81viEc8lsUQciQbQxDRxD7J6eYRdWy9w4PuAV6svLS6WK55A4Ll2kLAs0rmiwzUejTiLpQxMWO4cYvrubIlzLW1+FEoVDFPxKgOpFudEjAzGp4qOuE5GI5ijxN3EUDrv3Gzf3Rq3JlojAhz+cW7ZqpgjBYFC3kPKAJYFyhJH4vK0awqAI6Z2pOXcasNUzJHFI+F5XY67VcYwDPR1JLF1bArDE3ks7uVfvDuSJeIqAZPcrVbRbrV6Il+w5pFY1B2XZAOYzpWQzpXQz7l6M8gtpmR9yQfMkU55/ncfNLe3U8JuIse3VjrCriXIciTeeDviiPIMqMzvzYAWRzMIpJMkYhEkYu6iTAZTVmQ5IoMvQGBkC2Wh6dQfsGfVLbc7cDu/t0u53PmDl89dQhzl2DFHHmFnGMBpPwt8xs/ufQXf/fuLzu/nH7sPzjpuL2HdBO/+/n1Yl846vz/ymeMxv0vOHvPs1nG840euYDtsXg/+cObrpOv+/t+ex0/vX+/8/rW37o8PH7NMqqxpmnjLN+/Gjry14EYM4MnzT/JMpDw8um4X/v3njzq/H7tsLq4740ipev2uKcf6ImU5cuONCFROrPndauTfrH1fVDLGtgIUShWnXzkxR47VS+wSZHHfOjYlFXe0i7phncQcactRfZEvWu0b8/WLVEsc6VxJbF0PEDcpBYHAnSMF5UlfTVFjWkXYZR3u7meX5W6aplO+g7KatUtybxZ0QPYMwkRA5wfcTiRyq/F2FsQnzgMZ3ME7G7mB7xdH7Um18oG7IolgR3dnE25XBgCPrNsFANhzbjsAYPXGUalygLXQrrPvxdqjzyr/6Ppd0uWfeHUEALDcLrt2y7jUhY4Ej9rc97C5P6HAffPIFHZk8khEI1jU04qKCfxzw4h0eT/3f20clUriOFkoO33SbzlSERikLAClwGZSnogilfuiiLCKRQxHkDtWLwWXIG2hIxYsGWFHu/SIW62iLUd1BUmVYET84khungmyHKkIhMA5UlKgOHN71eY1wLquzJ3f7/KlCkr2fBBGXDULWhzNIGQDOj8g71YL8uu2xaNVf2fXHxD3I3laLWjg0s+StjwFDL5SxXQCb4NQqZhOMj+au+zAB6zdzbPbxgEAH3v9cgDA01vGpC8hfXrLGABLGL1p77kAgGe3pqXKAsBTW6y6Tz14IXrbEyiUK3hhu9wN76VyBc/bt8Gf8bplNp9xhbrHAAD7zk/hqOXW/WbPblPhbpX/wJFL0BKPIJ0r4dVdWX4huAt8a9yNGepxEtPJH23upa61UTlO7z+tFokYzgka0X1RtLCK2IqK5GiSu4jTa7WyuMsLQ9rqZToB2Voc1ROkfQ3fSY2U5BwZNL/Lzo/5kpvgN2iOFM/tfMu+rLALw51+dntCnXuzoMXRDEImIKIfUOjAAeUjVMZpXvlKxXTcVx6zr6w4YnCXtd4ElacHEq887XZrDyHsAGAwncPoZBHRiIF3HrQAhmEtUrI5c160xcl+Czqx33zLPq0iMOjye/V3AADWD09IlV0/nEWhVEF7IopTVs0HAGwYzkpnanbr7sK+81M2d3lx9eKQVX7Voi4s77O5S9wuT2KkaIFAjgqrZBym48ycXEcKMUfe+q1niTJ07woo26WQs8afkA+gXIICcWSapve0GnGr6dNqdUWFpIcwqt1qgHgTFjS/k/k1X6pwM0XTG2N6XqSt6zyQmCT/5rWW+V02AaYTT5qIOhsJFe7NghZHMwhB1hNA3nQadFrNU57TCSftI+j+8h2SGbKDzK4AZToV7aoCuEftUzyi8qTuWMRAMuYNBpfhDgDrdliL+bI5behqjWOBHSv06rB4kQfgWEr26GvH3vMsgSErbsoVE+t2Wu/de6DDcevJCAyLu1V2xUAKc9oTjijcuEvuEtQNFPd9HO5ydU8WStg8MmVzTzluPZnPTiwsPe3ViT9lrhUIOl4sm5iuQl1RQrvlZDMWu/dcBYgjKctRtbBzhSFfHE3kSyiUXXekaejEpo2AadpuNcO7bMpaUJw5LsDyA/Bda8Sq35aIeg5akABn8fxcnSrFy12UJynotJr1/1yxws0rVuu61ixocTSDwDJ9yguU4N1Bu8QAInVHI24eDICRSJFTnukSFARVs9xyMqbXLDX46IBz2WByANg4YomBpXOsxX1Zn3Va6FVJgfHq8KRdrh1L7ZNGQ+m8lPVm29gU8qWKHfPThj0UrC8W90mbexsMw8AyO/ZHxrUFABvt91ncrbKbRial4obI5+5pi6O3PYE9++SF3XhAYjmVawWCrC+yt32PTxVBPh4tcHok7wNMByT0I//PlyrC753HXXQse9S+Rb0lHkFbIubGHOkkkHVFpWIJACMaHHMUxvoSj0ac+ZY3x2VscVM9v8qtDU7IhH/zKnvgJuA0saywE4VczFRxJH1a7corr5R+6Kc//elQZGY7WG41adNpjuwO/OXFA8jpwImoR2CQZ4mO8tfOPTgYvaMlhh2ZvIC7LQoTwYNPJuZoky0wltjCZtmcdjz0yi5ly9HSOe3obosj1RJDJlfC5pFJrBhIcctuHrXqXtTTimjEcKwvxJoky30pxf3pLeNS3E3TdIXdnDYs6LZSABRKFezI5J3LXEXcSbvtMVde2AUJhIgd4Dw+VcT4VMHJOh2EoKy9sknx6FvG6ZOhsjeNB3HvSMacpKfjU0UnFw6vfHeA1Usk7IhliXxuk1gydMxRXWES8elzq3VIx2VWx0Vav8eRK+a55Ym4qT6sI2s5YggUxZhSmnsiFnFyc2VyJc+ltF7u/INGu704+uEPfyj1PsMwtDgKiSzD8iNrOnUGUJX5Mmr/nSMwGOKGnMQplCrc481sq5diwCDD9BqGu+yODgA27aoWR4Cc9SVXLGO7fZv68r52GIaBJb1teHZbGht3icXRFtsttbDHcuURgfHqriwqFdPjp+dxX+xwl7d67coWMJEvwTCs8rFoBAu7W7FpZBIbd2XF4miECDsijuTdakGuJcCyoIxPFYXuqSCBIuvaCioLuJYjUcxRkEvPMKxs1yPZAsYmi07G7SAE5Z0Jy5241XTMUX1Brg/xn1brdDafohNfjM1rMorhCX7KEqdsVdiCVbfotBtr8ykTz1osV5wDMUHze75UEHAPnttTEnN7MyEtjjZs2FBPHhpwB0C1uJG7wkN4YkzSNeUpS/0+kSsh2REsjlhH+aUTWNZgemUNPjJpkWBH2kLgxybKNQVAyTVFYns6W2LOaaulcyxxRJ7LA7G+EHGzuKcVsYiBXLGCoUxOmCvJ5U5cgjZ3CcsRec+CrlbH0rF0Ths2jUxi08gkjtpjDrf8llFL2C3qtTiS4/zDE5bo4iWyZAmU7tY4NkLeghIkMGRdclXCjAiUbPjyI9mCBHe2OFJ1J7riSFuO6gpbfLKO8vM2YaVyxUlbEca6zrKOO5YjyXgn//zaKRFMTouXIMvTrmxBKia0mrsOyNaQBNM9pHjckpVrKIxfOBoxnHvCpNxyIU6r0UnCwpheWfFOdE4NUf3VliPrX5mg5o2US424JInQkRJH9nsW29aXWDTiWB22jfGzNRfLFWwdm/JwJyJJpm7y+YgorJV7qiXuBIRvt3mxEHQRJ+AKjjDWH+JqmiryA7qZwoxcXisIihZzZ5cvlitO6onpEHbardYYODFHjIBs/hzlfjdhNq+OdZyxeZ0o8HPB1RL3Q0RfMhapujFgWrjv7pYjP7Zs2YI///nP2LRpEwoF70Twgx/8oGZisxG1RPWbpsnOUi2h0FllAWtATRbKoaw3MtynimUnOLbqqKkSd++OLmYHO+aKFWTzJc+xaxr0vXVEGMzvtiwhmVxJaAEZtK+bWNDtulHowGYRNtvWl8W9roVoQXcLto5NYfv4FHg3pm0fs64cScYizt1gC23uQ2nrb7xrRFzubt1LVcSRz+pFnpUezGDr2BTXpTgeYPkB6Nu62SIhX3ITSHZ5bjm3ArpN0yrPilliu9XIUX51y4/FXSxw6L/RlqcuX0A3K2ZJu9WaBCI+fZYjmQ0cCaj2334AyHkGmHmK7LKmaZ3w9M+fBCy3msudLaxZJ5FpPuG4u+0mur2hGQglju6++268853vxB577IEXXngBBxxwAF599VWYpolDDz10ujnOGkwws5iKB1++VHHu5Qqj0FkdmPDZmcnzBUoNPm3yN8Oovs1ehjtP2MkEO24bt8RJX0fCWZA6kjGkkjFk8iUMjuec3ENBGLTjjeZRMSZEKG0TWE8AYMuo1/oCwHaljQrLE+4Lulud2KS+jgQihpU8c9dEnnsBazB3SyhtF1itTNN03GqLe1xxNb+rBS8MZpw4LBZYAqXLvpCSFxRNyhqGt89FIgZSSetKBF5Ad1DMD0Adp5c8rVbNXV4cpVpi3mPZiZhz1xUvoJsljgxtOaorSMxRxJ8EUkogBAdUA3L5gjKMOa4lHnHvR8uXmOJInGBY7FYLXBsk5mcWd8KlYkJ48W0zEMqtduGFF+Jzn/sc1q5di5aWFvzhD3/A5s2b8eY3vxnvec97ppvjrAE7IFs8+OjFvy0eZmcTPHjo12SC7phHTSWEVUciVrV7kOHOqtuqPyrkPmRbT/wBtCQYeUhwESmxvgxQwcuyZYtl61QY4AZkA8D8bjm3msvdFQGxaAT9qRYPtzDcRWXHp4qOe4i2PM13xJWcW40lUHhZsp2LhlviVQHrXQrWG5blJ2xAd7eES5BVNhIxHEsSj7tfmOmYo8bAzZAdJmwh+Cg+QFvX2d8fS9yQ+9Gs8urzu3vghV03b22QOTDD4t6WiDppO2aiay2UOHr++efxkY98BAAQi8UwNTWFjo4OXHrppfj2t789rQRnExyFzbD8FMoV5n1btLr3LxZyOxue9UUccMh0q5FgRQl/vL8sXXdo7hLBjoPjljiZxxBHIgvIjnR1efL/0ckiN+fNjkwepgnEowZ6qaOwJAnl9nG+wAiy/ACu2BFzry5P/j+YznHjGIh46mmLe6wcC+y6twnqDjrxBci5plhlAUpc8cQRo7z0cfrJ6jQCANAl4RJk1W09T0XY2f1dxxw1BiTmyGc5kpnjWMf46fJSlvkQc6QnpnOavQoyqQBYbjnDMNCRmLlB2aHEUXt7uxNnNH/+fKxbt8752/Dw8PQwm4VwO6HP8kOZG1kK37WeVJviZSw/QfeqEZABwNtdMI/y29wLnPT4rARn9POkjopyd2UccRRgPQFckSBtOaIERldr3MnWTcRTEMiz+1MtHlE7X1LcsLjPV+buWp767f8XShWuBWTI/lx+ixs5XSdyCbIsKE5QcwjLD/2alMDwBVT7436CUChVMFWsDqimf6+Zu4zlyeZqEkuGqcVRXWG3b8R/Wo2ynrA2E6x0I/RrPLcaSaLbnqie3935OXiOyxUrzJhOqdPAHO5ylv3gg0Ze7jOv74YSR0cffTQefPBBAMDb3vY2fPazn8U3vvENfPzjH8fRRx89rQRnE9xF3jtpek6MMRS2jEDgqXvyN77ZlzN4mX5ldzCzBi9XmMlYraS4c9xqDOuLazniL/KkPC0SDMOQck+5Zb2xMcRNJetWC2P1KpUr2JmptnolY1EneF2Ou08cdYvrzhXLTu4Uv0BRcU35T4sBcvmCWAKFxP0A7ESSnngn327Y5c52CfK4hxKG2nLUEBC3WsR3YssfOxMEVqoUQFGgtFT3GVI/y3JFNp+GUR1yQdfNFHYc7lIHZkhy4oDyLndxot5GI5Q4+sEPfoCjjjoKAHDJJZfghBNOwE033YRly5bhmmuumVaCswk860+HoBPJ7Exk/MJ+qxVdnuUTp2+M9guUWDSC1jg/FQArORr9PC53xp1y9Gu88oMCgUHcboF150vOpORPmDjQKRZHQVYnwLUcDU/kuUfSWW41J+aJI1CGJwqomJb4JjfCh+PuE3aUS5A14RLhETFc6yKBTJZrVp4h+jUZy5G/PB33wxIoTkB1gAtbhXvNVi9/zJG2HNUXJAmkoR47IxO3w8+QLZ6fRZvP9kR1fyWCpVwxnc2KH/yYThm3nHjzOxMtR6HCw/fYYw/n/+3t7bj66qunjdBsRb7k5mVJJasnTecaDcYACrrUkC4LCDowp7woWRf9OsstN1UsMwc/zx8vd9qNXb5dYuIZErjVBtNsyxERCB3JWFX9jluOI1BYrqne9gQS0QgK5Qp2ZHJOBmpmeQZ3nvVm0HHpJauO+8/rTOL57SLujHgn+/dcsYJMvuQkmqNBH4X3T9jkKD/PesKNOaohIBuwrD9jk0VmeZKCIOi6hG6J60dYmcGlufs/u+1WM/RR/vrCDLYckdiZTL6EiVwJ/QHZK6TiIqVO5AasDQKBkuVsumlLUiZXCjwhycpBZ3G3k0iGPk0s9ko0CzWdnSsUCtixY4eTHItgyZIlNZGajfAmCavuoCnBAHDcYkF+XYXTbkHlUwKfNuHkvzGa5r6Tcz+alFtMwmwbWF7AHajNcsRyi3nK81xTpG6fuDEMA/2dSWwZncJQOlgcVSqm0K3GizkaZLjFVLn7hVlrIorOFus4/Y50LlAcccUJJRBY+U9qtb6wjuJ7yjPccrLcWZDhzrI8VSqmsxD5k0B25bYC6+5h1huEnZk8RiYLWD6nnZtBPgjliokNw1kkYhEs7mmDapqabL6MTSNZLOhuDWwLEYbSOYxPFbGsrx2JqBr3Ytni3p6IYkF3qxT39uIogOrTaoA1z2TyJWFMaFBAtcw1GlJeBcYcybr3ErAspR3JGCbyJWTzpcDUFzLiJkyCYbr8TAzIDiWOXnrpJXziE5/Aww8/7HmdTGRlfTu0MkjnaolHEAsY6KLdhZRPu8BOtsXb2bQLMmTzOj/NiW32ZU8cchmyOWbbBL98rlh2dvJVAqPT69oKWjwGGeIGkHNNBR3Fp+vfMjrFFGe7sgWUKiYMA1WTGm05Yn3nLGHl4S5j9UoFl0/nJjCUzmOvgK0078QWea1csRKbpgLElXvprLq4KVMCI6h+kVuOJ27osqx78dxLZ6stT268VHDMUiZXAvFUOm61iPWcfUfuBn51d2A5FubaP2EQBbBXyLIA0A5g3xrKD9g/YRAHsLdimWX2v0aUF/fDCHvIczavUteHiOdI0fzKSmTbnoxiIl/izO/BKWZoPryTcjLceWkMmoVQ4uiMM85ALBbDbbfdhvnz58+4zJYyuOqqq/Dd734Xg4ODOOigg/CjH/0IRx55ZNP4uOo+eAdFBhXbNSU22/KyqPKC7jqcixX5lp8gsyvNPc1INMbbFdFuNdYiz+fOF0dEILTEI+hs9ZaXcW2xYoYAObcar/yAwHpDuPd1JKvS+hOxNlUsI50rBS7kPGE3TyHmiCUMX94xwbRcOW61ANdUSzzq3PY9NlkMFEcitxj9Hj9oqwxPnLFcY45LjxMMbprWWA16D89qJUpDQF5viUecS6CjB52Ox7Y+hhSm0NueCBS7NEyY2Dw65YzbSMQ6pW4Y1hU0QQs4jUK5jA3DkyhXTEQMwLQ/bzIewbI57YgK1oORyYIjukndANCXSqC/Q8x948gkJvPk5JhVPmJY1+a0MhJnEuRKZftCZ2/drYkolva2IcLhvnl0Ehum2jDU/7qqv4liZ1hXaABi1z99FJ8rUMJuXpMxDIFn2ZcIqGbM7XRyYj7314hbbc2aNVi9ejVWrlw53XwagptuugnnnXcerr76ahx11FG4/PLLcfLJJ+PFF19Ef39/Uzi5QcXBg1tkfeGJo9Z41MmimmVkUZVJpMi0WjEuNazmzjc5BwlD+iRIrlhBq+8oq2maVP3sNAYs7nRAs194GYaBga4kNo9MYXA8WByxTroBwLwuy5oT5sQX/UyWwGAFYwOWwOhus2JnBsdzgQsxr25HmDGEXbFcwfCEZTnqD7B6kdeGGGkMeOKGvL4jk8f4VBGLA/7Our6Dfk0kMNoS0SpRqVI+qO5kLIrWeBRTxTLGp4qB4ijowlyCMFaro45+M34f/wM+97ungAJw+UkH49RDFgaWB4Br/rEeX//L80jGIvj5Rw7Hkct78en/fRJ3PDeE/okk7jj3TYHxVIB1wvE9Vz+Cp3Jj2H9BJ371iaOwayKPf//5oxieKODfVi7C995zELPuFwcz+D8/ehCFcgVnHrsnzj9pH9zwyKv46q3PAbuAG999FF6/Vx+z/A/vfAlX3v0y2hNRXPfxI7Hf/E78569W48FXhrEk14a//ecbmfNQvlTGO3/0IF7KTeDwpT245mNHYNOuSXzgF48iM1HCxw5chq++c39m3Zfe8ATufG4Il7VVrxGi2BleQLXjVmNY9vOlinPgJcxxet7a4OHOimeVCKgWhXsEnZSzuEc9dcwkhDqttt9+++3W+Yx+8IMf4JOf/CTOOOMM7Lfffrj66qvR1taGX/7yl03jxNtZAGLfLi9uxzAM7nFPemfCuoKDVzfPp63CPWjiaIu7J0GCTNaThbLjZmBdfcKrm2e5AYD5na2e97HK89xqO9L5wFNbE/kSsnaG6UBxJXBtibiLrD8u92CXHsAWZsMTVvLKWMRAX3t1+QFB+apEhj6IYm9kXVuqZQE3bihM3fTrYeoPW/bfDluET5+wAgBw0S3POBcp+/HctjS+ffsLAIAvv2M/vGnvuWiJR3Hlvx+CPee2Y0cmj4tueSawLAD89IH1eGrzGFItMfzio4ejtz2BFQMp/ORDh8EwgN+v3oJ7XhgKLFsoVXDuTWtQKFdw/Mp+fP7kfRCJGPjY65fjg0dZcaqf/e1TTHfo6o0j+H/3vAwA+OZpq3DEsl60J2P48YcOxcLuVmwamcTX//I8k/sP73wZLw1NoK8jgZ9++DB0tcaxalEXrvz3QwAA1z38Kh5bvyuwbDZfwnPb0gDCZbnOSG4Ag1IB0HNXmJhSkVvN2bwycsmxrv+gX8sWyoFznGPxCjgpZ5W3A7pnYMxRKHH07W9/G5///Odx3333YdeuXUin056fmYxCoYDVq1fjxBNPdF6LRCI48cQT8cgjj1S9P5/PN+Tz8XzSgNg3Szp2kF8X4OejoC9+Dd6ZWKKF1YFZ1574y4ssT0HCMBLhZ1Elz4wYCDSpi0zWrIBoAmIBYQkU1mkzAM4VHoVyBSPZ6hgS8sxUMhbYdrJutSBxQ3NiufVY16YA4gzfhHt/Khk46Q3YMVA7MsF181xL9Oui4/Q815awbB3Ejbf+4LghmRxNYer+zAkrcOSyXkzkS/jUb55Esew9KFMsV/C53z2FYtnEW/YbcAQJYFkaf/DegxGNGLjt6e3481Pbqp7//PY0Lr/rJQDAV//P/k6yTwA4YlkvPvH65QCAC/+4NlDgXHn3y3huexo9bXF86/RVHgvJl96+L/boa8dgOoev3vpsVdlcsYzP/e5pVEzgtEMW4l0Hu5axzpY4vvueAwEA//v4Jtz74o6q8qs3juBnD1jJir/57lWe1BXH7dOP9x1u2Sc//4enMRkgEr5z+wvYOjaFhd2tOGFlteVIdKKXe2JMkArAXRuigWNN1q3G2niLQjZ4Lj3yeVipAIRWqxnsVgsljk488UQ8+uijOOGEE9Df34+enh709PSgu7sbPT3sG8RnAoaHh1EulzEw4A3lGxgYwODgYNX7L7vsMnR1dTk/ixcHGflrR19HEifvP4Ajl/cG/l1ktuWdNgP4QXu8i18B6rQaY2dBOLGEmXO/WoiTdl7u1Ys07Q4MikcS7YpYV4cQkNfJ/Wd+8ARGIhZBXwc7maKTHTvALQW4AiOMW41+nVWeJ+y62+JOAHpQhm+Xe3DdruUouN1IwHFQUDJQm0ggoqPAyHLNy5FEP5MVFD3uXB2iLq7ypTJyxQqzfv9JPRb3oM8djRj44fsPRmdLDE9tHsMP73zJ8/cf37sOz21Po7stjm++e1XVeDlocTc+dbwVYv3lW57x9JtcsYxzfrMGxbKJE/cdwGmHVrvtPnfyPtijrx1D6TwuvPlpD/9/bRrFj+97BQDw9VNXORsHgrZEDN9/70GIGMDNT27F35/1zsXf+/uL2DCcxUBnEhcHuL5et2cfPvEGS5x94fdPY5TajEzkSzj3pqccYXXS/vOqyn/pHftiflcLNu6axCV/fs7ztwdfHsb1j2wEAHzr9FXc2BlR2EPQHCm6RkMUM0TmTVHdYQ/McAOqqTk7SFzx4kkB11vwmnGr3Xvvvbj33ntxzz33eH7Ia68lXHjhhRgfH3d+Nm/eXJd6jtlzDn764cPx2ZP2Cfy7KOCPd1qNfj3IrUYnCQsSGPSuKNA9JHSrkQGgftLOy716sRGajAU7Op64oV8PshyVK6YjmlgChedecsQNw2o1j4r7CWp3kVuNnIALEmb06ZQg7oZhcN1yImHWZws7EpfkRy3Wm1zRzQkWVL4j6d52H1TePS1WH8sRz63nya4d0GfJM4tlM9DF4tYdLCoXdrfi26dbVpSf3L8OD79ihT888NJOXGm7pC555/6BR7YB4Kzj9sKBi7owPlXEZ37zJHJFy11y8Z+exYtDGfR1JKqsPgQt8Sh++L6DEYsY+OvaQVz/8KsArPv7PvObJ1ExgVMPXoC3Hzg/sO5DlvTgP9+8JwDggj88jfU7JwAAtz+zHdc8tAEA8K3TDmS2+/kn74O9+juwI5O3LWRWMPAX/vA0No1MYmF3K776ruCYos6WOL7/3oNgGMBNT2zG71dvAQBsHpnEeb9dAwD48NFL8cYVwWf7RNbxCdGBG94GUBRyIbjbTXqOFHIPtuyT08yBG29OZm/rmeI8Sc1CqIDsN7/5zdPNo2Ho6+tDNBrF0JDXLz40NIR586p3FMlkEslk8ETSSIhSxMsG3fE6MFvdW2VLtunUnyiMd9RzOrjLTBy8kxissgA/Zgjgu7Z2TeSdEzvEQuTHvM4WPLstHXgc382v1Fr1N8AVPflSBeNTxaogWZFLcICT60jk0iPcN41MBosjctkuo26ygLFM9SLrDU9gkNNi0YgR2GcMw0BnSwyjdiJHv3gUCzO5E2NhhB2xOnW2VCe/BCzLbSxioFQxMT5VRJvPmhpY9+QIsPo6oDgFHP8lnLJqPv79yMUYfuJmPPOr3+GpZW/CD16Zh3LFxPsO7sM7h68B7gZw3JcAck/Yy3cCmx5BfMnr8IP3HoV3/r+H8M/1O3HL9/8LyVgEtwy/FYaRwHf/7SD0DT0MPPYPYNERwD6nuDzu+ToOMiv44gmn4tI7N+Ortz6HXc/dizmDD2L/qcUweo/FJe88wHrvfd8GynngmLOBNttavvlxfDb6N0TmxnDVzoNx+k8exnH79GP+2h/js9Eccod8AscRl9a2J4HnbwXmrAAO/ncAljj71crHccvYM/jVC8fj364uIB4xMLHpKXw+/ihOOeQodLYc7/J97KfAxBBw8AeBOXvidXv24ctHxTD5xI1Y88c7cd+LH8Gj60cwPJHHud3/wH+3/RPYEQP6qw8iiazjIgsKT1zxbgCgXxdajgK8AnT5oLrzpTIKtnuWN79nC2UBd/7n5uVJahZCWY6efvrpwJ+1a9fi5ZdfRj7PTprXbCQSCRx22GG4+243H0ilUsHdd9+NY445ponM+JBNER9md+CaTflpBNjlRW618CftADoBZvViwzP5Au6ALpQryJfYsTOioOYdgQLBem1uKhmYmwrgiyvXchQsvsmJM2F5oVuN7RbzJ3AM4h4UszRo3zfHEkck8WOa4R4a48TdAAKBQQkEVhoRJ8t2QOwLL+bHW3dwf3XTEITnzqrbMAw3y3Ygd5Kdmyr/xC+Buy8BHviO89JX3rE//q3rBfyHcTNyrzyIYtnEW/efh0vfvheMB78P/OP7AP29rL/Peu3VB7BXfwrXfPQIdCUjeH/ut3j3xG/QFi3jO6cfaImTTY9Y733Fl1PpHz8A/vF9nHHEXPznm61bFIqvPoaPlf+Ad7U9jV994ki3zR75f9Yzpkbd8tvWIPbQD/DpBS9iv/mdGJ0s4o9PbsVHo3/H2bE/4Zyju933Dj1rlX/2Zg+F+S/fiDMjt2BpfBxPbR7DExtHsTK2Df8dvQXLt//Vy/dfN1jPGNvkvPSxlRWcHfsT/i36AG57ejuGJ/JY0d+BM3seR/zhHwIj6xAE50RvwGagWK448ThBtx8A/HQpsgde2PduWvMec37nlKc3leK4IXXupD1eM0kgDz74YG5uo3g8jve973346U9/ipYWft6KZuC8887DRz/6URx++OE48sgjcfnllyObzeKMM85oNjUmRAIjw8kSTb/ODfhjlCWm02yhjGy+hD7fPVyuW46/MwniLjopZ/Eiuyp2zJFo4iA8SW4YwMo2TAKGmdYXyjXlP2YrEif03wIFhmP5CbYckfLkOP7KeZ3O61MFK38RwBY4vCSUctzZbjny2nyWOGp1rY1TxXKVBUQ2IFskjljgurY4CSgBV/SMTxUCj1bLWo6CTrvJch+eKMh/9sM/Diw8DHjqN85LrYkoTnz7e/HKv3qxIHYYrj7wMJy8/wCM4hRw1JnWm+jPtfR11sW1i48GYLn57/zscXjqpn9HuWLilncdi6Xz+qz3LjrCesaSo73kjvovwKzASLThwlPm4637z8OLj4zguWwUJxzyZiTmtHs5l/JAS5f72rwDgKPORHLeKvzpva/HH/+1BeuHs5ic+CDQUUEsRbm05q60OMz1hSEc/EFgcheuPOBk/OalCMqmiQ8smQusKwK9e3jfu+o9wLI3Al2LnJcivcuAo85ET7kH/xXdE4t7W/Fvhy1C4p//Biw5EuhZVvWdAPzYRs9pM2HsDSfsQWRZL5QDE4/ybhAA+DGlhE9rPPj2A4s7e37nBXNbr89cy1EocXTzzTfjC1/4As4//3wnceLjjz+O73//+7j44otRKpVwwQUX4KKLLsL3vve9aSU8HXjf+96HnTt34itf+QoGBwdx8MEH4/bbb68K0p5J4J0Ys3L9kN2B+u7CsfwwOrBVv2U6DarfOerJ8isTn7jopJwooJsT8McSR9GI4eSdmciVnNvmASsZXbFsZZjuZ8Rg0PeEpae8Sf1E8UoA/zi9jEAZ6GzBC4OZqqBo8ry2RJT5vRFewxN5FMsVT04fUbwS/Tced1b51rjrHkpPlTziyDTNaREYLJccXT7QLUfyDDFy+fjjfmjuongn6/UYs24ZccTlPhlgeWrrBfY8zvqhED3g3djrgHd7s1gn2oBTvlVd6cq3Wz8U5nS2Y84nr65+74q3WD9+vPWbnl8PWdKDQ5Z8GMCHq9/7lkuqX1v6OusHVgbr9x1BTtN9s/q9iw63fvx48/kArKzfn6LPzuwdkOD3DedUv9a/L3DKt7AUwAX068f8d/V7KfBOfJHXWLcfACLLPn9+puf8bKE6o7zQui7BnTU3i7mXuNwdqxPn9oZmIZQ4+sY3voErrrgCJ598svPaqlWrsGjRInz5y1/G448/jvb2dnz2s5+dkeIIAM4++2ycffbZzaYhDZ66zxX5WUg95XlBcxxxRC6+5e0OhDFDAdydLL2Mo/gi7iKzLeE+Vaz2iZMFfk57dYZpAjqZ4lAm5xFHonglQBD3I7C+AGxxxUteSTCnPeEIlOGJvOfotSgNgPW3YKuXaZpC7oZh3W4/ki0gnSt62miyUHaS2olyDQULBHYSRQLeibMxwWmzdvuOwHJA3I8o3snizo5Z4l066+cedByed+GuRp1RyFrWrnir9UOBd+LLjbthf2d8yz7fcpSMRZxxns2Xq8WRyC0nwV20cWZz51uOiFuNd3tDsxAq5mjt2rVYunRp1etLly7F2rVrAViut+3bt9fGTsMBfRTfH8PhOYrPEBi8oGjX8hNydyCdBFL9KL71N3awoiiHB4+7KOaHgNwd5j+xtl1gPQG8d5zRoDNMc603jJilwfSUsGwkYjgWMRZ3GZegv+7xqaJzHJ1Xf6f9nfitP0Q0xKNGYOoIoHa3WncNri3DMJhXkMjEO00Xd+nyG/4BPP5zYOtq5jM1pgG3nAl8Zznw5P9U/UlufmRfbSJzYIY1x9FJfoPiMkXzuwx3nmiphXtLPALirePdn9kMhBJHK1euxLe+9S0UCu6urFgs4lvf+pZzpcjWrVtntJtqdwPpnMVydbItOoFk0AkYQM4vzLW+SOwOhIMvhFvM+hs7WNG5tDbE4HVPi/Hj4lgCZfuY9fvCbn7MEEAEhSsOd2SsDNPxqIE57cHuHbq833rj5GfiWJ1o7n7L1XY7oHoBhzsrwzdph562eNXJRRrEOuK/U69WgcG7dFamvCgo2lN+ks2dBZmj/LVzp/rMM38A/vo54OW7mM/UmAYY9nIZcMCANz/WvPm0BY/c/OzdgNIxnUzXFmfzysuOLarbeo1f3jAM7mdvJkLZsK666iq8853vxKJFi3DggVZOjbVr16JcLuO2224DAKxfvx7//d98P62GPOgTY9l8ybMo1SxuyMWxnMErYzplH9f0nhijg6LlxBH7JIhoZ2LVb8dr+bjLxAwBVLZnn8DYZgsMnlusszWGlngEuWIFg+M5LOuzglLJaa/+VAtT0ALs+9nkuQefWNs2RtxiYnFEMnyTrMIyFjOAPrHmbXcV11I64HZ7lbidoCzZKgLHX5646cK6xUSB6F7uXpdgsVxxxoun/PyDgP3eVR2crDG9OO0XwOnXuCKJAr0B88fO0FdosCBzYkxqfveVl4np5F0eKwqoFnGXm99jSOdKM+7EWihx9LrXvQ4bNmzAjTfeiJdesrKwvuc978EHPvABpFIpAMCHPxwQhKcRGtGI5YKYtPNJ0OnvnQzTEmbbIHWfkRgArDvKvKfN2DEcBP4TY1JmW068lQx31t1wMgHRAJWMkRIopmk6IoFnfSHJFF/dZeULcsWRJVZ4wgpgJ5F0ufNdgkHcc8Wyc53Jgm52/YlYBHPaE9iVLWAwnXP6HLFiibiTE2ssyxHPekLER8W0gjU7qTgKKXHEiFnKl8qYtA8vsLJz089mudVkLD+ZfCmcsHNilrz9lXYRdtIL3eFnWD8a9UVUPEeR+9HoODWZzad7R1nIOY5xnF4pptO+H40WdnLcOUkgZbmPz7wTa6Gjn1KpFP7rv/5rOrloCNCejDniiIabYVoi4C9gdyATkM3aHeRLFZScYPDgwReLRpwTY9m898SY6E44gH+aQiqYnGF5ck5sCRZ5IjCItQUAdmULKJQqMAwJ640tjmiBQ9xaorrdE2dWfeRKD5lgcC/3Kapuq2xrPCoM7B3obMGubAFD6Rz2X9DlKS+qmwgavwVFxnrSEo8iGYtYCTAnix5xNKZgfWGJG8Pg9znW5bMqVivTtPosHcRfC3dSNtUSY5560mgOWuNRRAxbzOe8pzOlBAJn8yrjGWBZ9mlhxY7ptMqWKyZyxQpaE9WWfamNNycVgExA90zLki0tjv785z/jlFNOQTwex5///Gfue9/5znfWTEyjGqlkDDsz+SrfsMitBdAnvth+Ye7uoCV48NKDUWQ2Djox5liOOGV5pynUuIezHC3uaQMAbBl1bzon8UZzO5KOYGFhfoC4IkJpvqDu3rYE4lEDxbKVk2mRzUV0lL6aOyWOxki8EfukG839ue3pQO6szN4ErJgj5yi9QJh1tcaxI5PH+FQR9Kns0aDj7AFlAbYwY2WoriofQhwlYu5mYHyq6BFHo+ROOUYaAS93r1tNpm6NOuKZP1pB7yveAuxxrOdPJCg6k7Ou5aGvppVxLdW6eWVZ9h3LD6dsW9y6+NY0La5B4kjqpB1n8xo2oLuZkBZHp556KgYHB9Hf349TTz2V+T7DMFAuz7xL5F4LYJ1IkPXr0u+loRaz5KubGri8xSbVEsPwRL5aHBF/OkfcpCQCslWPyZqmiU0jlthZ0tvGLAsAi3osEbB5ZMoxO2+1BcZ8jkuNYLH9/M2UuNomaX2xTpy1YOvYFAbHLXGUK5Ydy5E8d7furWPiYGw57nyXnntazfu9BQYVB4CII7/1hsT99HAC2VmpAALzBDHqpt9fzV1cnoijoPp72jmn1Rjcx1nc//xp4KW/A8dfBByqwxnqhnX3AE/+ysor5RNHgDUHEnFEQyYuUmbzGiagW3RvJUCS/Mac+xbpe/dk3GrcNDES9acYm9dmQ9o2W6lU0N/f7/yf9aOFUf3AyhQtY7alBUKl4j1toXIigWW14pldvdz94kh8EqOdE5Atwz1oV7Ujk0e+VEHEABb28EXCwp5WGIYVS7DLjtVxTnsJxA3gCphNu1yBQcQKsQTxsLjX4kfEHLFgdSRjHhdlcFnr+Tsyeee03HbJmCER98UC7qLTarygZoDjXiICQ8Zy5Lu+RJTjSFS3rPUmqHylYrrCTsZyVOVWs61O/lipqRFgYhAoVefS0phG7HUi8PrPWBnCA8AUKCTPkUxAdogDL3R5f+iBzPxI/73K8lQgln1x3X7udHJi7vzOCZtoJpQc14888ohzGo3ghhtuwPLly9Hf34//+I//mNH3qu3uYAUWk1MGnZyYI1r5T/pu+5Y78RXsF5axWgHuAKjmruAWKwTkeFI4aUdzJ0JjQXcrMwEkQTIWdU59EWGw0RYLiwWWG4ASGHZZ0zSxYTgLAFje184sR0De86pdhjxncW+b0C3W0xZ3JjbiWnt1l/UckbgJ4l4qV5w2WCbg7sQcMcSNrMCgT4yVK6Yjtlg309NlSxV3gqa51CrMZMvTJ84y+ZJzckg25ojeyDCvPTn5m8B//gPY/91cTho1Yv9TgbdcCix/U+CfWe4luSzTwZtH0zSFd1/Sz2a51XjxqBb34BsYZMqzxNFkoewkJ5aZ32eaW01JHF166aV49tlnnd/Xrl2LT3ziEzjxxBNxwQUX4NZbb8Vll1027SQ1LLACi2UEQjIWce7GqSqvZDliDB6BOHJMpyG4k2eTLKoEpXIFU0V+9lgWd2IJWTpHLBAA13qz2RYY63ZOAAD2kBA3S+07pbaOTaFUrmB0suhMQiK3GAAss8u/anN2uEuUNQyjyjW2fqcljvaY2yHB3bUcmaZpfYaKiWQsIozVIm6v0RC5gui/0wLFsgRZ/+e5tlrjUcSjRlX5MQWXnr+sCvegXEfEatQaj3LzQ5Fnk5N6fu5VF952LwHmHwi093E5adQXrFsMZI7D0xtfegM4VZQUGEzLvNjqBLjixz+/ZyXKM+Od7N/JFU5s7ru5Ww0A1qxZgxNOOMH5/Te/+Q2OOuoo/PznP8d5552HK6+8Er/97W+nnaSGBeaJBAmBwkq2Va6YjuAIk0fDMRlzBi6Pe9rhzl/oSDgTPQBpF5/UaQqK+0Yn3kgsbgDXykKsJioCoz+VRDIWQbliYttYzrEaze9q8QQ/srDUEUdZD3dZYUdcd1tGLIGzngi7ueLPToRVJl/C2GTR4b50Ths3xgywgskBYDTrDSyWSeII8AVGKhnjWvwMw3AsS3RQ9rhz9Qi/v7LEkSz3oPIy7kDAPann566vDmkyKmWgmAPK1UHTgGsdZ20++Se2rHmgVPEm+SVzu1hgBMdlylr2xeJKbDnyh1wQj0YH56QczW23Fkejo6OerNf3338/TjnlFOf3I444Aps3b54+dhoesE5dpR3rC3/SDOqE9C6Ha/Zl1O3kWOL40wGesHOPJ7NAp8enXWNkV52IRTy5k2S4b5YMxiZYYguRV4ezyBXLTgJIGYERibjWm00jk9hoi5xlc+SEGXGrbRjOwjRNN+ZHkjsRURuGJ+27zkowDDmXXks8igE7l5LFfVKaOwk6HpkseHbD4ywLiA8knooWV8QKJSoLBF8A6+YpEliOWEHR0tzjAdz5F956uVfXzxRmL99lXWkxskH4XI0acMdFwDcGgHsDLsIF70Sv2LrdHnD0H5AXGKy4TBlxQ57vr5v+nbf59Cf5JUhLeAXo8jMtCaSSOBoYGMCGDdYALBQK+Ne//oWjjz7a+Xsmk0E8rnc19UIHI27HubVZ0AmD3EukQyaiAoHB2FnInIYAxKZXEfeg8jLHVIFgYfbKDst6srxPTmDsPWAlN31pxwRe3ZWFaVqnsXhXf9AgQuTlHRkndmiZZN1EwGVyJYxOFinucuJq74EOp+71dt0Lulq5rp1g7hOO5UgUbwS44qZQqnjcoTK5fujyuyiBIRPQTEBcZ/Tls65bTd7yQ4SdaZrSbrXe9mQAdznLEc2PPi3H5P7wFcCfztJ3q9UbzvUhlcA/M0/0kkMnwhNj1ckUZWIy6b/7XXoy8aQAe/MqlSqFmn9p69GE5Kadd6l6M6Ekjt72trfhggsuwD/+8Q9ceOGFaGtrwxvf+Ebn708//TT23HPPaSepYUHoVhOJo5bqUwEyRy0Btk9cxmTs5e43vcoN/o6AmCWZSYfmRiadUrmCF4cyAIB953dyyxI4AmMog5eHiFuqQxgQTbDvPEtcPb89jecHrbr3lHDJAUBrIurEPD3x6ogTeyTLfYUt7F4YzGDdDnmXGsHKeZ0O9xcG0wCAvSS4t1LuIZKRu1SuOAu+6KQdEZ4jAQJDJG4AV0CNTFaXFwVUE8tSmQroTk+VnISnInEWzF1e2AVzZ+SHWng4sNdbgNR84XM1asDxFwEXbAaO+2Lgn5knemvYxMmETFh/j3vqcuqWnJ+DNp+maVIxpezxQrv8AoWd5Em5mWY54rP24Wtf+xpOO+00vPnNb0ZHRweuv/56JBLuQP/lL3+Jk046adpJalgQubY6JXcHQR1YeNrM5xMnVgeZNAL089luNdFpivATh7/sS0MTKJQq6EjGpE5sAZYbqT0RRbZQxu9WbwEgL04AYL8F1nuf3jLuLNAHLuqWLn/gwm5sHpnCb/5pua0HOpNCcUGwcl4K0YiBnZk8/vrMoMUnFPcxPL/dEnarFnUJyxmGgd72BLaP5zA6WcDi3jZnsY8YYpHQGyAwZJIoEsxN2ZaniWrLkcjy0xKPIBGNoFCuYDRbQEcyhuGsdRI31RITWt2Cucu7BPvsXDO7JtzTv2Osk3YnXix8nsY0IN5q/TDAOk6flXCrAdb8viOT94gEd26XO20WduMcxF3m9gOa+1Sx7CkvEzJB1z3TYo6UxFFfXx8eeOABjI+Po6OjA9Got8F+97vfoaNDbjesoQ6WwpY56gm4Cp7uhLLixu8Td8SRrNUqIAOs95iquriSFmb2s4tlE/lSGQ+vGwYAHLa0RxhUTBCLRnDwkm489MouPPDSTgDA4Ut7pMpadfUCsKw3ABCPGth/gbxAOWRJN/6ydjvueWEHAOCIZb3SZdsSMey/oBNPbxl3uB+mwJ3U9c9XRwFYOU9W9MuN8542SxwRkUCESm97wjk9ycKcDiJuKIGg4Jqa014tMMj/+zr4CSwNw8CcDpf74t42h7uoLAD0dgQIM8dyJCGO2qvLk//Plahfo/EIOpKeL5VRKFc8f2eWD5zj5AQGK1EuKS87R2YD5ldAHFPaYd/eEDQ/h5nbZwJCXdDT1dVVJYwAoLe312NJ0vj/7Z17dFXlmf8/557bSciNhEASCFe5FUpxBJWLMpDpTbQ/bLW6ShdLp1M7o1NHp6KrlXFaW6+1dSo6tfxWO7Y/i7SOzkJHtPbnBX9e0BZBgYICGkgIkOSc5CTnnJxz5o93v/tycpLz7gCG/Nb7WStLsnn23s+Rs9/9fZ/3eZ/n9CJnD3Z1nslkHEl7Q5FrdqHS+waca+J2cWbuVstzvmxCmj0zSaYySufnypdS9b04qwnkE0bk56qynfD0DbD795ZxJiOOPX0DxLut4/ue49b0I1zifQUQkY8Lp1bB1puEbeykZXvgRXHs7V+Zh6rDIe4t+y3f9z9KNR2c11QpBqyDrwrbNx91Ov38BnG88zAAy6aPZZ5nP9/3P8pa37MsmVpt2b54p7A9vt86dvTP4tirDwCwdJqw/6bvSX4Y/AWLS49ZtsfeF7Yv3e30YftP4ekbmJjYZ1babvS0snHMf+B/6YdO29cfFtf46A3HYTOpOuYUR1K4DIXM24n09ZM0XjBuIkdSXB03hFkmk6E9KsSRisCQIkieI4WVSp5ZrmW1DlPYqfguc5bEPeP9VrVtFXGmOQN8+BL84fuw99mcf50rL9OxozaPwMg1vqtHfsS97bWF7PdXXtrKMb4WB315J5GlZsqGbQOBy4lzrurgI4nuXjiKKM2x+8YuMPIr9IGzC9XIj91mOEtbuQoCynM9HrWZCTh3q6kOHD6vhyJD2LV09prRmwuLDsGOTQNe6OzYJH76bQVNj/6ZmUe2cEFwHwCfn1vH2NICePuXwjZhE1LH3hPHPnzJcdnPZ/7IV/0vUOqJsXbxRHHw+F5he+APTh/e3SyO94go15SxJawa181X/S/QHNzJFz5VZ9nu/p2w7W61jnUeFsf2bAXg8s/UUxT00ex7k694n6ekr82yjbQI2/f+0+nD3mdgxyY8HYf42yVNAFTTyYWRp2HXFqftX54T1zhhCLSOQ/D87VzetxmAkz3i312+7KVwGYoxhQGzhIPc9XVMiptwfoFgCgxD1HTH+81t0lVhlWU5cf5x43wpslR8l6KwN5mi18hZOhbtc+G7Iey6naIy4PMMXBL8zRXwk08Loa05cxx8FV66C/Zvy/nXQ42vRUFf3khprvHdbU4mOBOb1XNKhxjbFd4NucpuqCZk298r2d0bRhJXy2qakUUOivZ2DK4ERg51r1peHmRoNj48cZTTdyvilW9mMmQyuaLvsUTKnMl7PVAw/WIoLIEJC5zGy4yES3t+QeNiWLaeJcXTuYu5fHGeIU6W3CTqn4RsS2QTzhXXqJnpuGxo6bc51HaCO6YsYfE5RkmMuvnCtmqK04dF10FfxJFke/Xqz7HrlR5mNM101kc691oRuSqztWetmi6uWzYeENv+//O68+l65WukKuL4Kpos24omYVtib5cJzL8KJi2F6hlcNbORCeVFhBP1cLJf9JeyM/fL4nPXzhG/dx+DV+7ngmAdsNwUN/JlX6kQ/fB6PZQXBTnRk+BET4KxpQWmOBqrIDCyl6bkvYuDPkfX9EHPNwVKVuRIwfeSkN/MWTrRE2dCsMidsMtaEjxuRq1CA5+Vzo/g5AFI6e4EZ5TxC8Sz1rAo51/nisxHFKP6YBvfc4qjoQVGyO8zv2/Rvv4BUSi3eZluzgXb+N47cHxXXVYDUZ4lX37VJ4UWR6MI+aWJJVIkU2kCPq8lMIL5BYa1PXl4kaNcOxoiigmuueq2qO5mGOx8t763R+PEutq5N/AQcU8ImrYMbCDp8cCyfx54gYnnw8TzqQEutx9f8k8DbesXip9szr+eRqDRfqxuvvjJ5ry/G3CopGEes6+cN9D23GsGHqueNuBzTK0Jw5f+caBtRVPuzzzvSvOPHmD5jLHAWGDuQNu5lzt/Lx0H532T948CEWtLu5ulKRARmBM9CVPUtkfcRF+c2+nl8liVwrmQa1nNyDlS8F0mo7dGRM7ShPIi2iMuhJ3MWRrge457X7pRRC6rp+e9ruYUmLZS/AxCOEd7J9XxEQaLrquLq9LCAMe743TFkow3mkqr9K4Uvg8c21XLVjh9d79bTRY9jfen6YolzxpxpJfVRhH2XSryoVNNegOreJy97ovqwwO5ozeq7Rik731Jq1CYaiK53Xd7xWAzcqQQBZC+xyIdfMn3Mqs9L+c9R3MKlE2A5jv58JxvANBuLClZSc3q4giESMhkMrR3qwsMuTTVEUvQn0qb0RfVhGZrWc0Qdj3qkaNs33sTKTNKWx3O3/DXWhKUUa8hfK+dDQ3nQaF6kr3m9DP0+KggMHJE1+UYl28nsv0esp9ffypNX9JIBldMyLb73iUbHbsoWprLd6XxfZCiqyOJFkejCJ/XY6pw+SVysy6cK2zrZnaQ/QC4KYoXDvmRJYEixuzCnBWp+J7j4elyMfBI/1oTIX6QvIKfeS7Pc4bmdFA3RgiBI52GOHIpMOw71jpiSTO/TiVyVF4UxOsROfYdsaQpMFQTms3Ikbm0pZ5z5PQ9YeYbhfxepRedPLc73k9fMmXeWydjn73IMaY73k+/sYHAVfRliOj6cMZ3+3VUGyUP992QO1/K/ZKiFkeaYWPNLpwCQ0Wd5xIYHS6K6sleVR1Gcm2PbWdEvgfIaxN2Ulyplpe3X9/pu/t2DC19IR5JfYHf+C7Je47mFEmnGV8CkOGo0W7F7Ut+rBFlaYvETYExpigwZDV3ic/rsUVv4tZONcVlNTNylLVbzb3vfVauVGlIqXBoOOQnaBTQPNGTGNr3vc+IHZf2HZOa089r/wYbyuF3f5vzr+2itytLoOQTJ2AXKDlqBeVp/2E/X95Tju2lBf68yeCy6GlPIkWi372wGzpfSosjzSdA9uzCfPjcLKvZZwdSHOXpNQUDw7ZyeS7o91IQyP9VyvY9YvquLszkvcX9B+k1NYTv7VFxfr7BQnOK9EXgX8qZ/vNpBBFtT3oTKdqMnCHVZbVxZUJgtHb1mgJBZUlNIoVMa1ffKUeOjkXcnW/53mfzPf+SGoicpWqb7+1D+b71Jti8Fjp0b7UzTiY9aPsQv89rCgE5xna6GF/lGJ4rOq4irqy0CfluUF8WCxf4zZ2h1vh+avlS7oShbPWjxZFmmMgHKJI1OyhXSBK1q3u5ZbLTfIDc5/3YZxYqs+Hs2YWM/KhUei7Lurf9/m5aSXRGu6nlBFXe7jxnaE4JvyUCyoPiZfJRR8wUR+PLB680bKfWEBhHu/pMcaIqMAAzMfVIp3W+28hRtK+ftkifmTMkr+nO9z7Dd3VhZ/neayZz5/R9wkJovABC+auWa06BT38NbtwHn7tnUBNznMkxRuYjV95Oh9lqx/2ynJtWO16vZ8AYOzzfxTOSTmdMgehqfD+LIkd6t9ooY0Do1NjNUqEwO5APTzpjbZl0s6wmH3wpatw8PDBwdiFr36gUxZP3iMb7SaUz+Lwe0w8351dG3uOJgltoSdQAq5X81gwDXwBuOgD+EOEHd9DW3sM7hztIZ0ST4yqFIpAA48qEQDja1Udb1L3AqDMERktnjI86RE86VWFWWuAnXOAn2tfP6x+KJauK4qCzjMKQvktx1EvbMKJeMl+rpbN3aN/XbFK+puYUCJWInyEYUxTg8Ekrqm7tVnNfK6g/lTb/7GaMy15WU4kcSbuOWNI8bzj5UvLzRvv6zZQLNzmhZ5M40pGjUUb2jgZTICio8wJbI9CumOg23uXiASozl9WS5jXAhTgqlDlHYnZhtlNQmBXJe2QyYh2+L5kyd2Ko9KqSny/aGyeZ8ZHy6HnBGcXjgeIqCIUZZwgU2X5k3JgC5bYtsuFuS2cvH7T3ADChQq0fHlhioqWjl49OirynBsXzPR6Pafv6BycAS7CoUG+ce/hEjMNGs+D6Yfh+8HgPrUbkSdV3zchQlrW0JSPzKmOUnDzKYoh2oeAmemMt6RmrAorjs+W7+8nvwBUNq6aYSn6gJY4SeSw/ObQ4GmVkK2w30RdwbpmMJay+P0p5OwPWtNVzfuy+R0zf1SM/Qb/XrHLd1Zs0fbDv4BsK2c9qe3IaU+O/4pqSh5R81pw6dUb059X9otq3mxd8TbiAwoCPVDrDy39pB2BSlfr5jca93jzYQW8yhcfjUuAYjYn/uLfduF6x8rkNFUV4PCLa+dYhEXmaWKl+vrzXy385TiYDhQGfcn0ozRmg9V14+T7Y/eSgJoNF15VyjozJo5gA9lsbTgoD+H35X9VybI8MY1lN+D7I+O4i8iMj+yddTNrt99CRI5ccPHiQdevWMWnSJAoLC5k8eTLf+973SCScKnPnzp1ceOGFFBQUUF9fz1133TXgWps3b2bGjBkUFBQwZ84ctm7d+kl9jNOCnF3IHQ0dLppZglNcyRlG0GcJj6GQX/ThzCycvmdFvRSFndN3a1akku+U/YD7/aPiqz+6ef1h+MO/MissIj5Hu0T0Y1pNWPkSXq+HxkohUNqMvJtJVerNraca92rpFFGj+vIipZmsZPLYYsf5U2vU710Q8JnC0PS9Wl0cyXvJezdVF+f+rv98BTx0AXR9rHxtzTBoeRte2AA7Hx/UJPsl7yYpOeT3mRtbIn1J28TX/dgO9nxS9WU1+3nDWVYDEdnvcDHxtd9DiyOX7Nmzh3Q6zcMPP8zu3bu5//772bhxI+vXrzdtIpEIK1eupLGxkR07dnD33Xdz++2388gjj5g227dv54orrmDdunW88847rF69mtWrV7Nr166R+FjDosysJyG+fG6W1cT51uygM2aFfJUEhu0LbE+4U3nws+8tfJfJ5O7PN3dSKA4c2QOEykxMc4r8v5/BS3fzqXDUcXiaC4EBMLPOas3i83qYOlb9/MbKIoK2f+s5490lLc+uc9q7EXbg9L0o6HMVNZuS9TkH9b1tN7S9C+mzq6v5/3dUToF5RkudQRiTlZDtZseX3a4zljylsd3+X9XI/hhb5Mi+rKfie8A2we605S0N1/ezgVGReNHc3Exzc7P5e1NTE3v37uWhhx7innvEzoHHHnuMRCLBL37xC4LBILNmzeJPf/oT9913H9deey0ADzzwAM3Nzdx0000A3HHHHWzbto0HH3yQjRs35rx3PB4nHrd6FkUikTP1MZWoMLbyyiUpMyFb+Uso7OxLU8rLYkVWQne0r99V2FX4bnQqj4lqx+59t8RZwOdx5bu0m+k5yBW+P5DsbQLOVzpXM0zmXA59nTQ1NlLFDm4N/AfxTIBFTb+xbN7aBIe2w+zLYPrfiGO9HbD1ZpG3dNkjnDuxgt+93cKXvC/xhfAeivcnYNZqYZvshaf+Qfx59c9EIjjAu0/Avv8mMPWv+czEBrYfOIGHNP8YvRu2lMDn77eSa99/Gt57CpqWin5ykt//HUvjccawkk6EKDo/8zZseVJUpF64zrJ9+npIxGDlHRCuFccOvMjNPY8wwVfJptTfsKCxnIDPKz5bbwdcdCuUTxS2h7aL/xc1s+CCGwBRu+z+MZuh5xgP9q9mfoPRt+7jHfD6RqiaCktvhisfh1QSSmpO9V9MMxRGC6GhkONMRyxBKp0xa/0oj5HFIdoicU7GEq4229jvMZzdasJ3uSSYJBrvJ2P0gFWd/FYUB4klerN8d/du0ZGj00BXVxcVFVbzy9dee40lS5YQDFpfpFWrVrF37146OjpMmxUrVjius2rVKl577bVB73PnnXdSVlZm/tTX1w9q+0lQaWummbKpe+UHoMh6eOXDoxr6DPl91uygN+E6IdvyXTSv7Td2M7jNl+ochu/Sx4meVq72P895icH/zTWniYtuhc/eTXj8dC6ZWcqlvle5JPAGDZW26MnHb8G7v4X2Pdax/rg49u5mAFbOqqWiOMgc7wcsi/9RREokqaRh+1tn/ZnWneLY0T9zxbkNgEgOndK6VRxP2Zbk294Tx1p2OP3f9QRFe7awYooQRs2zainr/kDYfvSG03b3k+J43BYlO3mAqW1bWezfC8BXFgo/2PNfwra307LtOCSOHXS2tbnY9w6X+l6loaCXz84xmhBHPha2B14Uv09aAlMudjZK1owIdoFiL4io2i/MPka63W0mJ76RviSpdMZcHnOfj2qN7QUBLwUBtWVo+7tJRr2Ul/R05Oj0sH//fn7605+aUSOA1tZWJk2a5LCrqakx/668vJzW1lbzmN2mtbV10HvdcsstfPvb3zZ/j0QiIyqQKm0NKSO9SQx9ofwA2FsayIdBdWkKxJc4lkjRGUsOXZgu572tRqCyynZhwKf+8JVYva7kdmpV32WBtv3x8fy4/zKKyicyU+lMzengxtWL2P/iehqqs5aGZl8GNTNFJEYSLIFVP0C0uxUz0s3fWMTJXT1kQkvxTFho2fpDhi3gsX2PpjWLSMq4T/GFiXU0VhZRFPDAB4ZtwCbQJl8kokg1s5y+/fUdkEnx3ZmL+GJbinMnVUC7V9yvKqvJ60W3CcFVVGkdq/8rWPUDzvHUsql8IcunjxXHl94MiR4orbNs6+aL645pcFw2vOImPjp6lH+Z+TmrCn7NbGEbHofm7MJe50gWHS0rDJjVzvNhH5+tOnDqCdUeo13OyZ7EMFIPLIHidmwXvst+gHFXNezs58p2OarvhDPJiIqj73znO/zoRz8a0ub9999nxowZ5u8tLS00NzezZs0arrnmmjPtIqFQiFDo7OlnVGnUh+mIJcyHLxzyi3C9AtW2qr8y0U814Q/ETOBIVx8neuJmWwXVonr2mcVJl4nk2b7Lfj2qolDa7uurZ19/PUvD1VyrfKbmVCkqrWTKJf888C+mXCx+7IRKYNF1jkOTq0uYvHz1wPP9oQG2ADQuFj8GcyeMEX+oyWFbv1D8ZHOeaJpbCiyRmq5uvvjJ5twcY1HtHKidwwRggv34grUDbcfOED9ZeOZfRX327Son5/7MmjPLe0/Bk98UQv6qJ3KaSIFxott9uxqwxvfjPXEzdUI1+uL3eaksDnLc6OXnZjew3e5Ed552NYP6bk3crXurbtYR7XIS/Wnao3FXJS/OFCMqjm688UbWrl07pE1TU5P55yNHjrB8+XIWL17sSLQGqK2tpa2tzXFM/l5bWzukjfz70YB9dnDAqPuimvQG1pe9PdpnJnfXlKpvba4pDfHeUdFKwe0DZJ8dtBo7l4bne5weo1pxTan6w1tTGuLwSVFvRuYsaTQajRKZFCSiIs9tEORY2t4dN/vpVbuKvlgCpdNl9AVEpOd4d4KDx2PEEinDJ7X7S9+PRa12Ne58l5H9uOuEbNkup6Wzl/ZuLY6orq6murpaybalpYXly5ezYMECNm3ahNfrjJQsWrSIW2+9lWQySSAg1Oq2bduYPn065eXlps0LL7zADTfcYJ63bds2Fi1adHo+0CeAmB2EON4dZ+fHnYA7dW9GX6JxM0zvRhzJlggHT8TMdgqqodfSAj8hv5d4f3p4vtvEkdzy6sb3saUFhEgQIkkBemePRqNxwZQV8PdvO5dks5BjVDKVYV+byD+rcjHGyQrqbZE+c1nMjUCpDofY0xpl15EuQPRMKwqqvealiOqIJTlilI8Yru+yXY5b31s6rR6KI82oSMhuaWlh2bJlNDQ0cM8999De3k5ra6sjV+jKK68kGAyybt06du/ezeOPP84DDzzgyBe6/vrrefbZZ7n33nvZs2cPt99+O2+99Rbf+ta3RuJjDRtZxO6tQ0bF4TI3AkF+geNmnytXAsPoa/VuSycAIb9XqektiNmBbOdg+a6eROp8+MQD5CrqFS7gK74X2VlwDV9v/6HyeRqNRkMoLJY0SwfP9Qr4vGZT5Z0fC4EynHY3Rzp7TYEyzkXRUjk+y8mnm/HRnhv17rB8N9rddPRyxFgZqFPsQ2i/1+sfnGTLjo95/+jI7gwfFQnZ27ZtY//+/ezfv58JExyr92SM/YZlZWU899xzXHfddSxYsICqqiq++93vmtv4ARYvXsyvf/1rbrvtNtavX8/UqVN58sknmT179if6eU6VurJCdn7cxQ5DYKg2whS2YtbTHe9nT6uY2bhbmhIPwJsfinvXVxQp1UiS1I0p4MPjPTbf3bdjaI304TfaT7iLeoVoQ4SaM95R8dXXaDSjjJrSAo53J3jjoKiKXq/Yyw8sMfHh8R5zs42b8V2225GtetyM7R6Ph9rSAg6fjNl8V1/ekr7vOhIhlc7g8bgbn+X4/us3DtGXTLPinBp+/rXPKJ9/uhkVb4i1a9fmzU0CmDt3Li+//PKQNmvWrGHNmjWnybORQc4kZGM/N5GjwqCPseEQx6JxEv1i67OblggTjW3Ysu2I215PMlJk+a7+4FcWBykM+OhNpkimRPNZNwNHQ0Uxd6aa+WVqJZedU8fIPXYajWbU0XkY9j4jdiTO+V+DmjVWFrH7SMQcXx2lK/Igx3IpjAoDPuVSKWCJGXNsd9GuRtgXcfhkbJi+O8f26pKQ8i49sESk7Jkpq9OPFKNiWU3jpKnaWTl3UrW7isN2QVNVEnS1lT/73m5mReJ85xfeTTsFeyNQEJ/DzcM3ubqYDF6S+PH4z54diBqNZhTQvheeuRm2/2RIs6aq7DFSXWAUBHyOCd+kqkFaxgxCtphpqnInMLLt3fheVRJ0pFhMcnnvbN8nu2gTdCbQ4mgUMnNc6ZC/5+Mcm3222MlHTWnI3EaffS0V7L56PXBOrVvfrfYNk10IK3DOomS/Ko1Go1EiXAuzLhV1sYbA3valMOBzHb2xt5yZVedufJxWE8aupSa7aLUDTt8rioOul+Wcvrtr1ZP9LtGRI43F3mdhQwU8utJ5/NGV4vjeZwEhEBZ5d7M/dBXPhG5x7vj65SXCdtcW69hHb4pjP/k0gChmB/x74F7+z9HPwdu/smzbdgvbe7NqrjyxDjZU4Hnj3zl/iih01+Bp48vPzIM7nYXreOrvxTVeud86Fm2DDRUsfdwqvTiurJDCF9YL2xd/YNnGo+LYhgpI9lnHn9/AfXsv5hb/YwBcMKUK0inLNnbSsv2/d4tj/2Ul5Af9Xg4WXMnPAj+m4fhLaDQajTK1c2DN/4YVtw85Tl7y1By+5vtvQAidYOSQsFUcJx/+YCV/CV0NwPwGsdOaZ76jNE6WFQbYULSF/aGrWO9/jIUTjS4S6bTSOHn+lCoA3gt9nTdTl+OxNzN+7d+E7e+/4fwcd00Wx9v3mf5e6XuB296+AB6/2mn74znC9sg71rE/Pw4bKhj39NWEbCsBc8aPYSTR4uisIiNqaaRTzsPplDiOWMstCvr56sIJ+D1pxpdl1ZHIpIWtbIxjHpfXgJWzarhoxlhKgl68WNd12Gb7IK9LhmuXNFFTGuLyBRPw2K6r4oMnk+Jby6fg93r410tn22zTA2xzXdebSVE/JsSM2jBfnDd+cFv5/zLrumlvkGbfm1w1vwKNRqMZNoOMk55MioWNY2isLGL9Z2dYtorjpJcUPk+a6TVhLvv0+Czb/OPksumV+D1p5k8odUT5VcbJpuoSVs+rw+9J4yP7XrnHVPt1v37+RGpKQ9SXF+DNZZtOD+nDj788j3FlBdzcPN1VysSZwJPJZL/BNEMRiUQoKyujq6uL0lJ3Ic+8JPtEQ0pfAIqrrOM9x0UPqcJyCBjJ1/1x4tF2QoEQlNhqRfWcEG0MCsdYvZb6ExA7AV4flIy1bGMnRR+rglIIGiHMVFLcz+OFcM1A21DYatiZ6oeedtEgVDbbBNEzKtkr7ELGMlg6Bd3HAMiEa0mk0oT8PujrEg07g8XCDxAPULdRrDNcixkn7ouItgvBIigwQraZDESNkg4lNSDrX8WjEO8W/w8Kx1i+RY6K/4eF5fn+NTQajSY3Z3ic7E+nITwOv+x8MBLjJEBxNfgMgRXvFvbZ42e0VVy/uAp8AZKpNN5kDF8iKirYF9kmot3HxGcsqgS/MbFPxMTny7Y9A7h5f2tx5JIzKo40Go1Go9GcEdy8v/Wymkaj0Wg0Go2NUVHn6GxCBtoikZGt3qnRaDQajUYd+d5WWTDT4sgl0aioKl1fXz/Cnmg0Go1Go3FLNBqlrGzoUgM658gl6XSaI0eOEA6HXRXn0mg0Go1GM3JkMhmi0Sh1dXUDmtdno8WRRqPRaDQajQ2dkK3RaDQajUZjQ4sjjUaj0Wg0GhtaHGk0Go1Go9HY0OJIo9FoNBqNxoYWRxqNRqPRaDQ2tDjSaDQajUajsaHFkUaj0Wg0Go2N/wEjq/0sCbqbUwAAAABJRU5ErkJggg==",
|
|
"text/plain": [
|
|
"<Figure size 640x480 with 3 Axes>"
|
|
]
|
|
},
|
|
"metadata": {},
|
|
"output_type": "display_data"
|
|
}
|
|
],
|
|
"source": [
|
|
"import numpy as np\n",
|
|
"import matplotlib.pyplot as plt\n",
|
|
"\n",
|
|
"fig, ax = plt.subplots(3, sharex=True)\n",
|
|
"\n",
|
|
"t = np.linspace(0, 5 * 1 / 4160, 1000, endpoint=False)\n",
|
|
"data = np.array(200 * [255] + 200 * [128] + 200 * [200] + 200 * [20] + 200 * [255])\n",
|
|
"carrier = np.sin(2 * np.pi * 24_000 * t)\n",
|
|
"\n",
|
|
"ax[0].plot(t, data, color=\"C1\");\n",
|
|
"ax[0].set_ylabel(\"Pixel values\");\n",
|
|
"ax[1].plot(t, carrier, color=\"C0\");\n",
|
|
"ax[1].set_ylabel(\"Carrier\");\n",
|
|
"ax[2].plot(t, data * carrier, color=\"C0\");\n",
|
|
"ax[2].plot(t, data, color=\"C1\");\n",
|
|
"ax[2].plot(t, -data, color=\"C1\", linestyle=\"dotted\");\n",
|
|
"ax[2].set_ylabel(\"Signal\");\n",
|
|
"\n",
|
|
"for a in ax:\n",
|
|
" a.get_xaxis().set_ticks([]);"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"id": "b11ba0ea",
|
|
"metadata": {
|
|
"slideshow": {
|
|
"slide_type": "subslide"
|
|
}
|
|
},
|
|
"source": [
|
|
"The pixel values (\"baseband\") and the carrier are signals, and the modulation is performed by *multiplying* both signals."
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"id": "fca54469",
|
|
"metadata": {
|
|
"slideshow": {
|
|
"slide_type": "skip"
|
|
}
|
|
},
|
|
"source": [
|
|
"We remember:"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"id": "12803f83",
|
|
"metadata": {
|
|
"slideshow": {
|
|
"slide_type": "fragment"
|
|
}
|
|
},
|
|
"source": [
|
|
"$$ \\text{multiplication} \\,\\circ\\!\\!-\\!\\!\\bullet\\, \\text{convolution} $$"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"id": "e02e20a9",
|
|
"metadata": {
|
|
"slideshow": {
|
|
"slide_type": "skip"
|
|
}
|
|
},
|
|
"source": [
|
|
"During modulation, the baseband spectrum is convolved with that of the carrier."
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"id": "1d1b4bf0",
|
|
"metadata": {
|
|
"slideshow": {
|
|
"slide_type": "subslide"
|
|
}
|
|
},
|
|
"source": [
|
|
"The carrier's spectrum looks like this:"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 2,
|
|
"id": "b61fb512",
|
|
"metadata": {
|
|
"slideshow": {
|
|
"slide_type": "-"
|
|
},
|
|
"tags": [
|
|
"remove-input"
|
|
]
|
|
},
|
|
"outputs": [
|
|
{
|
|
"data": {
|
|
"image/png": 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",
|
|
"text/plain": [
|
|
"<Figure size 640x480 with 1 Axes>"
|
|
]
|
|
},
|
|
"metadata": {},
|
|
"output_type": "display_data"
|
|
}
|
|
],
|
|
"source": [
|
|
"n = 8192\n",
|
|
"f_s = 16440\n",
|
|
"t = np.linspace(0, n / f_s, n, endpoint=False)\n",
|
|
"carrier = np.sin(2 * np.pi * 2400 * t)\n",
|
|
"\n",
|
|
"X = np.roll(np.fft.fft(carrier), -n//2)\n",
|
|
"f = np.roll(np.fft.fftfreq(n, 1/f_s), -n//2)\n",
|
|
"\n",
|
|
"fig, ax = plt.subplots()\n",
|
|
"ax.plot(f, np.abs(X));\n",
|
|
"ax.set_xlabel(\"Frequency [Hz]\");"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"id": "c2a53d61",
|
|
"metadata": {
|
|
"slideshow": {
|
|
"slide_type": "skip"
|
|
}
|
|
},
|
|
"source": [
|
|
"We see two peaks, at plus and minus 2.4 kHz. During convolution, they create two copies of the baseband:"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 3,
|
|
"id": "75ba74c8",
|
|
"metadata": {
|
|
"slideshow": {
|
|
"slide_type": "subslide"
|
|
},
|
|
"tags": [
|
|
"remove-input"
|
|
]
|
|
},
|
|
"outputs": [
|
|
{
|
|
"data": {
|
|
"image/png": 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",
|
|
"text/plain": [
|
|
"<Figure size 640x480 with 1 Axes>"
|
|
]
|
|
},
|
|
"metadata": {},
|
|
"output_type": "display_data"
|
|
}
|
|
],
|
|
"source": [
|
|
"box_width = 4160 / 2\n",
|
|
"f_c = 2400\n",
|
|
"boxes = np.where(np.bitwise_and(f_c - box_width < np.abs(f), np.abs(f) < f_c + box_width), 4096, 0)\n",
|
|
"\n",
|
|
"fig, ax = plt.subplots()\n",
|
|
"ax.plot(f, np.abs(X))\n",
|
|
"ax.fill_between(f, boxes, alpha=0.3)\n",
|
|
"ax.set_xlabel(\"Frequency [Hz]\");"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"id": "9ea4c83a",
|
|
"metadata": {
|
|
"slideshow": {
|
|
"slide_type": "subslide"
|
|
}
|
|
},
|
|
"source": [
|
|
"This signal is then transmitted in the satellite band (137-138MHz) using *frequency modulation*"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"id": "35b858ed",
|
|
"metadata": {
|
|
"slideshow": {
|
|
"slide_type": "fragment"
|
|
}
|
|
},
|
|
"source": [
|
|
"We receive it using a *software-defined radio* and corresponding software to demodulate the fm signal."
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"id": "7f01bcc4",
|
|
"metadata": {
|
|
"slideshow": {
|
|
"slide_type": "fragment"
|
|
}
|
|
},
|
|
"source": [
|
|
"**Your task in the project is to undo the amplitude modulation.**"
|
|
]
|
|
}
|
|
],
|
|
"metadata": {
|
|
"celltoolbar": "Slideshow",
|
|
"kernelspec": {
|
|
"display_name": "Python 3 (ipykernel)",
|
|
"language": "python",
|
|
"name": "python3"
|
|
},
|
|
"language_info": {
|
|
"codemirror_mode": {
|
|
"name": "ipython",
|
|
"version": 3
|
|
},
|
|
"file_extension": ".py",
|
|
"mimetype": "text/x-python",
|
|
"name": "python",
|
|
"nbconvert_exporter": "python",
|
|
"pygments_lexer": "ipython3",
|
|
"version": "3.11.13"
|
|
}
|
|
},
|
|
"nbformat": 4,
|
|
"nbformat_minor": 5
|
|
}
|