{ "cells": [ { "cell_type": "markdown", "id": "2802cad5-f014-4566-953d-2ae6b6e62d6e", "metadata": { "tags": [] }, "source": [ "# Lab 4: The human experience of sound\n", "\n", " Last updated 8/12/2024 " ] }, { "cell_type": "markdown", "id": "9b6c0fd5-9380-4d32-bf67-2210d89aa79b", "metadata": {}, "source": [ "## 00. Content \n", "\n", " Mathematics \n", "- converting back and forth between trig and exponential notations\n", "- combining components of the same frequency by factoring\n", "- writing complicated functions using just one term per frequency component\n", " \n", " Programming Skills \n", "- N/A\n", " \n", " Embedded Systems \n", "- N/A\n", "\n", "## 0. Required Hardware \n", "- N/A" ] }, { "cell_type": "markdown", "id": "0cccb145-a8ce-46bb-b694-c5b74518114e", "metadata": {}, "source": [ "

Write your name and email below:

\n", "\n", "**Name:** me \n", "\n", "**Email:** me @purdue.edu" ] }, { "cell_type": "markdown", "id": "537365ee-5c23-4e78-afca-55e7e2fae8a9", "metadata": {}, "source": [ "# 1. The human experience of sound\n", "\n", "Let's talk about sound. Sound is one of the basic, fundamental ways we experience the world. It can't be broken down into smaller experiences, it can't be explained except by analogy to other feelings. We can explain a bit about what causes sound. By exploring this, we will be able to better understand what makes things sound the same or different. This will also serve to explain why Fourier series are such a powerful tool for understanding sounds.\n", "\n", "This may go without saying, but we hear with our ears. To understand sound we need to understand ears a bit. Look at this diagram.\n", "\n", "> Diagram of the middle ear\n", "\"diagram\n", "\n", "> BruceBlaus, Blausen.com staff (2014). "Medical gallery of Blausen Medical 2014". WikiJournal of Medicine 1 (2). DOI:10.15347/wjm/2014.010. ISSN 2002-4436., CC BY 3.0, via Wikimedia Commons\n", "\n", "\n", "When the ear drum moves, the auditory ossicles transfer that motion into the cochlea. The ear drum moves when the air pressure in the middle ear is different from the air pressure in the ear canal. The middle ear is filled with air, and connected to the outside through the auditory tube into your nasal cavity. The auditory tube is usually closed, but opens up throughout the day at various times, such as when swallowing. This lets any gradual changes in air pressure balance out, so your middle ear doesn't inflate or deflate like a balloon. This gives us an important insight about what sound is.\n", "\n", "**Sound is caused by *changes* in air pressure, not by pressure alone.**\n", "\n", "Sound does not allow us to sense air pressure directly. This is one indication of why calculus will be such a helpful tool for understanding sound. Calculus is the mathematics of changes.\n", "\n", "Once a motion is transmitted from the ear drum to the cochlea, it wiggles the fluid in the cochlea which in turn wiggles tiny bundles of hair inside the cochlea. When the hairs wiggle, they produce an electrical signal which travels to the brain. Each hair bundle sends its own signal, giving you a unique experience.\n", "\n", "To understand this, we will use an analogy with an old style of meter called a vibrating reed frequency meter. Watch this short video of someone using this tool to measure the speed of an engine.\n", "\n", "https://www.youtube.com/watch?v=AsSi6FA8wFI" ] }, { "cell_type": "code", "execution_count": 2, "id": "31002f7b-cdc7-4272-9c2c-bfd2bd68063e", "metadata": {}, "outputs": [ { "data": { "text/html": [ "\n" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "%%html \n", "" ] }, { "cell_type": "markdown", "id": "10d8eded-03fa-466a-8115-307dcba04f8c", "metadata": {}, "source": [ "The device consists of a series of metal reeds which are tuned to vibrate at a specific frequency. In the example above, the reeds which are tuned to vibrate at 51 vibrations per second are moving most strongly, indicating that the motor is turning at 51 cycles per second. The reeds which are tuned to vibrate at 47 vibrations per second do not wiggle as much. The hairs in your cochlea work in much the same way. Depending on the frequency of vibration coming into the cochlea, different hairs will wiggle and you will get a different sensation. This leads us to another important concept.\n", "\n", "**Sound is experienced as a collection of *separate* frequencies experienced *simultaneously*.**\n", "\n", "That is, we can stimulate specific groups of hairs in the cochlea by making vibrations at specific frequencies. Another important concept is that you can only experience a sound if you have hairs in your cochlea which are sensitive to it. In most people, there are no hairs which are sensitive to vibrations faster than 20,000 vibrations per second. On the other end, most people don't have hairs which are sensitive to vibrations slower than about 20 vibrations per second. The scientific unit for something happening so-many-times-per-second is \"Hertz\", abbreviated as Hz. That is,\n", "\n", "**Sound is only experienced when vibrations occur within a certain range of frequencies. Most people can't hear vibrations slower than 20 Hz or faster than 20,000 Hz. Many people can only hear vibrations between 200 Hz and 4,000 Hz.**" ] }, { "cell_type": "markdown", "id": "667c2279-1bdb-40e4-96dd-c471f11f4b1c", "metadata": {}, "source": [ "# 2. Multiple sounds, simultaneously\n", "\n", "Let's build some sounds and see how we can combine them. We will combine a a middle A with a C and F, to form the F major chord. We will start with five seconds of time, sampled at 44100 hertz." ] }, { "cell_type": "code", "execution_count": 2, "id": "b92fc630-a9ea-4dca-993b-be3047930a9f", "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "\n", "t = np.linspace(0, 5, 5*44100)" ] }, { "cell_type": "markdown", "id": "f3f92dfb-f484-4a5e-b24e-ba8fc79af6db", "metadata": {}, "source": [ "Recall that middle A has a frequency of 440 Hz, and the notes on the chromatic scale are in a geometric sequence with common ratio $\\sqrt[12]{2}$. We will take the C which is three steps above middle A, and the F which is four steps below middle A." ] }, { "cell_type": "code", "execution_count": 3, "id": "c68c39ac-5bbd-4347-a6b2-dcd52deceb09", "metadata": {}, "outputs": [], "source": [ "a = np.sin(2*np.pi*440*t)\n", "c = np.sin(2*np.pi*440*2**(3/12)*t)\n", "f = np.sin(2*np.pi*440*2**(-4/12)*t)" ] }, { "cell_type": "markdown", "id": "0405330a-56fb-4e2b-b89c-3d6f06d589e7", "metadata": {}, "source": [ "Let's plot each of them and give them a listen. Note that in order to keep the `Audio` objects from being automatically deleted, we need to keep a reference to them somewhere." ] }, { "cell_type": "code", "execution_count": 4, "id": "c3a767fa-71c6-4e95-a58d-24204f6cb1f8", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "The note A:\n" ] }, { "data": { "image/png": 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\n", 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\n", 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" }, { "data": { "text/html": [ "\n", " \n", " " ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import matplotlib.pyplot as plt\n", "from IPython.display import Audio\n", "\n", "\n", "audio_playbacks = []\n", "for name, note in [('A', a), ('C', c), ('F', f)]:\n", " print(f'The note {name}:')\n", " plt.plot(t, note)\n", " plt.xlim(0, 0.04)\n", " plt.show()\n", " audio = Audio(note, rate=44100)\n", " audio_playbacks.append(audio)\n", " display(audio)" ] }, { "cell_type": "markdown", "id": "0b0ec83d-ef82-4a9a-878f-ac80533a26ea", "metadata": {}, "source": [ "To combine them, we can just add up the curves. Let's see that now." ] }, { "cell_type": "code", "execution_count": 5, "id": "77b9bde0-48bf-4b26-94e4-0ec166d3aaa3", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" }, { "data": { "text/html": [ "\n", " \n", " " ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "f_major = a + c + f\n", "plt.plot(t, f_major)\n", "plt.xlim(0,0.04)\n", "plt.show()\n", "audio = Audio(f_major, rate=44100)\n", "audio_playbacks.append(audio)\n", "display(audio)" ] }, { "cell_type": "markdown", "id": "25d19471-3f22-4023-8d15-cedffb1f1891", "metadata": {}, "source": [ "### Exercise 1 \n", "\n", "Wikipedia has [a helpful list of the major chords](https://en.wikipedia.org/wiki/Major_chord#Major_chord_table). Pick another chord from the table and write some code to play that chord using sine waves." ] }, { "cell_type": "code", "execution_count": null, "id": "577ac1ad-2875-4c79-93fc-82954694fed2", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "id": "b2c7f4e4-a7e6-491a-8b01-55073b7a29a0", "metadata": {}, "source": [ "### Exercise 2 \n", "\n", "Notice that even though we added the notes above together, the y-coordinate of the curve in the chord is still near zero the whole time. Explain why that is. Why didn't adding the curves up shift the whole plot upward?" ] }, { "cell_type": "code", "execution_count": null, "id": "63017ee2-4f7f-4fd1-b72f-f458c66e43e6", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "id": "29ea0509-6347-4652-9dd0-325b7e3266e0", "metadata": {}, "source": [ "### Exercise 3 \n", "\n", "Try adding a constant number to the sound curve for one of the sounds we have made. Play the sound back and compare. Does it sound at all different? Describe your experience qualitatively. Then, explain in terms of the anatomy of the ear why these two curves should sound the same." ] }, { "cell_type": "code", "execution_count": null, "id": "3549f255-221f-4e25-bf7d-66d9570c2fbb", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "id": "17cbcf29-c404-4808-8b64-38596b803e66", "metadata": {}, "source": [ "# 3. Phase and waveform\n", "\n", "There is another aspect to hearing which is essential. Up to now, we have been using only sine waves to produce sounds. There is a good reason for this, and it lies at the heart of Fourier theory -- over the next several labs, we will explore how we can use sine waves to describe an arbitrary shape of curve. We call the shape of a sound wave its **waveform**.\n", "\n", "There are three numbers which characterize a sine wave: its amplitude, frequency, and phase. The amplitude of a sound wave it related to its volume, that is, how loud the sound it. We have already explored how pitch is related to frequency. What about phase? How do we experience this? Let's explore an example. Begin with 5 seconds of time, sampled at the standard 44100 Hz." ] }, { "cell_type": "code", "execution_count": 6, "id": "9695a99d-85d3-4730-9598-acd53904c3c4", "metadata": {}, "outputs": [], "source": [ "t = np.linspace(0, 5, 5*44100)" ] }, { "cell_type": "markdown", "id": "7d8b6518-25c8-4c34-927c-7d55dd987534", "metadata": {}, "source": [ "To avoid having to mess with irrational numbers for now, let's hear A3 which has a frequency of 220 Hz, and combine this with a note at 330 Hz, which is very slightly higher than E3. In music terms, we are using a \"perfect fifth\" (notes with a frequency ratio of 3:2) rather than an \"equal temperament\" (where the notes form a geometric progression)." ] }, { "cell_type": "code", "execution_count": 7, "id": "f1ecb01f-7590-4e6c-b261-f37176b1fb3f", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" }, { "data": { "text/html": [ "\n", " \n", " " ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "a3 = np.sin(2*np.pi*220*t)\n", "e3 = np.sin(2*np.pi*330*t)\n", "\n", "plt.plot(t, a3+e3)\n", "plt.xlim(0, 0.03)\n", "plt.show()\n", "audio = Audio(a3+e3, rate=44100)\n", "audio_playbacks.append(audio)\n", "display(audio)" ] }, { "cell_type": "markdown", "id": "e36de569-13cc-46f4-a52d-c7d7cedb5c42", "metadata": {}, "source": [ "What if we adjust the phase of the E note? Let's try shifting it by, say, $\\pi/4$." ] }, { "cell_type": "code", "execution_count": 8, "id": "f1dffdaa-a7c4-4233-957b-692901991b12", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" }, { "data": { "text/html": [ "\n", " \n", " " ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "e3_shift = np.sin(2*np.pi*330*t+np.pi/4)\n", "\n", "plt.plot(t, a3+e3_shift)\n", "plt.xlim(0, 0.03)\n", "plt.show()\n", "audio = Audio(a3+e3_shift, rate=44100)\n", "audio_playbacks.append(audio)\n", "display(audio)" ] }, { "cell_type": "markdown", "id": "283d6827-3cdb-46dc-8b5d-895550149b02", "metadata": {}, "source": [ "The curves look visually similar. To the ear, they sound exactly the same. It is a distinct pattern of pressures, we can certainly distinguish the waveforms visually. They are the same sound. This is an important fact.\n", "\n", "**We do not experience the phase of a waveform as sound.**\n", "\n", "This helps justify why we don't bother with cosine waves when it comes to sound. After all, sine and cosine are related by the identity\n", "\n", "$$\n", "\\cos(x) = \\sin(x+\\tfrac{\\pi}{2}).\n", "$$\n", "\n", "That is, any cosine wave can be expressed as a phase-shifted sine wave.\n", "\n", "# 4. Simplifying sine waves\n", "\n", "Let's explore how we can take a sound wave which may be expressed in a complicated way, and write it as a simple sum of sine waves with different frequencies. You, me, and two friends are starting a band where we each play the Keytar. Each of us plays a note at the beginning of our performance, given by the following formulas.\n", "\n", "\\begin{align*}\n", "f_1(t) &= 3\\sin(2\\pi 220 t)\\\\\n", "f_2(t) &= -\\cos(2\\pi 220 t)\\\\\n", "f_3(t) &= \\sin^2(2\\pi 220 t)\\\\\n", "f_4(t) &= 2\\sin(2\\pi 440 t + \\tfrac{\\pi}{6})\n", "\\end{align*}\n", "\n", "We all share an amplifier, and the resulting sound coming from the amplifier is given by the function\n", "\n", "\\begin{align*}\n", "f(t) &=f_1(t)+f_2(t)+f_3(t)+f_4(t) \\\\\n", "&= 3\\sin(2\\pi220t) -\\cos(2\\pi220t)+\\sin^2(2\\pi220t)+2\\sin(2\\pi440t+\\pi/6).\n", "\\end{align*}\n", "\n", "That looks like a mess! Is there a simpler way we can make the same sound? Let's try plotting the curves. We will plot each instrument's sound separately, then combine them." ] }, { "cell_type": "code", "execution_count": 9, "id": "1da60ea4-fe5d-4f4e-867b-32244e2577ea", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "the waveform of f1(t):\n" ] }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "the waveform of f2(t):\n" ] }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "the waveform of f3(t):\n" ] }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "the waveform of f4(t):\n" ] }, { "data": { "image/png": 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gb4vVIuuuaWmo96FKn3riPMZjd9pRyIiC0SHJfgmPixe2M46Jbyz2jb3frj3Gcdnp9PcZ8OU6P/UUAJGpceFcK4PRGM3ecEoHP0iYdka1Uh6lfI51rWxHGNelapHdUdxu9rBa358zlH/nkt3OALVSPigwcCGHzlEs1YrYYZww47HAXne/4ZM/c0/MsLEAvLZw6pD9IpOlgGdcByOBvS5fhc20o5AImdXwtQcoFXKoFCeOdaFa5DXggbGYLGQXYz9t+OQ84EThUY5iuVZijVj3Ipy3i/7a7QywEGoHEWGBGVTttCVI2D/2nDpGY2/dhXXICJkzophejy7k7nYUPgoOT5qFahH94ZjtEptGbwgh4NxRePRDad/fFqq8Tk8u5IXKwbZwGtjpibngyFhMT/5FZ45iFmM/0VHI5zBfKTiJKBam5jE3QJCfG9YRfo1DpqlNT0/B+dgv1YroDEboDXlsS9Pv+2mgC7hfK9xydzuKiIhigdnw7c1o8u+0+/u4cKmHc/LvdQ8aC24j3h+O0RmM9vWXt1ktz76QpyMwblQ5KTAIoX0ZHTEv5HDCXOrkjijmy4V9h8ItVAto9oZs1XuyTxZnEFFEgQRu5w3sz+lwt0Wux/nK5CpiCeL2OrwOfOGb3VFUirkDvD7AN5hywoQnZq2URyFH7LTQdLJpiXnyy8nnMqKYTsqH9czKWHDlWyT94BIkSF5/euyXa8WAJ+eQvQhjIdvSYIoqZhVRxI29zClxyE6nj/lyIUiYA/wgNCrKqxRzKOZ5bctuZ7BvzbuQu95RTHcA98SMmvxE5ADB9PdxlVInJ/2w1x2gmCdUiqHJLxFM111/ST2zMBbDsUC7z0MNyL5frrvLUUQl5b3fS4Gj4tITNSYA49hHgKr5Cq9xHY/FzCKKabDDvb8liPArB20L15gA0VQdt3Ddmf3rRLRORM/EvP5WItoN3YD3cyqfOxqLyAkDODB8DhGyECKSSlmsepwo14moez6y8G6n9WSh6oW93IYvCr1yTv7dzsGFzG3Et9sDFHKEeml/whzgM3xREavUw1tZFW1cAQdOL6QnnyPMlwtsOpr9IcbioGNdrBbZqxCXI4AbwEg9yQi/Wtj394UK79gfphzFvwbwjpRn/jJ0A97/qvKhUY5ioeLG8E1zyJx8eKs/wjCiLdyJrb3uMJZ+4OJEo3I6gOwvd5VVYZ2cHPJidb9jrRTzKBdybGh/N6JeH/B4a857xncjqM0F5rGXTm96jnE6vd0YHYvVIhq9IdulZVGOVTpAlxEFAMwz2pbByNsLdCgchRDiLwBscXxWWEYiPqLgQhdxVApnRCGrH6IWWPg72IoXUexHL/VSATmaAfXEWJUSVa8f1smlp9Ed7ks0SuEsW5ZGelrPfKXgtGQZcBNRzJULB+r1OddK/PwqQgi+fEujOzyA9PkjiqTomxu4HZzHnDLLHMV3ENHTRPQHRPStcQ8R0WNEdJGILg4GB43FxLjyJehK+dw+Xh9gdhQ973PmynETkwe97nUPJjRzOcI8Y/4gybFyV6JFUXXh72Arze4AcxGOgnPsJ5UvU6iyXEB/OGYrxYzMUfjGgxMkRCHXhSof9RQXsfKP/fDAepRrh6viba87BJE31vv0VPhAVRx1zi2zchRfAHBOCPE6AL8E4PfiHhRCfEQIcUEIcUFQ7oDhC0oxGSf/whT9AHAbC8+pTRslF7RQVPUDpxFPchSN3pDl6Iu9mAiM3Vj0hpgvR/cXpw4gKqLw9DYZkGXXz3O57q9GdxAZgXHmp5LmV/h1W2n2hgect8y3cAKeuXIhOONLCitVF9Nf3DITRyGE2BNCNP2fnwBQJKLVtPeNI6gngH8hT9M1UsceUymmNAbTyEIuOi6uei8inAZ8WoixRDLquIAFxuoX2V9xiI/P8A0jI4r5SpFtTOLaIseeg0qJMxbVolfmzWWUPOPqNgKT/TGtR459g8EhjccCzd7BiALwDp/kuidkr5sA3Lo8tuVIOQoiOkk+ZCeiR3y9myrvjQx1GasGmt0B6jETZiyA7sC+ImmCKve3Zc5Hs1xGqREzMTlLV+PoB85qNNkf00ZcLuxWj2lXfnd4wHkD3thzIH3Aa0uOvL05YZFt4XAUcZVV3GXezd4wcq3MV4psuYNgrZSn1wofqGr2o50R4M05NuDWOVhcAnjrcTAS6DCcLhFUITreR8GSASGi3wTwVgCrRHQNwD8FUAQAIcSHAfwwgH9AREMAHQDvEYruNKqj6+U8Wn2+iRmFLOZCaL86tch1RaKgacNXL3ufy2GUesMRuoOD9APgTaJLG01rHUB8zfYcI0KOMxb5HKFazAc5Hw49kcaiXECT0RnNlQsHqE0JGhoMbWlE7MiXwmn4mt0hzq7UDuooF9DujzAai307w410+N9Vro2wjvDrVjpiojz5N74I/2BxCRDKHXWGqJXsTPBexDEhLoTFUQgh3pvy+ocAfMjks6O9PidKGuH0cunA3+ekEe8NrS8EacRMzLo/SRoME1PqiJqYcxW+cDrWsQZon8NReGM7bSwAPsMnhE8/RFJPBWZndHARc1JPQQQW1V+M0VEjwbECQKs/tEa2zd4QlWJu345pYAJEeOZXdITv/Y0zohjgTIxjDX8PG2nEFEtwy129Mxs4yOsD3oJoMiXPmr1BjOHjSzZOFvJ+PbkcsS3kuFI8qZdr8rdi6IewsbCVZkzyX+rhQPudgYeA5yKS2fVSAd3BmOWMpKjqGsCVo4iKvnnHPin65jLiUe0IqDpGUBU1v+olRsfajXacEiBy9FfLpzanqza55a53FHFGiYunjlvI3KFuvZSPDMvnmJJnQaVQ1MQs59HqDXkS8wlJQIDL8HljG1WR5DlWvoR5HE8N8ORCGr3oEtyAemJoi5w/kRFYucDivEf+0SlxzghgAlUxe1vKhRwKOWLREVDBMU6PlXqKKC4J09q20uqNUI+gNrnlUDoKXpQ0ikWuAFd4GE1xAN7iZuVdo1ASc2I+mXqyN67N3gD5HEWiJM/p2evYS3AU8wF65XFIiUCE0bHGcu6MUUuUM5rnBFW9YaQOImKjUONKlgG+6FtSm9GMCG9/RY07t9z1jiJu8rf69tv5e8MR+qPxjMLp6MGcqxRZwmmJGqtFtwtZIphpYe0vPwKLQklzZZ7+iqMDgRBC5gAJMbx+qZBDuZDjGfvAiMeBKg7nHW9cOfsraa3USwWesU8CCX5EYRt9dwdjCAHUEuYXF/UUNe7cctc7irhwWgigbVlellT9IPWycKIxCU3AM+IcVErHP1F1ugwT4FvIQgi0+sPIpGmtyNdfzd4otr/mfBrNWkdgLOIruLj0RBkkqZuDemr2higXcpFXYXL3VzT15I09l544RzHPHFHEgVAhYH1CsQRu0euRsb8yR+FJPaJ8jMsjtxJCdsmP80z+6B2tUjcHEmsHjsJdf7X7IwgRjVxz/imsXFVP8REYT38l8tSs+ZZ4w7dQKTjXMVf2Tii2TcwHx9BEUnUy3+K6LVxj70dgCWvFVo8EbtERviyN5umvKHqLW+5qR5EjOrD9HeDb0dwIyjAPdnSlmEOOeDjkRgJKqjMl5tsSwcREYIB9fyVRHABfGW5c2arUzUUJAfE8tfweNpKUAAa8/uIwrkn0Q4BeLRFyXIn3Ph1MVEri2DOuR5e2JQm4SdvCRz3Z7fNSkbvcUUT/XSIB20mTxFUSERuCSUJJ85UCC/0QUE8RCIYrokgyrlIPF4ccZ/i4DtNTq3rimV9xho9r7OPKVgG+/S0SzCT2F8OFUo0Ep8cVTTZ7yRE+YG9bkoAbEbEBxLicIbfc1Y4ibpcn10KWPGK8Eec588fjqeM4d57kWas/Qil/cKOS1AEwRhQxu0m5Sn2TwumJ0+NByEl7QmzRvoxY49rCSaUkRayA/dg3E6LvciGPYp6s+6s/HKM/HMf3V8k9cONaK0nATerJqp6YJBdTG8y1+SbJWHh/z1sji/FYoNmPD6fnKl7pqu25L51+/FEjXJN/UiKZYPhmwFMDDGi/N0C1ePBwQwDBjXdc/ZUUgbGgyn48/cBVs59EPcm/20ctKToqPP2VXK7OAxJaCdQTwNNfQois6gmIdxRcVEraQubYrNQeeAngqEohgA/xtfujyAoLTwcPh5yU/Pf0MKGkhIXMhfabvVGscS3kc6gW7RPzadRTrZRnORguiX7gc6zJRpxj7JWASM++LD4pAptnYisk9RQH3jj6qzccYzgWWUQRAfYAcPKu6ZPf1iC1e7JMLp5zBxg40cEoflLKnI4lGgv6K45zZ3Cs47FAq59g+AI+3JYaSD6QjYMPTzN89RIPVRd3U5/UAfDk82oxpwsAPFSKCnAD7Me+3R8m0qfh72IqSeXqUg9Xf33TOwrX1FPTv4EqbjA56rbbChMG4JmYcZOfq3S1ERi+BJRkHbL7xiKNc7dONsZHYIA3LtYgIWXsa6WChwotS1dbvXjDx1XFk8aFc9COSWdWAXxHqySNPRdVlzb2dYb9LWlViJxydzuKGPRSKeaQzxGL4ZsrxZ+TUmdInqU6igqP4Wv1ko9DZzHiChGY7SKOu4tCCtcu805CBAbwcMjB2BeTS1dtNo6Oxt69BvF5Nr6Kt0RHUbGPJpvddCACTBLrptLpx489V2JeUorxOYoi31r5Zi+PzccYcCIPIXMYviRvzEE/dAaSq0yhBhgMXxpCblouZHlSZdQmIsBDr/2RXemqNGizQHxx7QB4zuDqpPDU0oi0LQxGK+ESHiB05wlDxOoaiKRRKROQ4C6iALy2tBnorUKOUCpEm9i5ct66NFo6miyiSLgExStdtd1mP4qsc5bCUbqaSj/4+m2TmiqTnyOhWU+MwGTS3LwtSRuVgNlRT17+wH5MgGT6AbDj3JsplXvlQh6lfI7BuA6TgQhL9C33HriLjsZ+BBYH3ACvpNV27Fu9dMfa6o+sbEtahM8pLI6CiH6diNaJ6JmY14mIfpGILhHRl4joYaUvl3Byrof47DxyN8VY1EreuS+9oTmH3E7Yyu/psDeugI/4YigOgI8TjaOEPB32CznVuEoUbrm5yysnTjAW5QKL8waSxp4holDgqTnG3osokseej6pLXis2Y98dJs8vQI69fX+lAbfRWFjZlsZhcxQA/jWAdyS8/k4AD/r/HgPwKyofGkc9AR6VY2ss2v1RLH8M8EzMtOqHwFhwVHIkRkf2EVjaAWQcVSnBGTkx/ZX3w3n7/hrFGiRAoko7Hd3ByDuuIQbxBBGYTUShwFNzlGKm9Ve9nPdLwe2j73iqTq5Hd0BEvmYdTQ5GiVV1HEUGhy6ZLYT4CwBbCY88CuBjwpPPAFgiontSv1xCSFEr5gOjYirtwQiVhAlTDdA+x8SMr6UPP2cqrVQOmSOiGAXGLUqqDG1RXcj2EUVyf9XKDPOrn2wsJMViY/g6KfPLey3P41hTxt42+u70R8iRd0lRlNQYosmkw/omeuzHvtMfpuhgjCYt791WkVnlKE4BuBr6/Zr/twNCRI8R0UUiuthp7MZ+YL3MYSyGySjJHwAbCiJt400xn0Mpn7Nqy2gs0B+OU6Mj58aVYfIH1SJJNJplNCmE8BFfCqrs2+enEhPmrDmdJCNuH32nVYnJdWQLqmoJObBZADf5mv1ejfgNnZ4O+2gyAAlHqOopauQjV6AQ4iNCiAtCiAsnj6/GfmC1xMMhpxkLwG5iplFPgLcA7MLp5Eoh77VCUIVjrGeQvEmNgxpIqxSSr9lwyP3RGKOxSO2vsS1CHiQngDkiCllam+aQ7KOjlLZwoP1Bcom31G/TFrW1Yt9frZScDkv0PRihmKfIY2i4ZVaO4hqAM6HfTwO4YfOBHBxyOkJmmJgKg1m3RPtpvD7gRxQMHHKaAQdsIzD3HPKkv9Kdnp1RSqus4siBpTtW22hyPBboDsYpyX+esU/qLxl925xSq7pWWHb+p+TAwt/HTMcIlQQdnDIrR/E4gB/zq5/eBGBXCHHT5gOrLCgpveoJsDs+uZNCPwAcEYVa1CIs783upiU0GVBlWqUQYI/4VPqrXrJPzKs6Vp6cThJ6tdsXMNk8lg6qbNuStla83JHrZDZToYxSBGbHJCTp4BSWLAgR/SaAtwJYJaJrAP4pgCIACCE+DOAJAO8CcAlAG8B/ZaszXGURx2kmiVI9tdw5az2Yyd3sbfCx33SVSAsVJ21JMl5Jksbrc3DInZRKIcBr53qja6xD1bEC9ohvbb4c+3opn0PB8oQBJcNXtIsolPqrKPNT5m3ppswvwGcSLCN8IAUk+PlPU9sCqBVLABwRmPtENsDkKIQQ7015XQD4SQ5dUmolrw65PxqjXNA3fEr11DOgHwAPPVslgBVRkvw+xwz1tPvJVWJcHLJaBOa28oXjZjivLbXY14nImhbq9EeghEohwD767irkQbgiijTDVysXLJ138kkJgL1tAWQy233pfdpa4ZK7emd2ksgOMjWwqiEowEA9pTiKermAtkVyVgshGyIYlcqqYj6HYp6szi5SMhaWjrWtEIEFCNmyKkVl7G0jsFoxn4h8bfc4qNBbHOdWtRU4d9v8QdqmPqkDMLctAVuRmKOw35yadmwPpxxaRxEMpuHEVK2n9p61LflTQMgMJZJp+yjCz+rrSK8WAbz+tKVrlBwrR6WQSn/ZjIsKlWIZUbRTqms8HROEbKYjfezld7ChnjoKnLt1BKYw9ta2RYHe4qA203JgnHJ4HYUf1pkacRWUJBGyLSeatpCtq54G7hGySrUIwGDEFR2rDberRtXxIGSliMKynFjFeXvPWoIqhX0U9tRTmqOwpZ6SN/VJHYC501OJ8EsFLz9lM7/SjgnhlMPrKCwnporX916350STwlypw8ZYBKdIqhg+h1Qd4BkT11VitWIeg5FHhZmI6iY1wNxYqFB18jvYRpOp/RVs7rIb+8TomyE5qxJNclBP1RSqzjZ/oFJ+LfXYld6n5/O45PA6CstdrWk7psN67Hebpuvo9M05ZNXacMBtOC1ft538qTqCaNJ0IaePve0eB1Wqrm4JEtJ2TAMM0bfC2Jfy3h0xptGkym55+R3s6Zp0qg4wL41uD9TGvmZbtqzQFi45tI5ikpy1pFIU0JhteKjijIZWHLJKLb1dvkXqSE02Fjmop3QkBsC4AECnv1xTdTXL0mglIGIbfSs4ViKyOp57sls+3YjbnZSglgfxnnUbfXPkpzLqKUXq5Um5p4moD2bBKkGnyrsCFhNzMESpkIu9zziswzacTlvI1qWYio4VsB/7JJAg9zi4nl+2V9SqRqzh72Siw/scd2OvA9xc7v4G7EujddaK6ZgIIbKqJxWpWqMkRcRnMZgqm/qkDsBuYro3FopUStl+Q5SqYzXl9juDEcopjpWIrBayFhCxzIGlzS/bChtlp1cuGEffOijcJj+lQtVVS3ZUXdotjVJsTvXtDccQIt1+ccmhdRST5Kwp/ZBeKST1mCIYlU19AE8FV9pRw+VCDjmy4PUVygoBr7rKdcmf7eGDqkcf1C045LQrcAMdZc9YGOenBsnHqgA80WTapj5Alkbb0YHpY28ZfatEFJb5T+W1YlEoo7IfhFMOsaPwJ78pgtGoejKlBpRRUtFuYqocy+HtAjZPnOrxrm4rhYL8gQV6VTn6oGZRwaVTJWZzSq2OY7UZ+7RNfVKPsXFVpGs42pJ0EyRgn5/SoR3tI/wsmZ0olWIOZIOQFVGSTZWFMu9qvRlOjavk4JCVyj0d01u2yUaVAgMAVpcXqeRBgMnhg6Y3nakWS8hnjXQM0uktwOfcXVfVWeYmVZLZfPkpdzkKOZZJR+pwyqF1FLLKwsq4qqIkxxNmcuqqDUpSMHw2E3MgJ2YK/VDKozf0Kli0dSjSD8HJrhaRnopjrRXNo0mVTX2AXf6gPxxjOBbOqSfV/qpb3Hki5356VZ19viWtLbb5qY4G4LGOWjLqKV1sjk9WqacGYHUImS5CtkEXShGFlWMdevdVp1ySYuP0dOgawHxzl+pharWyeX5KFSTYjL2qY51E344dKwNCTo8o7Kgn1WjSJj/V6qtdKGRTyKC6VrjkUDsKu4mpltCsFfPoj8YYGOxx0KmlB2yTs+lOr14uGO87UY3AbBCyTh4k/Ly2HoVNfVKPedSitqHTyrEqHN0C+AjZAiSoGtdZVYnJ76Qrqpv65PewqUJUASLVokX0PVCbX1zyTesolFGSBSeqm8x23hZLxKfE69sgZMVKoUohDyLb/lJJZptHk7OgnnRQZa1kXrqqWq9vRaUoVgrZJLNVN/UBtvkpVeBmHhl3+h5wPVTJbCJ6BxE9T0SXiOiDEa+/lYh2iegp/9/Pcei1SjQr1FNLHYDhQlZO0M0omW1xPLeOM5LPm+gA0hPAuZyPkB0mgAG7Xfmq9xnb7KFRjVilHptD7tIqhTwdBXQHY4yN8lPq5eryO+nrUJtfgF1+Sr24xIamVaO1ucTaHRFRHsAvA/g+eHdjP0lEjwshvjL16F8KIX7AVl9YbMo9lXlqCwSjckkKYH9OjuqZL57hc5vTsZv8OgjZwogrO72C+aY+zfll0l+qlULyGec0bSh3lHRpT5SoggSbk1215lc5j81mX1sH4OcMy2q0tnxeW4csLjlEyexHAFwSQrwghOgD+DiARxk+N1Vsyj11jAVgSQ2kDKbNOTnD0Rj90VgZwZj2l8o1lYDdYXo6CNm21FcVhZvmp1TphyrH/FLtL+eO1QZUpe+WD+swAQmqm/qkHptCmbQycqkDMNs/dRiT2acAXA39fs3/27R8BxE9TUR/QETfGvdhRPQYEV0koosbGxuJim02rKgcrQGEB9Mcwbg0fKr0lnzGpupJKUHHQD253DUdOFaNhWzaFveOVa2kFJhVfsrO6an0lzxhwCTSU93UB9idMKB6L73NwaaqERiXcDiKKAgwTVJ+AcA5IcTrAPwSgN+L+zAhxEeEEBeEEBfW1tYSFVetysvS74nwdJgjGJVLUqSYUilywSglz3xUaXJchMoO4PD3MJn8AZWiYMRNK2x0HKtNormrmAOzKfVVLcGVz5j0l6wU0qPRTB1FejvkCQNmOtR5/VlRm/J5Xen0h6gUc8ilRGBcwuEorgE4E/r9NIAb4QeEEHtCiKb/8xMAikS0aqvYNjx0ncz2qkUKqSWlgKSF3Ca1qqUChAC6A4NSX43KF8AsnFY5zjqsxzW9ZZM/UDUWNvkp7ZyOVaWQ22jS2/2tho49Gs2knFhv7G1obdcVgqqOlUs4HMWTAB4kovuIqATgPQAeDz9ARCfJt5ZE9Iivd9NWcc0CIatuUqsVzb2+6oQBzA2fLu8KmHHIOseEAOb0QyFHKClFYKaoUiOisB57RYRsmJ/SrnqycqxqUQtg7lhVaRTbtqjOY/M9DumHdIa/hykInRXtBDBUPQkhhkT0AQCfApAH8OtCiGeJ6P3+6x8G8MMA/gERDQF0ALxHmB6XGZJaCCHrbDwJjj7QMnxmVU+qyaZaKY9G123li40R76iWSFrsCdF1rK4jsHAVj650+iOcXKgoPWucn1IslgDMOXfdqCX8Hh1RzYMA5icMTPpLw4gPRpjTruBSrRKzoZ5mdxcFwOAogIBOemLqbx8O/fwhAB/i0BWWMDWg4yj0UJKl4VP0+tViHut7PSMdgNuFLIRQnvyFfA6lQs6oDFdn8pvunJ3Z2Cvu/pZ6jHJgg5F3gF3KXo1Ah3+cuQoVKsVkfpki5JV6SelZU1pIh9oMl3nrOIrRWCgDV5tTanVAFYcc6p3Zppyo6p22gN0FSTo3UJnucZD15Cpo3/S4iP5ojLHGJSmmC7k9UOddZ4GQ7aJJnejILD/V0QBItbLZceZam9Qs7ppWpTalHuc5HcM9Drp7W8LfS0uPBgjlkEPtKEw7WmfC5HKESjFnXJWibPgM9zjIttQVNviYUk86xgKABeeuVoIL7EfIOqJTVmhDDegZPnMqRWdMAP2x17n3YBbUptTjcuc/YGNb1DbZAkAxn0Mxb3acuU7EyiGH2lGYImRtw2eBYJwnszUrOeT30tKhubnHuCpFw7iaXvjT0Ygmbag61X06gNcWExpN9YA7wBztz2J+ee/Ro+qM8kaDkXJJqSlbMbm3xW00eRirnu6YVIxRkvrkB8yTZ7rJbJMKLtUzcqQOwMBYaPaXTUWSjmMFzMfeJULuDvz7jDWiI9f0lm00qTKPrRDyTCIwtd3yng6zzYM6Eb6nxwwkdLMchbrYhodaRtzx5K+W8kZ7HHTCadPjInR2tHp6zMsXdcYE0N8IqVVSapif0p9f5hvItPvLdTRpcG/2aCzQG6pXLtrkp3SKS7z3mIIq9bViRGtrRJMccjQchWZHd2U4rciJ2tRtK+uQ0ZFmW9p9tTNy7HTMyLEO1BHfxOmZLWTlCq68fgWXfgRmWsWjR28B+mOvUykEmDk9nQSwfM4kP6UDREz7a5YgNIsoFMW0KsWIczcpKTXgkPURzFD5pE7zKjHvedWTKk13AWtVChmjfbXjv6WYjL2Z4TOsqtPgwgGbKh4NUGVoXHWcnkl+yoTaNI3A1IsM9POfo7FAfzjOqp5UxbQqRddReJe+6JeUjsbCOYesE07LA9W0OXdt+sE9NWC6kHUqq6Qe98n/AjqDkfY9DlrUpoVjDb8/VU8pH8wXVdFPAJvnW9zPL72xrxgAkVnfRQEcekdhN5g6Rtz1hLFpi6oO0wPV9B2rPqqUlULa1IBBW3SqRUw45AAha1CbgAktZIKQ9SsEValNqcfYGTnOT+mUlNqzFeqUs7n9yqqelKRckJfGu6t8AbzBNK6s0kBi4ffp6NFBFpWifumqTokkYGYsekO/UkibqtOn0XT6y4RDnhVI0ErOGnPuev1VNbhyVbsK0SI/pbrmJ4c1GqJ9jaonY+CWUU9qIg9UM9mZXbrrUJLZ8dy6x5eYtEWnBBfw2tzXPFBNd/LPAoV730efQzapFJLfTVXGY70IzMYZ6URgNYOqJ1lcojz2hjSaztib2hZdGq1aygftV9ahmQPjkEPtKADJ7+qH07ooyXVJqc1CVjmpMqzHeYLOwIjr7AAGbKgBvR2tRslsTZAgixF08mDdoR79UCkY8voD794DVbHL6bhfK67HvtVXP38LmA0I5ZBD7yhMqIF2X71aROroj8YYalyJqZtwMk026iJkIwSjyVOb3JutnTey6i/XjtXM6eno0Y1acjny9jgYUU+aOR3D/tIu/HAdTRrk2nTO3wLMChl0QSiHHAlH4dq4miTPTHh9+d10RBclmSIYPbpGvy2mdI0RqtQACSaFDDq36AEhKkXjfCxdxyqfNaHR3FOb+lWI4fepiM4VuFJMLhMzWY/AJEJU0yGLJbKIQllMq1J0FxigNzF1J795Mlt9kxrgVeKYbIjSjcC876bvKFTHxfSwRpOFbIJcSfEKXE+HQQRmwFObHEWjTdP6UYsOQjapqgu/T0mHQX8ZgSrNYgkTwNPRBKEccugdhSlC1kEWNoZPVc+EQ9bMtyjezSzF5FwhE3oL0J38enSNfFa73FO7v8yS2bViXvneBxMqRde4ymdNaCHdfB6gh5B1DZ9JfsokAjONjnSpuvD3UxGTsbcVFkdBRO8goueJ6BIRfTDidSKiX/Rf/xIRPcyhFzBESZrGYnIlps7E1ONdJYes05b+cIzBSOhRKSZVYppRiwk1YDL5zduip6M7GGsjZJ08iDxATg+I6O3VACxoWuegaoh8jlDSSADr6tCN8AF5bpVmMrunX4UIuM1PcYi1oyCiPIBfBvBOAA8BeC8RPTT12DsBPOj/ewzAr9jqlTJLHtG14dNNngWTX+MGLrNko2FOR2NcdCurpB7dklLv9jF9w6eD9nVODQYmUaeJ4dON9LTHXpdKMVwrOhGYjL5dG1dvPepHrEa2RWN+dQ8p9fQIgEtCiBeEEH0AHwfw6NQzjwL4mPDkMwCWiOgeBt3Gtc6z8vo6hk93Ievc1CdFOiOdA9V0J78JlWKC+HQRsgmvbzr2ZsZV37HqtaUwk5xO+PupSKc/QkVDh0kFl6Q2dUCCSVm89tgbsBW6ERiHcGg6BeBq6Pdr/t90nwEAENFjRHSRiC5ubGykKjc9tM1kIesaJdVLUqToHqZnipJGY4HBSJNKmVEy22UpphG9ZUCj6VKbpUIOhRxp3Uuge/mWfFZnfgWHz80gmtSlUWa1VmZF1enO46pGBMYhHI4i6ttOWyGVZ7w/CvERIcQFIcSFtbW1VOUmCNmYc9cIQ3V1AP7xB66NhYnh001mm1Ry9IcggubmLr3DGk2NK6C3Gc7E8Ok7Pf1ociY6inKt6Bs+HdEtWzamNg1si+qlRVJH+PupiO565BAOR3ENwJnQ76cB3DB4xkgkQu4rboYLeOoZIGTdya97plSrZ1IppG/4jKknzXJPXZSkbSyMKqtMx14PJOgi5I5/wZVuW7RyYAEX7hYhdwzuf9bNTxkls0v6l4np5vNMbuk0ASK2wuEongTwIBHdR0QlAO8B8PjUM48D+DG/+ulNAHaFEDcZdGsjZKP6c8N9FGbhtEFtuGMEoxsdmRyoZkQ/aDpWM+pJf+y7BreP1bWjSf0ITNex6p5bBJgjZNfRtwm1qXvRl7ypz6z0Xi9ineVmO4DBUQghhgA+AOBTAJ4D8NtCiGeJ6P1E9H7/sScAvADgEoBfBfATtnql6E5MI67SgEoxph8cJ4B1D6AzicBMDlTr9EfKFyNJMe0v94UM+gjZJN+iG4HVigWtwxpn5Vh1UThgAhL0ytUB/Y2QJlTdhNZWj1pMgIitsBwWIoR4Ap4zCP/tw6GfBYCf5NA1LboL2eQs9+BKTMc8onGCTutYAs3+Mjyp0sTwmeiYRYmk915NxGcw9i0dHQMDajPUlvlKMV2HkWM122VuEn3fanTVdczA6ZkAkUpRXpXgNv9pK4d+Z7ZcLKoH3Ume2iR5pjWYGvc/S9G9VEh3U5+nQ8/wmZ5UqcuHtwd6m9QAE4RskgA2S/7rOz29UkwTIKJbtmxy+JzRuWizAAkDvStwAXO2QieZTaS/0dYEiNjKoXcUuhfYmO5q1M4fGC5krWS2EfXkH7GgaSz0HaveRshOf6h9EYuu0zOJJnVpx/5wjOFY6IMEbWNhQG9p0o4mh8+ZXCamW1IKmCWzTcAhoG9bjAoZNIsMDl2O4k5L1dhYGCAYTT5c2/AV8xj6tesqYlryF35vqg6DSiGpR7dE0gRVAjqGTz85a4rCtWmhsgkQ0R8T+V4VMTl8Tjc/JYQwcnq60bcJXaNbFt8x2AALzIamtZVD7yh0y/FsIopZcO6ADic6RLWY197UJ7+fmo7ZRGCmOR3AreErF3LIkQZVZ2gsdB2rCRAxRcgmNJqqjt5wjLHGFbgTHe7Xo+78avUM14rmLYqHdR/FHRXdzV0mPDVgOphmCEZ1j8NsnJFhBGZQuup6Ibf7Q+Q0jv8GfISsYfjMczqa88soAayXbzF3FDll2tE4AivqXSZmlNPRti1mY1/RAFWmEZitHHpHoZs8M+GpvefVDV9wSYprhGyEwu/WnI7ZTnZAnRpo+/X6ukcf6Iy96e1j8pRa1cS8XQSmasT1iyUACapUqU3zqrrw+1P1zAJUmdK0RfVbJ/sjLwLLqp40RXcXcFDuaZA4ndXkV52YLQNkkc8RSoWcetQyMEN82seRaJ6PBMzGsUo9+glNs7ao0k9Whk9Dh8nhczr7W4ydkW50ZFJVZ1r15BBUmUZgtnLoHYUpQjZKZjuma0wmpu7kB/RoIfOFrF5OPBjp36sBmFEDJiG7TvmiycYuwKRseajvvLWrnvSO/5Zi4lhNiiXC708Tk6o63cvEbAplXNOBtnLoHYVEyDrUgC5PDeglG23oGu/96hNTF71IPfoT06zkT+VANZu9GoCe4TNBYt7Y6xkL1/mDzgwQsk0E5j4Por8fSFeH7mVik2S2yTlfboGurRx6RwHod7QJT62TbDS5fSz8vBbiM0HIGqW+NgtZCK+qJU26A7MFpr/L3CwJaJLMdpmfCiIw19ST4VERVY17L0zvf9YFCbp3XoT1KK+VwRClgnfOmZ4OdduSUU8WolO33RnoXVUoRedKTJuSUu87ukOVUo/OAiOTCEyDFjI2rppHWkuQoCta1ICh4dNByKb9NTmsUT2ZbTS/NO69sF0rWgDRwLjqFjKYAjf1OWyWMLeVI+EoqhrUgA39AKgZpVmgSsA7Ztxk8uuU+prz1Opn/pjy+tqFDDNIZncMF7JOrs20skp3M5xVxKobgRlG3yp6xmNhVE4MyLFXXyt1w5zhYCQwUCj1NQUitnIkHIUuNWA6YeT7VXQANobPLYeshZIGZqhSpy3GCNm/GW4WYz+rqie1+WW2FwjQT5ya9tcsiiUAtdLo7tCsJF6+ZxY5HUANhMp+1TlPikOOhKOYTXionj8wrqfWQJVCCLQHI6MJo2v4THXI96voCL9HR3TRq1nVk/q5VZ3+CGUjnlrfsZqCBB3DZ+ooVI+iMTmvDNDLT9nML53jzE03whmBKs0IzFaOhKPQqUhqGR7RO9nY545D1tnj0B95m7OMOHdN+sGEqtNZyKZ0jfcePfSqW2AgdehUcJkmzOX7VXTI76Ur1aIGH25wAjKgB6pMIzAd42patgrogaqWJa2tE01m1JOB6G5YsfH6Ohyyy9JCm+qHakl9J6gpStI5UM0K8ZUKSlUpMgIzHXvVCi6bhLn3fvWcjmtaqN2zo1JUAI/JeWXAbIolAN3Ng+YRK+C2kMFWrOIXIloB8FsAzgN4CcB/JoTYjnjuJQANACMAQyHEBRu90+JRA455V43NSpPw0EyPyuQ3Ddnle7SoJ8OoRb4/TVoWjtXbPJi+wHrDMYTB4XPAfsSXdgufaVWdDqqcgAST6Ei/kEFfh54RN5nDOpeJ2TpWnbL4WqlmpANwG4HZim1E8UEAfyKEeBDAn/i/x8n3CCFez+0kAO8QMq0drUYUhx41UMrnUNA8+gBQz7eYJgG993h17qqlvu4Nnx315Jyn1ixdNdFRzOdQzKsl5oOjIgxyR6o5iqBSqGwOElQNnymNonqZmL1jdZ/TAdTXikkEZiu2juJRAB/1f/4ogB+0/DwjmUXVkw414NWfm09+vRDUPN8iq0HS9Jjs/pbtV6G4bFCSquGzqxTS49xN0Z5qdGRTIqmaz5Nzw32+ZWgUsXp63IME3T00VslsxbUya9oJsHcUJ4QQNwHA//94zHMCwB8R0eeJ6LGkDySix4joIhFd3NjYUPoS1WIePYUrMYXwUJLpsReAurEwHUzVkzcDVDmDUl/TTX2qOjr9ESpF/UohQP3cKtNTgwE9PtwUVQJAvaw29jYRmGohg+ndCoAX4QPqEZgVqFIxroaHdALQukzMy+m4jcDuxF0UgEKOgoj+GMDJiJd+VkPPm4UQN4joOIBPE9FXhRB/EfWgEOIjAD4CABcuXFA6czlchzyXECp3B5Kndmv4TJEF4E3+7XY/9TmbhLkeNWCWzJYHqqnlKMwvi/cqktQjMPeO1YynBjQMn2UE5rxYQuO6XRvHql744TtWExotBBBLCacTmF4tAOhFYCYnRnNIas8JId4e9xoR3SKie4QQN4noHgDrMZ9xw/9/nYg+AeARAJGOwkTCHHKSo2hZblQC1DfF2Bi+6ztqE8Z73l2+RUZgJv0lD1RTolJs6JqSWiFDyyqno765y9bwtXtq/WWyV0Pq6Pilvkm77U2vwJU65PdMk1Z/hKVaSVsHoH7CQBAdGSXmJ5eJLaIY+5xN1KJ7fMusj+8A7KmnxwG8z//5fQA+Of0AEdWJaF7+DOD7ATxjqXefqHLIpufKAHrn5LR65l5fFfHZ8a7esKc5vUkEZmH4FNGr6U5THR0AjPhwPcQ3C9rRfH7VSgWMxgL9lOMigvnleLNlx6ItytHRwH1bbEviw5+Rpucw5ij+DwDfR0RfB/B9/u8gonuJ6An/mRMA/oqIngbwOQC/L4T4Q0u9+0R1MG0SwDrn5JiicEC9HM+OelKr25avmyYbdZyeCR0I7EfISWJbTgxo5CgMKA5AvWbfBlWq0o4BqLLYbOk8n6cIElq9odEFTIB6W9oWQCSoeLuLk9lWMYwQYhPA2yL+fgPAu/yfXwDwOhs9aaK6Gc6GepJ6lGiO3hBnls14atUKLpuJqYpgbI6KkHqUEbIx9TTZDJe0x4GLp06Sgc9Tm+RBAK/cVYV2tKW3AG9slxKmaKvnntqUz9hVCKobV92DLQH1c5hsd0wrF2UYnhhtK0djZ7YmSpoFlWLsjBQruDr9IYiASlF/CPUjMPP8gWuUpFqRZLUJUrO/TBey6sZRm/5SBVWm90QA6kfRCCGsy2PVc4b2jjVJbNdKTTXXZnhitK0cDUeheKS1DQoH1E+StOKplRGMlwA2QUnq4bRdBFZTTGbb0DW6Y2/CU6teiTmh6szHvqXYXzbIVX5Gkths6gPUKpJ6wzHGVjkwxWS2hTOaXCamOL8cl/p6ayVzFEaiWpFkGx56CMa14VOrgGhZVVapGVebHa2eHg1qwIJ6AtScnilPrXol5syoOsPD+jwdapc92Z5SqpLPsykuAaB8mZiNY1VPZttdKKRSIWhzXpmtHAlHocu5u0yeSZ7a3PCpVXC1+0MrtAcgFcHYokrlnI7FTnbVhdzqmV3AFNaTalx7thFrHn0F2rHd46CeUhByz5JzVxj7lmWxhGr0bRNR6MwvwK4taTpsToy2lSPlKFQRn3kYmj75JxSH+4lpOmHKhRyIgG5aWyxqw+X7nOd0NMoXbUJ2FcNnTdWpGnEOalNh7At+rsFMTzotxJEzBNTG3sbhyc9IkmDsLUCVcglulqMwE1XqyeYgPUDN8NkaC1XD5yUBzXQQKVIpAao0pznSjEV/OMZwLFA3LSmVnHsKJWiz+xtQHXtbkKAeTdps6PQ+Q8GxWlAcKoaPo1gCSO+vVt98n47qKcgtSxCqktOx7S8bORKOopTPIUdqvL4NSlJJZlvTW4rJxpZFHgSQR1+4qxQC1PYF2KIk1VJMe8OXXsHFQW2GPydOvBJJS8OnkM+zdayqeRDriCIFJHT6I+M8W3CceYqOds+8ChHwQVWaDosSb1s5Eo6CiJT2H9geqOV5/bQJY76pL/y+9LDdPKIA1KgUmxJJwHMwaZfG2+5tUabqLM/IUang4mpLUuXTYDTGYCQYkv8qxRJ2a0U1+rbJ6Xifo5CjcEw7tvrevS2mOTBPh+Ju+Yx6MhdVDtl0UgITFJ60C9i2RFKVRrPJUQBq5+TISqGycQSWvpBtUaUqh2xz/hagZvgmVTzm5dfhz4kSexSuHoHZgCqVPSGzir5tNvUB6k7PKmJVACIZ9cQgqhyyLe+adiWmzV0BgE5i3nJiqvaXVaVQuuGzOYPJ06FeyGDbX6pVPC6jo6C/DOkHuRlOpZTcrr/Sddgns9Od3nA0Rn84tgKISmPfGxmPCaAGQm37y0aOjKNQrXO3QhYKia2gRNJ11ZNlFY9S8szwzuSwDiA5OrJN/qtvhnOPKjv9EXIE8whMYX7ZOiP5XvcRmFrECnBQT/F6bCv35HtV2uIchFpGrDZyZByFymY428FUyR8Em/occsgDBpSklGy03NxTKSosZEuUFBxnroCQ7for3fC1enY8tQQXSfOYo0RSZTOcbY5CZTOczV3pgFqprwRudgAxPf8px95chwpNaw8STOUIOQq1ZLaNN1bhw9uW1MDkOPN0HbZGPB1Vmt0vLkVpITOgJBW0b234VCq4BuYbB4FQMrvntr+UChkYIjAgOZq0jcBUom/bqAVQG/v2wDbCVwGhWY7CWlQrE2xDUEAtOWuqR+U482Dy23KiClSdTWWVzkJ2mT+QPLWVcVWp4LLkqdWAiN1eIPle11SK6lqxrRQC0qhNhohCZa1Y3EED6IHQjHqyEFUO2XaBAemGjyxQktSTNGFs7jOWosYhz6K/uDjkBB1MPDWQ3hZbSihNh+35SJ4etf1AdihcoZDBMgJTuUzM9jQGQLWi0r6qDkiLwOz2atiIlUYi+hEiepaIxkR0IeG5dxDR80R0iYg+aKMzTtQ2+Njz1EAyh2yLkjw9yW2xrRQCFMNpppxOWn+FnzWRtM1wgXG1rKUPf1aU2Jy/Baht7mIzfAn9NRoL9IZjFuopqS0tizOrALXo2+YKXCkqyewWw74mQA2I2NgWU7F1Tc8A+CEk3H9NRHkAvwzgnQAeAvBeInrIUu8BUa3bdo8q7VASkL4DPKh8seFEFagULpSUjJDtUVK1mEtM/k8u4eEY+2QjbnupTK2cjF5ty6+B9KonLjrQ+6wUw2fZX2lof1JObBt9p1cI2uyYVjn+3SsumT3tBFg6CiHEc0KI51MeewTAJSHEC0KIPoCPA3jURm+USK8fV4fMgZJUyhdteX0gvYKLK0EHpCcbOainNN7VZq8GkL6QWaKW4PrYlIjCduzT8lMMTi9tD82kXt++iieNeuJYK4mgSvaX4REeQPplYv2h3c2GgNqeENs8iI3Mguw6BeBq6Pdr/t8ihYgeI6KLRHRxY2NDWUm1lMc4oQ6ZAyWpVPG0egyoMnXy86AkIN2IW01+pX0BM0CVjDmKJMfastx3AqQnmoPkrE0uJIV6mtBbbg0fT38lg4Rg7C33HIU/64AOpso9ID1ivWsdBRH9MRE9E/FPNSqIgoqxxdVCiI8IIS4IIS6sra0pqkgP3XgGM33yc6CktOPMJ07PfmJKxDUt47Gwvp834NxTqCfbyZ/KU7NST8lGySbK8/SkRUdDVIt55HLmEVi9VEAzZtw9HfaOVWUznO1BjUB69M1T+JHcluBeDYfOSL52J3ZlA0DqrBZCvN1SxzUAZ0K/nwZww/IzD8gkeTbCcsTrLYbJXyl69zgk8+EjzFdmE1HYtEWWccbpkZN/zvLaRQ/tu0VJaclGDpCgshGyxUANpNFCTcsSXMAb+/5wjMFojGLEjX+TElx7INJNilwGdsUlUk+S0wtyYAUbp5ccfXMANzmmSW1p9oaYuwMnxwKzoZ6eBPAgEd1HRCUA7wHwOLeStIXMQT2p3OPQsSwrBNLDaZ6J6fVDoxuDkiyPIpGS6vT6Q2sd1VIhmRJiKcFNdqwyB2abbExLNLd6Q2vnLfs7LpqUxsrGKCkVfnBQTynRd8uvFLKJwNLawkEFlws5FHIUOyaeHnvHaiq25bHvJqJrAL4DwO8T0af8v99LRE8AgBBiCOADAD4F4DkAvy2EeNbuax+UtIXc7MrJX7TUk3yPg+1x1kD6SZLt/gjFvPm9GsDECLg0FkD6pfHN3shaR62UXMHFSdXFzS+u4xXqKftbmr0h5iwj1vkU9Mox9ipVTxwIOXUPDUPEmtaWFsP8IiLUy4XATkXq6Y2sx95UrLQKIT4B4BMRf78B4F2h358A8ISNrjSReYG44w8CKsWyo9M3w9kv5PBJklHVQLZlq0AIVcbxrkyOIg0hN7sDnF6qWukIO72lWunA6zJqsqEE0yq4Al6fgapLM662qHISUcQhZPu1UsonI+TBaIzecMwARFJKyTmcUUr+0/audClz5QKaCce3NLqDI009zUTkpI6bmI0gorBNnMYjPiEEC0pKO0nSC0Ht2qGKKm1pIW/yp6AkBh1AEo02RMHiXg0gvYJrMr9c56fs55ekSJq9QeTrQVssEfJcpRC7HltM86uWkgPjiMAmG0dTIgpL2zJXju8vIYTVla62cnQcRYrhk+jJlnpKQny9oXf7GMfkB5JoDrvNPUAoeRZjXLmop7mUcLrZs89RBCAhxmBIY2GzVyNt17Rc4LaFDCoRK4fzBhCLXjk4d6mnkUZvMUbfkXq6PMANiK964jhWBfD6O85+yX0ctmNvKkfHUfgTLn5ieujJdvInUSlcxiIt2Wh7XADgtYMoQQdjRBFnwD2UZJ+cnUtzel2eJGCtnA9ohgM6AsdqmQMrFtAfjTGMybc0GXjqtOi71R+iUsyhEFERpaUnASRw5sCSom+OCH9CbcZFFPZVdYC31tIi/PnMUdjJvL9A4ycmD49YKxWCiXFQB8/kn0+hUtqW16ACPjVQiudE2SKKSryxaPdHEMIeVUpnloRebZ03kEwNcFFPEsjEFQA0e/Y8tVwDcUapwYDCgWSQwJUDS2MSWByFBKHdaKqOY7c8kDy/5BrKIgpLqRRzyCUgZA9V2pXJAcBCpZDK7doO5nzFd3oJiI9jh6aHYKLbwkc9FVPpB/v+Sq/g4lhgSlQKE80RFbUOR2N0B3YXVgHpFW8c9BaQDBL41ko6hWoNRPzoO349jlDK5yL3pOhIoqNgWiumcmQcBRElJk45qpGA5MnfYgoP5fdMMuIcbamX84mVLzmGI43nK97mrt7woB7OPAgQbyw4EsCA15Y4VMlRKQQk75iXkawtfZqWn+LqLxXHahvpSaovNqLoDq3pQGlb4iL8Zm/AtB7j+4vLtpjKkXEUgIfE4weTEVV2ow8f5ErQpVXxNLp8VEpS8n+ubJcABpLLlptsdE0KlcLkWOcrRYUqMds9NPH7gbjomlLBS8w3Y2ihBuNaSQNVXCBhL8KB94Yj9Edj6xwY4BnoJKqOk9pMsi1ZRMEgcylUCoc3nq8UMfR34UbpABjD6QSUJOkpG0kqX2TjqSvxuaOZ8dTdoVWpZ1hPEpVSyudQtjgqAkg+84cLiMjPSKKe2HIUKTkdl9TTpNLRPY3G4Sjq5QLGAugO3NkWUzlajqJSiKVS2CKKSjyC4apMSIoougOJkhgmZsLhcGw8dYIRbzBN/nyOvDN/kqgULtoxoaqOQ0dSaTSnsUiiHbnOFJqreIUfUcdzcxnxJFAVRKwcoCqpIokNVMW3RfYXh0MykSPlKNI4PhaeOoHf5apMqJXyyFG0Duk8FlxTTwxnMAHJC5krogDiSwvHY7lRiactewlnY3G0Y3L8u+P+miFIiKp8avYGqBbzyFsWlySBqkkOzJ56mqvEF2XsdQc8EX6wETK6v4AsomCR+XIBzZhkIxeVkohget5JlbYVSUmJ+UkS0H5i1lOoAS7eFYhOzHNSKXEcsjRSLLRjOT4xzzW/agk5nWBvi2MajbOcGIgBVUznFiWhcK69LYA39nGFDGzUUym+Gk2Wsdcs7iGxkSPlKNIQMsvETEEwHAlgID4xLycrG++ahCo5DFJFBfG5awsnXZO08YpjfwOQvMu8yUg/eLTQQR1cJbhSBxBn+Hgca7mQR6mQi5lfg33fw0ZSHatjmlYe22Nb3m8qR8tRxOQohBDePgrGhRw5MZlQJRCfmOc44C6sYzASkQh5FjkKjjOYpNRL0Qt5wlPzFDKEP3OfHrbKKj8H1omIwLp89EMcVcd1fAcQAlUxY8+1VuLQfpMxmT0fA0Tk+W5cxSVAjGPt8swvUzlajsKf/OOp5FlvOMZwLFgmzELCZjjOi0XmKtF12w1Gw5dYujoL+sF33hwRWFpEwYL4EgoZuHIU5UIelWIuMhfCtY8C8A78izRIfV4gAiSNPQ+NEjv2TOXXUkc7IjEv/8ZV9QTE2BamnKGpHDlHARwM21kpjoB6iubcubx+HI0m9S6wIBjvM6YNhkRJHAs56UwpjrsopKTldFiS2UkVXIyIb6FSjI4oekMU82RdggvEl3tyHhWRTj3Zz2HAR/szoJ68z4yxLQ51ALwRmIkcLUcRk9jirBYJdCTkKDgkbiFzU08AsDtllDqDEcaCJwkY7GqNqeRw7ShmN/Z8bVmoFiOjlr3OgAUgAJ4zavVHBy57cpHTiR57+8Mgw3qicxQjr7iEIQEcV8QigRsH9TShHd3S2iZie8PdjxDRs0Q0JqILCc+9RERfJqKniOiijc4kiTvDhmtzDwAU8zlUirnYUJfNWFTijCtfWxar3uSeRq/SccjXbWU+JhHIicLlBrLpXa1ch/UBE2PQmModyQQw59hHGYu97hALTGOyWI3OhexxRqwJ1BNXDszTE126KjdaciSAJWiaZhL2GIFbtZhHMU8HgBvgrUmu9WgithHFMwB+CMBfKDz7PUKI1wshYh2KrUw45P2TZo/Z8M2Vi5EcMtemPk9HnHEd+BPKPhiU/TE9MaWRWqjytCUucco5+SeJ+f0ImXMhxxk+zh3AQEpEweUoaj5IcLhW4jh3IQTr2Mcd1NnsDfjWY0w0KX/nyIERERarxVhHwRVNmoiVtRFCPCeEeJ7ry9iK3IQ2HYZyI+SFmOTZbmeAJUZn1BmMDtxLwFWzDUyMxfTE5O6vuMT8XpfRWMQ4Pfk7h4GV/T6NXvcC+sFtjsIzFkxjn9JfHONSzOdQK+UPtKXdH2E4Fs7nFzcQAQ6O/YQK5pvHUWO/1x0E6/VOyKxyFALAHxHR54nosaQHiegxIrpIRBc3Nja0lKROfqaOnos4RXQwGqPdH7FOfiCCE2VMmC/FRhR89IPUE4mS2nwLOakt8+WC9Q5gACgXcijm6QCq3Gl7OqPu6zaRhWr0DvC9LmNEkTb2TNFkFEJmByJ+9D1NO3I6irgzpRrMICGqv3rDEbqD8d1NPRHRHxPRMxH/HtXQ82YhxMMA3gngJ4noLXEPCiE+IoS4IIS4sLa2pqECWKx6C3W33d/39wBVclYkxUUtTM4oLrHVYDoQEPAqkgq5g5yoRMhcEzNq8o/HAo3ecCYImcu4xh03zR+xeqhy2vDtdYasYwJE91elaH+4YVjPjuscmH9Q5/RhersdvpyOBE3T/cVZ9QREr5WACr6D+yhSNQsh3m6rRAhxw/9/nYg+AeARqOU1tCRp8udzxJhsLOIbG819f5Oo0jVCbnYHbGfSx3GinHQN4CHtnSnn3egNIQSfjmDs2wfbwonElmol54ZvoeoZvs5gcpOhEIK36ikhP8XZX7OIKGT0s9cdBBc/AR5gfOieBRYdSzE07V7XO7aH43RiwFv3L2y09v2Nez2aiHPqiYjqRDQvfwbw/fCS4OxSKuRQLeYDoy1lr+txuxwbuwBv0sQZC67BXK570dFOZ7+B3WPMUQDRiI8bwSxUvaqU8GYl7gKDJJCwxMjtLlaLB5yeHCMuPdIZhKPJ3nCM/mjMRglNdEREYIxJ08UIzp0diPhMwnYEk8A1vyrFPMqF3IH51egO2CqrgJiIonvIHQURvZuIrgH4DgC/T0Sf8v9+LxE94T92AsBfEdHTAD4H4PeFEH9oozdJohEML0paqpWw295PDXAbPhlRbE85vZ12n40LB6KTZ7udAeqlPAoMlVWA1xYh9pcWcqNKaaSjHDjv2M8WIUvhzhvFGT7u/vIcq9v+WpZjH9IzGI3R6o9YQcJyRGS80+ZNMi/6FW/h0yW4+8tErOCJEOITAD4R8fcbAN7l//wCgNfZ6NGRuIXM2cnLtSL6fvJalt9xD2ZQkRSamEII7LQHWKnzTsxpJMZZjQTsD9ulk+NGlfMxHDK7o6gepB132wOUCzlUmE72jEL7LozFYrV4gKrb6w5wcqHCqyM2Yc67VsJGnBu4AT6TMNVf2+0+Vuq8wE0Ij5qd3ud0aMtj70ZZiEmecYZtUeiV3VFUD6KkRm+I4VhgmTGiiOOQOfsrqi3cCzmfI+++COcRRSkSIXPqkH2/L6JwQD/MYuyXal6Zd/jgyd3OAER89z/L9RAelx1HjvWgoxiwRvhRuTYXTk9XjpyjiOJE9xwYCwDYbk0QDLejKBfyqJXy+5yR1Mc9MaMQHyd6iUoEOkPIIR3dwQj94Zjd8DW6w337W9gdRUTFG3flHhDvKLjHRH5uWMdCpcjG60tHEaZpXcwvLze5P/rebvUD6otD4voL4CtZNpEj5yiiavZd0A/AFIJpe7w+x45pKctT6FUuBO6JudfZz4lut/tYZqa3gOgIzCVCdmIsIhbyTps/YQ7sT85uNr2fj9XLrHrC7RiOxmj2+EpKgVB0NDUunGNSKeZQKuT2GXEX82upejCa3G732SN8YP/82m4PUCvl2UqWTeTIOYrp8HA0FthhHsyoiiQXZ7FMV9hIw8EZUSzVihiL/TtON5t9HJvjNEj78xIAsNXqo1zIBUedc4jHIU/6a7IRjjE/FYy9O8O3VCshR14fSZE/H5tzF01utwcQAlhl1gEcHHtOsENEWK4VsdNyS9cs1T1aWxaxDEdjNLpDXkcREX1vNnus424iR85RLNdL6AxG6A48TnSn3ceYefJLwxMOdTdbPawwD+Z0Ga40gtzJM2CysEZjga12H6uMOoKIImT4Npo9rM6V2UqWAWClXsZmSMftZg8APwoHMBXp8Vai5XOElXoJt5uhiMJ3rLbX7IZlYcpRbLa8/lplBAlyrm4290dHnDoAH+13wmMvIzDGdV8toT8cBxv75Np0EX3vH5c+6xw2kSPnKNb8CbjR8Ca9nDCr83wdvRSxA/x2sxfoZtNT21+RtN3ip54kGpKIdafdhxBgjShKhRwWq8XAcAMyauF1rKtzJdxuTHRIfWvznCBBJk69/hJCeGPPOL8Az7ltNve3hduxrs6V0OwNA1C16cC4yn4JOz3ZFk7x1srEuN5u9lDMk5PqPbkmXeQMJ+tx/1rhBLomcuQcxapvFDb8RbbpAFWWfMpkKxTq3m7woyTPWISplD5yxFsmJxeydKybDigOqWcjwvBx62j1R+j4N8HJNrEiZH8hy37a7QwwGAl2kHBsrrQvOtpq8ZZhAmEj3tv3PydIkOtOjsV4LLDV4gcJy7XSvuKS240ejtXLrHdMSwcq+0k6phVGR1Ep5jFfKQT9BfhsBfPY68qRcxRrc14NuESWGw5QJQAcX6hgvdEF4E3+280ea9QCACcWytjtDALEt9XuY7HKVy0CAMf977ze2G8s2I3SXHn/5G/2WZErMHEIE8PXZ0eVxxf2G77AGXFHFHP7IwoXEdg0SAiib0Y9pUIOS7VJNLnbGWA4Fuwg4fhCOZjDgE9tMq/5E/7+kvU96Sh4d+RLOT4/aYsQgj1naCJHz1HIyR9EFHLyM0/M+XIwYZxN/nlvYsqFvL7XC/7GJatTVJ2r/lqbnzgKIQQ2Wz32yS9RfdjpHavz0jWVYh6L1SJu7XkgIQAi7NFkaV80ueWAp56eX5vNHgo5Yt/YtRoCCdJh8IOqyj5Q5YIKliDhlg8Q5Tw7ztyW8FrZ63h7p7hBla4cOUchUVd4YrqY/CcWKsGEmXDhzBNmQRq+ycSUk5VLSoUclmvFQMeEqnNAPYUm/2Ak2HnXgxEFP6oEPMMQOIqGo7GfL6Ph5w9kHsRVRLEeAgkr9RJrxAp4TjQc5QG8UQsQioz3JpEeN9jxckQTHet7XeSIl6oDPAcejImDAgMTOXKOopj3DN/tUERxbI5/8p9crODl3S6EEAGq5J78J+b3h7rre132iAKYnpheHoQzQQdM8get3hC3HU3+KM7dxQI7sVDBrZBBAtxEFIA3Hq3+CL3hmN15r9RLIArnp/ijPMCLHjam8iDc4yJpoVuNLsZjj67hjlqK+RxWaqVgrazveUUMHHedhEWCKi/y5q90NJEj5yiA/eh1w6cfuOX4fBm94Rh7naEzYxGEunve5F9v9HCCOaIAvP6Sk//mrueM2Cd/CO1Lx8ee/Pcd9e1GP/jfhaM4vlDex+uX8jn2XbPhsb+x0wEA3LNUZdUhDZ804rf2euw0CuBHFNPUkytHsdcNqGDu9Qh4uckNP/q+1XAF3MroDEZo9oa4uevpOrnIr0dHjqSjOD5fwcu+Mbq23capZd4FBuxHMC/7g3mc8TA1wKumKOQI640ettp9DMfCyUI+Pj9ZyNe3O7h3iX9SSrR/a6+Ha9ttAMBp5nEp5nNYnSvh5m4Hg9EY640u7nWwwE74hQzjscD6Xhdr87x5EAA4tVQDAFzb7uC67yhOORqX9dBa4R4TwHN6rf4Ie90Brm13UC3mWUu8AQQHGb682w2M6wnm9QjsTzS/vNt141hDlKBcK6eYQYKuHElHcWaliqtbbQghcHWrgzPLNXYdJ0IT88pWG0u1IvvO7FyOcHy+jJd3u7i86U2Ys8f423LPUgUv73UxGI1xfaeDUw7668yK95lXt9q4tt0BEXCvg8l/ZqWGK1tt3NjpYCyA0ysOxn6+jMHI25h4eauNMyv87ZDg5vp2B9e3paPgb8vp5SqubbfR6g2x3R7gtIOxP+uPwZXNNq5uec6I27EuVAsoF3K4tdfFla3WPr2ccnKhghs7Xd+2tIN5zSlyXcixX6oVg1Oq75QcSUdxdqWOrVYflzfb6AxGThayRF6Xt9q4stXGOQcTBgDOHavjxc1WMPnPHauz67hvdQ6jscDlzTZu7nacoJdTS1Xkc4TLmy1c2+7g5EIFpQL/9DvrO4orW+3gd26RY/DS7RYub7Zw3sGYzJULWKwWcX2njes7HRRyxJ4wB7y2vLTZwlWJXB1EFIGj2Grj6nbHiXElIpxeruLyZmjsHYCqc6s13G728NJmG63+COcd6Lhv1Z9fmy1c3+k4ifJ05Ug6inP+4P351zYAuDEW9yxWUC/lcelWA1ccIQsAuP94Hd9Yb+LF223kiJ+uASYT88+/toHBSOC+Vf62lAo53LtUwUubbby02XLWX2dXarix08Glde/OCBd67l+bAwB86doubjf7TgwSAJw/VsM31lv4+q0G7luts+eNAOD8ah3dwRif+cYmADgBPHI9vrTZwtWttpP1CAAPHJ/DpY0mLm+2sVjlj/CBydj/h6+uAwDOrfKDhOPzZdRKebyw0cKl9aYTcKgrtjfc/V9E9FUi+hIRfYKIlmKeewcRPU9El4jogzY6VeSVJ7zB/O2LVwEAD93Lc29uWIgIDxyfw+evbOPyZhvfcnKeXQcAvGJ1DnvdIf7y6xs4u1JzcoLkK/zJ/ntfvA4A+NZ7F9l1AMADa3N45sYuvnJjD9/qYEwA4FUn5zEWwO9cvIbFatFJjuLUchXlQg6ffPoGAK9dLuShexfx7I1dPHezgW9huvt5Wu5f88b+337hGvI5wqsczOP5ijcOv/+lm2j2hmz3WE/Lg8fncXmzjS9e2QlsALfI/vr/vuRu7IkIr1ir4+LlLVzb7jhbKzpiG1F8GsBrhBCvBfA1AP9k+gEiygP4ZQDvBPAQgPcS0UOWehPlFatzWKoV8eyNPazNl1lv7ArLt51exDPX9wAAD59ddqLj4XPe537xyg4unF9xomO5XsL9a3V8+fouCjnPAbqQC+dX8MJGC53BCN92yo0zeoM/Dl+5uYfXnVli58IB79C+151ewtNXdwAA337Ozdi/5tQC9rpDXN/p4NX3uAEirz+zhEKO8Mz1PTx4fI7tlr5pefjcMp694a2V151ZcqLjtacXMRoLfOXmHr79nJu1cp9vW754ZQcnFyrOaKEL51YC2+LKseqIlaMQQvyREEKeT/0ZAKcjHnsEwCUhxAtCiD6AjwN41EZvmuRyhO+8/xgA4M33H3NiLADg+x86GfzsbPKfWgyO4n7zA8ec6ACA735wDQDwxlesODMWb35gNfj5O+5305Z7FyeL982OdADA9776OADgweNzzo5X+O4H1oKf3/rK40501EqFAOR8V2h8uEWO/UKl4AyIyDns6XMz9vkc4S2+nu90aFu++8HJWPwdRwBRRzhT6T8O4Lci/n4KwNXQ79cAvDHuQ4joMQCPAcDZs2eNv8w/eeercaxexvvfer/xZ6TJdz2wiv/+bQ/ioXsWnFUl5HKED/3nD+Pzl7fxA6+914kOAPjA9z6AciGHv/d3zjjT8fozS/if/uNXY6FaxD2LbpAYEeGfv+f1eOLLL+NH33TOiQ4A+C/eeBYv73bx7jeccqbj7LEa/vd3vwbjsXBCn0r53979GvzGZy7jJ77nAWc6fujhU3jpdgvf/eCak1wLAFRLefzSe9+Al263nDq9n/n+V2GxWsRPfI872/I9rzqOn/n+V+Jb71284xVPAEDyEo7YB4j+GMDJiJd+VgjxSf+ZnwVwAcAPiakPJKIfAfB3hRD/jf/73wfwiBDiv0v7chcuXBAXL15UakgmmWSSSSYAEX1eCHGB8zNTXZUQ4u1JrxPR+wD8AIC3TTsJX64BCMPU0wBu6HzJTDLJJJNM7pzYVj29A8A/BvCfCCHaMY89CeBBIrqPiEoA3gPgcRu9mWSSSSaZzE5sq54+BGAewKeJ6Cki+jAAENG9RPQEAPjJ7g8A+BSA5wD8thDiWUu9mWSSSSaZzEissiRCiMjslxDiBoB3hX5/AsATNroyySSTTDK5M3Ikd2ZnkkkmmWTCJ5mjyCSTTDLJJFEyR5FJJplkkkmiZI4ik0wyySSTREndcHcnhYgaAJ6/09/DkawCuH2nv4RDydp3uCVr3+GVVwkhWA8Hu/N7w5Plee4dhneLENHFo9o2IGvfYZesfYdXiIj9OIuMesokk0wyySRRMkeRSSaZZJJJotztjuIjd/oLOJSj3DYga99hl6x9h1fY23ZXJ7MzySSTTDK583K3RxSZZJJJJpncYckcRSaZZJJJJokyM0dBRO8goueJ6BIRfTDidSKiX/Rf/xIRPZz2XiJaIaJPE9HX/f/dXF6sII7a9/NEdN0/mfcpInrX9OfOQizb9utEtE5Ez0y956iMXVz77oqx87+LUfuI6AwR/SkRPUdEzxLRT4Xec+jHL6V9R2H8KkT0OSJ62m/f/xJ6j974CSGc/wOQB/ANAK8AUALwNICHpp55F4A/AEAA3gTgs2nvBfDPAHzQ//mDAP7PWbRnhu37eQA/cyfaxNE2/7W3AHgYwDNT7zn0Y5fSvjs+dgxz8x4AD/s/zwP42hFbe0ntOwrjRwDm/J+LAD4L4E0m4zeriOIRAJeEEC8IIfoAPg7g0alnHgXwMeHJZwAsEdE9Ke99FMBH/Z8/CuAHHbcjTly1724Qm7ZBCPEXALYiPvcojF1S++4WMW6fEOKmEOILACCEaMC7T+ZU6D2HevxS2ne3iE37hBCi6T9T9P+J0HuUx29WjuIUgKuh36/h4IDEPZP03hNCiJsA4P9/nPE764ir9gHAB/xw8tfvUHhv07YkOQpjlyZ3euwApvYR0XkAb4CHSoEjNn4R7QOOwPgRUZ6IngKwDuDTQgij8ZuVo6CIv03X5cY9o/LeOy2u2vcrAO4H8HoANwH8P4bfz0Zs2nYYxFX77oaxAxjaR0RzAH4XwE8LIfYYvxuHuGrfkRg/IcRICPF6AKcBPEJErzH5ErNyFNcAnAn9fhrADcVnkt57S1IA/v/rjN9ZR5y0Twhxyx/oMYBfhReGzlps2pYkR2HsYuUuGTvAsn1EVIRnRH9DCPHvQs8cifGLa99RGT8pQogdAH8G4B3+n7TGb1aO4kkADxLRfURUAvAeAI9PPfM4gB/zM/hvArDrh0RJ730cwPv8n98H4JOuGxIjTtonB9KXdwN4BrMXm7YlyVEYu1i5S8YOsGgfERGAXwPwnBDiFyLec6jHL6l9R2T81ohoCQCIqArg7QC+GnqP+viZZuN1/8HLzH8NXgb/Z/2/vR/A+8UkQ//L/utfBnAh6b3+348B+BMAX/f/X5lVe2bUvn/jP/slf2DvOYRt+014ofsAHvL5r4/Y2MW1764YO5v2AfgueBTGlwA85f9711EZv5T2HYXxey2AL/pteAbAz4U+U2v8siM8Mskkk0wySZRsZ3YmmWSSSSaJkjmKTDLJJJNMEiVzFJlkkkkmmSRK5igyySSTTDJJlMxRZJJJJplkkiiZo8gkk0wyySRRMkeRSSaZZJJJovz/KcWi8wX84iUAAAAASUVORK5CYII=\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "the combined waveform:\n" ] }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "t = np.linspace(0, 5, 5*44100)\n", "\n", "funcs = [\n", " 3*np.sin(2*np.pi*220*t),\n", " -np.cos(2*np.pi*220*t),\n", " np.sin(2*np.pi*220*t)**2,\n", " 2 * np.sin(2*np.pi*440*t+np.pi/6),\n", "]\n", "\n", "f = sum(funcs)\n", "\n", "for name, func in enumerate(funcs, start=1):\n", " print(f'the waveform of f{name}(t):')\n", " plt.plot(t, func)\n", " plt.xlim(0, 0.03)\n", " plt.show()\n", "\n", "print('the combined waveform:')\n", "plt.plot(t, f)\n", "plt.xlim(0, 0.03)\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "6e96aedc-cb2a-440b-af22-cadd60a0a63b", "metadata": {}, "source": [ "Plotting it gives us two insights:\n", " - even though it has four parts to it, the resulting waveform is pretty simple.\n", " - $f_1$ and $f_2$ both look like they have the same frequency, and $f_3$ and $f_4$ look like they share a frequency as well.\n", "It looks like we should be able to make this sound using just two sine waves. Let's define a couple new functions,\n", "\n", "\\begin{align*}\n", "g_1(t)&=f_1(t)+f_2(t)\\\\\n", "&=3\\sin(2\\pi220t) -\\cos(2\\pi220t)\\\\\n", "g_2(t)&=f_3(t)+f_4(t)\\\\\n", "&=\\sin^2(2\\pi220t)+2\\sin(2\\pi440t+\\pi/6).\n", "\\end{align*}\n", "\n", "What do these look like? Is there a simpler way to write them?" ] }, { "cell_type": "code", "execution_count": 10, "id": "7668575e-b635-4764-878d-f48cc5e5a1c4", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "the plot of g1(t):\n" ] }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "the plot of g2(t):\n" ] }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "print('the plot of g1(t):')\n", "plt.plot(t, funcs[0]+funcs[1])\n", "plt.xlim(0, 0.03)\n", "plt.show()\n", "\n", "print('the plot of g2(t):')\n", "plt.plot(t, funcs[2]+funcs[3])\n", "plt.xlim(0, 0.03)\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "742445ab-83bc-461a-91ca-75f30d3f1bef", "metadata": {}, "source": [ "Sure enough, those look like pure sine waves! Can we figure out their formulas? This is not too bad with complex numbers. This is part of a general rule:\n", "\n", "**trigonometric problems are almost always easier with complex numbers.**" ] }, { "cell_type": "markdown", "id": "160bd681-f947-46a9-9d1d-0c059510c113", "metadata": {}, "source": [ "Remember Euler's identity, \n", "\n", "$$\n", "e^{ix}=\\cos(x)+i\\sin(x).\n", "$$\n", "\n", "It follows that \n", "\\begin{align*}\n", "\\sin(x)&=\\Im(e^{ix})\\\\\n", "\\cos(x)&=\\Re(e^{ix}).\n", "\\end{align*}\n", "This lets us rewrite $g_1$ using simple factoring.\n", "\n", "\\begin{align*}\n", "g_1(t)\n", "&= 3\\sin(2\\pi220t) -\\cos(2\\pi220t)\\\\\n", "&= 3\\Im(e^{2\\pi i 220 t})-\\Re(e^{2\\pi i 220 t})\\\\\n", "&= 3\\Im(e^{2\\pi i 220 t})-\\Im(i e^{2\\pi i 220 t})\\\\\n", "&= \\Im(3 e^{2\\pi i 220 t}-i e^{2\\pi i 220 t})\\\\\n", "&= \\Im((3-i) e^{2\\pi i 220 t})\n", "\\end{align*}\n", "Now we can just put $3-i$ in polar form, $3-i=\\sqrt{10}e^{-i\\arctan(1/3)}$. That lets us factor,\n", "\n", "\\begin{align*}\n", "g_1(t)\n", "&= \\Im((3-i) e^{2\\pi i 220 t})\\\\\n", "&= \\sqrt{10}\\Im( e^{2\\pi i 220 t-i\\arctan(1/3)})\\\\\n", "&= \\sqrt{10} \\sin(2\\pi 220 t-\\arctan(1/3)).\n", "\\end{align*}\n", "\n", "There we go! $g_1$ is just an ordinary sine function with amplitude $\\sqrt{10}$ and phase $-\\arctan(1/3)$." ] }, { "cell_type": "markdown", "id": "cee131dd-9abd-4cb2-881b-1ca03f5d3f25", "metadata": {}, "source": [ "### Exercise 4 \n", "We could have written $g_1$ in terms of two sine functions, $g_1=3\\sin(220\\pi t)-\\sin(220\\pi t+\\pi/2)$. In about two sentences, give an informal explanation of why you can't just add the amplitudes of the sine functions to get a sine function with amplitude 2.\n", " \n", " " ] }, { "cell_type": "code", "execution_count": null, "id": "cd5b5252-b39d-427d-a7d5-06a3c27f403e", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "id": "9a4a6fe8-ac3a-4837-9c80-e72403516cb6", "metadata": {}, "source": [ "### Exercise 5 \n", "Show that $3-i=\\sqrt{10}e^{-i\\arctan(1/3)}$.\n", "\n", " " ] }, { "cell_type": "code", "execution_count": null, "id": "ca38d64c-2a57-43d0-9f26-4ca88be47020", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "id": "3e3f3e22-480e-4c88-b463-5192a25167ce", "metadata": {}, "source": [ "To do the same with $g_2$, we will find it handy to have the following identity for complex numbers.\n", "\n", "$$\n", "\\Im(x)^2 = \\frac{1}{2}\\left( |x|^2 - \\Re(x^2) \\right).\n", "$$\n", "\n", "### Exercise 6 \n", " \n", "Using the identities $\\Re(x)=\\frac{x+\\overline{x}}{2}$, $\\Im(x)=\\frac{x-\\overline{x}}{2i}$, and $x\\overline{x}=|x|^2$, prove the above identity." ] }, { "cell_type": "code", "execution_count": null, "id": "598ba610-d606-4853-b338-d4d83ad3db3b", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "id": "4e69ad31-02c0-42bd-abf3-59e7568b1880", "metadata": {}, "source": [ "Using this the computation will be a breeze.\n", "\n", "$$ \\begin{align*}\n", "g_2(t)\n", "&= \\sin^2(2\\pi 220t)+2\\sin(2\\pi440t+\\pi/6)\\\\\n", "&= \\Im(e^{2\\pi i 220t})^2+2\\Im(e^{2\\pi i 440 t +\\pi i/6})\\\\\n", "&= \\frac{1}{2}\\left|e^{2\\pi i 220 t} \\right|^2 - \\frac{1}{2}\\Re(e^{2\\pi i 440t})+2\\Im(e^{2\\pi i 440 t +\\pi i/6})\\\\\n", "&= \\frac{1}{2} - \\frac{1}{2}\\Im(ie^{2\\pi i 440t}) +2\\Im(e^{2\\pi i 440 t +\\pi i/6})\\\\\n", "&= \\frac{1}{2} + \\Im\\left( \\left(-\\frac{i}{2} +2e^{i\\pi/6}\\right) e^{2\\pi i 440 t}\\right)\n", "\\end{align*} $$" ] }, { "cell_type": "markdown", "id": "8e52ab47-d43f-42bd-a7f0-1a898f438ef7", "metadata": {}, "source": [ "Once again we put the leading coefficient into polar form,\n", "\n", "$$\n", "-\\frac{i}{2}+2e^{i\\pi/6}=\\frac{\\sqrt{13}}{2}e^{i\\arctan(1/2\\sqrt{3})}\n", "$$\n", "\n", "which allows us to complete our task.\n", "\n", "$$\\begin{align*}\n", "g_2(t)\n", "&=\\frac{1}{2} + \\Im\\left( \\left(-\\frac{i}{2} +2e^{i\\pi/6}\\right) e^{2\\pi i 440 t}\\right)\\\\\n", "&=\\frac{1}{2} + \\frac{\\sqrt{13}}{2}\\Im(e^{2\\pi i 440 t+\\arctan(1/2\\sqrt{3})})\\\\\n", "&=\\frac{1}{2} + \\frac{\\sqrt{13}}{2}\\sin\\left(2\\pi 440 t+\\arctan\\left(1/2\\sqrt{3}\\right)\\right).\n", "\\end{align*} $$\n", "\n", "This gives us an alternate form for $f$,\n", "\n", "$$ \\begin{align*}\n", "f(t) \n", "&= g_1(t)+g_2(t)\\\\\n", "&= \\sqrt{10} \\sin(2\\pi 220 t-\\arctan(1/3)) +\\frac{1}{2} + \\frac{\\sqrt{13}}{2}\\sin\\left(2\\pi 440 t+\\arctan\\left(1/2\\sqrt{3}\\right)\\right)\n", "\\end{align*} $$" ] }, { "cell_type": "markdown", "id": "a5c3cce4-c933-491b-b7e6-fbb408e53016", "metadata": {}, "source": [ "Just to check our work, let's try plotting these forms side-by-side." ] }, { "cell_type": "code", "execution_count": 11, "id": "6bdc2ad0-31f8-47e3-826e-dc5ca294b142", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "alternate_form = np.sqrt(10)*np.sin(2*np.pi*220*t - np.arctan(1/3)) +1/2 +np.sqrt(13)/2*np.sin(2*np.pi *440 * t + np.arctan(1/np.sqrt(3)/2))\n", "\n", "plt.plot(t, f, label='f')\n", "plt.plot(t, alternate_form, label='alternate', linestyle='--')\n", "plt.xlim(0, 0.03)\n", "plt.legend()\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "d7cd1043-ba47-4c51-83d2-afde79b8d66b", "metadata": {}, "source": [ "They agree exactly, as promised. What's more, since we know that sound is not affected by phase or by a constant shift, we can get a much simpler waveform which sounds the same by dropping those parts.\n", "\n", "$$\n", "g(t) = \\sqrt{10} \\sin(2\\pi 220 t) + \\frac{\\sqrt{13}}{2}\\sin\\left(2\\pi 440 t\\right)\n", "$$" ] }, { "cell_type": "code", "execution_count": 12, "id": "aa116c5a-1b71-40fa-ae5a-20e2ced7db45", "metadata": {}, "outputs": [ { "data": { "image/png": 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6cw9pB/pZkcE0Ps/ao7s/G2VWi6MVhmBNAEqzLBNj+iJLE2DfeIw5MTY01JZWnGeZ6Lr9lQj5aIX0u8DBZ8UxQoDwGEKs1Z73ZiLMyQRCaiufczLKi5QIkomv39hXZCNc0BK0ChcGMDDz0EoLLMooExdtbIDxTJY6vk72qqOha5wLxJiMrRVo4zE/JW9qzeccDZ1u9MbWl2Lfkw4zTwJ3dWEouqVppTnmtBiT8eC69/ZlIpxrJ2gPyVkR1SV1VmLrz0o45XyFyTFCwBtZv7EnYwHyLpV8MQwXjlaeZ1FGGd/g4rwiE2FexpEO3gyrIaqLLMso4zH/uvf2ZiPMyjjt4hDMRd9fJVeCWNCz5i0hBKGU3p2r5Pz9ZcwlEN9ACGTCzMuEcthXnB9a2dS15/ENLs4rsuqsNPUwZUej3cLbyLHMxgrTVDZNFX8nctCJGLwQ0LWbYDy77i2XS+BJGIfUuX9EA43CPEsyts4sBLWx52QSX33Z+aGVWhtPPc/SJod0r37h1JeHwCegc/3uSGqdpQmQzOplvodgf1FZoIaXsXhi3VuxgJeaXxcOQ6EwLbEsI0zE1ysZ+7Jqf7mGwTrT99eijG14VvZkIsxqCRp55wq0gQsBWVmkIT3EE2Mbvh9JO9+cMqCV5lnahEJJRfyUffocyxu013QSqjlcaCzJGNnoBkIgrWi64bAElgDwRdMbvr1rIk1BBqnnnH9xtkoL6rJJrKdQAPwJ3ck6BJenqC2zLCMb7q/dqTALxPE1887vMa5bXQ1fYk2Uk4E9aeXXdLLCNHAh0CzOs0SUicT6zQCQ1jW1loMlqQFRWWRJrncQGfDFjUPq8MtTpx2a/uQ6ByQoS2BOJvBWnH/ZUFVCIJTYoKUpin+elwkqS853Qtbzcyxvwj0DRDOGVeNwgSYl3voyuU0szYDXvcqh6vA9ZvgqQxsrGcpqjqvkSodi4EKgUZjXueeNN/bOiTQFGaK04PDoDSnx1ZdY3MABaSA4NiTUVsdZv/HGjga8VHxpAq0CNGuXcGDmoZUX0aQgMbbxXPZllEN1GJyQWlkpGZsJgfS4EgK1ZYcrTI0SbtkiT5RU2LfhR3xxVU7e8UJgC2c9wEwyxAJJfFXnzmPgQsCIQtlMCBiS1PEbu17ELZsUXfF1DkgDiewMADUHm4ZAx8T1RTa+OAFEVNfUys7d3AC1wgJ5wozHwxu+PzMWYl7GcTt8HqBbmmwceACwc3yMnAxTdLrCpFN07UBiXT6NASOqRnO6f6OyuU8TwOdx0QikCbRL0KxeypF1jYELAVFd2jRKAFTo25xMOj+qRteeW4H1oa4GJnYoIZCbc/oh1aNQEhtvbIBAUrdqHO4XaBQXWJYRMhtwzwB+j5uaP02w7vyIGm99mSUZ29QSMBz2jZzDFSadohOh1KYfGZtQZ6Uw7+yz0iqpsxLZIDfIgCtmWDXOPCsDFwLe+hJLm4QigqIe8p4xfE7nn42M0+DGDm6APdkkSzJC1eGWQKukLsRwYvONHc0oTa286OxDqpUXyREhHdmYdgBU6QJZhXrp0g3MLFoN/O0SJXd8TZGy1dg5pqgtp142HeiWgDeyuRCYmtKFwIKzfTX1/BwFGSSdiGz6maCeXOnURL7BCgGtTaBVoOyOEfJtvLEBWsEM4dais+u76H0C3KHEph/ZmQoxLxO08s42ceuFeSrST2KDpDcD6YldACzNOrtqpajlWJZRUpGNlQwArx5V42TnnaFktPyJTT/i87goe1P4ag63avS5+Dfh0QF2jydYlFHHK0zN0iJ5GdnUtwEQ0x32+XlnnpXBCgH94mz64lt+TEQnCMi6sxuC13IA+KKbWwJ+j5uCJ4XH4VZNo7RMnvCWG3vHjp20paC86GxNzVNfJkeYsS3mEtH558XZU5dqWOah7y/p3/qstEJZok1nK0xt3ZkaiG/uc5qIBVggieZwurFdyZEnzFh4cyUjO7kTgGWHKkwDFgI5AOQW2g2AX+efSw6mHrRKDgB/ZHMhANAIpAk2nF0Co11ZpiBDW16cO9NRlojRcLhV42vkKRAlFtjc0kzp/PPieWceUqCjMLmCiS0/5o5NEKCOrBcuwaCsoZZXQiAU25wOEkIoq8bhChO1/LZnZXrHjFKYlpxp1QxWCFRzAIjg1tpNXDen5s4595DWdQdRcAvtBoDIBIn2ElLTLsGorEFW88oS2IJH93lcLLvGEE7mn1sN/FqFui+xqbMeYHKHorbyTuaf9bPiDm+tZAT0MOSlC849K43SAnkZIhkNbfm5ZjBNqOlshclVz21rNU8kwiwSd2yukyPoIHdo642dmVLm1NKcc831WnGJhnSTjG3OowP4khMERJP5BedmDbvqOfJyaxMXoOpPE6g5dx5GFErLn9zyY9nsFC3pouFg/lkaPHp067kYCtPsOeeelVZR1aUaC23hrAdc0QnGtBz1pnML4nkbBQpEiAe9m37G5RIUPGO4HBqGPFAhIHXtZruNPTGlNLXygnMPabO0pLjBLRyQAFGdfz575uSlGJYleBoFioRIbLGxAbRwlmhrCelU/rkTsZXY8mMuj4e8K+Fo/rleUnMJbkGhwAr/nJtzriUgqzqPvlXEFuAfm8Qvmpw970wNGsDXKlL3RDfNdzBQ9WccG4Y8UCHQKKuNHYhuvbED0RRNPDQdak6BwaOHSW2jPacm1CFdvOBcTc3XLFL3xLbd2O7YBCnyzBecmQRjBBJ4thECAGVfCl/NmZoaQK2oaJFwfBshYChMTk6urBcpyuC2lkA8raya82cdqjC16vhkHc23tfUPIMNZYu1lWm3n0cADFQLVgr6xt9FucLkouBMIJxde07WbrXh0gNS4ckIWnco/a22CWommd/uNHRqbwivanDrrUAutppyjvnBi24+2ghkizWUaLecdUoB6cYmK9DMW3TweHcAdStLE4+gwZFejQIkQyS14dFjlsJ91aECIzmRogcS2H/XElcJ0drnc3zFZwECFQL20TFO6icW2dgwD1Pxp/PUFx1IPrnqevAyT3JbnVFm4ji2DoUeVaIHt1yRhOOzPO9OqaegRW8FoYtvPuqLjpEWOU0vObAje6oQibr2/EIKC27n8M4CnVaLuDuF1b339GKG7JafSwHp043Z0I0A4pRSm0+ecp/wNVAi0yksUCDEW3ZpCAWiHsiS1ZZbKzqzF723kqbijG1bdXINgUvVPdWpUjRGx1YV2k9QLljm1DEa5mAMgvI3PCSCQnCRNnuPzzsxFkZVl3Vm/jRAA6gFVBkPTnKkw+VplWp6tLRoAIkphqjuVBtbPiie8/f5K6grTvAPDkAcqBLSKikLZKrzKgCc+QUbkObHoPHMKwN8q0fBsT6EgBBWfyupsOpAfNLSbrTKfDbijqiZKxaHxzzVdCITiW0efgYqq8QiNc+edp6kBiHqeAqFt6UZQDvsUOc7lHeirkZKAVqHti27/2UCClvAiHJrJ3aoon6avCyEQTavQ3bwDFaaBh4gWuuAGQfHPKfIcm3NgEoymKR69CwcRQCuUIUWeM8vOO6Ttigrb9XaxsdFbgjq1b3JTn0s0uj21FUyq0hFLDuWf3Y0CJSIEN2hccjG8MV1hWnAgtdWs4EJD+LsQAkJQ9aWItJbIV5v9H5tJVHSfZmA7nyYgIkphcmIZjIEKAXc9T5EI0U0KYq1GNDWJW0hmnaipNYq40GhtU/7CgCs6QUbkODbvvIJl1YJeRnqbiC0A/DGawo+nMk/bgdRDq5qnKIMkwhtX3VyDiCqWV3JoGQxfs0DVE90y6c1AOKUUphPz+UswMpPQnfWuQHcKkxbKkCHH8QXnMQB1PWLLv0WpmA50asuJReQGKgS8rQJVd6SrjW1QD7l5Bx5SnRukCx4dIJhUmpoTN3atqBKs/JEuLAEhqAfSjJHjXM55Vo1WK1AiuGUiTwf6IW06NKom2CrS8HShPQPhMV1huuBALt0I2w11pzAZNPDxBecpTI2S3rWuGyHgj9J0+fHVFqg1230emTkMVAgEWkVqXW5sQ1OrOpF/NhElAKoXbErkOT7vPGqrs7G7MHFBxT9nyHHMgQKNeoGSDJIIdS8E/LUFijWHUQ9am6As0+oibBdWGv44sWplvZwDwB3sbi6B5BQZkeP4vPP2V7uSoyL9xLcJ2wVACBqBDGmR47TDItAGJwSkJNjuLh4d6BzSVnHWcVEPmu4g6saZCkBkHDeShVnnCbRWWYXtRrrg0QF8iQnSIs9xB1JbrnqJkght2AB8Hfwx2i6/movTBJpeXqW1TQXRDnSFqbzkPEugUlRnxdtF7gaAOzrOmChyzIEKk6aH7XZlaQJElMJ01GECbXBCoFnBQ4t2l85UY2Mn2sucLzirr21Vp1C6cqZCR6CVFp0nBNrVHAVCxLfJdzDgi0+SdeLFCbibJequrYuUdSAEWjjrTJrOpKVp7C9ZnKVcd1bdnWopB4C/SyFAJIsbjaU55wk0UVPRjd0KAX9ikozI8/yss8KQBycEdO2mm2w7APwR2p4QGZHjuQvO0grquhDoypkKHYHmqsw77pBSNbexRXScpChy5PxynwdmHt5WiYZ7497CG8EdGycrchxzmKbWbRnpDsJKCGREnmcvOOvCqetCIBhJdPeALtAqS+cclyjqrqtqu1uVKV8NT2yCcVeBZx12f/UsBIQQM0KIrwohDgshnhZC/FJXD+rOVFcXmamd3xUZJyPyHD7vzI3dLY9OWIVWOjHqwaXHo8e6NXHDGVxIZi+ccdwh9bfLtLxd8LU6XJFxJt0Fx/k3WmWDbuzS0vRH0LxhMiLnuAunUVYCLRzr1mpWClOsvcQFhzEAnmaRigjj2SbzuYPIOAkKjlOY7LAEWsB/llIeAO4Afl4Icc12Dxk8uqvbjY1K7Z/2Fnjm/PYb+0tPX+D3P3/4kjhhjPIE3fLoxsbOiPy2c2m2Nf7yG8f4P199gWqj/1EFnkaBkoh0x6NDZy6B+iLn8lsf0rlCjT/44rN85tFLE4sf1Mq0vV0GHgBEsmRFvitL87HTOX73X57h0VP9P9CVgkm6EWWhTbkLPLuNwiSl5B8fPct7vvgsc5fgkm1VdSHQRSkPoGMJZMjz3DZWTa3Z5n9/5Qh/+Y1jlyQR09sqUnOb218ApcXz20YInV6q8HufP8y9z/Q/pLQ7O2YLSCnPA+f1/xeFEIeBHcAzWz1XLS0TBrzdOlMBIhkm3ec4vM3F+S9PnOMXPvYoAJ978jz3/vIrCPq6vNQsoF0tUJIBEttUEO3AH0F6w0zJAk+dzfMDt85s+tHf+Ken+PhDKsrj6FyJP/7BG20Y8ebwtErU3FPdP9ARaDkOnyuwIxHc8GO1Zpsf/osH1zjFvuem6Z7GuiU0jRBVtG4yUw1ExoloBU7M5ag0Wpv2vX72QoEf+PN/p9HS+NhDp/jCL72MXanuaSezqJVyxIBgt0oGymreWSrxoW3Oykf+/SS/+c9PA/D15+f551+4G/c21WN7gVYrqIiaSJe+mg61leOps3nuuSq74ceklPzixx/tXJpzxTr/7fUHbBnzZlCWpol1189KihxHZktcN73xeuYqDX7gz/+d8/kaH/z6MT7yjtt5+ZWb92PuFbb6BIQQu4GbgG9t8N47hRCHhBCH5ufnqeop/f5I9xubyDhJqRx3lcbGXHqp3uK3P/sMN0zH+Zt33M6Z5SqfeKS/oXKm4tF1iEiWvcEKT57dPKHn0IklPv7Qad758r286xX7+PSjZ/tOH/laZZru7imUjqYm8lsK5/ffd5Sj82U+/JO3ccN0nD+590h/o7waKlpJdJmUBEAki0CSkEWeObfxXKSU/LdPP0nU7+FffvFu2prkg18/ZseIN0Vdp1CCXdRA6kC3ap69UNyUpjMss1dcmeFPf/BGnj5X4EtP9zlPol6kRLBrHh1/BHwR9oUqPHFm87Pyr0/Pcu8zs/y311/N998yzYcfONHfOmN6+QvNBN24+qw8dW7zubz3S88xX6zziXfdyc6xEH987/O9jnZL2CYEhBAR4FPAf5JSrjtBUsoPSilvlVLemslkOvHCXTuIACLjBFt5vLLJU2c3PqR/99Ap5ot1fvPN1/KKKzMcmIzxj4/2OcGsXqQkzQkBIjq1da6waY3xD3ztKKmwj1/+zit5x927cQn4TJ/n4tcqtE1pN2pjXxWu8Pgmh7RUb/Gh+4/zXQcnuOeqLD951x5OLVV49HT/qJSmTjt0G48OrLFqNrtwHj6xzLdP5fjlV1/JwR1x3nD9JP/82Lm+0g9G+YuuKRSAyDhxbYlSvcWJxY0p0Q89cIJqs81vv/la3nTDFBOxAP/4WH/3l6gXKBPsnkcHCGfYGyxvqTD9+dePsicd5qfu3stPv2wPjbbG557oY/Rdq4aHNtKUpanOym5/kW+f3HjvL5cbfPKRM3zfzdPctnuMH7ljJ4+d7q/v0BYhIITwogTAR6WUn+7mGcNBFDKp3QCkKPDwiaV1b7faGn/9wAlu3zPGzTvVz/2ugxN8+1Sur1qBaJQoi2D3PDpAJEOKHPWWxvOz62PsTy6W+bdn53j7S3YS9LnJRgPcvDPJV57tI0eoaYRkxRyF4g2CP87V0SqHTi5tqN1/8tBpivUWP/uKfQC88kAWr1vw5cP9KwxWyqv94QmZFwJXhje/cD50/3ESIS/fd7Oisl577QTFemvD/WgX2jqFkghvTLVtiEgWf7OAjyYPH18/tkqjxccfOsXrDk6wOx3G7RK8+ppxvvb8fF97KribJWouk9SZ7rA/n68xV1zvt/j2qWUePZXjJ166G7dLcNV4lF2pEF95to+F5/TMZxEwcVZ0auv6RJ1HNvElfeyhU9SaGj95924Avuugqml133P9m4sd0UEC+CvgsJTyj7t9rlUtoElBtIteAh3oh/SWVIOHNtjYXz48y9lclXfctafz2h17VcROPx14Vjd2uKnmsNEF8uFvnsDjEvzIHbs6r911RZqnzxUo9SusVKdQ6Ka412pEsuzyl8lVmrxwUdKYpkk+/M0T3LwzwY0zCQBiAS/XTMV55ET/1qRc0Cs8dlmeAOgUxLsxqfbXxTTK6aUKX3rmAj90286Oj+muK9IIAQ8f799crNCNxoVzRajCtzY4K5/69lny1SY/dffKWblzX4paU+sq8MIqPE3VS8AUIqqMPLDhnvnrB04QDXj4/luUYBZC8LL9aR4+sdw3ylGarIEEgDcAgTj7ghWOzZdZvkgxbbQ0PvLvJ7j7ijRXT6ifOzMWYlcqxAMvLNo29othhyVwF/CjwCuFEI/p/16/3UNaTXGDiVCXzlToWAIvyTZ55OTyuqJlf/3ACaaTQV59zXjnteun43hcgkObmF92wNsqm4pHB1TWcG2ZXXEPD7ywtvdosdbkE4fO8IbrJsnGVoqf3bgzgZTw5BbcaE8weHS/iY0NnUxIYN2Fc9/zc5xYrPCTqwQzwC07kzxxNtc3GqWTlNRNDSQDHU2twdlcdV2Dmb998CRCCH7szhXBHPF72J+N8PiZXK9D3hw11Y6x67Bd6ChML5uUPHRi7QWiaZIPP3Cc66fjHYsZ6Px/M6rCDvjaZRrd9BJYjcg4gfoCEb+H+y86K+fzVT7/5Hl+6LYZwqsKUd4wnaBUb3GsTzWH6hUlBNxmLE2AyDg7vOrZi++kLzx1ntlCfY1gBnVWnjybszzW7dCzEJBS3i+lFFLK66WUN+r/Pr/tc/UCRbPajb6xr4/XKdVbPLaKU37mXIFvHV/ix+/cvSa6IeB1c+2OOI/0eWObiUcHOgLttbvdPHhscc1l+A+HzlCqt9ZdnDdMJwAVntgPGNyzKR4dFPVQX2AyHuD+I2tbgP71AyeYiAV43cGJNa/fvCtBraltG+llFTUjd8MM3egLgT/G3qDiX79xZOXCKdaaHfpk6qIIqOunEzx+Ote3PAlXo0RVBLftxLUG+v66Nd3k9FKVU6v8Ave/sMDR+TI/8dLda4o3TsQDTMYDfLuPVrO/XbFwVsYRtRx374nwjSNruwt++JsnkFLyY3fuXvOIYXU+dro/ClOlY2kmzD0YGSepLRP2uddQu1JK/vIbx9mbCfOKiyKBrt0RZ7ZQ35AKswMDyxgW9SJlggS85hxEAFdHq/g8Lj77+Eoq+V8/cJyg171huOW1UzGe2yJKolcEtDJtCxsb4FUzUKi1+IZ+eTZaKi/g9j1j3KBvZANjYR87x0J90wo6dV0saDeiNMdrr53gq8/NU9ALsD0/W+QbRxb40Tt3rbvArtuhaJrt4titwhBoITPOVIBIllh7id2pEP+yyrH48YdOUay1eOfL9q575IbpOItlZT30A25LFIraX7emFeXw2VVz+esHjpOO+HjD9ZPrHrtuR7yvdFBIltHM5G7AKoXJw6mllYi6Qq3Jxx48xeuvm2RmbO3fZ28mQtjn5ok+WWiVTvkLE3QjQCSLqzzHPVdnufeZ2Q6bcf8LCzx5Ns/PvGwvrotCdA9OqfP49CbBML1iYELA1SxRFeGuykh34PFDIIG/tsgrr8ryL0+co9Zs88JciU8/epYfvG2G+AYVI/dnI+SrTeZLdRtnoENKQrJqLkoAOtTDzakGY2Ef//CwSqD6+0OnOZ+v8XP37NvwsSvHo7ww1x8Tt2KE7YbNWwLUC7zlYJJGS+Ozj6sL54++9BwRv4cfvn3nukemkyH8HhdH5vojBFpGQ5kuuoqtgS7Qvv+WaR48tsSJhTLFWpO/+MZx7tybWieYAa7S+dt+rYunXaZuJmwXOgpTUstx664kn3rkDG1NcujEEl99bp6feOlu/J71gQz7xyOcXKz0xzksJWFZseRzAnj1TvB7XPz9wyrk+6++cZxivcW7XrH+rLhdgisnohzZIOjCDtTMlr8wEBmH0hxvun6ShVKDLz51AU2T/K8vH2EiFuB7b96x7pFrDCGwRVhpLxiYELDkIAL9jzjLT9y1m4VSg9/8p6d59yceJ+h18wuvvGLDR64cV5vuhX5siGYFN5qKZzYDfWN7K/O87fadfPHpC7z/vqP8wRee5Y69Y+tMQgP7smFOLFQ2DSvtBQaPHjDDo0NH67wxUeeG6Tjv+7cj/Mm9z/OvT8/yrlfs3bAvrtsl2JuJcKRPF6fhuOs6i9tAJAulWd566wwBr4v//o9P8SuffILFUp3/+l1Xb/jIvozyB/WrOqS/XablMelz8vggONY5K8cWyvz+5w/zXz/1BOMxP++4iHc2cEU2QluTfWnjWq8WcQtpLqIGOmcl0lziu2/cwT8cOs0Hv36U9993lDdeP8nBHRuv8d50pG8+gaYe4h6JJcw9GMlCo8Srr4iyNxPmj770HL/7ucMcOrnML796/4aCORrwMhEL9K2cycCEgK9dpml2Y4N+SOe4Y2+Kt79kJ39/6DTPnCvw3rfeQDqysZN5f1Zd0P24cLSqumysOFMBKM3xrnv2cWAyxnu++Cxhv4c//P4bNrWQ9mUiNNpaX1pTNqzkbkBHCIjyPL/3vddRrrf5X/92hJftT3fCQjfC/mykb5oa9SJlGcDrNeFzAmWhleYZjwX49Tdcw/0vLPCFpy7wn19zVYdnvhhjYR+JkJejfSqnbYluhI7C9PqDk7zu2gn+8v7jnM/X+NMfvGnTbOj9WV1h6sNZKeb1GkimfU56oEdplne/9iom40F+7/PPMp0M8ltvvnbTx/Zlw8wW6n2Jpmvp59483ajm4q7M87vffZAzy1U+9MBx3nzD1JaVA/akw33LFei5bIRVBNoV2gGLG/vsIwD87ncf5K23zpCO+JhObm5VZKJ+ogFPXzZ2pbRMBJOhYtChtijPEfF7+MzPvZTHTue4dipGNLD5xbUvo/5mR+dL7E7bW6qgVVXUjBUeHYDSHNceuJ2vvvseTi6WuXEmsWVS0BXZCP/8+DmqjbbtZT1cDdVLwPRfKJKFeh6aVX70jl3cuXcMTa5YkxtBCMG+TISj/bBqdLrRVO6GAV1hcrkEf/b2m3n09DLTyRDjsc3bbe7VrZojsyW4zuqgN0a5sEwa8Jh1purUFqU5MlE/n/+ll/HU2Tw3TCe23Dd70+qsHJsvcf20yd+5DWStQEu6iESsK38v3beH+/7LPcwWatw4k9iSGt+TCfOFJ/tTTntglkBQmizuZUDn1EAdvhtnElsKAONzO8dCnF62v5icUf7CY1a7gY6mBiqK6Y69qS0FAKxQD/0od9zWtZuwmYgaWKOpgRK6t+4e2zYrdFdKrduZPqyLu1mkKizSjdDZY1dko1sKAAN70+H+mOutOl5a4LNuCQC4XIJbdo1tKQAAQj4P4zF/X86KEXhgKncDlMIUTHbWJOL3cMfe1LaKQz/PiqyXKBEkaia6ETq+QGNdphJBbtqZ3NY3uicVZrnSn453AxMCIWpoljZ2FpplqJvTuqaTwb5UFK2V1cXpMetMhY6mZgbxoJewz92fSJR6gar0ETWTmQoQSgPC9FwM4d2PC8fbKlE3m7sB64RAt5hOhpgv1m3vH6vpvg3TzlRY2V8mo+Kmk6G+nBWDbjQdUQM6TWcuW96IGOrHWRGNEmVMhu3COoWpW+yx2epfjcEIAakOirS0sfU/YtncIZ1JhjizXLU9TNSogWRau4GOE9IMhBDsSAb7JASKlAkQMkvNuD0QSlk4pErYnF6yfy6+toUEPlhlrpuby46kmsuFbcppm4URimiabgR1VpqVlUzwLjGTDPbF52SE7fpNlMTuwILCFPC6SYV9fZmLu1mkYsXSDKdBuEzPZWfKwu/qEgMRArKthIC1jb3CD5rBzFiIektjvmhvmGjD2NhmI2pgDbVlBjsSQc71QQi4GiXKImQubNeAhblkIn4CXldf6KBAu0zDauABmFYyphKKZrFbOBsRW6YzU8GyVTMzFuJ8vmp7NrdBN5opid3BKmrLDKb6dFY8VkrFALjcynI2OZfppEnr3AQGIgQ0rRchYM2c6midNl84bT193HREDXTCxWiY4yz7ZQm4myVrPDpYtmoU9WD/XAJahZYVn1PYmpIxnegP9WDEo3stWZoW55IMokn7rZqOEIiZzN0AxylM3naZhpUQd7A0l5DPwy98x8Yh8L1iMEKgrUK2TGemQk+cLWC7adiuGc5UizwnmJ7LVCJIrtK0vT+xp1W2xqOD5UM6nQxyJme/JRDCZDVUA26vJWprIh5ACDhr8/6ql5SlaU0IWFSYDF+NzX4BWddzN6wqTBZ8gVMJpTDZTQP7rYa4gyWFCeDdr73K2u/bBgO1BEx1FTMQSumcmrk/ohEVMVewOWu4VqAuvUTCvTghTfLPeu0auzUcyzw6rGxsk4dtIhZg1uY10dptwrIGVoQAWBJoPo+LbNRvuyVgtC4NhBPmH7aoME3E1Vmxu6evqBepSh8u7/rkwW1h0Rc4lQhQabTJV+2NrAloFVpmC+EZsKgw9QuD8QnoQsCSM9XlViZ70VwHpFjAQ8DrYtbuPqr1IiUChDdJvtkSUb2oWtFc/K/BD56x+cLpTbsZh3Yd6ubqm4zHAiyU6rbyz5VyHpeQYDYz1UBk3PSaQH+oh5549OAYCLdlhclu4exqWHSmwoqvxuS5NxQmu4VzUFZpW4luBMsKU78wUCEQNJuUZCA6YXozCCGYiAVs125cjSIVQuuKPnWFuF4nJG+um9MOg3+2mXoIahVrmamwoqkVzF2e47EAUsKCjXWdjF4Cbis+J1DrYnJNYIV6sBNtq5mpAC6XunBMnpWw30PU77FdYXI3S1RdFoVAzOJZ0RUmW8+K1iZEzXy9MAORcdCaUO1ftVYzGKgQMFXmdzVi01Awf0izsYDtdFBPGzuQAG8Y8mdMPZaJ+nEJ1UzbToQw2TN1NeJ60/iCubmMx1SpDzudkDU9gc8VtKA9g9pfpVlometGNxkPcCFfs5V/lrUSLekiajYz1UBsh8Wz4re9dLG3VaZqJaIGVhQmk/vLoLbO27i/esrdAIhNqa8W1qUfGEyegKZMf1M9U1cjPm364gT6Ygl4WmVqVoWAEGpzm9zYbpdgLOxn3s5D2qrjo2UtdwNWhIBJTa0f1IMRVmmJbgT9wpGmKaFsNEC9pVG002FfV13FNqv1sy0snpXxPvhqfK2SdZ+TPwqBuOn9lQorhcnO0HCj2q6l6EaAuF4jyMK69AMDSxYrSz9RM13FViO+Q3HPNXOlVSfiAWYL9mpqPTlTQWlqFqiHbNRv68ZuVIxCeBaFQHRSOexNbuyOw95GgWbkbvisZKbCCvVgUlPLRNV+tnNdhJ67YYluhBUhYHLPj8cCtoeIBrQyTavOVFAWmsn95XYJ0hF7z0q1pGgcV7BXhelyFgJamzIh8ynXBixqndmon3pLszVSwN+umG+Xtxpxa+Z6Juq3lQ4y6rpY1m7cHiUITG7sVNiH2yVsvXCMMr8BK6GIYPmQZnUhYCflaLkGkoH4DLSqUFnfZ3grjMcCzBXtVZgCvficQK2LSasZ1Fmxs5dI1QjbtUo3hjPg9l3eQkBIjYroIQMuZu2QGvygnWZuQFos82sgNq3CxUzyz3ZbAoYQ8Fjd2KBrnadNPeJyCbJRv61r0omosSoEOk5I874awNYLx9MqU7dKN8IqgWZuXcZjfpptaWvRsrCsWKsXZsCiw14pTPYpGXWDbrQStgvKYR/bcXkLAWTbWsq1ActOSEMI2LchVJnfHjc2Eorntv3oamR0IaBp9mhqNV27sVQIz0DcmsNe8c/2O+5CVjJTQTUICiQcQQf5rBbCMxC3JtDsPiutVpswVTSzfTdWI7YDqkvQMJfElrGZDjKoU8t0I1j21fQDg7EE0Kx1FTMQnVDxz1bNdbs2RKtBgIZ1ZypYDn3LRP20NMlyxZwFsRmMQnh+q85U0Df22Y7jv1tkbdbUtJrqixCO2DAXM48EvfjcLlvn4tMq1nM3wLIT0ojasksIlEtFPEKz7nOClbmYFM7ZmJ+FUsM2hanTv9qqpQkjIeCSGg2zPVPX/AC3CrMyGymgdx5bKtsjBJo67WA5MxVWWTVm/RtKU7OLelip8Jiw/kNi0yphrLJg6rFUxM9S2R5hBioztSwDuDw99EyKmY/aEkJ0LDS7EOwlMxVUhr0nYJoOSoXVWVks2bMu5VKPuRtg2arJRPy0bVSYDEvTcp4TqHNfPAdt+7uemcXAfAKtXnh0sCRJwz43Po/Lto1dKRjOVDssAWv8s11OyLbVrmKrYdGhmo74WCo3aNukqbkaBeuZqQZ64J9tFQK98uhCWDorqYgq7WCXcDaaL5luLbkaFvdXJmpEoNmzLoYQiMQs5jmBmovULGWm243BWAJovTlTQXesmNNuhBCkwz4WbdrYlV66ihnwR1R6f+6kqceyNvPPK+UJEtZ/iMVDOhb2oUnI2aSpeVo9JPAZiM8o/rleNPWYrUJAaxOmZj0pyYAFIRDxe/C5XSzYZDUbdKOlQngGolOAMH3uszGbfTW1IhXpJ+S3UAPJgIPCRAcmBHrSbgCSu9QfsG0ueiEV8bNoE4VSKytLoKeNDTC2F5aOmXokbXMkiqwXaEtBNNqDQEvonO3yCVOPrdB09ggBb7PcW+ABqDUBWDpu6jE7hUCHbuxZCMxA7pSpR4QQpCI+lmyymhtGWGUvzlSPT83F5FnJROz1BYpGkbIIWs/dgBX/hsl16QcG5BiWvTmIAMb2qQ5lJv+IYzZaAvWyESWQ6O0HpfaZvmwMass2Lr1epEQIv7cHHj2YVBz00lFTj6XCSqNasOnC8VltKLMaHSFgbi7psI/lij1OyHIhB4Cr17OS2qeqbxrlDrqEnWelUw3VSvOl1UjthUWT+6tDbdkjBHrqu2EguRsQpvdXPzCwHsM98egAKb3BwuIL5h6L+GzzCaw4U22wBPJnoNl9JIYQglTYZ5sQcDVKVHvJ3TCQuqKHQ2rPXPy9ZqbCihAwOZekTm3ZkZDY4dF7tTSNs2JWOEf8tgkBW+hGUMrf0lFTGdAGtWXXXNytcu90o8cPiZ2m769+YIBCoAfaAZR2A+YvnLCPxXLdlkzIVlUJAVs2NtI0jZIM+Vi2a2M3S707U0HNxeTGHtMtgUWbNLWQ1mMCHyhfTWTCtIW2Mpfe16XS6SrW41kZ6+Gs2EQ3Gs2XQj1bAvtUuRgTFTiFECTDXtvOiq/VY6kYA+n9l7cQ8PSq3YRSqqCUaUvAT62pUWm0e/v9gNaJqOlxY3eoB3NcZypin7muuorZIARS+1TEg4kOUGMh/eK0yUIL9RpRY2Bsr2nt2RACdoQjdmog9exz2gMIS8LZNrrREAJW+iKshlULLeRjqWxP9rO/Xe4txN2AYTUPuK/AwIRAzxtbiBXT0AQM/tmOza3VC2hSEO15Y+9RX03OJRny2Rb77Gv3mJlqoEM9dC/QPG4XyZDXFkug1WoRpob09ag9g+KfTQrmpI0CrVE26MYelQxvUDkiLVCnlUabqg0Kk6iXqOFFeCwWjTRgWDWmqS2fbT4B1b/aJiHQKFlqNWknBicEesnmNNAD/2xHExNRL1IiiN/r7u0HhcaUZTP/nKnHxsL2RW/42z0mJRno0HRHTD1ml9ZZKhZwCYnolW4Etb9Ks1DNdf9IxD5LoN2hG+04K+ZpupSNNJ2rUaCMDUpGcreqFrBgbn8phckeSyAoK2heOxQm46wMlhIamBCwXNxrNTJXqZhhEyWl7cyEFI0SFRFEiB5CxQyMXwuzT5t6ZCzso1hv0Wj13pqx58xUA6krVEnpuWfNPRbx2xId1HM11NXIXqu+mlgXwxKwQ6D11FXsYmSugvnnQeteq7fzrPTUfGk1PD7FpZs8K7b5N6QkLCvWu4qtRvpK9XXucO8/qwcMTAj0zKMDTN6gvl54qutH7IxE6bnM72qMX6c2g4lDaif/HKKC9Nmg3XiDanNfeMLUY3ZFOnUS+Hp1pgJMHFRfZ7vfXwGvm5DPbQ/d2MlMTfT8s5i4DpplU/TWmI1nxdsqU+81d8PA+EFTawIqaqtQa/Xcy7pRK+MRWu+5G6ASXoNjps+K3RiYEAjbIQQmrlNfTfwRDe3GjkxIlZRklxC4VtV9N3NIbfJvSK1NhCqylwqPqzFxPZw3KQQi9mhqnczUXkpiG4hO6of0SVOPjYVtitpqlKhIP35fjzw6qDUBOP9414+kjbNiw7r03HxpNSauUwyAiR4JxlnJ9UgJlXUlQ/Qa4g7Krzl5vak16QcG02MYQShkw+UZnYBw1tSFE/QpTc0OE9fbLtvjTIUVgXbu0a4fsUsIVEo2ZaYamLxeFccqd19IbizsJ1dt0upVU9OFgC0+JyHUupg8pHYlWYl6sbe+G6uRuRpcXlMKk52WQEAr0bSDRwdLyp9tZ0WnG912KBmg2Iy5w6b7idiJgQiBNi57eHSA6Vvh1L+besSu+HrbnKmgLAFfFE5+s+tH7NvYOaCHdnkXY8ct6uvpb3X9SCrsQ0p6dt4ZCXw9Z6Ya2HmHoh5M+J3GwvZEbdmWuwGKS5+4Dk4/1PUjYZ8bv8eeJKugVqHltWl/Td+q/E4nuz/3Yzb5aqp20o0AUzdBuzFQa8AWISCEeJ0Q4jkhxAtCiF/d7vPSTtmz+2WwfHzjQkxSKm30Ip49GfaSsyGjMyDL9oSKgSqPvfOOzQVauwXlxTUv2a7dBGzSbnbcAp4gHP/6xu83KutKGCRCXgDy1d7m0rIrM9XArrtUtcdTmwi06vI6LW4sZE9WuqdV6r0G0mrseTmceRga5fXvSQml+TUx60IIkiGfLYX9QrKCZtdZCcSVQDv5wMbvt5vrqKIxm6K26mWbcjcM7H6Z+nr8a5v8wqLpJjpm0fNtLIRwA/8H+C7gGuCHhRDXbPWMJuwUAnerrxdfOPUS/O13wx/ugw/cDcWVWNxE0B5NLSQrtO1ISjKw66Uw/ywULuoyduFJeN9N8Id74dPv7Ai1RNCLEL0LgZrRLs+uje3xK4G2kRB49KPw3v1qXQ79dedlI6qmV85W6kIgHLXYVexiTN+maJRj9619XdPgs78E79kNf3ItnHus81bSJkvAtsxUA3teDlprvQZdOA9/8Up47xXwodeusXoSIW/P1lmjaficbLIEAHbdvbFAO/lN+ONr4A/2wBd/rSPUOgmJPZ4VW/purEY4rRzdGwmB+/8U3rMH/mAvPPNP9vy+DWDHbXw78IKU8piUsgH8HfCWrR6w1RIYP6iamTz1qZXX2k34xE+oS+iOn1flGD7/nztvJ0Je8r1eNlqbsKz11lDmYhx4k/r61KdXXsudhv/7/apY3i0/AU/8PXz7I4BKsooHvT0LgY5200tryYux/zUw98za8LfDn4V/+nllAs+8BD73nzt5HoYl0OuFI+tKCATsmosvBFd8Jzz9mbUW5Zf+OzzyYbj5x1TT8E//TKei7VhYJVnVmr0lWfnbZZoem+gggJ13gi8CT6/aX/USfOwHVI7KS39RXaxf/u3O23aclVLZ6Cpm4/66+vXQqsGzn1t5be5Z+PgPQSAG170VHvwzeO7zACR0IdArDWwIgaAdPicDV3ynEl6rFFUefD98+TfhytdC9mr4x59f+76NsOM23gGsLvB9Rn9tU2iix+Sq1XC54MYfhqNfURVFpYR/+U/wwr3whj+C1/2e2tyHP7vmwunZLKwUcQlpnzMVVPzz5A3w2EeVplnNwUffCs0q/Min4I1/qjTTB/5Xp4XjWNjHUo9zMWogBezI3TBw/Q+AywOP/I36/swh+NTPKKro7Z+A7/+Qujy/+T5gtSXQ21xEvUgFP8LdQzXUi3H9W5Wj++hX1PcPvh8e/D/wknfBm94Hr/t9WHgenv8iYB9NF5A2ZaYa8IXg4PcpgVbNKYrxUz+lfB5v/TC85nfh5h+HR/9vx6lvh9Xcab7US9+Ni7HzpSoLWleIKJyHj36/6qL2o5+B7/6Ayi6+/08B8HlcRAOentek07/aLroR4KYfURbao3+rvn/288qKOfAm+IGPwPf+pcosPvRX9v3OVbBDCGzk4V1XDEMI8U4hxCEhxKGysNHEBbVx3T74zH+Az/ys2sQv/xW49R3q/Vt+UjmSnvh7QF04+Wqzp3K/pU5XMRs3NsCdv6g06M+/Gz7yZpVN+IN/C9kDKlrltp9WPpCzhwC9JkqP/HNTb5xtqxAIp+G6H4CH/xK+/ofwf78PouPww3+ncgkiWbjmLfDUZ6DVIK5bAr3SQa5mEdv319VvVBUfv/Ar8KX/AV/8VfXaa39PrclVr1fhpI//HWBfwlhQVu3j0Q3c/jNKg/7Mu+AfflQJrte/F658jXr/tp9WLUIPfxZQClOv/rOq3lqy53phq+FyKSF84htw72/A37xR+Wfe9g9qrdweuPUn4cxDnbBrO6K2Ov2re+kqdjHS+5U1cP+fwn3/UwnmqRvhez6ofIXpK2DvPfDkJ+z7natghxA4A8ys+n4aOHfxh6SUH5RS3iqlvDUzPmXDr12FxAy84Y+VU/WJf4CX/xf4jv+28n5sUmnQL/wboBqCaxKKNev9PVfa5dloCYDS1G54m5L6Syfghz4Ge1+x8v7+1yiBduReAJIhb89liw3txpbcjdV4ze+oDf6V34XIOPzYP0Eks/L+gTdBPQ9nHibq9+B2CXI9OoY9zbJ9CXydH+pXB7K8oCyXa79XWTIu3aJ1e5TZfuxr0G6S7Di5ra+L1DSVmWonhQLKofqdv6Uu/yNfgtf+Ptz2Uyvvj18L8Z3qPRSNkqs0eqq6a/icbMndWI3b3wn7X6ss41peWctTN668f9Xr1Vf93Cd05a8XyHqRpnTjD9isaLzhj1X5mPt+X63RD/+9stwMXP0G03WsuoUdNvPDwH4hxB7gLPBDwNts+LnmcNPb1UGUmtIyL8bee5RGWl1eoR6qKxqoWdTsaJe3EVwu+J73wz2/quoJ+S/SBENjsONWRXe98teJBb0cPm+uBeLF6Gg3dpq4oKyBn/2Gap2Z2KUuy9XYfbcSaMe/hth9F4lg705Ib8umQngXY9ed8P88o7TNxM717+97lfIRnH6IREglZvVi1VRrFUKibS/daOCuX4Lrf1BZz6GLHOhCqHP02Eeh1SAR8tJsSyqNNmG/teui0fE52XxWPD54298ryzg6qSzM1UjtU7WGjn4Fbv8ZEkFvz3Sjq666iiXsCnE3kNwFv/CwinJM7lH3wGrsf7W9v28VerYEpJQt4BeAfwUOA/8gpTRX2MMuhNMbCwBQQkBqcPKbtjghbQ8VuxjJXesFgIG996i44kaZRLB37UbUi1SlD7e3h56pm8HtUYdxI44+mIDJGztRRHY4If3tkr0RNWt+eHRjAQAq8gbg5AOd/dWLVbNCN/ZBCIBKtLxYABjYfRc0KzD3dMeq6YUSWsndSFj+GZtCCFVe+mIBYGDvPXDiAZDSFmrLZUdXsc3g8auzcrEAACXMbvuZvvxaW8J0pJSfl1JeKaXcJ6X8f+34mbZj6iZVffDcY51IgV60AoNH9/djY2+HHTcrgXb+CRIhL6V6bzVRXI2iPV3FrGDmJUqgaW0SNpTGtjWBzwyCCUjth3OPEQ/27t/o0I12+5y6gZHsd+YQ8WDvUTXtfgQedIsdtyjKcemYbgn0JgQ8TZtzN8zgDe/ty48dWO2gSw5vUFVSPP/YiqbWw4ZYCRWzmUfvBlM3qa/nHl2VZGV9Lu5miYpdNZDMYvIGpXUuvkAy1PshDcoKLTtzN8xg6iY49ygBr5uA19XTmhhCoG+W5laIz0A4A2e/bYt/o+NzitmUu2EGkzeqr+ceJR7yUag1afcQEOJr29R8yUG4fIQAqAvn3GMkO5qade1mxZmasGNk5hCdgOiU2tg2aJ0eOys8moVRCfb848SDvWen2lbm1wqmblKhpMULxHvkn42uYl67efRuIARM3awrTL1n2krd5+S3Mw+lW2QPgNvfOStSQrFm/az42mWa/aIbB4TLTwiU54i1VUp5Lz4B2dFuEnaMzDzGr4W5w51D2ku5BVsL4ZlF+koV233+cWUJ9KBx1hotlZk6KCFglJ6ee6ZnX02nq5idSUlmkL1aWWcB5QDtRckQjaI9XcWswO1VgmDuGRLB3q0a27qKOQiXlxBI7wfAs3yUWMDTm0NVd6Z67SjzawWZq2DxCAm/WsJeDqnKTB2QEHB79A5xL5AIeak02tRb1jJty6U8LiHtz93oFumr1Nf554n3SG11aiANgm4EyByAdoNEXdXk6sWqcTWKVBgghaI31LGDBg7aWQPJIbi8hEBKCQF14fTmhHQ1SpT7FSXQDTJXQatGuq1SyXva2FqF9iCcqQb01ocdq8biXMqdzNQBWQKRrCputvAciWBv+RvtfmSmmkFGCTTf0hFCPndvdKNdXcWsIr0fCmcY86rzbtXalFISllW0QVmafcLlJQTi04ofXDjSsxPS1q5iVqBrnYmSSiDphUYJyQraoJypoITz8gmSAfWtVZquZpT5tTspqVsIodZl4YgKR7SDbrQ7ga9bdFofPttz/oa3VaLmHuD+0s9Kuqaq21i1aqr1OiFR70/uxgBxeQkBl1vXOo8S77FErqdZpu4aUFglQEYd0mDhGEJY5znbmiRMFTlQIXAFaC0mtDnA+iHtJPDZVeHRCtJXwvxzKtO2l+znWpGWdOH2DWiP+SMq+GDpmJ5pa30utnYVswJdoCUqSmGyelbKhRxgU1cxB+HyEgKgC4EjPTshVajYAC/OYBICcVz5k8QCXvIWL85SuYxftFTlxUEhdQUA6dopwLolYETUDCSs0sDYHijPkfK1qDU1y5VERaOo6Ea7M1PNILkblk/0XE460K7QGpTPCdSaAKGy4d+wNpfKIHM3+ojLUAgo6mEsIHpKgBmoM9VAcjcsn+wpE7JsNJTZLDv5UiC1D4BE9SRgPdKpWR5g7oaB5G4AdqCsGqtap7tZojaoBD4Dyd2QO9lzY5mgrNC2q6uYFXj8EJ3EnT9F2Oe2vCZVvQaSbV3FHILLUAjsA63FjGuJQq1lOXEkYGe7PKtI7FKaWg+ZkMbGdocS9o3LLEJjEBwjVFJCwKrWaWSm2tZVzAoSuwAY79Fh72mVqQ4qd8NAcjcUzpEKaJbnoZypZXubL1lBYpeuMPksz6VuNF8aJN3YB1x+QiCuCp5OiXnAuqY2cGcqqPpCuVMkgh7LlsDAnakGEjN4imfxuV2WD+lKrfdBWgJKCKSa5wHr/g1fvwrhmUFyFyDZ6V4kV21aqiRa17uKDdyZmtwFuZPEg17rlqZBN46EwJAjoYRAtm3dCam1NcIMMDPVQGIXtOvM+IqWfQKNjjN1wEIgPoPIn9bj6y1SD3WVmWp7tUozCGfAGyJWU9XUrQpnf7tMY5Bhu7BCbclZ2pqkWDdfer1Y6kNXMStI7ILCWVJBYVnJaBo1kAZ9VmzG5ScEYqrpWbKlm+sWDmmlVsHXrzK/ZqAf0t2uecuXTaNiJCUlbBqURcRnIHeaZLCHJL56kQqBlTr/g4AQkNhJqKKckFbnEpADKoS3Gvr+yurUlpX8DaMGkq1dxawguQukxh7vkuWz0tYT+EJ2NpRxAC4/IeDxQ2SCWF2Z61Y2drmgyk4MLDPVgM4/72DOcqe0dqfM74A3dmIGmmWmA3XLmpq7WaIyaGcqQGIX/pIuBCzOJaQ5gG6MjIMnQKqhrBorAq3jTB043ajOyk7XgnX/Rr/6bgwYl58QAEjMEKronK0FfnClq9ighYCqbZ9tz+mFscyb653M1EHVQDKg+2p2eaxrap5mkZrdrSWtILkLV/6U5U5pmiaJOIFuFAJiO4g2DOrU/LrUi31oLWkFyRWFqWDRv0FdnRXPoJU/m3F5CoH4DL7yWcDaxq4UlfY88I3tDUBwjERbNQW3RD0YQmDQdJDuq9npXrTs3/C1HFLmNzaFqBeYCrQs7a9ytUpQNAZPNwLEpgjVDOrU/LrUjEJ4g+bRo5OAICMXaLQ1qhbyN1yNIiWCGzd9GWK8uGbTLRIzuIrnEGiWLs5GWWk3A9/YALEdxJoq0slShmq9SBM3YrPOTJcKRtQW1v0bvnaZ+qB5dFCZtsDeQMHSXEoGj+4EjTM2ha9yAbCmMLWqDqEb3V6IZEm2FgFrc3E1ilQGWSqmT7g8hUB8BtFusCdQsrQZ+touzyxikyuamoW5iEaRMgPOTAXVT9kTZFybs1xJNKCVB+9MBYhNArDblx9uZypAbApX6YJlhcnI3RhYIbzViE6uKEwW1sXTKg+uq1gfcXkKgZiuqfmLlja2UebXGUJgCn/VeqSTu589U81ACIhNkdB7PVhZl6CsDD4pCToRaDOenDUKpZOZ6gBLMzqF0JpMeUsWhYCDImpiOwjVdf+GhXXxOiF3ow+4PIVAVGlqu3wFSzHphnbjiCiB6BSe6gI+mpa4dFXh0SEbOzpJVNfUzGrQmiaJDLKr2Gro+2tSLFtzpuq5G45IStIVpiv8RUtnRejOVK8jrJrJjsJkxULztyuDLYTXJ1zWQmDak7ekPRuhYgPNTDWgUw9ZkbNUbmHgFR5XIzpBqG74N8zNpVxvOiMzFcAXgkCcDEuWLpumLgQckZSkC4E9/ry10MpGkTpeFZo9aEQn8dRz+GlYsmoCWvlF11UMLlchEM6AcDEhlq3FcdeLNKUblzdg/9jMQj+ku705axvbCYXwDEQn8FfnAGn6wikVC7iERAQccHECxHaQai9QrLdotTVTjzqLbtSpLfeyJYVp4M2XVkM/KxNiyZLCFJIV2iMh8CKB2wPhLBmsbmwHlPk1YESi+AuWNDVHaTfRSVztGjEqpqmHSkmvhuoE2gEgOkm8payagsn8jQ6P7gS6MZwBl4cplzWrxtMsOSN3A1YYALd5hUlKSUgOuO9Gn3B5CgGA6ARj2hK5SsN0pq1jnKnQoYOmPdYsgZCsDrbM72pEJwDIimXTc6k6pRCegdgkYYPaMinQHEU3ulwQnSTLUg/OVKecFYPaKpguIlepN4mKKgy6BlIfcBkLgUnirQU0CaWGOU3N4yRnaiAB3hA7XMumN3azranMVCfw6LDiUHXlTFs1dd0S8IUdckijUwTqC3hombc26wU0KXANssfDasSmSGmLlpQMRxTCM6Dvr50e8/ur1Okq5pD9ZSMuYyEwQaRhLRLF13KQM1UIiE4yLpZMb+xypUJANBGOEQLKEtjtK5jWOpudzNSE3aOyhtgUAkkG87kCqqtY0Bl0IyiFqTlvqVNaUCvTdIoQCMTAF2GH23zUVlUvf+GI3A2bcfkKgdgU/sYyPpqmN4Rfc5AzFXRNzXzNnXJB39hO0W50IbDTaz4SpVnJARCMjtk9KmtY5YQ0K9A8zRIVp/DoAJFxwk1r+RshrewcuhGUwmTBF1h1Uu6Gzbh8hYB+4WQwn9ATdEJXsdWIZIlrKtLJTGGsilMK4RnwhcEfZ8qC404zMlNjDhECkSwAaWFeoHlaJWouh/DoAJEsvlYRPw1Tc2nrhfA0J/Ho0QnGyJnOqenkbjjF52QjLmMhoPjBcQsJPWEndBVbjXCWSHPJdGGsetkohJfo08AsIDZpaU2kXghvoK0lVyMyDkBG5E0LNFUIz1mWAECavCknd6nWcE7uhoFIlnjbvNXcMOjGyEgIvHigWwLjwpxpWG+pdnmOyEw1EMnia5cJUjN14RhdxRxRCM9AdIK0NE+hiHoBDYFwyrqEMwDs8BbN041tB/Ho0LFqMsJccmW5mHdW7gZAOEu0tUyl0abR6j5/w1G5Gzbj8hUCEZ0OEuZMw2KpjF80nRUlYGhqJqmHRsXQbhL9GJU1RCZItBdNX5yiUaDspDK/bi8Ex5jyFExbAo4phGegIwTM0XSVot58yUkUikWFycjdcIzPyUY45MQMAKEUCDc7POaSrCpOKvNrwKAeMCcEWroQGHhrydWIjhNpLlGsNU1l2noaRWc5UwEi44y7zFEooOduOIluXE1tmdhfNac0lFmNVb4aMyHVmk43OqJemM24fIWAywWRLDvc5kxcQwh4Qk4SAop6yFjc2I5ISjIQGccjm8Qpm8q0dVQhPAORjOLRzWicna5iDhICOrWVFeaCKBp6RI0jCuEZsKgwUVcJfO6AQ+hGG3H5CgFYpamZ0G70je11lIlraGrmkmAMZ2rASc6uNXPp/sLxtUrU3Q66OAEi4yRlzpT2XKrWCIm6szJT3V4IpZg26d+oG82XnGRprvZvmJiLq16gTABc7n6NbGC4vIVAdIIMOVPas8Gj+5zkTA2lkQjlEzChdYpOVzEHhSN2SkfkTM0loJWc5UwFiIwTby+Z8jmVCg5NSoqMM+421ymtbdCNTuLRw6tCd03MxeWkUjE24/IWApEsSWku07bZ4dEdRKG4PRBKMS7M+TdEo0gFB2WmQscSyGJOgw5pFVpOiQwyEM7g02o0a8Wu8zeMpCS3kyxNgEjWdPZzh0d3QkMZA2GlMJm1ND2tEtUXYVcxuOyFwATRdp5Cpdb1I4YzNeAwB5GIjDPpMReT7mmWqDopKQnW0kEmLLSILNP2Ok97BkjKHKV6d/6NupGZ6jRLIJxljGVTayJrDukvvBpuL4TGyJrM31ClYhx2VmxCT0JACPGHQohnhRBPCCE+I4RI2DSuS4PoOC40PNXFrjW1tlOjBCJZxl3mHMMqM9Vh2o0/ivSGFB3UpdZZa7ScVQjPgME/0/1c6iV1cXqdRDcCRLIk2sumqC1RL9DChfA5a4+JyDgTbnOhu7522Xk+J5vQqyVwL3BQSnk98Dzwa70P6RJC19QS2nL3mbY1B7XLW43IOGPSnLPLUYXwDAgBkawpIVAsFfGKtrNyN8BS1nBDr4HkiK5iqxEZxyfrNPV4+W7gahQp45C+G6sRzjDuMkedOqrvhs3oSQhIKb8kpTTs3AeB6d6HdAnRSRjrvkyBq56nhVvVuXESIhmScplcuXtNLaA5qMzvKojIBJPu7i/OlQqPTrs4V5Ksut1fHbrRSRQKdARaoL7Ydf6Gp1Gk4jRLEyAyTspk6G5Iq6CNhMC2eAfwhc3eFEK8UwhxSAhxaH5+3sZf2wP0Q2pG63Q3ipQIO0+7iYzjkw1aeiG1bhDUymheBx7S6Djjovskq6qemeoOJvo4KAsIpZDCpUeidDeXtr5+ESc5U2EVtZXvOn/D2ypRcznw4oxkScpl8uV6Vx9vdfpuOMzStAnbCgEhxJeFEE9t8O8tqz7z60AL+OhmP0dK+UEp5a1SylszmYw9o+8VqxNHujyk3maBiiM3tpqLp9qdgJVSKmeqP9HHQVlEZJyUiXK/tU5SksMsAZcbLZRWUTVdzsWohhpwUlglWMrf8LdLziqEZyCSxS/rNLqktoqVGlFRRQYS/R3XgODZ7gNSyu/c6n0hxI8DbwReJc3UMXYCvAHa/jjZVvcN532tIlW3wxyQ0MnqjDSXaLY1vO6t5Xul3iJKxVlJSQYi40RkmWql1NXHG0ZXMadRKIAIZ8kUcjzXLd1Yy9HEg9dxdKP5InKBdplqYEc/R2UNhsJUWejq46X8IknA7aRquzai1+ig1wH/FXizlLJiz5AuLbRw1lRiUrBdpO5AHt2sE7JYzOMVbQg57+I0Esbc5e6smpYTczd0uKLjetRWt3RjgZJwIN0YHEMKt6kiciFZdlbfDQO6whRsLNDuor94Ja/TjU48KzagV5/A/waiwL1CiMeEEB+wYUyXFK7opKkU8pBWpum0eHQwXTqinF8EHNZLwIA+F19trquPGzx60Gk8OkBknIwodE2heJpFZ9KNLhftUKbrJD4pJWFZoe1QSxMgRZ5ibfu5VIvqrDjR0rQD29JBW0FKeYVdAxkUXLEJxsWzXfsEwlqJBZ8DN3YwiSY8uqa2/VwqBV0IhB3GPUPnkIbqC2iaxOXaWivWqkbuhgMPaSRDilzXUVv+ZoGaU+PRI1nShTynuhBotUabCBVnNZQxcFHUViLk2/LjdZ1u9Dtxf9mAyztjGBCRrLo4uzikbU0SpYL0O8wBCUpTC6ZI0138c12PqPE7UbvR6aAUOUqNLiJR6nk0KfA4LUQUIDKOlxbNynJXHw+0i9Q9DlQyUNRWtzV3CoUcbiFxOamhjAE9aqtb6rRVVmclGE31e2QDwWUvBIhOEKDRiTDZCoVCAb9oghMvG5R/o1s6qKlv7IATN3YohcRFVnRZP6heoCIc1FBmNXSrxlvpjtoKaSVn0o2s+De62V+lDt3owLPictMKpLou893WE/gicQeeFRvgwFNziRExnJCz2360qG9sx8Wj63BFx/WaO90IgRwAYac0Zl8Nl5tGIE22y3ILbic2lDGgUw+e6vaRKCthuw68OKGTZFWobB9fX9GroXqd1EtgFbRQRs8P2p4BkNUcAMHYSAi8OKEfUncX8fVlnUf3hh1IoQDu2ARp0V1NFKlrN+FEus+jsoaWYdV04d/wNYvOayhjQLcEgo3thUC92SZGGZxW/sJAZBwP7Q49shWqBo/uRLoREDq11VWkUy2vSq47LWzXJoyEgM4/B2vbC4FaQW1+X8SB2jPgimRJizyFchdVUWs5wKHRQQDh7usH+VolR5a/ADpKRqK9TG2b+lR5I2zXqUlJemilqwur2cjdCDrUmeqJTXRNnbobBcpOrBJgE0ZCQD+koW40tZLuIHJiKCLoTsg2jdLith8V9TwlQo7tlOSKTXadvxHUijQcyqMTSNAW3q6ckOWcTjc6NR7dRFa6YS2E4w6pDnARXNFxVSmgi4AQTyNP2YlhuzZhJAQCCVrCR1xbpt7aWlNr6u3yQk7lBnWBRml7J6SnkafsVB4d8CUmFf9crm772YhWpOlL9H9QViAEjUC6K63TiEd3Ko/eKSJX217J0PRoqHDCmUKAyDhe0aZR3n4uvlaJmhOrBNiEkRAQglogrSJRttHUOlECCacKAXVI3V04IR1b/kKHOzaBW0gaha21znpL8ehOruvSCqmG89vtr3rRKH/hTLrRUDLCze37b4iamotTgyg6ClNxe4Up2C5Qd2Lms00YCQGgEcioXsPbaGpGlIDfiQlW0NnY/i78G4GWQ8tfGNAFmixe2PJj+VKZiKhB0KEUCiDDWT0rfWvqoVEywnYdur/8UVqugMrf2KZTmruWU3Sju6d81P6hozB1IwScG7ZrB0ZCANAi413xz656nho+8AYu0chMQhcCwcb2Jm6gXXIujw4dh72rvPUhLeeU1eNyKo8OuGLdhe62dArFsaGIQlDzp1XC2DYKk6eRp+RysPasCwF/bXurOSzLaE6sEmATRkIA1cSkm0gUV73gaB4df4ymy0+0uYi2TWGsiCzRcrIQ0AWabxtNrZJXh9iR5S90+OKTjFHYNmpLczrdCDRDutW8jUDzNQuOphs7ClN9ayFQb7aIUUZzYuazTRgJAcATHycpShSKW5cu9jYLVJ0cJSAENV+KlMhT3MJc1zSVlKQ5mEc3kvi2O6S1gnrfH3NmvgOANzau+ze2oR70xuyOpRsBGc50FekUbBeoeRx8cQbitISPyDb+jWKphF+0ECMh8OKGLzkFQKOwNf/sdzqPDioShfyW/o1iuap4dCdvbG+AqjtCqLk1tWWEwwYcLAREVFEP7eLW8fWilqdMwLk8Ospq7ibSKdQu0nQyhSIEVX+KMXJUGptHBZbyzqcbe8VICACBxCQA7fzWQiDcLlDzOnsztEOZbTNtjfIXLqdGbuioeNPEW1trai09KSkcd64QMPhnsY1/w93IUxbOVjK88XFSoki+XN7yc1FZouXUsF0dKiBk6/pBhs/JqVUC7MBICABCd0KyTSZkVCvQ9Dt8M0TGyYg8y1tZAjkVPeR1aiiijlogTZoc1S0ybbWKiqiJODUeHTr8s7eyddSWt5Gn4naw9gz4dYWpkd9coNUaLeKUHB22Cyp0d7t2mVXdEgg4NOnNDoyEAHT4Z88WmlqzrZGgSDvgbCHgjU8wRpHl4uaaWiWn5umPZy/VsCyhFcqS2a6IXC2nykg7tfwFQFgXAttEooRaOarexCUYkHV44+qsaFtQW/l8Dq9oI5y8JgARFbq7tEXWsOHHCSfGL9WoLjlGQgAgnEFD4Nsivr5QyBMUDQg5W3sOJCdxCUl5efNDamzsoMOFgBbWQ3e3OKTuWk61Y3RiGWkD/gh1V3BbJ3eknafhcArFoLYobb6/SjqF4nawgxvAG5vcVmFqldRcImMjIfDihttD0RUntMUhLS2ri9MVdjD3DAQSSlNrbOHfaOrlCaIO39iu2ARB0aBY2LxqpbeRc3Y8uo6KN0W4ubSpf0NKSVwWaAWcGx4KdKgtsUVpkqoeseWNOHsu3ShMUqcbHVv+wgaMhICOkjdNpLV5JEpF50A9Dt/Yhn9D2yrSSW/gHk06Wwh444p/ri+f2/QzvmaRipPj0XXUdf9Gobpx6G6pWiMhyhBy9v7qUFtbFJGr6aU+Ag4/K4Gk7t/Ind/0M+7qImUCCG/wUg3rkmMkBHRU/Snirc01zpruTPXHHK4RdKGpieoSNXy4/A5OfGPlkNa3OKTBVo6G18Ghrjo0vXTEQnnjhiz5RbW/RNjZFyfeABVXBH99c4WprguBcMrZSoarozBtbgm4a8sUhbOd9b3CuQHJlxjNYJZU/gi1ZpuAd315ZUO7cTqFYmhqni2ckJ7aMgURJeDw+uiR9DQA7fzGQqDZbCJv/w80k/s5fPjwpRyaKQQCATzxXWTOPsDzpQb7NtAjSsvKcvNGnU03AlR8KSIVFborNthD7aI6K/HU1KUemjkYReS2CAjxN3OUnZz0ZgNGQkCHjKj64hcKVWZS62O1DQdRLDVxqYdmDr4QNVeIwBZCwNdYpuRO4Gy3sConDWzqhDx9+jTpvTcQTGSIZHdfuoGZgJSSxcVFFna9mpnDf8FyoQisd5hWdbrRH3P6qqiExLGKSrIK+ze4QsrztKVwdAIfsBK6uwW1FWrlqDndWd8jRnSQDndsAq9ok1vaRCvQ6447tpfAKpS9qS39G6FWjqoncekGZBWBBA28uDdp0l6pVkmH3Qi37xIPrHsIIUilUrT1/JLy0sa+GqNkdjjpfCHQ1kN3F0obU1ue6iIFEXVsw6IOvEEqrjCBLQJCIu08DX/i0o1pABgJAR1+vXREaf7Mxh+oLlEggnB7L+GorKEeSJOSy1QaGzsh1cZ2dr4DAEKQcyc3LY0t2y2EEAgHl1kA1oyxkdvYyd0q6qGIDnfWA534+oXSxqG7vvoiBfcQ7C9U1FZkk9IkUkoSskg74OxQ114xEgI6wjp/uVkkire+TNE1HA6iVmiccZZZ3OCQGqGITk96M1DypgltUhpb01QmsdOFAIDQtWKtsLF/Q6voYbtDYAl44xNERZVcbnnD94PNZSqe4dhftUCGlFzasP9zqVwmIqrIoPOt/14wEgI6YroTsrVJaGWgmaM6JA4iLbaDSbHE4gbmeqVaIyYqQ7Ox6/40ifbGUVtSFwKuAdJB73vf+zhw4ABvf/vbt/6gUELAU9pYyXBVlygTwOVzfihiQLeay4sbzyXaXqbmHw7tuRWZVGdlg4TEwqKeG+TwUNdeMRICOoyaKJt1soq0lqn6hmMzeBLT+EWT4tJ6rTO/pJysLqeHIupohrKk5DKNlrb+TU295vYMjqL7sz/7Mz7/+c/z0Y9+dOsPutw08BKobGwJeGtLFIYkFDGU2QlAa/n0uveklCS0PK0hUTJkdAcTLLFYqKx7zzg/vqjDw8J7hPPt6EsFf4QKAdybFPka05Y4Hrz5Eg/KGgJpdUhrC6eAa9a8V1g4xxTgiw8B9wwQzpIUJc7nC0ymEmveklJZAm6Ph9/+7NM8c65g66++ZirGb77p2k3ff9e73sWxY8d485vfzDve8Q5++Zd/ecufl/NmiNQ3jnQK1BcoesaY7GnElwa+pNpfFM6ue69SrSpLMzQcF6cnOY1HaBQXzsLOtYKrsqyEQHDM4aGuPWJkCaxCzp0isIETslKtMiaKtMPDcXGGM7sAaC2vd3JXFtXBDaZ2XNIxWYVbzxrOz6+nHoTUaOPq8O2XGh/4wAeYmpriq1/96rYCAKDkHyfZ2ljJiLYWqfiH4+Ikpi7Fjait/IK6OF2R4ZhLIL0bgNriqXXvGf7BWGb6Ug7pkmNkCaxCyZsi0lwfLpabO0sIcEWHQwgEUptrao0h29j+Dv98houtGmSbNm7csKXG7hTUgpNkiw/RbGt43Wv1r2R7iYXgrQMamUn4QhREjGB1PbVVXFSveYcg3wEgMr65wmSUXklkZy7pmC41RpbAKtQDaWIbOCFLugPMEx8GYx1EOEMDD57SeiGgFdUhTWR3XuphWUJEj9qqbhC1JaSGJhwei74KMraDcZaYz6/ln6uVCglRQhsSSxMg780Sa6zP36jqJT6CQ1J6OWgoTPn1QsBVnqVIEF/Q2Y1+esVICKyCFh4nJXNUL2o3V1nSKZRh4QZdLpbdGQKV9U5uV2mWPBF8gdAABmYehha2UZEvl9TQxPAYswb/vHBhrUN1eU5974o5PBt9FcqBcZKt9UKgvqSEdXxIlAwCCaoENqS2fNU5ll3DEeXUC0ZCYBXcsXGiosqFhbVx6TVdC00OkVlY9I8Ta6x3Qvqq8+RcwxHDDao0toZAXhS6KzUNF200l/OT9wyEM7sBKMwdX/N6YV4JAX9yOPw0AK3oFONygWJtbcMfLXcGTQrGJncNaGQmIQRLnsyG1FaosUDRMxxRTr1gJARWIaAfwqXZtU4io/fwWHZILAGgHpogrS3Q1tbWrw835il6HV7TZTXcXgoihvuiIl/FwjIuJAw4g/vEiROk0939PeMTuwGoL6y1BKq69hwaEmc9gCsxQ1xU1ilM7tI5lkQcry8woJGZR9k/Qby53qqJtRapBYbDwd0LRkJgFSLjewAoXTi25nVP6QzzJPEM0cbWdP554aL451h7kap/iIQAin8O19dqasvn1Bo5uW7QxYjoUVvt3Fr+ubms6Mb4kDjrAfyp3QDkzr6w5vVg9QJL7uG6OBvhSTLawppcFKlppLQlGsHhcHD3gpEQWIXkzNUAaAtH17weqZ5j0TM8fC2AJ7lL8c/nVqiHdqtJRlukGR2eywagGN7JRHMtZ1ucOwmAyzM8QkAEE5QJ4iuutQRk7iRV6SOVHZ51ie24EoDqhSNrXo825ij5h+vilIlpsiLH7FKu89ry3BkCognJIaG1esBICKyCPzlNFT+e3FpLING4QCEwHJFBBgIT6pBWzj/XeW3x3FE8QkMkdw9oVNZQj+9lijkK5ZVesLVFdZG6vf5BDcs8hGDOu4NYdS3dGCidYdaVxeUenuOYnFYKE4trhUBKW6AWGq6z4k7vByB39vnOa8tn1bx86b0DGdOlhC27TgjxbiGEFEIMF89wMYTggnuKaPnkymtam6ycpx4eHn8AQGLmAADN+RVzffmM2tiB7HBtbFdqH24hWTy1cki1/Bkk4PEOjyUAkAvuIttYSwdFa2dZ9g3X/vKEkywRx1c40XmtXl4mSgUtMlxCIDJ1FQDVVQpTaVaxAbGJ4TorVtCzEBBCzACvBtan3A0hlgLTpFYd0uLCGby00eJDEvKmI5GdoSp9uJdXqK3KnLJwEpNXDGpYlhDUrZri+Wc7r/nyx2njxuUaHu0ZoBbbzaSco9WodV7LtC5QCQ+PU9jABe808cqKwjR/4hkAPJnh2l9JXWHSFlYUpubiCQDS0/sHMaRLCjtO0J8AvwLI7T44DKhGdzPRvoBsq9C32VNKOwhn9wxyWKYhXG7OuycJrNLUtMXjtKSL8Znh0m6SO1WmcHN2hXqIl08MVY6AAVf6CtxCcuGkEmiN4hJRKrRjw6VkAORDu8g2VhISc6eUEIhNX7PZI45END7GPIk1CpMrf5oFGScRH47Kwb2gJyEghHgzcFZK+XgXn32nEOKQEOLQ/Pzm7dwGDVf6CryizbxOnZTOqI09ttP5ZQkuxnJwN5naic733sJJzosMocDwRDkBZDIT5GQEuagfUk1jonVmKIVAfEZdkEsnngBg8bTqjexODZeSAdCK7yHFMrWS6ivQnHuethRM7D4w4JGZx5x3mlhpxRcYLp1k1jO5YQ/lFxu2FQJCiC8LIZ7a4N9bgF8HfqObXySl/KCU8lYp5a2ZjHNDyCI7bwBg4cghAOTcs1Skn6ndVw5yWJZQGruWKTlLs6RiucfKL3DON3yXjcslOOPdTaKgtOfa4mmC1ME1fEJg8oqbaUo3rTOPAZA7ofSn6M7rBjgqa/BNKYF24ci3AfAsv8BZkSUZG74yC0uxq9nZPAbtFkjJZP0Yi6F9gx7WJcG2p0hK+Z0bvS6EuA7YAzyuS8tp4NtCiNullBsX5R8CTF55K/XPeWidPgT8GKH885x0TXPANzyZqQbEjpvgNMw//xBT17+SidYZnk2/YtDDsoT52EHuWvoktOrMn3icGUCs7iPwhV+FC0/a+0snroPv+p/bfux3fud3+OhHP8rMzAzpdJpbbrmFd7/73Rt+Nh6P8ZyYIbyoxto6/xRV6WNm7/BZmsn9d8CDUDr6LbjpVcTLx5n1zrBzCLXnZvYGgoufpHj2aQKxDDFZpJ66etDDuiSwTAdJKZ+UUmallLullLuBM8DNwywAANLxCM+L3UQWHgetzXTlMOdCVw16WJaQ2KuqUpaOP0zx5KN40JATBwc8KmuoT9yEjxblU49ROfotNCkckSNw6NAhPvWpT/Hoo4/y6U9/mkOHDm37zNnglUyUnwUpCS8+yVGxk2TU+R3FLsauXXs4LTN4zx+CepEdzZMsxIZPmAEEdqmzsvj8g8w/9yAA3qkbBjmkS4bhs6f7DCEEZ0LX8Mryv9I49TBhWaEyftugh2UJV+7ZxQtyCu+p+1lwu4gCkf3DaQlE9t0Jz8DC0/fhPfctnmcGj3tVBdEuNPZ+4P777+ctb3kLwaC6xN/0pjdt+0wpewvxk1+idfphpivPcG/0exhG0ez3uDnivZqbc4+Re/5+Emgwc/ugh2UJe66+geUvRGgd/TqNYIq69DJ5zZ2DHtYlgW3xdbpFsL4Y/xCiuPs1+KnT/uTP0JaCyIFXDXpIlhDwunkidCcz+UdIPfMRntVmOHjVcIXvGTh44ABPa7tIPvUhdhUe4XDoNkc47aQ0HxQXvPa70KSg+Q8/hY8W9Z0v78PILg3mJu4h0V7E+8VfoSQDZK65Z9BDsoTJRJh/d9/KjtmvsuPkP/EIB7hiyrm+SzsxXEHWlwjTN76aI9oOgqVTfFXezA3XDF+0g4GFq34Yl2wTa8zyleibiQaGz7cBkAj5+LfIm4jVL+BGI3/VDwx6SADcfffdfPazn6VWq1Eqlfjc5z637TM3XXM1X9BuJ1g6xXFtnB03f9clGGl/ELnxLczKBOHyKb4oXsr1e4cr6W01ju76QYJamXA7x2Pj34PbNXgl41JgRAdtgDuuGOdtoV/n9uJXOLPvB/nO8OC5Z6v4jjvv4B0P/Rf2iPPsu/unBz2cnpC4+6f5758rc16O8at33kVraX0jkEuN2267jTe/+c3ccMMN7Nq1i1tvvZX4NrHl6Yiff939Kzx77OM8Fn0Ff7NneBPtX3X9Xn7kc/+DOxrfonT9T/L9nuHVK2972Wv5uef+IzFR4eV3/9Cgh3PJIKyYs73i1ltvld040AaJx07n+NQjZ3jXPfvYkRg+p91qfPKRMxxfKPFLr7oS3xAf0kZL40+//Dz7MhG+75ZpDh8+zIEDg7fSSqUSkUiESqXCy1/+cj74wQ9y8803r/nMxWM9s1zhz792jO+7ZZobZxKXeMT24oEXFvjS0xf4j6/aTyoyRLWcNsBfP3CcSqPNf3jFPlwOtASEEI9IKW3tQzoSAiMMLZwiBN72trfxzDPPUKvV+PEf/3F+7dd+bd1nnDLWEYYb/RACIzpohBF6xMc+9rFBD2GEESxjeLmBEUbAWnTOpcYwjHGEyxcjITDC0CIQCLC4uOjoS1ZKyeLiIoEhq9c0wuWDER00wtBienqaM2fO4OSChKCE1fT08HQNG+HywkgIjDC08Hq97NkzfAXxRhjBSRjRQSOMMMIIlzFGQmCEEUYY4TLGSAiMMMIII1zGGEiymBCiCDy37QeHF2ngRVFMbxO8mOf3Yp4bjOY37LhKShm18wcOyjH8nN1Zb06CEOLQaH7DiRfz3GA0v2GHEML2UgsjOmiEEUYY4TLGSAiMMMIII1zGGJQQ+OCAfu+lwmh+w4sX89xgNL9hh+3zG4hjeIQRRhhhBGdgRAeNMMIII1zGGAmBEUYYYYTLGD0LASHE64QQzwkhXhBC/OoG7wshxPv0958QQty83bNCiDEhxL1CiCP612Sv47SKPs3vt4QQZ4UQj+n/Xn+p5nMxepzfh4QQc0KIpy565sWyfpvNzxHrZ3VuQogZIcRXhRCHhRBPCyF+adUzQ79228zPEWunj8Xq/AJCiIeEEI/r8/vtVc+YXz8ppeV/gBs4CuwFfMDjwDUXfeb1wBcAAdwBfGu7Z4E/AH5V//+vAu/pZZwOnN9vAe8exJzsmp/+3suBm4GnLnpm6Ndvm/kNfP163JuTwM36/6PA8y+ys7fV/Aa+djbMTwAR/f9e4FvAHVbXr1dL4HbgBSnlMSllA/g74C0XfeYtwEekwoNAQggxuc2zbwH+Rv//3wDf3eM4raJf83MKepkfUsqvA0sb/NwXw/ptNT8nwPLcpJTnpZTfBpBSFoHDwI5Vzwz12m0zP6egl/lJKWVJ/4xX/ydXPWNq/XoVAjuA06u+P8P6P/Zmn9nq2XEp5XkA/Wu2x3FaRb/mB/ALuon3oQGa3L3Mbyu8GNZvOwx6/WyZmxBiN3ATSpuEF9nabTA/GPzaQY/zE0K4hRCPAXPAvVJKy+vXqxAQG7x2cczpZp/p5tlBo1/zez+wD7gROA/8kcXx9Ype5jcM6Nf8nLB+Pc9NCBEBPgX8Jyllwcax2YF+zc8Jawc9zk9K2ZZS3ghMA7cLIQ5aHUivQuAMMLPq+2ngXJef2erZWcMk17/O9ThOq+jL/KSUs/oiasBfoEzDQaCX+W2FF8P6bQqHrF9PcxNCeFEX5EellJ9e9ZkXxdptNj+HrB3YtDellDngPuB1+kum169XIfAwsF8IsUcI4QN+CPjniz7zz8CP6Z7uO4C8bqZs9ew/Az+u///HgX/qcZxW0Zf5GYuk43uApxgMepnfVngxrN+mcMj6WZ6bEEIAfwUcllL+8QbPDPXabTU/h6wd9Da/jBAiASCECALfCTy76hlz62fFs72BB/t5lKf71/XX3gW8S654sv+P/v6TwK1bPau/ngL+DTiifx3rdZwOm9/f6p99Ql+0ySGd38dRJnUTpbX81Its/TabnyPWz+rcgLtRtMITwGP6v9e/WNZum/k5Yu16nN/1wKP6HJ4CfmPVzzS9fqOyESOMMMIIlzFGGcMjjDDCCJcxRkJghBFGGOEyxkgIjDDCCCNcxhgJgRFGGGGEyxgjITDCCCOMcBljJARGGGGEES5jjITACCOMMMJljP8fBWWg0XhrP3EAAAAASUVORK5CYII=\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "f:\n" ] }, { "data": { "text/html": [ "\n", " \n", " " ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "g:\n" ] }, { "data": { "text/html": [ "\n", " \n", " " ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "g = np.sqrt(10)*np.sin(2*np.pi*220*t) + np.sqrt(13)/2*np.sin(2*np.pi *440 * t)\n", "\n", "plt.plot(t, f, label='f')\n", "plt.plot(t, g, label='g')\n", "plt.xlim(0, 0.03)\n", "plt.legend()\n", "plt.show()\n", "\n", "print('f:')\n", "audio = Audio(f, rate=44100)\n", "audio_playbacks.append(audio)\n", "display(audio)\n", "print('g:')\n", "audio = Audio(g, rate=44100)\n", "audio_playbacks.append(audio)\n", "display(audio)\n" ] }, { "cell_type": "markdown", "id": "122c857a-e0c1-456d-81eb-c978cec0749c", "metadata": {}, "source": [ "Now we can make the same sound with just two keytars, freeing up one band member to learn the harmonica and another to learn the tambourine.\n", "\n", "### Exercise 7 \n", "\n", "Use an approach like the above to rewrite the function \n", "\n", "$$\n", "f(t) = 2 \\sin(2\\pi 440 t) - 5\\sin(2\\pi 440 t+3 \\pi/4) \n", "$$\n", "\n", "as one sine function." ] }, { "cell_type": "code", "execution_count": null, "id": "e607b652-5519-46d2-ae88-568f5feb0dd1", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "id": "3807638c-6d53-4ac3-b401-8478298ff0df", "metadata": { "tags": [] }, "source": [ "### Exercise 8 \n", "\n", "In a short paragraph, explain a procedure you can use to figure out the phase and amplitude of a signal composed of two sine functions of the same frequency." ] }, { "cell_type": "code", "execution_count": null, "id": "f8ab60c1-4fef-4b36-9191-807127385e6f", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "id": "b39a31e3-6c09-4c88-99b5-2d39b8aa47cf", "metadata": {}, "source": [ "### Exercise 9 \n", "\n", "Reflect on the section above. Why would you want to rewrite a sum of sine functions as fewer, combined sine functions?" ] }, { "cell_type": "code", "execution_count": null, "id": "306e29f9-731e-4c22-9f9e-a8530873ec14", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "id": "a309b449-94d6-47ad-b7d4-cd42e550a647", "metadata": { "tags": [] }, "source": [ "### Exercise 10 \n", "\n", "We showed how to rewrite a function using sine functions. Explain how we could do a similar procedure, using cosines instead. What would be different, what would stay the same?" ] }, { "cell_type": "code", "execution_count": null, "id": "b9ce79ef-c3ed-4be6-9e26-682cbd4d6fc2", "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "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": "3.9.13" } }, "nbformat": 4, "nbformat_minor": 5 }