["$ 2d..E$ ","A2BrCDBrfeECABBeaj(CC|FG5886}l~aP58894}XCP588894}XP59766}aCP6464}3CP5665}cCECPG588976}*ZCE~EP5R%CCP6868847}4Ai~~CCP566656665686464}555*B(BZBBCjBeCKaX","2D array."," A glowing platform appears at the water's edge. The platform is solid. You step onto it. Suddenly an entire dimension is illuminated\u2014a new world is revealed.","In this 2D world,"," an element is addressed with X and Y. Consider now C#. 2D arrays can store any element type. Jagged arrays can also represent our 2D space.","Let us begin."," Here we show a two-dimensional string array. We initialize it. Then we use the indexing syntax to access all elements and display their values. ","To access a two-dimensional array element, please use the syntax array[0, 0]. Each dimension is indexed starting at zero.","Result: ","The program creates a 2x2 string array and then prints out all 4 elements (with no loops)."," .NET 4.7 (2017)\n\n","C# program that creates 2D array","\n\nusing System;\n\nclass Program\n{\n static void Main()\n {","\n // ... Create 2D array of strings.\n ","string[,]"," array = new string[,]\n {\n {","\"cat\"",", ","\"dog\"","},\n {","\"bird\"",", ","\"fish\"","},\n };","\n // ... Print out values.\n ","Console.WriteLine(array[0, 0]);\n Console.WriteLine(array[0, 1]);\n Console.WriteLine(array[1, 0]);\n Console.WriteLine(array[1, 1]);\n }\n}\n\n","\n\ncat\ndog\nbird\nfish","Debugger."," Above we declare a 2D array. The syntax is somewhat confusing, with curly brackets and commas. Here is what we see in the Visual Studio debugger. ","Screenshot: ","The compiler sees the string[,] array as a string[2, 2] array. It inferred the size (good job, compiler).","GetUpperBound."," This method receives the highest index of the specified rank (passed as an argument). It returns an int. This is probably not best for a simple 2D array. ","C# program that uses GetUpperBound","\n\nusing System;\n\nclass Program\n{\n static void Main()\n {\n ","string[,]"," codes = new string[,]\n {\n {","\"AA\"",", ","\"BB\"","},\n {","\"CC\"",", ","\"DD\"","}\n };","\n\n // Get the upper bound.\n // ... Use for-loop over rows.\n ","for (int i = 0; i <= codes.","GetUpperBound","(0); i++)\n {\n string s1 = codes[i, 0];\n string s2 = codes[i, 1];\n Console.WriteLine(","\"{0}, {1}\"",", s1, s2);\n }\n }\n}\n\n","\n\nAA, BB\nCC, DD","Length-based loop."," The fastest method for a 2D array is to do some arithmetic. In this example, there are five rows. GetUpperBound(0) will return 4. ","If we take Length, which is 10, and divide by 2, we get 5. We can iterate until we reach 5.","C# program that uses length-based loop","\n\nusing System;\n\nclass Program\n{\n static void Main()\n {\n ","string[,]"," words = new string[,]\n {\n {","\"ONE\"",", ","\"TWO\"","},\n {","\"THREE\"",", ","\"FOUR\"","},\n {","\"FIVE\"",", ","\"SIX\"","}\n };","\n\n // Loop based on length.\n // ... Assumes each subarray is two elements long.\n ","for (int i = 0; i < words.","Length"," / 2; i++)\n {\n string s1 = words[i, 0];\n string s2 = words[i, 1];\n Console.WriteLine(","\"{0}, {1}\"",", s1, s2);\n }\n }\n}\n\n","\n\nONE, TWO\nTHREE, FOUR\nFIVE, SIX","GetUpperBound, int example."," We cache array bounds in local variables for better performance and clarity. Here we get the two dimensions of the array and iterate through them. ","C# program that uses int array, GetUpperBound twice","\n\nusing System;\n\nclass Program\n{\n static void Main()\n {\n ","int[,]"," codes = new int[,]\n {\n {200, 400},\n {2000, 4176},\n {20000, 40000}\n };","\n\n // Get all bounds before looping.\n ","int bound0 = codes.","GetUpperBound","(0);\n int bound1 = codes.","GetUpperBound","(1);","\n // ... Loop over bounds.\n ","for (int i = 0; i <= bound0; i++)\n {\n for (int x = 0; x <= bound1; x++)\n {","\n // Display the element at these indexes.\n ","Console.WriteLine(codes[i, x]);\n }\n Console.WriteLine();\n }\n }\n}\n\n","\n\n200\n400\n\n2000\n4176\n\n20000\n40000","No initializers."," We can create an empty 2D array by specifying its dimensions. All elements have the default value (for ints this is 0). ","We can use a 2D array reference like int[,] to refer to any array size. The element type must match.","C# program that creates arrays, no initializers","\n\nusing System;\n\nclass Program\n{\n static void Main()\n {","\n // A two-dimensional array reference.\n ","int[,] array = ","new int[2, 2]",";\n array[0, 0] = 1;\n Console.WriteLine(array[0, 0]);","\n\n // The same reference can hold a different size of array.\n ","array = ","new int[3, 3]",";\n array[2, 2] = 1;\n Console.WriteLine(array[2, 2]);\n }\n}\n\n","\n\n1\n1","Arguments."," A method may receive a 2D array by specifying the type of the elements. The dimensions are not used in the argument list\u2014any 2D array of the correct element may be passed. ","Changes to elements in the argument will also affect the original version. Only the reference is copied to the new method.","C# program that uses 2D array as argument","\n\nusing System;\n\nclass Program\n{\n static void PrintFirstElement(","bool[,]"," values)\n {","\n // Display value of first element in first row.\n ","Console.WriteLine(values[0, 0]);\n }\n\n static void Main()\n {","\n // Any array size of the right element type can be used.\n ","bool[,] values = new bool[100, 100];\n values[0, 0] = true;\n ","PrintFirstElement","(values);\n }\n}\n\n","\n\nTrue","Loops."," 2D array loops are complicated. It is easy to cause errors related to invalid indexes. Here our 2D array is a four-element box, composed of two pairs. ","Next: ","To begin our for-loop, we acquire the upper bound of the zero dimension, and the upper bound of the first dimension of the array.","For ","for","Caution: ","The loop will not continue to work correctly if the array reference itself is modified or the array data is resized.","C# that loops over 2D string array","\n\nusing System;\n\nclass Program\n{\n static void Main()\n {","\n // Instantiate a new 2D string array.\n ","string[,]"," array = new string[2, 2];\n array[0, 0] = ","\"top left\"",";\n array[0, 1] = ","\"top right\"",";\n array[1, 0] = ","\"bottom left\"",";\n array[1, 1] = ","\"bottom right\"",";","\n\n // Get upper bounds for the array\n ","int bound0 = array.","GetUpperBound","(0);\n int bound1 = array.","GetUpperBound","(1);","\n\n // Use for-loops to iterate over the array elements\n ","for (int variable1 = 0; variable1 <= bound0; variable1++)\n {\n for (int variable2 = 0; variable2 <= bound1; variable2++)\n {\n string value = array[variable1, variable2];\n Console.WriteLine(value);\n }\n Console.WriteLine();\n }\n Console.ReadLine();\n }\n}\n\n","\n\ntop left\ntop right\n\nbottom left\nbottom right","Nested loops."," These are not always necessary. For example, if you are using a 2D array with only two elements in each row, you can index into positions 0 and 1 from a single for-loop.","Performance."," GetUpperBound is slow. You may not want to call it often. I took a benchmark comparing one million repetitions. It shows the performance decrease with GetUpperBound. ","Thus: ","Using the Length property for a loop boundary is faster than using GetUpperBound.","Benchmark ","benchmark","Memory: ","I have also tested the memory usage of jagged and 2D arrays. This helps us determine which one to use.","Jagged vs. 2D Array ","jagged-2d-array-memory","2D array benchmark result","\n\nLooping with GetUpperBound: ","142 ms","\nLooping with Length/2: "," 47 ms","Rank."," Every array has a rank. This is the number of dimensions in the array. A one-dimensional array has a rank of 1. We access the Rank property from the Array base class. ","We design a method (Handle) that receives an array reference. It then tests the Rank of the parameter array.","It handles both 1D and 2D arrays in the same method. It uses GetValue to access the array elements.","C# that uses Rank","\n\nusing System;\n\nclass Program\n{\n static void Main()\n {","\n // ... A one-dimensional array.\n ","int[] one = new int[2];\n one[0] = ","1",";\n one[1] = ","2",";\n Handle(one);","\n\n // ... A two-dimensional array.\n ","int[,] two = new int[2, 2];\n two[0, 0] = ","0",";\n two[1, 0] = ","1",";\n two[0, 1] = ","2",";\n two[1, 1] = ","3",";\n Handle(two);\n }\n\n static void Handle(Array array)\n {\n Console.WriteLine(","\"Rank: \""," + array.","Rank",");\n switch (array.Rank)\n {\n case 1:\n for (int i = 0; i < array.Length; i++)\n {\n Console.WriteLine(array.GetValue(i));\n }\n break;\n case 2:\n for (int i = 0; i < array.GetLength(0); i++)\n {\n for (int x = 0; x < array.GetLength(1); x++)\n {\n Console.Write(array.GetValue(i, x));\n }\n Console.WriteLine();\n }\n break;\n }\n }\n}\n\n","\n\nRank: 1\n","1\n2","\nRank: 2\n","02\n13","Add row, add column."," You cannot add a new row or column to a 2D array\u2014the array is fixed in size and a new array must be created to add elements. Here we introduce AddRow and AddColumn. ","AddRow: ","This allocates a new 2D int array and copies the current array into the new one. It then copies a separate int array as a new row.","AddColumn: ","This allocates a new array with an extra column and copies the previous array. It copies an int array into a new column.","These methods do not \"add rows or columns\" to a 2D array. Instead they create a new array and add to that.","For optimal performance, consider using a List and adding int arrays to that. Or add Lists of ints to a List in a 2D list.","C# that adds row, column to 2D array","\n\nusing System;\n\nclass Program\n{\n static int[,] ","AddRow","(int[,] original, int[] added)\n {\n int lastRow = original.GetUpperBound(0);\n int lastColumn = original.GetUpperBound(1);","\n // Create new array.\n ","int[,] result = new int[lastRow + 2, lastColumn + 1];","\n // Copy existing array into the new array.\n ","for (int i = 0; i <= lastRow; i++)\n {\n for (int x = 0; x <= lastColumn; x++)\n {\n result[i, x] = original[i, x];\n }\n }","\n // Add the new row.\n ","for (int i = 0; i < added.Length; i++)\n {\n result[lastRow + 1, i] = added[i];\n }\n return result;\n }\n\n static int[,] ","AddColumn","(int[,] original, int[] added)\n {\n int lastRow = original.GetUpperBound(0);\n int lastColumn = original.GetUpperBound(1);","\n // Create new array.\n ","int[,] result = new int[lastRow + 1, lastColumn + 2];","\n // Copy the array.\n ","for (int i = 0; i <= lastRow; i++)\n {\n for (int x = 0; x <= lastColumn; x++)\n {\n result[i, x] = original[i, x];\n }\n }","\n // Add the new column.\n ","for (int i = 0; i < added.Length; i++)\n {\n result[i, lastColumn + 1] = added[i];\n }\n return result;\n }\n\n static void ","Display","(int[,] array)\n {","\n // Loop over 2D int array and display it.\n ","for (int i = 0; i <= array.GetUpperBound(0); i++)\n {\n for (int x = 0; x <= array.GetUpperBound(1); x++)\n {\n Console.Write(array[i, x]);\n Console.Write(","\" \"",");\n }\n Console.WriteLine();\n }\n }\n\n static void Main()\n {\n int[,] values = { { 10, 20 }, { 30, 40 } };\n Console.WriteLine(","\"CURRENT\"",");\n Display(values);","\n\n // Add row and display the new array.\n ","int[,] valuesRowAdded = AddRow(values,\n new int[] { 50, 60 });\n Console.WriteLine(","\"ADD ROW\"",");\n Display(valuesRowAdded);","\n\n // Add column and display the new array.\n ","int[,] valuesColumnAdded = AddColumn(valuesRowAdded,\n new int[] { -1, -2, -3 });\n Console.WriteLine(","\"ADD COLUMN\"",");\n Display(valuesColumnAdded);\n }\n}\n\n","\n\n","CURRENT","\n10 20\n30 40\n","ADD ROW","\n10 20\n30 40\n50 60\n","ADD COLUMN","\n10 20 -1\n30 40 -2\n50 60 -3","Dimensions."," In C# we can also specify arrays with more than two dimensions. We can use another comma in the indexing syntax. It will work as expected. ","Multidimensional Array ","multidimensional-array","Flatten array."," A 2D array can be flattened into a 1D array. This can yield some performance improvements. But it makes a program's syntax more complex. ","Flatten Array ","flatten-array","Lists."," You can use the generic type List to simulate a jagged or 2D List that is dynamically resizable. The syntax for this nested type is somewhat more confusing. ","List ","list","List: nested ","nested-list","A List can solve problems that would otherwise require confusing 2D array resizing and copying.","Jagged array."," An array element can have any type. This includes other arrays. With an array of arrays, we construct a jagged array\u2014this gives us great flexibility. ","Jagged: Array of Arrays ","jagged-array","Research."," In the CLI standard, I found material about the types of arrays. The Framework determines the type of an array by its rank (dimension count) and its element type. ","So: ","Both parts are considered in determining type. Arrays are not all the same type.","The rank of an array is the number of dimensions. The type of an array (other than a vector) shall be determined by the type of its elements and the number of dimensions.","The CLI Annotated Standard","2D arrays"," have many uses. And they can be used in many ways: we showed several indexing approaches. It is easiest to use Length, but GetUpperBound is sometimes needed.","A review."," We created 2D arrays and looped over them. We mutated them. We benchmarked them. Before you use 2D arrays, research jagged arrays. These can improve your code."]

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3gvNNp03Nrhy0f3Qm0j51O56UcCLfogl7W4+cPpK3MdvjXHVZKAOewwN1rz0GO: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.DCYx8Mdh1Azham84I+WtCq+zSYamhfmm4O2zbasDyggYrszp1dVjEum4jPNGwo/5YZ0FKCt517uD+bmKHY3RYlzON6schLWy3fbbMu439cDCJf4dl7xy2GR02brk76ddh0RQwAKBRQD+WtqCUtxxWnR22hn6oc/r98w6LP5OhxC5: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?rtTQhrCDkRoNzO1gpIYKFevapUYDXF+lhiu2hts9jukKreEVwHQLrOGcHqmxMUytAkoNB6bUK7TUmBwOg0dqqNnmcBjBNcyapM0xKQqt0StghwNqj60xWY3DgSu0Rgcf0DRk4Iqt0ajq0Ceu6Qqu0ZsvkV5hSFIuc6M4TJ1So35hpMaDi5Eag4uRGvKp/+oXCWe7NgAZ9D8)ASUVORK5CYII=%iVBORw0KG;)NSUhEUg?AOQ?ABrCAM?ABQb96y)YFBMVEX::9/f729:6+v/z9P7v8P/o6v7s7v/e4P7+/v7W2f7q7P7g4v7m6P7j5P7O0f7l5v67wf61u/7EyP5vb2+rsf6jqf1PT0/S0tKurq6UlJSRmv0nJyeKkv2aof0CAgIxwEfw?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@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;uAC6zLCCuUCEZZQ1U1zanS47uFEcn3vKxTGXfuy7grFMrf+PQj1XrHk0fu06zNFFlJicAYFKQs+C6sjh3+L6mbuT8z6wv7LCOH/sb+Gvy77SaDVkQfcgpd2xbcnkjF0GmlLJCOrbNNUFd218MQS6XEDf0z/K4IFN11CM01Tr8hin3hGRjFlVB9FTY6UC6evl: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)AElFTkSuQmCC%iVBORw0KG;)NSUhEUg?AMg?ABbCAM)BdDpB)GFBMVEX:/9YVfW/vvqSkPj60LHy6vD3snr1n1Oi0Zbi?AEBUlEQVR4XuyY0arDMAxD+yA5:/Hl3VU4AbhLRe2GaK3zMbambGX9mgkjKfi6C0MgZh4Fr4MwBjBBRCOu/D9Hz4WQPBrIOOhhRlhBxCJCzPSC0SKRwZ1bAGyQYDTJECfw2cO4MKnEfhPENkUINUsBabdf4phZk1pqsDjSmSKT8IM4m1qEI6sSLkpZEmQwzpQHmUdFjYlCGYDOkpvYQRvch8JOpsaxFvQdURiUWO5I1k0IJ4jkE7TjCiFmFoCxRVemx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?MfZ2EjzbzaPqI89HF21VF3JReJtsRHDT1QGElRIUY5ALYalj04tR/sprfFW2t3UhC2BQZe+cWdrjbpjpfouUtq020oaeppXmGaSY4NnjgJDvwH+Jlwh24vW2qnaAV80dVQDCRSFD7yeJ/d5EDERgHcSHhRHB5v++PEGP5wj9Yx6/ZdFP442nO4h7QEZ4sJ8A2Yn5Fe3lXx0chSxAR9r/fqug6cuGOMHKTyZRakRPys3VU55fllP6frnhuu2lWRTfiLNkDjho2L3ctRx5toy9t18j4ChqYaWpjqpGKQXD3eTO8b8fCTXdmdfXuz2W+P0rb7Zkz2WjBoyrd/mtr0a6h+XMtL83t+qLtGBlbFRC3B91rZIhDMrWRSpBERBxVdLLJOE8dixFxcH059WXj1VLX6xjCWN7Zi98mf6dF9KijQ+JnppoGYpRcey0ijk3bcL/ovsSESbiZn/AHUbuP5B/RlHFCyIiskREQEREBQpUIVQl8LHGG+klIByu+Ulmvpfn9l90S/Kq8Ken2idPLLUyx17FhTZvuhOR2p8SxbLH4uejtpzVfkV+ObyfTU9RBPCFRSMM42fdYW+9ntw+q8qt2gNJIUgbraE1Q8n4gAE3BuY23UQ/wAo5Ne/NbUVRDsmlpqWschqTcujyEXFjvpf6tL9llHsDYYRH7IDRBvSmOaGTLiuxG2VybHhtj0ZU7026l78PQhGSmgllq3jGUnKaoOMWHp8XchHm64a2aaWOkrNmysO/No96Q+USvjJxP0fryWMreHJZnpt++8MClyCUiEQL3xln5LF/bRUil2EFTTUdI0hhtIJKeH2d3PAQ883vPywh5Wt9rIh8ZUwzU9ZUU9RHupo5SzC+XXzZcnYubOy9DYrOFSdRliUYFusdSYupN/SN117a2TLEEm0aiV5poC9nry+L/t6js7E2hCK8scqeRpDBsh+bk7O3MVleqys45/jy/VfCw0408g0zM0dgx7/ABeb1XvnbFfJ+BKgp6SfK3Dh01fU+a+slZ8LN3XTj9KP5Vk972K7jzezWWUjtk+V3EbPbu78mWl9WuzW6s2qyld2kZ2a99bfRF3dH5WV1lATlHfr6tZaqQREQEREBERAREQEREBERAREQFClQ6FUJfmUGxKOKsap3ku8CR5ObCOeeXltZl+nL8jrZPEW4r4qcgjrJXb8OjDHeeb3nF5RDHkXR1X5Ndbm1cN7urp1T0mwdnHJUzRy1FRSgMI5mRu/tGfA2Ls7u7Xy9F6sOyqMdnPQSNvoZ3aWXmLET2JsdbizaWXkHs2u/FfxOCKnIwf3JVbvlpAMQmWHPE8tO+q6doVXiCmpqiojKDdiLYF/FDT83HymZHwsF+XqqNmp0WyqCWWpnpjlCSB6eXCNyhClyy3ZgPw9Xfzc3XdR7IoabcVNPEJyAxbmpb5Zm+H+VxtosKqlr6qlo/fbqQXjKrpzvuZxs29iPDi72t1XNXUFJ7RIZ7WqaX2xyijHJsRA8RCCELYgwELOL876IOrbMMOIVUgkZxs+8jECMjh+PydRbVu/JfNbaoYwjp5aOZqihCJ9wQvkQw34cn6j2fn3X1H4dUb4pvxKqECOXeRcPklt7sdOHEm4S5tey5qyGjo8aiGSCk1Yd3PpDJ29WL1b7qMoizc07v8ATp29jqtdLx6/eRfbOLEy+a8JRkIVRFAMGZC/A4uLvc+WLL6Za4T9kY+MkNGHZWZm7WUopXEREBERAREQEREBERAREQEREBERAREQVXx0Hhja2LnVTU+/Iif3WeON+H4b8ua+yUJZL5V1fs+PqfDm2t2HsU9MMmYbwpc/y78eNh8ztyUy+H68Z95LJCdIDjug4nNi14uVtOi+vXLXk4QNiBScTaDa/XVRxJcn5+OwK723adZ7U+dQzYmMh+7H5Qj5C/0XXTbMqjlpqfak8cs4MxDjfA5h8snl6N0fqvZn3sjVgRDvI8WHDHVztrZ+rd1MjlGVP7L77dxl8fMNMv6rKq7xZPD8lXWS15TnvIzbde8LgcBcCxblibPqywbw7U1dI4z1ATjPCMVXk75WFn8mnA5N5u6+jjgGJqmXIc5r8QtjZ7ciVaWMY6XeYbvIOMb3Z3b4vug8PZm0NqbL38JuPwDDwtqzO9sdPlX12z9oyVkUE1nEZWbhJtW11uvPniiKNykFvLa737W1su2kHAoQ+VhG30Uwr11KrdSrK7SihSiRERAREQEREBERAREQEREBERAREQEREBc1a77nyuT3byrpWNVfcv8A/dHQfP5tuJpoAenOSTzX1PW2XDfmtZYSOohlF2HdO/oT+jf5XnsEnsTR7xtzI4EHTHj4xv3ddBRxUMsG8Mt2JyYmRPwZcrj1VVhgk9ommjJhhGQ/dk1hzx8z/MzutwzqKZt8zRmbfA97dnZZu/BUyQZRSRZZCNny082ul3Q6sYqUZh9/w34dXezXf7oqyE6molODOPGIh3pWe5emvK69SB/fD9V5Gz54N/LFllPIzS878Pb0XqwP70fqpVyr1VKzVlfTKZLqVW6soaypREULCIiAiIgIiICIiAiIgIiICIiAiIgLmrs9xwEwvf4vo66Vy15QjC2/xxyZuLlfWyDw4hjp6KTcEEhxuWZW/iM/y90aQKs4TxfdcYcr3LRvssIpIggmo5heL8z32HC7M/O3V10NKW9g3bhu6i/EDOQlo2BX5N6sqpc7b8d7uAEopCOIsW945W5vr36raEBjEAw3ZY5nHbkWgv8AS9lQwAKetI5B.yfebh3uPKwv/Ms6mpkjwORsary8DXF4+5Iq1jpYIZh3QYndyL1/Rd0D+9H6suWAanMzqWEdGwEP3ddUH5o/VWjPL7vSVrqiur1hjV1ZUZXVW+KVKhSoaQRERIiIgIiICIiAiIgIiICIiAiIgLKojKSPEWZ9brVEHix7KqAhlpyLKMnLd8mcc9X5P3Wcmyqk4o47bvds+JATNazdv5nXvKEK8WDZksZyykI5zOxdNNOV+uqyfZtTJVtLILYA/Dq2tuX0XuqqnTPKvNelm7furRU0omJW6rvUKdMrlkqysitZTajHFKsyhWZVbYwUqFKhoIiICIiAiIgIiICIiAiIgIiICIiAiIgKFKIKqHVkUq6UUWV0sivFVSpU2QmKFKKVC8giIiRERAREQEREBERAREQEREBERAREQEREBERAREQQilEQhFKICIiJEREBERAREQEREH/2Q==!A%iVBORw0KG;)NSUhEUg?ANI)9C)AD94GjJ?ADQklEQVR4Xt3awW4yMQwE4P+heLq8VJ7HZ5/nOtf8DS61QIFJCt0I5kKlKM1+8tpit/3XLiEBd7cedwfYVG63kG1/WpAIt0H8PosYb8G0Cp7Bi0nJGcRHqNT8GsWrQ19L4ggijpM7ZGD2d6Rm6ya5Q5foWJI26R2qRAeTtMmliaJEf0ty01kmmSjRfhKWSRAl2k5y0QxyR248ggTLeET0RpDWu4lmh5HcAbJlCElyAPzZROi5DDuKRMq5dHsm2WQNMFg+inQvy2dStN9+EkS3q+YfcHeTKEiqTKJK2EBqgiR22Hgtq/4eJH9A4u0A3X3j4QlSehOwh4Rfk/yccaflQ+XuIc550t1nb2RBDiHpiazDCwg9Q7GzbSPR1o9EiHAOR+Rw7iHBfnffdVAtp9OpfOXxLs8cQKKbrY9wdpGjgyJtluR/QYI9SlsoUj1NkvATdx5NmjsQWSTrQFVbRtBzNIkr4w5fonoNsO+CfVu/f4yOc++fxdrtQrRk8QvAajlvsBaJX1fLKRjlfGp8SpLPipJUNOk2UAs/HZr6SJDqComzjRQmlG6qWCRVtVBPpUSdxqRYwJcRkmSYFQWpA84qihsPjdF3/aOohUgNQ5LKmRwWno8qLxkPud27qZwi/pBkeYXdLBauCp56XnVW3H9TJIMWJQm0GioqkiVJLbQYD9ckC07OhzJNMmhRmtgZHVVfSArP@TN1JmYJJkUJSlqw1eSAlfM6l2Sd6x114XEqwDDMmmRhWiKRHKWlM01IKXQY5T/Exe6+Nre6WZdVHM+tNDZmJQyRcIdUjZTSZJ+ujDO0Xk+PFLytIggyRsvBkQdkALdlz1JyoRJUV5/PlvYkASgWwCsjYcyIOUhLUmqANCicHtM21KZ8Pge9xSJtWuqlXukFt4kyTL5VI1W4hlne0WilZKkX+Rp0WZStNIzJKhv7Mc+1UbnrZCUaAHz+tcp+QVipZeUaCspW+mJiQd77pL2v+Y3vFi0/524cV60n0RqUZK0aD+J8XwNkg/+om4Pvv75newjDS5PPAPCprKVpMOPI3l7JxJmSPw4Etqnkbx9Gsnbm5Fc33XvRmpU/yf+fqQewsX/5r8bKUIiZe4A21vmP24hqdv1SRFy)AElFTkSuQmCC!