test.cpp

/*======================================================================
** You can use this file to test if your code is working
** properly by designing your own test case and test code.
** 
** You are allowed to modify this file as much as you would like.
** For grading, we will use our own filled version.
**======================================================================*/

#include <iostream>
#include <queue>
#include <sstream>
#include <string>

#include "binary-search-tree.h"
#include "avl-tree.h"

using namespace std;

// Assert Macros for test cases.
#define ASSERT_TRUE(T) \
    if (!(T))          \
        return false;
#define ASSERT_FALSE(T) \
    if ((T))            \
        return false;

string get_status_str(bool status) {
    return status ? "PASSED" : "FAILED";
}

// Function for getting the tree as a string
std::string breadthFirstTraversal(BinarySearchTree::Node* root) {

    // If no nodes, return an empty string.
    if (root == nullptr) {
        return "";
    }

    // Init a string buffer, and queue for traversal.
    stringstream ss;
    queue<BinarySearchTree::Node*> queue;

    // Seed the traversal.
    queue.push(root);

    // Walk through the tree, looking at each level inorder.
    bool first = true;
    while (!queue.empty()) {

        // Get the node.
        BinarySearchTree::Node* cur = queue.front();
        queue.pop();

        // Push this value into the string buffer.
        ss << (first ? "" : " ") << cur->val;
        first = false;

        // Add the left and right children if they exist.
        if (cur->left) {
            queue.push(cur->left);
        }
        if (cur->right) {
            queue.push(cur->right);
        }
    }

    string level_order_str = ss.str();
    return level_order_str;
}

// Define the test suites (implementation below).
class BinarySearchTreeTest {
private:
    bool test_result[8] = {0,0,0,0,0,0,0,0};
    string test_description[8] = {
        "Test1: New tree is valid",
        "Test2: Test a tree with one node",
        "Test3: Insert, remove, and size on linear list formation with three elements",
        "Test4: Test removal of a node with one child",
        "Test5: Insert multiple elements and remove till nothing remains",
        "Test6: Test removal of root node when both children of root have two children",
        "Test7: Test depth with many inserts and some removes",
        "Test8: Lots of inserts and removes"
    };
    
public:
    string getTestDescription(int test_num);
    void runAllTests();
    void printReport();

    bool test1();
    bool test2();
    bool test3();
    bool test4();
    bool test5();
    bool test6();
    bool test7();
    bool test8();
};

class AVLTreeTest {
private:
    bool test_result[6] = {0,0,0,0,0,0};
    string test_description[6] = {
        "Test1: Test single left rotation",
        "Test2: Test single right rotation",
        "Test3: Test double left-right rotation",
        "Test4: Test double right-left rotation",
        "Test5: Test multiple rotations on insert",
        "Test6: Test multiple rotations on remove"
    };

public:
    string getTestDescription(int test_num);
    void runAllTests();
    void printReport();

    bool test1();
    bool test2();
    bool test3();
    bool test4();
    bool test5();
    bool test6();
};


//======================================================================
//================================ MAIN ================================
//======================================================================
int main() {

    // The test suite has some tests implemented for you,
    // and place holders for where you can put your own.
    BinarySearchTreeTest bst_test;

    // You can check the description for each test to see 
    // what we will be testing for with the following method.
    // Alternatively, you can also navigate to the line above 
    // where the test description is stored to read it.
    cout << bst_test.getTestDescription(1) << endl;

    // Tests can be run one at a time to get their result
    bool result = bst_test.test1();
    cout << "Test1: " << get_status_str(result) << endl;

    // Or you can run all of the tests at once and generate a report.
    bst_test.runAllTests();
    bst_test.printReport();

//     Uncomment and use this for lab 3.2 when it is released.
//    AVLTreeTest avl_test;
//    avl_test.runAllTests();
//    avl_test.printReport();

    return 0;
}


//======================================================================
//====================== Binary Search Tree Test =======================
//======================================================================
string BinarySearchTreeTest::getTestDescription(int test_num) {
    if (test_num < 1 || test_num > 8) { // check range.
        return "";
    }
    return test_description[test_num-1];
}

void BinarySearchTreeTest::runAllTests() {
    test_result[0] = test1();
    test_result[1] = test2();
    test_result[2] = test3();
    test_result[3] = test4();
    test_result[4] = test5();
    test_result[5] = test6();
    test_result[6] = test7();
    test_result[7] = test8();
}

void BinarySearchTreeTest::printReport() {
    cout << "  BINARY SEARCH TREE TEST RESULTS  \n"
         << " ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ \n";
    for (int idx = 0; idx < 8; ++idx) {
        cout << test_description[idx] << "\n  " << get_status_str(test_result[idx]) << endl << endl;
    }
    cout << endl;
}

// Test 1: New tree is valid
bool BinarySearchTreeTest::test1() {

    // Test set up.
    BinarySearchTree bst;

    // Check that the internal state is set correctly.
    ASSERT_TRUE(bst.getRootNode() == nullptr)
    ASSERT_TRUE(bst.root_ == nullptr)
    ASSERT_TRUE(bst.size_ == 0 && bst.size() == 0)

    // Try some allowed function on the empty tree to ensure they handle this case.
    ASSERT_FALSE(bst.exists(0))

    // Compare the tree's representation to the expected tree.
    string expected_level_order = "";
    string tree_level_order = breadthFirstTraversal(bst.root_);
    ASSERT_TRUE(tree_level_order.compare(expected_level_order) == 0)

    // Return true to signal all tests passed.
    return true;
}

// Test 2: Test a tree with one node
bool BinarySearchTreeTest::test2() {

    // Test set up.
    BinarySearchTree bst;

    // Try to add data to the bst.
    ASSERT_TRUE(bst.insert(5))

    // Check that the root has changed.
    ASSERT_FALSE(bst.root_ == nullptr)

    // Try to remove an element that isn't present.
    ASSERT_FALSE(bst.remove(4))

    // Check to see if 5 is in the tree.
    ASSERT_TRUE(bst.exists(5))

    // What is the max value of the tree.
    ASSERT_TRUE(bst.max() == bst.min() && bst.max() == 5)

    // Check that size is expected.
    ASSERT_TRUE(bst.size() == 1)

    // Compare the tree's representation to the expected tree.
    string expected_level_order = "5";
    string tree_level_order = breadthFirstTraversal(bst.root_);
    ASSERT_TRUE(tree_level_order.compare(expected_level_order) == 0)

    // Return true to signal all tests passed.
    return true;
}

// Test 3: Insert, remove, and size on linear list formation with three elements
bool BinarySearchTreeTest::test3() {
    // Implement a test case which does the above description.
    return false;
}

// Test 4: Test removal of a node with one child
bool BinarySearchTreeTest::test4() {
    // Implement a test case which does the above description.
    return false;
}

// Test 5: Insert multiple elements and remove till nothing remains
bool BinarySearchTreeTest::test5() {
    // Implement a test case which does the above description.
    return false;
}

// Test 6: Test removal of root node when both children of root have two children
bool BinarySearchTreeTest::test6() {

    // Test set up.
    BinarySearchTree bst;

    // Insert a bunch of nodes into the tree in the following order.
    BinarySearchTree::DataType in[7] = {8, 3, 10, 1, 6, 9, 15};
    for (auto val : in) {
        ASSERT_TRUE(bst.insert(val))
    }

    // Remove the root.
    ASSERT_TRUE(bst.remove(8));

    // Check the resulting tree.
    string expected_tree1 = "6 3 10 1 9 15";
    string expected_tree2 = "9 3 10 1 6 15";
    string tree_level_order = breadthFirstTraversal(bst.root_);

    // Depending on implementation, resulting tree should be one of the above.
    ASSERT_TRUE(tree_level_order.compare(expected_tree1) == 0 ||
                tree_level_order.compare(expected_tree2) == 0)

    // Return true to signal all tests passed.
    return true;
}

// Test 7: Test depth with many inserts and some removes
bool BinarySearchTreeTest::test7() {
    
    // Test set up.
    BinarySearchTree bst;

    // Insert the first node and check the depth.
    ASSERT_TRUE(bst.insert(0))
    ASSERT_TRUE(bst.depth() == 0)

    // Insert a node into the right sub-tree and check resulting depth.
    ASSERT_TRUE(bst.insert(10));
    ASSERT_TRUE(bst.depth() == 1)

    // Insert a node into the left sub-tree and check resulting depth.
    ASSERT_TRUE(bst.insert(-5));
    ASSERT_TRUE(bst.depth() == 1) // should still be one since we're ``balanced``

    // Inserting additional nodes into tree results in a depth increase.
    ASSERT_TRUE(bst.insert(-2));
    ASSERT_TRUE(bst.depth() == 2);

    ASSERT_TRUE(bst.insert(-4));
    ASSERT_TRUE(bst.depth() == 3);

    ASSERT_TRUE(bst.insert(-1));
    ASSERT_TRUE(bst.depth() == 3);

    ASSERT_TRUE(bst.insert(1));
    ASSERT_TRUE(bst.depth() == 3);

    // Check that the resulting tree after inserts is what we expect.
    string expected_tree = "0 -5 10 -2 1 -4 -1";
    string tree_level_order = breadthFirstTraversal(bst.root_);
    ASSERT_TRUE(tree_level_order.compare(expected_tree) == 0)

    // Return true to signal all tests passed.
    return true;
}

// Test 8: Lots of inserts and removes
bool BinarySearchTreeTest::test8()
{
    // Implement a test case which does the above description.
    BinarySearchTree bst;
    int insertList[10001] = {7064, 8490, 3780, 5356, 1950, 7713, 2865, 5541, 4183, 7860, 5620, 1685, 525, 7469, 646, 1426, 3309, 280, 7084, 1397, 6000, 4781, 2776, 4135, 5431, 6384, 1474, 5246, 7671, 4973, 5301, 4719, 8070, 3290, 1275, 751, 733, 755, 251, 3357, 4019, 147, 4867, 1859, 7, 3019, 6310, 4028, 4595, 1299, 2500, 4574, 8147, 151, 9041, 1006, 8112, 9814, 1528, 1324, 4448, 9298, 2710, 3568, 2482, 9707, 5349, 9776, 9742, 831, 6345, 3562, 3777, 3084, 2698, 445, 2645, 3225, 5467, 1900, 9106, 4545, 2102, 3489, 112, 152, 2981, 4155, 8410, 5876, 1423, 2627, 4844, 5222, 7954, 5385, 3585, 4200, 6666, 1377, 9432, 8961, 5051, 9512, 8833, 2914, 2340, 5020, 3821, 4230, 2026, 154, 358, 3221, 4424, 5723, 1535, 9764, 8779, 9540, 6216, 962, 7536, 8218, 3317, 9977, 4880, 3738, 8688, 656, 5435, 4938, 5182, 7812, 4557, 2546, 1260, 8680, 9900, 3531, 6100, 3430, 9293, 8871, 3048, 9916, 3250, 3789, 59, 7520, 6006, 9537, 1509, 9421, 7274, 9348, 6225, 5030, 376, 1578, 8198, 415, 6793, 3689, 1205, 8852, 1615, 2431, 1292, 8667, 9190, 2172, 3473, 8153, 2601, 1348, 8605, 9655, 8869, 3182, 6512, 7013, 6773, 6212, 7609, 1069, 9133, 7888, 102, 3609, 2497, 8144, 3551, 9609, 6251, 2491, 608, 4928, 7228, 4895, 8508, 9637, 1671, 4589, 39, 6381, 2837, 9944, 7210, 6131, 5146, 8107, 5443, 3313, 3751, 8341, 8935, 3575, 5196, 5082, 3810, 4496, 1941, 1091, 8008, 7350, 4371, 7131, 8960, 6039, 6026, 8203, 634, 9646, 5875, 7158, 9457, 7174, 7322, 5250, 2416, 8902, 4809, 5616, 4151, 7459, 8577, 6184, 5902, 7845, 811, 6238, 4380, 3852, 7227, 2846, 1529, 8359, 4393, 9594, 4071, 8066, 8514, 7120, 6064, 7981, 914, 1724, 2135, 2202, 2850, 777, 6156, 7188, 8167, 6061, 32, 9819, 9398, 1223, 2157, 8028, 8256, 6917, 8590, 2044, 7738, 8793, 913, 9170, 8499, 4121, 8340, 8753, 9910, 5451, 6716, 2861, 9789, 1797, 4992, 8742, 3033, 4580, 2140, 3756, 5096, 8179, 8319, 2286, 2528, 3720, 908, 5790, 9686, 1927, 4807, 2117, 1159, 1850, 2879, 2530, 7632, 4572, 7307, 6910, 3428, 9987, 1933, 7776, 1230, 4614, 1325, 1640, 4751, 5763, 3429, 191, 4540, 2905, 4222, 6170, 3462, 7292, 5828, 7662, 871, 5846, 8240, 7558, 4170, 6558, 9597, 6123, 4986, 1565, 2657, 6043, 4268, 8073, 2986, 4728, 9346, 8588, 7839, 7948, 1579, 6121, 7889, 5750, 5492, 2258, 7427, 336, 9721, 8358, 7620, 2586, 6684, 4145, 4784, 5091, 9176, 790, 8081, 3226, 2214, 9019, 9464, 6925, 2237, 7979, 4409, 2867, 7918, 9834, 3157, 3496, 8942, 4303, 6956, 2767, 275, 5634, 2453, 2902, 5003, 5089, 6390, 9438, 3749, 7937, 6727, 9690, 5497, 9946, 3992, 778, 2736, 2141, 5513, 1675, 3399, 109, 5742, 2729, 1657, 4413, 3189, 9811, 6719, 4377, 4191, 1368, 4010, 5162, 4394, 4948, 7550, 8404, 5112, 5142, 9935, 9141, 2930, 8925, 7588, 3183, 7698, 8720, 1976, 9251, 2409, 2532, 6448, 3123, 5611, 8916, 6706, 2415, 1566, 4162, 6400, 1925, 6204, 6441, 4555, 4650, 1264, 2253, 5597, 2425, 6785, 1202, 9886, 2442, 6280, 1779, 6081, 2230, 6387, 7896, 8899, 4989, 6393, 2999, 1945, 8992, 9786, 2890, 8506, 6639, 2477, 7442, 7761, 338, 1059, 5572, 7259, 1283, 8782, 332, 2715, 4123, 2582, 9249, 3324, 7401, 1876, 7176, 2296, 4647, 8947, 1533, 4926, 485, 6376, 1369, 9702, 216, 6700, 5121, 3022, 5411, 5555, 5269, 7964, 3699, 6325, 8211, 4216, 4193, 7791, 6177, 3844, 8318, 402, 220, 1896, 2428, 5087, 7220, 2571, 6491, 5940, 4868, 9291, 1627, 4249, 3539, 2192, 4032, 3895, 3396, 2270, 4287, 8889, 6240, 5208, 9056, 6206, 143, 6150, 6049, 5799, 9833, 5531, 980, 8752, 3722, 3308, 3255, 5376, 5026, 4435, 1449, 884, 7281, 2602, 6733, 9575, 4489, 8873, 1842, 7031, 7050, 1682, 5976, 1757, 8364, 2515, 692, 2432, 5285, 2111, 2194, 8910, 208, 7337, 7328, 1747, 8944, 4318, 4425, 4381, 110, 6539, 1949, 5031, 1861, 9327, 4067, 995, 7346, 3890, 6259, 7565, 7883, 1910, 8723, 2412, 1948, 218, 1304, 5236, 4158, 300, 764, 9781, 6636, 2305, 2928, 8170, 8242, 413, 9664, 4363, 1101, 1522, 122, 9374, 3580, 5836, 2798, 9909, 8236, 4359, 2472, 7316, 506, 2895, 8383, 2364, 2419, 9032, 7638, 2759, 7256, 3185, 8646, 1505, 4581, 2803, 3752, 8367, 9422, 3707, 3929, 9724, 5506, 7391, 8715, 4396, 5595, 4132, 1895, 9954, 2768, 7902, 7876, 6978, 5382, 7797, 5180, 3980, 1594, 7366, 2548, 7764, 3029, 4825, 6411, 7217, 4148, 688, 367, 4658, 2239, 6188, 6525, 1499, 5711, 1988, 2199, 6166, 7549, 7999, 2040, 2143, 6669, 1103, 1082, 3118, 2163, 5556, 9075, 9511, 7584, 8419, 5813, 8452, 6247, 7445, 4933, 6808, 9194, 4610, 9095, 6173, 6721, 8473, 9333, 1568, 9631, 2360, 701, 2128, 8714, 1686, 785, 8771, 54, 6523, 6084, 7490, 5350, 9874, 107, 6372, 5470, 4620, 4824, 2987, 8160, 1555, 26, 4049, 1872, 9172, 9300, 564, 7984, 6196, 5909, 1206, 2139, 845, 4332, 2410, 8618, 1126, 2022, 3925, 8617, 4720, 5880, 1745, 2483, 4009, 8548, 197, 7027, 6584, 9242, 3525, 1060, 8231, 8113, 8253, 2447, 95, 6749, 3108, 3790, 1431, 5688, 3348, 6063, 8886, 5164, 3050, 5161, 7306, 8600, 760, 2386, 3667, 1071, 1562, 720, 79, 1469, 2378, 8208, 9620, 3475, 8844, 7351, 3175, 6053, 9, 1364, 1683, 28, 868, 767, 6307, 2051, 134, 2982, 943, 7341, 9449, 6542, 5821, 3754, 1918, 9239, 3424, 7613, 4239, 5280, 1915, 1543, 1232, 9136, 8395, 7987, 3907, 2675, 2696, 635, 8186, 9269, 2280, 2569, 3270, 6232, 3627, 7905, 164, 6083, 2779, 8757, 8266, 257, 3792, 1313, 7878, 7670, 189, 8659, 6637, 8194, 5066, 3679, 6891, 5203, 5898, 1951, 2512, 491, 8032, 4263, 3035, 3206, 9000, 6447, 9243, 5491, 2261, 2363, 5762, 9542, 5913, 3879, 3865, 285, 8460, 9993, 2325, 5207, 8098, 6614, 5895, 1557, 9913, 7438, 3279, 8426, 6067, 8048, 2240, 982, 633, 5907, 614, 9820, 6826, 1413, 7068, 6548, 1680, 9031, 1173, 8068, 3584, 7234, 5290, 6592, 3215, 3365, 1766, 8557, 8092, 4959, 4947, 7597, 5692, 1999, 8740, 1507, 1105, 1012, 7864, 2854, 7567, 7524, 3353, 355, 6572, 8626, 7241, 843, 1791, 9116, 1508, 6303, 8131, 2786, 8510, 8168, 3558, 1841, 4097, 6988, 4953, 5707, 9334, 9408, 3846, 3379, 2251, 3801, 1489, 8926, 6741, 45, 6738, 8357, 2834, 7616, 5834, 6532, 4803, 6333, 1559, 1203, 8118, 3849, 584, 2934, 6479, 6457, 8686, 6016, 1807, 9479, 3106, 5992, 5273, 3773, 8310, 6969, 8023, 5516, 8209, 6524, 4594, 8354, 1975, 5993, 8882, 9749, 7190, 9583, 903, 7321, 1256, 9774, 5200, 2760, 4320, 6660, 7206, 5328, 168, 3336, 1032, 2565, 5070, 7359, 5275, 3240, 1434, 6772, 61, 4663, 4811, 8953, 5522, 3654, 715, 8229, 6993, 212, 9873, 1317, 5967, 5968, 3608, 2093, 9973, 2267, 2454, 2130, 2245, 4644, 2932, 3499, 929, 9477, 5213, 9617, 834, 6338, 6537, 4713, 4723, 2316, 8213, 6796, 1136, 2393, 9642, 9404, 3959, 5627, 600, 2728, 859, 7744, 6916, 3180, 1461, 7069, 155, 9288, 2462, 3228, 9488, 4047, 6565, 9595, 5576, 349, 7697, 2813, 4160, 3315, 3868, 5594, 3507, 828, 2541, 6245, 9328, 2629, 2138, 3620, 2795, 5843, 1571, 1268, 5422, 1782, 2862, 2161, 5073, 4804, 7677, 9039, 1729, 8580, 6607, 9584, 9375, 3155, 9769, 2228, 334, 2896, 2588, 2888, 46, 5922, 5358, 2459, 4554, 6130, 2467, 2345, 1494, 2788, 1022, 7795, 4008, 4398, 3583, 1244, 4849, 2170, 547, 1833, 351, 4411, 3085, 960, 1432, 7481, 787, 9639, 7238, 5781, 414, 347, 5390, 4689, 3302, 8922, 4722, 5837, 1839, 5397, 9463, 1574, 9761, 808, 8829, 1156, 7590, 529, 8122, 6490, 1822, 9318, 545, 9560, 766, 4041, 9395, 305, 7778, 394, 2652, 3040, 1564, 4752, 1227, 9278, 565, 2975, 6944, 7908, 1883, 9483, 5251, 870, 7509, 9286, 526, 7478, 793, 2390, 1133, 9208, 1781, 5447, 380, 1419, 996, 8516, 2988, 5995, 6538, 9941, 3191, 104, 159, 6921, 8504, 9544, 2556, 7541, 7368, 4335, 3147, 7219, 5178, 7862, 4152, 7636, 6948, 3447, 8669, 2332, 5486, 21, 2413, 7811, 8634, 2508, 8207, 9431, 6765, 8633, 1343, 5084, 85, 5701, 9366, 7757, 4996, 7118, 2753, 5410, 8639, 1497, 5383, 9475, 9213, 9891, 1339, 4416, 5012, 301, 3787, 2471, 2385, 5855, 5332, 7480, 1013, 5145, 7145, 1435, 4768, 4925, 9274, 5452, 7049, 6383, 7456, 9665, 4837, 3759, 7330, 5053, 5851, 7242, 1063, 6882, 9619, 7975, 4192, 7393, 388, 1257, 8376, 3617, 3088, 6896, 1502, 505, 5511, 5639, 5661, 4969, 6816, 7946, 270, 5664, 1010, 1190, 14, 9253, 1849, 1473, 2679, 2074, 4818, 1563, 7784, 4745, 7619, 7387, 1506, 8609, 4309, 4690, 5065, 5455, 9263, 2735, 469, 166, 3686, 130, 7105, 2502, 2088, 4219, 7574, 948, 4456, 9356, 6148, 8920, 9705, 2693, 5709, 7519, 3478, 1542, 7658, 6843, 2125, 1045, 6997, 3862, 2624, 42, 3480, 2152, 7126, 6075, 3010, 4288, 9324, 2008, 2662, 3878, 4506, 9612, 8088, 9859, 267, 3012, 1319, 2590, 3415, 1963, 5211, 7678, 1512, 7994, 7066, 6481, 5292, 5523, 4289, 4422, 5914, 3510, 7834, 2229, 9632, 7403, 4405, 5395, 1631, 8887, 4701, 771, 6630, 9578, 721, 7760, 2326, 8220, 4171, 2132, 8265, 9283, 3982, 7828, 192, 4708, 8576, 8813, 2839, 4564, 1946, 9720, 3518, 7198, 8766, 648, 8415, 7204, 8595, 6193, 9316, 7088, 7294, 691, 3016, 416, 6965, 5156, 990, 7841, 4588, 8881, 8475, 1281, 9844, 2440, 9199, 163, 2937, 567, 341, 1019, 6577, 4783, 8875, 5926, 4317, 4640, 9538, 6564, 9343, 4427, 9320, 4060, 9314, 9895, 5107, 932, 1551, 2697, 465, 9385, 4245, 9692, 5004, 8674, 2874, 1004, 2435, 4149, 8785, 683, 7564, 1236, 1831, 476, 7518, 9680, 6786, 7512, 409, 8291, 9723, 1155, 840, 8982, 9610, 7331, 1465, 2535, 5210, 9378, 8956, 5143, 9588, 6028, 56, 4389, 3234, 3911, 9626, 5408, 4271, 258, 236, 5563, 6195, 5632, 1702, 9836, 6784, 6890, 8918, 5678, 9138, 3458, 8411, 3092, 1443, 2226, 9222, 1816, 184, 4977, 822, 8196, 9846, 716, 232, 6329, 4876, 9489, 9883, 8149, 3411, 8911, 4495, 7051, 6674, 9055, 9167, 8232, 1765, 8712, 91, 7288, 588, 6813, 9514, 4514, 1323, 231, 9731, 8206, 7925, 5437, 6726, 2872, 8451, 4791, 4224, 6806, 5969, 2124, 4676, 1908, 2, 1514, 8246, 1092, 223, 9325, 887, 6267, 1328, 8429, 4905, 9048, 3043, 2534, 3163, 1096, 844, 7501, 4990, 8465, 9230, 9765, 77, 363, 7143, 523, 6135, 1321, 4656, 9500, 810, 4853, 6018, 7560, 1759, 9424, 7358, 4577, 4680, 639, 2066, 5225, 8689, 3174, 3732, 9358, 6186, 9663, 8180, 4587, 2875, 9751, 5365, 2380, 6488, 7338, 1649, 5343, 6966, 4279, 7675, 3251, 3334, 704, 3195, 4258, 7071, 3599, 1971, 2039, 2880, 1921, 7587, 4292, 8564, 4014, 4232, 4816, 1676, 1433, 5312, 6453, 1520, 3266, 9058, 6187, 2178, 320, 2804, 7362, 5681, 6574, 1593, 289, 7544, 7008, 1458, 9596, 6975, 8035, 6963, 5013, 4705, 9233, 1521, 6227, 1396, 3083, 2771, 4215, 9554, 1065, 9796, 5355, 2983, 7804, 35, 7774, 1818, 405, 6992, 9342, 3065, 1301, 2092, 2343, 8840, 9471, 8713, 1605, 8969, 3573, 5650, 981, 2167, 1262, 739, 8553, 313, 8400, 623, 4083, 8822, 4358, 105, 8924, 5042, 3703, 3495, 6730, 867, 4599, 2933, 5806, 9868, 4070, 9038, 1648, 6830, 6268, 5604, 7855, 7433, 3323, 1240, 7100, 2527, 8594, 5937, 3005, 4062, 3975, 1936, 2523, 8162, 5415, 8331, 3977, 7325, 9142, 5450, 2407, 3514, 5105, 4113, 4000, 2817, 3669, 4896, 7725, 1819, 7944, 8401, 4108, 8954, 3081, 7005, 7922, 5706, 6768, 9012, 6138, 5048, 6181, 690, 366, 2493, 700, 183, 2373, 9553, 2883, 3807, 9060, 9137, 7652, 1163, 8562, 7009, 5590, 6253, 7966, 2612, 2816, 4290, 5904, 1865, 7471, 5575, 1191, 88, 1989, 6065, 9175, 4796, 5485, 7886, 9788, 7450, 4711, 1181, 1483, 8420, 9394, 5309, 7575, 5022, 7995, 5552, 8408, 1952, 1704, 6044, 177, 9088, 1760, 9756, 8055, 2557, 9624, 1711, 2016, 5131, 8682, 812, 3800, 8928, 5953, 3333, 4044, 5202, 4544, 5714, 816, 2260, 9931, 4828, 2750, 1018, 4717, 9096, 9044, 3708, 3054, 9083, 3405, 3840, 7887, 8677, 1047, 5981, 1561, 6021, 6055, 9223, 8798, 4385, 1289, 1112, 2071, 4354, 963, 803, 5381, 6451, 3142, 1518, 2599, 3231, 2622, 3346, 2197, 5224, 6515, 7455, 9127, 2746, 9118, 9259, 9847, 9147, 8369, 2859, 4700, 255, 1388, 699, 4750, 277, 2514, 9615, 6626, 3671, 9447, 5859, 4642, 5293, 5874, 371, 711, 7347, 6336, 9354, 928, 4715, 5212, 8082, 4, 7340, 207, 3623, 7160, 9218, 4858, 6960, 3716, 9107, 4063, 9143, 2785, 2285, 2649, 847, 7466, 7821, 3647, 8678, 6, 8185, 4408, 6587, 1097, 3466, 5671, 1608, 6297, 8552, 8106, 5474, 6546, 7517, 1994, 4769, 7880, 1160, 33, 8541, 5069, 7786, 3839, 6871, 2379, 3244, 4908, 9778, 9248, 5603, 7258, 2034, 5803, 694, 8030, 2561, 1898, 8898, 4575, 7603, 5424, 6618, 3826, 3340, 4532, 9890, 243, 4924, 1525, 8193, 3177, 5229, 3014, 6990, 9636, 7614, 5192, 3502, 9257, 9738, 9867, 8295, 8114, 1639, 3047, 7295, 5095, 3521, 1038, 8760, 7263, 9809, 9465, 5829, 2195, 7815, 306, 3133, 7906, 6605, 6320, 7047, 1381, 2651, 6526, 5796, 5138, 4616, 4952, 9023, 9860, 976, 3419, 4980, 8563, 4421, 6213, 1670, 880, 9069, 4821, 2956, 9152, 1987, 3653, 856, 7260, 2968, 2262, 1051, 4710, 5067, 456, 2148, 9998, 1774, 430, 3245, 6924, 9459, 7561, 5118, 8482, 2863, 8080, 3165, 9508, 7149, 9750, 4695, 9340, 2238, 2844, 3104, 7727, 5519, 6752, 9264, 9839, 8797, 7611, 4247, 4417, 5877, 1573, 7235, 3540, 5917, 2293, 9214, 5577, 7846, 6324, 4870, 7477, 5605, 2782, 6366, 2506, 2446, 8099, 4889, 536, 3299, 6115, 6068, 4269, 5151, 1446, 8863, 5104, 9586, 2212, 8385, 2985, 4278, 7506, 2621, 6147, 7914, 3252, 2055, 542, 6496, 2372, 7246, 7076, 4937, 6025, 8535, 6395, 5945, 7355, 2210, 3823, 813, 1581, 7146, 8381, 659, 8769, 3247, 2119, 60, 4134, 1838, 5502, 5017, 9854, 4869, 448, 4439, 3412, 8155, 7685, 9572, 1164, 3769, 6757, 9582, 1429, 9678, 2050, 9851, 5753, 4227, 2805, 7641, 7982, 5122, 6272, 898, 2522, 6949, 975, 2980, 7583, 2990, 3717, 3542, 242, 6257, 2711, 9555, 5878, 2778, 1058, 3833, 9813, 8691, 5818, 8444, 6962, 4504, 8547, 389, 5134, 8249, 5363, 9307, 7953, 1073, 31, 6258, 9492, 2090, 4770, 9099, 6703, 4080, 6134, 894, 5456, 4802, 850, 5869, 3586, 9102, 3150, 4226, 373, 7668, 4225, 8344, 8450, 9604, 1903, 3194, 509, 3930, 3474, 5927, 2492, 8412, 8045, 72, 2021, 2648, 3612, 4243, 1864, 1638, 6795, 8328, 5591, 6151, 5980, 9411, 5824, 7019, 5500, 5288, 4477, 8222, 7214, 3841, 2977, 866, 4509, 5061, 1161, 6926, 8014, 1116, 5372, 5165, 4124, 3553, 1844, 8365, 4167, 3276, 837, 2291, 5609, 9045, 6036, 5521, 8350, 2827, 8064, 4369, 8636, 3537, 5327, 8129, 5726, 9518, 3943, 3427, 1456, 1899, 1858, 8663, 2967, 964, 8509, 6566, 6483, 7513, 1801, 6113, 1929, 4196, 1840, 9795, 3786, 1107, 4624, 7768, 7819, 4213, 1020, 4353, 4147, 4362, 9530, 5538, 4758, 7508, 5403, 9858, 94, 5810, 4664, 9592, 1892, 6095, 5347, 6717, 7353, 297, 3891, 2793, 2924, 7790, 4388, 7251, 2103, 3603, 5103, 994, 9752, 8454, 7271, 3132, 3785, 3373, 5128, 2550, 541, 3422, 6114, 3044, 5109, 2950, 9109, 6142, 958, 7706, 7897, 9112, 1309, 5808, 5682, 1428, 3880, 3798, 8493, 6070, 9303, 3253, 1511, 3934, 7973, 7695, 2168, 2744, 3216, 7106, 6782, 9945, 2639, 8413, 2847, 6829, 3256, 3778, 4774, 7413, 5584, 4187, 7078, 7663, 9650, 2290, 3704, 2991, 3897, 7397, 5505, 3950, 5997, 3192, 6254, 3744, 9996, 6863, 2300, 2659, 9815, 2095, 3356, 8800, 9526, 6446, 3287, 9741, 2176, 5405, 3892, 3630, 2603, 8572, 9525, 5433, 3077, 9539, 3, 4119, 660, 7722, 4775, 1887, 8279, 5674, 7297, 839, 2110, 5977, 6769, 8736, 7594, 2181, 3273, 6497, 4734, 517, 1481, 4339, 3920, 4578, 7484, 4490, 3007, 1267, 2358, 1932, 9600, 3737, 8239, 7701, 8806, 8138, 121, 7183, 2365, 8741, 8212, 5607, 5625, 50, 5613, 7080, 3114, 80, 7360, 8427, 1437, 2025, 854, 7137, 6357, 9784, 7872, 7691, 436, 1040, 8432, 5792, 1379, 4878, 4618, 2713, 6141, 5771, 7502, 1854, 5175, 5524, 841, 4806, 7211, 4099, 3808, 1752, 2303, 2819, 8931, 1171, 5802, 7302, 1758, 8786, 1690, 5085, 5241, 1728, 6149, 9889, 6051, 2187, 4444, 7485, 2866, 9974, 5242, 6439, 8201, 3643, 5346, 317, 5916, 1291, 8140, 141, 3817, 8317, 6300, 2876, 4822, 6386, 6647, 2906, 6127, 9959, 3485, 1491, 3433, 1452, 4401, 6957, 6433, 7679, 2560, 7378, 4195, 7817, 8615, 178, 6889, 4779, 7376, 4316, 451, 5331, 6057, 6214, 6787, 6807, 411, 4665, 2274, 4468, 5077, 8762, 8492, 5157, 4498, 5892, 7552, 7101, 9302, 3938, 4747, 1172, 3670, 9785, 488, 3375, 3779, 2559, 64, 7773, 6340, 4645, 5468, 9861, 6662, 1195, 4034, 5857, 440, 1273, 5820, 3766, 4106, 2145, 5708, 5624, 949, 4585, 6707, 7015, 9309, 199, 3109, 7371, 278, 9373, 3719, 9396, 5471, 1048, 3985, 5295, 5833, 6783, 872, 8856, 2369, 2732, 8638, 9481, 3607, 5645, 6870, 2043, 5216, 9297, 5153, 3296, 7308, 4759, 2109, 2620, 6781, 9203, 3381, 2473, 1335, 5306, 2308, 8896, 3220, 2836, 4596, 179, 3304, 738, 1296, 3072, 4698, 6625, 8469, 1645, 6191, 9110, 2368, 3306, 6295, 4011, 4138, 5952, 6288, 9080, 2218, 7203, 5308, 5209, 7912, 6426, 1055, 9963, 1730, 1868, 7826, 923, 8447, 4086, 331, 213, 703, 1154, 1699, 4294, 1314, 9853, 3945, 1439, 4606, 543, 5570, 4176, 2998, 9184, 1751, 7762, 9130, 2384, 5464, 5657, 7579, 6350, 9284, 7798, 5253, 3685, 864, 7849, 7637, 6779, 221, 8368, 3662, 1966, 6335, 6838, 4735, 9709, 1866, 4406, 5939, 7208, 9563, 1656, 5715, 1050, 4165, 4375, 4088, 2886, 6171, 7545, 3774, 1166, 4915, 3793, 7018, 3176, 2031, 4407, 8774, 9517, 7980, 3440, 2789, 5687, 2641, 7373, 2643, 7919, 3464, 8029, 8587, 2609, 6947, 427, 5686, 6504, 8623, 7487, 1485, 6836, 6260, 3845, 1210, 762, 4255, 4426, 9960, 6373, 4163, 4524, 5929, 9391, 7493, 5899, 2936, 7813, 4487, 9406, 4643, 2169, 1140, 9276, 2126, 3668, 5113, 3224, 1863, 2762, 489, 2913, 2747, 4944, 8095, 4687, 594, 9339, 1630, 2524, 5501, 5695, 3436, 3712, 6183, 1720, 9215, 3236, 3922, 941, 5498, 1209, 8494, 734, 7810, 1738, 442, 158, 481, 618, 1998, 4501, 1148, 9247, 4912, 4873, 661, 4877, 6228, 5416, 7615, 6023, 6656, 4551, 4571, 9370, 5946, 3961, 1853, 4442, 1218, 5881, 9717, 2668, 9321, 7029, 6534, 4174, 5536, 7364, 5942, 6475, 3695, 8853, 5044, 4055, 9938, 5277, 9467, 5240, 598, 9810, 9675, 4845, 561, 27, 7097, 2209, 2174, 3953, 7489, 6286, 7430, 7704, 458, 7117, 1358, 3713, 6654, 1288, 6635, 5794, 8503, 2545, 630, 8356, 4950, 6995, 7177, 4831, 3459, 8975, 2244, 5785, 6689, 7165, 449, 5583, 490, 9030, 1026, 2904, 1901, 3520, 5024, 3280, 8610, 4881, 1736, 3614, 5633, 2488, 125, 8312, 3470, 4559, 3330, 7720, 5459, 7735, 9669, 8281, 7006, 4930, 8370, 7557, 8986, 5615, 8847, 3069, 248, 4971, 3289, 8862, 1003, 70, 9329, 7539, 8158, 1617, 1517, 5928, 4712, 5108, 6199, 2553, 924, 7763, 2948, 92, 4031, 9236, 9188, 5947, 9393, 6923, 7805, 4569, 5481, 5844, 4480, 4140, 9054, 8999, 853, 2219, 8648, 3058, 4220, 9683, 7225, 9124, 4776, 3172, 3554, 4510, 3113, 2056, 8991, 4794, 6124, 9962, 9295, 4376, 1271, 5725, 3680, 8912, 6964, 8445, 6938, 1389, 3017, 629, 4827, 552, 4503, 6527, 4293, 8396, 6362, 7728, 5866, 3528, 1486, 5867, 8050, 2755, 7923, 7577, 2160, 4841, 217, 9599, 3921, 6210, 5842, 5910, 512, 3509, 8945, 7201, 7939, 579, 202, 3848, 2783, 4143, 443, 2180, 5120, 467, 7483, 8891, 8909, 9021, 175, 5550, 8351, 7186, 1199, 675, 1654, 2397, 6382, 1351, 2400, 8371, 8989, 2064, 5461, 2225, 4666, 9187, 967, 8500, 7542, 5060, 1122, 8133, 2011, 9003, 3385, 8624, 5528, 9347, 9914, 5238, 2820, 8934, 6091, 9543, 4206, 8694, 7830, 3690, 8303, 649, 5047, 5668, 3204, 4671, 66, 6463, 662, 2929, 9304, 9455, 3767, 3913, 3028, 9541, 8625, 1607, 381, 8838, 6355, 9189, 7710, 6089, 8962, 8037, 3721, 5600, 4142, 7001, 1308, 3666, 6014, 7814, 7423, 5720, 215, 7711, 9401, 1287, 3158, 4050, 4497, 5765, 4922, 6634, 263, 7468, 3784, 7686, 6731, 8957, 8022, 4718, 400, 7437, 7942, 8681, 7402, 8219, 5849, 4516, 2347, 6688, 7030, 9476, 8864, 3149, 9866, 8976, 1488, 9715, 2185, 1422, 2162, 7250, 1366, 4994, 9451, 7464, 429, 5705, 4474, 3894, 4846, 5512, 1375, 5747, 6287, 5389, 5921, 6790, 6464, 7083, 3291, 6914, 5010, 3935, 727, 3656, 3051, 6226, 8234, 6878, 7871, 3788, 8755, 329, 6555, 1962, 4310, 2501, 677, 7600, 6492, 9412, 9001, 4238, 8524, 9250, 5965, 2067, 2165, 3342, 7400, 9729, 1544, 7179, 5936, 9989, 8065, 7314, 4635, 3560, 7284, 9494, 3915, 795, 6172, 9648, 5125, 1411, 4133, 9602, 3587, 377, 9696, 3628, 8057, 9689, 3726, 461, 3320, 562, 6602, 946, 6609, 1168, 672, 1740, 7426, 9766, 1644, 7911, 4188, 1106, 8581, 8866, 9046, 7125, 7339, 1916, 2455, 7224, 6301, 5592, 7874, 2297, 9074, 3161, 5370, 5860, 4157, 3075, 8830, 4323, 8818, 1978, 741, 3657, 4785, 7901, 8363, 3831, 5374, 2791, 5018, 9869, 7674, 2773, 5313, 8754, 846, 1263, 9198, 1804, 8176, 5398, 6774, 861, 7818, 8204, 577, 3439, 1767, 2858, 8583, 2306, 2007, 7788, 1652, 3771, 1053, 8178, 2664, 6462, 250, 8536, 5666, 927, 8121, 1496, 404, 9035, 6318, 330, 9232, 8554, 6008, 4727, 3957, 5400, 5979, 8474, 471, 7566, 628, 7755, 5173, 2146, 5822, 2673, 4184, 1111, 9904, 3655, 6354, 823, 1231, 6982, 654, 3002, 7141, 9549, 4128, 1926, 7462, 2893, 1436, 2215, 5384, 326, 346, 7596, 8708, 6005, 2595, 8777, 3597, 4798, 9842, 5072, 1327, 8480, 2266, 6215, 5326, 1229, 5826, 8613, 934, 3984, 5191, 374, 2706, 3881, 3407, 5369, 2614, 7754, 4542, 6675, 6434, 5755, 9082, 9607, 316, 9068, 7107, 5733, 62, 3742, 7098, 3600, 2243, 2533, 8746, 2942, 775, 9417, 9850, 6814, 5696, 4800, 1928, 3500, 1931, 2156, 2331, 8543, 6449, 1153, 1843, 6476, 8768, 1523, 3071, 7479, 131, 6623, 9502, 2544, 9527, 3491, 1584, 737, 3164, 2769, 6847, 8537, 984, 7707, 6271, 6681, 3341, 1942, 6697, 7312, 2310, 8983, 2618, 2832, 4754, 4156, 204, 6991, 1380, 7187, 8125, 2450, 8441, 560, 7254, 6513, 3709, 344, 9985, 3955, 2978, 644, 1033, 8644, 8724, 917, 137, 5773, 2615, 8021, 875, 3990, 2075, 7453, 6959, 284, 1800, 7809, 3794, 7310, 2028, 4511, 9779, 4355, 5436, 3919, 1212, 1099, 1015, 1510, 5896, 298, 6234, 8003, 713, 8959, 8387, 788, 1503, 2946, 8987, 1968, 3770, 7016, 2234, 858, 6748, 8040, 1660, 8940, 8390, 2619, 8268, 3565, 5704, 6007, 2823, 1897, 6477, 7252, 4093, 5052, 7525, 1959, 6919, 9691, 3060, 8488, 6179, 1115, 3020, 3905, 7890, 1070, 1310, 9773, 7205, 4109, 2423, 9433, 5140, 4386, 2346, 2962, 1691, 1098, 4862, 3127, 9529, 9503, 7947, 8307, 1552, 7151, 3198, 6176, 4379, 3449, 6242, 6971, 4244, 8683, 6427, 5071, 3258, 5621, 6563, 3896, 4341, 7898, 8878, 1036, 8603, 1749, 1848, 4842, 4390, 1726, 167, 264, 7239, 7655, 4277, 4212, 5457, 8578, 4917, 2604, 6541, 8725, 3294, 6621, 9355, 7848, 9462, 5905, 2745, 8743, 5659, 931, 9114, 2607, 8466, 3432, 1076, 7458, 3278, 1878, 1714, 4087, 2801, 7446, 3853, 2046, 1541, 6045, 7806, 6750, 2993, 3549, 3417, 1944, 6082, 9893, 9849, 362, 9078, 7521, 3781, 4929, 246, 81, 8734, 1402, 2065, 7949, 2441, 8103, 3888, 3444, 3601, 9807, 9547, 3066, 3806, 759, 8398, 8559, 1259, 3441, 8515, 7692, 9400, 2094, 7739, 5321, 1344, 4646, 8665, 156, 9049, 6876, 3791, 5527, 7231, 7950, 3529, 2763, 1183, 2910, 2396, 9556, 1021, 7650, 1213, 5640, 3976, 171, 2521, 6777, 2420, 4082, 6169, 6024, 2616, 1719, 4414, 3389, 3380, 728, 6585, 883, 5654, 8654, 4302, 196, 7877, 8927, 8087, 6030, 8767, 8585, 3741, 7586, 9255, 9601, 1961, 8907, 2576, 6892, 4048, 6931, 8244, 3222, 8988, 1189, 4186, 4321, 1805, 5206, 7313, 9202, 3505, 6243, 970, 7538, 2712, 8083, 7879, 1221, 9258, 8041, 6159, 9317, 30, 1812, 2116, 6905, 6827, 824, 4319, 4875, 5698, 8304, 3202, 2443, 8990, 9986, 9353, 6974, 9104, 5189, 874, 8606, 8868, 1084, 8784, 5399, 3128, 7943, 9275, 2334, 6440, 7381, 7653, 5409, 5566, 256, 2734, 8565, 421, 6500, 7693, 6358, 4042, 8783, 6833, 9103, 5337, 4927, 1723, 5679, 7139, 1225, 1597, 9649, 8013, 833, 3504, 8191, 2731, 3293, 2617, 4343, 1090, 149, 3453, 8053, 1677, 9460, 3665, 7743, 4583, 1226, 8285, 484, 7467, 9456, 4978, 4207, 2671, 1466, 1464, 9672, 1661, 7858, 5099, 1732, 7236, 3111, 210, 7431, 1484, 7956, 5691, 5291, 7154, 9076, 6742, 1187, 3494, 7461, 3316, 5264, 1826, 325, 3530, 7020, 3503, 5171, 4592, 8275, 6631, 3981, 435, 7085, 7460, 3187, 5266, 7440, 8810, 4328, 8745, 4543, 1405, 5832, 7024, 5195, 5000, 6828, 3972, 8248, 8858, 3159, 1977, 5841, 6821, 6133, 2552, 4455, 8955, 6069, 5484, 7077, 2666, 2742, 4911, 1444, 4074, 3143, 9168, 4105, 8272, 3611, 9653, 8388, 7148, 3698, 3260, 4246, 1904, 4904, 2137, 9081, 2001, 3130, 947, 9735, 9466, 4473, 1214, 3400, 5717, 5694, 4780, 6615, 5116, 8679, 553, 1184, 2718, 6663, 5262, 8298, 274, 7820, 7182, 9519, 3498, 4984, 2912, 3154, 2013, 9063, 8409, 3455, 8079, 604, 5670, 321, 8458, 2610, 7386, 6824, 1717, 2894, 4217, 6241, 1909, 4919, 6062, 8831, 9666, 9231, 6003, 1062, 8867, 4235, 3864, 4177, 3445, 2359, 1109, 1002, 9418, 7932, 6835, 5838, 5888, 1235, 6010, 1490, 2153, 6339, 2451, 1025, 4072, 1029, 5440, 4466, 7770, 7667, 2057, 5233, 9362, 4965, 6852, 6845, 4064, 4283, 7352, 7554, 9077, 8111, 3932, 3675, 3248, 1780, 5935, 1799, 4534, 5046, 8084, 595, 3835, 5286, 3343, 8486, 7150, 2540, 848, 7929, 2722, 2263, 5316, 4941, 8109, 6936, 4430, 450, 6651, 791, 2613, 3898, 5749, 9875, 5934, 8652, 1538, 229, 7404, 4527, 3193, 3954, 9552, 7038, 7289, 7836, 7656, 460, 5100, 6610, 9146, 4451, 8651, 1222, 8165, 6078, 4987, 7324, 8127, 6551, 9983, 5136, 2496, 7661, 4465, 2204, 7377, 5643, 6472, 6567, 8448, 9442, 8374, 937, 4566, 7319, 7496, 8146, 3269, 6489, 9772, 8182, 272, 1042, 5340, 2878, 9923, 6935, 9306, 3227, 792, 8890, 2127, 5954, 6404, 7934, 4107, 342, 7859, 4531, 7645, 9196, 3339, 9131, 696, 8790, 4813, 1880, 8591, 4907, 8202, 6894, 9728, 902, 4539, 7023, 6696, 446, 3987, 5368, 754, 3581, 3885, 4733, 4175, 2743, 3230, 385, 8397, 9480, 387, 8476, 5458, 9166, 8009, 6837, 9651, 3619, 5234, 5770, 6058, 1385, 5759, 1393, 4940, 8915, 7116, 8520, 7042, 3476, 4918, 6048, 3857, 1341, 7634, 3681, 4515, 4936, 4897, 916, 8245, 605, 601, 2660, 6117, 8227, 8631, 6677, 5774, 8233, 6487, 9533, 1982, 3368, 899, 2433, 8619, 7147, 8731, 7191, 8392, 3492, 3715, 2149, 4146, 8205, 2724, 802, 2177, 3952, 7361, 1582, 6435, 1438, 1894, 4453, 6443, 770, 8970, 6316, 6314, 9205, 3354, 8974, 8839, 2009, 7444, 5421, 8324, 4520, 2381, 4275, 8380, 7854, 6201, 8308, 5172, 4210, 6396, 5406, 3335, 3688, 7264, 1817, 9863, 7282, 2995, 6693, 9323, 1835, 4988, 2780, 8315, 8261, 8372, 5055, 9792, 2777, 1312, 2430, 2134, 905, 144, 4848, 2376, 6249, 6771, 8321, 299, 8971, 324, 9331, 6805, 6652, 452, 3268, 3564, 4366, 6229, 23, 7624, 7555, 498, 956, 7301, 4364, 9040, 673, 9022, 237, 4906, 3311, 1575, 4122, 8726, 954, 8538, 9574, 3590, 4685, 4173, 5586, 8776, 610, 719, 9244, 8545, 3830, 136, 6763, 6928, 5713, 3591, 4068, 36, 5525, 1387, 9623, 335, 4443, 7599, 422, 9336, 9982, 1845, 6097, 7492, 3467, 6985, 4436, 8664, 8941, 8599, 368, 4764, 4433, 7935, 3327, 2954, 5078, 624, 7245, 8271, 2105, 7157, 1034, 5296, 4732, 433, 3382, 4253, 4463, 6299, 6275, 4819, 4091, 3087, 4018, 6739, 6723, 2030, 5354, 5718, 2362, 2048, 9716, 1354, 4704, 1035, 9312, 8438, 9059, 1401, 7028, 9825, 1453, 2704, 5951, 9268, 4538, 520, 9369, 682, 5520, 8378, 1242, 7383, 2856, 6690, 7892, 4508, 6510, 7388, 8789, 4347, 7327, 4530, 5882, 1297, 8521, 327, 5539, 8076, 87, 877, 7605, 7296, 4605, 6391, 1219, 3264, 9484, 9644, 779, 7153, 6918, 3484, 6531, 3629, 2190, 4866, 4662, 9153, 1694, 7503, 4648, 8874, 4349, 5147, 3061, 4724, 4356, 5887, 7726, 2684, 493, 2394, 9927, 6788, 6898, 2091, 7067, 9282, 5155, 8012, 7646, 4154, 6160, 6866, 575, 464, 5300, 7086, 1100, 7261, 1, 4921, 2907, 7582, 789, 5278, 9585, 3285, 4679, 8628, 5317, 7676, 1265, 674, 8697, 3702, 9221, 9613, 1912, 8051, 5761, 9968, 6680, 2897, 2273, 8166, 3804, 6767, 1852, 4039, 4069, 9823, 6939, 6334, 5680, 786, 9191, 7969, 5432, 6522, 5446, 4479, 5056, 8526, 7129, 4189, 3321, 7298, 4615, 3038, 1964, 8732, 7144, 6506, 3179, 5596, 9848, 4790, 8108, 8756, 4078, 6797, 6276, 7917, 393, 1943, 2925, 647, 4651, 585, 4832, 8573, 581, 5244, 6415, 1001, 4399, 501, 2136, 1602, 8763, 5193, 9439, 101, 6042, 9970, 6736, 776, 6521, 6236, 7041, 1775, 1672, 9495, 1400, 7494, 9121, 5999, 2757, 6875, 2284, 5986, 978, 6230, 8799, 455, 3727, 1298, 7344, 2578, 9382, 5114, 5776, 4391, 3145, 9532, 6264, 6246, 1477, 4649, 6927, 3782, 7062, 2271, 9643, 276, 4740, 9212, 9770, 4415, 2282, 8685, 573, 7808, 4418, 9929, 7752, 988, 2448, 7921, 2033, 3170, 6729, 4893, 6219, 6881, 5831, 8707, 774, 9571, 7057, 966, 5662, 5736, 9051, 3803, 3899, 6285, 2686, 5767, 1295, 747, 7580, 2059, 9710, 2966, 1701, 915, 4326, 6802, 1619, 9593, 9089, 7703, 596, 3624, 5858, 9791, 6066, 7591, 3262, 950, 4023, 4004, 1746, 3053, 8184, 8289, 9569, 997, 2947, 9760, 6994, 4546, 474, 4110, 5911, 5123, 1874, 3967, 1360, 68, 9611, 9156, 7787, 2961, 6559, 5760, 5973, 4281, 1815, 6811, 7095, 974, 1482, 7920, 9389, 6801, 9726, 259, 5260, 8200, 591, 7870, 6664, 2104, 702, 2159, 5542, 8533, 9436, 4963, 193, 969, 4454, 7168, 8848, 1061, 9976, 162, 8134, 357, 6732, 8177, 5444, 2083, 6119, 8391, 589, 1545, 5915, 3168, 8819, 5775, 5367, 310, 1743, 5641, 7730, 4500, 7842, 1980, 4136, 3908, 5768, 339, 65, 9660, 712, 1237, 8860, 7192, 8796, 8276, 5619, 9241, 9482, 1635, 7033, 8384, 2356, 3003, 9461, 6424, 1613, 1673, 1888, 2465, 9299, 6038, 8093, 815, 4744, 5943, 3723, 2418, 2647, 7082, 2014, 650, 7277, 3310, 849, 7837, 3875, 5023, 2797, 9154, 6972, 587, 8052, 1669, 1086, 9727, 7425, 4856, 3912, 9101, 6549, 6735, 7511, 7659, 2726, 5360, 4298, 599, 6929, 1665, 4568, 1829, 4731, 5801, 5132, 3847, 8172, 9042, 5848, 1365, 9734, 5618, 5758, 5970, 1837, 1326, 5703, 3858, 1180, 603, 6653, 2120, 6458, 3750, 857, 7528, 2335, 6009, 2633, 7531, 5333, 205, 2996, 9687, 337, 483, 6076, 2487, 5454, 9921, 9806, 9446, 3283, 5127, 7829, 1359, 3134, 1367, 307, 4693, 9260, 9746, 7012, 6104, 5672, 375, 201, 318, 7112, 8805, 1398, 2311, 7527, 6321, 4829, 3678, 2198, 668, 2720, 9670, 185, 8643, 911, 2567, 4492, 9899, 3697, 8512, 9474, 4942, 4836, 6641, 4101, 5058, 7771, 6471, 9407, 516, 2232, 6252, 1023, 4181, 8199, 8846, 7061, 2656, 7280, 3682, 6517, 6846, 5150, 5488, 671, 8049, 9700, 9308, 7199, 3664, 9267, 769, 3454, 2939, 470, 5475, 3625, 384, 1463, 2851, 5263, 6533, 9443, 2233, 627, 8574, 5442, 6590, 1504, 7380, 4526, 2976, 8025, 4815, 1549, 3277, 1650, 6755, 114, 5101, 6377, 2361, 5336, 2989, 9888, 2323, 5990, 9667, 3672, 6237, 8171, 8709, 6278, 4340, 8719, 486, 1302, 5215, 6480, 6403, 4073, 7621, 535, 6701, 8137, 2941, 6174, 9659, 4058, 9279, 1340, 5862, 7133, 7734, 3633, 1733, 7142, 3809, 9472, 1421, 2408, 4985, 1554, 6756, 7585, 8834, 5267, 9780, 7109, 3100, 153, 8379, 5353, 1793, 7156, 2377, 2935, 2265, 3946, 6922, 7395, 5606, 9862, 3635, 6071, 5298, 9892, 4015, 9922, 9066, 2923, 4312, 3642, 2594, 893, 1586, 5054, 2955, 6202, 5769, 2800, 8930, 9139, 6580, 926, 7960, 6298, 6673, 395, 425, 4126, 6429, 5154, 271, 9371, 4898, 2283, 6261, 6968, 1121, 5791, 4916, 8269, 3319, 1245, 4203, 809, 2945, 2337, 3700, 37, 4684, 5279, 379, 3903, 5284, 5532, 2389, 1862, 1646, 7718, 2481, 897, 4384, 2049, 3383, 8017, 2702, 1969, 1459, 138, 8972, 7070, 9165, 9561, 1970, 8216, 1247, 2766, 8913, 2843, 8673, 5419, 7535, 2721, 2269, 5589, 1688, 7941, 186, 1315, 5588, 1081, 6601, 5565, 9777, 9016, 745, 539, 9640, 9748, 1495, 6569, 5554, 554, 2164, 8770, 5025, 508, 951, 5637, 8322, 5564, 1448, 7510, 3082, 5011, 2719, 5941, 1634, 4935, 6556, 7392, 725, 495, 8455, 8808, 7553, 7682, 4843, 7747, 6596, 2525, 2605, 5815, 8827, 6004, 7654, 8828, 9271, 821, 4653, 2147, 6182, 612, 7666, 1923, 6508, 55, 6157, 1238, 3775, 6399, 9150, 6020, 8477, 412, 2339, 7930, 5873, 3355, 8539, 2309, 3344, 7170, 1700, 749, 4204, 6220, 2916, 6155, 4449, 9894, 6582, 3596, 7099, 3594, 7962, 5754, 4360, 7326, 9120, 8837, 8946, 6841, 6853, 1095, 8696, 8142, 670, 5466, 6337, 6860, 8851, 6099, 1005, 1371, 4513, 7910, 3146, 5348, 6699, 7007, 2479, 1990, 8933, 1626, 4412, 1057, 1960, 6378, 6648, 2466, 6884, 4861, 9350, 8921, 9281, 869, 4556, 8751, 4590, 3988, 7978, 1540, 6616, 3063, 356, 6950, 6715, 49, 4090, 3901, 2623, 3900, 4528, 5889, 2003, 8716, 7644, 6262, 8262, 2644, 921, 5315, 940, 8795, 7529, 9581, 4350, 7059, 2077, 8570, 3910, 9841, 4826, 7651, 6851, 7111, 2078, 2173, 5879, 3246, 7408, 5751, 5413, 5092, 1303, 3971, 6110, 4601, 1867, 2884, 2835, 7715, 1786, 7696, 9790, 5402, 4259, 4488, 6822, 6702, 3160, 5783, 6554, 555, 2915, 2831, 7601, 6906, 1285, 8463, 6751, 9990, 6643, 5582, 9280, 2259, 8951, 4481, 7957, 9313, 4683, 2294, 1958, 4221, 5647, 5963, 5473, 6190, 9498, 8489, 1250, 9920, 2587, 1891, 9520, 613, 4431, 9387, 5039, 3000, 6579, 2940, 8575, 7573, 1580, 8995, 1997, 2468, 9564, 3232, 955, 9173, 1017, 2632, 3203, 5477, 5158, 4854, 6908, 8418, 9227, 6530, 4307, 7309, 8978, 9753, 8608, 8635, 607, 5194, 6388, 3205, 194, 3387, 5245, 8845, 3369, 9061, 3650, 4037, 5111, 1290, 9504, 7865, 933, 4562, 1500, 5553, 1455, 5185, 9837, 4991, 2688, 2281, 6667, 5482, 7329, 9392, 4997, 5257, 7398, 195, 3527, 4348, 431, 7382, 6419, 3394, 2208, 2206, 3188, 2809, 4760, 6561, 1770, 3497, 268, 4882, 6873, 2806, 1536, 6290, 8330, 4029, 9957, 1642, 9579, 7058, 5081, 1599, 3148, 1763, 5793, 2543, 6583, 5933, 6728, 7035, 1322, 519, 5587, 2235, 6912, 9510, 403, 6422, 9004, 6410, 287, 4707, 7162, 3408, 7073, 3013, 9711, 9193, 5243, 961, 1027, 472, 568, 514, 619, 6575, 6900, 3074, 889, 9053, 9277, 7551, 3683, 8192, 2158, 1087, 4423, 233, 876, 5721, 4085, 5702, 3606, 2770, 993, 5853, 4094, 5741, 473, 900, 6109, 6812, 3747, 4046, 5439, 9065, 9559, 6359, 6646, 1821, 7409, 1307, 1753, 2519, 7783, 4659, 6794, 4603, 352, 9737, 5476, 4117, 2182, 4257, 7178, 7669, 3563, 1440, 510, 1234, 1394, 6344, 3937, 8780, 807, 2581, 6059, 1334, 8074, 2315, 3743, 757, 3352, 9621, 7418, 262, 5254, 5804, 2678, 4823, 6645, 9129, 5325, 2650, 2434, 370, 3413, 7476, 4233, 1587, 1382, 4254, 9828, 4265, 2518, 5780, 47, 1008, 998, 4979, 5798, 2429, 5795, 2860, 2061, 3535, 8007, 2542, 459, 6930, 1820, 8004, 5602, 9171, 7885, 4261, 2572, 2118, 1266, 5417, 8544, 7628, 1664, 7122, 1278, 3137, 8773, 2917, 2366, 4558, 9043, 9413, 1445, 5631, 2585, 3080, 7705, 5699, 655, 2292, 8485, 4229, 7017, 3122, 3517, 1668, 9117, 2469, 5430, 7037, 4084, 4447, 2892, 8042, 9630, 7175, 428, 4725, 1992, 3078, 6682, 5697, 800, 8428, 1689, 7694, 8870, 7851, 3036, 9972, 2790, 7750, 3199, 2452, 3171, 9645, 1814, 3460, 7683, 5364, 4696, 8825, 1790, 5514, 3701, 4703, 6132, 1907, 7237, 9148, 345, 3469, 9589, 6046, 4494, 4211, 5545, 3042, 3490, 8519, 3153, 7598, 684, 9262, 4295, 2756, 8772, 2951, 3639, 4688, 9940, 8555, 3056, 6803, 5924, 5930, 1789, 1785, 663, 9885, 4525, 5489, 2957, 6073, 1258, 1416, 3488, 1169, 9178, 8684, 4799, 3725, 8701, 1703, 8690, 8885, 1666, 1239, 323, 2188, 1846, 9403, 7384, 4114, 2781, 3301, 2636, 2829, 7108, 2084, 6098, 206, 1589, 3548, 1094, 4737, 9405, 3057, 4315, 6642, 8917, 3298, 9473, 7486, 6425, 7741, 3861, 6740, 9712, 9871, 3062, 985, 735, 7938, 7546, 1425, 496, 1331, 4291, 7025, 2889, 7630, 5734, 9108, 8225, 6351, 2201, 5644, 4956, 3265, 9767, 2739, 1674, 1349, 4437, 1722, 4284, 1857, 4694, 1410, 878, 4890, 8254, 1347, 8067, 1534, 9901, 9113, 4190, 1550, 7681, 7336, 8567, 3951, 1149, 532, 3860, 5535, 2498, 9426, 7940, 5261, 5393, 2796, 3410, 7475, 3534, 2395, 748, 6120, 4976, 1139, 9390, 2661, 8895, 2608, 7822, 7909, 3402, 7415, 253, 862, 7857, 2784, 626, 6379, 9111, 3009, 5608, 9020, 7673, 9722, 5923, 3648, 3637, 1124, 5991, 667, 6122, 6712, 8695, 6576, 386, 5807, 597, 3626, 6011, 9662, 7021, 8893, 8478, 6369, 3978, 4102, 5237, 9879, 8788, 365, 7893, 4864, 9367, 7907, 8019, 5045, 2920, 6178, 4297, 6292, 5037, 9434, 7794, 6599, 291, 5919, 2490, 3144, 2236, 5186, 9487, 8998, 9693, 3141, 6529, 5407, 3438, 2716, 1074, 4116, 1329, 3931, 4445, 9629, 3052, 7689, 369, 4296, 4092, 6305, 7134, 2631, 8394, 657, 2328, 5956, 4600, 3094, 7997, 3305, 6205, 2681, 2577, 3223, 8456, 3403, 8423, 8314, 3550, 7996, 9026, 2276, 5137, 4593, 7093, 97, 7135, 7789, 7533, 784, 6844, 4772, 8854, 9603, 4678, 2953, 7629, 1524, 5414, 5817, 2321, 9160, 3960, 2349, 636, 4523, 2539, 9017, 4541, 9967, 9656, 2246, 3645, 1492, 6370, 3939, 7447, 8288, 1211, 8325, 3178, 3086, 8305, 6346, 533, 8908, 5314, 7180, 5667, 7081, 7451, 3649, 9676, 736, 6283, 814, 426, 8287, 9587, 1905, 8059, 3451, 9453, 3426, 9671, 2242, 350, 5598, 3350, 1832, 1836, 2189, 8820, 4901, 7269, 9246, 513, 6465, 1591, 9468, 2738, 4077, 2870, 676, 7290, 1558, 3129, 977, 9322, 8257, 1794, 6456, 2299, 3696, 4378, 5449, 1806, 1333, 8525, 1621, 1392, 1983, 4561, 6027, 6273, 7213, 9955, 2032, 730, 1130, 67, 540, 5490, 7075, 9100, 6678, 6705, 2427, 10000, 5063, 4702, 695, 8758, 4857, 9969, 8593, 6880, 8765, 502, 1737, 2203, 9206, 8124, 128, 8966, 5786, 611, 53, 1150, 799, 198, 3393, 3030, 309, 1157, 7472, 419, 1984, 2495, 1830, 5884, 1442, 4584, 9007, 3526, 836, 2123, 1198, 4721, 8903, 9771, 9622, 9029, 3592, 6909, 6505, 3307, 3673, 7389, 2437, 9521, 4792, 5689, 4483, 3089, 8950, 1501, 9454, 5001, 6911, 1320, 9855, 1519, 2357, 7010, 7140, 2097, 5239, 987, 580, 8026, 2677, 8148, 3755, 9905, 7275, 6657, 1655, 7974, 1620, 780, 1647, 7602, 503, 5228, 8089, 8949, 1556, 83, 8747, 9534, 1885, 617, 9341, 1803, 4169, 9590, 8620, 5503, 7733, 7643, 5303, 3437, 1228, 9775, 5129, 3099, 3538, 230, 2787, 3731, 4755, 3190, 1796, 2166, 3059, 4493, 5739, 7354, 879, 6217, 1000, 3948, 3443, 697, 6644, 9292, 7714, 9551, 7991, 3615, 239, 6263, 3916, 4429, 392, 6695, 9952, 5445, 3541, 3162, 6289, 5567, 5256, 1744, 1450, 2868, 1539, 7799, 6407, 5094, 7396, 5310, 1468, 441, 9094, 9119, 7055, 1934, 5015, 3468, 3219, 3461, 9200, 8283, 6501, 5610, 6604, 2812, 235, 8710, 2887, 9633, 8727, 9261, 3210, 103, 9491, 2658, 7884, 6686, 9988, 4457, 9458, 7737, 4137, 1252, 5201, 6495, 18, 7243, 8542, 2849, 2063, 7933, 6854, 1663, 9266, 9161, 6385, 133, 2045, 2774, 2183, 1196, 4033, 5560, 9360, 8120, 3813, 768, 1330, 9747, 6571, 6072, 4459, 1141, 4252, 3582, 907, 7349, 5944, 2114, 9625, 3267, 3936, 2108, 6743, 2382, 9870, 5059, 4968, 3914, 7835, 3286, 8528, 7195, 5646, 544, 4280, 4598, 7032, 9566, 2100, 3209, 2828, 9381, 6661, 1632, 3676, 4522, 9831, 2965, 4547, 7746, 1870, 6012, 3442, 6108, 295, 1612, 2155, 6050, 8116, 9158, 9093, 6983, 3799, 4623, 707, 6348, 8163, 6940, 5740, 466, 6094, 9123, 6360, 5184, 1249, 1415, 4194, 5827, 2082, 4673, 6581, 4185, 5097, 3661, 238, 2974, 7802, 4793, 5727, 1851, 6086, 8100, 6710, 7435, 8433, 9067, 9204, 5690, 9545, 8540, 1890, 4955, 9211, 6724, 8173, 140, 6628, 8703, 9995, 1937, 5814, 3949, 2606, 1625, 8592, 2096, 7775, 3126, 7916, 9429, 9452, 9577, 1628, 6281, 7562, 2748, 117, 3772, 6899, 9444, 2971, 6714, 8389, 8235, 2864, 8020, 7951, 5712, 7827, 1138, 1610, 2010, 4622, 5635, 5871, 7626, 2733, 3281, 4285, 9745, 100, 796, 8311, 5559, 6758, 5391, 51, 4329, 528, 3397, 8255, 3233, 1044, 2122, 6694, 1827, 9934, 2070, 8175, 1200, 8468, 2439, 6218, 7578, 2591, 6363, 5380, 8, 8598, 6722, 2304, 2250, 3001, 4130, 3023, 3360, 9410, 494, 1457, 2277, 7570, 2848, 4863, 9132, 1179, 5839, 3329, 4839, 3999, 499, 4838, 2692, 5756, 1078, 4202, 8393, 5673, 5141, 63, 4630, 1467, 6323, 6402, 1079, 2457, 4306, 8069, 2019, 3595, 3728, 7571, 2494, 3825, 6952, 1679, 7748, 9627, 3827, 6945, 1698, 4057, 4788, 9090, 9252, 5294, 2370, 1567, 5549, 2005, 9345, 7365, 2374, 1902, 651, 4899, 4036, 2725, 5088, 9797, 16, 1194, 2295, 6792, 7491, 5728, 269, 9183, 8297, 3724, 7976, 8655, 7419, 7968, 1355, 9882, 290, 9635, 3138, 5574, 9606, 480, 1088, 1208, 2952, 2058, 9699, 4053, 6315, 7742, 2287, 7132, 2142, 8313, 7899, 9485, 7060, 576, 6368, 9072, 1011, 8047, 5394, 7688, 5341, 6595, 7285, 5800, 2484, 8161, 1316, 4834, 1713, 5870, 9219, 6633, 5959, 7247, 7803, 7515, 5789, 3893, 3091, 8932, 406, 9915, 3472, 58, 1697, 4486, 7523, 6850, 6915, 75, 1609, 1068, 9115, 5144, 7278, 5014, 8323, 294, 5465, 4749, 865, 3917, 2944, 4112, 7209, 4627, 4859, 7044, 9872, 7952, 244, 8294, 1370, 8197, 9122, 2154, 5334, 3965, 9573, 6140, 2342, 5685, 4201, 8647, 3906, 6934, 6622, 4035, 5797, 5139, 752, 3818, 5463, 2307, 2264, 4304, 5955, 7986, 7961, 4299, 5925, 397, 3359, 2438, 7311, 2193, 8348, 4040, 1585, 6139, 5868, 7928, 7230, 2029, 7756, 7244, 7971, 582, 2672, 6573, 1487, 8296, 9999, 8110, 5735, 4891, 8728, 2830, 6022, 4017, 5281, 4198, 7096, 1075, 4573, 9924, 187, 6428, 3282, 4368, 4026, 9531, 4095, 5299, 4597, 569, 3358, 7215, 3795, 8502, 999, 3692, 3090, 4502, 5540, 5964, 1882, 5938, 8188, 2845, 5533, 3993, 4324, 5028, 408, 7463, 1707, 4743, 6029, 6144, 615, 5515, 1125, 556, 8467, 5320, 2247, 708, 4765, 407, 7721, 487, 5307, 418, 9217, 7454, 1251, 4619, 7568, 6308, 2098, 566, 521, 4655, 5214, 722, 1390, 7867, 116, 3571, 7581, 2555, 7891, 7123, 4115, 6405, 2319, 8997, 9092, 8483, 9744, 1254, 9917, 9383, 6302, 157, 8604, 8132, 1248, 8497, 123, 8877, 8135, 6987, 5179, 5098, 5102, 5009, 1810, 2596, 9377, 5835, 5345, 3116, 5730, 5062, 5159, 9768, 1201, 5626, 3998, 7399, 5998, 9164, 922, 8787, 972, 4609, 3811, 4591, 4852, 7048, 3677, 7712, 8143, 135, 3025, 7781, 1342, 8077, 1847, 5966, 8739, 6136, 7155, 8888, 2520, 1725, 6671, 2458, 3962, 8824, 8823, 4537, 1404, 8662, 9618, 6137, 9098, 9162, 6624, 6364, 4342, 5777, 3859, 3136, 378, 7221, 1007, 3968, 4027, 2504, 678, 1532, 939, 2960, 6598, 6547, 8892, 550, 7212, 6937, 906, 9177, 9877, 9845, 9365, 5110, 1009, 1049, 8883, 7717, 9801, 9235, 9608, 4958, 2869, 6672, 8286, 6111, 3207, 283, 5897, 3347, 2505, 621, 9490, 6485, 6886, 3944, 5693, 3805, 4629, 9363, 936, 2406, 3819, 424, 1604, 2984, 4621, 9091, 2885, 4833, 1311, 6482, 731, 7422, 1064, 3693, 640, 1215, 7300, 315, 1108, 3753, 8274, 4089, 2564, 5908, 9430, 5778, 2329, 571, 5472, 6418, 6770, 3366, 8977, 7563, 5453, 3884, 3871, 2536, 8154, 9975, 8210, 4020, 1527, 2667, 6798, 4763, 6162, 8737, 7022, 5529, 6951, 4469, 4970, 6341, 6670, 2918, 8362, 3318, 5177, 4267, 8656, 5168, 7495, 2871, 1471, 8189, 176, 304, 6665, 4237, 991, 2695, 4352, 2320, 1217, 4762, 6655, 4954, 9757, 5148, 5387, 8273, 8224, 983, 6603, 5509, 8730, 9085, 7499, 689, 6913, 8096, 4617, 6998, 8658, 2634, 2997, 6221, 4964, 6322, 7390, 2391, 1577, 9084, 1158, 8333, 9326, 8327, 9008, 1123, 5174, 1705, 9908, 3815, 7193, 3733, 1357, 2399, 3098, 5274, 830, 930, 9201, 5518, 6054, 8462, 7589, 8859, 9507, 3367, 9159, 5499, 2573, 4748, 781, 2351, 145, 8416, 360, 5983, 6208, 4797, 120, 7385, 3761, 9605, 9736, 1479, 2727, 896, 7729, 6077, 5057, 860, 7504, 2004, 7955, 6153, 4946, 1412, 9570, 9794, 4059, 7482, 7152, 9493, 669, 1493, 6080, 9523, 6211, 3711, 5133, 9681, 2901, 1641, 9732, 4327, 3829, 6060, 1204, 4668, 3388, 9548, 4560, 7665, 3757, 6943, 2252, 8666, 296, 2689, 5344, 7185, 438, 2761, 2411, 2840, 4865, 9911, 9647, 5729, 586, 3872, 3570, 2101, 4325, 5469, 9034, 8104, 2703, 6775, 5648, 3119, 9002, 606, 5259, 8973, 9932, 2538, 4714, 3618, 8230, 7769, 1280, 2460, 5885, 1037, 8937, 7926, 4961, 1135, 3613, 1712, 6223, 1143, 3386, 8505, 8150, 106, 6746, 3288, 5152, 8641, 5392, 4129, 13, 2150, 9674, 5483, 4314, 4410, 5580, 2402, 4812, 5160, 4766, 4999, 4205, 5517, 8425, 2705, 6973, 4934, 6047, 9805, 5338, 4383, 1662, 5, 9073, 3481, 2216, 8457, 6856, 5652, 6658, 5743, 4814, 8373, 3516, 9086, 687, 9818, 4677, 7873, 5117, 7367, 7913, 7074, 3486, 9364, 6745, 111, 4817, 5198, 71, 6442, 7856, 6266, 537, 8159, 5265, 7173, 4761, 249, 6470, 2054, 7759, 9079, 4913, 6430, 4228, 3477, 838, 6090, 7443, 7079, 8529, 686, 6762, 7115, 8038, 160, 7470, 698, 5371, 2350, 11, 8750, 2503, 2638, 2478, 8472, 7375, 9294, 6349, 2289, 7054, 5569, 7184, 2205, 2220, 3271, 8872, 6102, 5677, 7434, 3120, 4611, 410, 5543, 6374, 5038, 2646, 2737, 1146, 2891, 3824, 9614, 2970, 1243, 3131, 5655, 4419, 9338, 5861, 7130, 8046, 6687, 7572, 3487, 7034, 1220, 4787, 3524, 1391, 1695, 5373, 1373, 6468, 5982, 1792, 9384, 4131, 8470, 3241, 5638, 8566, 9568, 3370, 5989, 7421, 2992, 4164, 6535, 7420, 6528, 9486, 4932, 4923, 3964, 6375, 5546, 8214, 2926, 9979, 1706, 6222, 8346, 6112, 4805, 6269, 6365, 8518, 2052, 5614, 292, 4729, 8342, 4397, 1906, 5324, 3371, 241, 2611, 9010, 8063, 6421, 9958, 756, 758, 7576, 1132, 4286, 3991, 5918, 9352, 4098, 818, 8060, 475, 1914, 1441, 2113, 4742, 3710, 1922, 4012, 7700, 7072, 4471, 4484, 6452, 2255, 3079, 6291, 2107, 200, 5487, 4446, 3115, 3181, 9128, 6197, 4801, 9897, 8511, 8984, 1633, 8101, 2821, 8044, 6545, 5683, 4153, 8258, 9743, 783, 8584, 1974, 9179, 1031, 7379, 7334, 7779, 4276, 3646, 6553, 311, 6239, 3328, 9826, 1755, 2445, 7753, 3095, 8721, 2562, 8226, 6294, 740, 4983, 7412, 3135, 732, 2417, 5731, 308, 2642, 6493, 3471, 4256, 9682, 890, 7990, 6244, 8693, 8072, 8550, 1787, 534, 6347, 6737, 214, 2551, 8119, 3969, 5283, 211, 2422, 234, 6231, 1996, 3545, 5746, 6105, 1056, 7299, 89, 1478, 6981, 4139, 1346, 8336, 7094, 2327, 4626, 7432, 1345, 3812, 8764, 3021, 3515, 4322, 4345, 8906, 1192, 2475, 3579, 1954, 8422, 5080, 2963, 3338, 6640, 631, 4966, 9535, 7723, 5568, 4025, 4888, 8443, 1336, 863, 3729, 4756, 5167, 5252, 6789, 3409, 7530, 4830, 7699, 5548, 6282, 118, 6560, 7207, 1778, 6502, 2709, 7993, 8812, 6192, 9703, 4404, 3434, 7163, 9126, 6955, 8627, 5115, 6158, 641, 2053, 2563, 1119, 5819, 8446, 8692, 9994, 8251, 7091, 1424, 2979, 5816, 9926, 1884, 9981, 5732, 8569, 9878, 8039, 1708, 6093, 348, 9688, 3561, 3395, 8484, 8309, 4003, 8320, 3739, 2838, 1128, 4628, 6861, 7441, 3423, 8900, 8223, 4006, 6764, 6834, 1185, 3361, 8809, 563, 5738, 1270, 6356, 9550, 8326, 9928, 8164, 2815, 2597, 7852, 8718, 6437, 7526, 5788, 6825, 1548, 9515, 3674, 7792, 500, 4613, 188, 3300, 6401, 17, 6408, 3714, 7998, 965, 5996, 842, 620, 8948, 1279, 680, 9800, 7092, 2464, 2456, 1643, 9567, 6855, 9229, 1384, 9036, 1174, 9843, 8865, 8601, 5199, 8993, 9881, 2682, 3797, 2336, 2964, 2398, 1592, 7522, 3986, 6885, 5676, 5375, 806, 2388, 7881, 2106, 1795, 9240, 8181, 2171, 5544, 4272, 4782, 1920, 8487, 8556, 4654, 4855, 6778, 5601, 5270, 5932, 8010, 9149, 6831, 3814, 979, 3572, 224, 6979, 3037, 1420, 7592, 9186, 8801, 6617, 3064, 7672, 7610, 7394, 8671, 5226, 1362, 2470, 7844, 6989, 3314, 1709, 1043, 6597, 7648, 2730, 5271, 9714, 8062, 8832, 3588, 3522, 2799, 782, 9652, 4962, 8282, 3217, 353, 5593, 2068, 3566, 228, 901, 7807, 3836, 6799, 7457, 9824, 2144, 9782, 4886, 7800, 5268, 4214, 4223, 2826, 1947, 4887, 9829, 6293, 7167, 5886, 6198, 9427, 1828, 6858, 3621, 4981, 2510, 3610, 5093, 6650, 9840, 8243, 7270, 3745, 8031, 1696, 1170, 3406, 5903, 6459, 5219, 3636, 3457, 1113, 1939, 7335, 3139, 5255, 6074, 7635, 9673, 3349, 6013, 3856, 9835, 5636, 9062, 399, 9812, 6284, 6958, 9402, 9799, 2723, 2480, 8884, 6311, 44, 8733, 5231, 920, 3956, 5124, 5782, 7087, 4672, 2042, 2717, 4884, 1938, 1110, 3638, 1855, 9827, 1877, 2121, 9180, 9265, 4262, 9399, 8876, 7287, 1756, 7103, 6819, 7161, 3372, 4382, 4208, 8650, 2186, 6107, 3536, 3997, 8807, 4273, 2898, 5779, 8459, 29, 4637, 3867, 1659, 9755, 8075, 312, 8437, 5651, 5086, 2708, 3838, 570, 8011, 3851, 288, 5429, 3544, 2254, 1480, 2958, 1678, 8217, 7840, 4536, 226, 9991, 1120, 4432, 5630, 1823, 2275, 4005, 457, 3519, 9698, 3832, 41, 6511, 57, 5856, 6371, 8252, 5404, 2589, 5480, 6330, 5948, 8612, 2852, 4400, 4120, 7680, 2047, 8729, 5852, 2626, 8169, 1378, 1824, 7816, 616, 8513, 6326, 3909, 227, 5462, 7608, 444, 8302, 8642, 3197, 7172, 7046, 9145, 7505, 2213, 5166, 5434, 1762, 9701, 4308, 9344, 1427, 4476, 6668, 7411, 3421, 4305, 6709, 4241, 6953, 7534, 2794, 5573, 3552, 8738, 8221, 3364, 4847, 6185, 4021, 7026, 6019, 2222, 518, 8115, 4065, 6941, 1054, 8085, 2072, 4957, 286, 772, 8228, 5183, 4995, 705, 1995, 4240, 7766, 3093, 6474, 8621, 6079, 7357, 5978, 4441, 2855, 9224, 9245, 8241, 9965, 7785, 4081, 6002, 3933, 1454, 6842, 8263, 4333, 2574, 9052, 2085, 2221, 5282, 7625, 9725, 4168, 1684, 8174, 6817, 5988, 9733, 3378, 9562, 909, 8568, 3834, 9047, 9097, 8001, 6999, 4467, 8375, 9528, 52, 7690, 3983, 1147, 971, 6203, 3096, 2278, 4739, 5579, 4485, 2584, 6194, 1809, 1350, 9311, 7452, 7967, 4372, 1134, 7595, 3616, 7216, 798, 6832, 3125, 9947, 8965, 1825, 322, 4529, 3854, 6818, 2020, 2087, 6804, 8936, 209, 8622, 9006, 4795, 4579, 1137, 12, 5149, 1913, 4434, 6498, 3663, 7863, 1016, 2080, 717, 7642, 124, 7992, 8481, 3431, 1386, 6877, 973, 1788, 7793, 3574, 265, 6255, 8471, 7102, 2017, 3420, 99, 9157, 492, 6588, 6562, 1991, 3303, 1104, 3923, 7448, 2387, 6101, 1197, 3513, 8672, 3631, 8352, 6869, 1986, 6519, 7843, 8938, 6416, 4197, 5297, 3046, 3589, 1856, 9864, 2882, 804, 8284, 9616, 1930, 6092, 453, 7607, 4344, 9289, 8015, 2256, 4840, 5719, 8027, 8817, 8377, 1475, 4182, 4336, 2314, 5612, 3734, 8616, 5188, 5423, 5040, 2752, 8803, 5287, 7253, 8078, 9685, 8264, 7894, 6420, 6977, 7127, 6649, 1253, 1089, 2330, 2312, 2217, 1127, 8290, 5883, 340, 5075, 1953, 8706, 622, 4860, 9718, 7514, 6032, 9884, 3107, 4726, 8804, 819, 1176, 9270, 4512, 2691, 6461, 7507, 8145, 6676, 4681, 7959, 5766, 4879, 9713, 4199, 4519, 6720, 9730, 5016, 918, 3555, 5840, 447, 6041, 6840, 531, 681, 5900, 3870, 8036, 7189, 6031, 6659, 1588, 3974, 5642, 2969, 3167, 9419, 2133, 6161, 3482, 7265, 148, 7293, 851, 3011, 4054, 2485, 3076, 86, 666, 181, 632, 1286, 3718, 6897, 4311, 1361, 5891, 8589, 4370, 9658, 1773, 3274, 6423, 8495, 5041, 8702, 3243, 1622, 9509, 8461, 8247, 3015, 2640, 9704, 8280, 7218, 1924, 1595, 3855, 6189, 9496, 2566, 6414, 7825, 6883, 2775, 2035, 4567, 2825, 6128, 8006, 1233, 6872, 6815, 9192, 9887, 6725, 6037, 7772, 1873, 8501, 7749, 7853, 8238, 240, 6180, 8775, 6946, 6304, 5205, 1277, 173, 3547, 8090, 420, 1560, 6954, 6536, 2741, 3694, 5949, 7240, 9930, 5547, 2129, 6146, 7796, 1972, 7751, 8532, 7977, 8748, 8000, 8139, 8406, 7989, 8630, 4777, 2908, 4266, 8332, 8704, 4521, 7838, 986, 432, 5823, 3576, 2911, 9448, 8698, 6306, 6455, 463, 6711, 8571, 1784, 6627, 2421, 3450, 7617, 9220, 7283, 3140, 1741, 6466, 1693, 685, 4960, 4639, 4051, 4440, 2575, 8338, 2489, 1513, 5812, 3331, 219, 6753, 2015, 2683, 8596, 5068, 1383, 2012, 5005, 3979, 8637, 3425, 1224, 2486, 3776, 5190, 4428, 4972, 2687, 497, 1935, 1783, 8711, 8259, 8843, 4338, 5002, 2414, 6879, 6859, 390, 4903, 6397, 5304, 6933, 1754, 4607, 3284, 4450, 3887, 4871, 477, 5339, 4150, 1798, 4013, 1653, 3758, 8558, 2006, 4505, 8527, 1476, 8033, 479, 4392, 245, 7780, 5508, 9706, 1598, 3418, 4141, 6116, 3242, 9014, 6820, 7963, 3401, 6327, 398, 5957, 5675, 302, 9817, 643, 3031, 3556, 9638, 1118, 73, 361, 1973, 4507, 1692, 3578, 3765, 6118, 4993, 6606, 2401, 8579, 2973, 7716, 797, 578, 6578, 5629, 1080, 3018, 2099, 142, 6823, 9135, 723, 3398, 9234, 3928, 8700, 8836, 3102, 4553, 5684, 2115, 4563, 5083, 478, 2842, 7543, 9057, 9025, 6503, 6632, 7970, 2663, 9816, 8157, 2461, 4300, 1152, 992, 6309, 7500, 1186, 1272, 3567, 8826, 1651, 1363, 6450, 8386, 2079, 4914, 225, 4691, 9939, 895, 1808, 6518, 9787, 744, 6052, 266, 2927, 8002, 1600, 7202, 945, 2257, 4001, 2714, 2248, 8058, 9984, 9501, 9351, 4608, 9195, 1182, 664, 2463, 3996, 9315, 658, 222, 5845, 1376, 1177, 5864, 6406, 8479, 527, 3275, 5599, 2579, 5571, 5901, 1889, 8517, 7547, 5787, 4535, 7498, 609, 1175, 8126, 9028, 1658, 6331, 6317, 8430, 8360, 7226, 2279, 5658, 6033, 6001, 8421, 4038, 7465, 5218, 1940, 4462, 93, 3970, 8417, 2994, 1131, 4111, 9580, 6509, 4692, 3435, 7136, 7931, 7429, 165, 6015, 2449, 2931, 1611, 7540, 1318, 319, 2949, 8316, 7660, 3506, 3828, 5950, 2943, 5420, 401, 3101, 5006, 2685, 7945, 15, 9237, 7537, 602, 9997, 8102, 7847, 8005, 1569, 5558, 1893, 8187, 8086, 8964, 1869, 6986, 6902, 5984, 5330, 4334, 4461, 6143, 3105, 6638, 886, 3110, 6718, 3039, 8967, 645, 7831, 1246, 7627, 4066, 6126, 6810, 4125, 5034, 4669, 1981, 1727, 2089, 150, 7657, 4652, 5289, 6734, 8061, 8811, 8436, 637, 279, 2824, 9783, 1734, 2972, 935, 7965, 1395, 6106, 2073, 750, 9499, 126, 4549, 8105, 4270, 1985, 6392, 5428, 4550, 5557, 9207, 3463, 3004, 2751, 1451, 8382, 9013, 6274, 1624, 3783, 328, 9951, 8675, 4736, 6473, 9668, 2516, 113, 1570, 4902, 2814, 4625, 9380, 9254, 3337, 3169, 161, 1403, 8607, 6544, 3902, 6620, 76, 5526, 6761, 7405, 7548, 8649, 3942, 1860, 773, 4022, 3687, 8043, 4660, 2630, 4357, 1241, 8337, 2700, 3736, 7159, 5049, 4482, 2903, 5425, 9469, 2344, 827, 4030, 2909, 8850, 2179, 9050, 5494, 6163, 10, 7417, 9310, 4631, 6901, 6904, 9144, 3249, 7303, 8943, 8024, 7291, 1721, 1576, 3448, 2635, 753, 7345, 20, 1338, 873, 5724, 7056, 3008, 5764, 9793, 281, 2436, 4337, 1178, 2959, 4387, 5357, 7758, 9335, 423, 8657, 6040, 6265, 3325, 180, 5379, 3414, 2690, 4518, 3211, 5032, 4699, 9763, 8403, 726, 4974, 1114, 9070, 3598, 7305, 1276, 5217, 5622, 4248, 5181, 9361, 2558, 9857, 6152, 1129, 5276, 6409, 2509, 7801, 4260, 454, 78, 2654, 8366, 6034, 3362, 6088, 4682, 1886, 1216, 5362, 4900, 9238, 2426, 6154, 3045, 4633, 4738, 548, 372, 2772, 3604, 9425, 4282, 9388, 4636, 2060, 2076, 6970, 2353, 9802, 1028, 3763, 2302, 7649, 6444, 8293, 7497, 5448, 5854, 8405, 8821, 2600, 8453, 8904, 5197, 9416, 1165, 2922, 7972, 4346, 4716, 5351, 763, 19, 7782, 5971, 6685, 9005, 8660, 5504, 6586, 5745, 7736, 1167, 9437, 7439, 383, 2338, 6436, 9415, 9376, 1337, 592, 3511, 9445, 9798, 3200, 24, 4789, 7623, 8897, 3263, 7924, 4464, 5204, 5126, 3882, 825, 439, 8929, 8496, 3622, 4931, 2002, 1955, 8407, 9027, 5748, 9694, 4975, 4810, 4079, 5388, 3994, 1282, 1372, 7255, 9943, 5359, 172, 5757, 882, 1718, 6514, 3735, 6893, 4264, 5912, 5135, 5033, 6256, 4885, 1408, 9256, 1470, 182, 6343, 4883, 9181, 4052, 3121, 7286, 8301, 9174, 7958, 6868, 746, 1409, 3322, 8054, 1052, 1637, 4313, 504, 43, 7232, 2131, 9641, 3640, 912, 2758, 1406, 6791, 9228, 1085, 3073, 4851, 8705, 3883, 9948, 3186, 2670, 6540, 9759, 1305, 7474, 1623, 482, 3295, 8016, 8334, 3605, 5322, 1748, 8156, 3886, 2086, 7861, 5163, 2676, 8267, 5811, 511, 530, 2184, 9169, 2301, 3557, 572, 2583, 3237, 5412, 9852, 4945, 6887, 8097, 2740, 6352, 9009, 9272, 2333, 3577, 8237, 2653, 718, 8645, 7983, 8439, 8431, 462, 247, 8491, 4250, 6328, 3404, 5230, 8128, 9151, 2873, 3924, 942, 7372, 3218, 7882, 5305, 2674, 7866, 261, 7414, 6570, 4706, 9209, 9754, 3658, 7823, 5847, 3173, 8183, 34, 9634, 5008, 3254, 7559, 8952, 2833, 9912, 6976, 4773, 9740, 2036, 5302, 4910, 7410, 5985, 3889, 9949, 1546, 4458, 6469, 4103, 7832, 8794, 8994, 4767, 1102, 7767, 9708, 5130, 6932, 4949, 1515, 5656, 1739, 9697, 9591, 7090, 4043, 8250, 7900, 2318, 2900, 1526, 6704, 3748, 115, 3730, 6600, 5342, 6367, 9522, 9450, 8939, 9357, 5426, 891, 6754, 4612, 5258, 8778, 1616, 4786, 3652, 6942, 1083, 2272, 3332, 4586, 7348, 2348, 5495, 7631, 6499, 9290, 6895, 6277, 3156, 3049, 3374, 1414, 8761, 7138, 835, 8260, 8190, 4874, 2069, 2367, 6759, 2511, 7200, 260, 343, 4301, 9497, 7732, 5460, 8292, 5665, 9087, 5493, 801, 4251, 6438, 3532, 2810, 2355, 9838, 8611, 3391, 3602, 3376, 9409, 9163, 9956, 293, 6017, 5974, 1077, 7473, 8195, 6296, 5752, 9332, 8880, 6342, 7315, 3103, 3235, 1447, 5961, 3152, 8464, 8744, 282, 1269, 2024, 8440, 8522, 1144, 2227, 6507, 4104, 4632, 3446, 2288, 3989, 9903, 3966, 9978, 7449, 6413, 2298, 829, 6445, 551, 7915, 9992, 6486, 7765, 9657, 3112, 5090, 5700, 794, 5561, 3877, 8861, 5050, 2765, 6864, 7833, 4582, 665, 9598, 1407, 5441, 9936, 7323, 354, 3927, 6594, 652, 8355, 8979, 5507, 9273, 2200, 2669, 9105, 48, 7036, 8056, 3416, 4697, 7516, 7428, 8215, 557, 820, 1742, 3213, 724, 3705, 9739, 3918, 892, 5248, 1710, 7089, 3684, 1284, 7268, 7065, 9803, 1353, 4576, 944, 5649, 3634, 6809, 7868, 8968, 2392, 6865, 1813, 6279, 9980, 314, 8835, 108, 5401, 2547, 9368, 7114, 6494, 9285, 3995, 4096, 6800, 2580, 2598, 1072, 5319, 90, 2694, 1618, 434, 6168, 4365, 2680, 2792, 3869, 6920, 9719, 8699, 1332, 3641, 1716, 9225, 4667, 5865, 679, 5617, 437, 1417, 5386, 4420, 3822, 8670, 3802, 8735, 9516, 546, 9918, 6248, 4850, 5272, 2211, 9033, 8034, 5805, 8855, 5562, 1596, 559, 9856, 3055, 9964, 2175, 5850, 3963, 7119, 3483, 1881, 2081, 4076, 9386, 1687, 2570, 6035, 6996, 4548, 6848, 4361, 9919, 9423, 6431, 2899, 3456, 953, 4533, 4007, 5551, 2919, 3958, 6516, 9441, 4209, 7824, 1731, 2018, 127, 3259, 1472, 9661, 3843, 9933, 9155, 1768, 549, 959, 7333, 5249, 3796, 5894, 706, 1919, 7011, 1979, 2151, 3874, 7569, 6766, 2405, 1399, 1306, 7249, 4472, 3837, 2241, 8435, 7622, 7639, 4920, 1067, 8130, 7532, 303, 3512, 2354, 7709, 9372, 9576, 558, 1162, 9524, 4746, 3326, 8781, 7014, 9808, 1636, 910, 7731, 1811, 1629, 4808, 6520, 5043, 5221, 5396, 9330, 8546, 4452, 3546, 5975, 9876, 9305, 2707, 3363, 5021, 9024, 4982, 693, 6129, 7045, 2625, 7110, 8919, 8300, 8343, 3820, 6412, 9758, 7369, 8151, 7356, 3006, 7985, 6849, 3392, 5479, 4330, 8985, 9470, 2701, 6874, 7052, 2811, 6679, 9695, 6125, 4641, 4374, 4061, 7124, 8597, 2037, 5027, 7332, 3816, 9011, 8339, 4602, 146, 4835, 4178, 1530, 709, 1965, 3151, 8399, 6380, 132, 7003, 8815, 938, 2444, 7267, 2341, 6087, 5585, 3973, 4403, 3261, 9349, 7317, 7724, 5496, 6713, 3068, 6332, 5825, 1761, 8914, 8306, 3067, 254, 5335, 5378, 9435, 2568, 5079, 8278, 4100, 8894, 5169, 7633, 3926, 574, 5029, 4661, 7687, 3166, 714, 3377, 5994, 8722, 8687, 2371, 2023, 3706, 7171, 9071, 9925, 5035, 6903, 1764, 7063, 8923, 7169, 1274, 9478, 9565, 8958, 9505, 6319, 5890, 6165, 4675, 7121, 7248, 7424, 5510, 3543, 8136, 359, 5530, 5653, 9902, 2531, 4166, 6361, 5669, 2526, 7664, 7000, 417, 2637, 8345, 3873, 2655, 7318, 3746, 1777, 524, 5418, 5744, 6611, 1776, 5863, 4367, 1606, 7850, 3593, 3947, 885, 1601, 4478, 4967, 3041, 9397, 583, 9804, 5007, 1583, 5076, 174, 8498, 5377, 9865, 5235, 8980, 3493, 8402, 9018, 3351, 9210, 4402, 3508, 7004, 382, 2628, 8879, 4179, 8335, 2853, 3904, 5906, 4002, 4475, 5537, 119, 1430, 4351, 6862, 9226, 6484, 4951, 805, 6608, 4820, 6235, 7342, 3850, 6613, 1352, 2938, 8717, 4236, 9937, 642, 8094, 4709, 9830, 8141, 7164, 3390, 396, 3659, 904, 38, 98, 3691, 1293, 4604, 1300, 5578, 6744, 1750, 7272, 1014, 2699, 4741, 888, 5534, 7257, 6691, 9679, 2554, 729, 4998, 9064, 1145, 6776, 6312, 3032, 2513, 4159, 8676, 8277, 1879, 6629, 4045, 4024, 515, 6612, 1041, 1715, 2881, 8349, 2424, 4552, 7436, 3479, 4438, 8551, 9337, 590, 6454, 761, 5318, 5232, 1917, 2764, 9506, 7903, 1460, 8981, 1681, 8123, 881, 7936, 1261, 9880, 3533, 3272, 742, 2352, 6209, 4395, 3239, 364, 8561, 6692, 4470, 9185, 6780, 2808, 2507, 1772, 5722, 2375, 8361, 4753, 6085, 5074, 9037, 3034, 8018, 8353, 8792, 9536, 9684, 3212, 6096, 5958, 9546, 1911, 5716, 743, 3208, 9628, 8802, 1531, 3024, 4144, 9953, 5036, 7988, 9906, 7304, 3297, 3070, 6550, 4757, 6888, 3201, 8091, 139, 8816, 5660, 957, 3238, 2027, 7181, 6056, 40, 7407, 4274, 7604, 507, 1294, 6552, 1572, 2841, 7488, 2754, 9420, 4634, 9961, 273, 1498, 8270, 7684, 1957, 8963, 7647, 7745, 8759, 8582, 9301, 4872, 4234, 4686, 3257, 7233, 8586, 4242, 8841, 3384, 6961, 9216, 6467, 1374, 5170, 1802, 6224, 2322, 8531, 3941, 5329, 2041, 1735, 5830, 5872, 1516, 7708, 6867, 6270, 6432, 2404, 3465, 2537, 1030, 4118, 2324, 4016, 4127, 5581, 4460, 96, 82, 6839, 8560, 7223, 2802, 522, 5064, 8549, 2249, 6200, 9287, 765, 7276, 1356, 8791, 4499, 5019, 6175, 9762, 925, 9557, 1590, 5187, 2196, 7875, 7196, 7869, 4638, 5784, 6708, 5227, 2665, 7556, 8424, 6103, 3760, 69, 4161, 8414, 8629, 3651, 5893, 9821, 2921, 2207, 9832, 6145, 3117, 7904, 2877, 5352, 5427, 6619, 7222, 4894, 7618, 2403, 9654, 8653, 1871, 3124, 4231, 4172, 3312, 9822, 4909, 7194, 8640, 9677, 8614, 5478, 2818, 4657, 2223, 2383, 2476, 8661, 6984, 8152, 4218, 7262, 5323, 5962, 7593, 5663, 8849, 9950, 8434, 6398, 538, 8442, 1834, 8602, 5972, 2231, 170, 9125, 6417, 1024, 4570, 3740, 1771, 4730, 1046, 6233, 4565, 7927, 8117, 9296, 6389, 5119, 817, 8668, 9140, 3559, 3501, 9513, 2062, 3768, 9898, 1188, 2529, 6907, 4180, 2317, 5220, 653, 2593, 3866, 593, 9896, 625, 2499, 1667, 1614, 7406, 8071, 252, 6478, 25, 6967, 7128, 4943, 8842, 3027, 8347, 2474, 1039, 6394, 7002, 6313, 989, 2857, 4517, 4056, 1547, 9182, 3842, 468, 8857, 22, 638, 9379, 3214, 5623, 8749, 3345, 3569, 6557, 7777, 8507, 3876, 6683, 2749, 826, 5176, 3660, 968, 8814, 7273, 1603, 7612, 4670, 7266, 5366, 8905, 7053, 2822, 5809, 1066, 6760, 710, 8632, 7719, 952, 8449, 129, 5737, 1553, 3762, 2191, 5931, 919, 6250, 8901, 8523, 1462, 4331, 6207, 3196, 169, 5772, 6747, 4892, 7104, 3940, 0, 8530, 2313, 9907, 852, 7166, 391, 7702, 190, 1956, 5960, 5106, 5920, 7197, 3026, 4771, 2268, 5987, 4674, 8299, 1207, 2112, 2038, 2549, 9942, 7043, 6167, 7374, 4491, 2224, 6353, 3292, 7370, 6568, 5361, 1193, 9971, 5628, 2000, 5247, 74, 3097, 7113, 1967, 8329, 7320, 3863, 9440, 9428, 1142, 5223, 1993, 3644, 7740, 1117, 4939, 6593, 5438, 3523, 6164, 3452, 7040, 1255, 7039, 1093, 8996, 2517, 4778, 9558, 333, 7895, 9134, 7363, 9319, 5311, 4373, 3229, 7606, 9966, 2807, 8534, 832, 3184, 1151, 6460, 9015, 855, 9197, 6857, 7279, 1537, 1418, 2592, 4075, 7229, 6591, 1769, 9414, 5710, 7640, 6698, 84, 3632, 6589, 9359, 7416, 3764, 7343, 1875, 6980, 6543, 203};
    int removeList[10001] = {9189, 3511, 6700, 5547, 7362, 6933, 3481, 9363, 676, 4775, 5702, 7259, 1267, 6018, 4796, 9073, 2297, 1069, 2597, 2833, 9613, 1278, 4287, 3612, 2041, 2330, 8515, 9967, 1908, 6619, 3196, 3882, 2484, 4877, 517, 7852, 4209, 4884, 7961, 2728, 2926, 1746, 6033, 2628, 6670, 5067, 1053, 3000, 4675, 8121, 4368, 1607, 7707, 1489, 3551, 9483, 8574, 3620, 9080, 4482, 2637, 1369, 1162, 904, 2086, 6750, 7246, 8291, 4382, 7547, 4319, 1390, 5560, 547, 675, 9433, 7380, 6793, 1794, 5640, 4657, 9802, 979, 271, 2876, 8807, 4320, 6516, 2011, 6188, 880, 749, 3049, 3951, 9741, 9683, 3611, 4428, 1157, 8300, 5920, 3110, 4991, 1919, 3342, 2114, 102, 9195, 5432, 8476, 6638, 4266, 4168, 2912, 804, 5349, 8741, 9820, 9250, 9281, 9463, 3943, 2049, 3131, 3208, 6325, 9147, 5790, 1623, 3141, 3941, 1041, 1905, 1855, 2106, 8274, 6807, 7874, 8944, 7332, 8707, 4431, 376, 8218, 7203, 5882, 1048, 4727, 1176, 378, 9842, 7796, 1810, 233, 9920, 6496, 2369, 4776, 6553, 4165, 1858, 1671, 1774, 4777, 1873, 5704, 5339, 8363, 7108, 1032, 9782, 4792, 1565, 2284, 8773, 8307, 2871, 5853, 9668, 3119, 3194, 5604, 3603, 7054, 5720, 8416, 6838, 3224, 920, 9565, 4997, 1519, 1426, 1852, 8040, 152, 2880, 8217, 7422, 2414, 4377, 7948, 1818, 3437, 7051, 3881, 2928, 2252, 3956, 1704, 8287, 3816, 458, 338, 1479, 5943, 305, 5860, 3704, 7410, 2287, 9669, 2581, 6510, 4031, 6124, 7131, 3891, 7453, 3265, 6356, 7837, 948, 2476, 664, 3839, 5050, 1620, 4919, 9325, 9052, 5053, 9271, 6834, 5408, 4505, 2604, 7795, 6028, 8159, 5742, 1023, 7636, 6304, 7777, 5946, 8160, 2472, 894, 2714, 3460, 8536, 3526, 5723, 115, 346, 4054, 1759, 2856, 5628, 4191, 9348, 6946, 469, 1501, 9766, 8000, 2932, 7966, 2227, 3097, 4686, 8293, 1813, 3312, 9813, 5478, 992, 6949, 3405, 9554, 9698, 7689, 245, 5118, 5726, 442, 9141, 708, 5847, 2031, 9321, 3999, 9376, 7117, 812, 215, 4703, 3569, 5744, 2454, 2354, 77, 6705, 446, 1752, 7873, 6863, 6179, 767, 3136, 6239, 1031, 131, 480, 6831, 3360, 5894, 4332, 5207, 1523, 2286, 2405, 7458, 2209, 3406, 7092, 9152, 9139, 2083, 232, 9493, 1879, 9219, 203, 7913, 9375, 351, 7008, 2805, 5791, 4189, 7450, 9829, 4974, 7510, 4903, 3681, 1042, 4464, 1010, 630, 9957, 7815, 5484, 3889, 5907, 3440, 99, 2162, 5808, 1245, 4053, 9534, 6079, 519, 2595, 9532, 5312, 4388, 9979, 153, 1419, 1668, 6475, 2399, 1249, 6070, 8889, 8336, 1235, 8947, 7150, 1122, 6117, 9926, 4993, 1441, 2387, 6066, 4629, 9477, 5244, 2654, 6749, 776, 2659, 1944, 5125, 9599, 268, 5575, 8489, 6566, 3897, 1233, 4649, 4210, 426, 3371, 9075, 8139, 4503, 8098, 4063, 6637, 9315, 9239, 4586, 8508, 8895, 2708, 5024, 8543, 5348, 1553, 821, 9362, 2276, 5932, 9678, 6199, 5145, 1463, 4432, 8092, 4364, 1937, 9736, 867, 3752, 9093, 3788, 4276, 8242, 9498, 7490, 8539, 5026, 9385, 2797, 6416, 7344, 5149, 9457, 5413, 4617, 1020, 7830, 3650, 21, 6548, 4948, 2845, 4248, 7467, 340, 5286, 9686, 8874, 9687, 3498, 8120, 3452, 1657, 9410, 7738, 8957, 1603, 6285, 9290, 8087, 223, 5816, 4947, 8897, 3780, 2511, 5136, 2290, 3413, 2868, 4590, 8487, 2645, 9294, 456, 392, 3077, 2502, 6779, 4277, 4699, 8195, 1411, 8194, 1373, 9069, 8064, 2713, 7824, 4120, 7649, 7803, 7444, 2062, 2173, 7912, 3363, 5250, 445, 4955, 2411, 8649, 2160, 564, 2381, 4199, 693, 3193, 6924, 6027, 6926, 6828, 2406, 5569, 3333, 2642, 1695, 8710, 7075, 6392, 4280, 7704, 2840, 352, 5033, 9411, 8125, 9571, 1972, 5933, 7978, 9365, 947, 957, 9852, 7040, 6296, 6358, 502, 8727, 7296, 471, 6324, 3071, 6609, 9089, 618, 8643, 7990, 7302, 7585, 1027, 8445, 6286, 9718, 8252, 548, 1123, 998, 8828, 1758, 2220, 641, 6692, 8724, 7274, 6891, 9723, 8847, 2238, 714, 1602, 3214, 690, 9121, 7454, 2329, 9502, 3590, 4882, 4870, 9959, 2523, 6005, 8811, 7090, 569, 6472, 9167, 5043, 508, 8196, 8805, 3433, 4859, 3188, 4668, 7182, 3851, 5373, 7759, 2023, 5722, 9095, 5796, 6868, 5151, 2739, 2108, 2232, 6557, 2415, 3833, 1845, 2740, 9103, 8739, 2306, 4810, 9092, 6411, 7148, 1781, 7398, 4743, 742, 1942, 4880, 8109, 4475, 4682, 3906, 5134, 312, 5545, 4392, 2128, 4040, 5537, 3562, 8668, 5036, 430, 6057, 1138, 8808, 8411, 5004, 3074, 3596, 8888, 7865, 1952, 7929, 973, 9480, 6729, 9664, 3299, 9655, 3241, 7928, 4335, 8409, 4546, 3760, 8050, 4836, 1568, 4283, 6989, 2490, 518, 3934, 1328, 825, 2650, 7457, 5947, 8855, 5718, 6180, 5788, 3516, 4096, 9465, 3869, 4486, 4270, 570, 3094, 9564, 4094, 914, 5301, 2930, 5410, 6712, 5743, 2446, 5444, 9626, 3009, 9951, 6288, 7209, 4176, 3790, 5260, 1963, 3817, 6814, 6114, 6021, 4945, 1706, 2294, 978, 2722, 5166, 9975, 526, 3031, 6482, 6483, 8145, 5174, 3915, 4139, 6612, 7701, 5889, 4369, 861, 525, 8358, 7896, 5283, 8644, 1424, 4057, 9179, 8127, 2239, 3923, 5080, 9902, 1382, 9772, 4707, 4172, 6046, 6311, 9893, 3436, 4288, 4543, 5981, 9097, 3080, 9329, 2925, 9621, 9823, 6746, 6229, 8501, 4033, 5382, 2922, 6941, 9340, 8717, 9680, 9361, 5730, 775, 6826, 9076, 4290, 7638, 1098, 5470, 4987, 4753, 7623, 2732, 387, 5740, 3571, 7538, 9695, 8552, 9758, 8022, 492, 8165, 2987, 3862, 3109, 6016, 2251, 2197, 4397, 4921, 8690, 2317, 6297, 7857, 640, 4030, 927, 6846, 4951, 7391, 6581, 5480, 6627, 2712, 1680, 9484, 7831, 166, 9440, 5231, 2874, 129, 8112, 3171, 2470, 9059, 7541, 5392, 7329, 1985, 580, 5586, 9041, 1250, 8788, 4293, 9891, 5425, 838, 7979, 8940, 922, 9053, 1325, 7396, 6273, 9799, 9611, 484, 3486, 7811, 7962, 6152, 1408, 6242, 7629, 2615, 1691, 1601, 3380, 9633, 4141, 2458, 614, 3186, 2134, 1354, 3499, 9129, 4621, 5195, 5531, 4321, 68, 1988, 98, 8697, 2915, 350, 7419, 6498, 4926, 7232, 5892, 5405, 5377, 9201, 6259, 3533, 7644, 5546, 2885, 7100, 4133, 936, 8602, 3159, 5523, 1997, 886, 63, 1071, 3849, 2109, 9586, 4451, 8587, 2443, 76, 3169, 2766, 8809, 4078, 7709, 8613, 747, 8149, 1180, 5667, 6380, 9475, 8010, 7086, 711, 5589, 318, 7356, 6495, 4708, 3980, 2777, 2508, 1543, 3716, 3215, 9995, 9326, 5295, 4259, 5793, 8642, 7420, 7459, 4566, 9762, 4007, 9458, 9731, 4303, 2072, 5964, 451, 9590, 9604, 8753, 2831, 768, 9309, 314, 4077, 862, 5141, 8969, 5970, 9430, 1480, 4833, 2863, 259, 6301, 2350, 1511, 9617, 5555, 5650, 2171, 5837, 7, 4250, 2720, 2165, 4192, 4866, 4146, 6871, 2873, 4331, 1597, 30, 6035, 8596, 6340, 9509, 5351, 2146, 7717, 7508, 2950, 8496, 985, 7429, 8526, 1110, 244, 9765, 9928, 9223, 8381, 7472, 8451, 4823, 540, 6969, 7393, 7850, 5429, 7119, 7498, 2136, 3021, 8699, 5152, 467, 8377, 4310, 4805, 8870, 7383, 212, 5460, 5608, 4173, 8760, 8329, 3677, 1323, 1522, 2335, 6277, 5140, 736, 4510, 2911, 712, 7888, 9261, 6249, 2634, 3417, 8531, 7058, 122, 5758, 1371, 5221, 4887, 8564, 282, 1305, 1065, 1458, 3541, 2611, 4964, 6287, 8438, 8408, 4424, 9102, 4755, 9872, 7725, 5222, 8425, 4175, 7031, 7955, 7438, 286, 2651, 8579, 6858, 1782, 3744, 9756, 7012, 5680, 1816, 1496, 849, 1126, 6816, 8503, 7731, 9489, 820, 9555, 8422, 5786, 5169, 4315, 5639, 1640, 8247, 2195, 3121, 5558, 7553, 9965, 791, 5015, 9467, 2658, 7290, 9513, 7401, 7602, 7897, 1226, 8061, 1588, 4062, 5334, 5168, 7333, 3453, 1547, 3266, 3514, 1417, 7692, 2254, 2897, 5700, 7327, 8580, 7949, 7123, 4036, 6563, 7682, 2422, 7569, 1109, 984, 4691, 3010, 157, 4483, 3328, 3911, 5922, 5259, 9998, 8869, 3629, 7882, 6600, 2407, 9231, 8732, 53, 746, 6577, 3579, 953, 8032, 7005, 6308, 2224, 5437, 3400, 5496, 1834, 9387, 7960, 6515, 9573, 562, 5071, 638, 5693, 1175, 4826, 8168, 2890, 6058, 7677, 7471, 4294, 3528, 2600, 7833, 9166, 9666, 9679, 7784, 1248, 9924, 3831, 8355, 1124, 2164, 9332, 4230, 7760, 6542, 3866, 4407, 994, 741, 9506, 4047, 9503, 6822, 7084, 727, 860, 3597, 1341, 9138, 5290, 2824, 9407, 9810, 96, 354, 2970, 7868, 5738, 7184, 8499, 5624, 2899, 6758, 1471, 7250, 622, 2644, 4285, 2734, 5230, 7411, 5463, 5477, 7730, 7145, 5785, 6366, 3683, 7842, 3477, 7926, 801, 5593, 1661, 7945, 193, 3410, 8113, 9596, 9233, 6688, 9241, 8696, 6992, 3779, 6850, 6592, 3669, 7235, 8636, 3139, 8136, 8730, 3657, 2042, 3991, 6281, 9725, 7389, 8519, 939, 1699, 7288, 5128, 2598, 9194, 9579, 6955, 4196, 2315, 8600, 7756, 7474, 1823, 3871, 4187, 9197, 2549, 3184, 5669, 7351, 2887, 7079, 3987, 4815, 441, 2180, 1030, 5465, 9218, 1653, 3, 6476, 7485, 8365, 3922, 1717, 9720, 3015, 8096, 5430, 9729, 9896, 6827, 940, 5761, 8317, 6881, 5696, 1574, 7673, 1686, 7172, 5439, 7853, 423, 5397, 7622, 7536, 8049, 7667, 5066, 3574, 2030, 1846, 8977, 3252, 1105, 8973, 818, 9462, 1606, 1688, 2719, 4016, 1866, 2326, 5621, 7656, 7277, 6037, 6338, 5471, 2468, 3076, 1991, 5732, 2614, 7403, 6062, 7977, 6209, 3689, 5226, 7225, 8105, 6284, 589, 8714, 2682, 6929, 7110, 8269, 1786, 5746, 6359, 1263, 9644, 2709, 8593, 4461, 7330, 2104, 4557, 7298, 2009, 3324, 8698, 2921, 3162, 1216, 173, 7765, 8967, 6762, 5929, 2947, 5005, 7993, 4799, 890, 3331, 1631, 5866, 185, 2588, 556, 9538, 5912, 8179, 9933, 7161, 6821, 4560, 4439, 72, 8656, 1735, 6118, 1433, 7808, 3041, 6679, 6102, 8483, 6034, 8713, 2003, 4807, 2382, 8974, 384, 1304, 9403, 3088, 1645, 1130, 1561, 9144, 3976, 2491, 8937, 3079, 2681, 5855, 4596, 2234, 4881, 7739, 2493, 4846, 5561, 879, 9978, 7242, 4594, 6594, 5578, 7068, 3707, 1587, 310, 2572, 6457, 5419, 3856, 2716, 5664, 3199, 2033, 3011, 250, 8966, 2673, 4049, 4466, 4347, 7867, 431, 3560, 2019, 1837, 5954, 8926, 6556, 4066, 1563, 7564, 5657, 7626, 9135, 2962, 2956, 6116, 4664, 9526, 8755, 3073, 4570, 5591, 6586, 6444, 6166, 6196, 9100, 5241, 1777, 8192, 230, 668, 6408, 2296, 9500, 278, 468, 1672, 1867, 1215, 9964, 6009, 840, 4630, 5999, 43, 975, 3020, 3939, 9763, 1475, 5289, 3353, 4245, 5904, 8157, 6432, 8240, 1269, 813, 3748, 6024, 2132, 7849, 6448, 1179, 3311, 6892, 605, 2363, 7583, 9717, 9789, 5237, 3687, 5941, 9125, 4340, 9062, 2358, 3913, 3971, 5076, 3530, 3348, 7841, 8097, 2189, 9443, 923, 9751, 6660, 8839, 7143, 2483, 5873, 2345, 3503, 4394, 8524, 5717, 8353, 4314, 6396, 1236, 3284, 7404, 2280, 5917, 3025, 7613, 5833, 4961, 1400, 4350, 4782, 8609, 9046, 6636, 9389, 8231, 5513, 1217, 2906, 385, 8104, 9867, 5435, 7487, 2248, 831, 9544, 2200, 5440, 5297, 1778, 7645, 4127, 2638, 9980, 9568, 2605, 2866, 4423, 7770, 9468, 9420, 8406, 6040, 7563, 615, 1641, 3646, 1310, 1546, 1907, 659, 8740, 8935, 5814, 1589, 7129, 5913, 4912, 7003, 6332, 8637, 4380, 6065, 3819, 270, 5102, 7734, 6060, 5114, 2965, 4346, 8380, 1464, 4236, 2690, 6111, 5500, 2403, 9945, 8548, 443, 5386, 6595, 7473, 3233, 4786, 2579, 6403, 4671, 1694, 4438, 5367, 8945, 9952, 1860, 386, 2738, 2990, 2355, 8295, 4849, 9873, 8921, 4520, 5055, 8457, 1733, 8470, 9413, 1165, 4809, 3616, 8354, 5960, 1055, 6050, 6815, 3294, 9043, 1658, 6788, 3884, 6741, 3895, 796, 9478, 5940, 8391, 3431, 950, 4126, 9575, 9879, 4853, 1037, 4532, 4117, 4145, 1395, 3268, 4892, 2553, 8976, 4897, 6423, 4291, 3566, 704, 5635, 4855, 3245, 2641, 4307, 5899, 5092, 3230, 124, 6170, 1184, 6781, 8068, 4578, 365, 6312, 3643, 7509, 9278, 4246, 5171, 4689, 3144, 18, 460, 7346, 128, 6512, 8009, 941, 6568, 8001, 4019, 8970, 8115, 5824, 3670, 3730, 1118, 1667, 375, 6582, 5077, 7826, 8421, 7431, 9312, 4770, 1722, 9803, 8346, 7434, 9524, 2841, 1780, 4916, 3246, 6668, 3244, 5968, 5898, 52, 7385, 2730, 6441, 4149, 1957, 716, 2291, 483, 2691, 8245, 1428, 82, 8432, 587, 3880, 5436, 5827, 4931, 7828, 345, 9160, 1930, 4454, 7115, 3210, 5632, 7249, 5278, 4944, 1701, 4718, 3464, 9065, 7463, 8960, 7653, 9108, 6233, 1514, 8718, 100, 7531, 3840, 728, 7128, 5057, 2420, 5170, 5252, 1421, 5384, 8014, 2918, 3986, 853, 5516, 7972, 1000, 1443, 5605, 4401, 6777, 6292, 2153, 7477, 5568, 1259, 9050, 8405, 4444, 989, 1005, 2599, 5113, 7711, 7303, 7408, 5093, 2530, 4224, 6375, 8024, 3039, 3198, 9958, 9304, 7621, 2818, 5648, 9961, 2799, 8815, 5695, 1987, 9876, 1669, 6681, 2556, 9258, 5526, 3403, 3577, 2465, 9768, 6704, 7790, 3859, 5431, 1784, 5552, 5783, 1196, 5846, 962, 3656, 8266, 60, 2564, 7052, 3238, 7546, 6127, 3390, 5737, 753, 1446, 358, 4941, 6089, 5984, 2056, 8995, 1632, 5631, 6164, 6570, 1802, 1913, 7639, 9905, 7097, 3036, 7551, 9444, 8030, 9350, 1059, 75, 35, 5542, 3370, 9634, 6782, 4717, 2913, 6271, 9280, 5035, 4650, 5338, 2424, 4973, 1288, 6954, 5834, 228, 4243, 45, 5945, 1633, 3392, 9341, 4638, 2618, 6950, 4761, 8025, 6813, 9963, 1161, 9378, 5340, 1290, 119, 4633, 3205, 1384, 9225, 9393, 219, 9936, 9704, 6343, 5603, 8725, 5456, 103, 582, 2503, 1560, 7527, 7854, 7363, 3745, 410, 1494, 6442, 6234, 4157, 201, 8086, 2731, 4724, 9255, 3663, 9, 6464, 8373, 184, 4772, 6986, 5006, 3415, 691, 180, 8119, 7684, 9300, 1947, 5957, 1490, 5792, 9033, 7970, 8911, 7844, 6153, 3336, 7266, 8893, 4264, 9264, 3197, 673, 4271, 5645, 3393, 1716, 6140, 8571, 1284, 370, 3089, 9937, 3101, 1617, 3082, 8041, 145, 38, 8639, 5584, 1057, 4188, 5279, 4988, 7144, 7633, 8123, 7435, 3050, 3095, 2916, 6561, 7488, 2850, 3665, 3814, 1353, 9712, 4508, 3778, 4456, 9490, 2103, 3957, 2635, 4791, 7906, 8359, 6067, 7180, 1251, 200, 6069, 7557, 5686, 5825, 9912, 8282, 6329, 380, 3531, 7907, 2907, 1213, 7965, 5446, 8886, 7345, 3087, 1803, 7348, 1734, 4374, 7357, 7901, 4073, 1542, 1760, 1847, 1721, 9798, 6491, 1370, 9452, 8435, 5198, 1407, 6295, 7010, 287, 7018, 7307, 3322, 4050, 8790, 5691, 1095, 8904, 8914, 5703, 3347, 1918, 1888, 7953, 9739, 9016, 3701, 8327, 9663, 1074, 5876, 2348, 5800, 2480, 1724, 4329, 237, 5601, 6976, 7916, 2029, 7098, 3485, 1842, 7199, 6039, 5243, 8083, 7781, 2095, 9834, 2622, 2181, 3161, 6172, 702, 8654, 1840, 381, 391, 8249, 4005, 604, 683, 2437, 9844, 8778, 4435, 1537, 4171, 5061, 2299, 2107, 4198, 1146, 6981, 6291, 4967, 2014, 7515, 5812, 9303, 9133, 4592, 1381, 2467, 7149, 1854, 7029, 6963, 4083, 937, 3635, 2303, 6716, 9804, 1739, 9800, 5915, 9114, 751, 4282, 8226, 1224, 2888, 6003, 6790, 845, 6878, 7601, 1368, 3712, 1841, 1096, 8477, 6439, 9580, 6535, 3920, 7037, 3100, 1690, 6972, 4356, 9643, 7446, 6912, 4553, 7900, 7594, 7660, 3556, 9791, 4651, 6523, 1051, 9667, 4958, 9997, 7300, 4702, 4216, 323, 5844, 7275, 7305, 2202, 3128, 8393, 3863, 9553, 8877, 4023, 2250, 3543, 4378, 2451, 7596, 4767, 6183, 7588, 9335, 2089, 5031, 6985, 364, 3354, 4415, 4975, 7936, 689, 9049, 1204, 3572, 9032, 2384, 8151, 3722, 4226, 2626, 837, 1583, 5202, 6984, 2002, 8456, 3709, 8267, 5551, 5369, 2028, 169, 8678, 9699, 9338, 8626, 6187, 7672, 9494, 194, 866, 8443, 4933, 2366, 2203, 1931, 2328, 7890, 608, 7793, 5620, 4539, 2684, 1135, 7662, 1600, 4660, 588, 217, 9962, 1036, 3529, 9623, 1482, 402, 1787, 8141, 2047, 958, 1791, 1684, 8328, 2829, 105, 8101, 3166, 127, 4615, 1302, 2583, 3604, 4076, 8768, 2703, 191, 5211, 8931, 577, 2302, 3510, 6269, 2636, 6019, 4400, 1535, 8511, 8175, 6181, 5181, 6226, 7997, 9142, 4593, 987, 3630, 4742, 1906, 1936, 8133, 8638, 4646, 8943, 5414, 7835, 800, 3043, 2402, 9650, 488, 713, 9085, 4598, 4140, 7561, 6837, 4722, 1439, 3797, 1308, 101, 5859, 4100, 5016, 869, 826, 4354, 7364, 3416, 8471, 3104, 9925, 3962, 1212, 8509, 5988, 1350, 464, 5807, 9970, 6539, 3966, 565, 723, 9660, 2608, 5998, 6970, 183, 666, 186, 3873, 2864, 3047, 8246, 9165, 3254, 2246, 5347, 1868, 4391, 9589, 3997, 5983, 5649, 9792, 9816, 7632, 4585, 3236, 1375, 3768, 2432, 9944, 8551, 3091, 8751, 7767, 4959, 67, 1081, 9706, 9735, 5189, 7091, 3397, 9087, 9145, 7523, 1054, 1538, 6748, 5466, 6110, 7186, 9266, 2875, 4710, 1358, 4465, 4700, 784, 976, 2105, 2282, 7506, 2380, 7312, 4178, 5342, 2652, 7206, 2379, 5234, 4548, 4193, 4583, 133, 4822, 281, 324, 3610, 5461, 7655, 6282, 7111, 117, 6952, 2230, 686, 4925, 4090, 2452, 1459, 1280, 4656, 2955, 2167, 4412, 4939, 9044, 7839, 7864, 9086, 9163, 2903, 3092, 6724, 4220, 7674, 6265, 8662, 5502, 4022, 2627, 2960, 9419, 9870, 7237, 6726, 6240, 7376, 9471, 3754, 8063, 7087, 5299, 945, 9649, 5773, 875, 9543, 8757, 9320, 951, 4863, 1604, 6294, 6579, 816, 5862, 5779, 5327, 3480, 3209, 1708, 5269, 8802, 6808, 795, 9923, 5045, 3872, 2440, 1173, 3857, 2649, 2247, 1697, 539, 1425, 4242, 9022, 1880, 7211, 3017, 3396, 7539, 8412, 7151, 6155, 8148, 500, 6854, 1405, 7917, 6855, 4564, 1016, 4136, 3258, 5457, 4992, 3124, 4913, 8015, 4857, 7999, 2500, 5302, 8861, 5146, 7791, 1901, 1966, 3478, 1418, 1949, 9082, 7832, 8396, 6766, 6041, 9356, 9960, 7233, 6576, 4830, 450, 5662, 4873, 6667, 7823, 5135, 6254, 6073, 171, 1021, 6732, 3146, 8052, 9676, 6134, 7175, 1324, 9447, 7614, 1828, 1477, 4648, 3368, 2668, 1338, 3806, 6143, 8475, 3559, 2460, 1884, 9293, 83, 6678, 3154, 7134, 8171, 4979, 4201, 6530, 7251, 8865, 9051, 2552, 6532, 5329, 334, 2861, 4059, 3457, 4746, 283, 419, 8993, 8985, 8525, 2404, 3601, 7764, 903, 4679, 3908, 5097, 7248, 8043, 178, 2277, 6348, 5393, 107, 1270, 24, 8330, 437, 4730, 5776, 9584, 8772, 6434, 2741, 8781, 1728, 8054, 6167, 8362, 8981, 8144, 3412, 2917, 1397, 2755, 9339, 1870, 6469, 4904, 7681, 8582, 9425, 70, 6299, 8681, 6993, 276, 7726, 4359, 6658, 7216, 5977, 3919, 2249, 1312, 2694, 4891, 1639, 3212, 1273, 8905, 8792, 2006, 4379, 2768, 6765, 9232, 8013, 4899, 682, 665, 9234, 8389, 2878, 2575, 8894, 6640, 4153, 9105, 5091, 3113, 3517, 2591, 2092, 1977, 1508, 2751, 8544, 7213, 6357, 5344, 5158, 6774, 8420, 631, 476, 3742, 3420, 8334, 7753, 2143, 2088, 1562, 3974, 9592, 5633, 6474, 8304, 1088, 326, 5447, 288, 3502, 3766, 5361, 5926, 3753, 5959, 4872, 5218, 6104, 149, 2594, 8675, 9029, 6876, 6649, 6934, 1900, 4460, 7308, 2629, 5214, 3841, 4110, 2843, 4296, 2413, 3142, 2754, 3287, 4183, 9948, 4015, 9107, 2255, 1776, 1556, 5820, 5886, 1590, 4408, 8920, 6791, 4695, 5258, 6372, 8836, 7421, 6500, 6257, 8798, 7762, 7548, 3581, 5784, 8964, 5129, 2706, 2869, 7231, 1516, 6860, 2396, 1197, 4741, 9025, 2969, 2830, 1487, 4260, 3016, 1049, 6165, 4713, 7518, 1951, 6845, 7741, 2185, 40, 9070, 2578, 5565, 7938, 3524, 6794, 4480, 1510, 162, 1279, 4467, 2522, 773, 6390, 8002, 5823, 3042, 6241, 785, 3422, 165, 1264, 9796, 4878, 5540, 6020, 3739, 8093, 6996, 2927, 435, 3838, 7374, 7688, 566, 9098, 7153, 2808, 4561, 192, 9728, 9369, 7998, 9647, 5729, 9245, 6938, 7281, 4132, 961, 8744, 3693, 7118, 1061, 8619, 7154, 2678, 2055, 3558, 4155, 8082, 9482, 1170, 4197, 3910, 1166, 5865, 3737, 2798, 2610, 4402, 1258, 5383, 3222, 6217, 3367, 8350, 7331, 5366, 6538, 6606, 4490, 3084, 8504, 6190, 3048, 6211, 6119, 6231, 8344, 1221, 4749, 6939, 3843, 39, 6775, 5602, 4206, 5787, 2070, 2386, 7163, 8458, 2154, 7315, 4848, 8473, 2308, 5756, 2971, 9151, 8774, 3377, 1573, 9388, 8693, 9117, 9150, 8614, 3308, 6093, 5529, 8541, 3013, 8827, 5487, 3904, 253, 2037, 3133, 2670, 9301, 6487, 4631, 2112, 6958, 7096, 9382, 6054, 2498, 621, 1281, 1145, 4704, 3140, 8048, 6869, 6443, 5925, 6666, 662, 9088, 7992, 405, 909, 246, 9931, 7887, 1517, 1314, 799, 3964, 1638, 1108, 5503, 6076, 5564, 3459, 601, 6819, 2418, 3660, 2244, 8655, 3424, 396, 6931, 9078, 3147, 4275, 4163, 5963, 684, 4976, 9397, 7607, 9047, 4536, 9541, 6030, 7761, 8866, 6875, 5532, 3024, 8039, 4970, 7013, 7746, 9324, 3285, 3773, 7519, 5178, 7719, 9286, 1859, 7073, 7838, 2201, 6398, 2141, 522, 6735, 9159, 4652, 5617, 9831, 2469, 2764, 3825, 5916, 373, 6574, 1301, 8313, 6533, 2071, 335, 7533, 4386, 7771, 507, 6865, 3281, 1355, 5029, 6613, 9602, 2349, 1484, 1211, 8019, 6068, 7306, 6521, 5153, 5585, 5232, 8669, 6633, 254, 6909, 6302, 5522, 2981, 9357, 3219, 6753, 4565, 3713, 8791, 3972, 9418, 8016, 9318, 123, 4778, 8633, 8570, 64, 636, 4894, 8324, 231, 4018, 6810, 9187, 3847, 7766, 4803, 634, 2093, 6962, 92, 2048, 6784, 3035, 4229, 4404, 37, 8591, 2589, 1770, 1800, 5403, 2426, 6245, 7432, 85, 7743, 6126, 9954, 550, 1466, 8237, 6362, 5948, 6872, 7526, 1833, 5163, 7318, 1513, 5345, 9797, 6711, 2889, 9966, 1886, 5706, 336, 4653, 5931, 4662, 8167, 3537, 2208, 3438, 2334, 4166, 9885, 3190, 783, 3337, 2980, 847, 5536, 7367, 9567, 1275, 554, 3812, 8029, 7686, 1718, 8581, 16, 546, 7663, 7898, 5044, 8563, 2285, 7020, 7373, 9900, 8939, 5641, 6654, 4920, 9527, 5826, 5157, 1257, 9295, 2376, 252, 2972, 8185, 8312, 4468, 7700, 858, 1518, 9593, 6927, 363, 5550, 505, 7093, 5885, 7019, 1141, 7524, 8404, 7338, 9479, 7804, 5805, 5119, 777, 2680, 5120, 1876, 7072, 592, 6460, 1178, 2457, 1814, 6042, 9198, 1877, 1648, 4628, 632, 2323, 6560, 6908, 9262, 3086, 5903, 3061, 8348, 7021, 5452, 5656, 5368, 2567, 4962, 7840, 6722, 1762, 6266, 1809, 5745, 8787, 6470, 9906, 8664, 6368, 1360, 9591, 1437, 6374, 1757, 3053, 3384, 5341, 4410, 8990, 1644, 2081, 6389, 3729, 694, 4614, 4484, 7495, 9515, 8436, 3067, 3948, 6671, 5511, 9894, 4999, 9019, 6799, 3323, 58, 1187, 6555, 7637, 5139, 4950, 7661, 4914, 8427, 732, 5455, 8297, 1619, 7582, 4495, 7657, 3349, 4835, 3037, 382, 5022, 4544, 4938, 2190, 5597, 241, 6424, 3823, 4251, 6820, 3027, 1928, 3456, 6917, 6559, 6835, 2316, 1334, 1848, 7774, 8399, 9850, 3710, 5358, 7768, 8189, 1309, 5492, 4393, 7220, 4074, 1209, 718, 7245, 9244, 3680, 2810, 5320, 551, 4501, 292, 6772, 9719, 7089, 5856, 1378, 4667, 4669, 7675, 2647, 1058, 8398, 6198, 908, 9496, 9659, 4632, 6531, 6250, 5590, 329, 9514, 2509, 7085, 2666, 5096, 6853, 2902, 5616, 487, 5789, 5647, 5572, 1208, 7341, 5236, 3979, 4256, 4828, 5817, 7870, 2442, 6861, 2826, 6851, 7560, 5715, 3774, 1730, 3468, 8635, 8949, 6630, 8368, 3012, 8386, 9750, 3002, 7749, 854, 7352, 7806, 9837, 1073, 9472, 4430, 1046, 2207, 1434, 9112, 1087, 3592, 256, 567, 868, 6823, 7484, 1903, 5953, 1674, 8719, 5257, 9946, 377, 8316, 1598, 8533, 7293, 8674, 3414, 3108, 8402, 4856, 4316, 7517, 9818, 1540, 3826, 9220, 956, 8110, 2322, 3824, 8972, 4550, 5910, 2383, 1712, 2752, 4802, 7797, 2548, 1189, 1136, 6321, 8912, 8925, 1394, 1387, 5303, 4601, 3408, 2494, 94, 828, 5019, 9929, 261, 7139, 3678, 7323, 6685, 3740, 4281, 3898, 7240, 3846, 5673, 5539, 6412, 648, 8299, 9862, 6422, 4231, 2546, 2237, 4309, 8687, 6342, 348, 1622, 6038, 878, 6971, 7975, 6571, 912, 8689, 4101, 7944, 1431, 7869, 1240, 1363, 6770, 8229, 1745, 4114, 5508, 6085, 5491, 8132, 1315, 3584, 1047, 609, 5000, 2448, 9518, 2867, 6687, 3844, 6480, 3837, 2820, 4129, 4055, 7578, 3818, 9795, 2378, 4027, 6634, 6078, 8371, 5908, 7973, 1404, 4150, 1347, 8606, 3783, 9402, 5023, 2533, 73, 135, 6615, 2015, 6151, 4582, 2762, 680, 4588, 2939, 4723, 1531, 2155, 3921, 6979, 3373, 9770, 8682, 7179, 9622, 3365, 2881, 2193, 2488, 7935, 9875, 8155, 6957, 8832, 3338, 6543, 4885, 6175, 1743, 8859, 8746, 3291, 7780, 4455, 5265, 5400, 4595, 2535, 4568, 7750, 6697, 7107, 1362, 4990, 5804, 130, 9996, 4471, 6507, 700, 5781, 8215, 3617, 1710, 7083, 4758, 7892, 8490, 4045, 2693, 850, 362, 8538, 6894, 9793, 9381, 9096, 8646, 4079, 9636, 7745, 7109, 1410, 8735, 8190, 2839, 8672, 1635, 7375, 7590, 9370, 8801, 2954, 5836, 4576, 7136, 7202, 8070, 2044, 2022, 4554, 8453, 755, 1893, 8268, 2667, 161, 2489, 2123, 495, 4272, 4041, 2968, 5573, 5888, 9099, 8492, 1826, 3168, 2320, 9355, 3165, 2025, 5991, 4814, 5208, 6147, 7941, 4010, 4406, 1331, 8126, 8228, 1698, 6884, 4324, 1292, 9986, 4035, 7295, 8765, 6453, 3523, 7392, 2314, 1971, 9854, 509, 8388, 2283, 349, 297, 5488, 6061, 9883, 5472, 6212, 189, 2750, 8794, 7805, 8378, 1107, 4403, 7127, 8961, 3563, 482, 8989, 9563, 1256, 2547, 8222, 2774, 6319, 9646, 2715, 2784, 9323, 5304, 8292, 303, 7616, 4147, 3749, 5893, 3164, 5095, 3725, 5355, 125, 1887, 2736, 8260, 2222, 3757, 8983, 4499, 2005, 206, 1222, 750, 7690, 4138, 2485, 4890, 6247, 1461, 6787, 9619, 1693, 1692, 3874, 6844, 3916, 3717, 7651, 3648, 9734, 7782, 8759, 1357, 1729, 156, 5154, 9288, 4289, 2441, 3351, 2538, 7525, 9213, 8584, 1117, 7580, 6588, 493, 489, 7193, 1869, 1186, 8374, 5042, 8640, 2603, 2919, 8351, 8161, 9773, 7652, 2984, 3137, 235, 9911, 7355, 3870, 9769, 9700, 6406, 9969, 7470, 597, 6916, 9211, 2332, 4841, 6978, 138, 3989, 6554, 1754, 557, 5736, 2687, 5850, 9985, 2492, 4221, 9508, 8991, 4858, 8055, 4462, 2561, 9237, 7400, 8708, 2563, 6997, 900, 7532, 1342, 4879, 8632, 2110, 8890, 8003, 3945, 4241, 110, 5618, 3001, 4355, 8842, 7589, 6236, 5563, 910, 1714, 1956, 1792, 3746, 1585, 833, 1121, 9973, 1894, 2312, 4883, 4513, 7036, 8493, 8214, 7963, 8720, 5674, 7460, 9034, 2886, 4161, 6103, 4930, 9716, 5566, 4768, 8253, 8005, 355, 1134, 6910, 3924, 5215, 5316, 5087, 6105, 919, 3598, 9934, 6701, 4211, 3148, 2559, 5038, 1626, 79, 6804, 8369, 4109, 4328, 1801, 7014, 6991, 7016, 309, 9242, 1769, 1536, 6959, 8339, 9701, 613, 9858, 1835, 7247, 9279, 5343, 5930, 9848, 9651, 5328, 5698, 8512, 9208, 2718, 2988, 4985, 8761, 8910, 2098, 2743, 9302, 5292, 8971, 5445, 36, 4085, 9618, 3463, 9955, 1262, 2619, 3807, 1811, 2570, 7322, 3547, 6661, 7002, 9104, 2525, 2631, 6214, 2630, 9740, 9748, 1153, 8044, 56, 1940, 6768, 999, 4419, 852, 9788, 8102, 1885, 7740, 4343, 6508, 6251, 3218, 50, 8872, 6437, 3958, 9297, 8545, 6351, 2937, 2191, 7855, 2580, 7354, 343, 5117, 5714, 709, 720, 698, 3229, 3234, 5610, 4847, 5309, 9446, 3276, 9561, 7409, 9743, 8140, 3362, 5766, 2481, 4995, 7222, 4234, 4981, 8661, 1050, 2423, 8258, 1914, 251, 3570, 5997, 9847, 4491, 2253, 3607, 2084, 1416, 7710, 9721, 1029, 2688, 7041, 2931, 9811, 290, 9149, 7775, 6158, 4268, 3674, 4567, 7567, 5438, 4205, 3358, 2544, 8527, 9658, 3776, 9892, 8965, 1339, 5944, 4305, 379, 617, 6077, 6624, 3695, 2985, 5521, 9090, 5549, 5389, 1066, 1286, 3098, 5225, 5275, 2495, 4831, 1656, 2767, 1719, 5769, 1984, 3334, 9247, 1555, 7200, 7361, 5032, 1938, 9115, 4902, 3644, 8170, 9214, 8460, 2257, 9216, 8731, 3896, 5699, 7272, 8497, 9988, 5588, 8986, 4523, 8130, 2279, 5308, 5112, 3758, 3942, 8172, 176, 8992, 6193, 9519, 106, 9522, 6186, 606, 7423, 2370, 2998, 1102, 4487, 3711, 5668, 995, 6, 7292, 6994, 8987, 2783, 8879, 3203, 7736, 5962, 4659, 7802, 1272, 4043, 798, 4765, 8783, 444, 8426, 8309, 646, 1488, 2577, 8134, 5972, 9759, 300, 5277, 7969, 3160, 8862, 7820, 6014, 1298, 2995, 5782, 2069, 6698, 9587, 9656, 1935, 9056, 3666, 7919, 361, 9181, 2827, 4322, 2790, 4714, 4874, 6583, 1895, 2914, 1982, 3771, 2705, 3762, 2948, 1080, 4624, 1158, 7173, 7425, 8779, 5682, 8769, 9566, 9517, 3120, 1035, 1528, 3685, 3992, 5261, 4683, 1038, 7448, 4011, 8302, 4284, 428, 5924, 399, 7379, 2966, 1462, 6623, 8630, 990, 8942, 1974, 5126, 7158, 7287, 3003, 4422, 9352, 5468, 2815, 2663, 8383, 2963, 7130, 7112, 9836, 789, 8202, 8028, 7974, 3798, 4363, 5388, 6942, 6227, 4738, 2075, 5254, 4889, 5048, 3564, 757, 1749, 6843, 5233, 3217, 2593, 2008, 2924, 8080, 1827, 7562, 8154, 1398, 7263, 7735, 4559, 8651, 6684, 8916, 9752, 7813, 7615, 3728, 6026, 4640, 4095, 9441, 779, 5330, 6803, 5115, 4838, 275, 4362, 7309, 199, 6655, 9068, 4797, 3684, 2127, 8823, 9451, 8177, 8723, 5223, 3795, 2945, 4605, 3507, 5499, 9760, 2295, 3548, 9709, 8816, 6216, 6818, 8950, 6017, 8955, 6590, 7640, 5224, 1839, 3720, 9042, 8321, 5298, 1423, 8446, 4769, 1954, 6094, 9881, 4227, 5434, 3994, 242, 1805, 3794, 2758, 5801, 6961, 9533, 4760, 3277, 7191, 9002, 136, 20, 1812, 47, 3072, 202, 498, 34, 6995, 4789, 6197, 896, 2459, 5554, 7545, 5075, 7138, 4661, 926, 3996, 9314, 9084, 9557, 6549, 1101, 3637, 1028, 1228, 3130, 4670, 5748, 2590, 4056, 1564, 4477, 3605, 7669, 7566, 116, 7988, 6331, 8880, 5559, 8007, 1237, 9423, 1140, 3129, 8567, 9170, 4204, 6656, 7930, 7600, 6479, 4908, 1001, 1768, 6708, 9177, 3458, 1532, 3221, 5101, 2344, 819, 8107, 2992, 4551, 647, 9373, 3751, 952, 3855, 4763, 1967, 5861, 760, 2555, 1921, 6488, 5387, 8629, 1961, 5150, 2045, 4706, 2817, 7304, 7827, 938, 7922, 672, 2204, 3926, 5543, 8764, 6578, 2076, 9921, 7494, 5451, 9764, 1076, 5039, 787, 6841, 6391, 4398, 6544, 8276, 7386, 9343, 8272, 5927, 5574, 5994, 9516, 6990, 2510, 7104, 906, 3676, 824, 46, 3907, 6208, 4180, 9781, 8238, 2051, 1392, 1183, 2986, 4895, 3636, 1018, 3274, 7469, 7273, 8748, 4953, 1391, 1169, 6261, 3482, 4481, 8680, 3335, 2117, 9598, 2711, 4182, 8978, 2882, 3747, 2814, 3316, 2429, 895, 57, 583, 1925, 8854, 1188, 6786, 3968, 2096, 6550, 1365, 296, 266, 4771, 2346, 4144, 9670, 3228, 5306, 1152, 2352, 3727, 4535, 6562, 3321, 7985, 6202, 5083, 9005, 1820, 3614, 6965, 6354, 7328, 8566, 8323, 4443, 9118, 4619, 3652, 765, 2272, 8280, 7257, 1926, 3183, 4963, 8658, 3848, 2877, 754, 6982, 3731, 1896, 1843, 4750, 6451, 6107, 5025, 7685, 1524, 2035, 2944, 8366, 4922, 7325, 1359, 6745, 5247, 4396, 4690, 1231, 5517, 503, 8210, 9313, 1715, 8349, 1450, 6755, 2812, 1527, 5643, 7320, 5533, 9688, 1012, 6410, 9648, 7384, 3852, 9010, 5524, 4026, 6429, 4854, 5325, 8612, 788, 317, 2551, 2262, 5848, 1700, 2849, 1393, 7137, 5412, 9067, 1965, 438, 4326, 8634, 2727, 629, 9661, 3690, 3172, 1470, 4020, 1572, 5642, 4458, 3282, 2319, 9328, 3255, 5630, 4514, 7316, 1830, 3595, 5239, 7046, 4842, 1075, 8469, 9938, 1808, 1647, 4620, 6611, 7884, 7976, 6138, 6676, 7388, 542, 4389, 7492, 5996, 814, 4409, 5103, 996, 7751, 9238, 681, 6604, 4736, 6806, 78, 857, 4447, 9024, 25, 7387, 8331, 6413, 7598, 5489, 7415, 8261, 5869, 6136, 6449, 695, 8152, 8207, 5060, 2226, 2231, 9491, 8858, 7394, 2620, 593, 9947, 9525, 8692, 2292, 7060, 6132, 5512, 7714, 6905, 4968, 1621, 6631, 4635, 7483, 5124, 9006, 4515, 1502, 5282, 2587, 2182, 7577, 6128, 126, 8158, 8747, 5606, 8703, 6477, 1881, 8550, 1474, 3672, 9993, 3056, 5611, 3698, 9916, 7671, 545, 2082, 2271, 3185, 9336, 5475, 7579, 4907, 6528, 3535, 2729, 477, 3317, 6162, 3155, 3263, 9347, 9682, 5411, 9805, 2021, 2908, 674, 2496, 4448, 9869, 5596, 6778, 1969, 8841, 744, 9391, 1772, 4121, 8623, 7591, 8081, 2870, 1002, 1500, 2066, 8241, 4688, 6873, 8824, 3126, 1085, 2057, 7157, 7910, 6980, 6524, 5797, 6144, 620, 111, 3738, 6862, 7881, 3594, 2613, 1559, 3697, 9899, 1336, 1192, 6090, 6278, 1696, 4092, 8599, 6334, 964, 5607, 9654, 701, 9809, 8848, 6915, 8776, 8754, 9560, 8875, 8018, 5049, 356, 5952, 9697, 6643, 4524, 4522, 2430, 9523, 1227, 404, 3894, 7801, 4274, 4440, 2655, 6900, 737, 1092, 6947, 7056, 8012, 5428, 6968, 4164, 2375, 4600, 7230, 7792, 3555, 5064, 3491, 6605, 971, 9026, 462, 3418, 3260, 8315, 6454, 29, 5262, 2573, 9653, 1806, 7814, 168, 6572, 6313, 1456, 7737, 2518, 1507, 8982, 163, 9774, 2060, 9989, 4996, 8901, 6505, 5956, 4575, 870, 6381, 8341, 6101, 4417, 4353, 8500, 9711, 9530, 8251, 1453, 7270, 6792, 5123, 4453, 7433, 865, 2811, 9134, 3063, 7946, 1127, 4852, 5167, 3201, 3829, 653, 3122, 6290, 6100, 2723, 9113, 5835, 6306, 6763, 2198, 5193, 9540, 3688, 1143, 7496, 5987, 4219, 4080, 9439, 9855, 8091, 9542, 9235, 8679, 8235, 1666, 5845, 572, 3253, 7723, 7951, 5122, 8863, 5666, 9692, 5992, 688, 5949, 4604, 5453, 8289, 7162, 3756, 7646, 4627, 1844, 1132, 934, 2699, 3583, 9625, 1731, 7915, 4500, 7070, 3296, 1670, 2417, 5008, 5205, 4174, 7125, 1344, 9577, 9456, 9801, 6723, 2388, 9435, 6733, 697, 3954, 6956, 1326, 4489, 574, 4113, 815, 6573, 2679, 8565, 7816, 8045, 425, 2085, 6752, 872, 6628, 5280, 5942, 3892, 4502, 9609, 3447, 481, 5646, 9191, 6268, 9940, 8962, 6010, 3300, 9888, 924, 3065, 2434, 9203, 2543, 4647, 6135, 4081, 209, 439, 8795, 667, 5443, 943, 7876, 6095, 9185, 1413, 3118, 7276, 2425, 843, 3800, 8459, 1142, 724, 7664, 3901, 5313, 2994, 1737, 6004, 8479, 4794, 1445, 5538, 1785, 1435, 1303, 7895, 3170, 762, 19, 8209, 1321, 8825, 9307, 7368, 7836, 5479, 5270, 6075, 2828, 882, 1177, 8288, 8821, 9914, 9908, 3686, 5307, 4017, 8922, 1916, 6738, 3505, 8670, 3659, 6157, 1295, 6300, 6800, 9003, 5705, 5755, 4108, 6125, 1150, 8603, 2139, 1582, 7170, 3726, 8071, 6195, 7065, 2482, 8322, 142, 7241, 5346, 8941, 8715, 6141, 5567, 7971, 7848, 1296, 2951, 4225, 6378, 3028, 49, 2178, 4626, 3699, 6591, 6365, 8395, 8716, 3549, 3033, 4801, 7571, 1349, 9786, 3372, 5830, 6438, 1624, 1467, 6802, 8780, 1160, 9956, 3944, 4811, 3988, 8084, 4237, 6383, 8467, 9277, 7570, 9742, 7283, 4352, 2698, 1570, 2749, 794, 8785, 2707, 5390, 2632, 5731, 8585, 5268, 5186, 2419, 8254, 6177, 1558, 4135, 2657, 2333, 5088, 5099, 6047, 7968, 5778, 1356, 5688, 4680, 6693, 8706, 4351, 3625, 298, 8900, 7455, 9209, 7574, 9023, 1862, 6352, 8502, 5182, 4060, 2929, 1727, 9787, 2218, 5634, 5520, 7683, 5644, 8953, 6206, 265, 6243, 4552, 5159, 5450, 877, 6602, 3355, 3952, 8597, 5923, 6237, 3090, 1664, 7894, 2545, 6675, 8103, 5424, 1505, 4025, 4429, 4420, 8448, 6527, 2576, 3257, 5183, 8554, 3467, 9366, 7706, 1995, 9417, 4061, 4678, 9828, 9684, 8534, 1171, 7171, 9672, 4300, 3967, 9784, 7340, 5037, 6322, 8011, 6534, 4980, 6743, 214, 3423, 4426, 8946, 2858, 3085, 4692, 5840, 257, 7057, 6379, 9450, 917, 6360, 6983, 7819, 5426, 3787, 8736, 9983, 5822, 9624, 4795, 4185, 8485, 907, 3645, 2571, 4915, 9001, 7628, 2215, 4442, 5971, 1755, 3501, 7198, 3694, 4719, 5918, 5310, 9436, 9437, 7187, 3290, 8345, 5364, 7720, 8938, 8733, 8868, 8835, 3314, 3327, 8390, 763, 413, 7101, 9767, 9057, 9755, 6776, 9327, 6551, 4134, 4065, 7223, 8605, 9371, 9154, 4249, 9817, 3582, 3820, 4244, 5204, 4154, 5173, 5935, 781, 2163, 4488, 3914, 7891, 5676, 685, 1996, 5271, 264, 411, 7462, 9386, 6320, 5753, 4530, 5180, 3195, 4494, 2138, 2835, 8789, 10, 7513, 9520, 6673, 8611, 3588, 2526, 3045, 7160, 8927, 4124, 4116, 4273, 5442, 8867, 6279, 1090, 1767, 1702, 9127, 258, 9690, 113, 4360, 2933, 3703, 3736, 9248, 8379, 1476, 9101, 5857, 9368, 1343, 8856, 4673, 1017, 9662, 4064, 353, 510, 97, 291, 366, 5883, 3484, 9246, 6506, 7201, 4295, 2996, 4330, 1447, 5130, 671, 5082, 5798, 4405, 4107, 4672, 8169, 6045, 848, 1185, 3876, 280, 2447, 8641, 248, 5059, 7763, 806, 8204, 8066, 2377, 7799, 6417, 5073, 13, 3261, 5716, 1904, 3310, 2976, 8892, 8510, 8464, 306, 448, 182, 6987, 8667, 2940, 6889, 2064, 2486, 3005, 955, 2357, 2142, 6007, 5690, 7957, 5652, 6394, 71, 61, 5089, 8360, 4470, 901, 8308, 2240, 5098, 5187, 175, 4071, 3150, 5085, 9028, 967, 6731, 7584, 2124, 6426, 2170, 9111, 3864, 1070, 5052, 4949, 9992, 2206, 9840, 6307, 2444, 9027, 7370, 4745, 8219, 3275, 1133, 2733, 9392, 9148, 2435, 9202, 6773, 8338, 6616, 9913, 205, 3732, 7000, 6626, 9637, 7619, 5877, 2516, 6159, 9629, 148, 2371, 6252, 6603, 3500, 4263, 9353, 2477, 931, 7927, 797, 4739, 8488, 2318, 4663, 6682, 7009, 9000, 793, 9014, 54, 637, 7313, 7055, 2923, 2, 6435, 5967, 5315, 7465, 6839, 8392, 3845, 9168, 5710, 4177, 7063, 7476, 1438, 9009, 5142, 5068, 339, 1068, 2788, 8577, 196, 4478, 294, 6690, 1194, 7424, 4529, 359, 2361, 7038, 2169, 1993, 4766, 5372, 4122, 9317, 491, 5765, 2102, 255, 5027, 2397, 9794, 3613, 1753, 5979, 1797, 6764, 5160, 4203, 2689, 2529, 3444, 7445, 4764, 3700, 811, 3811, 4911, 3940, 561, 4721, 9035, 7049, 2592, 2281, 4728, 313, 8270, 4547, 7156, 8547, 9204, 7377, 3496, 3965, 433, 2183, 10000, 3647, 897, 3439, 3386, 3936, 4618, 2374, 4194, 4752, 87, 3134, 1449, 7282, 9785, 9146, 6055, 7166, 8418, 4612, 7358, 3383, 817, 3719, 9137, 972, 6063, 8162, 2474, 7812, 8073, 4344, 935, 5391, 5598, 2769, 7210, 1019, 5982, 4677, 4190, 2267, 1520, 6695, 6601, 8100, 657, 6189, 8059, 2838, 225, 9275, 220, 5021, 599, 3320, 4818, 3609, 4871, 3982, 8147, 197, 9943, 4104, 7501, 4304, 5319, 8387, 6545, 7449, 4012, 4781, 4709, 277, 6517, 9284, 4893, 722, 3809, 4365, 8340, 473, 9930, 4783, 1078, 2781, 1747, 9230, 118, 3059, 3434, 810, 6893, 6789, 5902, 5627, 553, 5300, 5811, 3489, 5311, 4476, 8851, 4687, 7586, 6131, 6344, 2574, 9094, 1592, 8074, 5692, 5989, 3125, 3399, 5363, 9481, 4780, 4125, 8361, 457, 2455, 1798, 7958, 5872, 7043, 1689, 5995, 585, 5407, 7047, 8777, 8803, 132, 6870, 7194, 7556, 2176, 6283, 3589, 650, 3115, 1388, 2675, 293, 4334, 1548, 4086, 5727, 6857, 9322, 9045, 8186, 3973, 3525, 6130, 9240, 1891, 9754, 9459, 1106, 2449, 4900, 7511, 3083, 5376, 3303, 7996, 8466, 960, 7299, 627, 4569, 5733, 1953, 4239, 6817, 3102, 3325, 2278, 6255, 7353, 4676, 3023, 6382, 4441, 635, 2168, 4986, 1139, 4318, 1151, 4731, 6051, 5749, 4325, 9081, 1586, 8996, 9263, 2313, 9761, 2219, 3770, 6625, 3631, 86, 2983, 2936, 4608, 6072, 6967, 1128, 735, 5875, 809, 9865, 7676, 190, 933, 2946, 8589, 3019, 5985, 4336, 3494, 6371, 5613, 9833, 9488, 4732, 1902, 4757, 6832, 9907, 6607, 6644, 1763, 7426, 6182, 2013, 6811, 4152, 4558, 5164, 7124, 6805, 928, 8034, 2676, 9838, 1766, 4167, 8833, 5217, 9039, 6145, 3885, 1103, 6513, 3404, 3781, 1655, 9889, 4390, 6336, 5747, 5362, 5937, 6522, 6246, 2633, 9374, 1244, 7679, 6173, 778, 1682, 511, 2935, 6783, 2275, 521, 1643, 8060, 9383, 9919, 8909, 8375, 5671, 9157, 7694, 5459, 8820, 9830, 1218, 8786, 91, 6150, 4099, 3270, 6149, 8283, 5229, 5458, 4862, 2825, 658, 9474, 8963, 8583, 2796, 3854, 7489, 7252, 5401, 2061, 4733, 4014, 579, 8431, 8557, 7858, 407, 1609, 2475, 544, 5854, 3724, 692, 1340, 946, 8468, 1915, 3364, 5868, 9511, 4928, 4820, 7103, 2821, 8437, 8347, 8549, 6178, 5819, 3259, 1243, 3764, 2973, 2569, 2554, 8812, 2585, 5851, 9691, 1939, 3216, 7159, 9473, 8899, 9448, 6468, 2540, 2147, 8657, 7024, 5072, 455, 7654, 7147, 6447, 7608, 1874, 7227, 9657, 1580, 6973, 6333, 4257, 7280, 2471, 7301, 9976, 4222, 8929, 315, 2765, 7886, 1351, 851, 9364, 8357, 1366, 90, 6936, 5842, 1207, 1912, 9486, 9176, 7754, 6347, 1454, 3426, 8568, 2347, 2298, 2893, 195, 2229, 3995, 7889, 8106, 4009, 1545, 6935, 4606, 8223, 1201, 1113, 95, 247, 1596, 803, 3145, 4655, 9783, 6642, 3937, 188, 5939, 9334, 7954, 8712, 1255, 7022, 1864, 8686, 6386, 2612, 461, 4001, 2801, 6262, 9414, 4977, 4521, 5399, 8652, 308, 4840, 9030, 6564, 6710, 1406, 9504, 524, 9600, 8793, 401, 535, 9703, 2223, 6049, 11, 4929, 3220, 6459, 8980, 5474, 1174, 42, 6088, 9221, 8814, 121, 2900, 5287, 3789, 2463, 9186, 4734, 3955, 4865, 834, 6948, 3014, 1203, 3066, 8183, 3429, 7001, 5219, 2725, 6031, 6463, 6184, 1964, 1660, 5541, 9605, 7321, 725, 3743, 5228, 6345, 9116, 6546, 9215, 2776, 1254, 2624, 3204, 5914, 6485, 8069, 2391, 8188, 7724, 9878, 2607, 3391, 8813, 5375, 5379, 6529, 4685, 333, 9807, 1052, 8486, 7339, 3801, 8559, 679, 6648, 3487, 5895, 5653, 8271, 1775, 2894, 7102, 1815, 6168, 644, 17, 5203, 7441, 3450, 2683, 4186, 993, 5255, 3200, 5288, 2795, 4051, 3232, 5003, 6674, 6663, 541, 944, 2036, 1297, 6224, 8958, 5017, 9935, 422, 4207, 6497, 7995, 2324, 7807, 2261, 2851, 3449, 6960, 1703, 4252, 2854, 5615, 2982, 372, 6552, 9036, 5133, 7914, 4450, 7994, 669, 9485, 2001, 5725, 342, 5921, 5579, 8415, 7342, 9470, 5469, 1011, 7035, 8193, 9259, 3890, 8164, 7414, 2747, 3381, 4255, 2816, 9199, 8659, 4519, 5100, 496, 5353, 1114, 2119, 4338, 7267, 6456, 893, 9131, 4118, 3879, 7146, 4143, 3649, 4525, 3152, 3512, 2834, 23, 1460, 6303, 6401, 7947, 1615, 3346, 3069, 415, 1491, 5599, 8844, 8314, 1539, 9228, 2068, 7437, 2356, 677, 4936, 3250, 8913, 3248, 2528, 8075, 269, 3639, 9882, 887, 3793, 5774, 1181, 7254, 639, 9909, 5191, 1294, 478, 7258, 9182, 4715, 2860, 1920, 5659, 226, 6940, 1014, 7337, 4434, 6867, 5780, 9576, 9845, 9405, 6629, 6339, 2942, 4969, 1575, 3515, 8876, 2809, 7062, 7480, 9953, 8200, 1332, 7980, 3034, 726, 1246, 7026, 6797, 7402, 7468, 6919, 5253, 2067, 4223, 3448, 4437, 4934, 3211, 7606, 5813, 8767, 8143, 1948, 9316, 2499, 7543, 1662, 3654, 1857, 109, 2791, 6326, 2789, 844, 628, 7535, 5519, 7236, 1990, 9038, 9130, 3618, 5482, 8216, 5199, 2368, 8290, 8743, 1983, 772, 4218, 3344, 2623, 6739, 5062, 9360, 1164, 8263, 968, 611, 5172, 9932, 8153, 143, 4021, 8035, 7620, 8701, 1554, 3175, 5897, 9401, 8277, 3432, 9843, 9941, 2311, 9910, 3568, 8273, 6298, 610, 6998, 3673, 7604, 8294, 4371, 654, 6740, 5143, 9319, 2524, 9790, 8505, 5525, 4751, 4427, 7851, 678, 6148, 5701, 4876, 4748, 8948, 7634, 7670, 8255, 782, 8721, 2059, 1372, 8532, 8704, 8709, 2520, 1116, 717, 28, 4784, 740, 9379, 9615, 6836, 1093, 7155, 4269, 6830, 9922, 1313, 74, 6677, 1420, 552, 1853, 2565, 4418, 0, 2305, 4032, 7610, 3339, 9226, 1468, 3565, 7818, 8463, 9950, 6715, 603, 8826, 981, 2748, 3469, 9174, 6761, 2744, 429, 8645, 2398, 3792, 8182, 1836, 9635, 7549, 3225, 240, 7482, 4452, 1225, 8410, 3240, 2852, 3902, 2401, 3062, 1962, 108, 2034, 88, 8555, 5614, 3708, 6397, 2674, 3786, 8397, 7028, 1241, 930, 2724, 4037, 5238, 3858, 6087, 584, 4798, 7862, 7872, 2150, 6620, 7758, 3461, 3361, 3388, 6504, 1125, 9549, 4868, 4579, 4909, 6490, 6848, 921, 1159, 2760, 6099, 9903, 5728, 4610, 8883, 5354, 5486, 6346, 1646, 3834, 7334, 4790, 6361, 2697, 4512, 6192, 204, 8873, 3532, 5507, 6703, 5759, 2879, 4115, 6367, 420, 705, 3279, 2802, 5132, 1316, 8906, 9744, 2813, 7284, 8903, 3912, 7493, 2058, 5263, 7866, 7757, 8248, 864, 9296, 1569, 3691, 651, 555, 1576, 891, 7113, 2991, 5326, 7825, 3827, 4574, 8578, 8413, 5121, 5196, 4202, 7504, 2803, 2016, 7452, 2664, 9190, 3060, 1403, 4875, 6610, 2337, 137, 1713, 9990, 9342, 4674, 1992, 5685, 8834, 8212, 7521, 4301, 2601, 3540, 988, 8517, 5144, 3249, 898, 2895, 7260, 8482, 6106, 8462, 5235, 1260, 6852, 5137, 4693, 3313, 9753, 1206, 9674, 5583, 6395, 6558, 9730, 1571, 4024, 7413, 1205, 6901, 2999, 4603, 7381, 274, 5852, 9581, 5381, 8540, 1182, 2091, 4046, 2054, 8631, 2896, 9627, 5623, 4262, 2099, 4989, 1525, 3421, 1277, 9421, 3189, 1642, 9868, 2161, 337, 1485, 289, 1112, 4292, 1276, 2763, 902, 5365, 4357, 7611, 7984, 284, 486, 3235, 7856, 7617, 1064, 5009, 1317, 2957, 5494, 2512, 905, 3455, 1512, 8465, 2568, 5175, 6083, 2039, 7478, 528, 9607, 9749, 6280, 977, 7748, 1440, 8742, 7798, 3959, 7486, 2221, 4, 224, 9298, 3237, 3661, 4555, 6461, 397, 7365, 4509, 9308, 3374, 822, 9427, 8256, 6599, 942, 9771, 7581, 6719, 7229, 7081, 8830, 2953, 8367, 6951, 2293, 2264, 2214, 2073, 5528, 5772, 2497, 9449, 2527, 6798, 842, 3653, 4581, 9594, 6430, 8400, 2080, 4008, 6001, 5483, 2759, 6108, 9536, 6289, 388, 5194, 4589, 1318, 6121, 1083, 6002, 6328, 6999, 9394, 2531, 9252, 3509, 6419, 6540, 9453, 4068, 406, 4493, 1924, 7880, 4265, 5515, 1975, 8343, 1210, 4233, 9409, 8979, 8318, 6473, 8590, 9178, 6097, 5881, 6337, 9217, 7030, 3682, 374, 6081, 586, 721, 9583, 8181, 4123, 1072, 7133, 6044, 8208, 3705, 7064, 3202, 4825, 2949, 743, 7165, 8262, 6639, 3998, 3909, 3821, 141, 9153, 4413, 9021, 7066, 6757, 8647, 5594, 3474, 3692, 2807, 7695, 2012, 3004, 9079, 6270, 9545, 6384, 5028, 1149, 5637, 1943, 8372, 6920, 6728, 5418, 7939, 321, 8784, 9991, 5220, 3977, 9285, 8414, 2373, 2211, 4642, 8333, 780, 6849, 513, 436, 7491, 8278, 8628, 3506, 5679, 5760, 4159, 4869, 8234, 8434, 5293, 8384, 4087, 8610, 2063, 9572, 6194, 4091, 5020, 3519, 9464, 3174, 5332, 2259, 4697, 7407, 739, 8601, 8810, 9454, 9826, 3116, 5490, 600, 2910, 3865, 9841, 9487, 8917, 8518, 7658, 6742, 2409, 187, 8156, 5197, 1750, 5370, 5544, 238, 8057, 4075, 2321, 9306, 3430, 2327, 2772, 5398, 5795, 6064, 6526, 2148, 6651, 9156, 5654, 8178, 1077, 1307, 9431, 1104, 210, 3628, 2145, 9060, 3813, 5317, 7931, 5884, 5473, 7507, 8244, 8516, 504, 5111, 3495, 568, 5719, 394, 1740, 573, 6025, 453, 408, 3442, 6587, 2097, 8819, 8131, 8088, 3626, 2609, 6327, 2453, 3550, 8994, 2487, 5350, 3520, 7516, 4311, 8608, 8685, 8951, 2126, 1605, 538, 4384, 5928, 1099, 7940, 6452, 1663, 5762, 8370, 2506, 1045, 7405, 3554, 9775, 9066, 6032, 2671, 9708, 5018, 9570, 9192, 6137, 7106, 7116, 6388, 5264, 6713, 2410, 1941, 3815, 2078, 7417, 1402, 2133, 8617, 1515, 4414, 512, 1415, 2582, 8594, 9578, 6525, 6220, 6161, 6662, 1793, 1909, 7778, 7650, 6672, 4370, 6450, 7105, 2274, 7099, 440, 5557, 1910, 4940, 3158, 6043, 9987, 1198, 4472, 4591, 5063, 3803, 5266, 5323, 2519, 4952, 7558, 2596, 4998, 4860, 6702, 4971, 5965, 8265, 7436, 112, 6048, 7297, 6364, 1044, 8197, 7289, 2339, 3366, 4716, 1675, 344, 899, 7152, 2040, 7691, 9311, 8417, 5396, 7568, 6244, 9055, 8711, 7911, 6129, 6420, 4238, 2625, 5105, 5655, 5661, 7871, 7829, 8078, 7909, 89, 2269, 6718, 3264, 3608, 4297, 1451, 3466, 6635, 6864, 2677, 8419, 3975, 6471, 559, 6219, 1927, 7451, 7693, 66, 4278, 4463, 9122, 7114, 4497, 6213, 2389, 7860, 8695, 1348, 5581, 9008, 1377, 81, 9851, 55, 9299, 9550, 8224, 4261, 4337, 6415, 8616, 7964, 1414, 2837, 6052, 9890, 3662, 6751, 3765, 7077, 2266, 6932, 8173, 4634, 5245, 1457, 2032, 4103, 3419, 3304, 3385, 9710, 6585, 4067, 327, 1989, 9694, 6974, 3006, 7696, 888, 5081, 8984, 3227, 7597, 1097, 2653, 1627, 2938, 9466, 6404, 6056, 3927, 7360, 7406, 7967, 8441, 9939, 7627, 4421, 1581, 9780, 9344, 9390, 5828, 7183, 6747, 578, 4286, 400, 7631, 211, 9110, 6928, 871, 3536, 7727, 5689, 3567, 7687, 7048, 1544, 4737, 9282, 1970, 9853, 3182, 5612, 5352, 7464, 4946, 7271, 5305, 2836, 3867, 4666, 9445, 4850, 892, 4267, 7800, 2952, 434, 766, 7552, 706, 9685, 9693, 9162, 4169, 7982, 4735, 3153, 8163, 9169, 1958, 2501, 4102, 9126, 1015, 6541, 2156, 5909, 670, 5938, 1683, 1195, 643, 7643, 8627, 6223, 8750, 3931, 5281, 9058, 7239, 2258, 7809, 1851, 9384, 8429, 6318, 3428, 4312, 4901, 3621, 7785, 6641, 4131, 3269, 3341, 9499, 5832, 9210, 7034, 7817, 8211, 5767, 8621, 3051, 8956, 2542, 2186, 1115, 7399, 9994, 3658, 8180, 2241, 3472, 3382, 9236, 596, 3117, 4526, 1738, 5421, 9158, 1897, 316, 3938, 347, 7226, 357, 3861, 3475, 1202, 2537, 4696, 2892, 2392, 3606, 6706, 5678, 8887, 1929, 6082, 3580, 9283, 4729, 4511, 748, 4416, 8799, 5056, 808, 9547, 8560, 2024, 3775, 1799, 2779, 758, 4785, 5409, 9548, 1533, 4927, 3679, 2050, 8572, 5576, 2213, 9846, 8762, 997, 2778, 9367, 4538, 8934, 2857, 4937, 730, 4003, 9287, 1168, 8332, 7190, 9642, 1465, 7575, 4093, 4411, 7120, 5530, 2735, 4474, 8038, 8176, 4599, 5248, 6341, 6156, 2116, 6737, 3946, 5626, 1242, 3231, 3267, 3875, 6796, 7397, 8691, 4038, 969, 1999, 2557, 4253, 2007, 9652, 3860, 3518, 7023, 1239, 7027, 6489, 9777, 3243, 7544, 8959, 6023, 5527, 4954, 7443, 1932, 3058, 7497, 4843, 2842, 9124, 3587, 3633, 1385, 3376, 7265, 8303, 403, 9977, 7810, 4744, 9460, 207, 158, 273, 3163, 4496, 3402, 3619, 8424, 6887, 5156, 6228, 710, 412, 954, 9539, 7499, 5829, 7773, 2427, 6899, 1034, 2289, 3395, 7722, 4004, 8440, 6665, 9610, 8829, 2456, 9398, 8085, 6029, 9702, 859, 2977, 4834, 6771, 3877, 367, 1039, 1613, 7456, 1804, 1086, 4160, 5818, 2309, 7732, 8326, 8800, 8507, 5147, 1549, 8907, 7514, 619, 3791, 65, 4563, 3106, 5321, 4333, 6721, 466, 8337, 3427, 4373, 6267, 159, 9608, 829, 3271, 8999, 3326, 3591, 7987, 2737, 571, 424, 8433, 6309, 8837, 6139, 764, 285, 8281, 1551, 6686, 5476, 9942, 9274, 9714, 9140, 4639, 7192, 5629, 8891, 5054, 1383, 7366, 5012, 6013, 330, 5757, 5422, 5858, 146, 84, 2934, 752, 520, 6402, 6646, 6966, 8553, 5065, 6988, 6537, 1154, 2993, 1771, 3735, 7659, 9173, 1955, 9207, 8198, 5336, 6377, 6205, 5333, 2135, 7481, 3804, 1917, 8111, 8845, 3777, 7505, 4395, 7592, 8734, 341, 279, 9358, 6414, 846, 516, 2961, 3176, 7291, 5625, 7573, 3715, 3905, 1526, 9331, 9012, 9918, 2260, 7565, 3306, 7559, 3359, 5969, 7427, 7618, 1541, 8264, 7416, 2367, 543, 4824, 883, 8225, 3054, 8622, 2898, 966, 3107, 2065, 9063, 5919, 8108, 4867, 2245, 3149, 7285, 1013, 9832, 6569, 1033, 5010, 2439, 7082, 427, 4779, 4712, 5467, 4983, 6376, 4069, 5423, 1552, 1707, 1004, 3593, 8561, 2794, 9824, 4829, 8975, 2461, 2157, 5708, 7372, 4097, 6659, 4541, 7716, 7572, 1831, 9469, 1503, 2847, 8342, 7950, 4935, 4787, 2027, 8796, 3759, 6717, 1998, 3918, 3470, 8738, 9253, 855, 2152, 6744, 1429, 1654, 6493, 2263, 6618, 2662, 8072, 3191, 150, 7794, 8752, 3632, 5950, 1960, 8138, 1311, 2212, 9249, 9155, 3984, 1062, 3441, 9884, 7395, 5406, 2855, 263, 2053, 7314, 4105, 1979, 6760, 2390, 602, 1616, 6154, 1327, 144, 575, 738, 3181, 6248, 2125, 8556, 832, 2865, 9727, 9982, 3332, 3288, 8284, 2974, 6400, 8243, 6163, 6944, 7599, 5148, 7647, 8607, 4052, 22, 1530, 7264, 6191, 9109, 8930, 5934, 655, 6736, 5335, 2964, 6874, 9406, 2943, 1883, 5416, 6086, 6433, 4313, 9106, 527, 9806, 9018, 1478, 802, 4339, 9337, 8257, 69, 3497, 260, 1265, 6650, 1448, 383, 218, 6230, 5213, 3929, 6022, 8852, 3641, 4910, 8033, 9707, 8537, 8004, 9746, 9681, 3357, 6727, 3627, 9861, 3925, 3850, 3947, 8521, 6589, 3963, 3763, 7788, 3462, 2473, 7729, 4641, 7440, 4088, 6499, 3401, 2978, 7088, 9537, 1137, 8065, 6458, 9641, 1293, 9461, 980, 2513, 3651, 7733, 696, 8090, 6696, 9011, 2273, 3340, 3398, 320, 1129, 6824, 1193, 8576, 6260, 6502, 6353, 2362, 5498, 8356, 9606, 3868, 532, 8385, 5433, 6866, 6734, 7934, 4034, 7542, 4681, 5802, 3446, 6509, 7772, 4112, 1483, 9004, 1821, 9040, 8666, 8726, 5571, 2959, 7821, 6922, 9171, 1119, 4978, 7017, 4756, 2832, 5155, 6200, 1742, 501, 6315, 4179, 2310, 9880, 5741, 699, 2233, 7986, 8494, 3714, 5665, 6440, 1878, 7612, 1352, 3828, 656, 2236, 6622, 7502, 6596, 5462, 3178, 8860, 2445, 1299, 8206, 7428, 3179, 1980, 1282, 4327, 167, 1711, 5206, 3978, 2331, 2359, 9442, 9072, 6466, 62, 4597, 2166, 8838, 6501, 4562, 8046, 4058, 1367, 395, 5107, 1838, 9632, 9354, 5713, 6842, 661, 5256, 9510, 7952, 1807, 9017, 911, 1822, 6428, 1091, 1687, 9492, 3114, 8924, 7522, 5079, 8998, 8129, 8079, 3527, 1625, 3578, 8017, 5251, 7256, 598, 2756, 1850, 8988, 5880, 48, 6809, 6123, 7071, 12, 7776, 41, 4072, 9732, 8688, 2853, 4827, 5867, 8056, 5212, 8569, 4816, 4607, 4345, 4806, 5707, 3096, 1261, 1994, 5481, 5200, 1665, 8472, 6176, 1744, 4942, 7195, 6455, 1300, 1396, 3784, 1219, 9495, 9272, 9812, 3223, 1865, 5891, 6904, 3302, 5192, 6977, 4517, 8902, 8233, 3026, 6207, 6232, 3443, 6691, 3750, 5069, 1199, 9128, 5768, 3903, 1751, 5951, 3638, 4367, 8423, 2192, 3112, 9776, 170, 1509, 6520, 3521, 2342, 5658, 6759, 2353, 5040, 4308, 2901, 5663, 1200, 7219, 3093, 5441, 9665, 9981, 7278, 234, 5777, 1933, 9521, 32, 3177, 2586, 9552, 5356, 756, 5104, 6335, 3585, 3599, 8174, 4577, 9270, 4381, 7294, 8882, 9631, 8364, 5534, 9196, 7412, 2188, 5505, 302, 1741, 421, 1863, 7920, 9689, 9915, 8117, 9546, 9007, 4542, 7447, 3030, 9562, 5672, 8135, 8598, 8997, 8588, 8694, 9927, 1634, 8818, 4726, 2225, 9529, 3830, 1163, 7033, 4747, 8683, 6201, 5051, 2179, 4611, 3022, 2643, 360, 6171, 8952, 9673, 8650, 2819, 687, 1172, 7044, 6925, 2385, 4740, 1871, 719, 663, 2077, 3718, 5267, 5318, 7061, 6409, 3623, 479, 1486, 2175, 2394, 2466, 4387, 873, 8722, 6903, 7500, 1156, 2341, 4485, 4701, 8749, 7609, 7336, 529, 9901, 731, 3899, 3761, 1934, 1892, 2672, 6174, 6725, 9887, 6689, 4972, 4556, 626, 1148, 7207, 3575, 1337, 8296, 8232, 4302, 6467, 5990, 1584, 8095, 523, 6921, 5337, 1287, 6436, 8442, 6203, 6263, 8089, 8137, 8495, 5955, 7648, 418, 3799, 5841, 4445, 7908, 3950, 9333, 3586, 4498, 3539, 1266, 6829, 1084, 6109, 5058, 6812, 93, 2692, 3040, 4580, 272, 8382, 3044, 5878, 5177, 3329, 1223, 3622, 7983, 7317, 3064, 1709, 3206, 3917, 6767, 4200, 5901, 5636, 1819, 9256, 4762, 307, 5074, 6113, 4804, 3755, 2395, 8676, 2336, 2210, 4254, 1649, 7224, 9291, 3508, 4774, 5764, 1783, 1651, 4473, 2228, 7350, 8401, 3032, 6478, 5735, 9886, 9821, 530, 537, 3297, 4965, 1889, 7702, 51, 151, 5070, 134, 4572, 9779, 8199, 3018, 2243, 9020, 2301, 3132, 5394, 4587, 9814, 8530, 1214, 3981, 2094, 3723, 7847, 2859, 6883, 5684, 3969, 5078, 3655, 6898, 27, 7942, 6008, 9808, 8205, 8928, 4228, 9345, 6580, 8729, 390, 9856, 3640, 104, 3052, 9377, 6699, 2753, 4098, 33, 5041, 2793, 959, 5660, 8775, 8898, 506, 1761, 239, 745, 3081, 2159, 8915, 8455, 7603, 2665, 3696, 6647, 7286, 2872, 5011, 6011, 2621, 1614, 449, 5272, 7846, 9897, 2562, 9269, 463, 3835, 5864, 4306, 8484, 9601, 8461, 3782, 8514, 5799, 1945, 2560, 9733, 7439, 9212, 1364, 3970, 549, 5775, 761, 8478, 3810, 1335, 7903, 5986, 8320, 3008, 8474, 4705, 6945, 2010, 6896, 1089, 417, 5378, 4156, 885, 9671, 8311, 3733, 7121, 3301, 2256, 8756, 7918, 863, 8620, 4684, 876, 9136, 6405, 4918, 7834, 4446, 8454, 1720, 4361, 4982, 6657, 4142, 6238, 1899, 1082, 2017, 7905, 497, 7067, 3180, 2786, 9227, 416, 8051, 1361, 5936, 1976, 7007, 5752, 9251, 5371, 9582, 7045, 2550, 9871, 7728, 8624, 2792, 5863, 3561, 7050, 2235, 5966, 3513, 3099, 2196, 9827, 9434, 7550, 8428, 3143, 2656, 1594, 8653, 2761, 9898, 485, 1922, 514, 7004, 221, 7752, 5007, 4148, 6373, 3262, 7705, 624, 5874, 7923, 1, 2304, 6632, 5506, 9180, 5454, 9143, 5227, 3542, 2505, 7378, 15, 4886, 9061, 4817, 1492, 1756, 1022, 2710, 1521, 1779, 5331, 3213, 9949, 6652, 7956, 6446, 319, 3226, 4128, 2462, 6091, 2288, 3407, 734, 1060, 7032, 4864, 5562, 2100, 6146, 9971, 5210, 8128, 5651, 4070, 771, 8968, 715, 3289, 3239, 3493, 9132, 8298, 8220, 2848, 6975, 3473, 9091, 1764, 9257, 7369, 1422, 9172, 6133, 6427, 1705, 4813, 9815, 3887, 5464, 1444, 6316, 2436, 3476, 2101, 6310, 5906, 4622, 7924, 6235, 3293, 5420, 3534, 4039, 44, 2026, 6122, 3808, 4341, 229, 2782, 140, 6000, 331, 8452, 5973, 6621, 5831, 8806, 2669, 645, 2151, 8020, 2521, 5870, 5108, 7442, 2408, 9222, 836, 7174, 9585, 4217, 5975, 3667, 7843, 1773, 8191, 6096, 7755, 1849, 9558, 5030, 982, 8213, 7635, 3949, 301, 3671, 3522, 8116, 5556, 5619, 2806, 8335, 5216, 7011, 1595, 7678, 7347, 2416, 6274, 9184, 963, 7787, 5980, 835, 1079, 6902, 5600, 8403, 7053, 9597, 2905, 856, 26, 660, 6221, 4549, 3356, 7512, 4537, 7708, 6514, 6890, 4181, 7875, 5404, 9857, 3451, 6465, 4372, 6907, 3007, 3283, 8449, 4235, 5161, 1578, 9351, 3900, 9183, 6953, 7991, 1252, 6795, 3352, 6387, 4504, 3990, 4808, 332, 5046, 3928, 4457, 5810, 2018, 2351, 4960, 3893, 7747, 7243, 9839, 5131, 7555, 4906, 3038, 6780, 9640, 5427, 4258, 4773, 9013, 3721, 7902, 5976, 3961, 4449, 6709, 9512, 5002, 3624, 616, 2617, 454, 6895, 6481, 2883, 5905, 1506, 4215, 31, 1389, 3557, 3075, 6218, 6906, 6425, 1008, 2199, 6598, 4943, 4924, 8542, 7343, 7921, 9614, 5849, 1681, 9984, 6914, 7933, 5357, 1333, 6059, 1268, 7382, 5510, 2421, 5821, 7132, 2823, 8480, 8919, 9747, 1577, 4130, 949, 4917, 2120, 7122, 4106, 1796, 889, 841, 1504, 5900, 9505, 2785, 6369, 6370, 2602, 563, 8529, 1469, 1950, 4195, 1412, 1319, 8250, 5806, 3538, 8822, 1432, 328, 6272, 7742, 9715, 6664, 2536, 5592, 249, 2131, 9031, 536, 1529, 3985, 1253, 7713, 3675, 3135, 8122, 6363, 607, 9895, 8705, 2431, 5179, 7534, 9054, 1959, 7576, 2433, 9559, 4469, 5677, 5771, 4623, 7025, 6683, 3272, 7135, 6565, 1732, 1652, 4658, 5887, 7359, 371, 7699, 4812, 1495, 8648, 5675, 8663, 5595, 7641, 5548, 465, 414, 9268, 1007, 3465, 5803, 991, 3822, 7698, 2639, 5324, 2702, 1618, 1817, 2721, 2340, 5084, 1829, 9696, 1430, 1190, 3305, 729, 9412, 2514, 3242, 4898, 3078, 1147, 4323, 7095, 2372, 8618, 3138, 4089, 9874, 3983, 2343, 2742, 3319, 3853, 6330, 9866, 1534, 6913, 8831, 2771, 5385, 7666, 155, 7142, 6547, 7197, 4425, 1890, 2775, 1629, 7529, 9330, 2646, 6317, 7042, 9722, 6756, 1497, 5013, 3702, 4534, 1274, 6492, 2365, 1650, 9726, 2661, 474, 5138, 7269, 5249, 4571, 2428, 7859, 8042, 267, 8843, 3445, 3785, 5176, 3251, 4528, 6885, 9396, 9305, 7744, 7779, 805, 5322, 5014, 3127, 8481, 2701, 2941, 3350, 4888, 6253, 8439, 6918, 59, 807, 1499, 4232, 7630, 4905, 6225, 9639, 5697, 576, 6112, 8027, 9422, 6204, 6645, 7074, 5911, 8745, 6694, 3157, 2904, 4111, 1247, 8352, 1386, 9243, 8376, 4573, 6720, 6036, 3886, 2822, 8595, 432, 9616, 533, 8850, 9395, 5974, 4000, 8407, 2052, 3173, 3488, 3479, 3273, 8142, 4479, 6653, 4788, 8053, 2205, 5448, 8936, 7324, 5577, 9738, 1427, 6593, 3573, 8737, 2111, 2606, 4665, 8187, 7593, 1320, 8878, 2787, 7279, 4492, 3315, 8546, 1131, 9677, 6169, 790, 8058, 2700, 4028, 6445, 4002, 4637, 3993, 1723, 7943, 5274, 1111, 8279, 7069, 236, 4162, 6462, 7253, 7244, 9424, 3454, 6730, 5246, 1442, 7466, 3435, 9455, 7932, 5750, 4507, 4247, 5296, 4240, 6847, 7164, 2074, 2616, 8150, 8849, 7169, 2140, 5879, 1628, 5110, 6393, 3664, 6222, 652, 1610, 6071, 4861, 4844, 4358, 9071, 7885, 4518, 3490, 5809, 9556, 9972, 915, 3504, 3953, 3471, 4845, 8227, 8513, 7076, 8908, 7181, 7185, 5622, 7989, 5190, 1981, 6567, 6293, 8660, 2174, 2504, 8076, 6305, 8528, 1579, 6431, 8062, 8026, 9588, 3295, 1330, 7319, 3425, 1685, 3642, 6519, 8684, 8430, 5683, 4366, 6707, 2364, 1043, 9426, 9289, 8871, 3552, 4759, 2038, 3832, 4170, 9408, 8450, 2479, 5, 3772, 5374, 6323, 9428, 2800, 6801, 5395, 7503, 9380, 9864, 5314, 2000, 177, 8885, 5721, 916, 1832, 4084, 1144, 2696, 5754, 9200, 4516, 6053, 147, 9206, 2660, 7665, 8573, 3123, 2338, 9416, 2393, 5961, 792, 2515, 2172, 4613, 5518, 9863, 8766, 4042, 4720, 4654, 8275, 7863, 7721, 7177, 6258, 6575, 4119, 7208, 8146, 9849, 1234, 2144, 932, 8840, 1875, 8118, 6964, 1677, 7080, 7189, 369, 9346, 5086, 3298, 9077, 5978, 9267, 7899, 7140, 8259, 3634, 1306, 5284, 2400, 7878, 4609, 6859, 929, 6074, 389, 9276, 1790, 9123, 9119, 7540, 1599, 6886, 4531, 7703, 7520, 7861, 5493, 7530, 7680, 9438, 7212, 5485, 8394, 4208, 1473, 4013, 2464, 6349, 7528, 770, 398, 6115, 9859, 913, 3343, 2121, 2584, 633, 6084, 7783, 3278, 4896, 6275, 9048, 560, 9349, 9476, 769, 8325, 4279, 6256, 4837, 2534, 9595, 874, 6536, 2507, 6399, 7537, 1436, 9737, 3553, 4006, 3247, 1637, 7893, 8604, 5415, 9745, 1882, 7221, 3741, 8201, 918, 8881, 2242, 4636, 9551, 5587, 3767, 7605, 5240, 4213, 9822, 5582, 2217, 4644, 965, 1748, 4459, 7587, 6511, 7311, 8728, 5535, 1968, 174, 5711, 1040, 9638, 5497, 2216, 823, 4044, 8884, 4349, 7697, 1322, 2745, 14, 4029, 7349, 1795, 6006, 9399, 6215, 5094, 7845, 7255, 7879, 839, 304, 3935, 3883, 1566, 6825, 6098, 4625, 2325, 4399, 8586, 299, 9705, 3307, 6614, 4819, 9415, 9612, 7786, 5553, 5165, 6879, 7039, 594, 9254, 9620, 733, 325, 8918, 7006, 9628, 4545, 5417, 2685, 2043, 612, 534, 1673, 8558, 4375, 5285, 6943, 7479, 5794, 2717, 3345, 649, 2118, 3409, 2975, 9904, 9188, 1271, 2770, 4698, 6930, 7167, 7204, 827, 6418, 595, 6355, 4602, 1856, 4932, 3802, 1725, 925, 9603, 6518, 2177, 8310, 1345, 8671, 7126, 4436, 5294, 974, 2862, 7390, 8932, 499, 5402, 8615, 6897, 3546, 198, 7217, 4821, 3544, 8498, 6160, 1063, 3070, 8221, 4527, 1452, 9877, 5694, 1611, 8094, 4616, 9630, 1024, 4082, 8036, 494, 4376, 295, 5188, 9501, 3280, 7078, 8625, 3545, 1291, 3256, 5504, 9825, 5871, 8239, 4994, 3103, 7218, 5106, 2129, 1978, 2079, 2997, 4433, 409, 9015, 5993, 3330, 6669, 7326, 4385, 2704, 1283, 1009, 3055, 4754, 1872, 7205, 8592, 9645, 470, 7715, 2450, 5047, 2149, 5380, 8763, 6407, 393, 2158, 9968, 1678, 1191, 3292, 8702, 8857, 1289, 9400, 4793, 6833, 581, 2920, 2967, 8523, 983, 6012, 8770, 4643, 2726, 2695, 5890, 1557, 2130, 3151, 1094, 5495, 7310, 8896, 9528, 4348, 2307, 4533, 1409, 9161, 1612, 4584, 1006, 6714, 5681, 7904, 5184, 5514, 2187, 1679, 8447, 3387, 2541, 7059, 3960, 8700, 2300, 6185, 4851, 120, 2194, 7094, 623, 160, 6923, 9260, 472, 1911, 7418, 881, 1550, 9037, 139, 986, 7261, 1329, 5724, 3933, 1167, 6856, 5815, 8184, 5838, 2412, 3394, 9074, 164, 9574, 2846, 4839, 8230, 216, 1493, 2478, 9507, 8236, 9310, 7168, 6617, 2270, 3379, 3615, 7262, 7822, 490, 3769, 208, 3389, 7430, 8665, 1472, 6421, 703, 5360, 4645, 3111, 3207, 9569, 2909, 8047, 1593, 4957, 3492, 2137, 5763, 830, 591, 6120, 1026, 3068, 8771, 1100, 8562, 7595, 1120, 5712, 7981, 8306, 6092, 2532, 7624, 2640, 9724, 3309, 5449, 8203, 5001, 7718, 7625, 368, 1380, 2804, 5090, 2115, 8301, 5201, 7234, 5509, 5359, 5116, 1374, 3411, 6484, 7769, 5291, 1788, 590, 7712, 3375, 9757, 5770, 8506, 2780, 5242, 5670, 8817, 1567, 6494, 2517, 3734, 7789, 5501, 1455, 322, 8285, 2884, 7883, 7959, 2891, 707, 8114, 4800, 3187, 459, 9535, 9860, 1230, 7461, 7215, 5109, 9164, 6276, 1861, 5276, 7668, 1379, 6608, 3046, 3600, 2046, 5751, 9292, 2648, 8782, 4923, 9064, 774, 2438, 6210, 2539, 531, 213, 8099, 1155, 4694, 7937, 2122, 2746, 9917, 2989, 7238, 4984, 8023, 5273, 8954, 4540, 7178, 7554, 5127, 8677, 1401, 2686, 114, 3483, 9224, 9229, 9083, 9974, 1025, 7877, 9404, 3156, 9675, 3842, 8491, 1789, 4317, 7188, 6486, 3878, 1726, 1898, 9531, 8008, 222, 5609, 6503, 6880, 311, 1591, 4711, 7196, 1346, 3029, 4383, 8286, 8575, 7141, 8305, 5839, 2087, 8319, 2757, 6597, 1636, 5185, 9120, 243, 3932, 1285, 2184, 6877, 7475, 1765, 8031, 1003, 2979, 3796, 3668, 9497, 5734, 5638, 5843, 2773, 9205, 5162, 2090, 1659, 1376, 1630, 475, 6769, 2958, 8673, 4832, 1220, 9778, 6680, 3378, 2558, 154, 447, 1986, 2020, 6015, 4725, 3286, 452, 8758, 759, 1736, 9713, 4048, 9372, 5739, 1973, 8535, 3836, 4151, 4342, 5209, 558, 6754, 1229, 3369, 181, 7214, 8037, 8006, 3167, 1608, 1825, 6584, 8797, 9999, 8522, 8166, 6882, 9265, 8067, 786, 3602, 4184, 2566, 1056, 9193, 9175, 1238, 3318, 7176, 8021, 1481, 1399, 8933, 6080, 8124, 7925, 2844, 5958, 2004, 1067, 262, 4158, 9835, 5709, 8, 642, 3105, 9429, 3888, 5687, 970, 7335, 8804, 1946, 625, 2265, 3057, 6264, 5580, 2360, 6350, 4212, 5896, 7015, 515, 7228, 1824, 9273, 2268, 179, 4956, 1676, 9359, 4299, 884, 6840, 80, 1232, 8864, 1923, 8923, 8846, 6385, 6142, 6911, 4298, 7371, 6314, 7268, 8520, 3706, 7642, 4137, 6937, 8077, 3930, 3192, 4506, 172, 6785, 9819, 6888, 2113, 5034, 5570, 8444, 3805, 1498, 9432, 227, 3576, 8853, 4966, 4214};
    for (int item = 0; item < 10001; item++)
    {
        //bst.print(bst.root_);
        ASSERT_TRUE(bst.insert(insertList[item]))
    }
    for (int item = 0; item < 10001; item++)
    {
        //bst.print(bst.root_);
        ASSERT_TRUE(bst.remove(removeList[item]))
    }
    return true;
}

//======================================================================
//=========================== AVL Tree Test ============================
//======================================================================
string AVLTreeTest::getTestDescription(int test_num) {
    if (test_num < 1 || test_num > 6) { // check range.
        return "";
    }
    return test_description[test_num-1];
}

void AVLTreeTest::runAllTests() {
    test_result[0] = test1();
    test_result[1] = test2();
    test_result[2] = test3();
    test_result[3] = test4();
    test_result[4] = test5();
    test_result[5] = test6();
}

void AVLTreeTest::printReport() {
    cout << "  AVL TREE TEST RESULTS  \n"
         << " ^^^^^^^^^^^^^^^^^^^^^^^ \n";
    for (int idx = 0; idx < 6; ++idx) {
        cout << test_description[idx] << "\n  " << get_status_str(test_result[idx]) << endl << endl;
    }
    cout << endl;
}

// Test 1: Test single left rotation
bool AVLTreeTest::test1() {

    // Test set up.
    AVLTree avl;

    // Insert a some nodes into the tree in the following order.
    BinarySearchTree::DataType in[3] = {1, 2, 3};
    for (auto val : in) {
        ASSERT_TRUE(avl.insert(val))
    }

    // Check that a left rotation occurred.
    string expected_tree1 = "2 1 3";
    string tree_level_order1 = breadthFirstTraversal(avl.root_);
    ASSERT_TRUE(tree_level_order1.compare(expected_tree1) == 0)

    // Add additional nodes and check that another left rotation occurred.
    ASSERT_TRUE(avl.insert(7) && avl.insert(11))

    // Check the new tree representation.
    string expected_tree2 = "2 1 7 3 11";
    string tree_level_order2 = breadthFirstTraversal(avl.root_);
    ASSERT_TRUE(tree_level_order2.compare(expected_tree2) == 0)

    // Return true to signal all tests passed.
    return true;
}

// Test 2: Test single right rotation
bool AVLTreeTest::test2() {
    
    // Test set up.
    AVLTree avl;

    // Insert a some  nodes into the tree in the following order.
    BinarySearchTree::DataType in[3] = {7, 4, 1};
    for (auto val : in) {
        ASSERT_TRUE(avl.insert(val))
    }

    // Check that a right rotation occurred.
    string expected_tree1 = "4 1 7";
    string tree_level_order1 = breadthFirstTraversal(avl.root_);
    ASSERT_TRUE(tree_level_order1.compare(expected_tree1) == 0)

    // Add additional nodes and check that another right rotation occurred.
    ASSERT_TRUE(avl.insert(6) && avl.insert(5))

    // Check the new tree representation.
    string expected_tree2 = "4 1 6 5 7";
    string tree_level_order2 = breadthFirstTraversal(avl.root_);
    ASSERT_TRUE(tree_level_order2.compare(expected_tree2) == 0)

    // Return true to signal all tests passed.
    return true;
}

// Test 3: Test double left-right rotation
bool AVLTreeTest::test3() {

    // Test set up.
    AVLTree avl;

    // Insert a some  nodes into the tree in the following order.
    BinarySearchTree::DataType in[3] = {8, 1, 3};
    for (auto val : in) {
        ASSERT_TRUE(avl.insert(val))
    }

    // Check that a left-right rotation occurred.
    string expected_tree1 = "3 1 8";
    string tree_level_order1 = breadthFirstTraversal(avl.root_);
    ASSERT_TRUE(tree_level_order1.compare(expected_tree1) == 0)

    // Add additional nodes and check that another rotation occurred.
    ASSERT_TRUE(avl.insert(5) && avl.insert(6))

    // Check the new tree representation.
    string expected_tree2 = "3 1 6 5 8";
    string tree_level_order2 = breadthFirstTraversal(avl.root_);
    ASSERT_TRUE(tree_level_order2.compare(expected_tree2) == 0)

    // Return true to signal all tests passed.
    return true;
}

// Test 4: Test double right-left rotation
bool AVLTreeTest::test4() {
    
    // Test set up.
    AVLTree avl;

    // Insert a some  nodes into the tree in the following order.
    BinarySearchTree::DataType in[3] = {1, 7, 4};
    for (auto val : in) {
        ASSERT_TRUE(avl.insert(val))
    }

    // Check that a right-left rotation occurred.
    string expected_tree1 = "4 1 7";
    string tree_level_order1 = breadthFirstTraversal(avl.root_);
    ASSERT_TRUE(tree_level_order1.compare(expected_tree1) == 0)

    // Add additional nodes and check that another rotation occurred.
    ASSERT_TRUE(avl.insert(11) && avl.insert(9))

    // Check the new tree representation.
    string expected_tree2 = "4 1 9 7 11";
    string tree_level_order2 = breadthFirstTraversal(avl.root_);
    ASSERT_TRUE(tree_level_order2.compare(expected_tree2) == 0)

    // Return true to signal all tests passed.
    return true;
}

// Test 5: Test multiple rotations on insert
bool AVLTreeTest::test5() {

    // Test set up.
    AVLTree avl;

    // Insert a some  nodes into the tree in the following order.
    BinarySearchTree::DataType in[10] = {11, 15, 26, 87, 40, 82, 69, 21, 23, 42};
    for (auto val : in) {
        ASSERT_TRUE(avl.insert(val))
    }
    
    // Check the new tree representation.
    string expected_tree = "40 15 82 11 23 69 87 21 26 42";
    string tree_level_order = breadthFirstTraversal(avl.root_);
    ASSERT_TRUE(tree_level_order.compare(expected_tree) == 0)
    
    // Return true to signal all tests passed.
    return true;
}

// Test 6: Test multiple rotations on remove
bool AVLTreeTest::test6() {

    // Test set up.
    AVLTree avl;

    // Insert a some  nodes into the tree in the following order.
    BinarySearchTree::DataType in[10] = {11, 15, 26, 87, 40, 82, 69, 21, 23, 42};
    for (auto val : in) {
        ASSERT_TRUE(avl.insert(val))
    }

    // Try removing some nodes to see how the balance changes.
    ASSERT_TRUE(avl.remove(87))
    ASSERT_TRUE(avl.remove(82))
    ASSERT_TRUE(avl.remove(69))

    // Check the resulting tree.
    string expected_tree1 = "23 15 40 11 21 26 42";
    string tree_level_order1 = breadthFirstTraversal(avl.root_);
    ASSERT_TRUE(tree_level_order1.compare(expected_tree1) == 0)

    // Remove additional nodes.
    ASSERT_TRUE(avl.remove(11))
    ASSERT_TRUE(avl.remove(15))
    ASSERT_TRUE(avl.remove(21))

    // Check the resulting tree.
    string expected_tree2 = "40 23 42 26";
    string tree_level_order2 = breadthFirstTraversal(avl.root_);
    ASSERT_TRUE(tree_level_order2.compare(expected_tree2) == 0)

    // Remove the ``right sub-tree`` and force a left-right rotation.
    ASSERT_TRUE(avl.remove(42))
    string expected_tree3 = "26 23 40";
    string tree_level_order3 = breadthFirstTraversal(avl.root_);
    ASSERT_TRUE(tree_level_order3.compare(expected_tree3) == 0)

    // Remove the remaining nodes in the tree, causing the root node to change each time.
    ASSERT_TRUE(avl.remove(26))
    ASSERT_TRUE(avl.remove(23))
    ASSERT_TRUE(avl.remove(40))

    // Check that the tree is now empty.
    string expected_tree4 = "";
    string tree_level_order4 = breadthFirstTraversal(avl.root_);
    ASSERT_TRUE(tree_level_order4.compare(expected_tree4) == 0)

    // Return true to signal all tests passed.
    return true;
}