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⠠⠁⠌⡐⠄⡈⠰⠀⢄⢁⠂⡁⢊⠈⠌⡐⠀⠌⠒⢈⠠⢡⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠐⠀⠂⠄⠐⡀⠄⠐⡈⠠⠀⠀⠀⠀⠀⠀⠀⠑⢠⠉⠔⣈⠔⡡⠊⠤⠉⢂⠡⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠠⠀⠂⠀⠄⠀⡀ ⢀⠁⡂⢐⠠⢁⠂⢉⠀⢂⡐⠈⠄⠌⡐⠄⡉⠤⢉⠰⢈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠠⠐⠠⠐⡈⢄⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠂⢌⠒⡄⢊⠄⡑⠠⠁⠀⠀⠀⠀⠂⠈⠀⠀⠁⠀⠀⠈⠀⠀⠠⠀⠀⠂⠠⢈⠐⡀⠂⡁⠄⠂⠄ ⢀⠂⠌⡀⠂⡄⢈⠄⡈⠄⠠⢁⠌⢐⠠⢂⠐⡄⠢⢁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⡑⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢊⠰⡁⠒⠌⡐⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠐⠀⠁⠂⣆⢁⡒⠤⠘⡀⠂ ⠀⢂⠐⠠⢁⠐⠠⠐⠠⢈⠁⠂⠌⣀⠒⠄⢡⠐⠡⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢀⠠⠐⡀⠈⡀⠐⠀⠀⠀⠀⠀⠀⠢⢑⠨⡑⠌⡀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢀⣬⣤⣃⠐⠀⠁⠀⠀ ⠀⠂⠌⡐⠠⠌⡀⢃⠂⠡⢈⠁⡂⠄⡌⠌⢂⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⢧⢫⡵⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⢀⠂⠁⠄⠀⠐⠀⠄⠀⠀⠀⠀⠀⠀⠃⢆⠑⡂⠄⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢹⣿⣿⡟⡀⠂⢀⠀⡀ ⢀⠉⡐⠠⢁⢂⠐⠠⠘⡀⠃⠌⡐⠨⠐⣈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⡀⠀⠀⠀⠙⢦⡹⢶⣹⢳⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤⠈⠄⡈⠀⠁⠐⠀⡈⠀⠀⠀⠀⠀⠈⠢⢘⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠀⠂⡉⢉⠡⠐⠀⠠⠀⡀ ⠀⠆⠠⢁⠂⠄⡘⠠⠁⠄⠡⢂⡁⠥⠁⠄⠂⠄⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠂⠩⠀⠀⠀⠀⣒⠭⢲⢬⠣⠋⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡐⢈⠐⡀⠌⢀⠂⢀⠀⠄⠂⠀⠀⠀⠀⠀⢡⠐⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢀⠀⠁⠀⠄⠠⠀⠌⠀⡐⠀ ⠠⢈⠡⠄⡘⢠⠀⠅⠊⠌⣁⠂⠔⣀⠃⡈⠐⡈⠄⠀⠀⠀⠀⠀⠀⠠⡁⠀⠀⠀⠀⠀⠀⠀⢀⣰⢣⡞⡽⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠄⠂⡐⠠⠀⠄⠂⠀⢀⠈⠀⢀⠀⠀⠀⠀⠨⠐⠀⡀⠀⠂⠀⠀⡀⠠⠀⠀⠁⠀⠂⠁⠀⡀⠀⠂⠀⠐⠈⠀⠐⠀⠄⠂⠀⠄ ⠐⠂⡐⠠⠠⠁⠌⢠⠉⠄⢄⡈⠆⠠⠐⠠⠁⡐⠈⠀⠀⠀⠀⠀⠀⠐⡁⢀⠀⣀⡀⡄⡠⢤⡳⣭⠳⠬⡅⠂⠀⠀⠀⠀⠀⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠁⠄⠂⡁⠠⠐⠈⠀⠀⠂⢀⠀⠀⠀⠀⠀⢁⠂⠀⠄⠂⠈⠀⠀⡀⠀⠂⠀⠠⠀⠠⠀⢀⠐⠀⠈⠀⠄⠁⠠⠁⢀⠂⠁⠠ ⢈⠐⠠⢁⠢⠡⠈⡄⠌⠂⠤⠐⣈⠢⠁⡂⠡⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⡪⢔⡲⢳⢭⢱⣏⡷⠬⣏⠱⡄⢇⠀⠀⠀⠀⠀⠒⠀⠂⠀⠀⠀⢀⠀⠀⠀⠀⠀⢂⠘⣀⠂⠄⠡⢀⠈⡀⠂⠄⢀⠠⠀⠀⠀⠀⠀⠀⠂⢀⠂⠁⡀⠁⢀⠐⠀⠁⡀⠐⠀⠐⠀⡀⠂⠁⠠⠀⢈⠀⠐⠀⠠⠈⡀ ⠠⡈⠄⡁⢂⡁⠆⡐⠨⠘⠠⠑⠠⢂⡑⠄⡁⠀⠀⠀⠀⣀⠂⠀⠀⠀⢎⠥⡣⢚⡑⠊⠁⠈⠘⢧⡃⠞⡸⢌⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⢢⠄⠀⠀⠀⠀⠂⡄⠂⠌⢀⠂⡀⠐⠠⠈⢀⠀⠄⠐⠀⠀⠀⠀⠀⠂⠠⠐⠀⠄⠂⠀⡈⢀⠠⠀⢁⠀⠂⠀⠄⠂⠀⠌⠀⠀⠌⢀⠁⡐⠀ ⠠⠐⡈⠄⢃⡐⠀⠆⡁⢊⠄⡉⢆⢁⠢⠈⡔⠀⠀⠀⠐⠠⠀⠀⠀⠄⣊⠬⠇⠉⠀⠀⠀⠄⠀⠘⢬⡱⢁⡏⢦⠁⠀⠀⠀⠀⡀⠠⢀⠦⡭⢜⠢⠌⠂⠀⠀⠀⠐⢈⡐⠈⠄⠂⡀⢁⠂⢁⠠⠈⢀⠠⠀⠀⠀⠀⠀⠀⠐⡀⢁⠠⠀⡁⠠⠀⠄⠐⠀⠠⠁⠐⠀⠠⠁⢀⠂⠁⠠⠀⠄⢀⠂ ⠀⡡⠐⡨⢀⠄⢃⠢⠑⡀⠆⡑⠤⠈⠄⡁⠢⠀⠀⠀⡈⠄⠀⠀⠀⠂⠜⣮⢹⣉⠆⠀⠀⠀⠀⠰⢲⡔⢃⡜⢦⠃⠄⡄⠀⢡⠀⢡⢊⡴⣉⠌⠀⡀⠀⠂⠀⠀⠀⠂⡄⡉⡐⠄⡐⠀⠌⠀⡐⢈⠀⡀⠄⠈⠀⠀⠀⠀⠀⠀⠄⠠⠁⠠⠐⢀⠂⠈⠠⠐⠀⠂⠁⠄⠂⠠⠀⠌⢀⠂⢈⠠⠀ ⠄⡁⢂⠔⡈⠄⢂⠢⢁⠰⢁⠒⣀⢃⠂⡡⢁⠄⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠁⠈⠂⢅⡲⣎⠵⣳⠤⠤⡌⡮⠧⣍⠔⠀⢈⢂⠴⢣⡑⡰⠁⢀⠂⠀⠀⠀⠀⠀⠀⠐⠠⡐⠠⡀⠄⠡⢈⠠⢀⠂⠄⠠⠀⠂⠁⡀⠄⠀⠀⠀⠈⠀⠌⠐⡀⠂⡀⠡⠀⠂⢁⠈⠄⠂⠠⠁⡀⠂⠠⠐⠀⠂⠁ ⢐⠈⡄⠢⢀⠃⢂⠜⠠⣁⠂⠒⢄⠂⠌⡐⢌⡀⠀⠀⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⢁⢏⡓⡥⡍⢳⡸⡈⠐⢠⠎⡜⣂⠑⡀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠄⠡⠐⡈⠄⠠⠀⠄⠂⢈⠐⠈⠀⠄⠀⠀⠀⠀⠀⠀⠈⠐⠠⠐⢀⠐⠀⡁⢈⠠⠀⠂⠄⠁⡐⠀⠌⠐⡀⠡⠈⠄ ⠂⠆⠄⡑⠂⢌⠂⡔⠡⡀⢉⠌⠢⢁⠂⡌⠂⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⠐⡄⠀⠀⠀⠀⠀⠀⠀⠂⠌⡐⠹⣅⠳⡁⠌⠂⠑⠐⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡈⢁⠆⠠⢀⡁⢂⠠⠈⠄⡈⠄⡁⠐⠈⠀⠀⡀⠀⠀⠀⠈⠀⠡⠀⠂⡁⠄⢀⠂⠄⠁⡀⠂⢀⠐⠈⡀⠐⠠⠁⠄ ⢂⡈⠒⢈⡁⢂⠅⠰⢠⠑⠌⢌⡁⢊⠄⢢⠁⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠱⢢⢄⣀⣀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢂⠈⣁⠂⠐⠠⢀⠡⠂⢀⡐⠠⠁⠂⠈⠀⠀⠀⠀⠀⠀⠈⠀⢁⠂⠄⡐⠠⠀⡈⠄⠐⠈⡀⠄⢁⠠⠁⢂⠁⠂ ⠄⡐⢁⠂⡌⠐⡌⠡⢂⢉⠒⠤⡘⠠⡘⠠⠀⠐⠠⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠒⠠⢈⠄⡁⢂⠐⠈⢀⠀⢂⠠⠁⠌⠀⡀⠀⠀⠀⠀⠀⠁⠂⠄⡐⢀⠐⠠⢀⠐⠈⠠⠀⠌⢀⠐⡈⠄⡈⠄ ⠂⡌⠄⡡⠌⢡⢀⠣⢈⠂⡑⠢⠡⡁⠰⠁⠀⠌⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠔⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠌⠰⢁⢂⡐⢀⠂⠡⠈⠄⡈⠄⠂⡁⢂⠐⠀⢀⠀⠀⠀⠀⠀⠐⠠⠐⡀⠌⢀⠂⡀⢁⠂⠡⠐⢀⠂⡐⠠⠐⠈ ⢂⠰⢁⠢⠘⠄⣂⠡⠢⡁⠥⢑⠡⢈⡑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⡀⢀⢤⡒⢴⡉⠀⠀⡐⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠌⡐⠠⠂⠄⠂⠌⠄⢡⠐⠠⡈⠔⡀⠂⠌⡀⠂⠀⠀⠀⠀⠀⠀⠀⠡⢀⠈⠄⠂⠐⠠⢈⠐⡀⢂⠐⠠⠁⠌⡀ ⢂⠡⠂⡌⡁⢎⠀⡕⠢⣁⢊⠄⡃⢆⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠐⠠⠁⠌⡐⠁⠌⡐⠂⢌⠐⡀⠂⠠⡁⢂⠐⠠⠀⠀⠀⠀⠀⠀⠀⠐⠠⠈⠄⠡⢈⠐⡀⢂⠐⠠⠈⠄⡁⠢⠐ ⠢⢌⠁⢆⡁⠆⡘⠤⡑⠤⢊⠔⣈⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢁⠂⠌⡐⢈⠠⢁⠂⡐⢀⠉⠄⡐⠠⢈⠐⡀⠂⠀⠀⠀⠀⠀⠀⠠⠁⠌⡐⢀⠂⡐⠠⠈⠄⡁⠂⠤⠑⡀ ⡁⢆⠘⡄⢢⠑⠘⢐⠱⠈⠊⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠌⡐⠠⢁⠂⠰⠀⠄⠂⠌⠐⡀⠂⠄⠂⠄⡐⠀⠀⠀⠀⠀⠀⠀⠐⡐⠀⠆⡐⠠⠁⠌⡐⠠⢁⠂⡡⠀ ⠰⠈⡔⠈⠁⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⠐⡁⠄⠌⠄⠃⠌⡈⠄⠡⠠⠉⠄⡁⢂⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⢃⠐⠠⠁⡌⠐⠄⡁⠂⠤⢁⠂ ⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠌⡐⠠⢁⠂⡐⢈⡀⠅⡈⠄⠠⠀⠂⠀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠄⢃⠰⢀⠉⡐⡀⢃⠢⢁⠂ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠌⠐⠠⢁⠂⡐⢀⢂⠐⠠⠐⠈⠄⢂⠈⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠌⠄⠒⡀⠃⠤⢁⢂⠡⠂⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⡁⠂⡐⠠⠈⠄⡀⠡⢈⠐⢈⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠣⠐⣈⠡⠒⡈⠄⠂⠀⠀ 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