⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⢒⠆⢀⠀⡀⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⢤⠲⢮⠷⠃⠤⠈⠄⡐⠈⢿⠿⡴⢤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡦⢄⠠⠠⠤⢦⠤⡄⠀ ⠀⠀⠀⠀⢀⣠⣄⣒⠦⡈⠄⣁⠢⢀⠉⠄⡁⢂⠄⡉⠄⢂⠌⡐⣈⠲⡤⣄⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠒⣁⠂⠄⡁⢂⠂⡐⢈⠀ ⠀⠀⠀⣀⢆⡳⠜⠠⢁⠐⠠⢀⠂⠌⡐⢈⠐⡀⠢⠐⡈⠄⢂⠔⡀⠂⠔⡈⠧⡐⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢾⣂⠡⠠⢈⠐⡀⢂⠐⡀⢮⠀ ⠀⠀⢠⡯⠌⠡⢈⠐⠠⢈⠐⠠⢈⡐⠀⠆⢂⢁⠂⠅⢂⠉⠄⢂⠄⡉⡐⠠⢁⠩⣽⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢮⠉⢋⠄⢂⡁⠢⠐⣀⠂⢂⠡⣿⠀ ⠀⢀⠳⣏⠠⠁⡀⠄⡀⠂⠌⡐⢡⣆⡉⠰⠈⠄⠌⡈⢔⡈⠌⠄⢂⡐⠠⢁⠂⠂⢽⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢺⡓⠛⠆⣁⠂⠌⢠⠀⡁⠆⠠⠘⡀⢚⣽⠃ ⠀⠄⠫⡅⠂⠄⠐⠠⠄⠃⣌⠶⣯⣶⡑⢂⠡⢈⠐⢨⣾⣷⢮⡔⠡⢀⠁⢂⠈⠌⢠⠉⡐⠀⠀⠀⠀⠀⠀⠀⢀⡤⢶⡾⡜⠧⢈⠁⠆⠠⠌⠒⡀⢂⠡⢈⡐⠡⠐⣈⢾⡁ ⠰⡈⢐⠠⢁⠂⡁⠒⡈⠔⣸⣛⢖⡣⠌⡀⠂⠄⢈⠰⣿⣯⢿⡜⢀⠂⠌⠀⠠⠈⠄⢂⠀⠀⠀⠀⠀⠀⠀⠀⣼⢣⠓⠠⠐⡀⢂⠡⢈⠡⠌⢠⠁⢂⢂⠡⢀⡁⠒⢠⢿⡀ ⢸⡐⠄⢂⠄⠂⠄⡁⠆⡈⣳⡝⢮⡐⠂⠄⡁⢂⠠⢘⣿⣯⠳⡘⡤⣬⣤⣁⣆⣬⣔⣢⠀⠄⠀⠀⠀⠀⠀⠀⢺⡁⠌⠀⢁⠀⠂⠤⢁⠂⡌⠄⡘⢀⠢⠐⠂⠄⡑⢨⢿⡀ ⢨⠑⡌⠠⢈⠐⡈⠐⠄⡡⢸⡙⣦⢧⡉⡐⠄⢂⠐⢨⣿⢇⠃⠀⠉⠙⠉⠋⠙⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⢺⡀⠄⢀⠂⠌⡐⣂⢤⣫⢿⣣⠀⠃⠤⠑⡈⠰⠐⢨⢿⡀ ⠀⠌⣰⡃⠄⠂⠄⡉⢐⡀⢂⠙⠚⠷⢁⠰⠈⠄⡈⠤⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠒⠈⠀⡘⢜⠳⢋⠟⣻⢿⡣⢈⠌⠠⠁⠤⢁⠊⢰⣻⠄ ⠀⠀⢷⡿⡀⢁⠂⡐⠄⡐⡈⠄⢃⠰⠈⠄⡑⢂⠰⠐⣿⠿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠀⠀⠀⠈⣽⡁⠂⠌⠡⡈⠐⡄⠘⡠⢿⡂ ⠀⠀⠘⣯⡱⣀⠂⠔⡐⠠⡐⠨⢀⠆⡁⢊⠐⡀⢂⠡⢈⠘⡰⣏⢶⣰⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠥⠘⡈⡐⠠⠁⠤⢁⡘⣿⠄ ⠀⠀⠀⠀⠱⣭⡖⣄⣂⠡⠄⡑⠠⠂⠤⢁⠂⢌⡀⠆⡁⠢⠐⣀⠂⢄⠰⠈⢗⡢⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⡃⢂⠡⠠⢁⠊⡐⠠⢘⣽⠂ ⠀⠀⠀⠀⠀⠉⠙⠩⠍⠓⢦⣈⡐⡁⢂⠆⠨⡀⠔⡐⠠⣁⠡⠠⠌⡀⠆⡉⠄⡉⢻⠥⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⡅⢂⠂⠅⠂⠤⠁⠌⢢⢿⡁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠚⠱⣟⡷⡂⠌⡐⠐⡰⠀⢅⠠⢂⢁⠒⡀⠒⡀⢂⡐⠡⠘⢦⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⢎⠠⠘⠠⠉⠄⣁⠊⢤⣻⠄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡷⣅⠒⡈⢐⠠⢁⣶⢶⣤⠆⢂⢁⠂⣁⠂⠄⠡⠌⢺⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⡃⠄⢃⠡⠌⡐⠠⢈⠄⣿⠄ ⣠⣤⣤⣤⣄⣤⣤⣤⣄⡀⠀⠀⠨⠷⣌⠐⡀⠂⠐⢂⣿⣟⣮⢏⡄⢂⠌⠠⣈⠐⠡⠈⢼⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⠡⡈⠄⠢⠐⢠⠁⣂⠘⣾⠂ ⣹⠎⠠⠀⠌⠀⠌⠹⡯⠄⠀⠀⣜⡳⣌⠂⠄⡁⢈⠰⣿⡿⡜⢨⢚⣵⠈⡐⠠⢈⡐⠡⢸⣟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⡅⠐⣈⠡⠘⡀⢂⠤⠘⣽⡁ ⣼⡀⠂⠄⡐⠈⠄⠡⠑⣈⡐⡰⢬⡳⢌⠂⡐⠠⢀⠘⣿⣷⢡⢀⠻⣾⠁⠤⠑⠠⠠⢁⠼⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠡⠄⢂⠡⠐⠂⡄⠙⣾⡁ ⣻⡵⢈⠐⠠⢁⡘⠠⠡⢀⠿⣹⢧⣏⠆⡐⠠⠁⠠⢘⣿⣽⢲⣈⠳⠙⢠⠂⠡⡁⢂⠡⢸⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠄⢡⠈⢄⠂⡁⠎⠠⠙⣾⡁ ⢹⡖⢂⠉⡐⠠⠀⡅⢂⠡⠘⠵⣻⣟⡎⠠⠁⠌⡐⠨⣾⢿⡳⠎⠠⠑⡠⢈⠡⠐⡀⠂⣽⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠆⠂⢌⡀⠆⠡⢈⡐⢩⢾⡁ ⠀⢈⠱⣎⠠⢁⠂⡐⠠⢁⠊⠄⡑⢏⡐⠡⠘⢠⠠⠁⢾⠃⠡⡈⢁⠒⡀⠂⠄⠡⡐⡡⢞⡓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡱⠈⢄⠐⡈⠐⠠⠐⢨⣿⠆ ⠀⠀⠘⣧⡐⠠⢂⠁⢂⠡⢈⠐⠄⠂⡄⢁⠊⠄⢂⠡⠂⠌⠡⠠⢁⠂⠄⢡⠈⢂⣼⠱⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⠵⡁⢂⠂⠄⠡⢈⠂⡱⣾⡃ ⠀⠀⠈⠡⢹⣹⡄⢌⠠⠂⠄⠌⡠⢃⠐⡠⠌⢂⢁⠂⠅⢊⢁⠂⡡⢈⠐⠂⡌⢢⠹⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⡁⠂⠌⡀⢁⠂⠄⢱⢻⡁ ⠀⠀⠀⠀⠀⠻⠝⡚⢆⠣⠌⢂⡐⠠⢂⠐⡈⠄⢂⠌⡈⠄⡂⠌⡐⣰⠋⠗⠋⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡐⠠⢁⠂⠄⠠⢈⡐⣄⢫⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠍⠶⣾⢷⡤⢁⠂⠜⡀⢢⣾⣶⡿⢾⠵⠢⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠷⠿⡞⠶⢧⢷⡻⢬⠳⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠐⠠⠈⠀⠐⠀⡹⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⢦⠁⡀⠀⢂⡽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠁⠀⠀⠁⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀