⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⡗⠀⠀⠀⠀⠀⠀⠀⠀⡀⠆⢀⠀⠀⢠⠐⡰⣞⡷⣶⢶⡰⢆⡶⢶⣖⡶⢦⡄⡐⠦⣤⢀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⢆⠁⠌⠀⠀⢠⠣⣜⣱⢯⡿⣽⢯⣟⡮⣽⣏⢾⣽⣻⡼⣆⠠⡙⢎⠆⡄⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠀⢠⠌⢦⢳⢣⣏⡻⣽⢯⣟⡾⣽⣖⢻⣎⢷⣯⢿⡽⣇⢮⢌⡫⠐⡀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡁⢢⠇⣨⢟⣣⣟⣾⣳⣞⡿⣾⣽⣳⢯⣧⡹⣷⢯⡿⣽⢯⣼⣳⣜⢧⡒⡀⠀⠀⠀⣿
⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⣈⡥⣶⣻⣞⣷⣻⣞⡷⣯⣟⡷⣯⣟⡿⣞⡷⣽⢯⡿⣽⣻⣞⡷⣯⢷⡹⡄⠀⠀⠀⣿
⠀⠀⠀⠀⣟⠀⠠⠄⡀⠀⠀⠀⠀⠀⠐⠣⠟⠽⠳⠟⣾⠳⠟⡾⡙⠳⠋⠝⢣⠛⡽⡹⢽⡹⣏⡟⢧⡛⡼⢳⡝⢯⠻⣵⠀⠀⣸
⠀⠀⠀⠀⣯⠀⠀⡈⡄⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀⠀⠈⠉⠘⠐⠀⠁⠀⠠⠀⠘⠄⠣⠇⠳⣩⠘⠡⠘⠀⠡⠌⠤⠱⠌⠂⠀⠈⢻
⠀⠀⠀⠀⣿⠀⠀⣴⢳⡄⠀⠀⠀⠀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⣿⡄⡆⢉⠣⢈⡰⢄⠀⡰⣟⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⣯⡝⣦⢒⣦⣛⡾⣄⣱⢻⡼⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣳⣟⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼
⠀⠀⠀⠀⠀⣷⡻⢅⡿⣶⣍⡿⢦⣍⠷⣹⢯⣟⡷⣦⣤⣄⣀⣀⠀⠀⠀⠀⢀⡀⣴⢫⣞⣷⣻⢾⣡⠀⠀⠀⠀⠀⠀⠀⣀⣾
⠀⠀⠀⠀⠀⠀⣿⡎⢿⣳⢯⡝⢣⢎⣳⣙⢮⣝⡻⢷⡻⢾⡽⣏⠿⣭⢛⡜⣣⡝⣮⢳⣟⡾⣽⣻⢶⣡⠐⣆⠲⡔⣮⢳⡹
⠀⠀⠀⠀⠀⠀⣿⡇⠀⠉⠊⠁⠈⡞⡴⢭⡺⢼⡙⢧⢋⠧⡓⡌⠳⠌⡒⢬⢳⠹⢎⡷⣫⢟⡷⣏⠷⣩⠓⢈⠣⡙⠤⢃⣾
⠀⠀⠀⠀⠀⠀⣿⣇⠀⠀⠀⠀⠀⠼⣱⢣⡝⢦⡙⡴⣊⡴⣡⢌⡱⣘⡜⣣⢏⡖⡠⠄⡁⠎⠐⠉⠐⡠⢂⠄⡐⢀⠂⣸⣿
⠀⠀⠀⠀⠀⠀⣿⠂⠀⠀⠀⠀⢈⠱⣣⠞⣥⢛⡼⣣⢏⡵⢊⠵⢪⢜⡱⢮⡼⣱⡌⡔⢠⢠⡐⣤⡑⠢⠐⣀⠂⡜⣾
⠀⠀⠀⠀⡿⠛⠀⠀⠀⠀⠀⠐⢢⡑⢦⡙⢦⣋⠶⣣⢎⡴⣋⡞⡶⢮⡜⣥⣙⣁⠋⠙⠃⠃⠉⢀⡁⢄⡰⢀⠣⣼
⠀⠀⠿⠙⠀⢀⠀⠀⠀⠀⠀⢀⢧⡝⡶⡘⠴⡈⢧⡑⢎⡵⣫⢞⡽⢣⠟⡴⢣⢎⡙⢎⡜⠬⢑⠢⡙⠦⣁⣦⣾
⠛⠀⠀⢀⠀⠂⡀⠀⠀⢠⢀⡏⣾⣹⢳⣝⢢⠑⢢⡝⣎⠶⣩⠞⡼⣍⢞⡱⢣⠌⡐⠀⡀⠤⣈⠧⡑⢆⣽
⠀⠀⠐⡀⠈⠄⢀⠀⠰⣎⠼⣜⢧⣏⠷⣎⠷⡘⡄⠚⣬⠳⣥⢛⡵⣚⢮⡳⢧⡞⣤⢳⣜⡲⡱⢎⠱⠈⠛⢿
⠀⠀⠐⠀⠌⠀⠂⠀⠸⣜⡻⣜⡳⣎⠿⣜⠯⣕⢮⡑⡠⠙⡔⢫⠜⣭⠺⡝⢧⠛⡌⠳⣌⠳⡑⠊⠀⠀⠀⠀⠈⠛⢿
⠀⠀⡁⠈⠠⠈⢀⠀⠀⣯⢳⣭⢳⣭⢻⣜⠳⣍⠶⣙⢦⢣⠌⡀⠋⠐⠣⠙⠂⠡⢀⠑⠠⢁⡐⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿
⠀⠀⡀⠁⠂⡁⠠⠀⠀⢚⡷⢎⡷⢎⡳⢬⡛⣬⠳⣉⢎⡱⢊⠴⡁⢂⠀⠀⠀⠀⠀⠌⡐⠢⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠙⠿
⠀⢀⠀⠡⠐⠀⡐⠀⠀⠀⣛⢾⡘⢧⡙⢦⡙⢆⠳⡡⢎⠰⡁⠆⠱⠈⠐⠀⠀⢀⠂⠐⠠⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠠