⠀⠻⡹⡿⡿⡿⣟⡿⢏⠻⡹⠌⡥⢁⠌⠂⡀⠀⠀⡀⠌⠀⡄⣀⠀⡀⠀⢀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢂⠂⢐⡈⢟⡶⢻⡞⣿⣿
⠣⡟⣼⡋⣝⠣⢓⡙⠞⣮⠳⢘⠱⢉⠘⡑⠊⠳⠙⡄⠋⠘⡉⠌ ⠣⠙⠆⠒⠒⠂⠀⠒⠐⠀⠂⠐⠀⠒⠂⡱⣌⠢⣇⣻⣞⣿⡣⢼⣿⣿
⢕⡺⢥⠃⣌⡒⢣⠜⣽⠋⠒⠀⠀⠀⠒⠠⠁⠡⢒⠒⠉⠈⠀⠈⠐⠉⠈⠁⠉⠀⠀⠀⠀⠁⠀⠈⠀⠉⡁⢵⣨⢷⣿⣿⣿⣿⡟⣯⣿⣿
⡓⠞⠧⠁⢂⠈⠡⠂⠀⠈⠄⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠄⠀⠐⠀⠂⡘⠸⢨⣿⣿⣿⢏⣽⣿⣿
⠡⢎⠥⠈⠀⠰⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠐⠂⣰⣿⣿⣿⣏⣽⣿⣿
⠀⣎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡉⣿⣿⣿⠻⢽⣿⣿
⠄⣌⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⢿⣿⣿⠎⣿⣿⣿
⠘⡄⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⣎⣿⣿⣿⠌⣿⣿⣿
⠐⢈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠝⠚⢉⠛⣿⣿⠈⢻⣿⢻
⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢣⡏⠰⢘⡞⣷
⠘⡀⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠈⠄⠈⣴⡻
⠀⡑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣠⣴⣶⣦⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⢌⣱
⠀⠁⠀⠀⠀⠀⠀⠀⠄⠄⠀⠀⠀⢀⣼⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⢈⢦⣑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⢎⡥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⢀⠀⢀⠚⡬
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠥⢈
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⢿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣎⢘
⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⡙⠉⢻⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⢦
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣷⣄⠀⠻⣿⣿⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡆⠀⢰⣶⠸⡀⠀⣀⣠⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡇⠀⢠⣷⠠⣽⢥⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣷⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠁⢀⠰⣿⢲⢹⣾⣿⡿⣿⡿⣿⢿⣿⣙⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡃⠈⡭⢷⠊⡈⠋⠉⣇⡧⠷⣿⢾⣿⣿⢿⢿⣿⣿⣿⣿⠿⣿⠿⡿⢿⣿⣿⣿⠿⢿⠲⣶⣾⣶⣤⣀⣀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣼⢣⠦⢝⣲⢿⣆⡶⢿⣹⡟⣿⣿⡿⢛⣫⣿⢿⡾⢳⢣⢛⡜⡱⢎⠼⢛⢿⣯⣛⣉⡿⠛⠾⡝⠯⢟⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠄⠐⣢⠍⣏⠻⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⡽⣻⢯⣿⣿⣿⣻⢷⣫⣟⡿⣮⣝⢯⠻⡽⢿⡿⣟⢿⢛⣻⣤⣀⠀⠀⠀⠀⠔⢤⣐⣤