⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠐⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠂⠁⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣠⠠⡄⢤⣀⡀⢠⡐⢒⡆⢶⡳⣇⡰⣒⢦⢒⢤⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢁⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢿⣹⢧⡙⢦⠱⣸⠽⣾⣷⣾⣹⡳⣓⣮⣝⣺⣮⢟⡲⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠈⠠⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢨⠑⠚⠬⢳⣅⢳⣹⣿⣿⣿⣿⣿⣵⣿⣟⣽⣿⣿⣿⡺⣭⣳⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠁⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣁⠪⣑⠎⡖⠴⣳⣻⡿⣿⣷⣿⣿⣿⣿⣿⢿⡿⣿⣿⣿⣽⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠑⣆⠹⣈⢛⢵⣻⡽⣿⣿⡿⣯⣟⡿⣯⣏⣷⣿⣿⣿⣿⣾⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠈⠠⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠢⡑⢤⢣⠱⣎⢲⢯⣿⣿⣿⣽⣯⣿⢿⣿⣽⡿⣿⣿⢿⣿⡟⣯⢻⡝⣾⡽⡄⠀⠀⠀⠀⠀⠀⢂⠡⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢁⢲⡉⢆⡣⡝⢤⢫⢿⡽⣿⣿⡿⣿⣛⡿⣽⡳⣟⠿⣿⡲⣬⢙⡔⢣⠞⠥⣛⣳⡄⠀⠀⠀⢀⡡⢊⡆⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢌⣢⠽⣎⡁⠙⠊⠑⠭⣟⡿⢭⡿⣫⠿⡵⢧⣻⣜⡳⣞⣻⡖⣏⢾⣖⡜⣴⢷⣰⣈⠄⣠⠀⠒⠌⠳⠬⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢢⠭⣿⢻⣗⣦⣔⣀⣤⣱⣛⢎⡱⠉⠓⣽⣯⣳⣭⣟⣾⣷⣾⣿⣾⣽⣿⣿⣿⣵⡞⡩⠆⠁⠀⠀⠀⢀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠁⢦⠙⠦⢏⣻⠷⣿⡟⢜⢲⣿⣿⣧⣀⣄⠈⠚⣵⣷⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⢾⠱⠀⠀⠀⠀⠈⠄⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠢⢌⠱⢢⡘⢡⠛⣒⠯⢟⡷⡄⠀⢉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣀⠀⠀⠀⠀⠁⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡐⠢⠙⡐⢬⠡⠎⣀⠉⠀⡀⠀⠘⠺⢯⢷⣿⣾⢿⣟⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠰⣁⠈⠤⠐⠀⠀⠀⢀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠠⠐⣂⣡⣬⣶⣾⡿⠿⣁⢀⡁⡄⣠⠈⠥⠶⣙⡯⣟⣮⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡄⡁⢂⠀⠀⠀⠐⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣬⣴⣾⣿⠿⠟⠛⠉⣄⠒⡖⣌⢖⡲⣜⣠⡛⣌⢧⢎⡲⢭⡺⣕⢳⡹⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⡂⠂⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠿⠿⠛⠋⠁⠠⢀⠐⣈⠒⣌⢳⢼⡡⢞⣽⡆⣷⣱⢎⡾⢹⡺⣥⢳⣞⡿⢾⣹⣟⣿⣿⣿⣿⣿⣿⣿⣿⢿⠲⠀⠀⠀⠀⠀⠐⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠁⡀⠀⡄⠛⡬⣹⣚⠽⣽⣎⠿⣼⢧⣋⢞⡵⣹⣼⣳⣯⣿⣿⣷⣿⣿⣿⣿⣿⣿⡿⣽⣏⣟⠂⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⠀⠀⡜⡰⠳⣜⢳⣎⠻⣦⣻⢏⡼⣃⠏⣞⢸⣫⢷⣻⣽⣾⣳⣿⣿⣿⣿⣟⢿⢾⣝⡳⢞⠂⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠆⡁⢂⠱⡹⢬⣓⠮⣓⠌⢧⢏⠲⠩⠌⢄⠣⣬⢳⡝⣯⣿⣿⣽⡜⡝⡮⡙⡬⠳⣌⠵⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⢦⠱⠈⣳⣽⣻⡽⢊⢇⠋⠈⠎⡁⠁⢈⠌⣳⢩⢧⣛⣼⣿⣾⣿⣻⢶⠃⠜⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠣⠁⢤⠣⠙⠜⠈⠂⠀⠀⠀⠀⠠⢁⠞⠡⢏⠜⣶⣻⣿⣟⡻⠏⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠀⠈⠌⠒⠙⠂⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀