⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⡼⢹⠃⠀⠀⠀⠀⠀⠀⣀⣠⡴⠾⠛⠛⠒⠈⠉⠑⠒⠒⠭⣿⠀⠀⠀⠀⠙⢄⠀⠀⠀⠀⠀⢸⠀⠀⢀⣀⣀⠀⠀⣀⣀⣀⣀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⣸⠁⣾⠀⠀⢀⣠⡴⠚⠉⠈⠁⠀⠀⠀⠀⣀⣠⣤⣤⣀⡀⠀⠈⣇⠀⠐⠮⢢⡈⢦⡀⠀⠀⢀⣾⠾⠽⠓⠒⠒⠀⠀⠐⠒⠒⠚⢯⠹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⣏⠀⡏⣠⢔⡽⠋⠀⠀⠀⠀⠀⠀⠀⠐⠉⠀⠀⠀⠀⠀⠉⠙⠲⣜⢦⣀⡀⠀⠑⡞⢹⠀⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡼⠞⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣘⢦⡺⡵⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠈⠉⠑⢷⣻⡉⠁⠀⠀⠀⠀⠀⠀⢀⣀⡠⠴⢒⣋⣁⣀⢤⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⢛⣿⠿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⣳⡀⠀⠀⢣⢧⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⢁⣀⣀⣀⣼⣸⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢣⠞⠁⠀⠀⠀⢤⠀⠀⠀⠀⠀⠀⠀⠐⡄⠀⠀⠀⠀⠀⠀⢀⣤⣺⠵⠚⠁⠹⣄⠀⠈⣿⠀⣀⣀⣤⣤⡤⠀⠀⠀⠋⠉⠛⠳⣶⢤⡄⠀
⠀⠀⠀⣀⡠⠤⠔⠒⠚⣿⠋⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⣀⣤⡄⣠⠞⠁⠀⠀⠀⠀⠱⣜⣆⠀⢹⢫⠟⠋⠉⠀⠀⠀⠀⢀⣀⡠⠤⠔⠓⢻⠄⠀
⠤⠒⠉⠁⠀⠀⠀⠀⠐⡏⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⣀⣠⠤⣷⣯⢟⡽⠋⠁⠀⠀⠀⠀⠀⠀⠀⠈⢿⣧⠘⡏⡇⠀⠀⠀⠀⠀⠀⠉⠛⠒⠒⠒⠲⡞⡆⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⣄⢀⣀⣀⣀⣀⣀⣿⡤⠴⠒⠚⣉⡥⠔⠊⠹⡌⠻⢄⡀⠀⢤⣀⠀⠀⠀⠀⠀⠀⠀⠳⡀⡇⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣸⡇⠀
⠀⠀⠀⠀⠀⣀⡄⠀⠀⣇⣄⣀⣀⣀⣀⣠⡴⣾⠻⡖⠒⠋⠁⠀⠀⠀⠀⢹⡉⢀⣿⣷⣦⣬⣝⣻⣖⡶⠦⠤⠴⢶⣿⡇⠸⢖⣲⠶⠆⠀⠀⠀⠀⠀⠙⠫⢕⣦⡁⠀
⠀⠀⣠⠔⠊⠁⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⡞⠀⠜⢦⡠⣀⠀⠀⠀⠀⠈⢣⠸⡟⣿⢀⣤⡟⠻⡿⡇⠀⠀⠀⣏⡜⡇⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠷⠇⠀
⣰⣿⠓⠀⠀⠀⠀⠀⠀⣇⠀⢲⠀⠀⠀⠀⣰⢧⣷⣾⣿⣿⣾⢷⣦⢤⣀⣀⣈⣧⠀⠸⣌⣻⡧⣤⡷⣷⠀⠀⠀⣟⠀⡇⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⣏⡳⠀
⡏⢧⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⠀⠀⠀⢠⣿⣿⠟⢹⠀⣾⡞⣇⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠉⠀⡟⠀⠀⢠⡏⢠⠃⠀⠀⢷⡠⣤⣀⡀⠀⠀⢀⣠⡤⠤⣽⠀⠀
⢱⠈⢆⠀⠀⠀⠀⠀⠀⢸⠀⡞⠀⠀⢀⠞⢿⢿⣄⠸⣄⠽⢵⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣽⠀⠀⣼⡠⠃⠀⠀⠀⠀⡞⠉⠁⠀⠀⠀⠀⠀⠹⣽⠀⠀⠀
⠀⢧⠘⡄⣀⣤⣴⡶⠆⣿⣼⠁⢀⡴⠋⠀⠈⢧⠉⠓⠈⠛⠛⠁⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⢹⠀⢠⡿⠁⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠶⣟⡀⠀⠀
⠀⢸⡰⡫⣷⠟⠁⠀⠀⠟⢻⠴⠋⢻⡀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠈⠑⠀⠀⠀⠀⡀⠀⠀⠀⠀⢸⠀⢸⠹⡀⠀⠀⠀⠀⠀⠛⠒⠦⠤⢤⣀⠀⠀⢀⡴⠃⠀⠀
⠀⠀⠘⡔⣇⠀⠀⠀⠀⠀⠀⠀⢛⠯⣷⡀⠀⠀⢹⣆⠀⠀⠀⠀⠀⠀⠀⣀⢀⣀⠤⠚⠁⠀⠀⠀⠀⢸⣀⡏⠀⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⣠⣞⠥⠖⠚⠁⠀⠀⠀
⠀⠀⠀⠘⡞⡆⠀⣀⠀⠀⠀⠀⠈⣆⣸⡳⣄⠀⠀⢟⠦⡀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⡰⢻⡾⠑⠦⣄⣙⢦⡀⠀⠀⠀⠀⢀⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢹⠷⣪⠋⠀⠀⠀⠀⠀⠁⢠⠃⠈⠣⡀⠘⡆⠈⠓⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠈⣇⡀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⣀⡤⠤⠞⠃⠀⠀⠈⠳⢼⣄⠀⠀⠀⠉⢓⣲⡤⠤⣄⣀⡴⠊⠀⠀⠀⣀⡽⠋⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⣧⡠⠤⠤⠭⠭⠶⣤⡀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⡿⣝⣓⣒⡒⠒⢖⠲⣖⣚⣩⠥⠖⠋⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠉⠉⢹⡀⡇⢠⢤⣴⣶⣷⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠛⠉⠉⠛⠓⠶⣾⣿⣹⣭⣿⣧⣀⡀⠀⠀⠀⠀⡇⣇⠘⠛⠛⠋⣁⡠⣿⡲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⠀⠀⠀⣸⠁⠸⣿⣷⠀⠀⠉⠙⠓⠒⠒⠳⣟⠶⣖⠋⠉⢀⣴⣿⠿⢭⣷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⠟⠁⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⢻⣿⡄⠀⠀⠀⠀⠀⣀⣴⣿⣷⣮⣙⣶⣿⠟⠁⠀⠀⢸⠈⠛⡶⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀