⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢱⠉⠙⡆⢹⢿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡈⠳⠒⠁⠀⠂⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢶⠀⠈⠂⢄⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣒⠭⠻⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡝⠭⢻⣼⣿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢛⢿⣿⣿
⣿⣿⣿⣿⣯⣿⡿⠌⠐⠒⠀⠠⣿⠉⠻⣝⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣶⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⢤⡀⠀⠄⠀⠂⠼⢺
⣿⣿⣿⣿⣿⠏⡞⠉⢳⣄⡀⠀⣿⠀⠀⠹⡄⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⢋⡿⠋⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⢀⡇⠀⠀⠀⠀⠀⠀
⡿⠿⡿⠙⢻⠵⢷⣤⢴⡙⢿⣦⢽⣾⡋⠙⣷⠀⠀⠙⢷⣄⠀⠀⣀⣀⣀⣀⣀⣀⣀⡀⢀⣠⠞⠁⢠⣟⣠⣤⣀⣀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀
⡇⠀⠄⠀⠀⠀⠀⠈⠉⠻⠷⠉⠹⣿⣡⣄⢸⡀⠀⠀⠀⢙⣿⠟⠉⠉⠉⠉⠉⠉⠉⢹⠟⠁⣠⣤⣏⣠⡀⣴⡟⠉⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣄⡿⢸⡇⠀⣠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡙⢯⡇⣹⠋⣷⣬⣿⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣶⡦⣇⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠷⣄⣿⣿⣴⠾⣿⡀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣻⡾⠋⠀⠀⢰⢶⠀⠀⠀⠀⠀⠀⣰⣶⠀⠸⢧⣄⣤⣿⣿⣿⡥⣼⣟⡾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠲⡄⠀⠀
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡇⠀⠀⠀⠘⣾⡇⠀⠀⠀⠀⢠⣧⡟⠀⠀⠘⢿⡇⢩⡟⢻⣦⣘⡾⣹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠒⠃⠀⠀
⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠟⣻⡟⢽⣿⣶⠀⠀⠀⠀⠀⠀⣩⣤⣴⣶⣦⢤⣽⡋⠻⠾⠋⣿⣴⠏⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠶⠋⠀⢿⡙⠪⣿⣿⡆⠀⠀⠀⠀⠀⣾⣈⣻⢿⣿⢈⡇⠀⠀⠀⠰⣿⠏⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠛⠶⢿⡟⠀⠀⠀⠀⠀⠐⣇⣀⠈⠛⣋⡾⠁⠀⠀⠀⠀⠙⠳⣶⡄⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠠⣤⣀⠀⣀⡀⠀⠀⢾⡋⠀⠀⠀⣠⠂⡿⠀⠀⠀⠀⢀⡴⠃⠀⠉⢉⣩⠟⣿⠿⠒⠛⠁⠀⠀⢾⡋⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⢙⡛⢓⢿⣷⣤⣤⣽⣷⡀⣰⠋⢠⣷⡦⣤⣤⣤⣞⠁⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠟⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢠⣴⠶⠿⡾⢾⠕⠙⣯⡭⣽⡟⢿⣅⣻⡄⠀⠉⠻⣼⡼⠏⠉⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢀⢀⣙⣧⠀⠀⠀⠀⠈⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⣠⣴⠮⠛⠉⢁⣴⠾⠳⢿⣄⣹⣦⡀⣀⣸⣀⡀⠀⠀⠀⠀⣠⡾⠃⠀⠀⠀⣀⣠⣬⠿⠉⠀⠀⠀⠀⠀⠀⠀⢻⣦⡶⠛⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠺⠛⠉⠀⠀⢠⣶⠟⠁⠀⠀⠀⠈⠉⠉⢻⣿⣜⣉⣩⡿⠲⠚⢛⣩⠶⠲⠤⢤⡤⠼⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠁⠀⠀⠀⠙⢷⡄⠀⠀⠀⠀⠀⠀⠀⢠⣠⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢮⣭⣁⣀⣠⡶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠃⠀⠀⠀⠀