⠀⠀⠀⠀⠀⢀⣠⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢀⣴⠿⢫⣯⣍⣉⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣰⠟⣱⡾⠛⢿⣿⣿⣷⠀⣿⡻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣸⡏⣼⣿⣿⣷⣤⡉⠻⡿⠀⡟⠿⡎⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⠀⡟⠳⣽⡻⣿⣿⡾⠃⣼⠃⠀⠉⠲⣌⢻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢿⡄⠻⣦⣬⣽⡾⠋⣠⡞⠙⢢⠀⠑⢦⡀⣸⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠈⠻⣶⣤⣤⣤⣶⢿⡉⠀⠀⠀⡀⠈⠙⣿⣿⢱⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠉⠛⠷⣌⡓⠯⡳⢄⡀⠈⢳⣴⡿⢻⣿⠄⠀⠈⠻⢦⡄⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⠙⠳⢦⠤⠵⢾⣿⣯⣿⣷⡃⠀⠀⠀⠀⠀⠙⢿⣟⠛⣋⣉⣉⣉⣉⣉⡉⠉⠉⢙⡟⠳⢦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢯⣕⢯⠲⣄⠀⠀⠀⠀⠀⠙⢿⣿⠟⠿⠻⠿⠿⢭⡇⠀⢸⠃⣰⣤⣌⡙⠳⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢶⣄⠙⠶⣔⠦⣄⠀⠓⣾⣷⠀⠀⠀⠈⢸⡇⠀⣾⠀⡟⠒⠈⠉⠓⠶⣬⣹⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣷⣦⣈⡓⢈⣓⣶⣿⠋⡄⠀⠀⠀⣿⠀⢀⡇⣠⣇⣀⣀⣀⣀⡐⢺⡇⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠛⣿⣿⣿⡟⠛⠿⠛⠋⢁⣴⣁⣤⠤⠶⠿⠶⠾⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⢾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠶⠶⠶⠛⠛⢻⡿⣿⡿⠷⠿⠛⠛⠛⠛⠛⠛⢩⡟⡁⢠⠖⠀⠀⡀⣠⡶⠻⣷⣄⣈⠉⠛⠻⠿⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⣠⢢⡀⢠⠆⣴⣿⡾⢋⡄⠀⠀⠀⡴⠀⠀⠀⣴⣋⣼⣵⣃⣀⣤⣾⡿⠋⣠⡾⢻⣯⡙⠓⢶⣦⣤⣈⠙⠛⢦⣤⡀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢠⣾⠥⢾⠷⢿⣾⡿⣿⣿⡟⢁⡞⠀⡤⢀⣞⡇⠀⣠⠚⢻⣤⣮⣤⣤⣽⣽⣽⣷⡾⣿⣶⣿⠿⠿⠿⣿⡷⣤⣍⣻⠶⣦⣈⠙⢷⣤⡀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢹⡷⡶⢺⣿⡛⡿⣻⢿⡶⠿⠺⡟⠛⠋⠉⠉⢻⡉⢹⣿⣦⣴⣤⣿⣦⣾⣾⣫⡴⣿⠟⣴⢾⣿⣶⣌⢻⣦⣍⡙⠳⣦⣍⡿⢦⡈⠻⣦⡄
⠀⠀⠀⠀⠀⠀⠀⢿⡗⠻⣿⣻⠻⡛⢻⡌⢻⡄⠀⠓⠀⠘⣦⡄⠀⠓⠈⢿⡘⠈⢯⠻⡼⠈⢿⡈⢷⣿⠀⣿⣿⣉⣿⣿⢈⡿⢿⡿⣿⢿⣿⣿⣦⣙⣷⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠈⢿⣄⣹⣥⣷⣧⣄⣿⣾⢿⡄⢷⡀⠀⠸⡾⡄⢠⡸⣌⣿⣤⣬⢦⡿⢤⡼⣿⠟⣿⣆⠹⢿⣿⡿⢋⣼⣇⣸⣿⣬⣻⣿⣿⣿⣿⣧⠛⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡄⣤⡽⡆⡄⢹⣄⢻⣟⣿⣿⣿⣿⢛⣿⣿⣿⣿⣷⡹⢬⡃⢀⢣⠘⣇⠘⣟⢳⣶⣦⠶⣿⣿⣾⣿⣿⣿⣿⣏⣿⣾⣿⣿⠿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡶⠾⠷⢷⠾⠶⡿⣟⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡶⠷⣾⠷⣶⡾⣟⠹⣿⣶⣿⠿⢿⣿⣿⣿⠿⣷⣿⡿⣿⣿⠿⣧⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⢲⡈⢳⡄⠁⠹⣆⡽⠿⠿⢿⡿⢿⠿⢿⠿⢿⣿⣷⣄⣘⠲⡜⠁⠻⣤⡿⠙⠋⢻⡏⠉⠙⣿⠉⠙⣟⠉⢹⣧⣴⠏⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠁⠀⠀⠀