⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣴⣶⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣾⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣀⠤⠤⠖⠲⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⣠⣶⠿⠛⠉⠉⠀⠀⠀⠉⠙⠿⣧⡀⠀⠀⠀⡟⢳⣾⣿⣿⣿⣷⣦⣉⡾⣩⣍⡑⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢀⣴⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡀⠀⠀⣿⢻⣿⣟⠈⣉⣿⣿⡿⣤⣹⣿⣷⠈⣧⠴⢖⣒⢶⡄⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⡠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⣟⢸⣿⣿⠿⣿⣿⣿⣅⣿⡏⢿⣿⣷⣶⣿⣿⣿⡒⣿⣉⠲⣄⠀⠀⠀⠀
⠀⢀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣷⠀⢀⡧⢸⣿⣷⢀⣀⣽⣿⡿⢸⣿⣼⣿⣿⢿⣫⣿⡿⣷⣿⣿⣷⣦⣍⠒⢤⡀
⠀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⡿⠋⠀⢸⡁⢾⣿⣿⣾⣿⣿⡿⠃⣾⢏⣿⣿⠏⣸⣿⣿⢣⣿⣿⡏⠛⠿⣿⣶⠌⡇
⣰⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣶⣶⠿⠛⠁⠀⠀⠀⠀⠙⠢⠬⣍⣉⣙⣵⡼⠿⣿⡘⠿⡏⣸⣿⡿⢡⣿⣿⢿⣿⣷⣤⠠⡦⠼⠇
⣿⡇⠀⠀⠀⠀⠀⠀⢀⣤⣾⠿⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠛⠑⢰⡇⣿⣿⣏⡀⠨⣝⣋⡼⠇⠀⠀
⣿⡇⠀⠀⠀⠀⠀⠀⣾⡏⠀⠀⢀⣤⣴⡾⠿⠟⠛⠛⠛⠻⠷⠶⣦⣤⣀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢍⡛⠿⣿⣷⣦⠙⡇⠀⠀⠀
⢸⣧⠀⠀⠀⠀⠀⠀⠘⣷⣴⠾⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⡛⠙⠛⠿⢶⣤⣀⠀⠀⠀⠀⠀⠀⠈⠑⠦⠬⢭⣼⠃⠀⠀⠀
⠸⣿⡆⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⠀⠀⠀⠉⠛⢷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠘⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠈⠻⣷⣄⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢠⣿⠃⠀⠀⣰⣾⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⡄⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠹⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⣿⠇⠀⠀⠀⢿⣿⣿⠃⠀⠀⠀⠀⣄⣀⠀⠀⣀⡀⠀⠀⠀⠸⣿⣿⡇⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠈⠙⢷⣦⡀⠀⠀⠀⠀⠀
⠀⠀⠀⢸⣿⡀⢰⠶⡄⠀⠉⠁⠀⠀⠀⠀⠀⠈⣯⠉⢉⡏⠀⠀⠀⠀⠀⠈⢉⡴⡤⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢶⣤⡀⠀⠀
⠀⠀⠀⠀⢹⣷⡉⠛⠐⢠⣤⣄⠀⠀⠀⠀⠀⠀⠘⣦⠞⠁⠀⠀⠀⠀⠀⠀⠙⢽⡓⠄⠀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣆⠀
⠀⠀⠀⣠⣤⣿⡿⣷⣤⣾⠁⠘⢷⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣴⣾⠿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡆
⠀⠀⠀⣿⣿⣿⡇⠀⢹⣏⠀⠀⠈⢻⡋⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠻⢿⣿⣏⡁⠀⠀⠈⢻⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠇
⠀⠀⠀⢻⣿⣿⣿⣄⣸⣿⡀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣆⠀⠀⠀⠈⠻⣷⣤⡀⠀⡀⠀⠀⠀⠀⢠⣾⠏⠀
⠀⢀⣴⠟⠛⠉⠉⠉⠛⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠘⣿⡆⠀⠀⠀⠀⠀⠉⠛⠳⠿⢿⠿⠿⠿⠛⠁⠀⠀
⢠⣾⠋⠀⠀⢀⣠⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣦⣤⣠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀
⣿⡇⠀⠀⢠⡟⠁⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢻⡇⠀⠀⠘⢷⣄⣀⣠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠳⣀⠀⠀⠀⠀⠉⠁⢘⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠈⢻⣶⣶⣶⣶⣶⠿⢿⣇⠀⠀⠲⣤⣤⣄⣀⣀⣀⣠⣤⣴⠆⠀⠀⢸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠘⣿⣆⣀⣠⡿⠉⠉⠙⠛⠛⠛⠛⢿⣧⣀⣠⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⢠⠋⠉⠉⠒⠲⢤⣀⣠⡀⠀
⠀⠀⠀⠀⠀⠀⣀⣀⣀⢀⡠⠖⠋⠉⠀⠀⠀⠀⠉⠉⠢⣄⠀⠀⠀⢀⠼⠤⠇⠀
⠀⠀⠀⣀⠔⠊⠁⠀⢨⠏⠀⠀⠀⣠⣶⣶⣦⠀⠀⠀⠀⠀⠱⣄⡴⠃⠀⠀⠀⠀
⢸⣉⠿⣁⠀⠀⠀⢀⡇⠀⠀⠀⠀⢿⣽⣿⣼⡠⠤⢄⣀⠀⠀⢱⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠑⢦⡀⢸⠀⠀⠀⡠⠒⠒⠚⠛⠉⠀⢠⣀⡌⠳⡀⡌⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠉⠉⣆⠀⢰⠁⣀⣀⠀⠀⣀⠀⠈⡽⣧⢀⡷⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⡤⢄⠀⠈⠢⣸⣄⢽⣞⡂⠀⠈⠁⣀⡜⠁⣩⡷⠿⠆⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢯⣁⡸⠀⠀⠀⡬⣽⣿⡀⠙⣆⡸⠛⠠⢧⠀⡿⠯⠆⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣀⡀⠀⠀⡤⠤⣵⠁⢸⣻⡤⠏⠀⠀⠀⠀⢹⠀⠀⠀⡊⠱⣀⠀⠀⠀
⠀⠀⢀⠜⠀⢘⠀⠀⠱⠲⢜⣢⣤⣧⠀⠀⠀⠀⠀⢴⠇⠀⠀⠀⠧⠠⠜⠀⠀⠀
⠀⠀⠘⠤⠤⠚⠀⠀⠀⠀⠀⠀⢸⠁⠁⠀⣀⠎⠀⠻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⣀⣀⡴⠤⠄⠴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀

ㅤ
ㅤ⠀⠀⠀⠀ ⠀⢀⣤⣄
⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⡆ ⣠⣶⣿⣶⡀
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⠋
⠀⠀⠀⠀⣾⣿⣿⣧⠀⠻⣿⣿⠿⠉
⣰⣿⣿⣿⣿⣿⣿⣿
⠸⣿⣿⣿⣿⣿⣿⠏
⠀⠈⠛⠿⣿⣿⡟