⠭⠵⠖⠀⠀⠀⠀⠀⠀⠀⠠⠀⠠⠀⡠⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠄⠠⠀⠀
⠀⠂⠀⠀⠀⠀⠀⢀⡀⠀⠀⠁⢠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠠⠀⠀⠔⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠀⠀⠀⠀⠀⠀⠀⠀⡀⠉⠳⢦⣀⠀⠀⠀⠁⠀⠈⣐⠲⠶
⠀⠀⣀⠠⣒⣼⡵⠋⠀⠀⠀⡴⢃⠀⠀⠀⠀⠀⢀⠐⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠣⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠂⡀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈⠑⠐⠁⠢
⡶⠞⠊⣽⡵⠟⠁⠀⠀⣀⡞⠀⠀⠀⠀⠀⠀⡠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠈⠀⠑⢄⠀⠀⠤⢀⠀⠀
⠀⣠⢟⠟⠁⠀⠀⢀⠄⡼⢀⠀⠀⢠⠀⠀⡔⠀⠠⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⠁⠢⢀⣀⠀⠀
⡼⠡⠂⠀⠀⣀⡴⡱⢊⠁⠀⠀⠀⠂⠀⡜⠀⣆⢠⣼⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⡀⡀⠀⢦⡀⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⢹⣿⢟
⠀⠁⢀⠤⢊⠏⡰⢁⠊⠀⠄⠀⠀⠀⢰⠃⠘⢨⣽⣿⠀⣸⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠐⠀⠤⡀⠀⠣⠂⠀⠀⢆⠀⠀⠐⡄⠀⠁⠂⢢⠀⠀⠀⠀⢀ ⠈⠢⣀⠢⡀⢣⠑
⣠⠔⠁⠠⠂⠐⡡⠃⢀⠔⠀⠀⠀⠀⡎⠀⡇⡞⣿⣿⠀⢿⣼⢠⣸⣇⠀⠘⣤⡀⠀⢃⣆⠐⡌⣶⠄⠀⢷⣀⠀⠈⢷⣄⡠⠽⣴⡀⠀⠳⡃⠀⡷⡄⠀⢡⡙⢇⠠⠀⢣
⠁⠀⠀⠀⠰⡴⠁⠀⠙⠀⡄⠀⡄⢀⠇⢀⢁⣿⣿⣿⡾⡞⣿⢸⣿⡿⡄⠀⢹⢳⠀⠘⡼⣆⢸⣼⣿⣦⠈⢿⣧⠀⠈⢿⣷⣄⠹⣧⡀⠀⠙⣄⡙⣌⢦⡀⢳⣮⡳⣤⠀
⠀⠀⠀⢀⡖⠁⠀⠀⠀⠸⠀⠐⠇⡀⢀⣾⣼⣿⣿⣿⣿⣧⣿⡆⣿⣷⣷⡀⠈⣿⣧⠀⢷⣏⢦⢹⣼⡿⣷⣌⢟⢷⡄⠘⣿⣿⣦⡙⣷⡀⡀⠘⢀⡝⠾⢟⢄⠻⡏⠛⠊
⠀⠀⠀⡜⠑⠀⠀⠀⠀⠀⢀⠜⢠⠇⣿⣿⣿⡏⢹⢹⣿⣿⣿⣽⣿⡟⣿⣷⠀⢹⣿⢧⢸⣿⡀⣳⣯⢷⣟⣿⣯⣿⣻⣦⣹⣍⣿⣿⣾⣷⣄⠀⠹⣧⠀⢸⣾⣏⠙⠄⠀
⠀⠀⢠⠅⠀⠀⠀⠀⠀⠀⡞⠀⡜⢰⢹⣿⢻⣇⠀⠈⣿⣿⣿⣾⣿⣇⠻⡇⢣⢸⣿⠈⢧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⣿⠿⣿⡿⣿⣿⣦⢻⠀⠀⣏⢿⡄⠀⠀
⠀⠀⠈⠀⠀⠀⠀⠀⠀⢰⠁⢀⠁⣸⣿⡁⠆⢻⣆⠀⠙⢿⣿⣿⣿⡈⠀⠻⡌⢻⣏⠆⠼⢿⠁⠀⢿⣿⣿⣿⣿⣿⡿⠁⠀⠈⣰⡟⠃⠀⣹⣿⣝⣠⣼⠀⠀⣿⢦⢻⡄⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⣼⠀⢸⣿⣷⠀⠀⠻⣦⡀⠀⠉⠉⠀⠁⠀⠀⠁⠈⠻⠀⠀⠈⠀⢀⠈⠙⠻⠿⠟⠋⠀⠀⣠⡾⠋⠀⠀⠐⢻⣿⡍⣽⡇⣀⢀⡴⠋⠀⠈⠋⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠰⢸⠘⢹⣧⠀⠀⠈⠻⠷⡶⠤⠂⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣶⣶⣤⣤⣶⡶⠟⠋⠀⠠⠐⠀⠀⣸⣿⣇⣿⡿⠤⡤⠂⢀⡴⢃⣠⡍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠘⠀⢹⢿⡄⠀⠀⡆⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢲⣾⣿⣿⣿⣿⡶⠒⠀⠀⠈⠁⠐⢤⡀⠀⣿⣿⡿⢿⠴⠒⠒⢛⣴⢻⡋⠉⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠈⣷⢀⠐⠀⠀⠀⠀⠻⣭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⠋⠉⠁⠀⠀⠀⡇⠀⠀⢠⣄⣤⣿⡇⠀⠀⠀⣠⡞⠹⠋⠸⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡟⠃⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⣿⠀⠀⠰⠆⠀⠀⠁⠀⡀⣸⣿⣟⣿⣿⡷⣶⠏⣿⣧⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⡀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠀⠀⢰⡇⠀⣀⣴⠟⠀⣿⣿⣿⣿⣿⣧⣿⢀⣿⣿⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⠢⣄⠀⠀⠀⠀⠻⠯⠟⠳⠆⠀⠀⠀⠀⠀⠀⣼⠇⠀⣨⣵⠾⠋⠁⣠⣾⣿⣿⣿⣿⣿⡟⢻⣼⠉⡇⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣾⣿⠛⣁⣤⣶⣿⣿⣿⣿⣿⣿⣿⠁⠁⠈⢿⠀⠙⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⣤⡀⠀⠀⠀⠀⣀⣤⣶⣿⣿⡿⣻⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣶⣶⣶⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣈⠛⠷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⡄⠀⠉⠳⠦⣄⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠉⠀⢀⡀⠀⠠⠚⠙⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢁⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠁⠀⠀⠀⠀⢠⠊⠀⠊⠀⡀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠼⢁⣴⢯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⡐⠀⠈⠀⠀⠀⣇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢋⣴⠟⣱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢏⡔⣻⠋⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠐⡀⠀⣤⣤⣲⡴⠖⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡖⡣⢋⡼⠃⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠄⠀⠀⣾⣷⣾⠿⠋⠀⠀⠀⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠟⣀⡞⠁⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⡀⠀⠉⠛⠟⠀⠀⠀⠀⠚⢠⣴⢦⠴⠀⠀⠲⠬⣕
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢃⢴⠏⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⡀⠀⠀⠁⠀⠀⠀⠀⣰⣴⣶⣿⠦⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢧⣾⠏⠀⠀⣴⠀⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⢰⣦⣴⠶⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⢫⠏⠀⠀⠘⣿⠀⠻⣿⣿⡿⠏⠀⠀⠐⠲⠃⠀⠀⠙⠉⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⢁⡞⠀⠀⠀⣼⣿⣁⠀⠈⠉⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠐⠟⠁⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀