⢀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⡀⠀⢀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣶⣦⣴⣶⣄⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠒⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠟⠙⢿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⣿⣿⣿⡿⠀⠀⠀⠀⢀⣤⣤⣀⣤⣤⡀⠀⣀⡀⢀⣀⠀⠙⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣦⣴⣶⠋⠉⢻⣿⣿⠟⠁⠀⠀⠀⠀⠘⢿⣿⣿⣿⠟⠁⠀⢿⣿⣿⠟⣀⣀⣀⠙⠏⠻⣆⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⢏⡀⢀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠟⠁⠀⠀⠀⠀⠈⠁⠀⠙⠿⠋⣀⠀⠀⣹⡆⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠁⠘⢿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣷⣾⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⣠⢦⣀⣀⠀⠀⠀⠹⣏⠙⠛⠷⠶⣄⣀⣀⣀⣀⣀⠀⠈⠻⣿⠟⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⣡⣶⣤⣶⣄⠀⠀⣠⠞⠁⠀⠉⠙⠛⠛⠶⠶⠾⠃⠀⠀⠀⠈⠉⠉⠉⠉⠙⣦⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠙⢿⣿⡿⠋⠀⢸⡇⢀⣶⣶⣶⣤⣴⣾⣿⣷⣆⠀⢀⣴⣿⣿⣿⣶⣿⣿⣿⣿⡆⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠉⠀⠀⠀⠈⣷⢸⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠘⢧⣄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠈⠻⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠈⢳⡄⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣄⠀⢷⣄⠀⠀⠀⠙⢦⡀⠈⠻⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠋⣿⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠎⣼⠃⠀⠀⠀⠀⠉⠳⣄⠀⠀⠀⠀⠀⣠⡶⢶⣦⡀⠀⠀⣀⣴⡏⠀⠀⠀⠀⠀⢀⣠⡴⠞⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠉⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠈⠉⠀⠀⠈⣁⣤⡾⠛⠛⢧⣄⣀⠀⠀⠀⠻⣥⡀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠃⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⠛⠛⠛⠛⠛⢛⣿⣿⣿⣿⣷⣀⡀⠀⠈⠙⠛⠶⢦⣀⣀⣙⡧⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣶⣄⠀⠀⠀⠀⠘⢿⣿⣿⣿⡄⠀⠀⢠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠿⠿⠶⢶⣦⣤⣤⣭⣿⣿⣿⣦⣤⣿⣿⣿⣿⣿⣿⠃⠻⢿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠸⣀⣤⠜⠛⠉⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠈⠳⣄⠈⣹⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡄⠀⠙⢿⡀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⣨⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⡆⠀⠀⠘⠛⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡄⠀⠀⠀⢰⡏⠀⠀⠀⠀⣾⠉⠉⠿⠿⠿⣏⠉⠉⠉⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠹⣿⣿⣷⣤⣤⣼⣇⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⠿⠿⠿⢿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠙⠛