⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⢶⣦⡀
⠀⠀⠀⣴⡿⠟⠷⠆⣠⠋⠀⠀⠀⢸⣿
⠀⠀⠀⣿⡄⠀⠀⠀⠈⠀⠀⠀⠀⣾⡿
⠀⠀⠀⠹⣿⣦⡀⠀⠀⠀⠀⢀⣾⣿
⠀⠀⠀⠀⠈⠻⣿⣷⣦⣀⣠⣾⡿
⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⡿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⢠⠏⡆⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣀⡀
⠀⠀⠀⠀⠀⡟⢦⡀⠇⠀⠀⣀⠞⠀⠀⠘⡀⢀⡠⠚⣉⠤⠂⠀⠀⠀⠈⠙⢦⡀
⠀⠀⠀⠀⠀⡇⠀⠉⠒⠊⠁⠀⠀⠀⠀⠀⠘⢧⠔⣉⠤⠒⠒⠉⠉⠀⠀⠀⠀⠹⣆
⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⣤⠶⠶⢶⡄⠀⠀⠀⠀⢹⡆
⠀⣀⠤⠒⠒⢺⠒⠀⠀⠀⠀⠀⠀⠀⠀⠤⠊⠀⢸⠀⡿⠀⡀⠀⣀⡟⠀⠀⠀⠀⢸⡇
⠈⠀⠀⣠⠴⠚⢯⡀⠐⠒⠚⠉⠀⢶⠂⠀⣀⠜⠀⢿⡀⠉⠚⠉⠀⠀⠀⠀⣠⠟
⠀⠠⠊⠀⠀⠀⠀⠙⠂⣴⠒⠒⣲⢔⠉⠉⣹⣞⣉⣈⠿⢦⣀⣀⣀⣠⡴⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢠⣶⣿⣿⣿⣿⣷⠀⠀⢠⣷⣶⣶⣶⣶⣶⢶⣦⡀⠀⠀
⠀⣼⡿⠟⠉⠀⠀⠹⢿⠃⠀⠀⠉⠙⠋⠉⠉⠉⠉⢹⣿⡏⠀
⡼⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡟⠁
⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⣿⡟⠀⠀
⣿⡇⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡏⠀⠀⠀⠀
⣿⣿⡿⠋⠉⠉⠙⢿⣷⣀⠀⠀⠀⠀⠀⣼⣽⠇⠀⠀⠀⠀⠀
⣿⣿⠃⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⢸⣿⠃⠀⠀⠀⠀⠀
⢸⣿⠀⠀⠀⠀⠀⠀⢸⣿⠇⠀⠀⠀⠀⣾⡟⠀⠀⠀⠀⠀⠀
⠀⠙⠿⢦⣤⣤⣴⡿⠋⠀⠀⠀⠀⠀⢸⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢠⣶⣿⣿⣿⣿⣷⠀⠀⢠⣷⣶⣶⣶⣶⣶⢶⣦⡀⠀⠀
⠀⣼⡿⠟⠉⠀⠀⠹⢿⠃⠀⠀⠉⠙⠋⠉⠉⠉⠉⢹⣿⡏⠀
⡼⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡟⠁
⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⣿⡟⠀⠀
⣿⡇⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡏⠀⠀⠀⠀
⣿⣿⡿⠋⠉⠉⠙⢿⣷⣀⠀⠀⠀⠀⠀⣼⣽⠇⠀⠀⠀⠀⠀
⣿⣿⠃⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⢸⣿⠃⠀⠀⠀⠀⠀
⢸⣿⠀⠀⠀⠀⠀⠀⢸⣿⠇⠀⠀⠀⠀⣾⡟⠀⠀⠀⠀⠀⠀
⠀⠙⠿⢦⣤⣤⣴⡿⠋⠀⠀⠀⠀⠀⢸⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢠⣶⣿⣿⣿⣿⣷⠀⠀⢠⣷⣶⣶⣶⣶⣶⢶⣦⡀⠀⠀
⠀⣼⡿⠟⠉⠀⠀⠹⢿⠃⠀⠀⠉⠙⠋⠉⠉⠉⠉⢹⣿⡏⠀
⡼⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡟⠁
⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⣿⡟⠀⠀
⣿⡇⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡏⠀⠀⠀⠀
⣿⣿⡿⠋⠉⠉⠙⢿⣷⣀⠀⠀⠀⠀⠀⣼⣽⠇⠀⠀⠀⠀⠀
⣿⣿⠃⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⢸⣿⠃⠀⠀⠀⠀⠀
⢸⣿⠀⠀⠀⠀⠀⠀⢸⣿⠇⠀⠀⠀⠀⣾⡟⠀⠀⠀⠀⠀⠀
⠀⠙⠿⢦⣤⣤⣴⡿⠋⠀⠀⠀⠀⠀⢸⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢠⣶⣿⣿⣿⣿⣷⠀⠀⢠⣷⣶⣶⣶⣶⣶⢶⣦⡀⠀⠀
⠀⣼⡿⠟⠉⠀⠀⠹⢿⠃⠀⠀⠉⠙⠋⠉⠉⠉⠉⢹⣿⡏⠀
⡼⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡟⠁
⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⣿⡟⠀⠀
⣿⡇⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡏⠀⠀⠀⠀
⣿⣿⡿⠋⠉⠉⠙⢿⣷⣀⠀⠀⠀⠀⠀⣼⣽⠇⠀⠀⠀⠀⠀
⣿⣿⠃⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⢸⣿⠃⠀⠀⠀⠀⠀
⢸⣿⠀⠀⠀⠀⠀⠀⢸⣿⠇⠀⠀⠀⠀⣾⡟⠀⠀⠀⠀⠀⠀
⠀⠙⠿⢦⣤⣤⣴⡿⠋⠀⠀⠀⠀⠀⢸⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢠⣶⣿⣿⣿⣿⣷⠀⠀⢠⣷⣶⣶⣶⣶⣶⢶⣦⡀⠀⠀
⠀⣼⡿⠟⠉⠀⠀⠹⢿⠃⠀⠀⠉⠙⠋⠉⠉⠉⠉⢹⣿⡏⠀
⡼⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡟⠁
⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⣿⡟⠀⠀
⣿⡇⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡏⠀⠀⠀⠀
⣿⣿⡿⠋⠉⠉⠙⢿⣷⣀⠀⠀⠀⠀⠀⣼⣽⠇⠀⠀⠀⠀⠀
⣿⣿⠃⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⢸⣿⠃⠀⠀⠀⠀⠀
⢸⣿⠀⠀⠀⠀⠀⠀⢸⣿⠇⠀⠀⠀⠀⣾⡟⠀⠀⠀⠀⠀⠀
⠀⠙⠿⢦⣤⣤⣴⡿⠋⠀⠀⠀⠀⠀⢸⣿

⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢠⣶⣿⣿⣿⣿⣷⠀⠀⢠⣷⣶⣶⣶⣶⣶⢶⣦⡀⠀⠀
⠀⣼⡿⠟⠉⠀⠀⠹⢿⠃⠀⠀⠉⠙⠋⠉⠉⠉⠉⢹⣿⡏⠀
⡼⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡟⠁
⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⣿⡟⠀⠀
⣿⡇⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡏⠀⠀⠀⠀
⣿⣿⡿⠋⠉⠉⠙⢿⣷⣀⠀⠀⠀⠀⠀⣼⣽⠇⠀⠀⠀⠀⠀
⣿⣿⠃⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⢸⣿⠃⠀⠀⠀⠀⠀
⢸⣿⠀⠀⠀⠀⠀⠀⢸⣿⠇⠀⠀⠀⠀⣾⡟⠀⠀⠀⠀⠀⠀
⠀⠙⠿⢦⣤⣤⣴⡿⠋⠀⠀⠀⠀⠀⢸⣿