⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢠⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣿⡇⠀⠀⣤⣤⣤⣼⣿⣤⣤⣤⣤⣤⡄⠀
⠀⣀⣀⣀⣿⣇⣀⡀⠉⠉⠉⢹⡿⠉⠉⠉⠉⠉⠁⠀
⠀⠛⠛⢻⣿⡟⠛⠃⠘⠛⠛⣿⠟⠛⣿⡟⠛⠛⠀⠀
⠀⠀⠀⣼⣿⣷⡀⢠⣤⣤⣼⣿⣤⣤⣼⣷⣤⣤⣤⠀
⠀⠀⣰⣿⣿⡿⢿⠄⢠⣾⠟⠀⢠⣤⠀⠘⣿⣄⠀⠀
⠀⣰⡿⠀⣿⡇⢨⣴⡿⠛⠶⠶⢾⣿⠶⠶⠞⠻⣷⠄
⠀⠿⠁⠀⣿⡇⠀⠁⣀⣀⣀⣀⣸⣿⣀⣀⣀⣀⠀⠀
⠀⠀⠀⠀⣿⡇⠀⠀⠉⠉⠉⠉⢹⣿⠉⠉⠉⠉⠀⠀
⠀⠀⠀⠀⠿⠇⠀⠀⠀⠀⠀⠀⠸⠿⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣿⡇⠀⠀⣤⣤⣤⣼⣿⣤⣤⣤⣤⣤⡄⠀
⠀⣀⣀⣀⣿⣇⣀⡀⠉⠉⠉⢹⡿⠉⠉⠉⠉⠉⠁⠀
⠀⠛⠛⢻⣿⡟⠛⠃⠘⠛⠛⣿⠟⠛⣿⡟⠛⠛⠀⠀
⠀⠀⠀⣼⣿⣷⡀⢠⣤⣤⣼⣿⣤⣤⣼⣷⣤⣤⣤⠀
⠀⠀⣰⣿⣿⡿⢿⠄⢠⣾⠟⠀⢠⣤⠀⠘⣿⣄⠀⠀
⠀⣰⡿⠀⣿⡇⢨⣴⡿⠛⠶⠶⢾⣿⠶⠶⠞⠻⣷⠄
⠀⠿⠁⠀⣿⡇⠀⠁⣀⣀⣀⣀⣸⣿⣀⣀⣀⣀⠀⠀
⠀⠀⠀⠀⣿⡇⠀⠀⠉⠉⠉⠉⢹⣿⠉⠉⠉⠉⠀⠀
⠀⠀⠀⠀⠿⠇⠀⠀⠀⠀⠀⠀⠸⠿⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣀⡀⠀⠀⢀⠀⠀⠀
⠀⠀⣿⡿⠿⢿⣿⠀⠘⣿⡄⠀⣿⠇⠀⢠⣿⠃⠀⠀
⠀⠀⣿⡇⠀⢸⣿⠀⣤⣼⣥⣼⣿⣤⣤⣽⣧⣤⡄⠀
⠀⠀⣿⣷⣶⣾⣿⠀⠀⠀⢀⣿⠇⠀⢹⣧⠀⠀⠀⠀
⠀⠀⣿⡇⠀⢸⣿⠿⠿⢿⣿⠿⠿⠿⠿⢿⣿⠿⠿⠀
⠀⠀⣿⣇⣀⣸⣿⣀⣴⡿⠋⠀⣶⡆⠀⠀⠻⣷⣄⠀
⠀⠀⣿⠉⠉⢹⣿⠿⠛⣶⣶⣶⣿⣷⣶⣶⣶⡞⠛⠁
⠀⢠⣿⠀⠀⢸⣿⠀⠀⠀⠀⣼⡟⠀⠀⠀⣿⠃⠀⠀
⠀⣸⡏⠀⠀⢸⣿⠀⠀⣠⣾⠟⠀⠀⠀⢰⣿⠀⠀⠀
⠐⠻⠁⠘⠿⠿⠟⠀⠿⠛⠁⠀⠀⠿⠿⠿⠋⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣷⡆⠀⠀⠀⢸⣿⠀⠀⠀⠲⣷⡄⠀⠀⠀
⠀⠀⠀⣸⣿⠁⠀⠀⠀⢸⣿⠀⠀⠀⠀⠹⣿⡄⠀⠀
⠀⠀⢠⣿⠇⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⢹⣿⡄⠀
⠀⢠⣿⠏⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⢻⣷⠀
⠀⠙⠋⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠘⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠈⠿⠿⠿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢠⣤⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⣀⣀⣿⡇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢀⣼⣿⣶⡶⠿⠟⠛⠛⣿⡇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠋⠉⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢠⣤⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⣀⣀⣿⡇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢀⣼⣿⣶⡶⠿⠟⠛⠛⣿⡇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠋⠉⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠺⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷⣄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀