⡗⣿⣿⡄⠀⠀⠀⠀⠀⢣⠎⠀⢸⣲⣧⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⠃⠀⡆⠀⠀⠀⢠⠀⠀⢸⣻⣿⣤⣾⣿⣶⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⠀⠀⠀⠀⠀⠀⠈⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠈⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⢿⣭⡀⠀⠈⠙⠻⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣧⢄⡀⠁⠀⠚⠛⠓⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡗⠉⠉⠉⠇⠈⠂⠲⠒⢺⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣷⠀⠀⠠⠂⠂⠀⠀⠀⣼⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡀⠀⣾⠿⢷⡀⠀⢰⣏⠙⢯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣷⡀⠙⠮⠇⠀⣠⣿⣿⣄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣦⣤⣤⣾⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⠟⢉⣿⣿⣿⠿⠿⠛⠛⠛⠿⣿⣿⣿⣷⠀⢄⠀⣀⢀⠀⡥⠀⠀⠆⠐⠀⠀⢀⢻⠅⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⣿⣄⠘⣿⠁⠀⠀⠀⠸⣿⣿⣦⠈⢻⡿⢹⡇⠀⠀⠀⠀⢀⣅⠀⡃⢨⣄⡤⠤⣴⣷⣷⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⢟⡉⠁⠀⠀⠈⠻⠀⢿⡄⠀⠀⠀⠀⠈⠉⠙⠀⢸⡏⠀⢿⡀⢤⣹⣣⣿⣿⠓⠛⠶⠟⣿⣷⣿⣿⡿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠃⠀⠀⠀⠀⠀⠀⠈⠻⠄⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⢸⣷⠸⠘⣸⣿⡏⠩⠀⢸⡀⠿⢿⣿⣿⡇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⣴⣶⣾⣿⣿⡄⢺⣿⡅⡀⣿⣿⣇⣴⡇⢈⣃⢸⣾⣽⣿⣧⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣄⠀⠀⠀⣠⣴⠂⠀⠀⠀⠀⠀⠀⣠⣤⣾⡿⠿⠿⢯⣿⣿⣾⣿⣿⡗⣿⣿⣿⠝⢿⣞⣛⣷⣿⢻⣿⣿⣬
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢀⣼⡿⠛⠁⠀⠀⠀⠀⠀⠉⠉⠋⢹⣿⣿⣿⠛⣄⣜⣓⣌⣿⣷⣶⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠄⠀⠀⢀⣶⠿⠋⠀⠀⠀⠀⠀⠀⣠⣀⣴⣶⣶⡿⣿⣿⣿⠇⣮⣿⣧⣻⣿⣿⢿⣟⠛⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⣿⠇⠀⢀⠜⠡⠀⠀⠀⠀⠀⠀⠀⠸⡏⠙⠛⠋⠁⠀⣾⣿⣟⠨⠈⠉⠉⢡⣻⣷⣿⣿⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠏⠀⢸⠀⠀⠀⢶⠃⠀⠀⠀⠀⠀⠀⢠⡇⢓⠀⡂⠀⣬⣷⣿⣿⣿⠆⠐⠀⠀⠛⠻⠋⠁⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡿⠋⠀⠀⠀⠀⠀⠀⢸⡠⡄⠀⠀⠀⠃⢀⣿⡇⣾⠿⣳⣿⣿⣻⡟⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠸⡚⠁⠂⠀⡴⣄⠈⠈⣷⠀⠀⣏⣿⣿⣏⠀⣀⡠⡤⠀⠰⢶⣶⠄⠂⠈⠛⠂⠛
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡏⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⣿⣀⣈⣙⣿⣿⣿⠾⠿⠿⢋⡂⠀⠀⠈⣤⣤⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⡿⠴⢶⣶⣿⠿⠇⠀⠀⠀⠘⣿⣿⣿⣤⣿
⠀⠀⠀⠀⠀⠀⠀⣾⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠈⢽⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠉
⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣿⣿⡿⠃⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢿⢿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣿⣿⠃⠀⠀⠀⠀⠀⠘⣷⣦⣄⡀⡀⣄⣠⣠⠄⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠹⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠘⣿⣷⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣇⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣸⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣆⡄⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⠀⠀⠀⠀