⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠴⠒⠒⠒⡶⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢴⢤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠝⠀⠀⣀⣐⣀⠀⠀⠈⢦⠀⡶⢄⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠘⣇⠄⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠓⠢⢄⡀⠀⠀⠀⣸⡇⠀⠀⣰⣃⠀⠈⢧⠀⠀⠈⡇⠻⡄⠀⠀⠉⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠛⠒⠦⣄⠀⠀⠀⠀⠀
⠀⠈⠳⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄⠀⢿⢳⣧⠀⣽⢿⣼⣇⡟⠀⠀⢀⡇⠀⠙⢮⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀
⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠘⣦⣬⣾⡟⠷⣿⡀⠻⣼⢷⣄⠀⡼⠁⠀⠀⠀⢸⣶⢀⡀⠀⠀⡀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠹⡄⠀
⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⣿⠀⠀⠀⠈⠙⢦⠀⠀⠀⠀⠀⢘⣏⡷⠀⠈⠈⠛⣆⠈⡑⣝⢿⡁⠀⠀⠀⠀⣨⣿⡿⣿⡿⠿⠿⢧⣀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠸⡄
⠀⠀⠀⠀⣿⡁⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠈⣇⠀⠀⣠⣶⣯⣅⡄⠠⣶⣾⡟⢃⢀⠻⣦⠀⣷⢀⡀⢠⢾⣹⡭⢶⣒⣀⡀⣀⣢⠮⠵⠄⠀⠀⢸⡄⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⣿⠄⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣿⠀⠀⢉⣴⠟⣿⣴⠞⣿⣯⣤⡘⣿⣿⣗⣁⠈⢫⠧⣷⠟⢁⡾⠋⠉⠈⠙⡿⡇⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠑
⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢀⣿⠀⢀⣾⠓⠀⠋⠁⠀⠉⡴⢋⣿⠹⣷⢍⠹⣷⣫⡞⠁⢠⠏⣿⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸⡃⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣿⠀⠀⠀⢀⣠⠞⠂⠀⢸⣿⡧⠀⠀⠀⠀⣸⠁⠈⠿⠞⠉⠸⡄⡀⠙⠛⢦⡏⢸⡏⢶⣄⣀⣀⣀⡇⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⣸⠃
⠀⠀⠀⠀⣿⠄⠀⠀⠀⠀⠙⠉⠙⠋⠉⠁⠀⠀⠀⠈⣿⠅⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⡸⢷⣄⠀⡀⠨⠻⣧⡾⠛⣯⠻⣟⠱⣯⡛⠉⠉⠀⠀⠀⠀⠀⠀⡴⠃⠀
⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡁⠀⠀⠀⠀⠈⠣⣀⡀⣀⡤⠞⠁⠀⢙⡷⡄⠀⠀⠈⠀⢠⣿⡾⠋⠀⠈⣿⠀⠀⠀⠀⠀⢀⣠⠞⠁⠀⠀
⠀⣠⣖⣋⣀⣀⣀⣀⣀⣀⣠⣀⣀⣠⣀⣠⡤⠴⠚⠁⠈⢧⢀⡀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⢠⠞⠀⡿⢀⡄⠀⠀⠀⠀⠀⠀⠀⣰⣟⣠⣀⣤⠤⠖⠋⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠛⢦⡠⠀⠀⠀⠀⠀⠀⣠⠔⠋⠀⠀⢧⣸⣷⡀⠀⠀⠰⠶⣶⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠒⠒⠛⠉⠁⠀⠀⠀⠀⠀⠙⠃⠙⠺⠤⠤⠾⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣷⠀⣴⡿⢿⣦⠀⢸⡇⠀⢰⣿⠀⠀⠀⠀⣿⠀⣾⣧⠀⣿⠀⢸⡇⢸⣿⣿⣿⠀⣾⡇⠀⣾⣿⣇⢾⣿⣿⣿⠀⣿⡆⢿⣷⠀⣾⡇⣾⣿⣿⠀⣿
⢸⣿⣤⣿⠀⣿⡇⢸⣿⠀⢸⡇⠀⢸⣿⠀⠀⠀⠀⣿⠀⣿⣿⣶⣿⠀⢸⡇⠀⢸⣿⠀⠀⣿⡇⠀⣿⢿⣿⠀⢸⣿⠀⠀⣿⡇⢸⣿⣠⣿⠃⣿⣿⣤⠀ ⣿
⢸⣿⠛⣿⠀⣿⡇⢸⣿⠀⢸⡇⠀⢸⣿⠀⠀⠀⠀⣿⠀⣿⣿⣿⣿⠀⢸⡇⠀⢸⣿⠀⠀⣿⡇⢸⣿⣤⣿⡆⢸⣿⠀⠀⣿⡇⢸⣿⣿⣿⠀⣿⣿⠛⠀ ⣿
⢸⣿⠀⣿⠀⢿⣷⣼⡿⠀⢸⣷⡆⢸⣿⣶⠂⠀ ⣿⠀⣿⡇⢻⣿⠀⢸⡇⠀⢸⣿⠀⠀⣿⡇⣼⣿⠉⣿⡇⢸⣿⠀⠀⣿⡇⠀⣿⣿⣿⠀⣿⣿⣶⡄⣿⣿