⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣼⣷⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢀⣠⠶⠟⠿⠿⠿⢿⢿⣶⣶⣶⣶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡧⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠓⠀⠀⠀⠠⠿⠖⠒⠻⣯⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⢠⣺⣿⣿⡇⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⡁⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⣿⠟⠃⠀⣧⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡰⠃⠀⡀⠀⠀⡀⣠⠀⠀⣶⣵⣷⣿⣿⣿
⠀⠀⠀⠀⢠⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⢸⡏⢻⣤⢀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⡿⠧⠦⠄⠠⢀⣤⣿⣿⣿⣿⠏⠈⠙⠛⢻⣿
⠀⠀⠀⠀⣼⣣⠀⠀⠀⠀⠀⠀⠀⢀⣾⢿⠀⢸⠀⠐⢿⣿⣿⣿⣛⣛⣻⣗⣖⣒⣲⣶⣶⣶⣶⣾⣿⡧⠤⣤⣤⣤⣤⣄⣀⣀⣀⣘⣧⣠⣶⣶⣦⣽⣿⡿⢿⣻⣏⠀⠀⠀⠀⢸⣿
⠀⠀⠀⢀⣿⠙⢷⣄⠀⠀⠀⣠⡶⠋⠁⡏⢀⡟⠀⠀⠀⠻⢿⣿⢀⣀⣠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠛⠛⠛⠓⠒⠶⠖⣤⡿⠿⣟⢿⣇⠉⣿⠟⠿⢤⣀⣈⠃⠀⠀⠠⣤⢿⣿
⠀⠀⠀⣸⠟⠂⢤⠈⠛⠒⠛⠁⠀⠀⣰⠇⣼⣅⡀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣠⠾⠋⢀⣠⣿⡷⠟⢾⡏⠀⠀⠀⠈⠉⠀⠀⣤⣄⣠⣾⣿
⠀⠀⢠⠟⠀⠀⠀⠀⠀⠀⢠⡄⠀⠘⣿⠀⡏⣿⣷⡂⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣠⡞⠁⠀⣰⣾⢟⠩⠤⠤⢼⣇⠀⠀⠀⠀⠀⠀⠰⠉⢠⣿⣿⡿
⠀⢠⠟⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⢸⠀⣷⣿⣿⣿⣦⣀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⠃⢀⣾⢿⠋⠀⠀⠀⠀⠀⠀⠙⠲⢤⣾⣿⠟⢀⣠⣿⣁⣠⣤
⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣼⡆⠻⣿⣿⣿⣿⡿⠗⠓⠒⠒⠲⠽⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⠟⢹⡇⡼⣿⡟⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠿⢿⣿⣯⣠⡇
⠈⠳⣆⡀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢹⡇⠸⢽⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣾⣿⣿⣿⣿⣿⡿⠋⠘⢸⣧⡇⣿⠀⠣⠀⠀⠀⠖⠉⠓⠶⢤⣄⠀⠀⠀⠀⠀⠀⠈⠙⠻⠇
⠀⠀⠈⠙⢦⡀⠀⠀⠀⠀⠀⡸⠀⠀⠘⡇⢀⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⠿⠋⣠⠞⠀⠈⢿⣇⠙⠲⠀⠀⣠⠖⠋⠉⠙⢶⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠔⠁⠀⠀⠀⢀⡬⠔⠚⠉⠉⠀⠀⠀⠀⠀⢤⡀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁⠀⠀⠀⠀⠙⠃⠀⣴⠞⠁⠀⠀⠀⠀⠈⠀⢸⣿⣿⣶⣦⣤⣤⣀⣀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⡀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠰⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠐⠄⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⢰⢋⣠⠴⢚⣉⡿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡴⠚⠱⡄⠀⠀⢨⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠈⠓⢤⣠⣄⡀⠀⠀⠈⢱⠞⠉⠀⠰⢏⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠏⠀⠀⠀⡆⠀⠠⣯⠉⠉⠉⠉⠉⠙⠛⠛⠛⠛⠛⠛
⠀⠀⠀⠀⠀⠈⣕⡯⠳⠦⢄⡀⠀⠀⠀⠀⢀⣀⣉⣉⣉⣉⡽⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⠉⠀⣤⡤⠚⠁⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠙⢦⣄⠀⠙⠲⡄⠀⠀⠀⣄⣀⣉⣥⣤⣾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠋⢧⠀⠀⠀⠀⠀⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⣸⡍⠳⣄⠀⠠⣄⣉⣁⣉⡴⠋⠀⠀⢀⣠⡴⠊⠀⠀⠀⠀⢀⣠⠴⢦⡖⠒⠒⠋⠁⠀⠀⠈⠳⢤⣄⣤⣼⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢯⢧⠀⠀⠉⠓⠒⠦⠞⠋⠀⠀⠀⠀⠉⠀⢀⣀⣀⡤⠴⠚⠉⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠩⢭⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡄⠀⠀⠀⠀⠀⠀⠀⠈⠸⠶⠒⠒⠋⢹⠁⠀⠀⠀⠀⠀⠀⠀⠀⠻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡅⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣦⣄⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀