⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⡒⣾⣭⣵⣿⣷⣶⣤⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⢀⣢⣤⡶⢮⣿⣱⣶⣿⣿⣿⣿⣿⣿⣿⣿⣷⣬⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢀⣵⣿⣿⣿⣿⣿⣿⡿⠿⠟⠛⠛⠛⠿⣿⣿⣟⣿⣿⣷⢄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⢠⣿⣿⣿⣿⣿⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⡹⡽⢿⣿⣿⣼⡆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⣸⣿⢿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⢻⣇⣿⣷⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢇⣿⣿⣻⣿⣻⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⢐⣀⢀⠌⣯⣿⣽⡆⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣾⣿⣿⣷⣿⡟⠀⣠⢶⣾⣏⣯⣋⡄⠀⠀⠀⠰⣿⠻⠿⢿⡳⣿⣾⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣿⣿⣷⠿⢳⣾⣿⣛⣉⣉⣉⡉⠙⢷⣤⣤⣦⣿⣾⣿⣿⣛⣿⣿⣶⣤⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⢿⣿⣿⣿⠡⠈⣟⠻⢟⣻⠏⠛⣀⣼⡗⠒⢶⡋⠿⢯⠟⢃⣿⣿⡿⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⢌⣻⢿⣿⠬⠂⣹⡠⠔⠒⠉⠉⢁⡿⠁⠀⠘⣯⠉⠛⠙⡾⣬⣱⠏⠄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠀⠞⢋⢿⢷⢇⡘⡭⠙⠲⠖⠶⠒⡻⢁⣤⡀⣤⡌⡳⠦⠼⠵⠾⠃⠀⠀⠂⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠘⣁⡈⢾⢸⡔⡄⠱⢀⡠⠄⠚⠉⠋⠙⠻⠉⠋⠉⠲⣤⠂⠂⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⡆⡬⣇⠒⢌⡐⠏⠁⠀⠀⢀⡤⣤⢤⣔⣢⡀⠀⠀⣃⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⠀⠀⠈⠳⡹⡄⠂⠀⠀⠀⠀⠐⠻⢛⠒⢋⠩⢛⠋⠀⠀⡘⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⠀⠀⠀⠀⠁⢿⣦⣁⠂⠄⠀⠀⠀⠳⢯⣧⡷⠋⠀⠀⣐⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡀⠈⠳⣟⣮⢖⣀⠀⠀⠀⠀⠀⠀⠀⢀⡰⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⢀⣠⣾⣟⠀⠀⠀⠈⠻⣯⢯⣟⡶⢤⢤⣠⢒⠲⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣤⣴⣶⣿⣿⣿⣿⣦⠀⠀⠀⠑⠌⢿⡾⣽⡻⢾⡱⣋⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⡿⠉⠛⢿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠈⠤⡙⣷⡹⢣⡓⣜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⠿⠿⠛⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⢣⠜⣫⢣⡑⣾⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⣴⣾⡿⠟⠛⠉⠀⠀⢀⠀⠀⠀⣰⣯⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠩⡐⢧⡘⣿⣿⣯⣅⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣸⣾⣿⡿⠋⠀⠂⠀⡀⠀⠀⠆⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⠄⠀⠀⠀⠈⠜⡿⠹⢿⣿⣿⣶⣤⡄⠀⠀⠀⠀ ⠀⣠⣾⣿⣿⠟⠀⠀⠀⠀⠐⢰⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠃⠹⣿⣿⡷⣯⢗⣦⡀⠀⠀ ⣾⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⡰⠀⠀⠀⣾⣿⣟⣿⣿⣿⣾⢿⣾⣟⣾⣯⣿⣿⣿⣷⣯⠀⡀⠀⠀⠀⠀⣸⣿⣿⡟⣷⡻⣿⣷⡄⠀ ⣿⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⣸⣿⠿⣼⣿⢿⣿⢾⣋⢿⣿⣿⣷⡿⣿⣿⣿⣿⡄⠉⠔⢠⣂⢀⢻⣿⣟⣧⢿⣟⣿⣿⣿⡀ ⡛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⢀⣿⣿⣿⣼⢯⡻⣽⣟⣼⣷⣽⣿⣿⣿⣝⣿⣿⣿⣏⠀⠀⠀⠀⡇⢸⢸⣿⢯⣞⣿⣿⡝⡋⡇ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣾⣏⣿⡜⠿⣶⣿⣿⣞⡿⣿⣿⣿⣿⣿⣯⠀⡢⠆⠀⡇⢘⠀⣷⡯⣿⣿⣿⣇⢅⠟ ⡇⠀⠀⠀⠀⠀⠀⠠⠑⠀⠀⠀⠀⠈⣿⣿⣿⣿⣼⣿⣿⠧⠻⣿⢟⠴⣟⢿⣿⣿⣿⣿⣿⡀⠈⡁⠀⠀⢸⠀⢿⣷⣿⣿⡿⢭⠀⠅made by defne ⠇⠀⠀⠀⠀⠠⠀⠐⠠⢁⠀⠀⠀⠀⢹⣿⣿⣷⣿⣿⣧⠀⠁⠀⠀⠈⠿⣿⣯⣿⣿⣾⣿⡇⣼⣿⡂⠀⢸⠀⢸⣿⣿⡇⠐⢲⠐⠀