⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠿⢿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⠈⠉⣿⣿⣿⣿⣿⡇⠭⠐⡢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡠⣪⡖⠉⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠈⠑⢬⣦⢄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⣺⣿⠏⢰⣶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡷⠀⢻⣿⣦⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡔⣽⣿⡟⠀⢀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⣤⠀⠀⣹⣿⣷⡀⠀⠀⠀⠀ ⠀⠀⠀⣰⣞⣿⣿⠀⠀⠘⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣋⠀⠀⢰⣿⣿⢖⡀⠀⠀⠀ ⠀⠀⢀⢻⣿⣿⡃⠀⠀⣾⡿⠂⠀⣰⣶⣦⠀⢠⣶⣶⡄⠀⠺⣿⠇⠀⠀⠹⣿⡽⣇⠀⠀⠀ ⠀⠀⡈⣿⣿⣿⠄⠀⠀⠀⠀⡶⣦⣬⣭⣁⠀⣀⣨⣯⣤⡶⠆⠀⠀⠀⠀⣾⣿⣯⠻⡀⠀⠀ ⠀⣀⣧⣿⣿⣿⣧⠀⢀⣠⣤⣀⡁⠙⠛⢿⣿⣿⠟⠫⠃⣢⣤⣤⣄⡀⢀⣾⣿⣷⣿⣶⣄⠀ ⢸⣿⢫⢿⣿⣿⣿⣵⣿⣿⣿⣿⣿⣧⢀⠈⠈⠁⠀⢢⣿⣿⣿⣿⣿⣿⡌⣿⣟⣿⣟⣍⣿⡄ ⠸⣿⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⡟⣸⠇⠀⠀⢲⠞⣿⣿⣿⣿⣿⣿⠉⡿⣿⢿⣿⡿⠟⠀ ⠀⠀⡎⣿⣿⣿⠋⠀⠙⠿⣿⠿⠛⢁⣻⠀⠀⠀⢘⣧⠈⠻⠿⠿⠋⠁⠀⠈⣿⣻⡇⡆⠀⠀ ⠀⠀⢁⢿⣿⣽⡄⠀⠀⠀⠀⠀⠀⠨⢝⠀⠀⠀⠐⡫⠃⠀⠀⠀⠀⠀⠀⢸⣿⣿⢠⠀⠀⠀ ⠀⠀⠸⢻⣿⣷⣧⠄⠀⣀⣀⠀⠀⡁⣵⣀⣀⣀⣤⠼⠄⠀⠀⣤⠀⠀⢰⣾⣿⠾⡟⠀⠀⠀ ⠀⠀⠀⢛⣿⣿⣿⣄⢠⣾⠃⠀⠐⣮⣟⣿⣿⣿⡝⢨⣸⠀⠀⠹⣷⡄⢸⣿⣿⠻⠇⠀⠀⠀ ⠀⠀⠀⠘⣹⣿⣿⣷⣿⠇⠀⠀⠀⠈⠉⠉⠛⠙⠉⠉⠀⠀⠀⠀⢻⣿⣿⣿⣷⡘⠀⠀⠀⠀ ⠀⠀⠀⠀⠱⣻⣿⣿⣿⣆⣀⣀⠀⣠⣤⡄⠀⠀⣰⣤⡀⠀⣀⣀⣼⣿⣷⣟⠿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠩⣻⣿⣿⣿⣿⡿⠁⠙⠿⠋⠀⠀⠛⠟⠃⢺⢿⣿⣿⣾⣽⡿⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠱⡻⡻⣻⣿⣽⣦⣠⣦⣄⠀⠀⣠⣦⣤⣰⣿⣿⣯⡟⡿⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⢞⢿⣿⣿⣿⣿⠛⠁⠀⢀⠙⡟⣱⣿⣿⣿⣿⠝⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢝⡻⣿⣿⣿⣷⣤⣤⣾⣿⣿⡿⣫⠝⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠭⣽⣛⡛⣛⣓⡫⠭⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠭⡫⣓⣛⡛⣛⣽⠭⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠝⣫⡿⣿⣿⣾⣤⣤⣷⣿⣿⣿⡻⢝⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠝⣿⣿⣿⣿⣱⡟⠙⢀⠀⠁⠛⣿⣿⣿⣿⢿⢞⠈⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠁⡿⡟⣯⣿⣿⣰⣤⣦⣠⠀⠀⣄⣦⣠⣦⣽⣿⣻⡻⡻⠱⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠁⡿⣽⣾⣿⣿⢿⢺⠃⠟⠛⠀⠀⠋⠿⠙⠁⡿⣿⣿⣿⣿⣻⠩⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠿⣟⣷⣿⣼⣀⣀⠀⡀⣤⣰⠀⠀⡄⣤⣠⠀⣀⣀⣆⣿⣿⣿⣻⠱⠀⠀⠀⠀ ⠀⠀⠀⠀⡘⣷⣿⣿⣿⢻⠀⠀⠀⠀⠉⠉⠙⠛⠉⠉⠈⠀⠀⠀⠇⣿⣷⣿⣿⣹⠘⠀⠀⠀ ⠀⠀⠀⠇⠻⣿⣿⢸⡄⣷⠹⠀⠀⣸⢨⡝⣿⣿⣿⣟⣮⠐⠀⠃⣾⢠⣄⣿⣿⣿⢛⠀⠀⠀ ⠀⠀⠀⡟⠾⣿⣾⢰⠀⠀⣤⠀⠀⠄⠼⣤⣀⣀⣀⣵⡁⠀⠀⣀⣀⠀⠄⣧⣷⣿⢻⠸⠀⠀ ⠀⠀⠀⢠⣿⣿⢸⠀⠀⠀⠀⠀⠀⠃⡫⠐⠀⠀⠀⢝⠨⠀⠀⠀⠀⠀⠀⡄⣽⣿⢿⢁⠀⠀ ⠀⠀⡆⡇⣻⣿⠈⠀⠁⠋⠿⠿⠻⠈⣧⢘⠀⠀⠀⣻⢁⠛⠿⣿⠿⠙⠀⠋⣿⣿⣿⡎⠀⠀ ⠀⠟⡿⣿⢿⣿⡿⠉⣿⣿⣿⣿⣿⣿⠞⢲⠀⠀⠇⣸⡟⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⠸ ⡄⣿⣍⣟⣿⣟⣿⡌⣿⣿⣿⣿⣿⣿⢢⠀⠁⠈⠈⢀⣧⣿⣿⣿⣿⣿⣵⣿⣿⣿⢿⢫⣿⢸ ⠀⣄⣶⣿⣷⣿⣾⢀⡀⣄⣤⣤⣢⠃⠫⠟⣿⣿⢿⠛⠙⡁⣀⣤⣠⢀⠀⣧⣿⣿⣿⣧⣀⠀ ⠀⠀⡀⠻⣯⣿⣾⠀⠀⠀⠀⠆⡶⣤⣯⣨⣀⠀⣁⣭⣬⣦⡶⠀⠀⠀⠀⠄⣿⣿⣿⡈⠀⠀ ⠀⠀⠀⣇⡽⣿⠹⠀⠀⠇⣿⠺⠀⡄⣶⣶⢠⠀⣦⣶⣰⠀⠂⡿⣾⠀⠀⡃⣿⣿⢻⢀⠀⠀ ⠀⠀⠀⡀⢖⣿⣿⢰⠀⠀⣋⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠛⠘⠀⠀⣿⣿⣞⣰⠀⠀⠀ ⠀⠀⠀⠀⡀⣷⣿⣹⠀⠀⣤⣬⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣤⢀⠀⡟⣿⣽⡔⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡀⣦⣿⢻⠀⡷⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⣶⢰⠏⣿⣺⡠⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢄⣦⢬⠑⠈⠀⠀⠀⠉⠉⠉⠉⠈⠀⠀⠀⠉⡖⣪⡠⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢄⡢⠐⠭⡇⣿⣿⣿⣿⣿⠉⠈⠒⠤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⢿⠿⣿⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀