⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡛⢷⣽⡀⠀⣀⠶⣄⡆⠀⠀⠀⠀⠂⠀⣰⣪⣠⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠓⠻⣿⡷⣇⠀⣮⠂⠀⠀⠀⠀⢶⠊⠡⢗⣵⡇⠀⣐⣀⠴⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣸⣇⢀⡧⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⠻⣀⣙⢢⣧⡀⢠⣄⡄⠀⣸⠀⢀⣴⢟⠇⠀⠹⠾⠽⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠙⠻⣇⡻⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠙⠛⠓⠂⠀⠚⠻⣷⣵⣄⡏⡆⡴⢡⠴⠋⠉⠛⢄⠀⠀⢀⣀⣤⡤⠀⠀⢀⠟⠀⠉⠒⠤⠤⠤⣄⠀⠀⠈⣩⢯⣏⣟⡳⢶⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠱⣀⠀⠀⠀⠀⠠⣶⠺⣻⡿⣿⣄⠃⠀⠀⠀⠀⠈⠳⣶⣿⣿⠏⠀⠀⢀⠇⠀⠀⠀⠠⠀⠀⠀⡼⡀⠀⠀⢿⢥⢚⢾⣟⡴⢹⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣔⠥⢊⣁⡉⢩⠂⠀⠀⠀⠜⢉⢽⣿⠋⠛⠃⠀⠀⠐⠂⢠⠿⡿⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠉⠁⠀⠙⠛⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣸⣹⣿⣿⣿⡿⠀⠀⠀⠀⠚⠋⢸⣹⠢⣀⣀⣀⣴⣦⣴⢏⠈⠺⣏⡯⣗⡦⣸⠀⠀⠀⠀⠀⠀⠀⠀⣸⠠⠴⠖⠒⠒⠲⢦⣤⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⢿⣿⣿⠿⣿⣿⣧⠖⢀⠀⠀⠀⣠⠋⠁⣴⣿⣩⣿⣿⣿⣿⣇⠂⠀⠀⠈⠀⠙⠿⡃⠀⠀⠀⠀⠀⠀⡠⠃⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠠⡞⡶⢲⡄⠀⠀⣰⢯⣶⣡⣦⢊⢤⣴⣟⠁⠆⢀⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⠀⡀⠀⠀⠢⣤⣶⡀⣿⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡨⠆⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣤⣄⠀⠀⡴⢿⣿⡆⠀⠀⠋⠷⠷⠿⠿⢿⣼⡛⢻⣆⣠⡜⣿⣿⣿⣿⢿⣿⣿⣿⣿⠛⠣⠀⠀⣠⣤⣀⣭⣿⣿⣟⡋⠀⠀⠀⠀⠀⠀⢤⡖⢁⣴⠾⡛⠋⠉⠀⠀⠀ ⠀⠀⠀⠳⣕⢷⢤⡓⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣻⣸⣿⣿⣿⣼⣿⣿⠋⠀⠀⠀⠀⠀⣠⡾⠿⠋⣿⡟⡏⡿⠂⠀⠀⠀⠀⠀⠀⠈⠣⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⣀⣀⣀⠬⠶⠀⣈⣢⣄⠀⠀⠀⠀⠀⢀⣤⣤⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⣿⢷⡀⠀⠀⠀⠀⠀⠉⠁⠀⢰⣿⡇⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄⠀⠀⠀⠀⠀⠀ ⠀⢫⡓⠭⠄⠀⠘⠒⠲⢕⡳⣄⠀⠀⠀⢠⢛⣿⢹⣿⣿⣿⣿⢻⣧⣶⣿⣿⢱⣶⣾⣷⣿⣦⠀⠀⠀⠄⠀⢀⡴⠻⡇⠀⢘⡄⡄⠀⠀⠀⠀⠀⠀⠈⡁⣜⠳⢤⣀⣀⡀⠀⣀ ⠀⠀⣬⣽⣮⣂⠀⠀⠀⠐⠚⠷⠿⣦⣀⠘⢯⣊⣿⣿⣯⣟⡾⣼⣿⣿⣿⣬⠻⠷⢿⣿⣟⣿⣧⣀⣤⠜⠊⠁⡇⠀⢀⡅⠀⡟⡏⠲⢄⡀⠀⠀⠀⣀⡴⠙⢷⣄⠀⠀⢣⠀⠈ ⠀⠘⢻⣟⠛⠙⠿⡒⠂⠀⢀⢀⣤⠼⣿⣿⠟⠻⣿⣿⣟⣿⠹⣾⣋⢻⣿⡿⣇⠀⠀⠈⢫⠙⠛⢿⡏⣆⣀⣴⣇⢰⡅⡇⣠⢯⠋⠀⠀⠈⠉⠙⠚⠁⠀⠀⠀⠙⢇⠀⡀⡟⢦ ⠀⡸⠛⠁⠀⠀⠀⣀⢤⡴⣺⣿⡯⢪⣿⠏⠀⠀⡀⠀⠙⠻⣿⡿⠿⠟⠋⠙⠛⠃⠀⠀⠘⡄⣠⣼⣷⣿⡿⠿⣏⣯⢹⣸⢸⣺⠿⢖⣤⡀⠀⠀⡄⠀⠀⠀⠀⠀⠈⢆⢇⢫⠉ ⢘⣄⠤⠔⠂⠀⣡⠔⣡⡮⠓⠁⠀⣾⡟⠀⠀⠲⣱⣽⠆⠀⠉⢻⣷⣄⠀⠀⠀⠀⠀⠀⠀⣷⣿⡿⣿⡏⢳⣺⣧⣿⣮⣿⣿⣿⡗⠒⠋⠀⠀⢯⣱⢤⡀⠀⠀⠀⠀⠈⠪⠞⠀ ⠈⠑⠢⠒⠤⠬⣰⡿⠊⠀⠀⠀⠀⡿⠁⠀⠀⢸⡵⠛⠃⠀⠀⠀⠙⢿⣧⡀⠀⠀⠀⢀⣼⣿⠿⠿⢚⣴⣾⡿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠉⠋⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣀⣾⠎⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠉⠁⠀⢠⣾⣿⣿⣷⣤⣿⣿⣟⡇⣽⣿⣿⠋⣿⢻⣿⢿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀