⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠚⠉⠈⠙⢧⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡤⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⡜⠉⢧⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠉⠷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡇⠀⢸⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⡎⠁⠠⡈⠈⠳⣄⠀⠀⠀⠀⠀⠀⡇⠀⣀⠧⠔⠚⠂⢺⠧⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⡇⠀⠀⠀⡡⠄⠈⠷⠦⠤⡤⡴⠄⡾⠋⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠧⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠺⢦⠀⠀⣠⣤⠀⠀⢣⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⣠⣄⣀⣠⡀⠀⠀⡼⠀⠀⠀⠀ ⠀⠀⠀⡤⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⣀⠀⠀⠀⠀⠀⡠⠉⢈⣄⠀⠀⠀ ⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠹⡄⠀ ⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣶⣆⠀⠀⠀⠀⠀⣰⣾⣯⣽⡷⡄⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀ ⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠳⠻⠍⠁⡇⠀⠀⠀⠀⣿⠹⠟⢻⠋⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣤⣀⣀⡞⠀⠀⠀⠀⠀⠙⠷⣄⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⢸⠀⠀⠀⠀⠀⣠⣖⣒⣦⠀⠀⠀⠀⠀⠀⠀⢶⣿⣿⡆⠀⠀⠀⠀⠀⠀⣀⣤⣦⣀⠀⠀⠀⠀⠀⡇ ⠘⠀⠀⠀⠀⢼⣿⣾⣿⣿⡇⠀⠀⠀⠀⣀⣀⡤⠞⠳⢄⣀⡀⠀⠀⠀⢸⣿⣿⣾⣿⡿⠀⠀⠀⠀⡇ ⠰⡀⠀⠀⠀⠉⠻⠿⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠻⠿⠿⠏⠀⠀⠀⠀⠀⠃ ⠀⠹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢱⡟⡞⡠⠀⠀⡖⢲⢶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀ ⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⢾⡀⠁⠀⡏⠀⠀⢇⠀⠀⠁⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⠀ ⠀⠀⠀⠈⢢⠀⠀⠀⠀⠀⠀⠀⠀⠛⠂⠘⠀⠀⠀⠈⠢⣄⡔⠋⠀⠀⠀⠀⠀⠀⣀⣠⠏⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠑⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡀⠈⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠐⡖⠤⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠰⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠅⠉⠉⠀⢨⠉⠉⠁⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢀⡀⣀⠀⠠⠂⠀⠀⠀⠀⠀⠐⠀⡀⠀⠀⠀⠌⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠊⠉⠉⠙⢆⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⠏⠀⠀⠙⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢀⣀⠊⠉⢒⠀⠀⡜⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡿⠀⢠⣄⠀⠀⠻⢤⡀⠀⠀⠀⠀⠀⠀⢰⠇⢸⠀⠀⠀⡾⠀⣠⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⠃⠀⢐⠀⠉⠲⣄⠀⢈⢶⣄⣀⣀⣀⢀⣰⡀⡯⠖⠚⠉⠉⠉⠹⣦⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⣾⠀⠀⢈⣀⡠⠴⠈⠉⠀⠀⠀⠀⠀⠀⠀⡎⠉⠀⠀⠀⠀⠀⠀⠀⠀⠙⡆⠀⠀⠀ ⠀⠀⠀⣰⢫⡔⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠲⠶⠀⠀⠤⠖⠀⠀⡇⠀⠀⠀ ⠀⠀⢀⡗⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⠒⠚⠃⠀⠀⡽⢅⠀⠀⠀ ⠀⢀⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠦⢤⣀⠤⠴⠒⠉⠀⠈⠲⡄⠀ ⢠⠏⠀⠀⠀⠀⠀⠀⠀⢀⣼⣯⣿⣯⢤⡀⠀⠀⠀⠀⢸⣶⣷⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠩⡀ ⢰⠂⠀⠀⠀⠀⠀⠀⠀⠸⡟⢓⢻⣚⠀⡆⠀⠀⠀⠀⠚⡇⣛⣟⠋⡄⠀⠀⠀⠀⠀⠀⠀⠀⠂ ⣼⠀⠀⠀⠀⢀⣀⣀⡀⠀⠁⠄⣈⡠⠈⠀⢀⣀⡀⠀⠱⠄⣁⣁⡐⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠔⠀⠀⠀⢠⣶⡾⣾⡶⡦⠀⠀⠀⠀⠀⠀⢀⣿⡁⠀⠀⠀⠀⠀⠀⢠⣤⣴⣦⣤⠀⠀⠀⠀⠤ ⢨⠀⠀⠀⠩⣿⡅⣽⡍⡯⠀⠀⠀⠀⠙⠚⠉⠀⠙⠒⠒⠚⠁⠀⢠⢸⣿⣩⣿⣭⠧⠀⠀⠀⡄ ⢸⡀⠀⠀⠀⠀⠂⠚⠂⠀⠀⢀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠒⠟⠖⠀⠀⠀⡴⠀ ⠈⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠙⡿⠹⢷⡆⠀⣿⠟⡿⢷⡏⡇⠀⠀⠀⠀⠀⠀⠀⢀⡠⠆⠀ ⠀⠀⢓⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⡴⠁⠀⢪⠃⠀⠀⣴⠃⠀⠀⠀⠀⠀⠀⠀⡔⠂⠀⠀ ⠀⠀⠀⠙⡄⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠙⠪⠶⠚⠁⠀⠀⠀⠀⠀⠀⡰⠈⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠑⠆⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠐⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⠋⠁⠉⠁⠈⠐⠦⢠⡤⠤⠠⠤⡠⡴⠠⠴⠒⠉⠉⢲⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⡴⠛⠀⠀⠀⠀⠈⣆⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⠖⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠚⠉⠈⠙⢧⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡤⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⡜⠉⢧⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠉⠷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡇⠀⢸⠀⠀⡇⠀⠀⠀⠀⠐⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⡎⠁⠠⡈⠈⠳⣄⠀⠀⠀⠀⠀⠀⡇⠀⣀⠧⠔⠚⠂⢺⠧⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⡇⠀⠀⠀⡡⠄⠈⠷⠦⠤⡤⡴⠄⡾⠋⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠧⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠺⢦⠀⠀⣠⣤⠀⠀⢣⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⣠⣄⣀⣠⡀⠀⠀⡼⠀⠀⠀⠀ ⠀⠀⠀⡤⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⣀⠀⠀⠀⠀⠀⡠⠉⢈⣄⠀⠀⠀ ⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠹⡄⠀ ⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣶⣆⠀⠀⠀⠀⠀⣰⣾⣯⣽⡷⡄⠀⠀⢐⠀⠀⠀⠀⠀⢳⠀ ⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠳⠻⠍⠁⡇⠀⠀⠀⠀⣿⠹⠟⢻⠋⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣤⣀⣀⡞⠀⠀⠀⠀⠀⠙⠷⣄⢠⠞⠁⠀⠀⠁⢀⠀⠀⠀⠀⠀⡇ ⢸⠀⠀⠀⠀⠀⣠⣖⣒⣦⠀⠀⠀⠀⠀⠀⠀⢶⣿⣿⡆⠀⠀⠀⠀⠀⠀⣀⣤⣦⣀⠀⠀⠀⠀⡀⡇ ⠘⠀⠀⠀⠀⣾⣿⣾⣿⣿⡇⠀⠀⠀⠀⣀⣀⡤⠞⠳⢄⣀⡀⠀⠀⠀⢸⣿⣿⣾⣿⡿⠀⠀⠄⠀⡧ ⠰⡀⠀⠀⠀⠉⠻⠿⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠿⠿⠏⠀⠀⠐⠀⢰⠃ ⠀⠹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢱⡟⡞⡠⠀⠀⡖⢲⢶⣤⡀⠀⠀⠀⠀⣅⠀⠀⠀⠀⠠⢀⡎⠀ ⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⢾⡀⠁⠀⡏⠀⠀⢇⠀⠀⠁⡏⠀⠀⠀⠀⠀⠀⠁⠀⢀⣤⠋⠀⠀ ⠀⠀⠀⠈⢢⠀⠀⠀⠀⠀⠀⠀⠀⠛⠂⠘⠀⠀⠀⠈⠢⣄⡔⠋⠀⠀⠀⠀⠀⠃⣀⣠⠏⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠑⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⡀⠈⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠐⡖⠤⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠰⠢⠀⠀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠅⠉⠉⠀⢨⠉⠉⠁⠀⠀⠀⠀⡇⠀⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢀⡀⣀⠀⠠⠂⠀⠀⠀⠀⠀⠐⠀⡀⠀⠀⠀⠌⡅⠀⠀⠀⠀⠀⠀⠠⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀