⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀ ⠀⠀⠀⢤⢸⡇⠄⠀⠀⠀⠀⠀⠀⠰⡎⢱⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢳⣼⣔⠂⠀⠀⠀ ⠀⠀⠒⢒⣿⣿⠒⠂⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠉⡹⢻⠿⡏⠁⠀⠀ ⠀⠀⠀⠉⢸⡇⠁⢠⣀⣀⠶⠶⠶⠶⠶⠶⢆⣀⡀⠀⠀⠀⠀⠀⣄⣀⡲⠶⠶⠶⠶⠶⢶⣀⣀⠀⠀⠺⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⠞⠋⢀⣀⡤⠤⠤⠤⠤⢄⣀⣀⠙⠳⣤⢀⡴⠛⠁⣀⣠⠤⠤⠤⠤⠤⣄⣀⡈⠙⢦⡀⠀⠀⢀⡀⠀ ⠀⠀⠀⣰⡼⠃⣠⠞⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⢄⡀⠃⢀⡘⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠣⣀⠙⣦⡀⠀⠀⠀ ⠀⠀⣰⠏⢠⡖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠘⢢⠀⢹⡀⠀⠀ ⠀⣤⠇⢀⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⠀⠀⠀⠀⠈⣷⠀⢣⡄⠀ ⢀⣿⠀⣿⠀⠀⡀⢀⡐⣲⠶⢶⡖⢾⡙⣏⠻⣍⠻⣍⢻⡙⣏⠻⣝⢫⡝⣫⢛⠶⠶⠶⢶⠶⣆⣄⣀⡀⢸⡇⢸⡇⠀ ⢸⡇⠀⣏⢻⡇⠀⠀⠈⣧⢛⠦⡏⠉⡼⣌⠳⣜⠳⣌⢧⣋⡘⢧⡓⢧⡚⣥⢋⡞⡭⣛⢬⢳⡙⣀⢻⡹⡉⢵⠀⢸⠀ ⢸⡇⠀⣿⣷⣇⣀⣀⡸⣇⢏⡞⣭⢛⠱⢎⡽⢸⢿⢿⣷⣿⢿⣿⣽⠂⡃⠀⠉⠆⠰⡍⢎⠧⣝⣦⣷⡗⣫⢿⠀⢸⠀ ⢸⡇⢀⣿⣟⡯⣙⠭⡳⣽⣾⣵⡿⠞⠀⠈⠑⡈⢌⡼⣿⣟⣾⣿⣿⠀⠃⠀⠀⠐⣠⠓⢼⣶⡿⣯⣹⠷⣭⢾⠀⢸⠀ ⠘⣣⠀⣿⡽⣷⣡⠷⡵⣫⣷⣿⣇⡘⠀⢀⠐⡤⢪⢥⣿⣿⣿⣿⣻⣟⣦⣄⡷⣜⣦⣿⢿⣯⣿⡽⢆⡛⣼⠇⢰⡜⠂ ⠀⠙⡆⠀⢿⣿⣏⡀⢸⠹⣿⣿⣿⣿⣶⣜⣲⣱⡿⣿⢿⡿⠟⠚⡷⢯⠛⢻⣾⡟⠙⣿⣿⡽⣯⢷⣩⢒⡿⠀⡞⠃⠀ ⠀⠀⠙⣤⡈⠛⣿⣮⣔⡿⣿⣟⡟⠈⡝⣯⢷⣯⢿⣽⣻⠉⠂⠀⠈⠠⡘⢦⢻⣷⣞⣯⣿⡽⣯⣟⡾⠋⣡⡔⠉⠀⠀ ⠀⢀⡄⠀⠑⢦⡈⠳⠮⣟⡹⣄⡓⣺⢴⣯⣟⣾⢯⢷⣿⣶⣄⣀⡰⢰⣉⣦⣿⢏⠻⢾⣳⡯⠷⠋⣠⡔⠋⠀⢀⣤⠀ ⠀⠈⠁⠀⠀⠀⠳⣤⡄⠉⠱⢶⣵⡿⢾⣳⣿⣾⣇⣨⡿⣿⣿⣿⣷⡧⡹⢍⡲⣩⡾⠷⠉⠁⣤⡴⠉⠀⠀⠀⠈⠉⠀ ⠀⠀⠀⠀⠀⢠⡀⠀⠈⠋⠤⣄⡀⠙⠳⢻⣳⣿⣻⣯⣿⣿⡟⣏⡒⢶⣹⠞⠙⠁⣠⡤⠜⠋⠀⠀⠀⠀⠦⠀⠀⠀⠀ ⠀⠀⠀⠀⠸⣇⡸⠄⠀⠀⠀⠀⠘⠻⠤⣀⡀⠛⠛⠥⠿⠶⠭⠞⠛⠃⣀⡠⠼⠛⠃⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠲⠤⠤⠤⠤⠤⠞⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⣀⣳⣾⣦⣃⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢸⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⣤⠀⠀⠀⠉⠼⢻⠻⠍⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣹⣾⣷⣡⡄⠀⠀⠀⠀⠀⠀⠀⠀⢶⠉⡱⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⢹⠛⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀