⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⢾⣻⡿⣿⣻⣟⡿⣶⡶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡿⢫⣑⣾⣟⣷⣻⢷⣻⢾⣽⣳⢿⣽⣻⢷⣦⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣄⡀⠀⠀⠀⢀⣾⢯⣷⢫⢱⣾⣻⣞⡷⣯⠿⣛⠛⡭⡍⢯⢩⢛⡛⠾⣿⣦⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⡍⠛⠱⢤⡀⠀⢹⡃⠀⠳⢦⡀⢠⣿⢯⣟⣾⢡⣿⢷⣻⢞⡙⣆⢳⣌⣽⣰⣙⠆⡏⢦⡙⢎⡴⢹⣷⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠛⣶⣼⡗⠀⠀⢱⣷⣿⡏⠛⡟⣿⢹⣯⡟⢱⣾⠛⠋⠉⠀⠈⠑⢫⡟⢻⣦⡝⣬⠒⢣⣽⣧⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠈⢿⣿⣇⠀⠀⣸⡟⠀⠀⠈⠻⣿⣏⡾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⢾⡹⢷⣪⠱⣌⢿⡆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄⠀⠀⠀⠙⣿⢆⣾⠳⡇⠀⡄⠀⠀⠈⢛⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⢰⡄⠄⢻⣿⡽⣷⠌⣾⣧⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⠀⠀⠈⡿⡥⢛⡇⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠷⠀⠀⠀⠙⢛⣻⣽⣿⣿⣞⡰⣿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡴⡖⠲⢢⢽⣧⡀⠀⢰⣯⠱⣍⣾⡀⠈⢣⠀⠀⠀⠀⠀⢀⣠⣴⡾⢋⣀⣀⠀⠀⠀⣿⡇⣸⣿⡿⣇⠞⣿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠹⣇⠀⠀⠈⠙⢽⣄⢸⡏⢧⣿⡣⢷⡄⠀⠀⠀⠀⠛⠛⣹⣿⢿⣿⠋⠻⣿⣧⠀⠀⠹⢿⣯⣿⣟⣿⣸⣿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢗⣄⠀⠀⠀⠈⢒⣿⡿⣇⡛⢦⢻⡶⣄⠀⠐⣷⣾⡁⠈⠸⣶⡀⣰⠿⣿⡇⠀⠀⠀⠛⠟⢞⣿⣿⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⢄⠀⠀⣇⠘⣿⣧⡙⡎⡵⢻⣞⣧⡀⠀⠀⠙⢄⠀⠳⡉⠻⣾⣿⠃⠀⠀⠀⠐⠀⣸⣾⡿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠶⣤⡹⣆⠈⢷⡱⣩⠖⣹⣿⡘⣿⡄⠀⠀⠀⠑⠂⠌⠐⠋⠁⠀⠀⠀⠈⢑⣾⣿⣻⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⡟⠋⠬⢷⡀⢿⡴⡙⢦⣿⢧⡹⣿⡄⠀⠀⠀⢀⣀⣀⡀⢀⣀⣤⡴⢺⣿⣟⡷⡟⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡶⣶⣶⣦⣵⣗⣀⠀⠀⢉⣲⢿⡱⣟⣿⢢⠕⣿⣧⠀⠀⠀⠀⠀⠨⡏⡙⢿⣯⣷⢛⣷⢯⣟⣷⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⡾⢫⣝⣶⢿⡽⠾⡽⢿⠟⠉⠳⣤⡸⣄⢸⣷⣿⠣⢇⠞⣿⣽⠀⠀⠀⠀⠀⠈⣿⠀⠀⠛⢿⣮⡜⣿⣞⡿⣷⣤⡤ ⠀⠀⠀⠀⣰⡿⡑⢮⣟⡿⢪⢕⣢⣳⡎⠀⠀⠀⢉⠓⠻⢼⣿⡟⢲⠸⡔⣿⢯⠀⠀⠀⠀⠀⠀⣻⠀⠀⠀⠈⠛⠷⣯⣿⣷⠯⠟⠁ ⠀⠀⠀⢠⣿⠒⣭⡿⣿⡸⡑⣎⣾⠿⠈⣰⢤⣄⠀⠀⠀⢼⣿⠱⡍⠶⣹⣯⣟⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣯⡙⣼⣿⢣⠧⣙⢼⣿⣄⠑⠠⠤⠜⠀⠀⠀⢺⡏⡗⡜⣣⣿⣳⢿⠀⠀⠀⢦⠀⣘⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣹⡷⣉⣿⣾⢣⠞⣡⠾⠿⢻⠀⠀⠀⠘⡆⠀⠀⢸⣯⡑⢮⣱⡿⣽⣻⣆⠀⠀⣸⣧⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢾⡗⡥⣿⢾⣃⠞⣹⠀⠀⠘⠀⠀⠀⠀⠘⡦⣀⠀⢷⡩⢖⡸⣟⡷⣯⣟⡿⣿⣻⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠸⣿⠰⣟⣿⡎⡼⣹⠀⠀⠀⢀⠀⣀⡴⠋⠆⠉⠓⠶⠽⡷⣬⣝⣿⣳⢯⣟⡷⣯⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⡧⣹⣾⢿⡰⢽⠀⠀⠀⠈⠉⣷⡀⠀⠀⠀⠀⢀⣼⠁⠀⠈⠙⣯⠿⠾⠝⢫⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⡷⣡⡿⣿⣌⡇⠀⠀⠀⠀⠀⢾⡧⠀⠀⠀⠋⠉⣿⠀⠀⠀⠀⢸⡄⠀⠀⠀⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⡄⠀⠀⠐⣿⡔⣿⣽⠛⠀⠀⠀⠀⠀⠀⣺⣟⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠈⢧⠀⠀⠀⠘⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣾⣿⡀⠀⣰⡿⣘⣯⢿⢢⠀⠀⠀⠀⠀⢀⣾⣏⠆⠀⠀⠀⠀⢈⡇⠀⠀⠀⠀⠘⣇⠀⠀⠀⢙⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣜⠻⢾⡛⡕⣾⢯⣿⠏⡧⣄⠀⠀⠀⣬⠇⣯⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢿⣿⣟⣄⣧⣿⣟⣿⢟⡸⢤⣿⡧⣄⣻⠟⠀⠘⢿⣠⢀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⢼⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⠳⢿⣯⣟⣾⣽⣭⣶⣷⠟⠋⠀⠀⠀⠀⠀⠀⠀⠈⠙⠚⠓⣿⠆⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣹⢦⣄⣤⡶⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠫⢤⡄⠀⠀⠀⡠⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀