⠀⠀⠀⢀⣟⢀⡿⠟⣼⢋⣟⠋⣿⢏⡾⣽⣿⠟⣱⣿⢏⡞⣿⣿⡿⠋⡱⠋⣱⢿⣞⣁⣾⣠⡟⣿⡿⠀⠀⠙⠿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣼⡏⡼⠁⢠⡏⣼⡝⣼⣟⣾⣾⣳⢃⣼⡿⣱⢫⣾⣿⠟⢀⣾⢃⡜⣡⢟⣾⣿⣿⡿⢲⣽⡇⠀⠀⠀⠀⠙⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⢠⢇⠆⣸⢰⣿⢁⣿⣿⣿⣳⠃⣾⣟⡜⢱⣿⡿⢁⣴⡟⡡⢋⡼⢣⣿⣻⣿⣿⢣⢧⣿⠀⠀⠀⠀⠀⠀⠈⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⡇⠘⡼⢀⢇⣿⡏⣼⣿⣿⣳⢃⣼⠏⠈⣰⣿⢋⣴⡾⢫⢞⣡⠟⢁⣽⣽⣿⣿⢃⢎⣾⡇⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⠀⢠⠃⡜⣸⡿⢠⢿⣿⣣⢇⣾⡓⢀⣴⠟⣡⣿⢟⣴⣱⠟⣡⣤⣮⣾⣾⣿⣣⢎⡞⡞⠀⠀⠀⠀⠀⠀⣠⣤⣾⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⡇⠀⡼⢀⠆⣯⠇⠜⢸⡟⠟⣰⠟⣴⡿⣣⣾⣟⣵⣿⡿⢃⢜⣿⣷⣷⣿⣿⣽⢯⢎⡜⠀⠀⠀⠀⠀⣴⣿⠿⠛⠉⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣸⠃⢀⡇⣸⢸⠹⢠⣣⣿⠁⣴⣧⡾⢋⣴⢿⣿⣿⠛⢀⢔⣡⢟⣿⣻⡿⣫⣿⠟⣡⠎⠀⠀⠀⠀⠀⠈⠉⡀⢀⣰⣤⣾⣀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡿⠀⢸⢠⡇⡎⠠⢸⢸⣇⣾⣿⡿⣠⠟⢡⡿⠋⣠⣶⡵⣟⢵⣿⣾⣫⣾⠿⢿⠞⠛⠀⠀⠀⠀⠀⠀⠀⢰⣼⣿⣾⣿⣿⣿⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠸⠃⡇⡏⢸⢡⠃⡆⡗⣿⣿⣿⣿⡾⢁⣠⠤⣀⣼⠟⢫⣾⣵⣿⣯⡿⠟⣁⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⢹⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣧⠇⣼⢸⣆⣇⣧⣿⣿⣿⣿⣶⣿⣵⣾⣿⣣⣶⠿⣫⠵⠚⠁⠀⣀⣤⣿⣷⣿⣷⡆⠀⠀⠀⠀⠀⡄⠉⠻⣯⣽⡿⡿⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢻⢿⠀⡏⣾⣿⢸⣹⢿⣿⣿⣿⣿⢗⣫⣵⣟⠯⠓⠉⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⡟⠳⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠃⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⡎⢰⠃⣿⠘⣼⣿⣿⣿⣿⣿⡿⠿⠛⠉⠀⠀⠀⠀⣴⣾⣿⣿⠛⢿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢰⣿⡇⡜⢸⣿⠀⣷⣿⣿⣿⣋⣠⠄⠀⠀⠀⠀⠀⠀⠶⠿⢟⣿⣷⣦⣴⠿⡏⠻⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⠀⡇⢸⡏⢀⣿⠛⢲⣌⡛⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⡇⠀⡇⠸⡇⢸⢸⠀⢠⠃⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⡇⡀⠇⢸⣺⡀⢸⡀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢨⡇⠀⠀⢸⣿⣌⠉⠙⠂⠒⠸⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⢖⣯⣟⣤⣧⡤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢺⠁⠀⠀⠘⣿⡟⣷⣤⣀⠀⠀⠀⠀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣴⣾⡥⠤⠒⣻⣿⡿⣿⡿⣷⣤⣻⣿⣿⣆⠀⠀⠀⠀⠀⠀ ⠀⠀⢻⠀⡇⠀⢠⣿⠁⣿⢿⡟⣿⡟⠒⠚⠁⠈⠳⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠣⢄⡀⡾⢶⣿⣯⠛⡿⠟⠥⣤⣿⣿⡿⠀⠳⡄⠀⠀⠀⠀ ⠀⢀⣿⠀⡇⢸⡎⣿⠀⣿⢻⡇⢿⡇⠀⠀⠀⠀⠀⠀⠙⠲⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⣿⡟⠛⠒⠾⣠⣼⢿⣿⡇⢠⡶⠃⠀⠀⠀⠀ ⠀⠸⡇⢰⠁⠀⡇⣿⡂⣿⢸⣯⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠦⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠻⠿⣷⠒⠒⠛⠒⠛⠻⣅⣼⡄⠀⠀⠀⠀⠀ ⠀⣼⠇⢸⠀⠘⣷⣿⣧⣯⣾⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠒⣶⣤⣤⣤⣤⡠⠤⠗⢦⠔⠶⠛⠡⠟⠒⠒⠒⠁⡰⠃⠀⠀⠀⠀⠀ ⠀⣿⠀⣼⠀⣴⢿⣿⣿⡇⣿⣿⡈⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡏⣿⠁⠀⠀⠘⡲⠶⠶⠶⣤⣴⡏⠉⢉⣤⣄⠀⣀⡀⠀⠀ ⠀⡏⠀⣿⠀⣿⡸⢻⣿⡇⣿⣿⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡿⠃⠏⠀⠀⢠⠎⠀⠀⣀⡴⠃⠙⢿⡀⡏⠀⣸⠉⠀⠙⠷⡄ ⠀⠃⢠⡏⠀⡿⡇⣾⣿⠁⣿⣿⡃⣩⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⢹⣿⡇⠀⠀⠀⠀⠸⣄⢠⠚⠁⠀⠀⠀⠸⣇⠳⣦⣿⠤⠒⠉⠉⠉ ⠀⢠⢸⡇⠘⣧⢧⣿⡿⢠⣿⡟⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣾⣿⠁⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⢻⣤⣿⡿⠀⠀⠀⠀⠀ ⠀⡎⣿⠃⣰⠻⢸⣻⣇⣾⠇⣸⢲⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡏⣸⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠡⡇⠀⠀⠀⠀⠀ ⢠⢣⣿⠀⢸⡇⣿⣿⣾⠃⣰⠏⡜⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠙⢿⣿⠇⣿⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡏⠉⠀⠀⠀⠀⠀ ⠈⣾⡿⠀⡽⢰⣿⠟⠁⣰⠇⢰⠁⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠙⠶⣿⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀ ⢰⣿⣇⡾⣱⠟⠉⣠⢾⡃⣠⠃⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠈⠉⠉⠉⠑⠒⠢⢤⡀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀ ⣿⣿⣾⣫⣥⡴⠾⢛⡩⢞⣡⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀ ⣿⠿⣛⣯⠭⠔⠊⠉⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀ ⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠘⣧⠀⠀⠀⠀