⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⣦⣴⡄⠀⣠⡀⢸⣖⣒⣲⣇⢰⡄⢀⣤⣠⣼⢉⣿⣿⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡁⣽⣿⣿⣿⣿⣏⣹⣶⣖⣶⣏⢨⣿⣿⣿⣿⣿⣽⣿⣾⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠉⠙⠉⠁⠀⠉⢿⣿⣿⣿⣿⠉⠉⠁⣀⣭⡿⠿⣛⣛⡛⠿⢧⣄⡈⠈⠀⠀⠃⠉⠀⠁⠁⠁⠀⠈⠀⠁⠀⠘⠀ ⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣀⣀⣀⣀⣀⣠⣽⣿⣿⠿⣿⣠⣴⣞⣉⣤⡤⠤⠤⠤⠬⣷⣤⣈⣙⣦⣄⣄⣀⣀⣀⣀⣀⢀⣀⣀⡀⠀⠀⠀⠀ ⡵⣝⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⣻⣤⣾⠀⠀⠀⣷⡾⠉⠀⠀⠀⠀⠀⣀⣀⣠⠤⠤⠿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠻⣮⢦⡻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣆⣀⡀⣿⣥⠤⠶⠶⠿⠿⠿⠧⠤⠤⠤⠤⠤⢼⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠙⢷⡵⡜⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢤⣾⣾⣿⣿⡇⠀⠀⠀⠀⣠⠀⣀⡠⠀⣤⠀⠀⠀⠀⢹⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠻⣾⣦⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣾⣿⢻⣷⣿⣧⠀⠀⠀⠀⠉⠀⠊⠃⠀⠉⠀⠀⠀⠀⡸⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠙⢿⣷⡜⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⢤⣾⣿⣷⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⣠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠻⣟⢦⠻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠿⣿⢿⣷⣿⣿⠿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⣠⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⢷⡳⡌⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⢶⣿⣿⡿⣿⣿⢶⣟⣳⣶⠤⠶⠛⠛⠉⠉⠙⢿⣿⣿⣟⠻⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣞⢦⠹⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⠿⢿⢿⡷⣿⡿:⢏⢻⡀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⡃⠀⠙⠻⢿⣷⣄⣀⣀⣀⣠⣤⣤⣤⣤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡳⡌⢷⡄⠀⢿⡦⣄⠀⠀⠀⠀⠀⠀⠀⠀⢿⢲⣿⣿⣿⣽⣿⢲⣿⠾⣷⣝⡻⢿⣷⣶⣶⣶⣿⣿⣿⣿⣷⣤⠀⠰⣶⠤⠭⠿⠿⠿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣾⢦⠙⣦⠀⠈⠯⢕⢦⡀⠀⠀⠀⠀⠀⠈⠛⠻⣼⣿⣯⣿⠟⠁⠀⠈⠻⣿⣿⣾⣿⢿⣿⠟⠉⣻⣿⣿⣿⣆⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣤⣀⠀⠀⠀⠀⠀⠈⢷⡷⡌⢷⡄⠀⠈⠳⢷⣀⣠⠤⠤⠶⠲⠦⣄⣿⣿⡿⠋⠀⠀⠀⢠⠀⠈⠻⠀⢠⣾⠃⠀⣰⣿⣿⣿⣿⣿⣧⣀⣤⣬⣿⣶⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠹⢳⢦⡀⠀⠀⠀⠀⠹⣿⣦⠹⣦⠀⣠⣾⣿⡶⠦⣤⡀⠀⣠⣾⣿⣇⠀⠀⠀⠀⢀⡏⠀⠀⢀⣴⣿⠃⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⢟⣆⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠿⠄⠀⠀⠀⠀⠈⢿⡷⡌⢳⣿⡿⠋⢠⣤⣶⣿⣿⣿⡿⣿⡋⢷⡀⠀⠀⣼⠀⠀⣰⣿⣿⣣⡶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⡆⠀⠀ ⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣟⢦⠙⣷⠒⠶⣿⡿⠟⠋⠀⠀⠀⢙⡆⠻⣄⢰⣿⣠⣾⣿⣿⡿⠋⠀⠀⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀ ⠀⠀⠐⣜⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢷⡳⣌⣳⠀⣿⣄⠀⠀⠀⢀⡤⠊⠀⣠⣿⣿⣿⣿⣿⡿⠋⠉⠉⡱⠂⠀⣆⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠈⠷⠀⠀ ⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⣶⣄⡀⠀⠀⠀⠀⠀⠀⠘⣦⣉⣉⣁⣼⣿⣿⠀⠀⢀⠎⣷⢠⠞⠻⢿⣿⣿⣿⠟⠀⠀⢠⠞⠁⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢹⣲⡀⠀⠀⠀⠀⢠⠏⠛⢿⣿⣿⣿⣿⠀⢀⡎⣴⢻⡏⠀⠀⠀⣸⡿⠋⠀⠀⡰⠃⠀⠀⣀⣿⣿⣿⠙⠿⢿⣿⣿⣿⣿⣿⣿⣿⣀⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠀⠀⠀⠀⠘⣧⠀⠰⢿⡿⠿⣿⠀⡞⣼⣧⠞⠓⠒⠒⠚⠛⠃⠀⢠⡼⠁⠀⢀⣴⣿⣿⣿⣿⠀⠀⠀⠙⠻⣿⣿⣿⣿⠏⠀⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⣄⡀⠀⢀⣙⡾⠷⠛⣻⡖⣧⠉⠉⠉⠉⠉⠒⠋⠀⣠⣾⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠉⠛⠛⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⢯⣭⣀⡴⠚⢉⣵⡿⠃⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡟⠓⠶⠛⠛⠀⠀⠀⣠⢖⣀⡤⠄⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀