⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣴⣶⣶⣶⡶⠶⠶⣦⣄⣀⣀⣠⣤⣤⣤⠶⢶⣶⠶⠶⣶⣾⣟⣋⣩⠭⢭⡭⠛⠭⠯⣭⣽⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⣻⣿⡿⠟⠉⠙⠟⠙⢿⣾⣿⣹⣿⣿⠿⠿⠿⠟⢿⣿⠿⠿⠿⠿⢿⣄⡀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣎⢿⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣤⡾⣿⡾⠋⠀⠀⠀⠀⠀⠀⠀⢠⡤⠾⠟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠂⠀⠀⠤⠀⠀⠀⠀⠀⠙⢷⣉⣷⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣻⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣾⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣟⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣷⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢰⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣧⡿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⣛⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣀⣠⣶⣤⣤⣦⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⢦⡤⠀⠀⠀⠀⣠⣶⡶⠿⠛⠛⠋⠀⠀⠀⠀⠙⠛⢻⣷⣶⣶⣀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣧⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⣽⣟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⡇⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠸⣿⣿⡟⠙⣷⣀⡀⠀⠀⠀⠀⠀⢻⡿⣧⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣼⣿⡟⠁⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣾⠟⠁⠙⠿⠟⠁⠀⠀⠀⢀⡼⠿⠷⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣇⠀⠀⠀⠀⠀⠈⣷⢿⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⣠⣶⠟⠛⠻⢶⣦⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣷⣿⣷⣶⡶⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⡆⠀⠀⠀⠀⢹⣾⡇⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⣿⡇⠀⣾⠟⠁⢰⣤⢀⣤⡙⢿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡄⠀⠀⠀⢸⡏⣿⡆⠀⠀ ⠀⠀⠀⠀⢸⣧⣿⡇⢸⡏⠰⣶⣞⠛⣻⡏⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠸⣇⣿⡇⠀⠀ ⠀⠀⠀⠀⢠⣿⣿⠇⢸⡇⠀⠀⣿⠋⠇⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣆⠀⠀⠀⣿⢿⣧⠀⠀ ⠀⠀⠀⠀⣸⣿⣿⡀⢸⡇⠀⠀⠈⠳⠶⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣷⡄⠀⠻⣯⣽⡆⠀ ⠀⠀⠀⢀⣿⣿⠟⠀⠸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠙⣦⡀⣿⣿⣿⠀ ⠀⠀⠀⣾⣿⡟⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⠙⣷⡿⢿⣹⡆ ⠀⠀⣰⣯⡿⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠸⣷⣾⣿⣿ ⠀⢸⣿⣿⣇⠀⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⢀⣿⣷⡿⣿ ⠀⢸⣿⣿⠁⠈⠛⠃⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⣠⣼⠋⠙⣷⣿ ⠀⢸⣿⣿⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠋⠀⠀⢸⣿⡿ ⠀⢸⣿⢿⡄⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢠⣾⢻⡇ ⠀⢸⣿⣼⠇⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣗⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠈⢻⣼⡇ ⠀⠘⢿⣿⡄⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠀⠀⣠⣾⣻⡇ ⠀⠀⢸⣿⣧⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⣿⣷⡟⠀ ⠀⠀⠈⣿⢿⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⣼⢿⣿⠇⠀ ⠀⠀⠀⣿⣼⡇⠀⠀⠀⠀⢸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣴⢏⣿⠏⠀⠀ ⠀⠀⣠⣿⣿⣧⠀⠀⠀⠀⠀⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⣴⡿⣾⠇⠀⠀⠀ ⢰⣞⣻⡿⠛⠉⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣶⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁⣀⣽⣼⠏⠀⠀⠀⠀ ⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠇⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣷⣿⣿⡿⠃⠀⠀⠀⠀⠀ ⢹⣿⣷⢤⣤⣤⣤⣤⣴⣦⣤⣤⣤⣼⣷⣤⣄⣀⣀⣀⣀⣀⠀⠀⠀⢀⣀⣤⣿⣥⢶⣤⣿⣦⣤⣄⣀⡀⠀⠀⣀⣀⣀⣴⣿⣻⣵⠟⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠉⠛⠛⠿⠞⠛⠓⠺⠿⠉⠉⠽⠏⠛⠿⠿⣭⣭⣭⣭⣭⣭⣽⣿⠿⠟⠛⠛⠛⠛⠛⠛⠛⠿⠾⠿⠿⠿⠿⠯⠿⠿⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢠⣤⠀⠄⢀⣀⣀⠈⠉⠉⠉⠉⠉⠉⠁⠀⠀⣀⣀⣤⣠⣄⣀⣀⠀⣀⡀⡀⠀⢀⠀⠀⣀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀