⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣗⢶⣶⣶⣀⣠⣶⣶⣿⣷⣶⣶⣶⣶⣿⡿⢻⣳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠯⠩⣷⢶⣞⠯⡽⠿⣿⣿⣲⣶⣲⣶⣾⢭⣿⢿⣿⣇⣾⣿⣷⣬⠻⣯⣿⣿⡿⠚⣁⠙⢛⠉⠻⣝⣤⡟⠳⠿⢿⢷⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⠞⠉⠉⠉⠉⠉⠙⣧⠀⡇⣤⢹⣸⡏⠀⡿⣿⣇⠘⣯⣇⢻⣽⣿⣹⠻⠿⠿⢿⣷⣿⢶⣿⣿⣿⠇⠀⢻⣄⡛⠃⠀⣹⣿⣿⣟⡟⣿⣟⣀⣀⡀⠀ ⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⢸⣄⣁⣿⣄⣸⢳⣤⣿⣿⢻⣄⣻⣿⣈⣿⣿⣻⡀⠀⠀⢀⣠⢽⡟⠀⠙⣿⠀⠀⢸⢛⡏⠀⠀⣾⢻⣿⠟⠛⠛⣒⡛⠻⣿⣆ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡏⠉⣿⡽⠟⢾⠟⣿⡶⠿⣿⣿⡟⠛⢿⣿⠛⢻⡟⢹⣿⢰⡇⠀⠀⡿⠀⠀⠈⠛⠁⠀⠀⣿⠀⣽⢸⣿⠿⠯⣟⡇⢸⢼ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⢻⠏⡇⠸⠀⣿⠁⢠⣿⣿⣧⠀⢸⡏⣷⠘⠇⣼⢹⣼⠀⠀⠀⢻⣄⡀⠀⠀⠀⢀⣠⣿⣶⣃⡞⡇⠠⣞⣣⠇⢸⣸ ⢀⣀⣠⣠⣀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠈⢰⣿⣀⣠⣿⣆⢀⣿⢿⣿⣄⠈⣰⠟⣧⣠⡟⢯⣼⠀⠀⠀⣠⠼⠟⣿⠷⠾⢿⣍⢉⣉⣻⣿⣿⣶⣶⣶⣶⡿⠋ ⣿⡟⠛⠛⢻⣞⣦⣤⣤⣰⡖⠒⢲⡤⠤⢦⡌⢋⣉⣙⡶⠿⠿⠶⢿⣿⡉⠉⡀⠉⠉⣉⡀⢰⠟⠛⠛⠛⠛⠛⢷⡿⢶⢶⣿⣤⣤⣤⡟⡏⠀⠉⣿⡿⠀⠀⠀⠀⠀⠀ ⢻⣧⠀⠀⠀⣿⠁⠀⠀⣿⠀⠀⣼⠀⠀⢸⣷⡏⠉⢹⡇⠀⣀⢤⣀⠀⢻⣾⠉⠉⠉⠉⠙⢿⡷⠤⢤⡞⠀⢠⣿⡇⠀⠀⡇⣧⠀⠀⡇⡇⠀⠀⣯⡇⠀⠀⠀⠀⠀⠀ ⢸⣿⠀⠀⠀⡟⠀⠀⠀⢿⠀⠀⣿⠀⠀⢸⡏⡇⠀⢸⡇⠀⠻⠦⠟⠀⣸⣿⠀⠀⣎⣻⠄⢈⡇⢀⡟⠀⠀⣼⢹⡇⠀⠀⡇⡇⠀⠀⣧⡇⠀⢠⣿⡆⠀⠀⠀⠀⠀⠀ ⠸⣿⡄⠆⠀⡇⠀⡆⠀⢸⠀⠀⣿⠀⠀⢸⡇⡇⠀⢸⡇⠀⣠⣤⡄⠀⠳⣽⠀⠀⠉⠉⠀⢼⡁⣼⠡⠀⢸⠇⢸⡇⠀⠀⣇⡇⠀⠀⣏⢷⣄⣼⣿⠁⠀⠀⠀⠀⠀⠀ ⠀⣿⣇⠀⠀⠇⢀⣷⠀⠸⠀⢸⣿⡄⠀⢸⣧⣇⠀⢸⡇⠀⢿⣤⡷⠀⠀⣿⠀⠀⣏⣻⡀⠈⣿⠇⠀⠀⠿⠶⠾⢷⠀⠀⠿⠟⡄⠀⣿⡶⠻⢯⣻⡄⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⠀⠀⠀⢸⣿⡄⠀⠀⢸⠊⢷⣀⠀⠀⢈⣀⣼⣇⣀⡀⠀⢀⣀⡼⣿⠀⠀⠉⠉⠀⢠⣟⣀⣀⣀⠀⠀⢀⣸⡷⠤⠤⣤⠁⠀⣿⣇⣀⣸⣿⡇⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⡀⠀⠀⢸⢸⣇⣀⣀⣼⠆⠀⠉⠉⠉⠉⠉⠀⠉⠉⠉⢉⣹⣯⠤⣼⣷⣶⣶⣶⣞⣋⣉⣉⣉⣉⣉⣉⣉⣉⣀⣀⣀⡿⠀⠀⣿⠉⠉⢻⡿⢷⡄⠀⠀⠀⠀⠀ ⠀⠈⢿⣷⣶⣶⠛⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠁⠀⣀⣤⣤⣤⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣀⣀⣀⣀⣴⠏⠀⠀⣼⡶⠾⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠉⠳⣄⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣿⠀⠀⢸⣡⠖⠚⠛⠛⠳⣦⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣉⣉⣀⣀⣠⠼⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢸⢻⠀⠀⢸⢿⡷⡴⢦⡀⠀⣹⡏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⣆⠀⠈⠙⠒⠚⠛⠁⢀⡿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠾⢟⣒⣒⣒⣒⣒⣓⡻⠝⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀