⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣴⣶⠟⠉⠋⠉⠉⠉⠉⠉⠛⠻⠶⣤⣀⠀⢀⡤⠶⠖⠒⠒⠶⣦⠶⠖⠛⠒⠶⣶⠛⠁⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⠿⣯⡉⠉⠉⠛⠳⢦⣄⣀⣀⣀⠀⠀⠀⠀⠈⠙⢷⣏⣻⠷⠂⠀⠀⠀⠀⢀⣠⡤⠴⢻⡏⠀⠀⡾⠶⠶⢦⣄⡀⠀⠀⠀⠀⠀ ⠀⠀⣤⣄⣀⣀⣀⣰⣿⣭⡮⠿⠇⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠷⢦⣄⡀⠀⠙⢿⣄⠀⠀⠀⣄⡀⠚⠁⡀⠘⠋⠀⠀⠀⠀⠀⢀⣴⡾⠟⠀⠀⠀⠀⠀ ⠀⠀⢹⡄⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⣤⣄⣽⣆⡴⠀⠘⠻⠌⠀⠈⠙⠒⠦⠤⠄⣰⠀⠀⠉⠙⢦⡀⠀⠀⠀⠀ ⠀⠀⠈⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⣿⠇⢸⡀⠀⠀⠀⠀⠀⢀⡴⠃⠀⠀⠀⠀⠀⠙⢦⣄⡀⠀ ⠀⠀⠀⠀⣩⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠞⠁⠀⠈⢇⠀⠀⠀⠀⠀⠈⠹⡄⠀⠀⠀⠀⠀⠀⠀⢈⣽⠟ ⠀⠀⣠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡄⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀⠻⡀⠀⠀⠀⠀⠀⣾⡋⠁⠀ ⠀⣰⢏⣀⣀⣀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⢠⡏⢻⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣆⣀⠀⠀⠀⠹⡄⡄⠓⠲⠤⠄⠩⠇⠀⠀⠀⠀⠈⢻⡄⠀ ⠐⠛⠋⠉⢩⡏⠀⠀⠀⠀⠀⢠⡟⠹⣄⠀⠀⡀⢸⡗⠋⣁⣽⣷⣶⣤⠀⠀⠀⠀⠀⣴⣶⣿⣿⢿⡀⠀⠀⠀⠻⠃⣰⡆⠀⠀⠀⢹⡄⠀⠀⠀⠀⠈⡇⠀ ⠀⠀⠀⣠⠟⠀⠀⠀⠀⠀⣴⡿⢻⡿⣿⣷⣜⡟⠻⠇⠞⢿⢡⣶⢹⡟⠀⠀⠀⠀⢰⣿⢳⢻⢹⠿⣧⡀⢀⠀⣠⣾⣧⣽⣦⢀⡄⣸⠃⠀⠀⣿⠻⣦⡇⠀ ⠀⠀⠘⠷⠶⠶⣶⠆⠀⠀⢻⡙⢜⣆⣛⡿⠈⠉⠀⠀⠀⠚⠒⠒⣿⡵⣶⠀⢀⡀⠈⣟⠛⠛⠛⠀⠈⠙⠛⠷⣿⣹⢽⢧⣿⡄⠀⠁⠀⠀⠀⠻⣄⠈⠁⠀ ⠀⠀⠀⠀⠀⠀⣿⡀⣀⣼⠳⣿⣦⠀⠀⠀⠐⠀⠀⣀⠀⠀⠀⠀⠀⣰⣷⣾⠛⠙⢿⣿⠃⠀⠀⠀⠀⠀⢠⠀⠉⠛⠋⣠⠟⢀⣀⠀⢰⡟⠓⠚⠛⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⠟⠉⢸⡴⠛⢷⣄⣀⠀⠀⠸⠿⠽⠇⣀⣠⣴⡿⠟⢹⡟⡀⠀⢸⢟⣷⣦⣀⠀⠳⠦⠆⠀⠀⢀⣨⣿⣿⠋⠙⣷⠞⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢸⣻⣿⣗⣒⣒⣾⢿⢻⣿⠻⣃⢀⣾⢿⣿⣶⣿⠟⣻⣄⠽⢻⣶⣦⣤⣶⣶⣛⣳⣋⣋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣇⣩⡅⠀⠈⣭⡄⣿⣎⣽⣿⣿⣿⣿⣿⣿⣷⣽⣯⢛⡃⠀⢘⣨⣿⣷⡉⠁⣀⣈⣳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⡿⣿⠟⡿⢁⣾⣻⣧⣽⣷⣿⣿⣿⣿⣿⣷⣿⣤⣨⣿⠁⠈⠉⠉⠉⠉⠙⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⡿⠿⠗⠿⠆⢮⣿⣿⣿⣮⢼⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣴⣾⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⢻⣿⣿⣾⣿⣿⣿⡿⢀⣿⡇⢾⣷⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⣿⣿⣿⣿⣿⣶⣿⣥⣻⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⠩⣿⣽⡟⠻⠿⠿⢿⣿⣿⠏⠿⣟⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠈⠀⠀⣠⡟⢨⡟⠀⠀⠀⢰⠟⠁⠀⠀⢠⢤⣩⢭⡄⠀⠈⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠄⡀⣀⣀⣿⣄⣸⡇⠀⠀⠀⣿⣄⡀⠀⠀⠸⣌⠋⣼⠃⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣬⠬⠟⠁⠙⢿⣧⣄⠀⠀⠀⠈⠙⠛⣶⠀⠙⠛⠁⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠀⠀⠀⠀⢹⣿⢧⡄⠀⠀⠀⢠⣿⣧⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⠋⠙⣿⣿⣿⣿⣿⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⣄⣴⣴⣿⣿⠇⠹⣆⣠⣶⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠙⠋⠁⠀⠀⠈⠛⠿⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠏⠀⠀⠀⠘⢿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠟⠉⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀