⠀⠀⠀⠀⠀⣠⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣰⠟⠉⠀⠀⠙⢷⡀⠀⠀⠀⣠⡶⠞⠛⠛⠳⣦⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⡾⠃⠀⠀⠀⠀⠀⠈⢷⠀⢠⡾⠁⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀ ⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⢸⡇⣾⠁⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀ ⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⡇⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣸⣇⣀⡀⠀⠀⠀⠀ ⢸⠀⠀⠀⠀⠀⣠⡞⠛⠛⢷⡀⠀⢠⡾⠛⡙⠻⣆⠀⠀⠀⠉⠙⠳⣤⠀⠀ ⣸⠀⠀⠀⠀⠀⣿⡀⠸⠇⣸⠇⠀⢸⣇⠀⠛⢀⣿⠀⠀⠀⠀⠀⠀⠘⣷⠀ ⣿⠀⠀⠀⠀⠀⠈⠛⠶⠞⠋⠀⠀⠀⠙⠳⡛⠋⠁⠀⠀⠀⠀⠀⠀⠀⣸⠀ ⢻⣄⠀⠀⠀⠀⠀⠀⠀⢶⣄⠀⠀⠀⣠⡾⠃⠀⠀⠀⠀⠀⠀⠀⣀⡴⠏⠀ ⠀⠙⠶⣤⣀⡀⠀⠀⠀⠀⠙⢛⠶⠚⠋⠀⠀⠀⠀⢀⣤⣴⣶⠞⠋⠁⠀⠀ ⠀⠀⠀⠀⠉⠙⠛⠓⠒⢺⡿⢻⡀⠀⠀⠀⠀⠀⠀⠀⣿⣦⡈⢳⣤⠞⣻⠀ ⠀⠀⠀⠀⠀⠀⣾⠛⢦⡿⢠⡿⣇⠀⠀⠀⠀⠀⠀⣸⠇⢈⡿⠀⢀⠿⠷⣄ ⠀⠀⠀⠀⠀⠀⣽⠟⣧⢀⠿⣤⡙⣧⣀⠀⠀⢀⣴⠏⠀⠻⡶⣿⢸⡟⠶⠛ ⠀⠀⠀⠀⠀⠀⠷⠾⣯⣸⠛⠾⠃⡏⠹⡟⠻⡟⢹⡇⠀⠀⠀⠘⠛⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢀⣀⣰⡇⠀⡇⠀⡇⠈⣧⣤⣤⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⠉⠉⠉⠀⣰⡇⠠⣇⠀⠀⢀⣀⡿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⠋⠀⠀⠙⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣠⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣰⠟⠉⠀⠀⠙⢷⡀⠀⠀⠀⣠⡶⠞⠛⠛⠳⣦⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⡾⠃⠀⠀⠀⠀⠀⠈⢷⠀⢠⡾⠁⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀ ⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⢸⡇⣾⠁⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀ ⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⡇⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣸⣇⣀⡀⠀⠀⠀⠀ ⢸⠀⠀⠀⠀⠀⣠⡞⠛⠛⢷⡀⠀⢠⡾⠛⡙⠻⣆⠀⠀⠀⠉⠙⠳⣤⠀⠀ ⣸⠀⠀⠀⠀⠀⣿⡀⠸⠇⣸⠇⠀⢸⣇⠀⠛⢀⣿⠀⠀⠀⠀⠀⠀⠘⣷⠀ ⣿⠀⠀⠀⠀⠀⠈⠛⠶⠞⠋⠀⠀⠀⠙⠳⡛⠋⠁⠀⠀⠀⠀⠀⠀⠀⣸⠀ ⢻⣄⠀⠀⠀⠀⠀⠀⠀⢶⣄⠀⠀⠀⣠⡾⠃⠀⠀⠀⠀⠀⠀⠀⣀⡴⠏⠀ ⠀⠙⠶⣤⣀⡀⠀⠀⠀⠀⠙⢛⠶⠚⠋⠀⠀⠀⠀⢀⣤⣴⣶⠞⠋⠁⠀⠀ ⠀⠀⠀⠀⠉⠙⠛⠓⠒⢺⡿⢻⡀⠀⠀⠀⠀⠀⠀⠀⣿⣦⡈⢳⣤⠞⣻⠀ ⠀⠀⠀⠀⠀⠀⣾⠛⢦⡿⢠⡿⣇⠀⠀⠀⠀⠀⠀⣸⠇⢈⡿⠀⢀⠿⠷⣄ ⠀⠀⠀⠀⠀⠀⣽⠟⣧⢀⠿⣤⡙⣧⣀⠀⠀⢀⣴⠏⠀⠻⡶⣿⢸⡟⠶⠛ ⠀⠀⠀⠀⠀⠀⠷⠾⣯⣸⠛⠾⠃⡏⠹⡟⠻⡟⢹⡇⠀⠀⠀⠘⠛⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢀⣀⣰⡇⠀⡇⠀⡇⠈⣧⣤⣤⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⠉⠉⠉⠀⣰⡇⠠⣇⠀⠀⢀⣀⡿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⠋⠀⠀⠙⠛⠛⠋⠉⠀⠀⠀⠀
⠀⠀⠀⣠⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣰⠟⠉⠀⠀⠙⢷⡀⠀⠀⠀⣠⡶⠞⠛⠛⠳⣦⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⡾⠃⠀⠀⠀⠀⠀⠈⢷⠀⢠⡾⠁⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀ ⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⢸⡇⣾⠁⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀ ⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⡇⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣸⣇⣀⡀⠀⠀⠀⠀ ⢸⠀⠀⠀⠀⠀⣠⡞⠛⠛⢷⡀⠀⢠⡾⠛⡙⠻⣆⠀⠀⠀⠉⠙⠳⣤⠀⠀ ⣸⠀⠀⠀⠀⠀⣿⡀⠸⠇⣸⠇⠀⢸⣇⠀⠛⢀⣿⠀⠀⠀⠀⠀⠀⠘⣷⠀ ⣿⠀⠀⠀⠀⠀⠈⠛⠶⠞⠋⠀⠀⠀⠙⠳⡛⠋⠁⠀⠀⠀⠀⠀⠀⠀⣸⠀ ⢻⣄⠀⠀⠀⠀⠀⠀⠀⢶⣄⠀⠀⠀⣠⡾⠃⠀⠀⠀⠀⠀⠀⠀⣀⡴⠏⠀ ⠀⠙⠶⣤⣀⡀⠀⠀⠀⠀⠙⢛⠶⠚⠋⠀⠀⠀⠀⢀⣤⣴⣶⠞⠋⠁⠀⠀ ⠀⠀⠀⠀⠉⠙⠛⠓⠒⢺⡿⢻⡀⠀⠀⠀⠀⠀⠀⠀⣿⣦⡈⢳⣤⠞⣻⠀ ⠀⠀⠀⠀⠀⠀⣾⠛⢦⡿⢠⡿⣇⠀⠀⠀⠀⠀⠀⣸⠇⢈⡿⠀⢀⠿⠷⣄ ⠀⠀⠀⠀⠀⠀⣽⠟⣧⢀⠿⣤⡙⣧⣀⠀⠀⢀⣴⠏⠀⠻⡶⣿⢸⡟⠶⠛ ⠀⠀⠀⠀⠀⠀⠷⠾⣯⣸⠛⠾⠃⡏⠹⡟⠻⡟⢹⡇⠀⠀⠀⠘⠛⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢀⣀⣰⡇⠀⡇⠀⡇⠈⣧⣤⣤⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⠉⠉⠉⠀⣰⡇⠠⣇⠀⠀⢀⣀⡿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⠋⠀⠀⠙⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀