⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⣤⣶⣾⣿⡇⠀⠀⠀⢸⣷⣶⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡼⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⢷⠀⠺⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⡇⠀⢀⠀⠀⠀⠀ ⠀⠀⠀⠀⣸⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠘⣇⠀⠙⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⡇⠀⢸⣷⠀⠀⠀ ⠀⠀⠀⠀⣿⠖⠀⠀⠙⠦⠀⠀⠀⠀⠀⠀⠀⠴⠋⠀⠀⢤⣿⠀⠀⠀⢻⣿⣿⣿⡇⠀⠀⢸⣿⣿⠀⠀⢸⣿⣷⠀⠀ ⠀⠀⠀⠀⠋⣠⡶⠛⣿⠻⣄⠀⠀⠀⠀⣠⠞⠛⣿⠻⣤⠙⠀⠀⠀⠀⢻⣿⣿⣿⠀⠀⢸⣿⡟⠀⠀⣾⣿⡿⠃⠀⠀ ⠀⠀⠀⠀⠀⢽⠀⠸⣿⡇⠀⢻⠀⠀⠀⣟⠀⠸⣿⡇⠀⡯⠀⠀⠀⠀⠀⢸⣿⠿⠇⠀⠀⣿⡟⠀⣠⣿⡟⠁⢀⣼⠀ ⠀⠀⠀⢹⣄⠈⠳⣤⣿⣤⠞⢀⣀⣀⡈⠲⣤⣼⣧⠞⠀⣠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⣠⣾⣿⡇⠀ ⠀⠀⠀⠀⠹⣧⣄⡀⠀⠀⠀⠀⠈⢻⠋⠀⠀⠀⠀⠀⣀⣴⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠟⠛⠉ ⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣿⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⠿⠿⠿⠿⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⠀⠀⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠛⠀ ⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣄⠀⠀⠀⠀⠙⢿⣿⣿⣿⡇⠀⠀⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠟⠀⠀⠀ ⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠙⠛⠛⠃⠀⠀⠛⠛⠛⠿⡇⠀⣼⣿⣿⣿⣆⠀⠙⠿⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀ ⣠⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣶⣤⣤⣤⣴⣶⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠹⣿⣿⣿⣿⣿⣿⠿⠟⠋⠀⠀⣠⣶⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀