⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡏⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠆⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡇⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣾⡿⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⢻⠃⢸⠇⠀⠀⠀⠀⠀⠀⣀⣴⠞⣫⣾⠟⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡟⣿⠀⡾⠀⠀⠀⠀⣠⣴⢟⡿⠋⣾⡟⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣯⣿⡇⡇⢰⡇⠀⣠⣴⡿⣻⡷⣯⣧⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⡇⣾⣤⣾⣿⣿⡾⣫⣿⣿⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⠘⢳⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⡳⢦⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⣾⣿⣿⡿⠿⣿⣿⣿⠀⣼⣿⣿⡿⣿⣿⠏⠁⢀⣠⣬⠿⠂⠉⠳⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⣾⣿⣿⠿⠿⠶⢦⣌⣻⣿⢄⣿⣿⣿⣿⠟⢀⣤⡾⢛⡡⠀⠀⠈⠛⠂⠈⠳⣄⠀⠀⠀ ⠀⠀⣴⣿⣿⣿⣯⣄⣀⣤⣤⣄⣭⣿⣾⣿⣿⣿⣯⣾⣿⣶⣾⠿⠗⠒⢛⣿⠒⠛⠛⠒⠻⣧⠀⠀ ⢀⣼⣿⣿⣿⣿⣿⠟⠉⠉⠙⠛⠙⠛⠿⠿⠿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣶⣦⣄⣸⣷⠀ ⢾⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⠈⢹⡇⠀ ⢸⣏⣿⣿⣿⡀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣾⣿⣿⣹⡇⠀ ⠈⣿⣿⣿⣿⠃⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⠁⠀ ⠀⢿⣿⣿⣏⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠆⠀⠀⢻⣿⣿⣿⠀⠀ ⣠⢼⣿⣿⡇⣤⣭⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⠷⠖⠒⠀⠀⣿⣿⠿⢛⣦ ⡧⣤⢹⣿⡇⠀⠈⢉⣻⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⣠⡴⣿⣿⣿⢿⣿⣶⣄⠀⠀⠀⣿⡟⡴⠻⣼ ⣧⠏⢧⣿⡇⠀⢰⡟⢹⣿⣥⣿⠿⡙⢧⠀⠀⠀⠉⠁⠐⢹⢹⣿⣾⣿⠇⢹⠀⠀⠀⣿⣿⣁⠀⢸ ⣧⢠⡖⢻⣷⠀⠀⢧⡘⢿⣿⠟⣠⠇⠈⢃⠀⠀⠀⠀⠀⠙⠤⠛⠿⠋⠐⠃⠀⠀⠀⡟⡇⢸⠆⣼ ⠸⣧⢣⡘⢻⡄⠀⠀⠈⠉⠤⠚⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣃⣠⠏⡴⠃ ⠀⠘⣧⠙⠚⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠉⢀⠞⠁⠀ ⠀⠀⠈⠻⣤⣸⡄⠀⠀⠀⠀⠀⠀⠀⠀⣧⣄⢤⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡗⠞⠋⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⡻⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⠀⠀⠀⠠⠤⠤⠤⠤⠥⠤⠴⠶⠶⠃⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⢀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣟⠳⣄⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⢀⡴⡟⢹⡷⣤⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡴⢋⣿⠀⠈⠳⣦⣀⠀⠢⠀⠀⢀⣠⠶⠋⠸⢀⣼⠇⠈⣇⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣴⣾⡇⠀⠻⢦⣀⠀⠀⠉⣛⡛⠛⠛⠉⠁⣀⣄⠴⠋⠁⠀⠀⣿⣻⣦⡀⠀⠀⠀