⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠶⠞⠛⠛⠛⠶⢦⣄⡀⠀⠀⠀⠀ ⠀⠀⠀⣠⡾⠛⠉⠀⠀⠀⠀⠀⠉⠙⠳⣦⣄⠀⠀⠀⢀⣴⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀ ⠀⠀⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⢠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⠀ ⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣿⢮⡻⣿⣵⣿⣿⣶⠀⠀⠀⣀⡤⠤⢤⣀⠀⠀⠀⠀⠹⣇ ⠀⣿⠀⠀⠀⠀⠀⡰⠊⠉⠉⠲⢄⠸⣿⣿⣿⣾⠃⣿⢿⣾⣿⣿⠁⣠⠞⠁⠀⠀⠀⠈⢧⠀⠀⠀⠀⢿ ⠀⣿⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠑⠬⣉⡉⣁⡠⠛⢦⣈⣉⣠⠞⠁⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⢸ ⠀⣿⡀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣾ ⠀⠸⣧⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⣰⠇ ⠀⠀⠹⣦⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⢀⣴⠏⠀ ⠀⠀⠀⠙⣷⡀⠀⠀⠙⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⣠⡾⠃⠀⠀ ⠀⠀⠀⠀⠈⠻⣦⡀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⢀⣼⠟⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠈⠳⣄⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁⣠⣴⠟⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣄⡀⠈⠳⣞⠁⠀⠀⠙⠢⣄⣀⡠⠖⠋⣀⣴⢾⣏⣀⣠⠆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⢿⣿⡶⢄⡈⢳⠀⠀⠀⠀⠈⣻⣶⣾⣿⣿⣶⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠙⣦⠉⠁⠀⠀⠀⠀⠸⠿⠻⣿⣋⣙⠛⠋⠀⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⢄⡀⣀⣼⣄⡀⠀⠀⠀⠀⠀⠀⠀⢈⣩⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⠋⠀⠀⣿⣿⣿⣿⠉⣿⣶⣶⣶⡖⢶⡿⠻⣦⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⡾⠟⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⡾⠷⣀⠀⠀⠀⠈⣿⣿⡟⠋⣉⠙⠋⠉⠙⣿⣿⣄⠀⠀⠀⣶⣦⣤⡆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⡿⠁⠀⠈⠓⢦⣀⠀⠹⡏⠀⠀⣸⣿⠷⣶⣾⣿⠟⠻⣿⣷⣿⡿⠞⠙⣿⣧⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⡿⠁⠀⠀⠀⠀⠀⠈⠛⠦⣌⡲⠤⠿⣇⣀⣹⣿⡿⠤⠶⠛⠋⠁⢀⡤⢚⡟⢻⣆⠀⠀⠀⠀ ⠀⣠⣤⡿⠁⠀⠀⡴⠀⠀⠀⡼⠀⠀⠀⠙⠻⣒⠲⠤⠤⣄⣀⣀⠀⢀⣠⡾⡏⢀⡞⠀⠀⢻⣆⠀⠀⠀ ⠀⣿⣄⠙⠦⣀⣰⠃⠀⠀⢀⡇⠀⠀⠀⠀⠀⠈⠑⠦⣄⠀⠀⡝⠻⣏⢰⠇⠘⠛⠀⠀⠀⢀⡿⢻⡆⠀ ⢀⣿⣿⣷⣦⣌⡙⢢⢄⣀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠀⠀⠈⠚⠀⠀⠀⣀⡤⠖⢉⣴⣿⡇⠀ ⣸⠏⠻⣿⣿⣿⣿⡇⣸⠉⠉⣒⠦⢤⣀⣀⣀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣴⡶⣯⣡⣴⣾⣿⣿⣿⣧⠀ ⢿⣦⣄⣈⣛⣿⣿⢀⡏⠀⢰⣿⣿⣷⣦⣤⣍⣉⣉⠉⠉⣩⠟⣛⣉⣭⣼⣶⣶⣄⣿⣿⣿⣿⠿⠛⠋⠀ ⠀⠀⠀⠈⠉⠉⠛⠛⠓⠶⠾⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⠾⠿⠿⠿⠿⠛⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀