⠀⠀⠀⠀⠀⣠⣿⠏⠉⢩⣿⠟⠋⠉⠉⣽⡟⠙⣿⣏⠀⠀⠀⠀⢀⣼⣿⣯⣿⡿⠋⠉⠉⠉⢹⣿⠏⠉⠉⠉⣠⡈⠉⠉⠉⠀⠀⠀⠀⣠⣽⣿⡟⠉⢹⣿⠉⠉⠁⠀⠈⣿⠀⠀⠀ ⠀⠀⠀⠀⢠⣿⠏⠀⢠⣿⠋⠀⠀⠀⢠⣿⠁⠀⠹⣿⡄⠀⠀⣠⣿⠟⢿⣿⠟⠀⠀⠀⠀⠀⣿⡏⣀⣤⣶⣿⣿⠇⠀⠀⠀⢀⣠⣶⡿⢟⣽⡿⠃⠀⣾⡏⠀⠀⠀⠀⠀⣿⠀⠀⠀ ⠀⠀⠀⢀⣿⡟⠀⢠⣿⠃⠀⠀⠀⠀⣸⣿⡾⠶⠶⣿⣿⣄⣼⡿⠃⠀⣾⡏⠀⠀⠀⠀⠀⢀⣿⣿⠟⠋⠁⢸⡿⠀⣀⣴⣶⡿⠛⣩⣴⡿⠋⠀⠀⣼⡿⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀ ⠀⠀⠀⣼⡿⠀⢀⣾⠏⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⣻⣿⠟⠀⠀⣼⡟⠀⠀⠀⠀⠀⠀⢸⣿⠃⠀⠀⠀⣻⣿⣿⠟⠋⠙⠛⢿⡟⠁⠀⠀⠀⢰⣿⠃⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀ ⠀⠀⢰⣿⠃⠀⣸⡟⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠰⠿⠁⠀⠀⢰⡿⠁⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⣠⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠇⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀ ⠀⢀⣿⡏⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠻⣷⣤⣤⣴⠆⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠘⣿⣄⣀⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⠀⠀⠀⠀⠀⠀⣸⣿⠁⠀⠀⠀ ⠀⢸⣿⡁⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣹⣿⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠇⠀⠀⠀⠀⠀⠀⢀⣿⣇⣀⠀⠀⠀ ⡆⠀⣿⡇⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠃⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠃⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⠀⠀⠀ ⣿⡄⣿⣿⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣄⣀⣀⡀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠁⠀⠀⣀⣤⡄⠀⠀⢀⣿⣿⣿⡿⠀⠀⠀ ⠻⣿⣾⣿⡀⠀⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⢙⣿⠆⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣧⣤⣄⠀⠀⠀⠀⠀⠀⣴⣿⣏⣠⣤⣶⠿⠟⠉⠀⠀⢀⣾⡿⠃⣿⡇⠀⠀⠀ ⠀⠙⢿⣿⣧⠀⠸⣿⡄⠀⠀⠀⠀⢀⣴⣄⠀⠀⠀⠀⣸⣿⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⠀⠀⠀⠀⠀⠀⠈⠛⠛⠉⠁⠀⠀⠀⠀⠀⣠⣿⠏⠀⢰⣿⠀⠀⠀⠀ ⠀⠀⠀⠙⠻⠂⠀⢹⣷⣤⣤⣶⠿⠛⠛⠿⣷⣦⣀⣠⣿⠃⠀⠀⠹⣷⡀⠀⠀⠀⠀⠀⣠⣾⠇⠀⢰⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁⠀⠀⣼⡿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣦⡄⠙⠋⠉⠀⠀⠀⠀⠀⠀⠉⠻⠿⠃⠀⠀⠀⠀⠹⣿⡄⠀⢀⣤⣾⠿⣷⣤⣠⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡾⠟⠁⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣷⡿⠋⠀⠀⠀⠉⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⢻⣇⠉⠻⢷⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠇⠀⠀⠀⠀⠀ ⣧⠀⠀⠀⠀⠀⠀⠈⣿⡆⠀⠀⢻⡟⠿⣷⣦⣀⠀⠀⠀⣶⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡟⠀⠀⠀⠀⣠⣴ ⣿⡆⠀⠀⠀⠀⠀⠀⠘⣿⡄⠀⠘⣿⡀⠸⣌⡛⠻⣷⣦⢿⣿⣿⢠⣶⣄⡀⠀⠀⢀⡀⢀⣀⣠⣤⣴⡶⠿⠟⣿⣏⣽⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣤⣤⣴⣶⣿⣿⠏ ⠁⠀⠀⠀⠀⠀⠀⢸⣦⡘⢿⣆⠀⠘⢿⣤⣈⣀⣀⣿⡟⠈⠛⠋⠀⠛⠻⣿⡛⠛⠛⠋⠉⢻⣯⡁⠀⣀⣤⡾⢟⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣏⠉⠁⢠⣿⡏⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣦⣤⣬⣽⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠈⠻⣶⣤⣀⠀⠀⠉⠉⣉⣩⣽⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣷⣦⣿⣟⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣍⣻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠿⠿⣿⣿⣿⡷⠿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⢿⣷ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⢿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣄⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡟ ⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣨⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⠋⠀ ⣿⣿⣷⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣿⣷⠶⣶⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣶⢾⣿⢿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⣾⠟⢛⣿⠃⠀⠀ ⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣶⣄⠀⢹⢯⡉⠉⠉⠛⠿⢥⣌⠉⢁⡴⠚⠁⣸⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⡾⠿⠛⠉⠀⢀⣾⣟⣠⣶⣿ ⣈⣿⠏⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣀⠈⢿⣧⣹⠏⠀⠳⣄⠀⠀⠀⠀⠈⢳⡾⠻⣄⣰⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⠛⠋⠉⠀⠀⠀⠀⠀⠀⠾⡿⠿⠛⢹⣿ ⢻⡟⠀⢀⣀⣤⣴⣶⡿⠿⠟⠛⠉⠉⠉⠻⠿⣾⣿⣷⣤⣤⣤⣉⣉⣉⣙⠛⠛⠋⠀⠀⢹⡿⠃⠀⠀⠀⢀⣠⣤⡀⠀⠀⠀⠀⠀⢺⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⣶⠿⠿ ⢿⣷⡾⣿⡛⢻⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⣿⣬⣍⣙⠛⠛⠻⠿⠿⠶⡶⣟⣁⣤⣤⣶⣿⣿⣿⡿⣿⣄⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⣶⡀⠀⢰⣿⠃⠀⠀⠀ ⠈⠁⠀⠙⣿⣿⡋⠉⠀⠀⠀⠀⠰⣟⣻⡄⠀⠀⠀⣀⣀⠀⠉⠙⠻⠿⣶⣤⣴⣶⣾⣿⣿⣿⣿⣿⣿⠟⣋⣁⡀⠈⢻⣧⡀⠀⢸⣿⠀⢰⣦⣀⠀⠀⠀⠀⣿⣿⣦⣿⡏⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⣿⡿⠷⢶⣶⣤⡀⠀⠈⠉⠀⣀⣴⠞⢋⣿⠇⠀⠀⠀⠀⠀⢀⣀⣉⣉⣻⠿⢿⢋⣩⣶⣿⠿⠛⠿⣷⣦⣹⣿⣄⣾⡏⠀⢸⣿⣿⣷⡄⠀⢰⣿⠛⢿⣿⠀⠀⠀⠀⠀ ⢠⣦⣄⣀⣀⣻⣧⡀⠀⠈⠻⢿⣦⡀⠀⠘⢿⣤⣤⣾⠏⠀⠀⠀⢀⣠⣾⠿⠟⠛⠛⠻⠿⠟⠛⠛⠉⠀⠀⠀⠀⠀⢹⣿⣟⣿⡿⣷⣦⣼⣿⡀⠹⣿⣦⣿⡟⠀⠈⢿⣧⠀⠀⠀⠀ ⠀⣿⣟⠛⠛⠛⠛⠁⠀⠀⠀⠀⠙⠿⣷⣄⠀⠀⠉⠁⠀⠀⠀⣾⠟⣿⡏⠀⠀⠀⠀⠀⠀⢰⣷⡀⠀⠀⠀⠀⣸⣷⡄⠉⠛⢿⣶⣤⣈⠙⠛⠃⠀⠘⣿⡟⠀⠀⠀⠈⢿⡇⠀⠀⢀ ⠀⠘⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣦⡀⠀⠀⠀⢀⡘⠛⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⣷⣀⣀⣤⣶⡿⠋⠀⠀⠀⠀⠈⠙⠻⢿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣤⣶⠟ ⠀⠀⢈⣿⣷⡄⠀⣾⠿⢶⣤⡀⠀⠀⠀⠀⠀⠙⠿⣶⣤⣴⡿⣿⣤⣿⠃⠀⠀⠀⠀⠀⠀⣸⡇⣿⣿⣿⠋⠁⠀⠀⠀⠀⠀⠀⣼⣿⡇⠀⠈⠛⠻⣿⣦⠀⠀⠀⠀⠀⠘⠟⠋⠁⠀ ⣤⣤⣾⣿⣯⣤⣼⣿⣤⣤⣽⣿⣷⣦⣤⣤⣤⣤⣤⣤⣭⣿⣥⣾⣿⣿⣦⣤⣤⣤⣤⣤⣴⣿⣵⣿⣿⣧⣴⣶⣶⣶⣶⣶⣦⣾⣿⣿⣤⣶⣶⣦⣤⣾⣿⣶⣶⣶⣦⣤⣤⣤⣤⣤⣤