⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠉⠀⠀⠀⢀⣤⣈⣉⣻⣿⡛⠉⠁⠀⠀⠘⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠏⢀⣶⣤⡀⠀⢸⡏⠉⠙⣿⢹⡇⠀⠀⠀⠀⠀⠘⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠃⠀⣾⠏⠙⣿⡶⢸⣟⠛⠛⠛⢸⡇⠀⠀⠀⠀⠀⠀⠸⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣄⠸⣿⣄⣴⡿⠁⣼⣿⡷⠜⣷⣿⠇⠀⠀⠀⠀⠀⠀⠀⢹⣿⣷⣤⣤⣶⣶⣾⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡿⠛⠁⠘⢿⣦⡈⠛⠟⣠⣷⠛⢁⠀⣦⡈⣿⣷⡄⠀⢀⣠⣴⣾⣿⠿⠿⠛⠛⠋⠉⠉⠁⠀⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⠟⠉⠀⠀⠀⠀⠀⠙⠻⣷⣾⠟⢿⣇⠹⣧⣼⡿⣟⣯⣷⣿⠿⠟⠋⠉⠀⠀⢀⣀⣤⣴⣶⣾⢃⣼⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣾⣿⣵⣾⠿⠛⠉⠀⠀⠀⢀⣠⣴⣾⡿⠟⠛⠛⠿⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⠿⠛⠉⠀⠀⠀⢀⣠⣴⣾⡿⠟⠋⠁⠀⠀⠀⠀⠀⠈⠹⠿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⠟⠁⠀⠐⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⠟⠋⠁⠀⠀⢀⣠⣴⣾⡿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢿⣷⣄⣀⠀⠀⠀⠀⠀⣰⣿⡟⠁⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⢀⣴⣾⠟⠋⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠙⢿⣿⣷⣄⠀⢠⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠄⢀⣠⣾⡿⠋⠁⠀⠀⢀⣠⣶⣿⣿⠿⠋⠸⢿⣏⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠹⣿⣿⣷⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠉⠀⠀⠀⣠⣴⣿⣿⠟⠋⠁⠀⠀⠀⠈⣿⡄⠻⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠻⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠛⠁⠀⠀⢀⣴⣾⣿⢿⡿⠃⢠⡤⠀⠀⠀⠀⠀⢸⣿⡀⠙⢿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣄⠀⠀⠀⠀⠀⣠⣾⡿⠋⠀⠀⠀⣠⣾⣿⡿⠋⢉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⠀⠈⢻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣷⣄⠀⣠⣾⡿⠋⠀⠀⢀⣴⣿⣿⡟⠋⠉⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡄⠀⠀⠻⣿⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣾⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⡏⠀⠀⢀⣴⣿⣿⡛⣁⣀⠰⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⡇⠀⠀⠀⠉⠛⠛⢿⣿⣿⠿⣿⠿⠿⠟⣿⠛⣻⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⢫⡞⠀⢀⣴⣿⢿⡉⣀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡄⠀⠀⠀⠘⡲⠶⢼⣿⣿⣧⡙⠷⢦⣴⠟⢀⣿⣿⣿⡿⠿⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⢏⡴⠋⢀⣴⣿⡿⠃⢶⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⡿⣿⣿⣿⡄⢠⠔⠋⠀⠀⠀⠀⠙⢿⣿⣦⣄⣀⣠⣾⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⢡⡞⠁⢠⣿⠟⡋⠃⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣟⠁⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⡿⢿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣰⣿⠟⣰⠋⣀⣤⣿⣿⣀⡇⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠋⠹⣧⠸⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡉⠉⠁⠀⠀⠉⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣼⣿⣋⣴⣷⡿⠟⠛⢹⣿⡏⢳⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣏⠀⠀⠀⣿⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⣷⠀⠀⠀⠀⠀⠸⣿⣦⣀⠀⠀⠀⠀⢀⣠⣶⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣾⡿⠟⠋⠉⠀⠀⠀⠀⠈⣿⣷⢸⡷⠶⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⡟⠉⠈⠙⠿⠷⠾⠋⢀⣾⣿⣿⠁⠀⠀⠀⠀⠀⠀⢀⣤⡾⢟⣫⣽⠇⠀⠀⠀⠀⠀⣿⣟⠛⠿⠿⠿⠿⠛⠋⣸⡟⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡄⢿⣄⣀⣴⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣷⣤⣀⣀⣀⣤⣴⣾⣿⣿⣿⠏⠀⠀⠀⠀⠀⣠⣾⣿⣵⠾⠛⠉⠀⢰⡄⠀⠀⠀⠀⢹⣿⠀⠀⠀⠀⠀⠀⢀⣿⢁⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣷⢸⡏⠉⠁⠀⠀⠀⣤⣾⠿⠟⠉⢹⣿⠛⠿⣿⣿⣿⣿⣿⣿⣿⠛⠉⠀⠀⠀⠀⠀⢀⣾⠿⠛⠉⠀⠀⠀⠀⠀⣸⡷⠀⠀⠀⠀⠈⣿⡆⠀⠀⠀⠀⠀⣼⣏⣾⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡆⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣇⠀⢂⢸⣿⠁⠀⢹⣿⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⣀⣠⣴⣿⣿⣇⡴⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⢰⣿⣿⣻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣷⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣆⠀⢯⠏⠀⠀⠈⠃⠀⠀⠀⠀⠠⣤⣤⣤⣤⠴⠶⣞⣛⢫⠿⢛⣩⡾⠋⠀⠀⠀⠀⠀⢹⣿⠀⠀⠀⢀⣿⡿⠁⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣆⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⢶⣿⣏⣉⣭⣿⠾⠛⠉⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⣼⠋⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡜⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡄⣸⡆⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡆⠀⠀⠀⠀⠀⢰⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃⢹⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⡿⢿⣿⣆⠀⣠⣶⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⠿⣷⣄⣀⠀⠀⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⠀⠊⠛⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠋⠀⠀⠙⢿⣿⣿⣽⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠃⠀⠈⠙⢿⣷⣶⣿⣇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⢠⡮⠁⠀⠀⠀⠀⠀⠀⠀⣠⣾⠿⠋⠀⠀⢀⣀⣤⣶⠿⠛⠋⢻⣿⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠶⢾⣿⣥⣄⣀⠙⠦⣀⠈⠛⢿⣿⣟⠿⢷⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⣰⠏⠁⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁⢀⣤⡴⠾⠛⠋⠁⠀⠀⠀⠀⠀⢻⣧⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⠀⠀⠀⠈⠉⠙⠛⠛⠾⠷⠤⠀⠉⠻⢷⣴⣿⣧⣀⡀⠀⠀⠀⣀⣀⣀⣠⠤⠤⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠋⣰⠏⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⠾⠟⠻⣷⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣶⣶⣾⣯⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡛⠻⠿⠿⠿⣿⣿⣭⣤⣤⣄⣀⣀⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡙⢧⣤⠀⠀⠀⠀⠀⣠⣾⡿⠀⠀⠀⠀⠀⣀⣤⣴⠾⠟⠛⠉⠁⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⡟⠋⠉⢹⣏⠉⠉⢹⡟⠀⠈⠉⠉⠛⠛⠻⠶⠶⣦⣤⣄⣀⠀⠀⠀⠀⠙⢿⣶⠀⠀⠀⠀⠀⠉⠉⠛⠛⠻⠿⣿⣷⠒⠒ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡛⣦⡀⠀⠀⢸⣿⣏⣄⠀⠀⠀⠐⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⢿⣿⠉⠀⠘⣷⡙⣄⠈⣿⠀⢀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⢀⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣠⡽⢿⣮⡳⣆⡀⠀⣿⣿⣎⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⠾⠛⠋⠉⠀⠈⢿⣧⠀⠀⠈⢷⣌⠆⠹⠀⣾⡟⠛⠷⠶⣶⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠁⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⢸⣿⠀⠈ ⣀⣀⣠⠤⠤⠴⠖⠒⠒⠛⠋⠉⠉⠉⠀⠀⠀⠀⠀⠙⢿⣾⣷⣄⣙⣿⣿⣆⠈⢦⠀⠀⠀⠀⠀⠒⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠘⣿⡆⠀⠀⠈⢿⣷⣄⣰⣿⡀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠒⠆⠀⠀⠀⠀⠀⠀⢰⣿⡿⣷⣤⣀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸⣿⠀⠀ ⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⡤⠤⠴⠖⠒⠚⠛⢿⣿⣿⡾⣿⣿⡆⠀⠱⣄⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⡤⠶⢖⠀⠹⣿⣷⣦⣄⡈⢿⡝⣿⡏⠁⠈⠐⠒⠤⠤⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠀⠀⠉⠛⣿⣦⣼⡿⠀⠀⠀⠀⠀⢸⣿⠀⠀ ⠀⢀⣀⣀⣠⡤⠤⠶⠒⠚⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⡄⠀⠈⢦⡀⠀⠀⠀⠀⠀⠈⢻⣿⣆⠀⠀⠘⡄⠀⢿⣷⣼⣿⠃⠈⣿⣿⠃⠈⠉⠉⠙⢻⣿⣿⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⣾⣿⠀⠀ ⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⡭⠿⣿⣧⠦⡀⠀⠑⡄⠀⠀⠀⠀⠀⠀⠹⣿⣆⢀⣠⣵⡾⣿⣿⡟⠁⠀⠀⣾⣟⡀⠀⠀⠀⠀⣾⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⣿⣿⠊⠉ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⡤⠤⠶⠒⠒⠛⠉⠉⠉⠁⠀⠀⠀⠀⠸⣿⡆⢱⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠘⢿⣿⡋⠁⣴⣿⠏⠀⠀⠀⠀⠉⠙⢿⣿⣶⣦⣼⣿⠃⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⣿⣿⡀⠀ ⢀⣀⣀⣤⡤⠴⠖⠒⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⠀⢇⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠻⣿⣦⡉⠻⣷⣤⡀⠀⠀⠀⠀⠈⢿⣧⣼⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠁⠀⠀⠀⠀⠀⢸⣿⠁⠀⠀⠀⠀⠀⠀⣿⣿⣧⠀ ⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡤⠤⠶⠒⠛⣿⡆⠸⡄⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣄⣸⡿⢿⣦⣠⡀⠀⠀⣨⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡄⠀⠀⠀⠀⠀⣿⡏⠀⠀⠀⠀⠀⠀⢠⣿⡿⣿⣏ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⠤⠴⠒⠚⠋⠉⠁⠀⠀⠀⠀⠀⠀⢸⣿⠀⢳⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⡿⠁⠀⣙⣿⣾⡂⣴⣿⠏⠀⠀⠀⠀⠀⣆⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡄⠀⠀⠀⢸⣿⠃⠀⠀⠀⠀⠀⠀⢸⣿⡇⢹⣿ ⠀⠀⠀⠀⠀⠀⢀⣀⣤⠤⠶⠒⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣇⡞⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⣸⣿⡿⠛⠋⠉⠉⠀⠙⢿⣿⣿⣄⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣷⡀⠀⢀⣿⡟⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⠀⢻ ⣠⣤⠤⠶⠚⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡏⠻⣿⣦⡀⠀⠜⠀⠀⠀⠀⠀⠀⠀⣰⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣶⢦⡀⠀⠀⠀⠘⡄⠀⠀⠀⣠⣾⡿⠋⢻⣿⣿⣷⠀⣸⣿⠃⠀⠀⠀⠀⠀⠀⠀⣼⣿⠀⠀⠈ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠤⠶⠒⠚⣿⣿⣦⡇⠈⠛⢿⣷⣤⣄⣀⡀⠀⠀⠀⣰⣿⡟⠀⠀⠀⢀⣀⣀⣤⠤⠴⠒⠚⠛⣿⣧⡱⡄⠀⠀⠀⠘⣄⣤⣾⡿⠋⢀⣴⡿⢻⣿⣿⣧⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⠀⠀