⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣰⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⣶⢿⣿⠿⠟⢛⢯⣿⡟⣿⣿⣶⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣴⣿⣿⣟⣶⣻⠥⠿⠭⠙⢫⣿⡟⣀⢹⢿⠻⣿⣝⣷⣄⠀⠀⣀⣤⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⠋⣻⣿⣿⣛⡯⣿⠀⢯⣩⡷⠚⣾⣟⣉⣻⣛⠀⠈⣙⣿⣿⣿⡿⣻⡏⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣤⣿⣿⣿⡿⠗⡉⠀⠀⠈⠁⣨⣿⣿⣿⣻⣙⣿⣻⣻⣿⢷⣿⣦⣻⣿⠃⠀⠀⠀⠀⠀ ⠀⠀⣰⣿⣿⣿⣟⣭⠄⡬⠛⠛⠛⠻⠾⢟⣹⠀⠈⠻⣿⣿⠛⢋⣝⣾⠿⣿⣿⡇⠀⠀⠀⠀⠀⠀ ⢀⣼⢿⣿⣿⡿⠛⢳⣀⡁⠒⢒⡤⠤⠀⢻⣿⡀⠀⢸⣿⢻⣾⣾⡏⠀⢰⣿⣿⠂⠀⠀⠀⠀⠀⠀ ⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡝⠷⣦⣞⠋⠻⢤⣤⣡⣤⣅⣿⡅⢠⣿⣵⣿⠀⠀⠀⠀⠀⠀⠀ ⠉⠀⠀⠀⠀⠀⠀⢈⣽⣿⢟⣿⡷⠀⣶⣮⡷⣄⡠⣄⠀⠀⠈⡙⣻⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣾⣿⣾⣯⣕⣷⣼⣹⣿⣿⣿⣝⣙⣻⣾⣷⡿⠿⠿⣿⡟⠆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣼⣷⠿⠿⠿⢿⣿⣿⣿⣿⣿⡏⢀⠀⣿⣿⡿⠛⠉⣽⣞⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⣠⣿⣿⣿⣿⣿⢿⣏⣉⢒⣏⣼⣿⣦⣾⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⣿⣿⠟⢻⣿⡇⠒⠄⣿⣿⣿⣿⡿⣯⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠙⠻⢻⣶⠟⡿⣿⣶⣾⣿⣿⣿⠃⠀⣼⠿⡿⢣⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡃⡠⡂⠘⣿⣿⣿⣿⣧⣍⣩⣿⣿⣆⠀⢿⠀⡄⡠⢧⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣼⡽⡬⢳⡽⣣⠃⣿⣿⣯⣿⣿⣿⣷⡜⡏⠛⠓⡿⡀⠏⢳⡿⣧⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⡷⣱⠂⣾⢿⣷⣿⣿⣿⡇⠹⣿⣿⣿⣿⣠⠞⡁⣤⠆⣴⣿⣿⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠳⡾⣶⣦⣻⣾⣿⣿⣿⣿⠀⢹⣿⣿⣟⣿⡀⣿⠙⠊⣾⣷⣿⡷⠄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⢩⠛⣳⣿⢻⡄⢠⣿⣿⣿⣿⣿⣧⣀⣤⣦⣤⠼⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⢐⢿⣿⡸⣿⡈⢹⣿⡸⡉⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⢸⣿⡇⣾⣷⠘⣏⣿⣷⣄⢈⠻⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⢸⠈⣿⡇⠈⣿⣆⣿⣹⣿⡌⠣⡑⢻⣦⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠀⡸⠀⢿⣷⡀⣽⢻⢿⣯⣿⣧⠀⠘⡄⠙⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠶⢽⡚⢒⣿⣧⣿⢸⣛⡿⣝⡏⣴⡶⠧⣴⣾⣿⣷⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢞⣉⣙⢢⢼⣿⣿⣵⠙⢿⢭⣿⢻⣾⣿⢿⣻⣾⡟⢻⡻⢧⣄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡴⢫⣷⢽⠿⠉⠛⠛⣯⡈⠁⠀⣾⣿⣿⡿⣿⣏⠉⠀⠙⠿⠂⠉⠉⢹⣆⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⣷⠝⠧⠶⠤⣤⣶⠟⠉⠷⣤⣶⡿⠻⣿⡇⣿⣿⡄⢰⠶⢒⣶⣶⡶⢾⡝⣧ ⠀⠀⠀⠀⠀⠀⠀⢿⠭⢼⣿⣿⣧⣛⣛⣛⣶⣚⣟⡠⠤⠔⠻⣷⣟⣛⣚⣛⣒⣺⣾⣷⢿⣾⠯⠿