⠀⡆⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⡆⠀⡆⠀⠀⠀⠀⡆⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡆⠀⡆⠀⠀⠀⡆⠀⠀⠀⠀⡆⠀⡆⠀⠀⠀⠀⡆⠀⠀⠀⠀⣀⣤⣶⡞⠛⠙⣿⠻⠟⣉⠁⠀⠀⠈⣿⠿⣟⡛⠛⠛⠓⠒⠒⠀⡆⠀⠀⠀⡆⠀⡆⠀⠀⡆⠀⠀⠀⡆⠀⠀ ⠀⡆⠀⡆⠀⠀⠀⡆⠀⡆⠀⠀⠀⠀⡆⠀⠀⠀⠀⡆⣀⣤⠶⠛⠛⠛⠛⢛⡿⠛⠛⠶⣤⣿⠀⠀⠀⠀⠿⠀⠈⠟⠳⢦⣄⡀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⡆⠀⠀⠀⡆⠀⠀ ⠀⠀⠀⡆⠀⠀⠀⡆⠀⡆⠀⠀⠀⠀⡆⠀⣀⡤⠖⠛⠋⣁⣀⣤⣤⡄⢠⡎⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠸⡟⣶⣤⣀⢀⠀⠀⡆⠀⠀⠀⠀⡆⠀⠀⠀⡆⠀ ⡆⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⣠⡾⣇⣠⣴⠶⠿⠟⣻⠿⣿⣿⠾⠃⠀⠀⠀⠀⣼⠛⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠆⢹⣿⣻⣿⣦⣄⡀⠀⠀⠀⠀⡆⠀⠀⠀⡆⠀⠀ ⡆⠀⠀⠀⠀⡆⠀⠀⠀⠀⠸⣯⣉⠉⠁⢠⣍⣻⡷⠶⣶⣞⣁⠀⠛⠁⠀⠀⠀⠀⢀⣼⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢸⣿⣷⡍⠉⠉⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡆⠀⠀⠀⠀⡆⠀⠀⡆⠀⠀⢹⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢦⠀⠀⠀⣴⣶⠯⢿⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠸⣿⢻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡆⠀⠀⡆⠀⢰⣟⡉⠉⠋⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠟⠛⠉⠙⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠈⣯⣿⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀ ⠀⡆⠀⠀⠀⠀⠀⠀⡆⠀⡽⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⣴⣿⣟⣧⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣼⣿⠀⣿⣿⣷⣀⡆⠀⠀⠀⠀⡆⠀⠀⠀⡆⠀ ⠀⡆⠀⡆⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣜⣓⡿⢠⢇⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡏⣿⣿⡦⣿⣿⣿⢿⢦⡀⠀⠀⠀⠀⠀⠀⠀⡆⠀ ⠀⡆⠀⡆⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠺⢿⣶⣛⡥⢀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⡯⣿⡇⠀⠀⠉⢳⣦⣀⠀⠀⠀⡆⠀⠀ ⠀⠀⠀⡆⠀⡆⠀⠀⠳⡤⠤⠤⢤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡾⢧⣄⣀⣀⣤⣶⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⢨⡧⢿⠀⠀⠀⠀⠈⠠⠋⠟⠲⢤⣀⠀⠀ ⠀⠀⠀⠀⠀⡆⠀⠀⠀⢹⢦⣀⠀⠀⠈⠙⠒⠦⣄⣀⣀⣤⠞⡹⠁⠀⠹⣿⠈⢹⠿⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠸⠇⢸⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⣬⡿⠂ ⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠈⢫⡉⠀⠈⠉⠈⠓⠀⠈⢁⡼⠁⠀⠀⠀⢹⡄⠸⠆⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⠀⠀⠘⠀⠀⠀⠀⠀⠀⣀⣤⠖⠋⠁⠀⠀ ⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢠⠞⠀⠀⠀⠀⠀⠀⢻⣰⣆⢸⣿⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠰⡿⠀⠀⢀⠀⢀⣀⡤⠖⠛⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⡆⠀⠀⠀⠀⡆⠀⠀⠀⠀⢼⠃⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣸⣿⡀⠀⠀⠀⠀⣶⣾⡇⠀⠀⢀⣀⣠⣦⡤⠤⠷⠚⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡆⠀⠀⠀⠀⡆⠀⠀⠀⠀⠈⣷⡤⠴⣶⢒⣿⠍⢩⢹⡍⣿⣿⣿⣿⣿⡉⣿⣿⣿⡻⣏⠀⠀⡄⣄⣸⣻⡇⠀⠀⠀⡌⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡆⠀⡆⠀⠀⡆⠀⠀⠀⠀⢀⣇⣇⡞⣅⣞⡏⣇⢸⠈⠃⣿⣿⣿⣿⣿⡇⢹⣿⣿⣧⠈⠳⣴⣿⠻⣿⣭⡉⠛⠛⠛⠉⠉⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⡆⠀⠀⡆⠀⠀⠀⠀ ⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⢼⢸⣿⠁⡿⣸⡀⣿⣯⠀⢠⣿⣿⣿⣿⣿⣇⣿⣿⣿⣿⣷⡀⠈⠻⣇⠈⠙⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⡆⠀⠀⡆⠀⠀⠀ ⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⢀⣏⡼⢹⣸⠇⡏⡇⡇⢹⠀⢸⣿⣿⣿⠿⠛⠛⠋⠉⠛⠻⢿⣛⠦⢤⣀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⡆⠀⠀⠀⠀⠀⡆⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣿⡧⠖⠛⠉⣀⡙⠳⢧⣠⠴⠚⠉⠀⠀⠉⠓⠢⢤⣀⣀⡤⣤⣜⣛⣖⣪⡽⣦⡀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⣴⣿⠿⠛⣩⣴⡖⣺⣿⣿⣿⢟⡯⠟⠿⠭⠭⠭⢽⣒⣤⣠⣒⣯⣿⠿⠛⠋⠉⠉⢻⣿⣿⣿⣷⣤⡀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⣾⠿⠿⣓⣒⣚⣋⠭⠭⠭⠭⠭⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⢹⢹⣧⣿⣅⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⡆⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀ ⠀⣠⢞⡭⠖⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⣾⣿⣿⣿⡄⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⡆⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀ ⢰⢣⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣽⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀