⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⣀⢀⣠⣄⢆⣠⢬⡰⣀⢤⡠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣠⠶⣶⣿⡗⣿⣿⡿⢯⡿⣿⢿⣽⢻⡟⣭⢺⡟⢯⡷⣶⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠶⣻⣿⣿⣟⣿⠷⠟⠓⠛⠚⠷⠿⣶⣫⣌⡏⠉⠉⢽⣘⣷⣿⣾⣳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣹⣺⣾⡽⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠦⣀⢀⣤⢿⣿⣿⣿⣿⡂⠀⣾⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡖⢶⣦⡄⠀⠀⠈⠻⢧⣟⣾⣿⣟⣉⣇⠀⠙⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⡶⣯⢿⣵⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣟⣟⣿⠇⠀⢀⣠⠤⠒⠋⠉⠉⠁⠀⠈⠑⠒⡀⣸⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣩⣟⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⢁⡠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢘⡽⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢴⣍⠠⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡧⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠊⠁⠀⠙⠻⣖⡮⢭⣓⣦⣤⣄⣀⣀⠀⣀⡀⣀⣤⣴⡜⠁⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋⠁⠀⠠⠀⠀⡼⡰⠂⠙⣽⠖⠲⣤⡭⡯⠯⣯⠭⡿⠓⠊⠹⡆⠀⠀⠀⠀⠠⢀⠆⠡⠈⠀⠀⠀ ⠀⠀⠀⢀⣤⣾⣎⢿⣧⢟⡀⠀⠀⠀⣠⠴⣿⠁⢸⡞⠀⢠⠇⠀⡸⡝⠀⣠⠞⠙⡇⠀⡈⢹⠃⠀⠉⢧⠀⠀⠀⠡⢇⠀⠀⠀⠀⠀⣼⠂⠀⠀⠀⠀⠀ ⠀⢀⣴⣻⣿⣿⣿⣧⣟⣧⣉⣦⢖⠋⣹⢴⡟⠀⣾⠀⠀⡎⡀⢀⡇⢀⠼⠥⠤⠄⣷⠀⡇⢸⠁⠐⠒⠚⢧⣇⠀⠀⢺⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠁ ⠰⣾⡷⣽⣿⣿⣿⣿⢋⠋⢏⡟⠀⡞⠿⣻⡇⢀⠇⢠⢠⣳⠁⣼⡱⠋⠀⠀⠀⠀⢻⣀⢇⢻⠀⠀⣤⣤⣾⡿⠀⠀⡘⡆⠠⣄⠀⠀⢀⠀⠀⠀⡀⠀⠀ ⠄⣧⣟⣿⣿⣿⣿⡟⣸⠀⢸⡁⢸⡇⠀⣾⠇⢸⢀⣾⣴⠃⣰⣿⣷⣶⣶⠿⢭⡄⠀⣯⣾⢸⢀⣽⣿⠛⣿⡗⡄⠀⡃⢸⠀⠀⠩⠤⠀⠑⠢⡐⠀⠀⠀ ⠈⠳⣯⣿⣿⣿⣟⣠⡇⠀⡾⠀⢸⣱⣀⣸⡃⢸⣸⡿⡇⠀⢻⢻⣿⣿⡽⠀⠀⠀⠀⠈⠿⣟⡄⡋⠋⢰⡇⡇⠉⣧⡱⡀⢣⠀⠒⠀⠉⠀⠐⢈⠀⠀⠀ ⠀⠘⢱⣻⣿⣿⢯⡿⠀⢀⢿⠀⡼⢱⣷⣾⢀⣞⡟⠁⡇⠀⡞⠀⠈⠓⠂⠀⠀⠀⠀⠀⠸⡝⢾⡀⠀⣾⢰⡇⢠⢹⡗⡱⡌⡄⠀⠒⠺⣀⠜⡢⠀⠀⠀ ⠀⠀⠀⣸⡿⣿⣿⠡⠀⣸⡇⢀⡇⢰⣯⡿⣿⢿⠀⠀⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠤⠈⢲⣿⢸⠁⢨⢸⡇⠈⢾⠘⡄⠀⠀⠀⠈⠁⠀⠀⠀ ⠀⠀⠘⢯⣿⣿⠋⠀⢀⡿⠀⢸⠀⣸⣻⣞⡏⡿⠀⠈⡇⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢏⢿⠈⠀⢸⢨⡇⠀⠀⠳⡹⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢈⢿⣿⠟⠀⠀⡾⠃⢀⢾⡿⣿⣏⢼⣇⢡⡀⢈⡃⢸⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢾⠏⣸⢸⠀⠀⡸⢨⡇⠀⠑⠀⠹⣪⡦⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⢳⡿⠀⠀⣼⢧⣺⢽⠃⣸⣿⢪⡿⣿⢸⡇⠀⡇⢸⣆⣀⣹⣶⣄⣀⠀⠀⢀⣤⣾⢃⡟⢰⡇⡟⠀⠀⡇⢰⡇⠈⠀⠀⠀⠹⣟⠆⠀⠀⠀⠀⠀ ⠀⠀⠀⠘⠁⡠⣎⠓⠁⢠⠏⣰⡿⠁⢼⣿⣿⣞⣷⠀⢧⣾⣿⣿⢯⣐⠢⠈⠍⢛⣋⠾⢁⠞⣀⣿⠀⡇⢲⢶⡇⣸⣀⣀⣠⣴⡶⣞⡿⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠀⣠⢞⡜⠃⠀⠀⡼⠃⢻⠹⣿⡄⢹⣿⣿⠿⣷⣌⡛⢾⣍⡩⠟⡡⢋⡞⣸⠇⢸⡇⣾⣤⠈⢧⣤⣀⡀⠀⡤⠀⠀⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⣀⡲⠗⠉⠀⠀⠸⡆⢻⣧⠈⣿⣇⠀⠈⣇⢹⣖⠲⠿⠭⠖⠋⢀⡏⢀⣼⠯⣽⣞⣲⣿⣿⠆⠟⠃⠈⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢤⣀⣄⢀⣀⠀⠀⠻⡈⣞⣆⢸⣿⣷⣤⣿⢾⣏⠀⠀⠀⠀⠀⣼⣷⣿⠟⡄⣿⡿⣣⠞⡁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠩⣝⠛⠳⢦⣵⣼⡌⠀⢯⣿⣿⣿⠻⣿⢦⡀⠀⢀⡼⣩⡟⠃⢸⢶⡷⠛⠼⠫⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠙⢶⡍⢫⡷⠀⠈⠿⢿⣿⡇⢿⡷⣿⡤⡚⢸⣿⣟⠃⠀⠉⠑⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠝⠯⠕⠆⠀⠈⠻⠿⢥⠀⢽⣯⠻⡷⠩⠽⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀