⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣀⣀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠉⣿⣳⢯⡽⣦⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⡤⡌⢎⠻⣯⣷⢯⣻⣄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢠⡏⠀⢣⠙⢻⣿⣿⡟⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠈⠾⠁⠀⣜⡏⢶⠲⡴⣒⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠇⠀⠀⠀⡐⢯⣜⢣⠟⡴⡽⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠉⢢⠀⠀⠀⠀⢠⡏⠀⠀⠀⡠⢏⡳⣬⢛⡼⡳⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢀⡟⠀⣰⢦⢀⡝⣎⢷⣱⢫⢶⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠠⠉⠁⣠⡟⡼⣷⣾⣿⣾⣮⠷⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣴⣧⣄⢰⡟⣼⡽⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⡇⢸⣞⣶⠃⠀⠀⠀⠀⠢⠞⡒⡳⢚⠀⠀⠀⠀⠀⠀⢻⣟⡇⢸⠹⣿⣿⣿⣜⣾⣿⡿⣿⣻⢿⡿⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠁⢀⠀⠀⠀⠀⡿⡌⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠁⢺⡇⠸⡀⠙⠿⣷⣾⣿⣷⣻⣷⣯⡿⣿⡿⣿⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣠⢉⠂⠀⠀⠃⠀⠀⠀⡿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡇⠀⠘⢄⡀⠘⢿⣳⡿⣟⡷⣯⣿⣽⣿⣯⣿⡀⠀⠀ ⠀⠀⠀⠀⢀⣠⣤⣶⢾⡟⣿⢻⣟⡞⠀⠀⠀⢠⠀⠀⠀⣷⣃⠄⠀⠀⠀⠀⠀⠀⠀⢀⢄⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⡄⢸⣷⣶⣼⣟⡷⣿⣳⣿⢯⡿⣽⣿⣻⠇⠀⠀ ⠀⠀⢠⣴⣿⣻⡽⣞⡽⡾⣭⢷⣞⣿⠀⠀⠀⢸⠀⠀⠀⣿⡽⣮⣢⢄⠀⠀⣀⣠⣶⣭⣦⣂⣄⡀⠀⣀⣠⣼⣟⣷⠀⡇⢸⣿⣿⣿⣿⣽⣳⣿⡿⣿⣿⣿⣿⣿⠀⠀⠀ ⠀⢠⣽⡿⣞⡷⣽⠾⣽⣻⣽⣿⣾⣿⠀⡄⠀⢸⠀⠠⠀⠁⠀⡀⣠⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢸⣿⣿⣿⣿⣿⣿⣿⣿⣳⣯⢿⣿⠋⠀⠀⠀ ⢠⢻⣿⡽⣯⣟⣾⣻⡽⣿⣻⣽⣿⢧⡳⣠⢡⢸⠀⠘⠈⡀⡀⣼⣿⣳⢯⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⡶⡆⠀⠀⠉⣸⣿⣿⣿⣿⣿⣿⣿⣿⣷⢯⡿⣧⠀⠀⠀⠀ ⢸⣿⣯⣿⡷⣿⣞⣷⣻⡽⣿⣿⠙⣾⣷⢧⣳⠇⠀⠀⠇⠁⠘⣜⠷⣯⣿⠞⣡⠀⣤⣶⣾⣤⡀⠀⣷⣾⣿⣿⣿⣾⣇⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢯⣟⣿⡀⠀⠀⠀ ⢸⣿⣿⡷⣿⣻⣾⣳⣯⣟⣷⣻⣿⣯⣿⠛⠛⠁⢐⡄⠀⠀⠀⠀⠉⠒⠒⠉⢰⢸⣿⣳⣟⡾⡇⡄⠛⠛⣿⣿⣽⠛⠛⠀⢸⣽⣿⣿⣿⣿⡿⠟⠋⢻⣿⡽⣾⡇⠀⠀⠀ ⢸⣿⣟⣿⣿⣯⣷⣿⣳⣯⣿⣿⣿⣷⣻⢄⠀⠀⢸⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⡻⠷⠯⠿⡁⠂⠀⠀⠛⠛⠛⠀⠀⠰⢸⣿⣳⣯⣷⡀⠀⠀⠀⢸⣿⡽⣟⣇⠀⠀⠀ ⠈⣿⣿⣿⣷⣿⢿⣾⣿⣿⣟⣿⣿⣿⠿⢀⢡⣾⡘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠹⣿⡷⣯⣷⠀⠀⠀⢸⣿⣻⣿⡏⠀⠀⠀ ⠀⢿⣿⣿⣾⣿⣿⣿⣿⣿⣾⠿⠛⠁⠀⢸⣿⢿⣿⣦⣃⣆⣠⣀⣄⣠⣠⣄⣤⣠⣄⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡶⠃⠀⠹⣿⣷⣻⢧⣀⣠⣿⣿⣻⣽⠃⠀⠀⠀ ⠀⠸⣿⣿⣿⣿⣿⠿⠛⠛⠃⠀⠀⠀⠀⣸⠀⠀⠀⠘⢿⣿⢿⣿⠿⡇⠀⠛⠛⠛⠛⠛⠛⠃⣿⢿⣿⣿⣿⡿⣿⡻⠟⢸⠀⠀⠀⢿⣧⣿⣟⣿⣻⣿⣿⣿⠟⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⡀⠀⠀⠀⣸⢯⣿⣞⡈⠸⠀⠀⠀⠀⠀⠀⠀⠀⣇⢆⣭⣿⡿⣽⠋⠀⠐⠚⢄⠀⠀⠀⠙⠿⠿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣌⠀⠀⠀⠀⠀⢻⣷⡿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣟⣏⣀⣀⣀⣀⣨⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠉⠉⠉⠁⠈⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀