⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢠⣾⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣼⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣼⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⢠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡁⢀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀⠁⠐⣽⣏⣽⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠿⣿⣷⣮⡲⣧⢿⢾⣻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣇⡀⢻⡿⢿⣿⣾⣯⣿⣿⣿⣣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣀⡀⠀⠿⠹⠿⠏⡿⣿⣿⣿⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠏⠈⠀⣞⣤⠀⠀⣰⡇⣿⣿⣯⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⣩⢩⣤⡄⠀⣸⢷⣿⣿⣟⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠈⠀⠀⠀⠀⣠⣪⣿⣿⣿⣟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⠠⣤⣔⣾⣾⣿⣿⣿⡿⠃⠀⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠄⠀⠀⠜⠛⠿⠿⠛⢛⣿⡷⣤⡠⡀⠀⢀⠩⣑⡤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⣼⣿⣻⢿⣽⣳⣔⠦⢢⣄⡽⢾⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠗⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣿⢿⣽⣻⡾⣽⢿⣎⢞⣁⠺⣷⣿⣿⣳⢀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣪⣿⢯⣟⣾⣳⣿⡿⣿⣻⣯⠎⠀⣾⣿⣿⣿⣿⣥⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠠⢂⣴⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣽⣿⣿⣻⢾⣷⣯⣷⣿⣿⣻⣿⣿⣮⣻⣿⣿⡿⣿⣾⣧⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⣿⢿⣽⠀⠀⠀⠀⠀⠀⠀⠀⠠⢐⣽⣿⣻⣞⡷⣯⣟⡿⣾⣻⣾⣿⣿⣿⣿⣿⣿⣞⢿⣿⣿⣿⣿⣷⠀⠀⠀⠀ ⠀⠀⠀⠀⣴⣿⢯⣟⣾⢦⠀⠀⠀⠀⠀⠀⣢⣶⣿⣿⢯⡷⣯⣿⣟⣾⡽⣿⣿⣻⣽⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡄⠀⠀⠀ ⠀⠀⡈⣼⡿⣿⣻⣽⢯⣟⡷⣄⢀⢀⣴⣾⣿⣻⣞⣿⢯⣟⣷⣻⣟⡾⣽⣳⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣾⣧⠀⠀⠀ ⠀⠀⢸⣿⣽⣳⣟⡾⣯⣿⢿⡽⣿⣿⣻⢷⣯⣷⢯⣟⡿⣞⡷⣟⣾⣽⣻⢷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀ ⠀⠀⢸⣷⢯⣿⡾⣽⣳⣯⠿⣽⣳⢯⣟⣯⢿⣽⣻⣾⣿⣽⣻⣿⡷⣯⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀ ⠀⠀⢸⣻⢿⡾⣽⣷⠟⠁⢀⣾⣿⡿⣾⣽⣿⣞⡷⣯⢷⣯⢷⡿⣽⣻⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣟⠻⢿⣿⣿⣿⠀⠀⠀ ⠀⡀⠁⠈⠻⠿⠉⠀⠀⣴⣿⣿⣳⣟⡷⣯⢷⣯⢿⣽⣻⣞⣯⣟⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠒⡐⣦⢾⣯⣿⡿⠀⠀⠀ ⠀⠀⠀⠰⠋⠀⠀⠀⠀⠀⠉⢉⠉⠀⠙⣯⣿⠾⣿⣾⣳⣟⣾⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⠏⠁⢀⢊⣧⣿⢿⣿⣳⣽⡇⠀⠀⠀ ⠀⠂⠈⠀⠀⠀⢀⠀⠄⡢⠴⢮⣤⣴⣼⣿⣿⠀⠀⠉⠛⠹⠿⣽⣿⣿⣿⣿⣿⡿⠟⠋⣀⠤⣒⣮⢿⡷⡿⣯⣷⣫⣾⠁⠀⠀⠀ ⠀⠈⠀⢸⣆⠀⠀⢀⡾⠀⠇⠀⠈⠀⡉⣿⣾⣿⣷⡀⠀⢀⠈⠆⡎⢿⡁⢇⢷⡁⡸⣾⣾⣿⣹⣾⣏⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀ ⠀⠀⢱⣤⡭⣦⣀⣼⠧⠨⣀⡀⠀⢀⣠⠞⠋⠉⡉⠀⠀⡏⠀⠃⢸⡈⢡⣼⣿⡟⡜⢯⣟⢽⣭⣭⡽⣻⣵⣿⣿⣿⠅⠀⠀⠀⠀ ⠀⠀⠈⠋⠘⣿⣿⣦⣤⡜⠋⠹⣿⣿⣉⣰⣆⣄⠀⠀⠀⡇⠀⠱⡌⣷⡸⡇⣿⣿⣾⣿⣿⣷⡻⣭⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣟⣾⣳⣯⢿⣦⣤⣿⣿⠉⠉⠀⠠⠀⢀⡀⢆⡀⢸⣿⣝⣻⠅⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢻⣷⣻⢯⣟⣾⣽⣻⢾⣄⡀⣤⣠⣧⠞⠛⠈⢁⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⣳⢯⣟⣾⣟⡷⣯⢿⣽⣻⢿⡏⠀⡞⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢹⣯⢿⡷⣯⢿⣿⣻⢾⣽⣻⢿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀ ⣀⡀⣀⣀⡀⠀⠀⢻⣯⢿⡽⣯⢷⣻⣟⣾⣯⣿⢾⣯⣟⣿⣟⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⡾⠟⠿⠆⠀⠀⠘⣽⡿⣽⢯⣟⣷⣻⣞⡿⣽⣻⣾⣿⣿⣯⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢹⣽⢯⣟⡾⣿⢷⣯⢿⣽⣻⣷⢿⣿⣽⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀