⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠉⠠⠀⠄⡠⠀⡄⢉⠉⡓⠲⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁⠠⠈⠄⠁⠂⠄⠡⢀⠂⡐⠠⢁⠂⠌⡉⠳⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⡙⢢⢁⠂⠁⠌⢀⠂⠄⠂⠄⡁⠂⠌⡐⠠⢁⠂⡐⢉⠳⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣜⢣⢎⡰⢁⠀⢂⠀⠂⠡⢐⣀⣁⠂⠄⡁⠂⠄⡑⢀⠢⢀⡉⠳⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣯⣏⢶⡑⡎⡔⢀⣢⠗⠋⠉⠉⠉⠙⠛⠲⠧⣦⣐⠈⠌⡀⢂⡁⢂⠉⠳⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⢮⡷⣱⢎⣽⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⣦⣂⠄⠓⡈⡐⠠⠙⠶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣽⣳⣎⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⣄⠄⠃⢌⡐⢈⠳⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣷⣶⣤⣤⣀⣻⣿⣳⡽⣾⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣾⣷⣌⡠⠐⢂⠐⡈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⡻⣟⡿⣿⣿⣿⣿⡷⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⢿⡻⣝⢯⣛⢿⣶⣀⢂⠐⠡⢈⠛⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⢯⣿⣿⣿⣿⣷⣹⠶⣭⢟⣿⣿⣿⢿⣦⡀⠀⠀⠀⠀⠀⠀⣠⣾⣿⢿⡻⣜⣳⢽⣾⣿⣿⣿⣿⣿⣷⣌⠐⡀⠂⠄⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⢫⣿⣿⡏⡹⣿⣿⣟⡼⣫⢞⡿⣿⣿⣿⣿⣦⣀⡀⠀⣠⣾⣿⢿⣹⢎⣷⣹⣾⣿⡿⢋⠭⣹⣿⣷⢻⣿⣧⠰⡁⠌⡐⢀⠻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣏⡟⣿⣿⣷⣡⡽⣿⣯⣷⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣎⣷⣫⣶⣿⡿⢏⡱⢌⠢⣽⣿⣯⣗⣻⣿⣇⠘⢦⡐⢀⠂⡈⢳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡞⣽⢳⡻⢧⣻⣼⣿⣿⢿⣟⡻⣝⣧⢻⣽⣿⣿⣿⣮⡗⣯⢻⣟⡿⣿⣿⣿⣿⣷⣦⣵⣈⢶⣿⣿⡳⣎⢷⣻⣿⡀⠀⠻⣆⠠⠐⠀⡙⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡽⣎⣷⣻⣿⣿⠿⣯⡽⣚⢾⣹⢳⡞⣯⠶⣝⣻⣿⣿⣿⣷⣫⢞⣵⡳⣞⡼⣳⢯⠿⣿⣿⣿⣯⡳⣽⡹⢮⣽⣿⡇⠀⠀⠘⢧⠀⠂⢀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣞⣵⣿⣿⠿⣭⢟⡶⣽⢫⡟⣼⢻⡼⣣⢿⡹⣖⠿⣽⢿⣿⣿⣾⡮⣝⢧⡟⡵⣏⡿⣜⣻⢿⣿⣽⢖⣯⢻⣼⣿⡇⠀⠀⠀⠈⢳⡄⠀⠀⠂⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣾⣿⡿⣭⢟⡮⣟⢾⡱⣯⣿⣷⣯⣾⣽⣷⡿⣜⣻⢭⣳⢟⡿⣿⣿⣿⣮⡝⣯⢳⡽⣎⢷⣫⢿⣿⣿⣜⡳⣾⣿⠃⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⢳⡝⣮⣳⣛⣮⣽⣽⣿⣟⣿⢿⡿⣏⢿⡱⣏⠾⣧⢟⡾⣹⡿⣿⣻⣿⣾⣹⢞⣭⡻⣜⢯⡽⣿⣿⣷⣿⣿⣶⣿⣿⣶⣦⣄⠀⠹⡄⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⡿⣭⢿⣿⣟⣷⣿⣿⣿⠿⠿⠿⠛⠿⠿⣿⣿⣷⣯⢞⡵⣫⣟⡼⣫⢞⣳⣽⣷⣿⣿⣽⡿⣿⣿⣿⣾⣧⣟⡽⣿⣿⣿⣿⣿⣿⣟⠿⣿⣿⣧⡀⢻⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⡿⣱⢯⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⠾⢷⣺⢛⣳⣿⣿⡿⠟⠋⠉⠉⠙⠻⣾⣻⣟⣿⣿⣿⣿⣿⣿⠃⣿⣿⣯⢟⣼⢻⣿⣧⢸⢂⠰⢀⠂⡸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⢯⣳⣿⣾⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⢻⡏⣿⣶⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢾⣽⣻⣿⣿⣁⠀⣿⣿⢧⣻⡜⣯⣿⣿⢞⢢⠱⣈⠆⣩⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣟⣯⣿⣿⡿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣿⣿⣭⣟⣛⣛⣽⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣾⣷⣟⡿⣿⢿⣛⣶⣻⣼⠿⡿⢮⣖⣣⢎⡼⣸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⠏⡀⢻⣿⣷⣦⣄⣀⣀⠀⠀⠀⢠⣴⣾⣿⣿⠻⣿⣯⣿⡻⣿⣿⡿⢿⣿⣶⣦⣤⣤⡀⠀⠀⢀⣄⣀⣠⣤⣾⣿⠀⠉⠛⣿⣯⣟⣾⣳⢿⣯⣿⢿⣮⢷⣯⡶⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⣷⣾⣿⣺⣿⡏⠛⠻⠿⠿⣿⣿⡄⠘⣿⣿⠀⠀⠀⠊⠻⣿⣿⡟⠋⠀⠀⠈⠉⠛⠛⣿⣿⠀⢀⣾⣿⠿⠛⠛⣿⣿⠀⠀⠀⣿⣿⠿⣿⣿⣿⠛⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣿⣿⠉⠁⣾⣿⡟⠻⡿⢿⣿⣿⣿⠀⠀⠀⠀⣼⣿⠃⢰⣿⡇⠀⠀⠀⠀⠀⢀⣷⠂⠀⠀⠀⠀⠀⠀⢠⣿⡟⠀⢸⣿⡇⠀⠀⠀⣿⣿⠀⠀⠀⣿⣿⡘⣿⣿⣶⣾⣷⣾⣶⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⣴⣾⣿⡏⠀⢰⣿⣿⠁⠀⢰⣿⣿⢿⣿⣧⠀⠀⠀⣿⡿⠀⢸⣿⡇⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⢘⣿⣧⠀⠸⣿⣧⠀⠀⠀⣿⣿⡀⣄⡀⢸⣿⣿⣿⣿⣟⡟⣯⢟⡻⣟⡿⣿⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⣿⣿⣿⣿⣿⠇⠀⠸⢿⠇⠀⠀⣾⣿⣟⢯⣿⣿⣧⡀⠀⣿⣿⡀⢸⣿⡇⠀⠀⠀⠀⠀⢀⣀⣤⠴⠶⢲⠶⠦⣄⡀⢿⣿⣆⠀⣿⣿⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣯⣽⣎⡷⣭⢻⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⣿⣾⣿⡟⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡞⡼⣿⣿⣷⣄⣸⣿⡗⢸⣿⣇⠀⠀⠀⣴⣾⣉⣀⣿⣀⣀⣿⣀⣀⣴⠟⠀⣿⣿⢄⣿⣿⠀⢠⣾⣿⢿⣿⣿⡐⢆⠲⣄⠲⢤⡉⣍⠛⠿⣿⣿⣿⣷⣯⣾⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⡟⣿⣿⣧⣤⣀⠀⠀⠀⠀⠀⠀⢹⣿⣿⢣⣇⠛⣿⣿⣿⣏⠀⠈⣿⣿⡀⠀⠀⠉⠉⠉⠉⠁⠈⠀⠉⠉⠉⠀⠀⢠⣿⡟⢸⣿⡇⠀⣼⣿⡟⢻⣿⣿⠘⡈⢠⡀⠋⡀⠀⡈⡌⢡⢀⡉⠛⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢹⣿⣿⢨⠙⠿⢿⣿⣿⣶⣶⣶⣾⣿⣿⣿⣿⣷⢺⣝⢧⡻⢿⣿⣿⣦⣽⣿⣿⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡿⠁⣸⣿⣇⣼⣿⡿⣝⣻⣿⣿⢢⡙⢤⠊⡵⢡⠣⡱⢌⠣⢎⡐⢣⠌⣽⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣼⣿⡏⢆⠫⡜⢢⠌⡭⡙⡍⢫⠍⡭⣱⣿⣿⣯⢳⡞⣯⠽⣧⢏⡟⡿⣿⣿⣿⣿⣦⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⢰⣿⡟⠁⢀⣿⣿⣿⣿⣟⡳⣭⢿⣿⡏⢆⡱⢊⠕⡤⠣⢅⠣⢎⡱⢊⠬⣁⣾⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⢋⢆⠳⢌⡃⠞⣄⠓⡬⢡⠚⣴⣿⣿⠿⣜⢧⣻⣜⣻⣜⣻⢼⣳⢳⣎⢿⡹⢿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣷⣿⣿⣿⣿⣛⠷⣎⡷⣭⢿⣿⡏⠦⣡⢃⠞⡰⢩⠌⠳⠌⢦⡉⠖⣴⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⠌⡎⡒⠥⢊⠵⡈⠧⣌⡑⣺⣿⣿⣟⣻⣜⣳⢳⣎⢷⡺⣵⢫⣞⡳⣎⢷⣽⣿⣿⡿⠓⡤⣿⣿⣿⣯⣽⣫⢟⡽⣫⢏⡷⣹⠶⣭⢻⣜⡷⣭⢿⣿⣇⠳⡰⢌⡒⢥⠃⣎⠱⣉⠦⡘⣬⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⡇⢎⡔⣉⠎⡱⠌⡜⣡⠒⣌⠩⡛⢿⣿⣿⣮⣗⢯⣚⢧⣻⣜⡳⣎⢷⣽⣿⣿⠿⣉⠴⢩⠔⡌⣛⢻⣿⣿⣟⢮⡳⣏⢾⣱⢏⡿⣜⢧⣻⡜⣮⢿⣿⣿⠰⡑⢆⠍⡆⠭⢄⠳⢌⡒⢅⣾⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣏⠦⣘⠰⣊⡑⠎⡴⡁⠞⣠⠣⡑⢆⢚⠻⣿⣿⣷⣯⡞⡵⣎⢷⣹⣾⣿⡿⢋⠴⠡⢎⢅⡚⢔⢢⠊⣽⣿⣿⣷⡹⣎⢷⡹⣎⢷⣫⢞⡵⣻⣜⣯⣿⣿⡧⡘⣌⠚⣌⠱⢊⡑⢎⠰⣾⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠸⣿⣿⣔⢂⠳⣠⠙⡜⣄⠣⡍⢢⠅⡓⣌⠪⡑⠬⡙⢿⣿⣿⣷⣽⣾⣿⣿⠏⡰⡉⢖⡉⠖⣌⠒⡥⢢⠙⣄⢻⣿⣿⣷⡹⣎⣷⣹⣮⣷⣿⣿⣿⣿⠿⡟⢫⡑⠥⢢⠍⣢⢙⠢⢍⢢⣻⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣦⣤⣤⣤⣤⣤⣤ ⠀⠻⢿⣿⣿⣶⣦⣍⡔⡨⠱⢌⠣⢎⡱⢠⢃⡹⡐⣉⠖⣨⠻⣿⣿⣿⠟⡡⢎⠱⡑⢬⡘⠥⣊⠱⣂⠧⡙⡄⠎⣿⣿⣷⣿⣿⣿⣿⠿⢟⡛⢍⠣⡜⢢⡙⠴⡈⢇⣃⢚⠰⣌⠱⢊⣶⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣟⡿⣽⣻⣽⢯⣿⣽ ⠀⠀⠀⠀⠉⠛⠻⢿⣿⣿⣷⣮⣑⡢⢅⠣⠎⠴⡱⣈⠦⣁⠎⣿⣿⡇⢎⡱⢌⡱⠘⡔⡌⡓⢤⠓⡤⢣⠱⢌⣱⣿⣿⡿⡛⠭⣑⢢⣉⠲⢌⠪⡱⢘⠢⡜⠢⢍⠢⢆⡩⢒⠤⢣⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣯⡍⣯⣿⣿⠿⢾⡿⠷⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⣿⣿⣷⣾⣌⣣⠔⣡⠚⣄⢺⣿⣿⠜⡄⢣⠒⡌⡓⠬⡐⡍⢢⡙⣐⠃⡞⣠⢺⣿⣿⢃⠽⡐⡡⢆⠢⡍⢬⠱⡌⢣⠱⣈⠓⡬⣑⣪⣴⣽⣾⣿⡿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢿⣇⣧⣿⣻⣼⣟⣼⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣶⣧⣔⣪⣿⣿⠘⣌⠱⣘⠰⢡⠣⠱⢌⠣⢜⡰⢩⠔⢢⢸⣿⣿⢌⠲⢡⡑⣊⠱⡘⢢⣑⣬⣥⣶⣷⣿⣿⣿⣿⡿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⣿⣿⣿⣿⣿⣿⡿⣿⢿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡿⣏⢾⣹⢻⠿⣿⣿⣿⣿⣿⣼⣀⠳⡈⢬⣡⣮⣷⣮⣵⣦⣼⣁⠞⡡⢺⣿⣿⢠⣙⣤⣦⣷⣷⣿⣿⣿⣿⡿⣿⢟⣟⣻⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣽⣳⣿⣿⣿⣷⣿⢿⣽⣻ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡳⡽⣎⢷⣫⢟⡶⣭⢻⣿⣿⠛⡅⠳⣼⣿⣿⣿⢿⡿⣿⢿⣿⣿⡇⠧⣹⣿⣿⣿⣿⣿⣿⠿⣟⢿⡹⣝⢮⡳⣏⢾⡼⣽⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣳⣿⣿⣿⣿⣿⣿⣿⢯⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣽⡳⣝⢮⡳⣏⢾⣱⢻⣿⣿⠱⢨⣿⣿⣿⢯⣝⡮⢷⣹⢮⣿⣿⣏⠒⣽⣿⣿⢻⣭⢳⣭⣛⠾⣭⢻⡼⣫⢷⡹⣮⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⣿⣿⣿⣿⣿⣿⣿⢿⣾ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⣾⣧⣻⡜⣯⢞⡽⣿⣿⣧⣿⣿⣿⢯⣳⢮⡽⣳⡝⣮⣿⣿⠧⣉⣾⣿⣯⣷⣾⣿⣶⣿⣽⣮⣳⣝⣧⣯⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣽⣟⡿⣿⡿⣿⣻⢾⣟⣾ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣷⣻⡜⣯⢞⣿⣿⣿⣿⣿⢯⣳⢯⡞⣵⣳⣛⢶⣿⣿⣶⣿⣿⣿⣿⡿⠟⠋⠙⠛⠿⠿⢿⣿⠿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⣯⣟⡷⣿⡽⣯⣿⣞⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣮⣯⣿⣿⣿⣿⣿⣿⣷⣯⣾⣵⣧⣿⣿⣿⣿⡟⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣟⢿⣽⡿⣷⡟⡿⣾⢽⠾ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠟⢻⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣻⣾⣿⣿⣟⣷⣿⣻⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣟⣿⣽⡾⣿⣿⣿⣿⣯⢿⣽⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡽⣿⢿⡿⣿⣿⣿⡿⣿⢿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣯⣿⢾⣟⣿⣿⣿⣷⣻⡿⣯⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣻⣽⣿⣿⣿⣿⣿⣽⢯⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⢾⣯⣿⣻⣿⣿⣿⣯⣿⣽⣟⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢷⣿⣿⣿⣿⣿⣿⣿⣯⢿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡾⣿⣽⡷⣿⣿⣿⣿⣟⣾⣽⡾⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢿⣿⣿⣿⣿⣿⣿⣿⢾⣻ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣟⣯⣷⡿⣿⣿⣿⣿⡾⣯⣷⢿⣻⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣟⣾⣻⢿⡿⣟⣯⣟⣯⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣽⣯⡿⣷⢿⣿⣿⣿⣷⣿⣻⣽⡿⣯⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣻⣾⣽⣻⣽⢿⡽⣾⣻⢾ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⢷⣻⣽⣿⣻⣿⣿⣿⣿⣞⣿⣳⣿⢿⣽⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⣯⣟⡏⣿⡿⡽⢷⣽⡿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⢿⣻⣿⣽⡾⣿⣽⣿⣿⣷⢿⣯⣿⡽⣿⢯⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣻⣿⣯⣿⣿⣟⣿⣼⣞ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⢿⣻⣾⢯⣿⢷⣿⣿⣿⣟⣯⣷⣿⣻⣟⣿⣻⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣻⣟⣿⣿⣿⣿⡿⣟⣿⢿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⢿⣻⣯⡿⣟⣯⣿⣻⣿⣿⣟⣯⣷⡿⣽⣯⣿⡽⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢷⣻⣾⣿⣿⣿⣿⡿⣽⣻ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣟⣯⣷⡿⣟⣯⣷⣿⣿⣿⣟⣯⣷⡿⣟⣷⣟⣿⣻⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣟⣿⣿⣿⣿⣿⣿⣿⣯⢿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⢾⣟⣷⡿⣟⣿⣞⣿⣿⣿⣿⣽⡷⣿⣟⣿⣾⣻⣽⢿⣿⣿⣗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡾⣿⣿⣿⣿⣿⣿⡿⣽⣻ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣽⡿⣯⣿⣽⣿⣻⡾⣿⣿⣿⣟⣾⣟⣯⣿⢾⡷⣿⢯⣿⣻⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣽⢯⣟⡿⣿⢿⣻⢿⣽⣻ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⡿⣞⣿⣟⣷⡿⣾⢿⣽⣿⣿⣿⣿⣽⡾⣿⡽⣿⣻⣟⣿⣽⣟⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣯⣟⣯⡿⣽⣻⡽⣟⣾⣻