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