⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⣟⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⣾⠟⠿⢿⣦⣀⣀⣠⣼⣿⣤⢼⣟⣦⣴⣶⡷⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⣿⣡⣤⣤⣴⢿⣽⡿⣽⣻⡾⣭⠿⣽⣻⡽⢾⡽⣷⣯⢿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⣿⣿⡽⣯⣛⡾⣽⣫⢷⣻⢿⡽⣛⣧⣟⢾⣿⢿⣟⣿⣻⣯⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢰⡿⣿⣟⡷⣯⡽⣶⢯⣻⣧⢼⣽⢻⡼⣞⣯⢿⣻⡏⠀⣯⣿⡾⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣴⡟⣾⡽⣞⣳⢯⣯⠷⣯⣟⡾⣯⢿⣝⣿⣻⣽⣻⣻⣷⣿⣟⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠸⣿⣻⢷⣻⣽⣽⣳⢯⢿⣹⢯⣿⣞⣟⡾⣞⣽⣻⣿⣻⣷⣯⣿⣻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⢯⡷⣯⣿⣽⣞⣯⢿⣻⣿⣾⣯⢿⣽⣾⡽⣿⣳⣿⣷⣻⡿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⣿⣯⣟⣿⣽⣿⣿⣾⣽⣻⡿⣿⣿⣿⣟⣾⣽⣷⣟⣿⣽⡷⣿⣟⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⣿⡷⣯⣿⢿⠙⣿⣿⡿⠿⡇⠈⠟⢻⣿⣶⣿⣯⢿⣽⣿⢿⣽⣻⣽⣻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⣿⣽⣿⣿⣀⠀⠈⠁⠀⡁⠀⠀⢾⣿⣳⣯⣿⣿⣿⡿⣿⣳⣿⡽⡟⢾⣻⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣻⣷⣶⣤⣄⣠⣤⣶⣿⣷⣿⣻⣿⡿⢿⣽⣿⣳⢿⣽⢿⡀⠈⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣏⣿⣿⡿⣼⣹⣿⣿⣿⣿⣿⣿⣿⢿⡹⠀⣸⡿⣧⢿⡾⣿⣎⣧⠀⠀⠈⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣿⠇⢯⣿⣯⣷⣿⣭⣿⣿⣿⣿⣟⣿⣿⣯⣿⣧⣀⣿⣽⢯⡿⣿⣽⣾⣽⣣⡀⠀⠈⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣸⡟⠀⢸⣷⣿⣿⣿⣿⣿⠸⡿⠙⠻⣯⣿⣷⣿⣏⢉⣷⣻⢯⣟⡽⣾⣻⡶⣯⢷⣄⠀⢨⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⣿⠃⠀⣿⣻⣿⣿⣿⠿⣿⣤⣴⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣻⢮⣟⣵⣻⢿⣳⡟⣾⢦⣾⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⣿⠀⠀⣿⠁⠹⣿⡁⠀⠘⠿⠟⠁⠉⢻⣿⡿⠿⠟⠋⢹⣿⣳⡟⣮⢷⣻⣯⣿⣿⣵⣻⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢿⣆⢸⣿⠀⠀⣿⡇⠀⠀⠀⠀⠀⣤⣯⡀⠀⡀⠀⠀⣼⣿⣷⢻⣭⣟⡷⣯⣷⡿⣷⢯⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⢻⠇⠁⠛⣿⣾⠛⠶⠋⢻⠃⠀⠉⣷⣾⣿⣞⣯⣟⡾⣯⣽⣟⡷⢁⣿⢯⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠁⣼⢀⠀⠀⡌⢰⠀⠀⠀⣯⠄⠀⠈⡟⠈⠉⢫⣿⡿⠽⣟⠾⠛⠀⣼⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣀⠤⢿⡆⠀⠸⡇⢰⠀⠈⡆⠀⣼⠃⠀⢀⣼⠃⠀⠀⠀⠙⠺⣦⡀⠀⠐⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣸⢸⠘⣿⡇⠀⠀⣧⡏⠿⠴⢇⣼⠁⠀⢀⣾⠇⠀⠀⠀⠀⠀⠀⠀⠉⠒⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣿⣼⣳⣿⣇⠀⠀⣿⣧⣄⣀⣿⠃⠀⢀⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⠋⠀⠀⣼⣧⠀⠀⢸⣿⣿⣿⣧⣤⣤⣿⣿⡄⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠀⠀⠸⣿⠛⠿⠿⠿⢿⣿⣿⣶⣿⣷⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⣟⣯⢿⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡴⢿⣳⣯⣿⠀⠀⠀⠈⣷⠀⠀⢀⣾⡿⣽⣷⣻⣾⢿⣿⣷⣤⣀⠀⠀⠀⠀⣠⣿⢯⣻⣽⣾⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣨⣷⣾⢤⣍⣧⠀⠀⠀⢰⠏⠀⣀⢼⣿⣟⣯⣿⣽⣻⣿⠿⢿⣿⡏⠉⠁⠀⢰⡿⣭⣟⣷⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣺⣥⣜⠉⠻⠾⠽⡀⠀⡀⣸⠷⣾⣿⣿⢻⣟⣿⣿⡿⣿⣿⣄⠀⠀⢹⡄⠀⠀⣿⣻⣵⣻⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠠⣞⡋⡹⠻⣟⣿⣳⣞⣿⣿⣿⣳⣤⣶⣌⣩⣍⣉⣤⣧⣾⣶⣾⣿⣆⠀⠀⣷⠀⠀⣿⣳⠾⣽⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣹⣷⣦⣴⠤⠤⠼⢤⣠⣤⣀⣉⣹⠚⠳⠯⠟⠻⣟⢫⣝⣭⢻⣿⡆⢀⠈⣧⠀⢹⣯⣟⣳⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠙⠻⢿⡿⣶⣤⣀⢸⣿⡿⣯⣿⠋⠉⠀⠙⣷⣞⢿⣻⣿⣿⣿⣿⠿⣆⠀⠘⢧⣼⣷⣫⡽⣟⣿⣳⣄⣠⣶⣶⣦⡀⠀⢀⣠⣄⣀⠀⢀⣀ ⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⢿⣿⣿⣿⣷⣿⣿⢿⡿⣿⣿⣿⣿⣿⡟⠉⠁⠀⠀⠘⠷⣄⠀⠉⠓⠛⢋⣽⣞⣳⢯⣟⢾⣱⢯⡿⣿⣿⣯⣿⣿⡿⠋⠉ ⠀⠀⠀⠀⠀⠀⠀⢸⣿⢯⣯⢟⣿⣿⢯⣿⣯⢿⣹⢯⣟⡽⣯⣿⡇⠀⠀⠀⠀⠀⠀⠈⠛⠲⢶⣶⣟⡾⣼⢏⡷⣞⣯⢯⣷⣻⣿⠟⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⣿⣻⢮⣟⣿⣿⣿⣿⣿⣿⣯⢷⣫⣟⡷⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣻⣟⡿⣽⣞⣯⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⣿⡽⢯⣞⣿⣿⣿⣿⣿⡿⣽⣫⢷⢯⣟⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠺⠿⠷⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⣿⣽⣻⢞⣿⡿⣯⢟⣿⣻⣳⣯⣯⣟⣾⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⣿⡾⣵⢯⣿⣿⡽⣛⣮⢷⣽⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣟⡷⢯⣻⣿⣷⣻⡽⣞⣯⣾⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣯⣟⢯⣷⣻⣿⣷⣻⡽⢶⢯⡿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⣿⣞⣻⢶⣻⣿⣿⣷⣻⢯⣟⢾⣟⡿⣺⡽⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡽⣏⡷⣏⣿⣿⡷⣿⣞⣯⢾⣝⣷⣿⡿⢻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣯⣽⢻⡼⣿⣿⣿⣿⣾⣿⡿⠋⠁⢹⣤⡿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⢳⢏⡟⣹⣿⣿⡿⡟⠋⠁⢳⠀⣰⡾⢇⠻⡘⠻⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣯⣾⣽⣿⡿⢿⣇⢱⣀⣤⡾⣟⣯⢷⣞⣣⣟⢣⡟⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⢻⠛⠉⢹⠉⠁⣀⣧⢾⣿⣿⢯⡷⣻⣽⢺⣧⢟⡶⡟⢷⣽⣾⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⣿⡾⣶⣞⢿⡻⣟⡽⣎⣿⣿⣯⢷⣛⡷⣞⢿⡼⢯⡿⠃⠀⢠⣿⣿⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣼⡿⣝⡷⣞⡯⣟⣭⢷⣹⢾⣿⣿⢯⡽⢾⣝⣯⣞⡿⣽⣦⢀⣈⣷⠽⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣿⢿⣹⢾⣭⢷⣛⡾⣏⠁⠀⣹⣿⣯⣽⣛⡾⣼⡞⣽⢧⣿⣾⢫⡟⡽⣻⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣿⣯⡽⣞⣧⠿⣭⢿⣹⣥⡦⣽⣿⣷⡺⣭⢿⣱⢿⣹⣞⣧⢿⣣⣝⡳⢧⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⣿⣷⢻⣝⡾⣻⣭⢿⣹⢎⡷⡹⣿⣿⣿⣽⣫⡽⣞⣧⠿⣼⣏⡷⢼⣙⠾⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⣿⣯⣟⡾⣝⡷⡽⡾⣝⢮⡳⣝⣞⣿⣿⡾⣵⣻⢽⣚⡿⣳⢾⣹⢧⢫⣛⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⣿⠘⢻⡾⡽⢾⡽⣽⣛⢮⡳⣭⣿⠻⣿⣿⣷⣫⢯⣏⡷⣯⢯⢷⣫⢳⡭⢞⣿⡆⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡠⣿⡀⣿⣝⡟⣯⠷⣯⡽⢎⡷⣱⣿⠀⠻⣿⡟⠛⣿⡞⣽⡞⣯⢯⡗⣯⡜⢯⣿⣷⠀⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡠⠒⠁⠀⣹⣿⣛⣮⣻⣭⣻⣵⣏⡟⣼⣳⡏⠀⠀⢿⣇⢰⣯⡟⣧⢿⣭⢷⡻⢶⣹⠳⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⡊⠀⠀⠀⠀⠻⣍⣛⠛⠉⠉⣉⣿⡿⠛⠛⠋⠀⠀⠀⠈⣿⣦⣻⡽⣽⢺⡭⣞⣽⣷⣧⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠁⠒⠂⠀⠀⠈⠉⠙⠛⠋⠉⠀⠀⠀⠀⣀⢀⠀⠀⠀⠘⢿⣯⣷⣭⣿⠿⠿⠋⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀