⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⡶⡿⣟⣿⢻⣽⢫⣏⡿⣹⣝⡯⣽⢫⣟⡽⣫⢿⣹⡟⣿⢿⡶⣦⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⢻⣿⣻⢽⣺⣵⢻⣝⣮⠿⣼⣛⣮⣽⢳⡽⣞⡽⣏⡾⣽⣹⡳⣏⡾⣽⡺⣝⣳⢯⣛⡿⣿⠓⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠖⠋⠁⠀⢀⣿⣳⢏⣷⡳⣞⣯⢞⡾⣽⣣⢿⡼⣞⢯⣳⢏⡷⣏⡷⣏⡷⣻⣭⢷⣳⣻⢭⡷⣫⣟⣼⣻⣇⠀⠀⠉⠓⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⠀⠀⠀⣼⣟⢧⣟⣮⣽⢳⣞⢯⣳⢳⣭⢳⡝⣮⢳⡝⣮⢳⣝⡺⢵⣋⢷⡺⡽⢶⣏⡿⣼⣳⠽⣶⢫⣿⡄⠀⠀⠀⠀⠈⠛⢦⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣤⣿⣿⠀⠀⠀⠀⠀⠀⠀⣿⡞⣯⣞⡾⡼⣯⣹⣎⣗⣯⣶⣏⢾⣵⣯⡞⣵⣯⣶⡹⣧⣿⡮⡵⣯⣷⡮⣝⣳⣯⣛⡷⣛⣾⣇⠀⠀⠀⠀⠀⠀⠸⣿⣶⣄⠀⠀⠀⠀ ⠀⠀⠀⣰⣾⣻⣼⡇⠀⠀⠀⠀⠀⠀⢰⣯⣟⢶⡟⣵⣻⡏⢹⣯⣾⠇⢸⠯⢾⠀⣿⠽⢿⠀⣿⠵⣿⠀⣿⣷⣧⢸⣷⣻⡏⢹⣻⣼⢻⡼⣿⠀⠀⠀⠀⠀⠀⠀⣿⢮⣟⣦⡀⠀⠀ ⠀⢀⣼⣟⢧⡷⣻⠁⠀⠀⠀⠀⣀⣀⣸⣿⣮⣿⡏⠉⢹⡇⢸⣆⣸⡆⢸⣤⣼⠀⣿⣤⣼⠀⣿⣤⣼⠀⣿⣤⣾⢸⣇⣹⡇⢸⣉⠙⣿⣽⣿⣀⣀⡀⠀⠀⠀⠀⢻⡿⣜⣯⢷⡄⠀ ⢀⣾⡟⣮⣿⣼⣿⠴⠶⠖⠛⠋⠉⠉⢹⣿⣹⢏⣿⣛⡟⣷⠾⣏⠿⡷⢾⣳⢻⢶⡻⢧⣻⢶⢿⣚⢿⡶⣟⢮⢷⡾⣏⢿⣧⣾⡟⣿⣻⢽⣻⠉⠉⠉⠛⠓⠶⠶⢾⣿⣽⣮⣻⢿⡄ ⢸⣿⢿⣟⡿⢯⣿⠀⠀⠀⠀⠀⠀⠀⣿⣳⢏⡿⣎⡿⢾⣵⡻⣜⢯⡝⣧⣛⢮⡳⡝⣧⣛⢮⡳⣝⢮⡳⣝⢮⡳⣝⢮⣳⣞⠷⣽⡳⡽⡾⣽⠀⠀⠀⠀⠀⠀⠀⢸⣟⣯⠿⣿⢿⡇ ⢸⣯⡟⣼⡽⣫⣟⠀⠀⠀⠀⠀⠀⠀⣿⡽⢾⣹⡳⢯⣟⢶⣻⢽⡮⣗⣳⣎⡷⣹⡝⣶⡹⣎⢷⡹⣎⢷⣹⢮⣗⢯⣏⡷⣞⣻⢧⢿⣹⡗⣿⠄⠀⠀⠀⠀⠀⠀⢸⡿⣞⣽⣧⣿⡇ ⠀⢿⣟⣧⣟⣳⣯⠀⠀⠀⠀⠀⠀⠀⣿⣽⢫⣗⡟⣯⣞⢯⡞⡷⣽⡭⡷⣞⡽⢧⣟⠾⣵⢯⣏⡷⢯⣏⣷⣛⣮⠿⣼⡳⣏⡷⢯⣛⣶⢻⣽⠂⠀⠀⠀⠀⠀⠀⢸⣿⣻⢷⣻⣾⠁ ⠀⠈⢻⣽⣾⣻⣿⠀⠀⡀⠀⠀⠀⠀⢿⣞⣻⡼⣏⡷⣞⢯⣽⣛⣶⢻⡵⣏⡿⣝⡾⣻⣝⡾⣱⡟⣯⣞⢶⣻⡼⣻⡵⣻⣝⠾⣏⡿⣼⣛⣾⠀⠀⠀⠀⠀⠈⠀⢸⣿⢯⣿⡽⠃⠀ ⠀⠀⠀⠹⣾⡷⣿⠀⠀⠀⠀⠈⠐⠀⢼⣯⢷⡽⣞⡽⣞⢯⣶⢻⡼⣏⡷⣏⡷⣏⣷⢻⡼⣝⡷⣫⢷⣞⡻⢶⣻⡵⣻⡵⣞⣿⣹⣞⣷⣻⣾⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠞⠁⠀⠀ ⠀⠀⠀⠀⠈⠻⣿⡄⠀⠀⠀⠀⠀⠀⢸⣿⢯⡿⣽⣻⣽⣳⡾⣯⢷⣯⢷⣯⢷⣻⡼⣯⣽⢾⡽⣽⣳⡾⣽⢯⣷⣻⢷⣻⡽⣞⣷⣻⣞⡷⣿⠀⠀⠀⠀⠀⠀⠀⣿⠟⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⠦⣄⠀⠀⠀⠀⢸⣿⢯⣟⣷⣻⣞⣷⣻⣽⣻⣞⡿⣞⣯⡷⣟⡷⣯⢿⣽⣳⣯⢿⣽⣻⢾⡽⣯⢷⣟⡿⣞⡷⣯⣟⣿⠀⠀⠀⠀⢀⡤⠞⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢲⣤⠀⠀⣿⡟⣾⢳⡟⣾⢳⡟⣾⢳⣯⣿⣽⣾⣽⣯⣿⣽⢻⡞⣷⣯⡟⣾⣽⣯⣿⣽⢻⣾⣽⣯⡟⣷⢻⡏⠀⢠⣴⡞⠋⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠶⣿⣿⡽⣯⢿⡽⣯⢿⣽⣻⣞⡷⣯⢷⣻⣞⡷⣯⢿⣽⣳⣯⢿⣽⣳⣟⡾⣽⣻⣞⡷⣯⢿⣽⣻⡷⠖⣋⡡⠢⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠻⠿⣽⣟⣾⣳⣯⢿⡽⣯⢷⣯⢿⣽⣻⣞⡷⣯⣟⣾⣳⣯⣟⣷⣿⡾⠿⠛⠋⠉⠀⠀⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠛⠛⠚⠛⠾⠓⠛⠛⠓⠛⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀