⣿⣽⣯⡿⡿⣯⣿⡽⣯⡿⣿⣯⢿⡽⣯⢿⣹⠯⠁⠀⢙⢯⢿⡽⣯⢿⡽⣯⣿⣽ ⣻⡟⣿⣿⣷⣿⣿⡿⣿⣿⢯⣟⡽⣞⣧⡟⣇⠀⠀⠀⠀⢸⢯⣞⡷⣻⣾⣻⣯⣽ ⣳⢟⣻⣿⢯⢿⡻⣟⢿⡵⣻⠾⣽⢞⣳⢿⠁⠀⠐⠀⣨⣟⠿⣼⡳⣟⢾⣿⣷⣾ ⣽⣫⢷⣫⢯⣻⣝⣯⣻⡼⡯⠛⠩⠉⠉⠘⠁⠀⠀⢌⡼⣞⣻⣳⡟⣽⣻⢯⡿⣿ ⢾⡹⢾⡽⣏⡷⣞⣧⠿⠙⠁⠀⠀⠀⠀⠀⠊⣍⠆⠀⠈⠙⠳⣳⢯⢷⣽⣿⣿⣿ ⡏⠃⠈⠛⠉⠃⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⢯⣻⡼⣿⣽⣿ ⡞⠀⡀⣤⢤⣀⠀⣠⣠⡶⣶⢮⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣯⢷⣹⡿⣿⡽ ⣻⣽⣻⣝⣻⡞⣟⣯⣻⢳⢯⡟⠁⠀⠀⠀⠀⠀⠀⣀⣤⠀⠀⠀⠙⢻⣼⣛⡷⣽ ⣳⢧⣟⣮⡗⣿⣹⢶⢯⣟⡯⠁⠀⠀⠀⠀⠀⠀⠠⣸⣞⣷⡀⠀⠀⠀⠘⢯⡽⡾ ⡽⣞⡾⣵⣻⢳⡽⣛⣮⠟⠀⠀⠀⠀⠀⠀⠀⠀⢤⣟⡾⣞⡽⣧⣠⡀⡀⠀⠁⠡ ⣹⢋⡹⡞⢳⢏⡹⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣏⢷⢋⣹⢳⡏⡿⣱⠂⢀⣰ ⢼⣡⢳⡹⢇⡾⡱⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⢦⢻⢤⠣⣏⠔⡧⣏⢦⢏ ⣞⡽⣞⠷⣞⣧⡇⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⢀⡟⣞⣯⢞⡷⣿⣾⢳⣏⡾⣞ ⢾⣹⢯⣟⡽⣞⠀⠀⠀⠀⠀⣀⡾⠀⠀⠀⠀⠠⣴⣻⣽⡾⣯⡽⣏⣾⣛⣮⣿⣹ ⢯⣟⠾⣵⡻⣽⠄⠀⠀⠀⢠⡿⠙⠀⠀⠀⠀⣽⢳⣯⣷⣻⡿⢯⣟⠿⣽⣧⣿⣿ ⣻⣞⣻⣳⠿⠁⠀⠀⠀⢠⡿⡕⠀⠀⠀⠀⢀⣯⣟⣞⣯⣳⣻⣛⡾⣻⣯⢿⣿⣟ ⢧⡿⣵⢏⡍⠀⠀⠀⢀⡿⣽⡓⠀⠐⢀⢀⡿⣾⣹⢮⡿⣝⣧⡟⣷⣻⣼⣿⣷⣿ ⣻⢞⣽⠁⢐⠀⠀⠀⢸⣽⠓⠂⠀⢠⣞⡿⣝⣧⣟⣿⡷⣻⢾⣿⣷⣿⣿⣿⣿⣿ ⡽⣯⣞⡦⠀⠀⠀⣠⣟⠎⠀⢠⣴⣻⣭⣟⢾⡧⣿⢿⣯⣿⣻⣿⣿⣿⢷⣏⡿⣿ ⣳⢟⡾⣵⡀⠀⣲⣟⠚⠀⠀⣼⣳⡳⡷⣞⣳⣿⣾⣷⣛⣧⣿⣳⣿⣟⣟⣯⣿⣿ ⣽⣫⣽⣳⠃⠀⣟⡦⠀⠀⣰⢯⣳⢟⣳⢿⣷⣿⣽⣯⣟⣼⣿⢯⣷⣻⣼⡷⣯⣿ ⣞⡵⣯⡇⠀⠈⣾⡵⣴⣞⣯⠿⣭⢿⣿⣾⢿⡿⢿⣳⣿⡿⣞⡷⣏⡾⣷⡻⢿⣿ ⢾⣹⢷⡄⠀⠠⡿⣝⣳⡽⣞⣻⣽⢻⣽⡿⣟⣯⢿⣭⢷⣻⣽⡿⣽⣹⣞⣽⣿⣿ ⢯⡽⣞⣇⠀⣰⢿⣭⢷⢯⡯⢷⣞⣯⠾⣽⣺⣧⣟⢮⣯⠷⣾⣹⢧⢿⡼⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠴⠊⠟⠉⣻⠿⢷⣄⣤⡄ ⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡄⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠁⠀⠠⠟⣿⡷ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⣻⣿ ⠀⠀⠂⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⡿⣽⣿⡿⠍⠀⠀⠀⠀⠀⠀⢠⣴⣦⠀⠀⡀⠀⠻⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣼⣿⣿⣾⠛⡀⠀⠀⠀⠀⠀⠀⠈⢛⠛⠐⠀⠙⣫⣷⢿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣌⣵⣷⣶⣿⡾⢿⣻⣿⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠉⠀⠀ ⠀⠀⡀⠀⠀⠀⢀⠀⢀⣁⣤⣷⣾⣿⡙⣿⡾⣿⣞⣉⣵⣾⣿⣯⣶⡄⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠈⠀⠈ ⢠⣤⣷⣤⣤⣴⣾⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣟⣫⣿⣟⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀ ⢈⣻⠿⠟⠛⠛⠷⠟⠛⠃⠐⡀⠄⢸⣿⣿⣿⣾⣏⣿⣿⣿⣿⣿⣿⣻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠸⣽⣿⣟⣟⣿⣿⣿⡿⡿⢿⣿⣿⣯⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣽⢻⣿⣿⣿⣿⣾⣿⠏⠀⠀⠈⠿⣿⣿⣷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠿⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣾⣿⣿⣿⠷⠀⠀⠀⠀⠀⠛⠯⣿⣿⣶⣤⣤⠆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠁⠀⠀⠀⢠⣴⣿⣿⣿⣿⣿⣷⣿⣷⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⠿⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣸⣿⣿⣿⣿⣿⠿⠁⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠇⠀⢠⣽⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⢀⣿⣿⣿⣿⠋⠀⢡⣾⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢁⣾⣿⣿⣿⠁⠀⠀⣸⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡂⣿⣿⣿⣿⠏⠀⠠⠤⢹⣿⣶⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠠⣽⢿⣿⣿⣿⠃⠀⠀⣨⣿⣟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣮⣾⣽⣿⠋⡀⢀⣾⡿⠃⠀⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⠂⠸⣿⡿⠀⠐⢀⣼⣿⡃⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣳⡆⠀⢀⣿⣽⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢘⣿⡇⠀⠘⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⣽⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀ ⠀⠀⠀⠀⠹⠟⠐⠀⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣷⣤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣤⣤⣾⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣦⠀⠀⠀⠀⣠⣤⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⣶⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣻⡿⠟⠛⠛⠻⠿⠿⠟⠉⠁⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠈⠙⣿⣿⣿⣿⣶⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣄⡀⠀⣠ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠉⠙⠛⢿⣿⣷⣿⣏ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⠛⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⠿⠀⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠃⠀⠀⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠇⠀⢀⣾⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⠃⠀⢀⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⠁⠀⠀⢸⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⡏⠀⠀⠀⢠⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠇⠀⠀⢀⣼⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⣿⣿⣿⡟⠀⠀⣠⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⣿⡿⠋⠀⠀⢰⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢻⣿⠃⠀⠀⣰⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣾⣿⠀⠀⠠⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀