⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣯⣿⣟⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣂⣹⣶⣶⣶⣦ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⡾⣻⣏⢺⡏⠀⣠⠆⠰⣾⣭⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣠⡤⡾⣾⣮⣿⣿⣿⣿⣻⣽⢯⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⢿⢷⣿⣵⣿⠀⠈⠉⢠⡼⠟⠛⠋⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⢷⢟⣟⣿⣿⣿⣿⣻⢾⣽⡾⣿⣽ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣿⡿⣿⣧⣤⣠⠾⠿⠀⢀⣴⣶⣿⠿⠄⠀⠀⠀⠀⣐⣶⣿⣿⣿⣿⣟⡿⡟⡟⣯⣿⣿⣿⣿⣽⣟⣷⢿⣳⡿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣷⣻⢿⣯⣤⣴⣾⣿⢿⣻⡿⣿⣿⠤⢤⣶⣿⡿⣟⣿⣟⡿⣷⣿⣇⡣⣫⢿⣿⡿⢻⣿⣿⣟⡞⠋⠉⠀ ⠀⠀⢀⣀⣰⣶⣶⡦⣼⣿⣿⣾⣿⢯⣟⣿⣻⢿⣽⡾⣟⣯⣟⣿⣻⣿⣾⣻⣯⣟⣿⣿⡾⣿⣿⢷⣿⣫⠦⣿⣯⡷⢃⣿⣟⡯⣘⠀⠀⠀ ⣤⡾⢟⢶⣻⣿⣟⣿⢿⣻⣾⣽⣾⣿⣿⣾⣽⡿⣾⣽⢿⣽⡾⣷⣻⣾⡽⣿⣻⢾⣿⣿⣿⣯⣟⣽⣟⣋⣟⣿⣫⣵⣿⡟⢜⣇⡉⠀⠀⠀ ⡞⣵⣯⣿⣿⡿⣞⣯⠿⠛⠉⠀⢀⣽⣤⡀⠈⠙⠛⢯⣿⡾⣽⡷⣟⡷⣟⣯⣟⣯⡿⣷⣿⡿⣿⣿⡿⢿⣿⡫⣿⣏⣹⣧⣾⡇⣿⠀⠀⠀ ⢭⣿⢿⡿⣿⣿⠟⠁⠀⠀⢀⣴⣿⣿⠟⠁⢀⡀⠀⠀⠙⢿⣯⣟⡿⣽⡿⣽⣾⣻⣿⣽⣾⣿⣿⣫⣡⡷⣿⣿⡿⣿⣿⡷⡿⣓⡭⠀⠀⠀ ⣿⣿⣼⣿⣿⠃⠀⠀⢠⣴⣿⣿⠟⠁⠀⢀⣴⣿⣄⠀⠀⠀⢻⣿⣽⢯⣿⣳⣿⣿⣿⣷⣿⣿⣿⣿⠿⡫⣿⣿⣿⣿⠏⣾⣻⡎⠆⠀⠀⠀ ⣾⣿⣿⣿⡇⠀⣀⠀⠈⠻⣿⣿⣷⣄⣴⣿⣿⣿⣿⣷⣄⠀⠀⣿⣯⢿⣳⣟⡷⣯⣿⢾⣽⣿⣿⣿⣿⣿⣯⣿⣿⢋⢺⠵⡟⡿⣅⡀⠀⠀ ⣻⣿⣟⣾⠅⣼⣿⣦⡀⠀⠈⢻⣿⣿⣿⣿⠋⠀⠙⢿⣿⣷⡶⢼⣿⣻⣽⡾⣿⣽⢾⣻⣽⣟⣿⣽⣻⢿⣿⣿⡿⡸⡦⣺⣾⣿⣽⠀⠀⠀ ⣾⣿⣯⣿⡇⠈⠻⣿⣿⣦⣴⣿⣿⡿⣿⣿⣷⣄⠀⠀⠙⠏⠁⣼⣿⣽⣾⣻⣷⠿⣿⣯⣷⣻⣿⢾⣯⢿⣿⣽⣿⣿⣯⣳⣿⡿⠋⠁⠀⠀ ⣿⣿⣷⣻⣧⠀⠀⠈⠻⣿⣿⡿⠋⠀⠈⣻⣿⣿⡷⠀⠀⠀⢰⣿⣿⣋⣩⣿⣷⣿⢿⣳⡿⡿⣯⣿⢾⡿⣿⣿⣿⡳⠖⠋⠀⠀⠀⠀⠀⠀ ⢹⣿⣿⣽⣻⣷⡀⠀⠀⠈⠋⠀⠀⣠⣾⣿⡿⠋⠀⠀⡀⣴⣿⣯⡗⣾⢟⣿⣟⣿⣿⣿⡯⣷⣿⠻⠿⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⢽⣿⣷⣻⣽⢿⣦⣄⠀⠀⠀⠻⣿⡿⠋⠀⠀⢀⣨⣿⣿⡿⣷⣾⡿⠿⣛⣏⣿⣿⣯⡟⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠛⠿⣷⣿⢯⣟⡿⣿⣶⣦⣤⣬⣤⣤⣶⣾⡿⣿⢯⣿⣿⣷⣿⣾⣯⡿⡿⣿⣿⣷⣻⣿⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⣹⣿⣟⣷⢯⡿⣽⣻⢿⣽⣳⣯⢿⣽⣻⢷⣻⣞⣿⣻⢿⣾⣷⣿⢿⣻⣟⣿⣻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣿⣟⣾⢯⣿⣻⣽⢯⣿⡽⣷⣻⣯⢿⣽⣻⢯⣟⣾⣻⣯⣟⣯⢿⣻⣽⡾⣯⣟⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⣿⡿⣞⣯⣿⣳⡿⣽⣻⢷⣻⣯⡷⣟⣯⡿⣽⣻⢯⣷⣟⡷⣯⢿⣻⣽⢷⣻⣽⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠸⠿⠟⠿⠉⠛⠳⢿⣿⣽⣻⣟⣾⣽⢿⣽⣻⣽⣟⣯⡷⣿⡽⣟⣿⡽⣯⡿⣯⣷⢿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣿⣳⣯⢿⡾⣽⣟⣾⣯⣷⢯⣿⡽⣷⢿⣻⢷⣻⣯⣟⣷⣯⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠙⠻⠿⠉⠉⠁⠘⠿⣻⣞⣿⣽⣻⢯⣿⣻⠾⠽⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀