⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⡾⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣅⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣻⢷⣯⢿⣽⣻⢿⡿⣿⣷⣶⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⣤⣄⣴⣿⣟⡿⣾⣽⣻⣞⡿⣾⡽⣯⣟⣷⣻⣞⡿⣽⣻⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣿⣟⣾⣻⣟⣯⡷⣯⣟⡷⣯⢷⣯⣟⡷⣿⡽⣾⣳⣟⣾⣻⡽⣷⣿⣾⡽⠿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣤⣤⣶⣿⡿⣿⣟⡿⣽⢾⣳⣟⣾⣳⢿⣽⣞⡿⣽⣻⢾⣽⣻⢷⣻⢷⣻⢾⣳⣯⢿⡽⣯⢿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠐⣿⣟⣯⣟⣾⡽⣷⢯⣟⣯⡿⣽⢾⣳⣟⡿⣾⣽⣻⡽⣯⢿⡾⣽⢯⣟⣯⣟⣯⣟⣾⢯⣿⣽⣻⢾⣽⣻⢿⣷⣤⡀⠀⠀⠀ ⠀⠀⠀⠀⣀⣿⣿⢾⡽⣞⡿⣽⣻⡾⣽⣻⣽⣻⣽⢾⣻⢷⣯⢷⣟⣯⡿⣽⢯⡿⣽⡾⣽⡾⣽⣾⣻⣞⣷⣻⣟⣾⣽⣻⣞⡿⣿⣤⡀⠀ ⠀⢀⣴⣿⢿⣯⣟⣯⣟⣯⢿⣽⣳⡿⣽⣳⣯⢷⣯⣟⣯⢿⣞⡿⣞⡷⣟⣯⡿⣽⢷⣻⢷⣻⢷⣯⢷⣻⣞⣷⣻⣞⡷⣯⢿⣽⣳⢿⣷⡄ ⣰⣿⡿⣽⣻⢾⡽⣾⡽⣾⢯⣷⣻⣽⢯⣷⣻⣟⡾⣽⡾⣯⢿⣽⣻⣽⣟⣷⣻⢯⣟⣯⣟⣯⢿⣞⡿⣽⡾⣽⣳⣯⢿⣽⣻⢾⣽⣻⢾⡧ ⣿⣿⡽⣷⣻⢯⣟⡷⣿⣽⣻⢾⣽⢾⣯⢷⣟⣾⣻⢷⣻⣽⣿⣿⣿⣟⣾⣳⢿⣯⣟⣾⡽⣾⢯⡿⣽⢷⣻⢯⣷⣻⣟⣾⣽⣻⣾⡽⠟⠃ ⠹⣿⣿⣳⣟⣯⢿⡽⣷⢯⣟⡿⣞⡿⣞⡿⣞⣷⡿⠿⠋⠉⣼⣿⣷⣻⢾⣽⣻⡾⣽⣾⡽⣯⢿⣽⢯⣟⣯⢿⣳⣟⣾⣳⣯⢷⣿⡄⠀⠀ ⠀⠈⠹⣿⣾⢯⡿⣽⢯⡿⣞⣿⣽⣻⣽⠿⠛⠉⠀⠀⠀⢸⣿⣿⢾⣽⣿⠟⠛⠉⠛⠛⠿⠿⠿⢾⣿⣽⣾⣻⣽⢾⣳⣟⡾⣟⣾⣿⠀⠀ ⠀⠀⠀⠀⣿⡿⣽⢯⡿⣽⣻⣞⣷⣻⣿⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣆⠀⠀⠀⠉⠉⠉⠛⠛⠿⣿⣽⣿⣾⡿⠀⠀ ⠀⠀⠀⣸⣿⢿⣽⣻⢿⣽⣳⢿⡾⣽⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣷⠀⠀⠀⠀⣾⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠉⠁⠀⠀⠀ ⠀⠀⢠⣿⣟⡿⣾⣽⣻⢾⡽⣯⣟⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⣿⡇⠀⠀⢸⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀ ⠀⠀⣼⣿⢾⡽⣷⢯⣟⣯⢿⣳⢿⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣯⠀⠀⢸⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀ ⠀⢰⣿⢯⣟⣿⣽⣻⣞⣯⣟⣯⢿⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⢂⣿⡿⣝⣿⣿⠀⠀⣾⡿⣹⣿⡿⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀ ⠀⣾⣿⣯⣿⣿⣞⣷⣯⣟⣾⡽⣯⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⡳⣌⣿⡇⠀⠀⣿⡷⣩⢾⡇⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀ ⠸⡿⠟⠁⠘⣿⣿⣞⣷⣿⠛⠛⠿⢿⣯⠀⠀⠀⠀⠀⣀⠀⠀⠸⠹⣷⣼⡿⠀⠀⠀⠘⣿⣴⡿⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⢿⣿⣿⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⡀⠀⠀⢈⠋⠀⠀⠀⠀⠀⠈⠛⠁⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⡟⠀⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡉⠙⠳⠶⠶⣤⣤⣤⣤⣤⣤⠶⠶⠖⠛⠉⢁⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀