⣴⠞⢋⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⡛⠲⣆
⡏⢰⣿⣟⡿⣟⣿⣻⢿⣻⢿⣟⣿⠀⠀⠀⠀⠀⠀⢀⣠⡴⠴⠶⠛⠷⠶⢦⣄⣀⠀⠀⠀⠀⠀⠀⢸⣿⢿⣻⢿⣻⡿⣟⣿⣻⣟⣿⠀ ⡏
⢷⠈⣿⣞⡿⣯⣷⢿⣻⣯⢿⡾⣿⠀⠀⠀⠀⣤⣠⣾⣛⣫⣄⡀⠀⠀⠀⠀⠈⠙⢷⡄⠀⠀⠀⠀⢸⣿⣻⢯⣿⢯⣟⣯⣷⢿⣽⡶ ⠀⡇
⢸⠀⣿⣯⣟⣷⣯⢿⣳⡿⣯⣟⣿⠀⠀⠀⢴⡾⠿⠟⣻⡿⠿⠿⢿⠦⠀⠀⠀⠀⠀⢹⣆⠀⠀⠀⢸⣷⢿⣻⣽⣯⣟⣷⣯⢿⣞⣿ ⠈⡇
⢸⡄⣽⣷⣻⡾⣽⣟⣯⢿⣳⣿⣻⠀⠀⠀⣸⡯⢀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⣿⡆⠀⠀⢸⡿⣯⣟⣾⢷⣻⣾⡽⣯⣟⡟ ⢸⠃
⢸⡄⢹⣷⣻⣽⣟⣾⢯⣿⣻⣞⣿⠀⠀⠀⣿⡀⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⣿⡷⠀⠀⢸⣿⣽⣻⢾⣟⡿⣾⡽⣿⡽⡇ ⢸⠃
⠀⡇⢸⣯⣷⣟⣾⢯⣿⣳⣯⣟⣿⠀⠀⠀⣹⣧⣿⣴⢤⣤⣤⣄⣀⣀⣤⣤⣤⢤⣤⣽⣿⣏⠀⠀⢸⣟⣾⡽⣿⣞⣿⣳⡿⣷⢿⡇⣾⠀
⠀⣷⢘⣿⢾⣽⡾⣟⣷⣟⡷⣯⣿⠀⠀⠀⣿⢹⣿⡿⡿⠲⠾⣿⡏⢻⠿⠟⠿⢷⡟⢸⢉⣿⠀⠀⢸⣿⣽⣻⢷⣯⡷⣿⣽⢯⣿⠃⡿⠀
⠀⣿⠸⣿⢯⣷⢿⣻⡾⣽⣻⣽⢿⠀⠀⠀⢸⡏⣿⡟⠂⠰⣾⣟⠁⠀⢠⣀⠰⠚⠀⠀⣸⡇⠀⠀⢸⡿⣾⡽⣿⢾⣽⡷⣯⣿⣻⠀⡿⠀
⠀⢹⠀⣿⣻⡾⣿⣽⣻⣽⣟⣾⣿⠀⠀⠀⠀⢿⣿⣿⣶⣿⠟⠻⠶⠖⠛⢿⣦⡄⢀⣤⡿⠀⠀⠀⢸⣿⣳⡿⣯⣿⢾⣽⣟⡾⣿⢸⡇⠀
⠀⢸⣄⣿⢷⣿⣳⣯⣟⣾⣽⢾⣻⠀⠀⠀⠀⠀⢹⣏⢸⣿⣶⣾⣟⣛⣷⣾⣿⠇⢸⡏⠀⠀⠀⠀⢸⣟⡷⣿⣽⢾⣻⡷⣯⢿⡿⢰⡇⠀
⠀⢸⡅⢾⡿⣾⣽⣳⡿⣽⡾⣟⣿⠀⠀⠀⠀⠀⠀⣿⡌⠟⣿⣿⠢⠀⠀⠀⠏⢀⣿⠁⠀⠀⠀⠀⢸⣿⣻⢷⣯⡿⣯⢿⣽⣟⡇⢸⠇⠀
⠀⢸⡇⢸⣟⣷⣯⢿⣽⡷⣟⣿⣽⠀⠀⠀⠀⠀⠀⠘⢿⣶⣾⣿⠀⠀⢀⣀⣴⡿⠃⠀⠀⠀⠀⠀⢸⣷⣟⡿⣾⣽⣟⣯⡷⣿⡇⣾⠀⠀
⠀⠀⣇⠸⣿⢾⡽⣟⣾⣽⣟⡷⣿⠀⠀⠀⠀⠀⠀⠀⠀⣙⣻⣿⣆⣠⣿⣟⣋⠀⠀⠀⠀⠀⠀⠀⢸⣿⣞⣿⣳⢿⣞⣯⢿⣷⡅⣿⠀⠀
⠀⠀⣿⠸⣿⢯⣿⣻⣽⡾⣽⣻⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⣿⣿⡿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⣷⢿⣞⡿⣯⢿⡽⣟⡾⠀⣷⠀⠀
⠀⠀⣿⠀⣿⢯⣷⣟⡷⣿⣻⢷⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⣿⢾⣻⣽⣟⣿⣻⢿⢠⡇⠀⠀
⠀⠀⢻⡀⣿⣟⡷⣯⡿⣷⣻⣟⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣟⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣞⡿⣯⡷⣿⣞⣯⣿⢰⡇⠀⠀
⠀⠀⢸⡇⠚⠋⠛⠹⠛⠷⠻⠙⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠟⢨⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠛⠽⠳⠟⠳⠋⠛⠁⢸⡅⠀⠀
⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⣀⣀⣀⣀⠀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀
⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⠃⢀⣿⣿⡿⠛⠛⢻⣿⣿⡟⠻⠻⣿⣿⢠⣴⣿⣿⠟⠛⠿⣿⡟⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀
⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣧⣶⣿⠟⠁⠀⠀⠀⣿⣿⣿⣇⣀⣀⡉⢱⣿⣿⣿⠁⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀
⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⢿⣿⣿⣦⡀⠀⠀⢸⣿⣿⣿⠿⠿⠿⠀⢾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀
⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⣀⣾⣿⣿⣏⠈⢻⣿⣿⣷⣄⡀⣾⣿⣿⣇⠀⠀⠀⠀⠘⢿⣿⣿⣶⣤⣤⣤⣴⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀
⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠋⠉⠉⠉⠙⠀⠀⠉⠛⠋⠉⠃⠋⠉⠉⠙⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀
⠀⠀⠀⠈⢷⣄⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⠞⠁⠀⠀⠀