⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⢀⣴⠖⠛⣿⠀⠀⠀⠀
⠀⣀⣀⠀⠀⠀⠀⢀⣠⡶⠟⠋⠉⠉⠉⠙⠻⢿⣋⠉⠉⠁⠀⢠⡟⠀⠀⠀⠀
⢸⡍⠉⠙⠷⠖⢛⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⡀⠀⠀⠈⢷⡀⠀⠀⠀
⠈⠻⡶⠄⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠘⣧⠀⠀⠀
⠀⠀⡇⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⢻⡄⠀⠀
⠀⠀⡇⠀⠀⠘⣇⠀⢠⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⢸⡇⠀⠀
⠀⠀⣿⠀⠀⠀⣿⡀⠘⠛⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣿⣀⠀⠀⠀⠀⣿⠀⠀
⠀⠀⢹⡄⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀⠀⣼⠋⠀⠀⠀⠈⠙⢷⣄⠀⠀⠙⢷⡄
⠀⠀⠈⣷⠀⠀⠀⣼⠷⣤⣀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠙⢿⡟⠶⠤⠟
⠀⠀⠀⣼⠃⠀⢠⡟⠀⠈⢹⡟⠛⠛⢻⡇⠀⠀⠀⣄⠀⠀⠀⠀⠈⢻⡄⠀⠀
⠀⠀⠀⣯⣠⡾⢻⡇⠀⠀⠈⣧⣴⠞⠛⠛⠛⠶⣤⣿⠀⠀⠀⠀⠀⠀⢻⡄⠀
⠀⠀⠀⠈⠀⠀⠈⢷⣦⣴⠟⢻⡏⠀⠀⠀⠀⠀⠀⠙⠳⣦⣀⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠈⣷⠀⠀⠀⠀⢠⡀⠀⠀⠀⠙⠷⠄⠀⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⢸⣇⠀⠀⠀⠀⢻⣄⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⢹⣆⠀⠀⠀⠀⠻⣆⠀⠀⠀⠀⠀⢀⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠹⣇⠀⠀⠀⠀⠹⣶⣤⣤⣤⠶⠛⠁⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⢹⡇⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⢠⡟⠁⢀⣠⡴⠞⠁⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣤⡼⠷⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀
⢀⣴⡶⣶⢶⣶⣶⣶⢶⡶⣶⢶⡶⣶⢶⡶⣶⢶⡶⣶⢶⡶⣶⢶⣦⡀
⢸⣯⢿⣽⠿⠂⠀⢸⣯⢿⣽⣯⢿⣽⣯⢿⣽⠯⠟⠹⠯⠿⣽⣟⡾⡇
⢸⣯⢿⣇⣀⠐⣷⣿⢯⣿⢾⣽⡻⠞⠉⣠⣤⣴⢶⡶⣶⣤⣀⠉⢻⡇
⢸⣯⡏⠉⢀⣴⡿⣽⣻⡾⠏⢉⣠⣞⡿⣯⣷⢯⣿⡽⣷⢯⣟⣧⡀⠱
⢸⡿⣷⣶⣾⣯⢿⣽⠓⢁⣴⡿⣽⣾⣻⢷⣯⢿⣞⡿⣽⣻⣽⢯⣷⠀
⢸⡿⣽⣳⢿⣞⠟⠁⣴⣟⡷⣟⡿⣾⡽⣟⣾⢿⣽⣻⣽⣟⡾⣟⣷⠀
⢸⡿⣽⢯⣿⠊⣠⡾⣟⣾⣟⣯⣿⣷⣿⣯⣟⣿⣾⣽⡾⣽⣻⣟⣾⠀
⢸⡿⣽⡻⠁⣰⡿⣽⣻⢷⣯⢿⣿⡦⠀⠀⠀⠀⣾⣳⢿⣯⢷⣻⣽⠀
⢸⡿⡽⠀⣼⢿⣽⣻⡽⣟⣾⠿⠋⠀⠀⠀⠀⢰⣿⢯⣿⢾⣻⣟⡞⠀
⢸⡟⠁⣼⢯⡿⣾⣽⣻⣿⡏⠀⠀⠀⡠⣾⣷⣼⣯⢿⣾⣻⣽⣾⠁⡄
⢸⠁⢰⣿⣏⡿⣷⣏⣷⣿⣇⠀⡰⠏⠀⢹⣿⢿⣾⡿⣷⣏⣷⠇⢰⡇
⠈⢀⣿⣳⣯⢿⣽⣾⡟⢻⡿⠋⠀⠀⠀⣸⣿⣻⡾⣽⣷⣻⡝⢠⡾⡇
⠀⣼⢯⣷⣻⣯⢿⣿⠃⠀⠀⠀⢀⣠⣾⡿⣷⣻⣽⢷⣯⡟⢀⣾⡽⡇
⠀⣿⢯⣷⣟⣾⣿⡟⠀⠀⠀⠀⠻⣿⣽⣻⢷⣻⡽⣟⠎⣠⣿⣳⢿⡇
⠀⣿⣻⢾⣽⣞⣿⣿⣿⣿⣿⣿⣿⣟⣷⣻⢿⣽⡻⢉⣴⣟⣾⡽⣟⡆
⠀⣿⣽⣻⡾⣽⣾⣳⣟⣾⣳⣯⢷⣟⣾⢯⡿⠞⣡⣞⣷⣻⣞⡿⣯⡇
⠀⢿⣞⡷⣿⣻⣞⣷⢯⣷⢿⣽⣻⡾⣯⠟⢁⣴⡿⣾⣽⡳⠿⠽⣷⡇
⢀⠈⢾⣟⣷⢯⣟⣾⢿⣽⣻⢾⡷⢋⣡⢾⣻⣯⣟⡷⡿⠃⢀⢠⣿⡆
⢸⣧⡄⠙⠺⠿⠽⠾⠿⠚⣉⣤⡶⣯⣟⣯⣷⣟⣾⣿⡀⠔⢹⡿⣷⠇
⢸⣷⣻⢿⡶⣶⣶⢶⣞⡿⣽⣳⡿⣽⣾⣻⢾⣽⣾⠈⠀⣠⣾⣻⣽⡇
⠈⠳⠿⣯⢟⡷⢯⠿⣞⠿⡽⢷⡟⡿⢾⡽⣟⠾⡿⢶⡶⢿⠷⣯⠷⠁⠀⠀⠀