⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⣀⣠⣴⣖⠲⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣤⣤⣄⣀⠀⢺⡇⠉⠉⢀⣴⣾⣿⣿⣿⣿⠂⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣍⣹⣿⣿⣿⣿⣿⠦⣽⣤⣴⣾⣿⣿⣿⣿⣿⣿⠉⡔⠀⠀⢀⠀⠀⢻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠸⣿⣿⠟⠩⢂⣾⣿⢻⣽⡾⣽⣯⡿⣿⣿⣿⣈⡓⣠⡾⠉⢱⠄⠈⣷⣇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡴⢻⠋⢰⠃⣸⣿⣽⠈⢿⣿⣿⡽⣿⣿⣿⣿⠋⣵⣿⣧⢶⠞⢼⣰⠋⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠗⠦⣀⣸⡇⡄⡙⠓⣿⡿⣾⡆⠸⣿⣻⣷⠹⣿⢯⣿⣴⣿⣾⣽⠃⢀⣾⣷⣆⠐⠯⡀⠀⢀⣀⣀⣀⣤⣶⣶⣶⡾⣿⣟⣷⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡀⠀⠀⠸⠈⣴⡟⢸⠁⡇⣦⢠⡿⢿⣿⣽⠄⠘⣿⢾⡀⢹⣿⣻⣿⣳⣿⣭⢠⡿⣯⣿⡿⣿⣇⡿⠟⠛⠛⠉⠉⠉⠉⠉⠁⠀⠀⠀⡏⠀⠀
⠀⠀⠀⠀⠀⠀⠠⠍⠰⠀⠀⠈⣑⡴⢣⠈⠁⢸⡇⡇⢳⠼⣟⣂⣿⣯⢿⣶⣾⣿⠇⣸⣿⣷⣿⣟⣾⡗⣾⣽⣿⠗⠁⣢⢹⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⣧⣄⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣰⣿⣟⠻⡄⠑⡦⠸⣧⢹⣧⣶⢷⣿⣍⠱⢾⠟⠾⡛⢰⣾⣿⣿⣿⢿⣯⣿⡿⠋⣁⣤⣾⡿⢨⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠂
⢀⣤⣤⠶⠶⠾⠿⠿⠻⠟⠛⡙⠛⡆⠻⣶⣜⡆⢻⣾⣿⡛⠚⠛⠁⠀⠀⠙⢦⡘⠺⠫⣿⣿⣿⣿⣯⣷⣾⣿⣿⣿⡿⢥⡀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡷⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠡⣐⠺⢿⣷⡌⣿⣿⣿⣆⠀⠀⠀⣄⣤⠄⠉⠑⠇⠈⠛⠛⠿⣿⣯⣿⡽⣯⡏⠀⠀⢻⡷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢺⣿⡟⢾⠋⣘⣿⣿⡿⢳⠠⠀⠀⠀⢀⣠⡀⠀⠀⠀⠀⠀⠀⠣⣄⡀⡿⠁⠀⠀⣸⣽⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⢰⠎⠱⣿⠏⣏⣇⡿⠿⣀⡎⠀⠀⣿⣶⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡟⢎⠀⢀⣀⠀⡆⢻⠋⠀⢀⡽⢙⢻⢉⠛⡋⠛⢿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠚⠋⠙⠹⢯⠽⣉⢞⢢⠓⡦⠵⣌⢃⢏⢷⣄⢲⠄⡃⢾⠀⠀⠈⢻⣿⣿⣿⡏⠉⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⡧⡍⣎⢎⣝⣲⡙⣬⠃⡎⣜⡿⣧⣼⣦⣿⣤⣀⣤⣾⣾⣿⣿⣿⣿⡆⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢠⡴⠖⠛⠉⠉⢹⣿⡟⠉⣙⣄⠊⢀⠄⢉⣻⣿⣯⣿⠻⣿⣿⠛⢿⣿⣿⣟⣿⣿⣆⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠛⣿⣿⡿⣽⣷⣎⡀⠀⠉⢀⠋⠻⡐⣻⠽⢶⣾⣿⡿⣾⣟⡿⢿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⠙⠿⣿⣻⣿⣟⣷⣦⡔⠋⠀⠰⠁⠙⢲⡌⣿⣀⣤⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⢾⡽⣾⣿⣿⣷⣅⠀⠀⠀⢨⣽⣿⠌⠻⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢃⣿⡿⣿⣿⣿⣷⢶⣶⣿⣿⣾⡖⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣟⣿⣿⣿⣽⣿⣿⣿⣽⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⣻⣿⣿⣟⣾⣿⣿⣿⣿⣿⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⢷⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⢫⠿⣻⣿⣿⢾⣿⣿⣿⣿⣿⣟⣿⣿⢿⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀