⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣀⣴⣾⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣴⣟⡉⢻⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡈⢿⡇⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠻⣿⡇⠸⠃⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⠟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠙⠁⠀⠀⠈⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⠋⠁⣰⣿⣿⣿⣿⡿⠛⠉⠉⠙⠻⢿⣿⣆⠀⠀⠀⠀⢀⣼⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣟⣡⣴⣾⣿⣿⣿⣿⡏⢀⣴⣶⣿⣶⣶⣄⣉⠉⠃⠀⢠⣴⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡿⠋⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⡿⠿⠛⠛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠃⠀⠀⢀⡤⠈⢻⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⢰⡿⠟⢋⣠⣴⠊⠀⣴⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣴⡞⠁⠀⠀⠀⢻⣿⣿⣿⣿⣿⠟⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣾⡇⠀⠉⣠⣶⣿⣿⠇⠀⣸⣿⡿⠋⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⠖⠀⠀⢿⣿⣿⣿⠏⠀⠀⠀⠀
⠀⠀⢀⣤⣶⣾⣿⣿⣿⣿⣿⣷⣴⠾⠿⠿⣿⣿⠀⢠⣿⣿⠁⠰⠛⠁⠀⣨⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⡄⢸⣿⣿⠏⠀⠀⠀⠀⠀
⣠⣾⣿⠋⠀⠀⠀⠙⠻⣿⡿⠋⠀⠀⠀⠀⠈⢻⡀⢸⣿⣿⠀⠀⠀⣠⣾⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣤⠄⣸⠁⠈⣿⡿⠀⠀⠀⠀⠀⠀
⠘⢿⣿⡀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠳⠸⣿⣿⡄⠀⢰⣿⣿⡏⢀⣼⣿⣿⣿⣿⠛⠛⠉⠀⢀⣿⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀
⠀⠀⠙⠻⣶⣶⣶⣶⣾⣿⣿⣦⣄⣀⣀⣀⣤⠖⠂⠀⢿⣿⣿⣄⢹⣿⣿⠀⣾⣿⣿⣿⣿⣿⣿⣶⠞⠁⢸⣿⡆⠀⣿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠉⠛⠿⢿⣿⣿⣿⣿⡿⠟⠋⠁⢀⣴⡀⠈⢿⣿⣿⣾⣿⣿⣇⣿⣿⣿⣿⣿⣿⣋⠁⠀⠀⢸⣿⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⣠⣴⣾⣿⣿⣷⡀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣛⠉⠀⠀⠘⣿⣿⠀⠇⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠿⠿⠿⠛⢛⣿⣿⣿⣦⡀⠀⠈⠛⠻⢿⣿⣿⣿⣿⣿⣷⣌⠹⣷⡀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀⠈⠉⠻⣿⣿⣆⢸⡇⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠺⢿⣿⣿⡻⢿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠈⣿⣿⠀⡇⠀⢸⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣷⡄⠈⠙⠻⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⢸⣿⠀⠃⠀⢸⣿⢡⠄⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⠘⣿⣿⣄⠀⠀⠈⠙⢿⣿⣿⣿⣿⣧⡀⠀⠀⠀⡟⠀⠀⢀⣿⣷⡟⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⣸⣿⣿⣶⡞⠈⢳⣤⣻⣿⠉⢿⣿⣷⠀⠀⢀⠇⠀⠀⣼⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⠁⠀⠀⢻⣿⣿⠀⠈⢿⣿⡆⠀⠀⠀⢀⣼⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠋⠀⠀⠀⣸⣿⡟⠀⠀⢸⣿⡇⠀⠀⣠⠞⠋⢀⣠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠟⠁⠀⠀⠀⢠⣿⡟⠀⠀⠀⢀⣿⠇⠀⠀⣠⣴⣾⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠀⠀⠀⠀⠀⢠⣿⠟⠀⠀⠀⠀⣸⡟⠀⠀⢠⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠁⠀⠀⠀⢀⣴⠟⠀⠀⢀⣾⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⢀⡴⠟⠁⠀⠀⢠⣾⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋⠀⠀⠀⢀⣴⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀