⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠘⣇⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣦⡀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠸⣧⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⠀⠀⠀⢻⣆⠀⠘⣿⣦⣤⣤⣤⣤⣤⡤⠄⠀⠀⠀⠀⢻⣷⡀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⡎⣿⡀⠀⠙⢷⣶⣤⣤⣴⣶⡿⠟⠃⣿⠇⠀⠀⠀⠀⠻⣧⡀⠀⠉⠉⠉⠉⠉⠁⠘⣿⣶⣄⠀⠀⠈⣿⣧⠀⠀⠀⠀⢿⣿
⣠⣤⣄⣀⣰⣇⠘⡇⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠠⠋⠀⠀⠀⠀⠀⠀⠈⠑⠄⠀⠀⠀⠀⠀⣀⣀⣸⣿⣿⣧⣶⣶⣿⣿⡄⠀⠀⠀⠸⣿
⠉⠙⠛⠛⡿⠿⠿⠿⠿⣿⣶⣶⣶⣦⣤⣄⡀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⢀⣤⣶⣶⣿⠿⠿⠛⠛⠛⠋⠙⠛⠁⢸⣿⡇⠀⠀⠀⠀⢿
⠀⠀⠀⠀⠀⠀⢀⡆⠈⠀⠀⠀⠀⠉⣹⣿⣿⠀⠀⠀⠀⠀⠊⠑⠋⠹⠤⠀⠀⢿⣿⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⢀⣤⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣷⣤⣄⡀⠀⠀⠀⠀⠀⢸⣿⠃⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢸⣿⡇⠀⢀⣴⣿⠟⠁⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣤⣀⣠⣤⣄⡀⠀⠀⠀⠈⠋⠙⠿⣷⣤⡀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢸⣿⣡⣴⡿⠋⠁⠀⠀⠀⠀⠀⠀⠘⠿⠟⠛⠛⠙⠉⠛⠋⠁⠙⠻⠛⠃⠀⠀⠀⠀⠀⠈⠙⠿⣷⣤⡸⣿⣾⠀⠀⠀⠀⠀
⣥⠀⠀⠀⠀⣾⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⡿⣇⠀⠀⠀⠀
⣿⠀⢀⣴⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡇⠈⠀⠀⠀⣰
⣿⠀⠈⠉⠉⣿⣿⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⢀⡀⠀⢰⡞⠉
⣿⡇⠀⠀⠀⢸⣿⣿⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠟⣿⣧⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢼⠟⣡⣿⢯⠄⣾⠀⠀
⣿⡇⠀⠀⠀⢀⣿⣿⣿⡻⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠃⠀⠈⠻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣧⡆⣰⣿⠋⣾⢠⣿⠀⠀
⣿⡇⠀⠀⠀⢸⣿⣧⣿⢳⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠁⠀⠀⠀⠀⢹⣿⠂⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣷⣿⣧⢸⡿⢸⣿⠀⠀
⣿⣷⠀⠀⢈⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣖⡀⠀⢀⣾⡿⠁⠀⠀⠀⠀⠀⢸⣿⠀⣠⣴⣶⣿⣿⣿⣿⣿⣿⣿⡟⠈⣿⡉⠀⢸⣿⠀⠀
⣿⠻⠀⢠⠇⠀⢿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⢁⣄⠀⠀⢠⡄⠀⢸⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⣠⣼⢶⣓⡾⠇⠀⠀
⠈⠃⢡⡿⠀⠀⠘⣿⣧⣼⣿⣿⣿⣿⣿⣿⡏⠻⣿⣾⣿⢸⣿⡆⠀⢼⣿⠀⣸⣿⡿⠟⠉⣿⣿⠿⣿⣿⣿⣿⣷⣾⣤⣄⡀⠀⠀⠀⠀⠀
⠀⢠⣿⣵⣿⠿⣿⣿⣯⣹⣿⣿⣿⣿⣿⣿⠇⠀⠘⢿⣿⣨⣿⡇⠀⢸⣿⣦⣿⣿⠀⠀⠀⠓⠀⣠⣿⠟⠉⠛⢿⠛⠛⠿⢿⣷⣄⡀⠀⠀
⣄⣿⣿⠋⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣷⡀⠀⢀⣴⣿⣿⠟⣿⡇⠀⢸⣿⠉⣿⣿⠀⠀⠀⢀⣴⣿⠋⠀⠀⠀⠀⠀⠀⢠⠀⠉⠻⣿⣄⠀
⣿⣿⠃⠀⠀⠀⠀⠀⠀⠼⣿⣿⣿⣿⣿⣷⣠⣾⣿⣿⣿⠀⣿⡇⠀⢸⣿⡆⣿⣿⠀⣀⣤⣿⣿⣧⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠘⢿⣧
⠻⡿⠂⠀⠀⠀⣀⣀⠈⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠘⠁⠀⠈⠿⠃⣿⣿⣼⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠘⡟⠀⠀⠀⠀⠈⢿
⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⣀⣀⠀⣀⣀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢀⣀⣤⣤⣴⣶⡶⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠿⠿⣿⣿⠿⠃⢿⣿⣿⣿⣿⣿⣿⣷⠀⠔⠚⠛⠛⠋⠉⠉⠁⠀⣀⣤⣤⣄
⡶⠿⠛⠉⠉⠁⠀⠀⠀⠘⡇⢸⣿⣿⣿⣿⣿⣿⣿⡇⣿⠀⠀⠀⠻⠏⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⢀⣴⣿⠿⠛⠻⠿