⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⣀⣤⣴⠶⠾⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⡇⣶⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⡠⠚⠉⠁⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⡇⠁⠀⠀⢠⣼⠳⠀⠀⢀⡴⠋⠀⠀⠀⠀⡠⠀⠀⠀⠀⠈⠙⠛⠷⢾⣿⣿⣿⣿⣛⣯⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢃⠀⠀⠀⢸⠈⠀⢀⡴⠋⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠛⡷⠤⠤⠠⠤⠤⠤⠤⢀⣀⡀
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠈⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⢠⠏⠀⠀⡔⠀⠀⡀⢀⢼⠃⠀⡄⠀⠀⠀⠀⠄⠀⢀⣄⣀⣠⡀⠀⠀⠀⠀⠀⠀⢱⠀⢀⠠⢠⠂⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠐⣣⠀⠀⢀⡟⠀⠀⢰⠁⠀⡐⠉⠁⢸⡀⡼⠀⠀⠀⠀⡈⠀⢀⣾⠟ ⣩⣿⣷⣦⡀⠀⠀⠀⠈⡄⠀⣠⠃⣀⠀⠀⠀⠀
⠀⠀⢀⠀⠂⠐⢁⠀⠀⣼⠁⠀⢀⠃⠀⠸⠉⠢⢄⣸⢻⡇⠀⠀⢀⠜⠀⣠⠎⢸⣿⣼ ⣟⣡⡼⠿⡿⣆⠀⠀⠀⠁⠀⢀⡤⠊⠀⣠⣤⡤
⠀⠀⠑⠀⠀⠀⠈⢂⠀⠇⠀⠀⢰⠀⢠⠃⠀⠀⠀⢸⡿⣧⣀⣠⣪⡴⠾⣥⡶⠛⠉⢻ ⣿⣿⣴⠗⣴⣿⠆⠀⠀⠀⠂⠁⠀⡠⠺⣿⠟⠁
⠀⢀⠂⠀⠀⠀⠀⠀⠙⡆⠀⠀⡇⠀⡟⠶⢶⣤⣀⡈⡧⠸⡿⢟⡝⣇⡾⠋⠀⠀⠀⠀ ⡄⣹⠟⠿⠟⠋⠀⠀⠀⠀⠀⠀⠸⣿⡞⠁⠀⠀
⠀⢢⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⠁⢸⠁⢤⡴⠶⠛⠃⠃⠀⠈⠘⠐⠁⠀⢴⣶⠶⠛⠛ ⢛⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠼⠋⢡⡀⠀⠀
⠀⠘⢠⠀⠀⠀⠀⠀⠘⡇⠀⣾⣠⡇⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠙⠻⣦⠀ ⠊⠀⠀⠀⠀⠀⠠⠀⠀⣀⠖⠁⠀⠀⠀⠱⡀⠀
⣠⠴⠾⠛⠒⠤⠄⠤⠔⢇⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃ ⠀⠀⠀⠀⠁⠠⠁⢀⣠⡽⠙⠉⠉⠋⠣⠤⢼⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⣖⡀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⢠⠂⠠⠃⠒⡹⠉⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⡀⠠⠀⠀⠀⠀⠠⣿⣿⣷⢀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⡠⠁⠀⠀⠀⡠⠃⡰⠁⠀⠀⢡⢢⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⢀⠔⠀⢀⣀⣐⡀⠀⠀⠀⢸⣿⡟⠀⠑⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⢀⡜⢁⡾⠁⠀⢢⠀⠘⡄⠣⡀⠀⠀⡀⠀⠀⡠⠃
⠀⠀⢀⣴⣿⣷⠤⠈⢄⠀⠀⠀⡎⠳⡀⠀⢂⠈⣦⣄⣀⣀⣀⣀⣤⣤⠌⠀⠀⠀⡴⠋⣴⣿⣿⣿⣷⡀⠃⠀⠘⡄⠱⡄⠀⣇⠀⡠⠃⠀
⢀⣠⣾⣿⣿⣿⠀⠀⠈⠠⠀⠀⠘⠀⠁⠀⠀⠀⢹⣿⠿⠖⠂⠀⡲⠋⠀⢀⡴⠋⣰⠾⣿⣿⣿⣿⣿⣿⡜⡄⠀⠱⡄⠘⢆⢻⣎⠀⠀⠀
⠸⣿⣿⣿⣿⣿⢠⠂⠀⠇⠀⠀⣀⢀⡀⠀⠋⠉⠀⠀⠀⠀⢀⠔⢁⣠⣶⢉⡴⠋⢀⣴⣿⣿⣿⡿⠿⣿⣿⡘⡀⠀⠸⡀⠀⢣⡹⣶⣶⣿
⠀⣿⣿⣿⣿⣿⡄⠉⠉⠀⡠⠊⠀⠀⠈⡑⠀⠚⠀⠀⢀⣀⠅⠒⠉⣔⠗⠋⠂⠀⠠ ⠟⠛⠍⠀⠀⠀⠈⢣⠱⡀⠀⢹⡄⠀⠱⡜⢿⣿
⣼⣿⣿⣿⣿⣿⡷⠂⠀⠔⠀⠀⠀⠀⠘⠀⠀⠠⠒⠀⠁⠀⠀⠀⠊⠁⠀⠀⠀⠀⠀⠀ ⠀⠊⠀⠀⠀⠀⠀⠀⢇⠑⡄⠀⢳⡀⢀⣻⡄⠙
⣿⣿⣿⣿⣿⣿⠀⠀⠌⠀⠀⠀⠀⠔⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡐⠀⠀⠀⠀⠀⠀⠀⠘⡄⠘⢄⠀⣧⢸⠿⣿⡆
⣿⣿⣿⣿⣿⠇⢀⡈⠀⠀⠀⣀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⡀⠀⠀⠀⠀⠀⣇⠀⠀⠁⠸⡼⣄⣸⣿
⣿⣿⣿⡿⠃⠀⢸⣥⠤⠂⠈⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⢀⡾⠀⠀⠀⠀⠀⠐⠀⠘ ⡀⠉⠀⠐⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢷⢻⣿⣿
⣿⣿⠟⠁⠀⡀⠊⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⢤⣶ ⣾⣿⡀⠀⢃⠀⠀⠀⠀⠸⡇⠀⠀⠀⢸⠘⣿⣿
⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠤⠤⠤⠂⠀⠀⠀⠀⠀⠀⠈⠣⠀⠀⢸⣿ ⣿⣿⣷⡀⣸⣶⣶⣶⣶⣦⣇⠀⠀⠀⠈⠀⢿⣿
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡿⠛⠻⢿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀
⣤⣴⣶⠾⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⣠⣤⣾⣿⣿⣿⡟⠋⠀⠀⠀⠀⠙⠻⣏⠀⠀⠀⠀⠀⠀⠀
⠉⢁⠏⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠈⠀⢄⠀⠀⠀⠀⠀
⠀⠂⠀⠀⠈⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡇⠘⠻⠿⣶⣦⣤⣀⠀⠀⡀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠉⠙⠉⠉⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢀⣶⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡟⠟⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⡎⢸⠀⢸⠀⢀⡄⢀⠎⢠⡴⠖⠲⡄⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠀⣠⠀⠀⠀⠀⠀⠀
⠀⠀⠀⡼⠤⢼⠀⣼⢀⣾⣇⡎⠀⠙⠦⠤⠞⠁⣰⠋⠁⣸⠃⣤⠒⠒⡂⢀⡤⢤⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⢰⢃⠞⠀⠀⠀⠀⠀
⠀⠀⠰⠁⠀⠈⠀⠹⠋⠈⠋⠀⠀⠀⠀⠀⠀⠀⠙⠶⠚⠁⠀⠻⠶⠞⠁⠸⣄⣤⠇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀