⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠔⠒⠒⠒⠒⠒⠂⠤⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠱⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⣀⣄⣀⣀⣀⡀⠀⠀⣀⣀⣀⣀⣀⡀⠈⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠒⡿⠛⠃⠀⠀⢠⠂⠛⣿⠟⠃⠁⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔⣛⣯⠭⡟⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⠞⢉⡰⠊⠁⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣠⠏⢀⡜⠁⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⠏⠀⠸⠁⠀⠀⠀⠀⠠⢬⡆⠀⠀⠀⠀⠀⠀⠀⠉⠉⠈⠁⠈⠀⠀⠀⠀⠀⠀⠀⣠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣾⠀⠀⡇⠀⠀⠀⠀⠀⢀⣤⠼⢦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠻⣟⠒⠒⠒⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛
⠀⠀⠀⡇⠀⠀⡇⠀⠀⠀⠀⡶⠉⠀⠀⠀⠈⢷⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡰⠎⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠉⠲⢦⢄⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⡇⠀⠀⡇⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠈⣆⠉⠙⣶⠦⢄⣀⣀⣀⣠⡤⠶⠋⠁⠀⡀⠈⣇⠀⣀⣀⢀⢀⣀⡀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⣾⠀⢀⣉⣉⣉⠉⠉⠉⠉⠉
⠀⠀⠀⡇⠀⠀⡇⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠳⣗⠒⠒⠚⠉⠀⠀⠀⣠⡌⠘⣀⠽⠤⠇⠒⠶⣖⡢⢭⡓⣤⠀⡜⠀⠀⠀⠀⠀⢀⡏⠀⡘⠈⠓⣤⠀⠀⠀⠀⠀
⠀⠀⠀⢿⠀⠀⡇⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠀⢀⠞⠀⠀⠄⠒⠺⠤⢴⢲⠀⠀⠀⠀⠀⠉⠁⣿⠀⡇⠀⠀⠀⠀⠀⢸⠀⢰⡇⠀⠀⠀⠛⣤⠀⠀⠀
⠀⠀⠀⠸⡀⠀⢸⠀⠀⠀⠹⠀⠀⠀⢠⡀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⣀⠋⠀⠀⠀⠀⠰⢲⠶⡶⣿⠀⠀⠀⠀⠀⠀⠀⣿⢠⠁⠀⠀⠀⠀⠀⣿⠀⢸⠀⠀⠀⠀⠀⠀⠻⣄⠀
⠀⠀⠀⠀⣇⠀⠘⡇⠀⠀⠀⣇⠀⠀⠀⠱⢄⡀⠘⡤⠶⠶⢄⣀⣀⠴⠉⠀⠀⠀⠀⠀⠰⢚⠤⠍⡇⠀⠀⠀⠀⠀⠀⢠⠇⡾⠀⠀⠀⠀⠀⢀⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠈⢳
⠀⠀⠀⠀⠹⡀⠀⢱⠀⠀⠀⠘⡄⠀⠀⠀⠀⠈⠉⠙⣤⣄⡔⢫⠁⠀⠀⢀⠖⢦⡤⠤⠔⠛⠢⡐⡧⣤⣀⠀⠀⠀⣤⠟⢀⠃⠀⠀⠀⠀⠀⢸⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣧⠀⠘⡇⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⣴⠁⠀⠀⢸⡀⠀⣠⠋⠀⠀⠈⠓⠄⠀⠀⠈⠁⠀⢸⡏⠉⠉⠀⠀⢸⠀⠀⠀⠀⠀⠀⣿⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠸⡀⠀⢱⠀⠀⠀⠀⣹⡀⠀⠀⠀⢸⡇⠀⠀⠀⠈⢣⡎⢷⠦⠤⣀⣀⡀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢀⠇⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢇⠀⠈⡇⠀⠀⢠⠁⣱⡄⠀⠀⠈⠃⠀⠀⠀⠀⢈⡗⠞⠀⠀⢀⣉⣉⣑⣲⣦⠄⣀⣠⢾⣁⣀⣀⠀⠀⡿⠀⠀⠀⠀⠀⣾⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠸⡆⠀⢸⠀⠀⠀⠛⢹⣸⡧⣄⠀⠀⠀⠀⠀⢠⡌⠀⠀⠀⠈⠉⠓⠒⠒⠠⢤⡈⢻⠀⠀⠀⠀⠈⠙⠛⡇⠀⠀⠀⠀⢀⠇⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⡆⠀⠀⠀⠀⢡⠓⠚⠛⠒⠀⠒⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠢⣤⣄⠀⠀⠀⡇⠀⠀⠀⠀⢸⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢯⡩⡍⠛⠶⠤⣀⡀⠈⢇⠀⠀⠀⠀⠀⠀⢀⣤⡤⠤⠠⠤⠤⠤⠶⠶⠶⠶⠶⠶⠶⠷⠶⠾⠗⠛⠘⠳⢄⡀⠀⠀⡞⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢹⡑⠶⣄⣀⠀⠙⠲⢾⣆⠀⠀⠀⠀⠀⠈⡇⠉⠒⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⢦⣀⡇⠀⠐⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⢿⠀⠙⠢⣄⡀⠀⠙⠛⠲⣤⡀⠀⠙⢢⡀⠀⠈⠛⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⡿⠓⠢⢄⡀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣦⠈⣆⠀⠀⠀⢙⣳⣤⠀⠀⠀⠈⢳⡏⠁⠈⠓⢤⡀⠀⠙⠳⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⣄⡀⠀⠈⠛⠒⠤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⣹⡶⠭⣍⡉⠀⠀⢷⠀⠀⠀⢈⡇⠀⠀⠀⠀⠈⠑⠦⣄⡀⠉⠙⠶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠲⠦⠤⠤⡠⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠔⠒⠒⠒⠒⠒⠂⠤⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠱⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⣀⣄⣀⣀⣀⡀⠀⠀⣀⣀⣀⣀⣀⡀⠈⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠒⡿⠛⠃⠀⠀⢠⠂⠛⣿⠟⠃⠁⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔⣛⣯⠭⡟⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⠞⢉⡰⠊⠁⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣠⠏⢀⡜⠁⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⠏⠀⠸⠁⠀⠀⠀⠀⠠⢬⡆⠀⠀⠀⠀⠀⠀⠀⠉⠉⠈⠁⠈⠀⠀⠀⠀⠀⠀⠀⣠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣾⠀⠀⡇⠀⠀⠀⠀⠀⢀⣤⠼⢦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠻⣟⠒⠒⠒⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛
⠀⠀⠀⡇⠀⠀⡇⠀⠀⠀⠀⡶⠉⠀⠀⠀⠈⢷⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡰⠎⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠉⠲⢦⢄⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⡇⠀⠀⡇⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠈⣆⠉⠙⣶⠦⢄⣀⣀⣀⣠⡤⠶⠋⠁⠀⡀⠈⣇⠀⣀⣀⢀⢀⣀⡀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⣾⠀⢀⣉⣉⣉⠉⠉⠉⠉⠉
⠀⠀⠀⡇⠀⠀⡇⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠳⣗⠒⠒⠚⠉⠀⠀⠀⣠⡌⠘⣀⠽⠤⠇⠒⠶⣖⡢⢭⡓⣤⠀⡜⠀⠀⠀⠀⠀⢀⡏⠀⡘⠈⠓⣤⠀⠀⠀⠀⠀
⠀⠀⠀⢿⠀⠀⡇⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠀⢀⠞⠀⠀⠄⠒⠺⠤⢴⢲⠀⠀⠀⠀⠀⠉⠁⣿⠀⡇⠀⠀⠀⠀⠀⢸⠀⢰⡇⠀⠀⠀⠛⣤⠀⠀⠀
⠀⠀⠀⠸⡀⠀⢸⠀⠀⠀⠹⠀⠀⠀⢠⡀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⣀⠋⠀⠀⠀⠀⠰⢲⠶⡶⣿⠀⠀⠀⠀⠀⠀⠀⣿⢠⠁⠀⠀⠀⠀⠀⣿⠀⢸⠀⠀⠀⠀⠀⠀⠻⣄⠀
⠀⠀⠀⠀⣇⠀⠘⡇⠀⠀⠀⣇⠀⠀⠀⠱⢄⡀⠘⡤⠶⠶⢄⣀⣀⠴⠉⠀⠀⠀⠀⠀⠰⢚⠤⠍⡇⠀⠀⠀⠀⠀⠀⢠⠇⡾⠀⠀⠀⠀⠀⢀⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠈⢳
⠀⠀⠀⠀⠹⡀⠀⢱⠀⠀⠀⠘⡄⠀⠀⠀⠀⠈⠉⠙⣤⣄⡔⢫⠁⠀⠀⢀⠖⢦⡤⠤⠔⠛⠢⡐⡧⣤⣀⠀⠀⠀⣤⠟⢀⠃⠀⠀⠀⠀⠀⢸⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣧⠀⠘⡇⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⣴⠁⠀⠀⢸⡀⠀⣠⠋⠀⠀⠈⠓⠄⠀⠀⠈⠁⠀⢸⡏⠉⠉⠀⠀⢸⠀⠀⠀⠀⠀⠀⣿⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠸⡀⠀⢱⠀⠀⠀⠀⣹⡀⠀⠀⠀⢸⡇⠀⠀⠀⠈⢣⡎⢷⠦⠤⣀⣀⡀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢀⠇⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢇⠀⠈⡇⠀⠀⢠⠁⣱⡄⠀⠀⠈⠃⠀⠀⠀⠀⢈⡗⠞⠀⠀⢀⣉⣉⣑⣲⣦⠄⣀⣠⢾⣁⣀⣀⠀⠀⡿⠀⠀⠀⠀⠀⣾⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠸⡆⠀⢸⠀⠀⠀⠛⢹⣸⡧⣄⠀⠀⠀⠀⠀⢠⡌⠀⠀⠀⠈⠉⠓⠒⠒⠠⢤⡈⢻⠀⠀⠀⠀⠈⠙⠛⡇⠀⠀⠀⠀⢀⠇⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⡆⠀⠀⠀⠀⢡⠓⠚⠛⠒⠀⠒⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠢⣤⣄⠀⠀⠀⡇⠀⠀⠀⠀⢸⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢯⡩⡍⠛⠶⠤⣀⡀⠈⢇⠀⠀⠀⠀⠀⠀⢀⣤⡤⠤⠠⠤⠤⠤⠶⠶⠶⠶⠶⠶⠶⠷⠶⠾⠗⠛⠘⠳⢄⡀⠀⠀⡞⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢹⡑⠶⣄⣀⠀⠙⠲⢾⣆⠀⠀⠀⠀⠀⠈⡇⠉⠒⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⢦⣀⡇⠀⠐⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⢿⠀⠙⠢⣄⡀⠀⠙⠛⠲⣤⡀⠀⠙⢢⡀⠀⠈⠛⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⡿⠓⠢⢄⡀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣦⠈⣆⠀⠀⠀⢙⣳⣤⠀⠀⠀⠈⢳⡏⠁⠈⠓⢤⡀⠀⠙⠳⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⣄⡀⠀⠈⠛⠒⠤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⣹⡶⠭⣍⡉⠀⠀⢷⠀⠀⠀⢈⡇⠀⠀⠀⠀⠈⠑⠦⣄⡀⠉⠙⠶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠲⠦⠤⠤⡠⠤
