⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠈⢂⠀⠀⠀
⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⠔⠀⠀⠀⠄⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀
⠀⠀⠀⢀⠜⠀⠀⠀⠀⡜⠀⠀⠀⡈⠀⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀
⠀⠀⡐⠁⠀⠀⠀⠀⡐⠀⠀⠀⢠⠀⠀⠀⠀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠰⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀
⠀⠌⠀⠀⠀⠀⡀⡐⠀⠀⠀⢀⠊⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡆⠀⠀⠀⠀⠀⠀⠀⠁⠀
⡌⠀⠀⠀⠀⠀⠁⡇⠀⠀⠀⡈⣘⡤⠤⠄⡾⠰⠀⠀⠀⠀⠀⠘⠀⠀⠤⣤⣼⣄⣀⣀⠀⠤⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⢰⠀
⠀⡀⠀⠀⠀⠀⠄⠐⢄⠀⠀⡇⠇⡗⡀⠀⡏⠀⠡⠀⠀⠀⠀⠀⢆⠀⡄⠀⢸⠘⢄⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠂⠡⠀⠀⠀⠀⠈⢄⠀⠢⣀⡇⠀⠠⠐⠄⠀⠀⠀⠑⢦⡀⠀⠀⠘⡄⣷⠀⡈⣀⠀⠑⠠⣀⠀⠘⣄⠀⠀⠀⠀⠀⠀⠐⢄⠀⠀⠀⠀⠘
⠀⠈⠓⢄⠀⠀⠄⠀⣶⠀⡄⢑⣧⠶⠶⠼⢦⡀⠀⠀⠀⠉⢄⠀⠀⢰⠃⢨⠁⢀⣀⣀⣀⠀⠁⢢⡇⠘⣶⣤⣀⠀⠀⠀⠀⠠⡀⠀⠀⠀
⠀⠀⠀⠀⠑⢄⢰⢰⡏⠇⣿⠸⡅⢰⣿⣷⡜⠙⣦⠀⠀⠀⠀⢂⠀⢸⠠⣡⡾⠛⡛⠉⠛⠻⢶⣄⡃⠀⠉⠛⠿⢿⣷⣦⣄⠀⠰⠀⠀⠀
⠀⠀⠀⠀⡠⣀⣲⠋⠀⠎⠋⠀⠑⠀⣾⡻⡇⠀⠈⠁⠀⠀⠀⠘⠀⡘⠀⠈⠠⢿⣿⣷⠀⠀⠀⢹⠇⢸⠀⠀⠀⠀⠀⠙⢻⡗⡄⠀⠀⠀
⠀⠀⠀⢉⠔⠁⠀⠀⠈⢀⣼⠄⠀⠀⠙⠓⠁⠀⠀⠀⠀⠀⠀⠀⡷⠁⠀⠀⠐⣾⡟⡽⠀⠀⠀⠜⢀⠆⠀⠀⠀⠀⠀⠀⠼⢣⡿⠀⠀⡄
⠀⠀⢀⠊⠀⠀⠀⠀⣠⣾⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠙⠓⠁⠀⠀⡀⠔⠂⠄⠀⠀⠀⠀⠀⢀⠒⠋⠁⠀⠀⡇
⠀⠀⠸⡀⠀⠀⠀⢸⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡔⠉⣠⠂⠁⠀⠀⠀⠀⠀⡠⠂⠀⠀⠀⠀⣸⡇
⠀⠀⠀⠈⠂⢄⡀⠈⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢎⠘⣿⣤⡇⠀⠀⠀⠀⠀⣠⠞⠀⠀⠀⠀⢀⣴⣿⠃
⠀⠀⠀⠀⠀⢀⠌⣱⣄⢹⣿⣿⣷⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠪⡙⠻⣦⡀⠀⢀⣾⠏⠀⠀⢀⠤⣲⡿⠛⠁⡠
⠀⠀⠠⠄⠂⠥⠖⢻⣿⣿⣿⢿⣿⠘⢷⣄⡀⠀⠀⠀⠤⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣧⡘⣿⡄⢸⣿⠀⠠⡊⢄⣈⡀⠠⠔⠈⠀
⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣯⠻⣿⣮⡻⣿⣖⢤⡀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡀⢴⣾⣿⣿⣿⣿⣼⣇⠘⣿⣤⠋⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠻⠷⢄⠉⠛⠛⢿⡈⢿⡕⠂⢄⣀⡠⠤⠒⠊⠁⠀⢸⣿⣿⣿⣿⣿⣿⣇⠓⠸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣀⣀⠀⠀⠀⠀⠠⠠⣀⠀⠀⠀⢀⡃⠤⠒⢊⠉⠙⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣮⠀⠻⣿⣿⡿⢿⣼⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠈⢢⠀⠁⢩⢥⡇⢀⠃⠈⠉⠉⠁⠀⠀⠀⠀⠙⢍⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠉⠳⢌⡻⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠡⠀⠸⣄⠑⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠈⠑⡍⢣⣀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⠗⢖⡁⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⡠⢺⠑⠤⠁⠀⠀⠀⠀⠀⡀⠀⠀⠀⠐⣘⠤⡌⠁⠒⡒⠢⠀⠀⠀
⠀⠀⠀⠸⣄⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠘⠈⣤⡞⢂⠀⠢⡀⠀⠀⠀⠂⠁⠀⠀⠀⠀⢁⠤⠁⡔⠁⠀⠀⠀⠡⠀
⠀⠀⡀⢖⠉⡒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠂⠁⣀⠔⣈⡘⢳⢄⠡⡀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠘⠘⢋⠄⠀⠀⠀⠀⠀⠃
⠀⠀⢣⢄⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠁⠀⠀⣜⠲⠭⠊⣤⣿⣾⠉⢒⡄⠀⠀⠢⠄⡀⠀⠀⠀⠀⠀⡖⢋⡀⠀⠀?