⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⠤⠄⠒⠒⠈⠉⠉⠉⠁⠀⠘⠿⠿⠃⠀⠉⠉⠉⠉⠑⠒⠒⠠⠤⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠒⠤⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠒⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣦⣴⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠊⠁⠀⠀⠀⠀⠀⠀⢀⢀⣀⡀⠀⡀⣀⣐⠠⠦⠆⠒⠓⠓⠒⠺⣿⣾⠗⠓⠚⠒⠒⠤⠦⠆⣀⣀⠀⠀⡀⣀⡀⡀⠀⠀⠀⠀⠀⠀⠈⠑⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⣿⣿⣷⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⣾⣿⣿⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠊⠁⠀⠀⠀⠀⠀⠀⠀⢀⢀⠴⢒⠈⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⡀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠑⠒⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠉⠀⠀⠀⠀⠀⠀⠀⠠⣀⠖⠊⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣴⣶⣆⣂⡠⠠⠦⢼⣿⣿⡦⠦⠤⠠⣰⣾⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⢀⢰⣴⣔⡔⠋⠀⠀⠀⠀⠀⠀⠀⠀⣰⣶⣦⡰⠤⠚⠊⠻⠿⠟⠀⠀⠀⠀⠀⠙⠉⠀⠀⠀⠀⠘⠿⠿⠋⠑⠓⠴⢴⣶⣮⡀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠦⣢⣦⣄⠀⠀⠀⠀⠀⠈⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⠀⠀⠀⠀⠀⠀⡀⣿⣿⡿⠀⠀⠀⠀⢀⢀⠀⢀⣀⠤⠻⢿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠓⠤⣀⠀⢀⢀⠀⠀⠀⠀⢀⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠈⠀⠀⠀⠀⠀⡀⡰⠊⠂⠀⠀⠀⠀⠀⠀⣾⣿⣾⠊⠀⠀⠈⠀⠀⠀⢀⢀⢀⠀⠀⢀⢀⢀⢀⢀⢤⣷⣷⣄⢀⢀⢀⢀⠀⠀⢀⠀⢀⠀⠀⠀⠀⠀⠀⠈⢱⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠑⢅⠄⠀⠀⠀⠀⠀⠀⠡⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⢤⠊⠂⠀⠀⠀⠀⠀⠀⢀⠦⠛⡛⠋⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⡦⠒⠒⠈⠉⠉⠀⠘⠿⠿⠃⠀⠉⠉⠁⠒⠒⢴⣾⣷⡆⠀⠀⠀⠀⠀⠀⠈⠙⠛⠑⢦⡀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⠀⠀⠈⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⠜⠀⠀⠀⠀⠀⠀⣀⡔⠁⠀⠀⠀⠀⢀⣶⣦⡜⠁⠀⠀⠀⠀⠀⠀⠀⢀⣐⠤⠓⠉⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠟⠋⠒⠴⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣾⣾⣦⠀⠀⠀⠀⠀⠈⡂⠂⠀⠀⠀⠀⠀⠐⢂⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⣠⠊⠀⠀⠀⠀⠀⠀⣘⢿⡿⠇⠀⠀⠀⠀⣂⣂⣢⠜⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣂⣢⣀⠀⠀⠀⠀⠻⠿⠟⡀⠀⠀⠀⠀⠀⠀⠑⡀⠀⠀⠀⠀⠀⠀⠥⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⢠⣷⣷⡅⠀⠀⠀⠀⠀⠠⡰⠃⠀⠀⠀⠀⠀⢀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢀⠀⣄⡄⠤⠕⠒⠓⠺⣿⣿⠗⠓⠚⠨⠤⢄⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠇⠀⠀⠀⠀⠀⠀⠘⢄⢀⠀⠀⠀⠀⠀⢨⣶⣷⡅⠀⠀⠀⠀⠱⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠘⡿⠿⠃⠀⠀⠀⣲⣾⣾⡀⠀⠀⠀⠀⠀⠀⡰⠋⠈⠉⠀⠀⠀⠀⠀⠀⣠⠔⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠉⠒⠤⣠⠀⠀⠀⠀⠀⠁⠉⠁⠙⢄⢀⠀⠀⠀⠀⠀⢲⣿⣿⡆⠀⠀⠀⠘⠿⢿⠃⠀⠀⠀⠀⠀⠱⠀⠀⠀⠀⠀
⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠐⡜⠈⠀⠀⠀⠀⠀⢹⠿⠟⠀⠀⠀⠀⠠⣠⠊⠀⠀⠀⠀⠀⢄⠄⣐⠜⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⡄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣀⢀⠀⠀⠀⠀⠀⠈⠑⡠⠀⠀⠀⠀⠈⠛⢛⡁⠀⠀⠀⠀⠀⠀⣂⠀⠀⠀⠀⠀⠈⢣⠀⠀⠀⠀
⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⡲⠁⠀⠀⠀⠀⠀⢢⠃⠀⠀⠀⠀⣐⣤⣔⠁⠀⠀⠀⠀⠀⢽⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⣀⠦⢼⣿⣿⡦⠆⣂⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠈⣂⣦⡂⠀⠀⠀⠀⠐⡂⠀⠀⠀⠀⠀⠈⠆⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀
⠀⠀⢠⠃⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⣬⣾⣇⠀⠀⠀⠀⠀⢿⣿⣿⠀⠀⠀⠀⠀⣀⠞⠛⠋⠀⠀⠀⠀⠀⠠⡠⠕⠊⠉⠀⠀⠀⠈⠙⠋⠀⠀⠀⠀⠉⠐⠣⣄⠄⠀⠀⠀⠀⠈⠙⠛⠣⡀⠀⠀⠀⠀⠀⣿⣿⡿⠀⠀⠀⠀⢀⣶⣿⣦⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠘⡄⠀⠀
⠀⠀⡌⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢿⢿⠟⠀⠀⠀⠀⡀⡎⠉⠀⠀⠀⠀⠀⡠⠃⠀⠀⠀⠀⠀⠀⢠⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⡀⠀⠀⠀⠀⠀⠀⠒⢄⠀⠀⠀⠀⠀⠉⢣⢀⠀⠀⠀⠀⠻⠿⢋⠀⠀⠀⠀⠀⢥⠀⠀⠀⠀⠀⠀⣁⠀⠀
⠀⢰⠑⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠠⡰⠁⠀⠀⠀⠀⠀⠀⡖⠁⠀⠀⠀⠀⠀⠀⠀⠀⢄⣄⡠⠠⡀⢄⠄⠀⠀⠀⠀⠀⠀⠀⠈⢢⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠐⢂⠀⠀⠀⠀⠀⠐⡆⠀⠀⠀⠀⠀⠘⡀⠀
⠀⡘⠀⠀⠀⠀⢠⣷⢷⡄⠀⠀⠀⢰⣤⣇⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⢲⠁⠀⠀⠀⠀⠀⣐⠎⠀⠀⠀⠀⠀⠀⢀⣠⣷⣯⠪⣩⣁⡷⢖⡊⢻⣗⠐⡀⠀⠀⠀⠀⠀⠀⠅⡂⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠈⡂⠀⠀⠀⠀⢀⣸⣴⡀⠀⠀⠀⣐⣴⡶⡄⠀⠀⠀⠀⠃⠀
⠀⡇⠀⠀⠀⠀⠘⢿⠿⠃⠀⠀⠀⢻⣿⡿⠀⠀⠀⢠⣬⣦⡠⠀⠀⠀⠀⢄⠇⠀⠀⠀⠀⠀⢠⠒⠀⠀⠀⠀⠀⢀⣵⣣⣎⣽⡣⢹⣿⡟⠄⣸⣿⣏⠉⠁⢠⣡⣄⠀⠀⠀⠀⠐⠰⠀⠀⠀⠀⠀⠀⠸⢀⠀⠀⠀⠀⣀⣥⣥⡀⠀⠀⠀⣿⣷⡿⠀⠀⠀⠘⠿⡿⠃⠀⠀⠀⠀⢸⠀
⢀⠃⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠸⣿⣿⠇⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⣈⢞⢟⠻⣻⣿⣵⣴⡥⠘⠄⠌⡉⠀⢰⣧⠙⠛⠛⠐⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠸⣿⣿⠇⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠁⡇⠀⠀⠀⠀⠀⠸⠀
⢸⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⣾⣗⢵⣷⢊⢃⠊⢟⠑⡀⠹⣷⣲⠀⠀⠉⠰⣴⢈⡾⠀⠀⠀⠀⠀⠨⡀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠠⡇⠀⠀⠀⠀⠀⢺⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⡇
⢸⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢱⣿⣿⡆⠀⠀⠀⠀⢺⠀⠀⠀⠀⢲⣿⣿⡆⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢰⣏⣿⣿⣏⠢⣿⣿⢆⠂⣪⡐⡘⠑⠄⢜⣶⢼⠋⠳⢣⣔⠀⠀⠀⠀⠀⡇⠀⠀⠀⠐⣴⣿⣷⡀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢨⣾⣷⡆⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⡇
⢸⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠈⢛⠛⠁⠀⠀⠀⠀⣸⠀⠀⠀⠀⠈⠛⡟⠁⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠸⣺⣌⣏⢫⣈⣺⣿⠔⣴⡿⣿⡐⣰⣦⡎⡉⣿⣾⡎⠌⠩⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠙⢻⠛⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠨⢻⠛⠃⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⡇
⠸⠀⠀⠀⠀⠀⠀⢤⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢀⣸⣄⡀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⢿⣿⢿⣿⣿⢋⠂⠅⠲⠨⠠⢐⢈⢸⡐⡄⢌⢉⢷⣷⠇⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⡀⣠⣇⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢀⠃
⠀⡆⠀⠀⠀⠀⠀⣼⡠⠀⠀⠀⠀⢠⣷⣄⠄⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠘⢿⣵⣯⣪⣦⣥⢡⡨⢤⣼⡔⠄⢥⢀⡢⡑⢕⣴⠔⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠠⠇⠀⠀⠀⠀⢸⣿⣿⠇⠀⠀⠠⣀⣺⡀⠀⠀⠀⠀⣄⣇⠀⠀⠀⠀⠀⢸⠀
⠀⡇⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⢿⣿⡿⠀⠀⠀⠀⠈⢣⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠈⢻⣿⣟⢿⢿⣏⣎⣿⣿⣿⣙⡿⢿⣿⡎⡜⠋⠀⠀⠀⠀⠠⡜⠀⠀⠀⠀⠀⠐⣘⠀⠀⠀⠀⠀⠀⡝⠁⠀⠀⠀⠐⣿⣿⡿⠀⠀⠀⢱⣿⣿⡇⠀⠀⠀⠀⠸⠀
⠀⢰⠀⠀⠀⠀⠀⠉⠋⠄⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⢣⢀⠀⠀⠀⠀⠀⠉⠻⠿⣿⣿⣷⡵⠽⣿⣷⣚⢪⠿⠋⠀⠀⠀⠀⠀⢄⠜⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⢢⠃⠀⠀⠀⠀⠀⢸⠉⠀⠀⠀⠀⠐⡙⠉⠀⠀⠀⠀⠀⡇⠀
⠀⠈⡄⠀⠀⠀⠀⠀⠹⡀⠀⠀⠀⠀⠀⠸⡀⡀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠘⢄⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠐⠈⠉⠉⠓⠈⠉⠁⠀⠀⠀⠀⠀⠀⢠⠔⠃⠀⠀⠀⠀⠀⢀⡰⠁⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⣀⣌⡆⠀⠀⠀⠀⠀⢈⠇⠀⠀⠀⠀⠀⢱⠁⠀
⠀⠀⢱⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⣾⣿⣷⠀⠀⠀⠀⠀⣱⣤⣄⠄⠀⠀⠀⢈⢢⢀⠀⠀⠀⠀⠀⠀⠈⠢⢆⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡰⠔⠁⠀⠀⠀⠀⢀⠀⠀⡖⠁⠀⠀⠀⠠⣠⣤⣎⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⡎⠀⠀
⠀⠀⠈⡆⠄⠀⠀⠀⠀⠈⡄⠄⠀⠀⠀⠙⠛⢏⠀⠀⠀⠀⠀⢿⣿⡿⠀⠀⠀⠀⠀⠀⣱⣾⣶⡀⠀⠀⠀⠀⠀⠀⠉⠒⠢⠆⣄⣄⣠⣶⣶⣄⣄⣠⠰⠔⠒⠉⠀⠀⠀⠀⠀⠀⢰⣶⣶⡎⠀⠀⠀⠀⠀⠐⢿⣿⡿⠀⠀⠀⠀⢀⡸⠉⠁⠀⠀⠀⢀⠰⠁⠀⠀⠀⠀⠠⡸⠀⠀⠀
⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠈⢂⠀⠀⠀⠀⠀⠀⠘⢔⠀⠀⠀⠀⠀⠙⠿⠟⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡸⠿⠿⠃⠀⠀⠀⠀⠀⡬⠃⠀⠀⠀⠀⢀⠐⡔⠁⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀
⠀⠀⠀⠀⠡⠄⠀⠀⠀⠀⠀⢘⣠⡀⡀⠀⠀⠀⢤⣿⣶⡅⠀⠀⠀⠀⠀⠳⣀⠀⠀⠀⠀⠀⠀⠀⠉⠪⢄⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⡠⠜⠉⠀⠀⠀⠀⠀⠀⠀⣀⠟⠀⠀⠀⠀⠀⢨⣿⣿⣧⠀⠀⠀⠀⣀⣤⠃⠁⠀⠀⠀⠀⢀⠏⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⢰⣿⣿⡆⠀⠀⠀⠘⠻⠟⡃⠀⠀⠀⠀⠀⠀⠈⢢⣬⣴⡠⠀⠀⠀⠀⠀⠁⠈⠒⠢⠤⣀⠄⡀⡀⡀⣀⣤⣄⠄⡀⡀⡀⠠⣀⠤⠖⠒⠁⠀⠀⠀⠀⠀⠀⢄⣦⣦⡖⠁⠀⠀⠀⠀⠀⠀⢤⠛⠛⠁⠀⠀⠀⢸⣿⣿⡆⠀⠀⠀⠀⠐⡜⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠣⠠⠀⠀⠀⠀⠙⠉⢆⠀⠀⠀⠀⠀⠈⠈⢢⡀⠠⠀⠀⠀⠀⠸⣿⣿⢇⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠒⢺⣿⣿⠗⠂⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡸⣿⣿⠃⠀⠀⠀⠠⣠⣀⡖⠁⠀⠀⠀⠀⠀⠀⡸⠙⠋⠀⠀⠀⠀⢄⠝⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠱⠀⠀⠀⠀⠀⠀⠈⠢⡂⠀⠀⠀⠀⠀⠀⣿⣿⣷⠁⠀⠀⠀⠀⠀⠀⠩⠲⢄⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠉⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡆⠀⠀⠀⠀⠀⢐⠜⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠑⡁⠀⠀⠀⠀⠀⠀⠙⢄⠀⠀⠀⠀⠀⠙⠛⠑⠦⡀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠑⢺⣿⣿⡆⡀⠀⠀⠀⠀⠀⢀⢀⢀⠀⠀⠀⠀⠀⠀⡀⣸⣿⣷⡔⠋⠁⠂⠀⠀⠀⠀⢀⢀⠀⣀⠜⠊⠉⠉⠀⠀⠀⠀⢀⡠⠃⠀⠀⠀⠀⠀⠀⢬⠊⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄⠀⠀⠀⠀⠀⠀⠀⠱⣄⠀⠀⠀⠀⠀⠀⠀⠈⢪⣾⣾⡄⠀⠀⠀⠀⠀⠀⠈⠛⠛⠉⠉⠒⠓⠬⠤⠤⢶⣿⣿⡦⠤⠤⠑⠓⠓⠉⠙⠻⠛⠁⠀⠀⠀⠀⠀⠀⠈⣾⣿⣷⠁⠀⠀⠀⠀⠀⠀⡀⡬⠊⠀⠀⠀⠀⠀⠀⠠⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣄⠀⠀⠀⠀⠀⠀⠈⠓⣄⣤⣄⠀⠀⠀⠀⠘⠿⠟⡃⢆⡀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⠀⢀⡢⠒⠙⠛⠋⠀⠀⠀⠀⣠⣤⣠⠚⠀⠀⠀⠀⠀⠀⠀⣄⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡂⠀⠀⠀⠀⠀⠀⢿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢱⣿⣿⣇⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⢀⣢⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣿⡿⠀⠀⠀⠀⠀⠀⣀⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡂⠀⠀⠀⠀⠀⠉⠀⠈⠲⢄⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠁⠉⠑⠓⢺⣿⣿⣆⣀⣀⡀⢠⣾⣶⡄⢀⣀⣀⣌⣾⣿⣿⠚⠊⠉⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⡀⡢⠖⠁⠀⠉⠀⠀⠀⠀⠀⣐⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠪⣀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠚⢄⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠁⠀⠀⠀⠘⠿⠿⠃⠀⠀⠀⠐⠈⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⡨⠒⠉⠀⠀⠀⠀⠀⠀⠀⡀⢠⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢄⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⠦⣴⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣶⣤⠤⢒⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⡿⠟⠒⠤⠦⣠⣀⠄⠀⠀⠀⠀⠀⠠⣠⣄⠀⠀⠀⠀⠀⠀⢄⣠⣠⠴⠔⠒⠻⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡠⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠒⠒⢻⣿⣿⡗⠚⠚⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠦⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠓⠤⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣄⠤⠓⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠤⢄⣄⡄⡀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⢀⣀⠤⠤⠒⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⠐⠒⠂⠢⠦⠦⠴⠤⠤⠤⠤⠴⠴⠴⠄⠒⠒⠒⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
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