⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⣀⠀⠀⠀⠀⠀⠀⢨⠀⠄⠒⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢄⢐⠐⢄⠉⠣⣂⡀⠈⠠⠀⠒⡠⠐⠠⢈⢏⢀⣀⠴⠁⠒⠐⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢐⡐⡄⠆⠱⠀⠋⢀⠀⠄⠑⠐⠀⠀⠀⢘⡡⢼⡲⠂⠃⠁⠀⠀⠈⢋⠄⠨⢘⠆⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⢠⡀⡂⠑⡀⣀⠆⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠚⡹⡐⡈⠀⠀⠠⠄⠠⢀⠁⡈⢀⠈⠀⢀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠒⢁⠂⢀⢒⠄⠊⠀⠀⠄⠈⠀⠀⠀⠀⠀⠀⡠⠀⠀⠢⠀⠀⠀⢁⠀⡃⠀⠀⠀⠀⢈⠀⠢⠀⠀⢓⡑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⡒⠅⠕⠁⠀⢀⠀⠀⢀⠔⠀⠀⠀⠀⠀⢀⠀⠀⠀⠆⠀⠀⢐⠀⢂⠆⠀⠀⠀⠀⠀⢢⠑⡁⠀⠀⠲⠊⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢔⠠⢂⠂⠀⡀⡁⠂⠐⢁⠁⢀⠠⡀⠒⢀⢔⠢⠀⠀⠀⠃⠀⠨⠀⠀⢂⠀⠀⠀⠀⠁⣰⡈⠈⢂⡀⠀⢃⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⠢⠃⠀⢀⡐⠀⠀⠊⠀⠄⡢⠐⠀⡠⠁⠀⠀⢀⠃⠀⠀⠡⠈⠠⡀⠀⠀⢂⠀⠀⠀⠀⠐⢴⠁⡄⡄⠀⠀⢖⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣈⠁⠀⢀⠒⠀⠠⠁⠀⢠⠚⠀⢀⠌⠀⠀⠀⠀⠈⠐⠀⠀⢀⢃⠀⠊⢁⠀⠀⢂⠀⠀⠄⠀⠈⡆⢣⠠⠀⠀⢀⠢⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⢆⠄⠀⠀⠄⢠⠠⠁⠀⠀⢸⢀⢐⠂⠀⠀⠀⠀⠀⠈⠠⠠⠐⠁⠀⠄⠀⡘⠀⠄⡀⡊⣐⠀⠀⠰⠀⠀⠐⠀⠀⢰⠀⠊⢀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⢺⢀⠀⠀⢐⠐⠔⠁⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡂⠀⠐⣀⠁⠀⠀⠀⢸⢸⠀⠠⡁⢠⢄⠀⠀⠀⢸⡀⠆⠀⢠⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠂⢐⠅⠀⠀⠰⠁⠰⠀⠀⠀⠀⠀⠀⠈⡡⠀⠀⠄⠀⠀⡀⢀⢑⠀⡄⠘⠀⠠⠀⠀⠀⠀⣰⠆⠘⢤⡊⠁⢉⡂⢀⠀⡴⡅⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠈⠀⢘⠖⠀⡀⠰⠀⠄⡁⠰⠀⠀⠀⠀⠠⠰⢂⢄⠐⠀⠰⢐⠄⠐⢀⣈⣄⢄⣈⢄⡀⠀⠀⠸⡇⡁⢮⠄⡀⣈⠇⠄⠠⠸⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡇⢐⠀⠨⠠⠀⢃⠄⠐⢄⠠⣤⢶⠪⡭⠏⠒⡅⠁⠸⣸⠀⠌⠪⡽⣽⡿⣿⠿⠯⡣⡬⢧⡙⠄⡑⡐⠍⡌⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢂⠀⠂⠀⢂⠠⠀⢲⠞⢿⣝⣹⡾⣻⡀⠀⠘⠈⠀⡸⡎⠀⠀⠙⣿⣻⣟⢗⠂⢠⢑⡽⣧⠔⠊⢣⢒⠄⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⡀⠀⠄⠀⠈⠡⡸⣵⢯⣛⠺⠄⠀⠀⠀⠀⠉⠀⠀⠀⠀⠻⡼⠽⠃⠀⠀⢼⠌⣘⠐⡩⢂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠸⠀⠠⠂⢟⡀⠋⠙⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⢿⡀⠞⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⠈⠑⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⡠⢴⣵⡿⣟⡐⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠘⠔⠀⠀⠀⠀⠀⡠⡤⡤⡖⢓⡿⡺⡱⠺⠹⠡⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⢀⠀⢿⡇⠋⠁⠀⠀⠀⢳⣀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠙⠁⠀⠀⠀⠀⠀⠀⠙⡥⣎⡄⣁⣦⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⡠⣂⣶⡖⠄⠀⠀⠀⠀⠀⠀⣄⠮⠍⡊⠉⠚⢞⣯⢑⣢⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣰⡴⡯⡻⢌⢻⣹⢄⠄⠄⠀⡀⢔⢎⠔⠂⡈⠄⠀⢈⠌⢻⣷⡢⣓⡕⠀⠄⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢂⣵⡾⡏⡏⠘⢊⢠⡓⠘⣔⡄⠀⣄⠦⠊⠓⠀⠐⠐⠀⠀⡠⠀⡦⢵⣿⣻⠌⠠⠊⠀⡀⡀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⣯⣾⡋⣊⡠⠃⡐⢰⠀⠀⠒⠌⡛⡂⠀⠰⠁⠀⠡⠁⠀⠀⡑⢈⠐⣙⢹⡯⣟⢷⢥⢱⠌⡀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣱⠾⡻⣅⠇⠎⠀⡔⢰⠌⠀⠠⡁⠰⠀⠀⢀⠃⠀⠘⢁⠀⠀⢰⠈⡰⣉⣆⠌⣷⠹⣷⢳⡳⣅⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⣰⣯⣾⢱⢉⠓⡜⠀⠜⠔⢀⠅⢀⠅⠀⠦⠁⠠⠂⠀⠔⠀⠄⢁⢠⠲⣜⡫⣃⠨⠰⡅⢜⡿⡿⡃⡇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢽⢞⡯⡃⡣⢌⡙⠆⠌⠴⠈⠀⠈⠑⠀⠠⡁⠐⠁⠀⠀⠀⠢⠀⠠⢎⡑⣧⠣⣉⢣⢢⡂⢸⠐⣿⠷⢘⠀⠂⠀⠀⠀