⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⠄⠐⠒⠒⠠⠤⢄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠂⠉⠀⢀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠈⠑⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠊⠀⣀⠤⠒⠈⠉⠐⢤⣐⢤⣈⣍⣅⢒⣤⣄⡀⠀⠈⠪⡑⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⡠⠊⠁⠠⡪⣢⣶⡳⡝⣾⡷⠽⠿⠷⠿⠭⣿⣾⡦⣄⠀⠈⢢⠀⠑⢄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠁⡠⠊⠀⠀⠀⠛⢾⣯⠽⠃⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠚⠷⡀⠀⠱⡀⠀⠑⢄⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⢀⣔⣤⢆⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠹⡀⠀⠈⢢⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⢀⢮⣾⡳⠃⠀⢠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⢡⠀⠀⠀⢣⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠮⢠⣎⠚⠃⠁⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠈⡆⠀⠀⠈⡇⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡬⢤⡎⠀⠈⠓⠢⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢣⠀⠀⠀⠸⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⣔⠀⠉⠒⠢⢴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⣀⣸⣀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⣠⣴⣦⣄⡀⠀⠀⠀⠀⠀⠀⠰⠁⠌⡔⠻⠷⣶⣤⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡎⠀⠉⠒⠤⡇
⠀⠀⢀⣀⣀⠀⡾⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢠⠃⡸⡘⠀⠀⠀⣶⡍⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠉⡏⠑⠢⢄⣀⠁
⠀⡼⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⠀⠀⠀⠀⠀⠘⣴⢱⠁⠀⠀⢠⠕⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⡇⢠⠇⠀⠀⣠⣾⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⣁⠇⢀⣠⣔⣶⡿⠟⠙⠒⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢀⠃⢸⠀⠀⠀⣿⡽⠀
⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⢠⣛⠔⠽⢟⠟⠁⠀⠀⠀⠀⠀⠀⠉⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⡏⢸⢀⡸⣄⠀⠀⠘⡇⠀
⠀⠀⠀⠀⠈⠉⠉⠛⠻⣿⠀⠀⠀⠀⠀⠀⢠⡿⠋⠀⢠⠊⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠙⡄⠀⠀⠀⢀⠔⠂⠉⠁⢠⣰⣤⣴⣿⣶⣄⢠⢃⠜⣿⡿⣶⣵⣧⢤⠇⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣽⠃⠀⢀⠃⠀⠀⠀⠀⡴⣽⣽⣻⣦⡀⠀⠀⠘⡀⡠⠊⠁⠀⠀⠀⠈⢺⣙⣿⣯⣿⣿⣿⠝⣁⡄⠁⠜⠑⠞⢭⠃⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⡄⠀⠀⢨⠀⠀⠀⠀⠸⢸⡿⣗⡿⡫⢿⡄⠀⢀⠞⠀⠀⠀⠀⠀⡠⢂⠥⣚⣩⣽⡿⠋⠁⠠⠛⠁⠀⠀⠀⢠⠃⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠁⠀⠀⢸⠀⠀⠀⠀⠄⠀⠨⣗⡞⣏⣿⣧⢠⠁⠀⠀⠀⠀⠀⡠⢎⣥⣴⣿⠟⠁⠀⢀⣀⣒⣤⢦⣄⠀⢀⠃⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⢸⠀⠀⠀⠀⢰⠀⠀⠙⠀⣴⣯⣿⠁⠀⠀⠀⠀⢀⡜⠁⣨⡿⠋⢀⡠⠔⠈⠁⠀⠀⠀⠉⢿⠇⡜⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠇⠀⠀⠀⢃⠀⠀⠀⠘⡄⠀⠀⠀⠑⢻⠃⠀⠀⠀⠀⢀⠎⣠⡪⠋⢀⣴⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣶⡀⠀⠀⠈⣆⠀⠀⠀⠘⢄⡀⠀⠀⡘⠀⠀⠀⠀⠀⠊⡰⡝⠀⣰⡿⠉⠀⠀⢠⠒⢄⣀⠀⠀⠀⢠⢸⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡀⠀⠀⠈⢆⠀⠀⠀⠀⠈⠑⣪⡇⠀⠀⠀⠀⡜⢰⠝⠀⡼⡟⠁⠀⠀⠀⢨⣖⢷⠴⡁⠀⠀⡇⡎⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢻⣦⡀⠀⠀⢱⢄⠀⠀⠀⣰⣿⠇⠀⠀⠀⠀⣇⣦⠃⢸⠐⠀⠀⠀⠀⠀⠓⠚⠉⠒⠂⠀⡜⡔⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠙⠻⢦⣈⠙⡿⡷⣤⣄⣬⠽⣼⠀⠀⠀⠀⣿⢿⠀⡜⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢎⠜⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠈⠉⠒⠛⠛⠛⠊⠁⠀⠣⠀⠀⠀⢘⣿⡄⢱⢠⠀⠀⠀⠀⠀⠀⠀⢀⠔⡡⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣘⠻⣛⢷⡀⠣⣷⢄⡀⠀⣀⠤⢒⠕⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠑⠤⣀⣉⡉⠩⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀