⠀⠾⡢⣄⡣⣴⣶⠴⢗⣶⣦⡶⠤⠀⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡄⠴⣤⣤⣶⢦⡤⣤⣤⢀⣤⣶⠀
⠀⠸⣵⢛⢻⣿⣶⠛⣶⠏⡀⢱⠂⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢺⡶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡔⠀⠙⣧⠺⢧⡿⡜⡛⢞⡌⠀
⠀⢠⡷⠀⠈⣿⠁⠁⡼⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢸⡏⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠐⢛⠀⠉⣛⠑⠀⢼⣇⠀
⠀⢺⡇⣰⠶⢍⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠘⠀⠀⢸⣶⣆⠸⡅⠀
⠀⢸⡟⡏⠘⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠐⡢⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⣄⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡇⠖⢹⢯⡇⠀
⠀⢸⠁⠇⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⢔⣳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣻⡌⢳⣤⣤⡁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢸⠈⡇⠀
⠀⠃⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⣠⡼⣿⣟⣽⣿⢾⣽⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⢹⣿⣿⣆⢻⣏⠻⠷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠁⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⡶⠋⢀⣿⣿⣿⣟⢙⢿⣆⠀⠀⠀⠀⠊⢠⣀⡆⠀⠀⠀⣾⣟⢚⣽⣦⠸⠂⠀⠀⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⠀⠀⠀⢢⣿⡟⡿⡅⠠⣻⣯⣤⠀⠀⠀⣤⠃⢳⢧⠀⠀⣼⣿⣧⡇⣻⣻⡄⠃⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀
⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⢀⢀⣶⣿⢄⠲⠁⢺⢻⣷⣻⣿⡷⢞⠻⡓⠙⠾⠾⢿⣿⣿⣿⢻⣀⣋⢁⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⣎⠋⠁⡟⣠⠉⣾⠷⢿⣻⣿⡇⡀⠀⠀⠀⠀⡄⢸⣿⣿⡿⡌⠙⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠀
⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡏⣦⣃⠄⠀⠀⠏⠰⠀⡏⢿⠇⢿⠂⠀⠀⢸⡇⢸⠻⠈⠀⠁⠀⠀⠀⠀⠄⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀
⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⢝⣷⡖⠀⠀⠀⠀⠀⠀⢌⢀⣿⠄⠀⠀⣸⡿⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀
⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⡎⢗⠀⠀⡐⡶⠄⠀⠠⣼⣏⠠⠀⠀⠹⠐⠈⢋⠀⠀⠀⠀⠂⠀⡃⠄⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀
⠀⠀⠀⠀⢨⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢵⠈⢗⠤⠌⣆⠀⠀⢠⡿⢿⣧⣿⡠⣢⣧⡀⠸⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡲⠂⠀⠀⠀
⠀⠀⠀⢀⠺⣰⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠭⢺⣤⣫⣶⣴⠃⠑⡄⠸⣧⠌⣽⣿⡝⣳⣻⣿⡆⡆⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡢⢭⠔⡄⠀⠀
⠀⠠⠀⠃⡙⣿⠁⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⢠⢨⡘⡈⠉⠻⣶⡜⠁⠘⣿⠚⡏⢹⣧⠍⢻⡟⡅⠙⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠈⢠⣩⡄⠀⠐⠀
⠀⠀⠀⠀⢪⣊⠂⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡇⠑⠠⠀⠙⡆⠀⢨⣿⡸⠁⠈⠑⠉⠺⣇⣜⠍⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠚⢿⠓⠀⠘⠀
⠀⠀⠀⡔⠮⠗⢢⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⢁⠀⠀⠀⠀⠸⣆⢟⣿⣧⠀⠀⠀⠀⡜⡿⢄⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠨⠛⠔⡬⠀⠀
⠀⠀⠀⠉⢢⡆⠉⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠈⠀⠀⠀⠀⠀⢼⣦⣸⣿⡇⠀⠀⠀⣷⡁⢋⠢⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠈⠐⣦⠂⠁⡆⠀
⠀⠀⠐⠦⠦⡷⠤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢻⣆⢿⡇⡀⢆⣀⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠴⣷⠦⠒⠀⠀
⠀⠀⢀⡄⣸⣏⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠹⢿⣷⣠⠸⣿⣿⣿⡡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢀⣭⡀⣄⠀⠀
⠀⠀⠀⣧⢿⡻⣦⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢸⣿⡾⠨⣿⣻⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡼⣻⢧⡆⠀⠀
⠀⢀⠈⣛⣿⢿⠟⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⢀⣿⣿⣇⡄⣿⣿⣿⣽⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢯⢹⡝⠋⠀⠀
⠀⠀⠀⠂⢸⠇⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣊⣁⣀⣀⡀⠀⢀⣾⣿⣽⣿⡗⣿⣿⣿⠺⣜⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠄⠀⠯⠀⡀⠀⠀
⠀⠆⠀⣠⣺⣖⣄⡂⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢉⢩⣭⣿⠇⣠⣾⣿⣿⣿⣿⡿⢻⣿⣿⡇⠽⣷⢝⡷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⢀⡔⠷⣠⡇⠀⠀
⠀⠀⠘⣝⣟⣩⣪⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣷⡯⣵⠿⣿⠿⣻⣿⣿⣿⣼⡾⡝⠟⡱⡆⢫⡛⢽⡿⢿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢝⣯⡌⣝⠝⠀⠀
⠀⠀⠠⠼⣟⣿⠇⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢿⢿⣶⣯⣿⣻⣶⠿⣻⣿⣿⣷⣷⣬⣞⣑⣄⣙⡓⠿⡿⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠬⣷⣿⠿⢄⠀⠀
⠀⠀⠀⣰⣏⣸⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠙⠈⠉⠍⠗⢓⣚⠲⠚⠋⠉⠁⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣩⣨⣴⠀⠀⠀
⠀⠀⠀⢀⣸⣁⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠈⢀⣅⠈⠀⠀⠀