⠰⠱⡀⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⢹⢆⣼⡆⠀⠀
⠀⠳⠻⣆⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣀⣒⣐⡦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⡞⣎⢹⠀⠀
⠀⠀⠱⡌⠢⡘⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣔⡮⠓⠋⠁⠀⠀⣠⢿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⢿⠘⣆⠀
⠀⠀⠀⠈⠢⡑⢌⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢾⡞⠁⠀⢀⣀⡤⣔⠯⠛⣁⣀⣤⣄⣀⠀⠀⠀⠀⠀⠀⢸⡇⠇⡘⡇⢸⡄
⠀⠀⠀⠀⠀⠈⡦⠅⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠯⠭⠝⠛⠊⣉⣤⣾⣿⣶⡦⣤⣀⣩⡮⠆⠀⠀⠀⠀⢸⢃⠀⠃⡇⡼⡇
⠀⠀⠀⠀⠀⠀⠈⠢⡀⠘⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⣄⣼⣏⣽⠯⠭⠍⡙⢽⡺⣷⡄⣳⠀⢀⠀⠀⣎⠆⠀⠀⠀⡠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡂⠀⠑⠢⢄⠀⠀⠀⠀⠀⠀⣺⠀⣰⣿⠉⣿⡉⢷⣄⠀⠈⠑⢕⢜⣒⢎⣀⢼⡆⠀⠏⢀⢠⠀⢰⠁⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡶⠆⠤⣀⠙⠢⣄⢀⠀⠀⠉⢳⣿⣧⡼⡇⠙⠒⠩⠿⣲⣂⣀⣉⣛⣂⣘⣿⡄⡘⣠⠃⣞⠠⠃⡰⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠙⠳⣄⠀⢸⡿⣧⡣⣷⡀⢀⣰⠀⠀⢠⠒⠋⡋⡆⣵⣭⢧⡱⠁⠜⡹⠀⠀⢠⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢽⣧⣀⠀⢀⣀⡈⠛⢳⢢⣾⣧⢃⠢⢤⡤⢮⣤⡤⡴⣱⡴⢛⣻⡶⢭⠋⡇⠀⡴⢱⠀⣰⢃⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠛⠚⠱⢄⠀⠉⠑⠪⠿⣿⣦⡀⢯⣑⡒⢚⡪⢷⣢⠶⢃⡤⠊⣠⠧⠀⠠⢧⠀⢱⠋⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠤⣀⠙⠍⣒⠤⠄⠀⠈⠻⣼⣢⣬⣧⣶⠤⡿⡗⠐⠓⠉⠴⡋⠘⠀⣠⡣⢔⢷⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣍⠙⢅⠀⠀⠀⣀⣀⡀⠻⡋⢙⢭⠂⠀⠈⠒⠄⢐⡟⠢⠔⠈⠔⠁⣡⠊⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠊⣭⠜⠢⣥⣀⣀⣘⣳⡅⡇⠀⢰⠀⠀⠠⡚⣔⢊⣠⡪⠾⠁⡀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠺⣀⡤⣤⠉⡷⡀⢠⡇⠀⣱⠛⠤⣁⠜⣠⠤⠚⠁⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢱⠒⠟⠦⠴⣇⡴⢞⣷⡸⡷⢀⡴⢂⠢⢼⢢⡨⠇⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠘⣄⡠⠔⡇⢷⡸⢹⢳⠁⣴⢱⠀⢣⠈⡏⠁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⡘⣇⣰⣧⢸⠆⡜⡇⣠⢧⡀⡗⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⣾⠇⡇⢸⢸⢸⢘⡇⣟⠃⠸⠙⠁⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠁⠀⡇⠀⢾⡆⠈⠪⡇⠀⣾⡄⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⢱⠀⠀⠱⠀⢸⠁⡄⠀⡃⠀⣟⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣖⠁⠀⠀⢣⡀⠀⢇⠀⠀⢡⠀⡇⠸⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀