⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠤⠤⠴⢶⣶⡶⠶⠤⠤⢤⣀⡀⠀⠀⠂⠀⠀⠠⠀⠀⠀⠀⠀⠀⢀⣠⣾⠁
⠀⠻⣯⡗⢶⣶⣶⣶⣶⢶⣤⣄⣀⣀⡤⠒⠋⠁⠀⠀⠀⠀⠚⢯⠟⠂⠀⠀⠀⠀⠉⠙⠲⣤⣠⡴⠖⣶⣶⡲⣶⣿⡟⢩⡴⠃⠀
⠀⠀⠈⠻⠾⣿⣿⣬⣿⣾⡏⢹⣏⠉⠢⣄⣀⣀⠤⠔⠒⠊⠉⠉⠉⠉⠑⠒⠀⠤⣀⡠⠚⠉⣹⣧⣝⣿⣿⣷⠿⠿⠛⠉⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠈⣹⠟⠛⠿⣿⣤⡀⣸⠿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⣇⢰⣶⣿⠟⠋⠋⠳⡄⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⡠⢾⣿⣿⣯⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁⢀⣿⣿⣯⢼⠓⢄⠂⢀⡘⣦⡀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣰⣟⣟⣿⣀⠎⠀⠀⢳⠘⣿⣷⡀⢸⣿⣶⣤⣄⣀⣤⢤⣶⣿⡇⢀⣾⣿⠋⢀⡎⠀⠀⠳⣤⢿⠿⢷⡀⠀⠀⠀⠀
⠀⠀⠀⠀⣰⠋⠀⠘⣡⠃⠀⠀⠀⠈⢇⢹⣿⣿⡾⣿⣻⣖⠛⠉⠁⣠⠏⣿⡿⣿⣿⡏⠀⡼⠀⠀⠀⠁⠘⢆⠀⠀⢹⡄⠀⠀⠀
⠀⠀⠀⢰⠇⠀⠀⣰⠃⠀⠀⣀⣀⣀⣼⢿⣿⡏⡰⠋⠉⢻⠳⣤⠞⡟⠀⠈⢣⡘⣿⡿⠶⡧⠤⠄⣀⣁⠀⠈⢆⠀⠀⢳⠀⠀⠀
⠀⠀⠀⡟⠀⠀⢠⣧⣴⣊⣩⢔⣠⠞⢁⣾⡿⢹⣷⠋⠀⣸⡞⠉⢹⣧⡀⠐⢃⢡⢹⣿⣆⠈⠢⣔⣦⣬⣽⣶⣼⣄⠀⠈⣇⠀⠀
⠀⠀⢸⠃⠀⠘⡿⢿⣿⣿⣿⣛⣳⣶⣿⡟⣵⠸⣿⢠⡾⠥⢿⡤⣼⠶⠿⡶⢺⡟⣸⢹⣿⣿⣾⣯⢭⣽⣿⠿⠛⠎⠀⠀⢹⠀⠀
⠀⠀⢸⠀⠀⠀⡇⠀⠈⠙⠻⠿⣿⣿⣿⣇⣸⣧⣿⣦⡀⠀⣘⣷⠇⠀⠄⣠⣾⣿⣯⣜⣿⣿⡾⠿⠛⠉⠀⠀⠀⢸⠀⠀⢸⡆⠀
⠀⠀⢸⠀⠀⠀⡇⠀⠀⠀⠀⣀⠼⠋⢹⣿⣿⣿⡿⣿⣿⣧⡴⠛⠀⢴⣿⢿⡟⣿⣿⣿⡿⠀⠙⠲⣬⡀⠀⠀⠀⢸⣀⠀⢸⡇⠀
⠀⠀⢸⣀⣷⣾⣇⠀⣠⠴⠋⠁⠀⠀⣿⣿⡛⣿⡇⢻⡿⢟⠁⠀⠀⢸⠿⣼⡃⣿⣿⣿⡿⣇⣁⣁⣆⣉⣓⣮⣀⣹⣿⣿⣼⠁⠀
⠀⠀⠸⡏⠙⠁⢹⠋⠉⠉⠉⠉⠉⠙⢿⣿⣅⠀⢿⡿⠦⠀⠁⠀⢰⡃⠰⠺⣿⠏⢀⣽⣿⡛⠉⢩⠉⠀⠈⠁⢈⡇⠈⠇⣼⠀⠀
⠀⠀⠀⢳⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠈⢿⣿⣷⣌⠧⡀⢲⠄⠀⠀⢴⠃⢠⢋⣴⣿⣿⠏⠀⠀⡇⠀⠀⠀⠀⡸⠀⠀⢠⠇⠀⠀
⠀⠀⠀⠈⢧⠀⠀⠈⢦⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣧⠐⠸⡄⢠⠀⢸⠀⢠⣿⣟⡿⠋⠀⠀⠀⡅⠀⠀⠀⡰⠁⠀⢀⡟⠀⠀⠀
⠀⠀⠀⠀⠈⢧⠀⠀⠀⠣⡀⠀⠀⠀⠀⠀⠀⠈⠛⢿⡇⢰⠁⠸⠄⢸⠀⣾⠟⠉⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁⠀⢀⡞⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠙⢄⠀⠀⠀⠀⠀⠀⠀⢨⡷⣜⠀⠀⠀⠘⣆⢻⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⣠⠎⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠑⠦⣀⠀⠀⠀⠀⠈⣷⣿⣦⣤⣤⣾⣿⢾⠀⠀⠀⠀⠀⣀⠴⠋⠀⠀⢀⡴⠃⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢄⡀⢸⣶⣿⡑⠂⠤⣀⡀⠱⣉⠻⣏⣹⠛⣡⠏⢀⣀⠤⠔⢺⡧⣆⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢽⡁⠀⠀⠀⠀⠈⠉⠙⣿⠿⢿⢿⠍⠉⠀⠀⠀⠀⠉⣻⡯⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠲⠤⣀⣀⡀⠀⠈⣽⡟⣼⠀⣀⣀⣠⠤⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⢻⡏⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠤⠤⠴⢶⣶⡶⠶⠤⠤⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⠁
⠀⠻⣯⡗⢶⣶⣶⣶⣶⢶⣤⣄⣀⣀⡤⠒⠋⠁⠀⠀⠀⠀⠚⢯⠟⠂⠀⠀⠀⠀⠉⠙⠲⣤⣠⡴⠖⣲⣶⡶⣶⣿⡟⢩⡴⠃⠀
⠀⠀⠈⠻⠾⣿⣿⣬⣿⣾⡏⢹⣏⠉⠢⣄⣀⣀⠤⠔⠒⠊⠉⠉⠉⠉⠑⠒⠀⠤⣀⡠⠚⠉⣹⣧⣝⣿⣿⣷⠿⠿⠛⠉⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠈⣹⠟⠛⠿⣿⣤⡀⣸⠿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⣇⢰⣶⣿⠟⠋⠉⠳⡄⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⡠⢾⣿⣿⣯⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁⢀⣿⣿⣯⢼⠓⢄⠀⢀⡘⣦⡀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣰⣟⣟⣿⣀⠎⠀⠀⢳⠘⣿⣷⡀⢸⣿⣶⣤⣄⣀⣤⢤⣶⣿⡇⢀⣾⣿⠋⢀⡎⠀⠀⠱⣤⢿⠿⢷⡀⠀⠀⠀⠀
⠀⠀⠀⠀⣰⠋⠀⠘⣡⠃⠀⠀⠀⠈⢇⢹⣿⣿⡾⣿⣻⣖⠛⠉⠁⣠⠏⣿⡿⣿⣿⡏⠀⡼⠀⠀⠀⠀⠘⢆⠀⠀⢹⡄⠀⠀⠀
⠀⠀⠀⢰⠇⠀⠀⣰⠃⠀⠀⣀⣀⣀⣼⢿⣿⡏⡰⠋⠉⢻⠳⣤⠞⡟⠀⠈⢣⡘⣿⡿⠶⡧⠤⠄⣀⣀⠀⠈⢆⠀⠀⢳⠀⠀⠀
⠀⠀⠀⡟⠀⠀⢠⣧⣴⣊⣩⢔⣠⠞⢁⣾⡿⢹⣷⠋⠀⣸⡞⠉⢹⣧⡀⠐⢃⢡⢹⣿⣆⠈⠢⣔⣦⣬⣽⣶⣼⣄⠀⠈⣇⠀⠀
⠀⠀⢸⠃⠀⠘⡿⢿⣿⣿⣿⣛⣳⣶⣿⡟⣵⠸⣿⢠⡾⠥⢿⡤⣼⠶⠿⡶⢺⡟⣸⢹⣿⣿⣾⣯⢭⣽⣿⠿⠛⠏⠀⠀⢹⠀⠀
⠀⠀⢸⠀⠀⠀⡇⠀⠈⠙⠻⠿⣿⣿⣿⣇⣸⣧⣿⣦⡀⠀⣘⣷⠇⠀⠄⣠⣾⣿⣯⣜⣿⣿⡿⠿⠛⠉⠀⠀⠀⢸⠀⠀⢸⡆⠀
⠀⠀⢸⠀⠀⠀⡇⠀⠀⠀⠀⣀⠼⠋⢹⣿⣿⣿⡿⣿⣿⣧⡴⠛⠀⢴⣿⢿⡟⣿⣿⣿⣿⠀⠙⠲⢤⡀⠀⠀⠀⢸⡀⠀⢸⡇⠀
⠀⠀⢸⣀⣷⣾⣇⠀⣠⠴⠋⠁⠀⠀⣿⣿⡛⣿⡇⢻⡿⢟⠁⠀⠀⢸⠿⣼⡃⣿⣿⣿⡿⣇⣀⣀⣀⣉⣓⣦⣀⣸⣿⣿⣼⠁⠀
⠀⠀⠸⡏⠙⠁⢹⠋⠉⠉⠉⠉⠉⠙⢿⣿⣅⠀⢿⡿⠦⠀⠁⠀⢰⡃⠰⠺⣿⠏⢀⣽⣿⡟⠉⠉⠉⠀⠈⠁⢈⡇⠈⠇⣼⠀⠀
⠀⠀⠀⢳⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠈⢿⣿⣷⣌⠧⡀⢲⠄⠀⠀⢴⠃⢠⢋⣴⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⢠⠇⠀⠀
⠀⠀⠀⠈⢧⠀⠀⠈⢦⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣧⠐⠸⡄⢠⠀⢸⠀⢠⣿⣟⡿⠋⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⢀⡟⠀⠀⠀
⠀⠀⠀⠀⠈⢧⠀⠀⠀⠣⡀⠀⠀⠀⠀⠀⠀⠈⠛⢿⡇⢰⠁⠸⠄⢸⠀⣾⠟⠉⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁⠀⢀⡞⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠙⢄⠀⠀⠀⠀⠀⠀⠀⢨⡷⣜⠀⠀⠀⠘⣆⢻⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⣠⠎⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠑⠦⣀⠀⠀⠀⠀⠈⣷⣿⣦⣤⣤⣾⣿⢾⠀⠀⠀⠀⠀⣀⠴⠋⠀⠀⢀⡴⠃⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢄⡀⢸⣶⣿⡑⠂⠤⣀⡀⠱⣉⠻⣏⣹⠛⣡⠏⢀⣀⠤⠔⢺⡧⣆⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢽⡁⠀⠀⠀⠀⠈⠉⠙⣿⠿⢿⢿⠍⠉⠀⠀⠀⠀⠉⣻⡯⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠲⠤⣀⣀⡀⠀⠈⣽⡟⣼⠀⣀⣀⣠⠤⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⢻⡏⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀