⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠀⠀⠀⠀⣠⡷⠋⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠃⠀⠀⠀⢰⠟⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⡟⠒⠦⢤⣀⠀⣀⣤⢤⡄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⢀⣆⠀⣰⠃⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⣇⣤⠴⠖⠛⠉⠙⠲⠾⣧⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢠⡏⢀⣮⠁⣰⠃⠀⠀⣰⢠⠃⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠁⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡀⠀⠀⠀⡞⠀⡼⠃⣰⠃⠀⠀⠀⣧⡎⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⢀⡟⠁⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡇⠀⡆⠇⠀⠀⣼⠇⢠⠆⢠⣯⠤⠤⣤⣼⡝⠀⠀⠀⣠⠋⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⢠⡞⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠘⡄⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⡇⠀⠇⠀⠀⢠⡇⠀⠀⢠⡏⠀⠀⠀⠀⣿⠁⠀⠀⡴⠁⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⢸⠀⡄⠀⠀⠀⠀⠀⠀⠀⠠⣇⠀⠀⢰⣰
⠀⠀⠀⢀⠀⠀⡞⣰⡟⠀⡇⠀⠀⠀⠀⣸⠀⢠⢀⡏⠀⠀⠀⠀⢠⠃⢀⡀⠞⠁⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⢠⡏⠤⠤⣄⣀⠀⠀⠀⠘⡄⠇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢦⡀⢿
⠀⠀⢀⡞⢀⡞⣴⣿⠀⠀⠇⠀⠀⠀⠀⡇⠀⡸⡼⠀⠀⠀⠀⠀⡼⢰⡿⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠉⠲⢄⠀⣇⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡹⢿
⢰⠀⣸⠀⣜⣟⡟⢹⠀⠀⢸⠀⠀⠀⢸⡿⠀⣷⣿⣦⣤⣤⣄⣀⣿⢱⡇⠀⠀⡀⠀⠀⠀⠠⠊⠀⠀⢀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢹⢸⠀⠀⠀⠀⠀⠀⠀⣀⡤⠞⠉⢀⡞
⢸⣰⡏⢰⢋⡟⠀⠺⡄⠀⢸⡄⠀⠀⢸⠓⢰⡞⠉⠉⠙⠛⠛⢿⣆⣴⠃⠀⢰⠃⠀⠀⠀⠀⠀⢀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡏⣇⠀⠀⠀⠀⠀⢸⣍⠀⠀⢀⣼⠀
⢸⣿⠁⣾⡏⠀⠀⠀⣇⠀⢨⢣⡆⠀⢸⠀⠀⠁⠀⠀⠀⠀⠀⢸⠈⣿⡆⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠊⠉⠙⠒⠆⠀⠀⠀⠀⢸⣹⢀⠀⡄⠀⠀⠀⢹⣆⣠⢿⡇⠀
⢸⡇⢠⣿⠀⠀⡇⠀⢻⡀⠸⡆⢿⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠙⠳⣀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⢤⣶⣶⣾⣶⣦⣄⡀⠀⠀⠀⠀⣷⠇⠀⡇⠀⠀⠀⡘⢼⡏⡞⠀⠀
⢸⠇⣼⣿⡄⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣦⡄⠀⠀⣿⠁⢰⠁⠀⠀⢠⠇⢰⢛⡇⠀⠀
⢸⣸⣿⣿⣿⣄⠸⣄⡀⡏⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣷⣤⠀⣿⠀⡼⠂⠀⠀⢸⡀⢸⢸⠁⠀⠀
⠀⣿⣿⣿⣿⣿⣦⡈⠒⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁⣿⢰⡇⠀⠀⠀⣿⠇⢸⣿⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣷⣤⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⠁⠀⠀⣾⣷⡄⡞⡏⠀⠀⠀
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠊⠀⠀⠀⡏⢹⠀⡇⡇⠀⠀⠀
⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⢀⣾⠃⠈⣴⡇⡇⠀⠀⠀
⢳⡀⢸⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣴⣶⡶⣶⣦⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣧⠀⢸⣏⡤⠞⠟⠀⣇⠀⠀⠠
⠀⢣⢸⢹⣿⣿⣿⣿⣿⢿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⣿⠀⡟⠉⠀⠀⠀⠀⣿⠀⠀⠀
⠀⠈⠃⠀⢿⢿⣿⣿⣿⠈⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⢻⠋⠁⠀⠀⠀⠈⠉⠙⠻⢿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣾⠟⠙⢸⠀⡴⠃⠀⠀⡞⢹⡀⠀⠀
⠀⠀⠁⠀⠈⠻⡿⣿⣿⠀⢾⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠋⠀⠀⣯⠞⠀⠀⢀⣼⠁⠀⡇⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣧⡈⢿⣿⣿⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠙⠒⠢⠤⠤⠤⠤⠒⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⠟⠁⣠⡀⢸⡡⠚⢁⡴⢿⠃⠀⣰⢿
⣦⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠈⠿⣿⣯⢻⣿⣿⣯⠳⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣾⣿⣿⠟⢁⣠⠾⠍⠒⠉⢠⡆⢸⠀⡞⢀⠔⠁⠈⠁⠀
⠈⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⡏⠙⠻⣄⠈⠻⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣶⣿⡻⣿⣽⠟⡛⠉⠃⠀⠉⠀⠀⠀⢀⡰⠋⠀⢸⢸⠇⠀⠀⠀⠀⠀⠀
⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠈⠳⣀⠈⠙⢿⣶⣤⣀⣠⣤⣴⣶⣿⣿⣿⣿⣿⠿⠋⣿⡾⠋⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠘⡟⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠘⣆⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⢘⠘⠛⠓⢦⠙⠿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠐⠤⠞⠁⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊
⠁⠀⠀⢹⠞⠙⢦⣀⣀⣀⣀⣤⡤⠤⠖⠒⠚⢹⡄⠀⠘⡄⠀⠀⠈⢳⡀⠈⠉⠉⠉⣩⠃⠀⠀⠀⠀⠀⠀⠀⣰⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠁⠀⠀
⠀⠀⠀⠈⠀⠀⠀⠻⡍⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠻⡀⠀⠀⠀⢣⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠓⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣆⠀⠀⠀⠱⡄⠀⠀⠘⣧⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⠀⠀⠀⠀⠉⠲⢄⡀⠀⠀⠀⠀⣀⡤⠖⠊⢻⡀⠀⠀⣀⡠⠂⠁