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⠀⠀⢻⠀⠀⠀⠀⠟⣿⢃⡿⢷⡙⢝⠷⡿⢸⠀⠀⠛⠀⠰⠀⠀⠀⠀⠀⠀⠀⠁⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢸⠀⡠⠀⣿⢠⡏⣿⠆⣿⣇⣿⠰⣟⣼⠆⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⡆⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢸⠀⠁⠐⣿⣾⢻⡿⣠⠏⣿⣿⣷⠿⣿⣀⣆⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⡜⠀⠀⠀⣿⠃⣿⢠⡏⣷⠹⠹⣿⣞⢹⡇⢿⣠⢀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠃⠠⠀⣤⠸⠀⣿⠀⡇⢿⠠⠁⣿⣿⣾⣃⣸⠁⠉⡔⣀⠈⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⡄⠠⠀⡇⣠⡁⢿⡴⣧⡼⠁⠚⢿⣿⠿⣿⠛⡴⣀⣇⠉⠀⠀⠂⠀⠀⠀⡴⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⡄⠀⡄⠀⡟⢠⠀⡿⠿⣸⣇⠘⠀⡆⡟⣼⢀⣏⠉⠀⢀⠀⠀⠀⠀⠀⠁⢀⢘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⡆⠀⠃⠀⠃⠉⡄⣧⢰⠃⡿⠠⠀⡇⣷⣿⠋⣿⣴⠀⠀⠃⠐⠠⠀⠀⠀⡆⣤⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⡒⠀⠾⠀⠀⠛⠀⠀⣏⡼⢀⠃⡼⠀⢇⡿⣿⣼⢃⣿⠊⠤⣠⠀⠀⠀⠀⠀⠀⡏⣛⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⡍⢀⠀⢠⠀⡴⣽⠀⠏⣠⢀⠋⡼⢀⣿⣿⠟⣿⣼⣀⠃⠀⠁⠐⠀⠀⡋⠀⠏⣿⣾⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠁⣿⠀⠈⠀⠀⢻⠈⢀⠁⠈⣀⠀⠈⢱⣿⣿⣷⣿⢉⡟⢾⠀⡀⡀⠀⠋⠐⠀⡇⣿⣿⢴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢫⡴⠀⠀⠆⠠⠀⠀⠄⠀⠇⠀⠀⣾⠁⣿⡿⣿⣾⣥⣼⢀⠀⠀⠉⠖⢴⠀⡁⠉⠟⡾⣷⣶⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⡔⡇⢰⠀⠀⠀⠀⠀⠀⠀⠆⠠⠀⡟⠔⣇⣰⣿⣿⣿⣯⣹⠈⡶⢠⣆⣼⢀⠁⡈⠀⠒⠿⡿⡿⢸⠰⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⡿⠛⣀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠁⡿⢫⠟⡛⣟⣿⣼⣧⣸⠁⡟⣸⠁⠛⠛⠟⠾⠁⠛⡿⣽⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⡈⠙⠠⠀⠀⠀⠀⠀⠁⠘⠀⠀⠈⠀⠀⣼⣄⣿⣹⣿⣿⣸⢋⣶⠛⡿⢘⠄⡶⢠⠲⡿⢴⠠⡟⣿⠻⡻⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠟⡃⡐⢀⠀⡷⠐⠀⠀⠀⠀⠤⠠⠀⠁⣤⠉⡿⢛⡟⣿⢻⡿⢺⡷⣾⢠⡥⣾⣤⣁⣟⣠⠀⠏⣠⠙⣿⣾⢤⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⢦⠬⢀⠀⠌⢀⠀⠀⠀⠀⠀⠀⠀⠛⠰⠁⣿⣶⢀⡟⣿⣿⣴⣋⣿⣡⠋⠛⣀⠛⠟⣻⠛⠏⣼⠇⠋⢻⠄⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠐⢋⠐⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠆⢠⠁⠟⣼⣀⣉⣟⣻⣿⣿⢻⠛⠿⡟⣾⠶⠿⣴⠤⠁⠞⠠⢈⠉⡤⢀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⢤⠁⠂⠤⠀⠁⠀⠀⠀⠀⠀⠀⠐⣀⠀⠃⣽⠉⠋⡟⢉⠏⡿⣾⠶⠤⡋⣴⢠⠇⡾⣠⠀⠀⣴⠀⠄⠿⠀⠀⠀⠀⠀⠁⠘⡠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡠⢅⠘⡀⠀⠀⠀⠄⢀⠀⠀⠀⠀⠀⠀⠃⠸⠀⠀⡟⢸⠁⠿⠜⠀⡓⣁⣿⢀⠁⠟⠠⠀⠛⠸⠁⠘⠉⠀⡷⣾⣬⠠⠀⠀⠁⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠊⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣴⠀⠀⠿⣿⢰⠀⠀⡅⢹⠋⠼⠠⣽⠠⠀⠀⠀⡄⢤⠆⠠⠇⡭⣿⣖⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⡁⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠁⡟⣠⠀⠀⠟⠨⠀⠀⠟⣿⣲⣷⡒⣥⣿⣴⠡⡾⢧⠙⠊⠀⠈⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠌⢠⠀⠀⠟⡾⢠⠀⡟⢿⠻⣠⠀⠀⠀⠀⠀⠀⠤⠀⠀⡀⠀⠀⠀⠁⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⡠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠀⠀⠀⠐⠀⠀⠉⡿⢛⠛⠟⣿⢶⠒⠋⢷⣿⣿⣺⣴⣤⣶⣩⠀⡄⠀⠅⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠊⡶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠐⠀⠀⠆⣤⢀⠁⣼⣠⢀⠇⣴⠁⠋⠿⣿⣿⣿⢠⠀⣄⠀⠈⡅⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⡿⣴⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⣼⠀⠀⠁⠉⠉⠉⠛⡿⢀⠟⠫⡿⣿⣿⣴⣣⢀⠀⡃⣼⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠿⣽⢺⠠⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠞⠀⠀⠃⡞⢶⠠⠁⡾⣠⣀⣀⡉⠋⡿⣿⢚⠀⡰⢗⠿⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠋⠚⣢⡔⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠄⢀⠀⠀⡜⢀⠀⠃⡼⠀⠁⠋⡹⠛⡿⣿⡰⠁⡎⠓⠄⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠋⠔⠀⠃⡴⠀⠀⠁⣈⠀⠏⢹⠀⡖⣤⢀⠥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢻⣶⣴⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠐⠀⠀⠏⠘⠀⡿⠀⡃⣜⠁⠄⣴⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠟⣷⣾⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢀⠀⠀⠃⠐⠀⡀⢀⠀⠋⠸⠀⡇⣠⠀⠄⢠⠈⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠋⠿⣿⣴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠛⠀⠀⡇⢰⠀⣿⠂⡶⣠⡇⢠⠀⠀⠀⠀⠀⠀⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠟⡾⣮⣴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠁⠘⠀⠏⣾⣡⡼⠟⣿⡀⠀⠀⠀⠀⠀⠀⠂⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⡿⡽⢖⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⡆⠀⠀⠀⠋⡗⣸⡯⢈⠠⠀⠀⠀⠀⠀⠀⠁⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠭⣖⢾⡠⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠁⠀⠀⡀⢀⠀⠻⠁⡞⣠⡟⣠⠀⠀⠀⠀⠀⠆⢠⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠟⡿⣮⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢀⠀⠀⠀⠀⣧⠀⠀⣿⠟⢸⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⡿⣾⣠⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣸⠠⣊⠀⡟⢀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⣷⢾⢠⠀⠀⠀⠀⠀⡄⠀⠀⠀⠏⠀⠀⠀⣿⠀⠃⣴⠁⢾⠀⠀⠀⠀⠀⠀⠁⢰⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠘⠐⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠠⠰⠁⠰⢛⠛⠠⠁⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠤⡄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⠠⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⣷⠀⠏⠀⠀⠸⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠠⠀⠀⠀⠀⠀⠀⡄⢀⠀⠀⠀⠀⠀⢀⠁⣄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠿⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠇⢀⠀⡘⢀⡇⢈⠠⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢰⠀⠀⠀⡄⠀⠀⠀⡀⠀⠀⡌⠀⠀⡾⣻⠀⠒⠀⡀⢀⠀⠀⠀⢀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠐⠀⠀⠀⠁⡀⠀⠁⣾⠀⣈⣿⠀⠀⠀⠁⠈⠀⠀⠀⢨⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠐⠀⠀⡀⠀⠀⠃⣰⢤⠉⢤⠀⢸⠀⠉⠀⠀⢀⠀⠀⡆⢸⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠈⠀⠀⢀⠀⠀⠀⡃⡿⢰⠀⡟⣦⢰⠀⠀⠀⣄⡛⢀⠀⠇⠸⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠛⠀⠀⠀⠃⠀⠀⡀⢠⠀⡷⠀⠀⣇⠙⠈⠀⠀⣦⢸⡃⢀⠠⡇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠘⠘⠀⠀⠀⠀⢤⠀⡇⣤⠀⠇⣠⢦⠛⢀⠀⠀⠀⣿⣸⢧⡎⠻⢡⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠸⠄⠀⠀⠀⠃⣾⠀⠀⣿⡀⠂⣛⣤⣷⠨⢤⣄⢳⡌⢿⠀⠳⣀⢸⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠙⠂⠈⡀⣄⠀⠓⢉⠀⣄⢿⠀⠀⣿⠏⠹⡔⣷⡍⢷⡉⢸⡀⢰⡿⠈⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⢿⠀⡀⢀⠑⠈⠀⣆⣬⠲⠯⠘⡄⣷⢸⠁⡀⣯⠻⡇⢸⠁⣸⣷⣷⢡⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣷⢻⠀⠀⠙⠀⣆⠤⠳⡈⢸⣄⣶⠸⣧⢻⣗⣦⢿⢈⡀⠓⢀⠠⡏⣿⣿⠈⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⣏⠻⠐⠀⣀⢀⠀⣈⣠⣆⢳⠘⣌⣾⣷⣿⢿⣙⠧⢘⠀⡀⢷⠘⡀⢱⡳⠘⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣷⠷⠈⡆⠠⠀⠉⡀⣆⠙⣍⣮⣶⣳⣯⣿⣿⣿⣷⠙⣇⢺⠁⠉⡀⣤⣿⡞⢹⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡷⣿⢿⠀⠀⣠⠀⠦⠛⣯⢿⠓⣌⣷⣿⣿⣿⣿⢿⣿⢸⠂⠙⠀⣄⢦⠙⣧⣿⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢤⡑⣎⠻⠀⠀⠀⠂⠈⢄⠳⡈⣤⣶⢻⢈⡒⣧⠿⡟⢹⡀⣿⠈⠀⢆⡓⢨⠀⣦⣿⢻⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢤⡷⢬⠓⠙⠈⠂⠀⡀⣤⠰⡀⣧⣷⢿⣿⣿⣷⣿⡛⢀⡆⢿⠈⣧⠙⠀⠈⡒⢀⠀⣥⡷⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢤⣅⢭⠳⠙⠀⢀⠀⠤⠂⡁⣈⣤⣿⣿⣿⢿⣜⣯⣿⣿⠸⠈⡄⣿⠘⡄⠹⡄⠦⠳⠙⡀⣷⡜⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡦⣗⢿⠛⠉⠀⠠⠀⠁⡀⣄⣦⣷⣿⣿⣯⣹⣭⣿⠻⣉⣠⣷⢹⡀⢉⣇⠸⠀⠉⡀⣤⠳⠀⢄⢹⢧⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣦⣓⢿⢿⠉⠀⠈⣀⢀⡀⣆⣿⣿⣿⣿⣿⣿⠿⡻⣙⣯⢿⠈⠙⢧⠙⠀⠁⣆⠸⠀⠢⠓⠉⠨⡀⣷⡜⢳⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣷⣿⣿⠙⠈⠈⠠⡀⢰⣀⣦⣿⣿⣿⣿⢿⣝⣿⣾⣷⣉⣧⠻⠀⠀⠣⠀⠀⠀⠀⠉⠀⠄⠠⠀⡀⣧⢿⣯⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣦⣟⣿⠿⠉⠹⢠⣄⡀⣦⣷⣷⣿⣿⣿⢙⣈⣽⣦⣿⣿⠙⠉⠏⠙⠀⠀⠀⠀⠀⠀⠀⠃⠈⠀⠀⣀⣦⠻⣍⠳⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⢯⠙⠀⣄⡤⢧⠈⣄⣿⣿⢿⣝⣿⣝⡿⣿⢿⡛⢿⡙⣀⢤⠰⠀⠀⠁⠀⠀⠀⠀⡀⠀⠀⡆⠳⣧⠿⣜⠳⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣷⣿⢻⠀⠄⡃⠘⣦⣦⠻⣟⣿⣽⣶⢿⡛⣌⣷⣿⣦⢿⠘⠉⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⣄⣠⢤⡷⢾⠛⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣧⣿⢹⠁⠈⡀⡀⣴⣷⣿⣾⢿⡻⣿⣿⢿⡿⣿⠻⣝⢧⠙⠀⠀⠀⣄⠀⠀⠠⠀⠀⠤⠳⡈⣄⢷⡹⣭⠳⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣷⢿⠏⠀⡀⡆⢻⣧⣿⣻⣿⣿⣶⠙⡻⠉⣆⠻⠘⠃⠈⠀⠂⠐⠀⠀⣀⣀⢠⣄⠦⡐⣤⣷⣛⢬⠳⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⡿⢿⠈⠀⣄⢱⣇⣿⣿⡿⣿⠻⣏⢮⡻⢙⠂⠘⡀⢠⠀⠀⠐⠀⠀⡁⢉⠀⢀⡳⢘⣻⣬⠲⠛⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣿⠙⠈⡄⠹⠈⣧⣿⣿⣿⡻⣎⢷⠝⣳⠹⡂⠉⠀⠘⣀⢐⡤⣤⣦⣶⠛⡻⣿⢿⠻⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣿⢹⡀⢰⡀⣸⣇⣿⣿⣿⣿⠙⣧⣜⠦⣙⢢⢻⣀⠓⡉⣉⣦⡷⣽⢯⠲⠛⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣿⠙⠀⠁⠈⣧⣿⣿⣿⣽⣷⢻⡃⣿⣤⠷⡙⢠⣤⣙⣦⣿⢿⠺⠙⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣿⢹⠂⠱⡇⣾⣿⣿⣿⣯⢻⡿⣼⠳⣟⢺⡀⠱⣦⣿⣻⢿⠛⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣿⡀⡁⢀⡇⣿⣿⢿⣿⡿⣼⡿⣿⢰⡟⠀⣧⣿⣿⢿⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⣿⢸⠰⡀⢸⡇⣿⢻⣾⡿⣷⢹⠇⣻⠀⠃⣄⣿⣟⠻⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣿⠘⡀⠇⢸⡇⣿⢸⡟⡇⣿⡎⢠⠏⢠⡀⣿⣿⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣟⠈⡇⢠⡟⣷⣿⣿⣧⣿⠋⠀⠞⢀⡾⣇⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⣿⠀⠁⡾⣇⣿⣾⣿⣿⠋⡠⠀⠀⠊⠃⡿⣿⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⡇⣿⡏⣿⣾⣧⢰⠀⠐⠀⠀⠀⡇⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⡇⢏⣿⣿⣏⣽⠀⡴⢀⠀⢃⡱⡟⣿⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⠀⠊⣷⠟⣿⣻⡼⢫⡾⣃⢸⠀⠀⡁⠖⣿⣿⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢋⣿⢸⠀⠻⡞⣿⣿⣿⣿⢹⣋⣼⣠⠀⠅⢈⡁⣿⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⣿⣾⠀⠇⡀⣿⣯⣿⣿⣾⣡⢞⡣⣞⢠⠈⠀⠟⣿⣼⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢀⠀⠁⡿⣯⣿⣿⣿⢻⡿⣴⢩⡟⣶⣠⠀⠏⣿⣾⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⣿⣸⠀⡀⢀⠏⢿⣿⣿⣿⣴⣯⣴⡏⣿⢀⣯⠒⡅⣟⣿⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣿⢠⠁⠘⠀⠸⣿⣟⣿⣿⣯⣿⣴⠏⣿⠶⠠⠄⣡⡏⣿⣾⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣿⣿⣳⠰⠀⠀⡇⣟⢿⡿⣿⣾⣟⣨⠋⣾⢤⣠⢃⠠⠉⡟⣿⣾⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⣿⣿⣼⢀⠐⠀⠟⢿⣧⣿⣿⣿⣿⣾⢥⣼⣡⣉⢉⠞⢀⡇⢿⡿⣾⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⣿⣯⣼⠀⠀⠀⠎⣥⣿⣿⢋⡿⣿⣿⣩⣞⠡⠟⠾⠾⣠⠆⣡⢟⣿⣾⣠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣿⣿⣼⠁⠀⠀⡋⠀⡏⣿⢗⡿⣿⡿⣿⣿⣾⣤⣦⣵⣶⣡⠞⢿⠻⡿⣾⣴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡿⣿⣾⢀⠀⠀⠀⠀⡟⢻⢟⡿⣴⣋⣿⣿⣿⣾⣯⣽⣉⠛⠟⣾⠀⠋⣿⣿⣴⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⡿⣿⣴⢠⠀⠀⠀⠀⠀⠎⣽⢉⠟⣿⢋⠟⣿⣿⣿⣿⢾⡷⣾⣤⣡⠟⣿⣿⣾⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⡿⣿⣴⠀⠀⠀⠀⠉⠁⠋⠘⠋⣿⢸⠇⣿⣫⡟⣿⣴⣩⣟⣡⠋⣻⠟⣿⣿⣿⣴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⡿⣾⣤⣀⠀⠀⠀⠀⠀⠀⠟⡾⢶⠧⡿⢰⠁⡟⣿⣿⣿⣿⣷⣴⣇⣿⣿⣿⣿⣴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠟⣿⣾⣤⢀⠀⠀⠀⠀⠀⠚⠂⠀⠏⣴⠀⠁⡿⣽⣯⣿⣴⣯⣽⣏⣿⡿⣿⣿⣴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠟⣿⣾⣴⣠⢀⠀⠀⠀⠀⠀⠂⠐⠀⠀⠏⣰⠁⠟⣽⠏⣼⢏⣾⢏⣿⣿⣿⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠟⡿⣿⣐⣤⠀⠀⠀⠀⠁⠀⠀⠀⠈⠀⠀⠋⢀⠋⣿⠋⣿⣿⣿⣿⣿⣾⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⡿⣾⣒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⣸⡟⣿⣿⣾⣿⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠟⣾⣶⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠃⡿⣡⣿⣿⣿⣷⣿⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠟⣿⣴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠏⣿⢇⣿⣿⣸⡿⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡟⣿⢠⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⡆⢸⡏⣿⣿⣿⣹⡞⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⣿⣰⠀⠀⠀⠀⠀⠀⠀⠃⠀⡇⠉⡵⣻⡿⣿⡀⢁⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⣿⣠⠀⠀⠀⠀⠀⡀⠀⠀⠻⠀⠁⡿⣧⣿⣿⢠⠃⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⣿⢠⠀⠀⠀⠀⠁⠀⠀⠀⠀⣄⠀⡟⣿⣿⢸⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣾⠀⠀⠀⠀⠘⠀⠀⠀⠀⠇⡼⡇⣿⣿⣻⢈⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣿⢸⠀⠀⠀⠀⠄⠈⠀⡄⢱⡅⣻⡟⣿⣿⢸⠃⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣿⠘⠀⠀⠀⠀⠀⠀⠁⡌⣧⣿⢳⣿⣿⢸⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢹⣿⣿⢸⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢻⠀⠀⠀⠀⠀⠀⣰⠀⡿⣿⣼⣿⣿⢽⠃⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣼⠀⠀⠀⠀⡄⠱⠁⣶⢷⡜⣿⣿⣿⢹⡀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⠀⠀⠀⢀⠀⡠⢆⡟⢸⣿⣿⣿⣿⢘⡇⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣤⠀⠆⠀⡄⢀⢹⡀⣧⣿⣿⣿⣿⣿⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣿⠈⠀⠀⡄⠹⠃⣿⣷⣿⣿⣿⢿⣿⣿⡄⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣿⢻⠀⠀⠐⣆⢶⡜⣿⣿⣿⣿⡿⣏⡿⣿⣷⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣷⢿⠀⠐⠀⠐⡟⣿⣿⣿⣿⠿⣜⣷⢹⣧⣿⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣿⠘⠀⡒⢀⣄⣿⣿⣿⣿⣹⣦⢻⡏⡾⣿⣿⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⣿⠙⣁⠀⣍⡳⣯⣿⣿⣟⣿⢻⣏⠻⡍⣷⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣿⢿⠒⠀⣄⣶⣷⢻⣿⢿⡛⢻⡌⢻⠀⣧⣿⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣧⣿⠹⡀⣦⣿⣿⣿⣿⣿⠻⡌⢳⡌⢿⡘⣧⣿⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣿⢿⡈⣦⡽⣿⣿⣿⣿⠻⠉⡀⣷⠸⣿⣼⣿⣿⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣿⠻⡈⣄⣶⣿⣿⢿⣿⡈⣤⢻⡟⠸⣧⣿⣿⢿⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣷⣿⠹⡀⣧⣿⣿⣿⢻⣀⢨⠉⣳⢄⣽⣷⣿⢿⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣦⣿⣿⠘⣆⣷⣿⣿⣊⣿⠐⡍⠀⡆⣹⣦⣿⢿⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣦⣿⣿⣿⠻⣧⣿⣿⢻⡉⣍⢿⠀⢦⡀⣧⣿⢿⠙⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣿⣿⣿⣿⣿⣿⢿⠙⣏⢺⠙⠀⠀⣤⣷⣿⠻⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣷⣿⣿⣿⣿⢿⣿⣹⣀⣦⠹⡀⣦⣶⣿⢿⠙⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣦⣿⣿⣿⣿⣿⡻⣷⢿⠘⡄⣽⣷⣿⢿⠛⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣦⣿⣿⣿⣿⣿⣿⠸⣿⢻⡄⣦⣿⣿⠻⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣿⣿⣿⣿⣿⣿⣿⢼⡇⣹⣦⣿⢿⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣧⣿⣿⣿⣿⣿⣿⣿⠛⡄⢻⣯⢿⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣷⣿⣿⣿⣿⣿⣿⣿⠸⣄⣿⢿⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⣿⣿⣿⣿⣿⣿⣟⠿⢻⣦⣿⠻⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⣿⣿⣿⣿⣿⣿⠿⣹⣧⣿⠻⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣿⣿⣿⣿⣿⣿⢹⢷⣯⢿⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣿⣿⣿⣿⣿⢻⣌⣿⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣿⣿⣿⣿⣿⣿⡷⣿⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⣿⣿⣿⣿⡻⣯⣼⣷⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢿⣿⢿⡅⣿⣿⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⣮⡹⣦⣿⣧⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣿⣿⣽⣷⡎⢻⣧⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⣿⣿⣿⢻⣎⢷⡎⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⣻⠊⣞⣸⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣿⣿⣿⣼⣹⣇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣟⣿⣿⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⢿⣇⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣤⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡿⣿⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣧⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⣿⣿⣿⡿⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⣿⣿⣿⣿⣿⣸⣟⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣿⣿⣿⣿⣿⣿⣿⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⣿⣿⣿⣿⢏⣿⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣿⣿⣿⣿⣿⣾⣏⣿⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡿⣿⣿⣿⣿⣿⣿⡿⣿⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣿⣿⣿⣿⣿⣿⣴⡟⣿⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⣿⣿⣿⣿⣿⣿⣼⣟⣿⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⣿⣿⣿⣿⣿⣿⣿⣫⣿⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡿⣿⣿⣿⣿⣿⣿⣿⣿⣾⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠟⣿⣿⣿⣿⣿⣿⣿⣿⣾⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⡿⣿⣿⣿⣿⣿⣿⣿⣿⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⣿⣿⣿⣿⣿⣿⣿⣿⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡿⣿⣿⣿⣿⣿⣿⣿⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⡿⣿⣿⣿⣿⣿⣿⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⣿⣿⣿⣿⣿⣿⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⡿⣿⣿⣿⣿⣿⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡟⣿⣿⣿⣿⣿⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⣿⣿⣿⣿⣿⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⣿⣿⣿⣿⣿⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣿⣿⣿⣿⣿⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⣿⣿⣿⣿⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣿⣿⣿⣿⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣿⣿⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢹⣇⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⣏⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡄⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⣿⣷⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣿⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣿⢿⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⢿⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢿⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

Hera and Zeus debated which gender enjoys greater pleasure in love. Hera said men; Zeus claimed women

⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁⠀⠀⠀⠀⢀⣠⠴⠲⡄⠉⠻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣀⢀⡀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⡀⠀⣀⣈⣶⣌⠙⢷⣿⢸⠛⣿⠏⣿⡏⠉⡧⡤⣄⣀⠀⢄⠀⠈⢲⣄⠀⠀⠀⠀⠉⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢠⢊⣀⣤⠄⠀⠀⠀⠀⢀⡠⠖⠉⠀⠀⠀⣀⠤⠚⠉⠀⠀⡰⠃⠀⣀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠖⠉⠀⠀⠀⠀⠀⠀⣀⣠⣤⠤⠄⠀⢀⡀⠀⠀⠀⢰⡏⠉⢿⢿⠙⣿⠛⣛⣛⣶⣶⣶⡿⢛⠋⠉⠉⠉⠉⠛⠳⣦⡀⠀⠀⠀⠀⢀⢠⠤⠷⠶⠾⠿⠿⠿⠿⠻⠿⠿⣶⣤⣈⡀⠃⢰⠉⠀⠀⠘⠃⢹⡏⢧⠸⣷⡀⠀⠈⠃⠀⠀⠀⠀⠀⠑⠢⢄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⡄⠀⠀⠀⠀⠀⢀⠀⠀⠀
⠀⠀⣠⠟⠉⠉⠉⠉⠉⠉⠛⣃⡦⠔⠖⠒⠒⠉⠁⠀⠀⠀⠀⠈⠓⠚⠉⠉⠈⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⢤⠴⠚⠃⠀⠀⠀⠀⣀⣤⠶⠞⣫⣽⣶⣶⠀⠀⠛⡇⠀⠀⠀⠸⣷⣀⣺⠉⠀⢿⣧⣤⣽⣿⠟⠁⠀⠀⣀⠤⠤⠀⠀⠀⠀⠀⢤⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣄⠀⠉⠛⣿⢷⣾⣤⣄⣀⠀⠀⠀⠻⡘⡆⣿⣷⣠⡇⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠤⡀⠀⠀⠀⠀⢪⣭⣤⣤⣤⣤⣦⣄⣄⣄⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⢀⡔⠃⠀⢠⡶⠚⠉⢀⡠⠓⢰
⠀⠀⡏⠈⣤⢤⠤⡤⠤⠓⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠔⠚⢹⡇⣿⣨⣟⡆⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠉⠈⣀⠀⠀⠀⠀⠀⣠⡴⠋⠁⢀⣤⠾⠛⠉⠛⢿⢑⢠⠀⠃⠀⠀⠀⠀⠙⠿⣿⣦⣤⣼⣧⢾⡟⠁⠀⠔⠚⠉⠀⠀⠀⠀⠀⠁⠈⠃⠀⠁⠀⠀⠀⠀⠀⠀⣀⣠⣴⣶⣶⠿⠿⠮⢿⠼⢦⠒⠶⣞⢧⡌⠙⢯⡛⠿⠷⣶⣿⣷⡹⣿⣿⣿⠇⠀⠀⠈⠦⣤⣤⣄⣀⣀⠀⠀⠀⠀⠀⠈⠑⢤⠤⠖⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠤⠔⠁⠀⢀⠜⢁⡦⠔⠊⠁⠀⠀⠬
⠀⠀⢧⡀⣿⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠁⠀⠀⢠⠞⠀⠙⣥⡄⠀⠀⠀⣀⡠⠤⠤⠤⠔⠉⠀⠀⣠⣾⠿⠿⣷⣤⣴⣿⣭⣤⣴⠾⠋⠡⣐⣷⠶⠟⡟⠙⢸⣦⡀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡧⡀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠋⠉⠁⠀⠉⠉⠻⢯⣽⣿⣷⡌⢳⠀⠈⢳⣻⣆⠀⠻⣦⠠⡀⢻⡻⣿⣦⣍⡁⠀⣤⡀⠀⠀⣿⣭⣍⣉⠙⠛⠷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⣠⠞⢁⡔⠃⠀⠀⠀⠀⢠⠴⠁
⠀⠀⠀⢈⠉⠀⢀⣠⠤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁⠀⠀⠀⣀⡴⣫⢠⠞⠉⣠⠇⡤⠖⠉⠀⠀⠀⠀⠰⣤⣤⣤⣾⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣬⠵⠟⣁⣤⣾⣧⡀⠈⢻⣿⣦⣄⡀⠀⠀⠀⠀⠀⢀⣤⣤⣴⣶⣬⣶⡒⠚⠲⢦⡀⠀⠀⠸⣿⣄⣠⣤⣄⠀⠀⠀⡀⠀⡀⠠⠴⠲⠶⠦⢄⠀⠙⢿⣿⡇⢸⡆⠀⠀⠱⣿⣧⠀⠘⢇⠹⣆⢻⡨⢿⣿⠀⠀⠈⠙⠶⠀⣿⡏⣿⣿⢦⠀⠀⠈⠙⢿⣶⣄⠀⠀⢀⣠⣤⡶⠾⠛⠛⠛⠛⠛⠛⠓⠆⠀⠀⠀⠀⠀⠀⠈⢢⠀⠀⠀⠀⠀⠀⠀⢠⡚⠉⠉⢠⠇⠀⠀⠀⠀⡾⠀⢠⠎⠀⠀⠀⢠⠔⠊⠁⠀⠀
⠀⠀⠀⢀⣤⠜⠋⣂⠴⠛⠃⢍⡇⠀⠀⠀⠀⠀⢠⠋⠀⠀⣀⠴⠚⠉⣨⣷⡿⠖⢯⣷⠋⠀⠀⠀⠀⠀⠀⠀⠀⠠⠬⠿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⢀⣠⣤⣤⡿⠿⣦⣄⡀⠀⠉⠙⠻⠿⢾⣿⣿⣿⣿⡿⠿⠟⠲⣭⣙⢦⠀⠀⠙⠳⣄⡀⣤⡩⣿⢿⡋⠛⡙⠈⠂⠉⠀⠀⠀⠀⠀⠀⣀⣀⣶⣄⠙⢿⡄⢿⠳⡱⡀⠸⡽⣧⡀⠈⠀⢹⡘⣷⢸⣿⠀⠀⠀⠀⠀⡀⢸⣿⡘⣿⣼⣧⡀⠀⠀⠀⠻⣿⣿⣿⠟⣩⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⢄⡀⠀⠀⠀⠀⠀⢣⡀⠀⠀⠀⠀⠀⠀⠓⠒⠂⠁⠀⠀⠀⠀⠀⠓⠓⠁⠀⠀⠀⠀⠘⠒⢲⠀⠀⡠
⠀⠀⠀⣼⠃⠀⣼⠵⠒⠒⠋⠁⠀⠀⠀⠀⠀⠀⠘⠒⠒⠊⠀⠀⠀⢸⠁⣸⠁⢸⠟⠁⠀⠀⠀⠀⢀⣠⣤⡤⠀⣀⠀⠀⠀⠀⢀⣴⠋⠀⠀⠀⠀⠀⠀⠈⠉⠛⠉⠉⠉⠀⠀⠀⠀⠀⣙⠻⢷⣴⣶⣤⣤⣶⢾⣿⡽⠒⠛⠒⣒⠀⠀⠉⠙⠛⠓⠛⠓⠂⠉⠛⠿⠿⢿⣭⣿⣤⣀⣀⣀⣀⣀⣀⣀⣙⣛⣿⣿⣿⣿⣿⣦⣿⡌⢧⠵⡙⣄⠱⣝⣷⣄⠘⢦⣧⠹⣞⣿⡀⣘⡇⠀⠀⢺⡀⢿⣿⣹⣿⣿⠸⣦⠀⠀⠀⢿⡿⢓⣿⠃⠀⠀⣠⡴⠊⢀⣀⠄⠒⠀⠀⠀⣸⣿⣦⣀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢀⡼⣧
⠀⠀⠀⡇⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⣿⢰⠹⣄⠀⠀⡔⠁⣴⡟⣻⠏⠀⠀⢸⣷⠀⠀⣴⠟⠁⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡨⠉⣽⣿⡿⠙⠋⠑⠂⠀⠀⠀⢠⡠⣤⣄⠀⠀⠀⠢⢄⡀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢿⠿⣿⣿⣿⣿⣮⣯⣽⣌⢦⡘⢮⡛⣧⡀⠻⣧⢹⣿⠐⣟⣧⠀⠀⠈⢧⠈⠻⣿⡟⣿⡆⠙⢳⡄⠀⢸⣇⢸⡏⠀⠀⣰⠟⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣧⡀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣤⠾⠛⠉⣠
⠀⠀⢠⠃⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠂⣦⠈⠉⠉⣰⢾⣟⠀⠰⢥⣄⢿⣇⣿⠀⠀⠀⢸⣿⣇⢸⡇⡀⠀⠀⠀⣀⣴⣿⡭⠖⠀⠀⠀⢀⣠⡴⠀⠀⠀⠀⠀⡺⣉⣥⠍⠀⣼⣹⡟⢁⣶⠀⠀⠀⠀⡶⣄⡀⠉⣗⡦⠤⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣤⣠⣀⣀⣀⡀⢉⠈⠈⠙⠛⠿⣿⣿⣿⣯⡻⣄⡙⢮⡻⣦⣌⢻⣿⠀⡏⣿⡄⠀⠀⠀⠱⡄⠉⠿⣞⣿⡄⠀⣷⠀⢸⠝⣾⡧⡀⢰⠏⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣷⣆⠀⢹⣇⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠉⠀⢀⠔⠊⠉
⠀⢀⠏⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠉⠀⠀⡠⠋⠀⠀⠀⣰⠟⠀⠀⠀⠀⠀⠈⠳⣽⡆⣠⣾⣿⣿⣿⡀⠐⣿⣏⡴⠊⢄⣾⣋⠀⠀⢀⣤⣾⢟⡁⠀⠀⠀⠀⠀⢸⡷⣫⣶⡀⠀⡿⡿⠤⡄⠀⠈⠁⠀⠀⠉⠙⠛⠶⠷⢿⣤⣤⣄⣂⣀⣀⣠⡤⠴⠖⢛⣋⣉⣉⣉⣡⣤⣤⣤⣤⣤⣌⣉⣛⡿⣟⣶⢦⣄⡀⠀⠙⠻⣿⣿⣦⡑⢦⡙⠪⣝⣿⣿⠀⡆⣿⡇⢆⠀⠀⠀⠘⣄⠀⠙⢿⣿⡄⢻⡆⢸⠀⣿⡇⣷⠈⡄⠀⠀⠀⠀⠀⠀⠀⣼⣿⢏⣸⡿⣾⣶⠾⣿⡄⠀⠀⠀⠿⣆⣶⠒⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⣀⠤⠚⠁⠀⢀⠞
⣠⠃⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢒⡆⠀⢀⠎⢀⡠⠖⠉⠀⠀⠀⢀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⢹⣗⣏⣿⣿⣿⠙⣷⠸⣾⣳⡇⠈⣾⣿⣷⠀⠀⠀⠀⠀⠉⠓⣶⢶⣤⣤⢀⣾⡫⣾⣟⠁⢀⣷⠇⢤⣤⣤⣤⣶⣦⣤⣀⠈⠙⡾⣶⣶⣤⣔⣖⣚⣯⠉⠀⠀⠐⠉⣀⣀⣠⣤⣴⣶⣦⣄⣀⠀⠀⠀⠉⠉⠉⠓⠛⠻⢾⣽⡲⣄⠀⠈⠻⣿⡿⣦⡙⢦⣌⢻⣿⠀⡇⢺⣧⠘⣆⠀⠀⠀⠘⣆⠀⠀⠻⣿⣌⢧⠸⡇⢹⡇⣿⠾⣯⣠⡀⠀⠀⠀⣠⣾⣿⡿⠋⠀⠀⠘⠿⢇⣻⣿⣆⠀⠀⠀⠀⠙⢷⣌⣧⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⣶⣏⠔⠉⠀⠀⠀⠀⢰⠃⢀
⠃⢠⠋⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⢀⡞⠀⠀⣏⠴⠊⠀⠀⠀⠀⠀⣠⠋⠀⢠⠎⠀⠀⢴⣤⣸⠇⠀⠀⣿⣿⠟⢡⡟⢀⣿⣷⣿⢿⡇⠀⣿⣿⡅⢀⣾⣳⣶⣶⣀⢸⣿⣾⣿⣿⡄⡿⠏⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠐⠯⣉⠙⠛⠦⢬⣲⣖⣺⣧⢯⣷⣦⣶⣶⣾⡿⠛⣋⡭⠟⢙⣂⣀⡀⠀⠉⠁⠀⠀⠠⠄⠀⠀⠀⠀⠀⠈⠙⢾⣷⣄⠀⠈⢿⣎⠻⣆⠹⣿⣿⠀⠈⢸⣿⠀⠹⡆⠀⢢⠀⠘⣆⠀⠀⠈⠻⣿⣧⢻⡘⣧⣻⡌⢹⡻⣿⣷⣤⣐⣿⣿⡟⢁⡞⠀⠀⠀⠀⢠⣀⡉⠛⠷⣄⡀⠀⠀⠀⠈⠿⡀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣹⠃⠀⠀⠀⠀⠀⠀⣈⡂⣆
⣠⠋⠀⠀⠀⠀⠀⠀⢀⡤⠊⠁⢀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⣿⠀⠀⠀⠀⠹⣧⣤⠀⡆⠋⢁⣴⣿⠃⣸⣿⣿⣼⣿⣷⠀⢻⣻⢧⣺⣿⠟⠋⣠⡴⠇⣿⡿⠟⠋⠁⠀⠀⢀⣀⡤⠤⠖⠚⠛⠛⠲⢦⣄⡀⠀⠉⠁⠀⠀⠈⠙⠻⢿⣿⣿⣽⣿⣿⢋⣤⠞⣡⡴⣚⣉⣭⣽⣿⣷⣤⡀⠢⣄⡀⠀⠤⣈⠲⠄⠀⠀⠀⠀⠙⢿⣷⣄⠀⠻⣷⡙⣷⡘⣿⡆⠀⠁⣿⣤⠀⢻⡄⠀⢳⠀⠹⣄⠀⠀⠀⠈⠻⣿⣧⣻⡿⡄⣾⣿⣾⠾⢾⣿⣿⡿⢀⡾⠁⠀⣠⡔⠀⡍⠈⣧⠀⣦⣌⡙⠂⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠤⠤⠤⠷
⡇⠀⠀⠀⢀⡠⠔⠊⠁⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⢀⣼⣧⠀⠀⠀⠀⠀⢸⠟⢀⣧⣶⣿⣿⠏⠐⢋⣵⣟⣻⣻⠿⡆⢸⣟⣿⣿⣷⠒⢋⡡⠖⠋⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢶⣄⡀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⡟⠁⢰⣿⠁⠙⢷⣿⣼⣹⣿⣿⣿⣷⣦⣝⠒⢄⡀⠑⢦⡀⠀⠀⠀⠀⠀⠙⣟⣦⠀⠙⣿⣌⢻⣼⡏⢇⢲⢹⣏⢧⠀⢳⠀⠀⠀⠀⠙⣦⡀⠀⠀⠀⠈⠻⣿⣿⡇⡿⣕⣿⣞⣿⣺⣿⠃⣾⢇⢔⡼⠃⣰⣶⠁⣸⠇⣼⣿⡍⡿⣦⡀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢀⠴⠊⣉⠤⠴⣶⡶⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⣀⣠⡼⠁⠀⠀⡴⠁⠘⣿⠦⣄⣀⠀⠀⠀⠰⣿⢛⣼⡿⠃⢀⣴⣿⡿⣱⣟⠉⢀⣧⢸⡝⣿⣿⣿⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠶⠶⠞⠛⠛⠛⠛⠛⠛⠒⣄⡀⠀⠈⠛⠦⣀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⠻⣷⣄⠀⠨⣙⢿⣿⣿⣿⣿⣿⣯⡳⢄⠙⠆⠀⠻⣦⡘⢦⡀⠐⡄⠈⢮⢷⡀⠸⣿⣆⠻⣿⡈⡎⣇⢿⡈⢷⡀⢣⠀⠀⠀⠀⠈⠻⣦⣄⠀⠀⠀⠀⠙⢿⡽⣷⢯⣿⣿⣿⣿⣾⡟⡔⣾⠉⢪⡿⡿⣰⡟⣰⣿⡇⢰⡇⠈⠉⠢⣀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⣟⣁⠤⠚⠁⢠⠜⠋⣠⠞⠁⠀⠀⠀⠀⠀⠀⢀⡜⢉⣿⠁⠀⢀⡞⡔⠀⢠⡼⠷⠾⣽⣿⣳⣾⣶⣿⡿⠋⠀⣠⢞⣿⠏⣰⡟⠂⠠⡾⠀⣾⣽⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣖⣧⡤⠤⠤⠤⠤⢤⣤⣄⣀⡀⠀⣀⣈⠑⠲⢤⣀⡀⠉⠂⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠈⣿⣿⣦⣘⢿⣿⣿⣿⣿⡻⣿⣿⣕⡓⣄⠀⠐⢌⢻⣄⠹⣦⡘⢆⠈⢧⢳⡀⢹⣿⣶⣿⣧⢹⡈⠸⣧⠈⢷⠈⢣⠀⠀⠀⠀⠀⢪⠻⢷⣦⡀⠀⠀⠀⠙⢿⣿⡏⡟⠟⣟⣿⣿⣶⢿⠀⣾⣣⣷⢟⣴⠟⢿⡇⣾⡇⠀⢦⡀⠀⣷⠀⠀⠀⠘⡄⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠇⢰⠀⣸⣫⣡⠤⠊⠁⡤⠚⣺⠀⠀⣠⠴⣶⣿⡦⢾⡟⠀⢀⡞⣼⢡⢀⢮⠃⢹⠀⢀⣮⣿⣿⠟⠉⠀⠀⠐⢕⡽⠁⣼⣿⠃⠀⠀⡇⣰⣿⡿⠋⠀⠀⣀⡠⢤⣠⣤⣤⣤⠀⣀⣤⣴⣶⣿⣿⣿⣷⣾⣤⣭⣹⡟⣿⢾⣯⣽⣗⣢⠤⣉⡱⣦⣄⣀⠀⠀⠈⠉⠚⠯⢵⣦⣄⠀⠻⣿⣿⣿⣦⡻⣿⣷⣝⣻⣦⣹⡿⣿⡈⢳⡄⢈⠣⡙⢷⣌⠳⣌⢧⠘⣧⢵⠀⣿⡿⢿⣿⣧⣧⠀⢹⡆⠈⢧⡈⠁⠀⠀⣀⡀⠀⢳⡀⠙⢿⣦⡀⠀⠀⠀⠙⢿⣤⣠⡇⣿⡯⣿⢸⡇⢩⣯⣶⠟⠁⣯⣘⣷⣿⣇⠀⡞⢣⠀⠘⣧⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠉⠒⠒⠉⠉⠛⠒⠢⠤⣠
⠃⠚⠀⠹⠉⠀⢀⡤⠊⠀⡠⠃⢀⠞⠁⢠⠏⠀⢑⡟⠀⢀⡾⣼⠃⡜⣨⡿⠀⣿⢠⣿⣿⠟⠁⠀⠀⠀⠀⡠⠟⠀⣼⡿⠋⠀⣠⠞⢠⣿⠏⠀⣀⣴⢛⣥⣾⡿⠟⠛⠉⠀⠈⠛⠳⠶⢶⣶⣶⣦⣬⣉⠛⢿⣿⣿⣿⣮⣏⠿⢿⣿⣿⣿⣷⣶⣮⣭⣝⣒⡶⠶⡶⢶⣶⣲⣿⣽⣦⣘⢿⣿⣿⣿⣾⣿⣿⣿⣮⣟⣿⣾⣿⣯⣽⣌⢢⡘⢦⢿⢷⣝⣦⣗⢸⣿⣆⣽⣷⣄⠙⠻⣿⣧⠀⢣⠀⢨⢧⡀⠀⠰⣏⠛⣄⠀⢹⣦⡀⠙⣷⣄⠀⢀⠀⠈⣷⣽⣷⣿⣿⣸⣧⣿⣌⣭⡤⠄⠀⠀⠀⠉⠻⣿⣰⡇⢸⣤⣦⣿⣦⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⢰⢲⣋⡠⠔⠋⠀⣠⠏⢀⡴⠃⠀⠀⡸⠁⠀⣼⢳⠇⢠⠃⣾⠃⢰⣧⣿⡟⠁⠀⠀⠀⢀⡴⠋⠀⢀⠾⠋⠀⣀⣀⡟⢀⡿⠃⢠⣾⢋⣴⠿⠋⣁⣤⣴⠶⠶⢶⣶⣦⣤⣲⡀⡐⣿⣿⢟⢿⢿⣦⣌⠻⢿⣿⣿⡿⣶⣽⢿⣟⡽⣿⣿⣿⣿⣿⣿⣿⣷⣷⣶⣦⣽⣭⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⢳⡀⢳⢳⣻⣽⣿⣾⣿⣿⣿⣿⣟⣷⣦⡙⢿⣦⠈⢧⠀⢧⢻⡄⠀⠹⣧⠈⢧⡀⢣⡑⣄⠈⢿⣷⡄⢣⠀⢸⣿⣿⣷⣿⣿⣿⣿⠟⢉⡤⠶⠂⠀⠀⠀⠀⠀⢉⣷⣌⡟⠋⢻⣿⣿⢻⣛⡛⠻⢷⣦⡀⠀⠀⠀⠀⠒⠲⠲⢤⣀⡀⠀
⠀⠀⠀⠀⠈⠉⠁⠀⠀⣠⠊⠀⡠⠊⠀⠀⢀⣰⠃⠀⢰⢯⡟⢀⡎⣼⣏⢠⡟⣿⡟⠀⠀⠀⣠⡾⠋⠀⠀⡀⠁⠀⠀⢘⡿⠋⣠⡾⠁⣴⠟⣡⠞⢁⡤⠞⢉⣡⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣶⣬⣹⢾⣌⡟⡽⣿⣦⣝⢻⢿⣾⣽⡿⣿⣽⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⠿⣿⡿⢿⠻⠛⠹⠉⠉⠉⠻⡏⢹⡟⢿⡿⢿⢿⣿⣿⣮⣿⣌⣆⢻⣧⢻⡶⣿⣿⡏⣿⣷⣟⣿⣿⣌⢿⣦⠘⣆⠈⢧⢻⡄⠀⢻⣧⠀⢳⡌⢿⡌⢷⡀⢣⣷⠘⡇⠀⣿⣿⣿⣿⣽⠻⡠⢠⡟⠀⠀⠀⠀⠀⣠⡖⣄⡀⠉⢿⣿⢷⣌⢻⡏⣿⣿⢷⣆⠀⠈⠛⠛⣋⣭⣶⣶⣤⣄⡀⠉⠻⢷
⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⣠⠞⠁⠀⡰⢫⣿⡟⠀⢀⡟⣼⢃⡎⢐⡟⣸⢸⣿⡟⠀⠀⣠⡾⠋⠀⠀⢀⡔⠁⢀⡤⠚⠁⣠⣾⡿⠀⣼⠏⡼⠁⡴⠋⣠⢞⣯⣽⣾⣿⣿⣿⣿⣿⣻⣿⡿⣻⣿⣿⣿⣿⣶⣽⣿⣿⣿⣿⣿⣶⣬⣙⡻⢷⣿⣿⣿⣿⣿⣿⡿⣿⢻⣟⡉⠘⣾⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠚⠿⡷⢯⠁⠢⠫⠿⢿⣿⣞⣆⢻⣸⣧⣿⣿⡇⡏⢿⣿⣿⡿⣻⣦⡻⣧⠸⣆⠈⢧⢻⡀⠰⣿⡆⠀⢻⡈⣿⡈⣧⠈⣿⡄⣿⠀⣿⣿⠯⣩⡟⢸⡇⣾⠀⣴⣆⡇⣴⢳⣟⣽⣿⣿⣦⡀⢙⢷⡝⢷⣝⣘⣛⣧⠿⢀⣀⡤⠾⠛⠉⢉⣉⠉⠛⢿⣷⣤⡀
⠀⠀⠀⠀⠀⢀⡴⠃⡠⠚⠀⠀⢀⠞⣡⣿⡿⠀⢀⡞⢠⡟⢠⠁⡞⢠⡏⢸⣿⠃⠀⡼⡿⠀⡠⠊⣴⠋⡠⠚⠁⠀⣠⣾⣿⢿⠃⣼⠏⡜⠀⠈⣠⣾⣿⣿⣿⣿⠿⠋⠉⠁⠀⠉⠉⠛⡻⢵⣳⢟⣿⡟⣿⣿⣿⣷⣻⡿⣿⣿⣿⣿⣿⣿⣶⣿⣿⠿⣯⡣⣹⡌⣿⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢮⡳⣄⣀⠀⠠⢌⣹⣿⡼⣇⣿⣿⣿⣿⣿⡜⣿⣟⢿⣥⢯⢿⡽⣇⠹⡄⠈⣧⣷⡀⠙⢷⠀⠈⡇⢹⣇⢹⡀⢸⡇⡿⠰⣿⢇⣼⣿⡇⣸⢁⡏⢸⣧⣿⢷⣿⡟⡼⣿⣿⢿⡇⢿⡶⣄⠻⢦⣉⡉⠛⠛⠛⠛⠶⠶⠒⣛⡾⠛⣿⣭⣅⡈⠻⠻⣿
⠀⠀⠀⠀⠀⠻⠴⠋⠀⠀⠀⡔⢁⡴⣻⡿⠁⢠⠞⠀⣼⣓⠎⡸⠁⣼⢁⣿⡟⠀⠈⣴⠁⣼⢁⡾⢁⠎⢀⡤⢀⣼⣿⣻⡇⡝⢰⡟⢰⠁⢀⣼⡿⢟⣽⣿⣟⠵⠶⣽⣿⣷⣶⣶⣶⣤⣬⣵⣈⡛⠯⣽⣷⣯⣿⣿⣾⠷⢷⣯⡿⣿⣿⡿⣿⠁⠸⢷⣼⣻⡍⠁⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⣭⣓⠒⠢⠄⠠⠽⠯⠾⣿⣿⣿⣿⣿⠺⣿⣯⢿⣾⣎⣿⢹⣆⢻⠀⠸⣾⣷⠀⠀⠀⢸⡇⣼⣿⣼⡇⣿⢧⠇⢸⣿⣾⣿⣿⢃⡟⣼⢁⣯⣿⣿⣷⣿⣧⣿⢿⡏⢸⡇⣸⢻⣝⠷⣦⣬⣭⣭⠿⣿⣷⡶⠟⢋⣥⠞⠀⠂⠀⠈⠉⠓⢦⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣰⠏⠀⠀⠇⠀⢀⣿⠏⠀⠁⣾⢁⡾⣹⡇⠀⣾⡇⢰⡇⣾⠁⡏⠀⡾⣀⣿⣿⡏⣿⢀⡇⣸⡷⡇⢀⣾⡏⣰⣿⡿⢉⣰⡾⠿⠉⠉⠁⠀⠉⠹⢿⣏⡿⡹⡿⣿⣶⣿⣹⡿⣿⢿⣿⣾⣾⣿⣿⢏⡾⡸⣇⠀⠸⡏⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⢿⣿⡇⡶⡶⡀⣀⠀⠈⢹⣿⣿⣇⣿⣷⣿⣿⣿⣸⡇⣿⠈⡏⡇⢹⠸⡇⠀⠀⢸⡇⣿⣿⣿⢁⣿⠀⢀⣿⡿⣿⣿⡏⣾⢱⢇⣾⡿⢁⣿⣏⢿⣿⢁⣿⠀⣾⢀⡏⢸⣿⢹⣶⣀⣀⣶⡿⣿⣶⣶⡿⠏⠁⠀⢀⣀⣀⣀⡀⠀⠀⠹
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⣆⣠⠞⠁⠀⢠⠎⠀⠀⠘⠁⠀⣠⡞⠡⠊⣠⣿⣷⠀⣿⠁⣾⢱⡏⣼⠀⡼⣶⣿⣿⠟⠀⣿⢸⠁⣿⠁⢀⡞⣵⣷⣿⢫⡾⢋⣡⣴⣶⣾⣿⣶⣶⣦⣄⣀⠈⠙⠷⣶⣍⣙⠫⢝⣟⠿⢿⣾⣿⡿⠛⣌⢦⡸⣳⡹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⡀⠄⢀⠀⠈⠛⢿⣿⣿⣷⢿⣿⣻⣯⢸⡇⣷⢳⠘⡆⢻⡀⠀⢀⣼⣿⣽⣹⣸⠇⠀⣼⣿⣿⣻⣟⣼⣷⡿⠟⣋⣴⣿⣻⠿⠛⣡⡾⢃⡼⢣⣾⡾⣻⠇⣼⠋⣽⡟⢉⢼⡟⠀⠀⠀⣠⠖⣋⣽⡿⣿⣿⣿⣦⡀⠀
⠀⠀⠀⠀⠀⠀⢠⠟⠀⢰⣿⡃⠀⢀⡴⠃⠀⠀⠀⠀⣠⡾⠋⠀⠀⢰⡿⠃⣿⠈⣿⠀⣿⣾⢠⡇⢸⣿⣿⣿⣿⠀⡆⣟⣾⠀⣿⠀⡾⣼⣿⡿⢥⣿⣶⣿⣿⣶⣯⣭⣽⣳⠿⣭⣛⠻⠿⣶⣄⡐⠬⣝⡓⣶⣬⣍⣳⣚⣿⢯⠀⠘⣦⣳⠃⠃⠙⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣾⣿⣿⣿⡆⣷⣿⢸⠀⡾⢾⡇⡀⢸⣿⣷⣛⣶⡟⠀⣸⣿⣿⣿⣿⣟⣽⣡⣴⣯⣭⣥⡤⣴⣶⣯⣥⠴⣛⣵⠟⠫⡠⢋⡼⠃⠰⠿⠟⢃⣿⠁⠀⠀⢀⣴⠿⠋⣁⣤⣤⣀⡈⠉⠻⣧
⠀⠀⠀⠀⠀⠀⢸⠀⠈⣿⡛⠀⡠⠊⠀⢀⡤⢒⠟⢠⣿⠀⠀⠀⢀⡿⠁⣼⣿⡄⢿⡌⣧⡟⠈⠃⣺⣿⣿⢿⡟⠀⠃⠏⣿⠀⣿⠹⣷⡿⣿⠇⣿⢋⡡⠤⠶⠞⠋⠉⢉⠹⢟⣷⣾⣯⣭⣤⣭⣿⣷⣦⣭⣙⣛⣿⣭⣿⣿⣽⣧⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣷⣿⣿⣼⣇⡇⢸⡧⣿⢹⣿⣿⣼⡿⠁⣴⣿⠿⠟⠛⠛⠛⠿⢿⣿⣿⣿⣶⣫⣭⣯⡵⠶⠛⠋⣡⠦⢿⣾⠛⠒⢚⠛⢊⣩⡾⠁⠀⠀⣴⡟⠁⢠⣾⣿⣿⣿⣿⣟⢷⣄⠀
⠀⠀⠔⢹⡇⠀⠸⠤⠜⣏⠇⣶⠁⠀⣴⠋⠀⠀⠀⣾⣿⠀⠀⠀⣾⠃⣸⣿⣱⣧⠘⣷⢻⡇⠀⠀⣿⣿⣿⡞⣿⠀⠀⠀⢻⠀⢿⠠⣿⡇⣿⠀⠿⢿⣿⣶⣤⡙⠶⣆⠘⠛⠓⠦⢭⣙⢛⡻⠿⠿⢶⣛⡛⡛⢻⣿⣿⣿⡳⣈⢞⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣹⡧⣼⢣⣿⣿⡿⣻⡿⢧⡼⢋⣡⠴⠒⠒⠀⠀⠀⠀⣀⣠⠴⠚⠉⠀⠀⣀⡠⠖⠊⠉⠀⠀⠈⣉⣽⣿⠿⢟⠟⠀⠀⣠⡾⠃⠀⣴⣿⣿⣿⡿⠿⠿⣿⣿⣮⣳
⠀⠄⠀⢸⠁⢘⠀⠀⣸⠟⢠⣿⠀⠀⣿⠀⠀⠀⠀⣿⣿⠀⠀⠀⡏⠀⣿⢟⣩⣿⡆⢹⣿⡇⠀⢰⣿⡿⣿⣧⢻⣧⠀⠀⢸⡇⠸⡇⠙⡇⣿⠀⠀⠀⢻⣿⣿⣿⣄⠈⢑⠤⣀⠀⠀⣐⠈⠬⠭⠭⣭⣴⡵⠶⢿⡿⡿⡘⣧⢻⢎⠿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⡟⣿⢇⡿⣿⣿⣾⣾⠞⠀⢨⡾⠋⠀⢀⡀⠀⠀⣠⢴⣛⣭⣤⣤⣤⣤⣤⡾⠁⠀⢀⣴⠀⢀⡴⠛⣉⣠⣤⠶⠋⠀⣠⣶⠟⠈⣠⣾⣿⣿⣿⠷⠗⠀⠀⠈⠻⣿⣿
⣀⠀⢀⠞⠀⠀⠀⠀⡿⠀⣸⣿⡄⠀⢿⡄⠀⠀⠈⣿⣿⡆⠀⠀⠇⠀⣷⠟⢩⢸⣷⡀⢿⣧⠀⠘⣿⡇⠸⣿⣧⡹⣷⡀⠈⣷⡀⠀⠀⠈⢿⠀⠀⠸⡜⣿⣿⣿⣿⣦⡢⡙⠲⣯⣖⡬⢍⣒⣒⠶⠤⢖⣒⣾⡟⢫⡱⣱⡙⣧⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣟⣾⣁⡿⣖⡿⢅⣴⣾⠟⢁⣤⠖⠉⢀⣴⣿⣿⣯⣭⣿⣿⣯⣭⡿⠋⠀⠀⣰⣿⢏⣴⠿⠖⠚⠛⠉⠀⢀⣤⣾⠟⠁⣠⣾⣿⣿⡿⢻⣇⣀⣀⣀⣀⠀⠀⠈⠻
⡇⡀⠊⠀⠀⠀⠀⠀⡇⠀⣿⠸⣧⠀⠈⠻⣦⡀⠀⣿⣿⣷⠀⠀⠀⢄⠉⠚⠛⠛⠻⢷⣮⣿⡆⡀⠙⢷⡀⠙⢿⣿⣮⣛⠷⣮⣳⡀⢠⠀⠘⣆⠀⠀⣷⣿⣯⣿⡙⣿⣿⣮⡑⠦⣉⣛⠻⠶⣿⣿⡿⡿⣿⣿⡏⠀⢳⣳⣳⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣾⣷⣿⣯⣾⣿⣯⡿⢫⠴⢋⠀⢀⣴⣿⣿⠿⠛⠒⠚⠋⠉⠉⠀⠄⠀⣠⣞⣫⡵⠟⠁⠀⠀⢀⣠⣴⡾⠟⠋⠁⣠⣾⣿⣿⣿⡿⣩⡟⣼⣿⠿⣿⠷⡿⠧⣿⢶
⠋⠀⠀⠀⠀⠀⠀⠀⡧⢀⣿⡄⠹⣧⡀⠀⠈⢻⣆⢻⣧⢻⣧⠀⢷⡀⣧⠀⠄⠀⠀⠈⣿⡟⣷⠈⠁⠈⠣⠀⠐⣌⣈⠉⠑⢎⠻⣧⢸⡄⠀⠸⣆⠀⠸⡞⣿⡜⣷⡘⢿⢿⣿⣷⣦⣭⣛⣒⠶⠶⢿⣿⣿⠋⠳⣄⠰⣧⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⡟⣱⡟⢠⠃⣠⡿⠛⢉⣀⣤⣤⣶⣶⣶⣶⣶⣶⠶⠛⠋⠉⠁⢀⣢⣤⠶⠾⠛⠉⠀⠀⣀⣴⣾⣿⣿⣟⢿⣷⣿⣯⣿⣿⣿⣷⡌⢳⡙⣦⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣇⠘⣿⣇⠀⠈⠻⢦⡀⠀⠹⣆⠻⣷⣿⣧⡘⢿⣿⠀⠀⠀⠀⠀⠘⠿⣿⣇⡀⠀⠀⠀⠀⠈⠳⣍⢧⠈⣇⢹⡏⣇⠀⠀⢻⣆⠀⢻⡝⢿⣜⣷⣌⣷⡙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣑⢆⠈⠂⠹⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⡏⣸⣿⠀⣎⢜⣉⣤⣤⣭⣶⣶⣤⣄⣀⣤⣼⠟⠁⢀⣠⡴⢖⣟⣉⠁⠀⣀⣠⣴⠾⢁⣼⣿⣟⣫⣿⣿⣽⣷⣝⢿⣜⠿⢧⣶⣶⣻⡀⡇⢹⡄⠀
⠀⠀⠀⠀⠀⠀⠀⠀⡇⡆⣿⠙⣧⡀⠀⠀⠙⣆⢀⠘⣆⠈⡻⣿⣿⣾⣿⡄⠀⢀⠀⠀⠀⠀⠈⠻⣧⠀⠀⠀⠀⠀⠀⠈⠻⣧⢽⠈⣿⢹⡀⠀⠀⢻⣦⠀⠻⣌⠛⢮⣻⢿⣿⣶⣿⣿⣿⣿⣿⣿⠿⠞⣛⣽⣏⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣿⣿⣼⣿⡛⢛⣉⣉⣭⣭⣿⠿⠛⣋⣭⢔⣠⠔⢋⣥⣶⠟⢉⣤⣶⣿⠿⠋⣁⣴⣿⣿⣿⣭⣭⣭⣭⣝⡛⠿⣷⡹⣷⣄⠙⢿⣿⣧⡰⣸⡇⠀
⠀⠀⠀⠀⠀⠀⠀⣠⣧⣷⠸⣦⡟⣿⡆⠀⠀⣿⣿⣇⢸⡇⠘⣮⣙⢿⣿⣿⣦⡀⠑⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⢹⡞⢲⡇⠀⢷⠀⠀⠀⠹⣗⢄⠙⢷⣄⣙⢛⠛⠛⢿⣛⠛⢋⣩⡴⢶⣛⢅⡏⣿⡼⣶⣆⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡛⠻⣿⣻⣯⣍⣉⣉⣡⣤⣶⣿⠿⠉⢀⣠⣶⡿⣋⣥⣾⣿⠟⢋⣡⡶⠟⢋⣡⣤⣉⣁⣖⡾⠩⣝⣻⣿⣷⣄⠙⣌⢿⣷⡌⠻⡻⣷⣿⣇⠈
⠀⠀⠀⠀⠀⢠⣾⣿⠋⢻⣇⠹⣧⣽⣟⡦⣄⢸⣾⣿⡇⡇⠀⠈⠛⣿⡟⠛⠛⠻⢿⣶⣦⣄⡀⠀⠀⠀⠉⢂⠀⠀⠀⠀⠀⢸⡗⣿⠀⠀⠈⢷⡀⠀⠀⠈⠻⣷⣢⣀⡀⠉⢉⣙⣽⠶⠛⠯⠵⣒⠛⢁⣼⣽⣿⣷⢸⡾⡗⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⢿⣯⣽⣟⠓⠚⡋⠉⣀⣤⣴⡿⣛⣥⡾⠏⣉⣥⠶⠞⣋⣩⣴⡾⠿⠿⢿⣿⣿⣿⣿⣷⣷⣬⡺⣵⢿⣷⡌⢫⡻⣿⣆⠹⣌⢿⣿⡀
⠀⠀⠀⠀⢀⡎⠀⣿⠀⢺⣿⣧⡙⢿⣿⣧⡀⢷⣿⠇⣷⠇⠀⠀⣴⡿⠀⠀⠀⠀⠹⣞⡉⠻⣿⣦⡀⠀⠀⠀⣇⠀⠀⠀⠀⢸⡗⣿⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠉⠛⠛⠿⠛⠭⠤⠴⠶⠖⢒⣠⣶⣿⣿⣿⣿⣿⡏⣟⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠪⢽⠛⠻⠿⠯⠯⣯⣗⣞⣭⣽⣿⣭⠵⡶⢞⣻⡭⡵⠖⠒⠒⣺⢿⣻⣿⢿⣿⣿⣿⣿⣿⣿⣿⡽⢿⣖⠱⣝⢿⣧⢹⡄⢿⣯
⠀⠀⠀⠀⡼⠀⠀⡿⣧⠀⠹⣿⣿⣦⣉⠻⣿⡉⢿⣇⠁⠀⠀⠀⠿⠧⠰⠚⠻⣶⠈⣿⡇⠀⢿⡝⣷⡀⠀⠀⢻⠀⠀⠀⠀⠈⣧⠸⠀⠀⠀⠀⠀⠙⢦⡈⠳⡤⠀⠉⠓⢦⣤⣄⡒⠒⠒⣚⣛⣭⢟⣫⣵⣿⢣⣿⣧⢿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠉⠛⠓⠒⢲⣿⣭⣯⣵⡖⣿⣿⣽⢿⣭⢭⣍⡙⢻⣽⣿⣿⣿⣿⡿⣿⣿⡽⣿⣷⡘⣦⠻⣇⢷⠸⣿
⠀⠀⠀⠀⡇⠀⠀⠃⢜⠷⣤⣈⣹⣿⣿⣿⣶⣿⣤⠻⣧⡠⡄⠀⠀⠀⡄⠀⠀⢻⡇⠉⢠⡴⠏⢻⡌⢧⠀⠀⣘⡄⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⢄⡀⠀⠙⠦⣀⠀⠀⠀⠀⠀⠉⠿⠿⠿⣯⣽⣞⢿⣿⠿⣽⣿⢿⣿⢸⣏⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠴⠦⡎⢽⢷⣶⣦⣿⣹⣻⢮⣙⢦⡹⣿⣿⣿⣿⣿⣿⣿⣯⣿⣷⢷⡘⣧⠘⡼⡀⣿
⠀⠀⢠⠞⠁⠀⠀⢀⣼⣷⣬⣭⣿⣿⣿⡿⠿⠟⠛⠳⣬⣙⢦⡀⠀⠀⠀⠀⠢⠼⠇⠀⠀⠈⠀⢸⡇⠘⡇⠀⣿⡇⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⠈⣞⣄⠀⠀⠈⠙⡒⠦⣌⡙⠓⠲⠶⠶⠶⠚⢛⣩⣴⣿⣿⠋⣸⡏⣸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣐⣒⠀⠐⠐⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠁⠁⠀⠉⠀⠘⠛⢿⡲⢭⡳⢯⡊⢿⣿⣿⣿⣿⣻⡿⣿⣿⣿⣧⣹⣇⠘⢻⡏
⣀⡰⠃⠀⠀⢀⠴⢛⣽⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡿⢿⡿⣷⡀⠀⠀⠀⠀⠀⣀⠀⢸⣷⠀⠣⠀⢻⡇⠀⠀⠀⠀⠀⠀⠈⠳⣧⠀⠀⢏⢿⣷⣄⡀⠀⠈⠳⣤⣍⣑⣲⡘⣹⠚⢻⣭⣷⣿⠟⠁⣰⣿⣧⡜⠃⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣒⠠⠀⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢈⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⢦⣝⠢⡙⢾⣿⣿⠿⣿⡿⢷⡟⣽⣿⢿⣧⢿⡆⢸⠇
⡿⠁⠀⠀⠀⢠⣶⠟⠀⠀⠀⢀⣀⣀⡀⠀⠀⠒⢤⡀⠀⠀⠈⢿⡔⠻⣝⣷⡐⠂⠀⠀⠀⣹⣶⠈⣿⠀⡆⠀⠸⣧⠀⠀⠀⠀⣦⣦⠀⠀⠙⣧⠀⠈⢆⢝⢿⣿⡷⡀⠀⠠⢬⣉⣉⣡⣭⣽⠿⠟⠋⠁⣠⣾⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠠⠠⠴⠦⠔⡢⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢄⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡷⢝⢷⡉⠪⣿⣯⣶⣿⣯⣿⣷⣿⡟⢸⢿⡎⢹⠸⠀
⠃⠀⠀⠀⢠⣿⠋⠀⣠⡶⠛⠉⠉⢩⡭⠟⡶⣤⡈⠻⣦⡀⠀⠀⠹⣦⡚⢯⡻⡄⢰⡆⠀⢸⣿⠀⣿⡄⠹⡄⠀⢻⣧⠀⠀⠀⣿⣿⠀⠀⠀⢈⠁⠘⢶⣷⢣⢯⢻⣿⣵⣒⣢⣄⣀⣀⣀⣀⣀⣠⣴⣾⡿⢿⣿⡻⢂⠄⠀⠀⠀⠀⠀⠰⠀⠀⢸⣼⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢭⠍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠩⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠈⠗⣌⠢⡙⣿⣿⣿⣿⣿⣥⣿⡇⠸⣏⢇⡟⠀⢸
⠀⠀⢰⠃⣸⠇⠀⠞⠉⠀⠀⠀⠀⣀⣴⣿⣿⡎⢻⣄⠙⡿⣶⣆⠀⢸⣷⡄⢻⣿⣼⡧⠀⠸⣿⣧⠹⣷⡀⢿⡀⢣⢿⣧⡀⠀⢹⣟⣆⠀⠀⠈⣧⠀⠰⡌⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢛⣫⡵⣛⠥⠂⣸⡗⢽⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡼⢒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⡀⠀⠀⠈⠩⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠐⠄⠑⠀⢿⣿⣿⣿⣿⣾⣟⡇⢰⡿⣼⢹⠀⣾
⠀⠀⡿⢠⣿⠀⠀⠀⠀⠀⣠⣶⡿⣟⣫⣿⢸⡇⠀⠟⢷⡌⠈⠻⣷⡀⢿⣿⡄⣿⣿⣯⠀⠀⠙⣿⣷⡹⣷⡈⡤⠄⢣⠻⣷⡄⢆⢿⣽⣦⠀⠀⣏⡱⣄⠈⠢⣌⠙⠿⠿⠿⢿⣿⣿⣶⡿⠯⠗⠋⠁⠀⣰⣿⠻⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢻⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⠀⠀⠀⣀⡀⢀⠠⡬⢭⣭⣩⡵⣶⣒⣗⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢁⠀⡀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢙⠀⢸⣿⣿⣯⣿⢿⣼⣷⣿⣻⠇⣼⢠⣿
⠀⠀⡇⢸⣿⠀⠀⠀⠀⣼⣿⡿⠛⣭⣿⡝⢿⣯⠄⠀⠈⢿⡡⣷⡼⣄⠈⠿⠁⢸⡟⢻⣧⡈⢦⡈⠻⣿⣿⣷⡼⣩⡄⠃⠨⣿⡌⢎⢷⡛⣦⡄⠸⣖⡊⠑⢦⣌⣙⠶⣤⣤⣀⣀⣀⣀⣀⣠⠤⠀⢀⣼⣿⢻⠒⡅⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠉⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠒⠀⠀⠀⠀⠀⠠⠀⢰⣶⠶⠭⠝⠛⠛⠛⢛⡛⠛⠷⠶⠤⣤⣤⣤⣤⣤⣤⣤⣤⡤⠤⠴⠤⣤⣄⣀⠀⠈⠀⠀⣀⠀⣀⠀⠁⠈⠂⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠭⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠤⠀⠘⣿⣿⣿⣻⣿⡾⠛⣡⣿⣼⣿⣷⣾
⠀⠀⡇⢸⣿⡀⠀⠀⠀⢸⣿⣠⣾⣿⠈⢻⣄⠉⠳⢄⡀⠀⢉⠘⠣⠽⠀⠀⣶⣾⣿⣾⣿⣷⣤⡙⠷⣮⣝⢿⣿⣖⢷⡀⠆⠼⣷⡈⢮⢷⣌⠳⣆⢝⠳⣔⠠⣈⡙⠛⠛⠛⠛⠛⠋⠈⠉⢀⣠⣶⣿⢿⣿⢸⢸⠁⠀⠀⠀⠀⠀⠀⠐⠠⠀⠀⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠐⠀⠀⠀⠀⠀⠐⠒⠂⠬⠤⠤⠀⠀⣀⠀⠀⠀⠉⠛⠲⠤⣄⣀⠀⠁⠐⠀⠀⠉⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠐⠀⢀⡀⠘⠀⠸⠶⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⢻⣿⣯⣩⢤⣴⣾⣿⣿⣿⣷⢸⣿
⠀⣸⡇⢸⣿⡇⠘⣦⡀⠈⠙⠠⣯⣿⠀⠀⠻⣮⠢⣀⠈⠉⠈⢣⡀⠀⠀⠀⠀⠒⠬⢭⣝⡛⡿⣿⣶⣌⡙⠷⣬⣻⣿⣷⣬⣌⢹⣷⡈⢧⢻⣷⣮⡳⣔⣌⡑⡦⣬⣉⣀⣀⣀⣀⣀⣤⣶⣿⠟⠋⢁⣼⢿⠘⢸⢹⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠤⠊⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⡀⠉⢡⢄⣬⣀⣀⣈⢠⣘⡐⡀⠀⠀⡀⠠⢦⠉⠋⠙⢒⣖⣲⣤⣤⣤⣬⡭⣭⣍⣚⣛⣛⠛⠛⠛⠦⣤⠉⠹⠻⢭⣟⣯⢭⣳⠦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣋⣿⣿⣿⣯⣽⣼⣿
⣾⠟⠀⢸⣿⣿⡄⠈⠻⣦⡀⢀⠸⣿⠀⢠⠀⠙⢷⣌⠳⣄⠀⠣⡙⣂⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠾⣍⣟⣳⠮⣿⣿⣿⣿⣿⣿⣿⣷⡄⠙⢽⣿⣿⣿⡽⡟⡶⢶⣬⣍⣉⣩⣭⡽⢟⡽⠃⣠⡾⢫⣟⡎⣽⢸⢸⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠤⠤⠴⠶⠖⠒⠒⠒⠒⠚⠚⠒⠒⠲⠶⠶⠶⣶⣤⣤⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠈⠒⠢⠶⠀⠀⠅⠤⣉⡁⠂⠉⠉⠁⣐⡠⠤⠌⢁⣀⡒⢂⣀⣒⡒⠒⠒⠒⠒⠲⢖⣲⠿⠭⠭⠽⢗⡲⠯⣭⣊⡕⣖⡭⢷⣪⣽⡒⢌⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣞⣻⠷⠯⣽⡻⣿⣿⠿⣿⣿
⡏⠀⠀⣸⡿⠻⣷⢶⣰⡌⢻⡄⢳⣿⠀⠈⢷⣄⠀⠙⢷⡈⠳⡀⠹⡌⠓⢤⣀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣭⣿⣿⣿⣷⣷⠶⠭⣽⣿⣿⣧⡈⠫⡻⢿⣷⣭⣭⣅⣁⣉⣋⣭⡥⠖⠋⣀⡴⢋⣴⣿⢽⡜⢧⠎⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠲⠦⣄⣀⠀⠈⠀⠓⠚⠀⠈⢉⣐⡐⠒⠲⠀⣀⠀⠠⠐⢂⠀⠀⠀⡂⠀⠐⠀⠀⠀⠁⠀⢀⢀⣀⠈⢉⣉⣉⠉⢉⢉⠉⠑⠛⠷⣍⡚⠳⢓⡭⢟⡱⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢿⢿⣿⣦⣈⠙⢷⣝⢿⣿⣯
⡇⠀⣴⡿⠁⡀⣿⢸⣻⡇⢸⣧⡄⢹⡷⡄⢻⣿⡿⢦⣄⠱⠀⠙⡄⢙⢦⣀⡈⠉⠛⠛⠻⠨⣭⠭⠿⣾⣿⣿⡯⠟⣋⡭⠭⣽⣛⣲⡟⣿⢿⣿⣦⡑⢤⡀⠀⣉⡉⠉⠉⠉⠀⢀⡴⣾⠟⢠⣾⢋⡿⢮⣧⢏⢀⡄⢻⡤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠶⢦⣤⣀⣀⠀⠀⠩⢌⡑⠤⠈⠓⠤⠤⣁⡀⢀⣂⣀⣈⣉⣁⣒⣒⡂⢧⣒⣲⠭⣑⣒⡤⠬⡙⣆⠐⠪⠭⠭⢌⣉⣉⠑⠦⣜⠰⢭⣲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣾⣿⡾⣿⣜⢿⣿⡵⡑⢝⣧⡙⣿
⠋⢸⠏⠐⠀⢀⠟⣼⡿⠁⢰⣿⡐⢈⣿⠹⡈⠻⣿⣷⡙⡷⣆⠀⠘⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠭⠓⣚⣋⡁⠤⠚⣩⣿⣿⡇⢹⡌⢿⣿⣿⣷⣿⠷⠿⠖⣋⣡⣴⡾⣛⡽⢋⣴⡿⡽⣸⢳⢧⡏⡎⢸⡄⢸⣿⠁⠀⠀⢤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠓⠲⢶⣦⡐⢦⡍⠍⣑⣒⠢⢔⣒⣒⣒⣒⠢⠤⠤⢭⣅⣙⡚⡯⣑⠺⢍⣒⢤⡠⠽⣖⣊⡑⠒⠦⢄⣉⠀⠈⠙⠷⣍⠛⢶⠄⠀⠀⠀⠀⠀⠀⠀⠈⣿⢻⡿⣿⡾⡿⣧⢿⣿⣝⣾⢸⡟⢸
⣹⣿⠀⢀⡴⠋⢰⠟⠀⣠⠏⢹⣿⢸⣹⣧⡙⣄⠈⢇⢙⡲⣼⣢⣾⣿⡟⠉⣭⣭⣭⣭⣝⣿⡟⠩⣠⣴⡾⠋⢁⣠⠴⢛⣭⡭⠽⣿⣿⡈⣿⡘⣟⣿⣿⣿⣿⣿⣿⣿⣿⣛⣯⣵⡾⣻⣿⡷⣳⢫⠏⡞⡸⢀⡜⠀⣾⡼⣀⡀⣠⣿⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣍⡳⠶⣤⠉⣒⣒⡒⡒⠮⠭⣭⣛⣒⣒⢲⠤⢍⢶⡿⢵⣮⡓⠮⢽⣒⠮⠭⢭⣛⡒⠦⣈⠑⠶⠄⠈⠹⣶⣜⢄⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠿⣗⡿⣿⣾⣟⣿⡿⢸⡴⠋
⣼⡿⢠⠟⠀⠀⣸⣤⠞⢁⡔⣸⣿⡎⣷⣛⢿⣦⡳⣼⡿⣿⣿⠯⣿⣿⠄⣼⣿⡿⠿⠿⢿⣿⠁⣼⡟⣽⢀⡴⣫⡴⢛⣭⡶⠗⣛⣿⣿⣷⣿⣿⡿⣷⣿⡻⣿⣿⣿⣿⠿⢛⣭⢟⣽⣿⢿⢡⢣⠏⣶⣡⠇⡞⣄⣼⣽⢿⡏⣹⠟⣩⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠐⠒⠒⠒⠲⠦⠤⢤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⠛⠷⠶⣤⣠⣭⡭⢭⣉⣓⠒⣒⣒⣚⣩⣙⣶⣦⣍⠳⢌⣭⣛⠖⠬⣍⣛⡓⠦⢌⡑⠊⢙⠢⠄⠀⠀⠈⢮⠻⣣⠀⠀⠀⠀⠀⠀⠀⢸⣿⢢⡷⢣⣿⣿⣿⣾⠃⢠⢤⣤
⢼⡇⢸⠀⢀⣸⠃⣿⢠⢿⣾⣏⣝⢿⣹⣿⣦⣳⣝⣾⣇⣿⣿⣿⡻⣿⢸⣋⣴⣒⣶⣒⠻⢯⠀⣿⠀⡇⣸⢡⢏⣾⣟⣡⢴⡅⣏⣧⢿⣿⣿⣿⣿⣿⣷⣈⣉⣭⣤⣶⠿⣋⣵⣿⣿⣿⡏⡎⡞⡜⡟⡞⡜⡞⡾⣟⣽⡜⡸⣣⡾⠁⠀⠀⡄⣄⣄⣤⡤⡄⢀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠉⠉⠛⠳⠶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⢀⠸⠄⠀⠀⠐⠀⠈⠉⠙⠛⠛⠻⠿⠾⠿⠭⠭⠭⠵⠛⠛⠛⠓⠚⠛⠛⠓⠲⠮⣭⣝⠲⣭⡹⠂⠙⠐⠀⠀⠀⠀⠀⠉⠀⠀⠰⠀⠀⠀⠀⣿⣿⣿⣡⢿⡷⣟⣿⣡⣴⢯⣾⡁
⠌⣷⢸⠀⡇⡏⢸⡇⢸⢸⠿⣿⡿⢾⣳⣙⣷⣿⣿⣿⣿⣿⣿⣿⣿⣾⡀⣿⣾⣍⠲⢌⠹⣆⠑⣿⢧⢳⣽⡈⣿⣏⣿⣿⣌⣿⣜⠻⣿⣿⣿⣿⣿⣿⣯⣭⣭⣭⣶⣷⣿⣿⣿⣿⣿⣿⡼⡼⣱⢏⢞⡜⡼⡹⣱⢫⢮⢜⡽⠋⠀⠀⠀⣼⢻⣺⣺⢳⣿⢻⡣⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠲⢦⣄⡀⠀⠀⠀⢢⡳⡚⢽⡢⣄⠀⢤⣀⣀⡠⠭⣤⠠⠀⠄⠉⣯⠑⠶⠑⠀⠀⠀⠀⠀⠀⠀⠀⠤⢄⠀⠀⠙⠻⢮⣝⣶⣄⣄⠀⠀⠀⠀⠀⠀⠀⣼⣟⠀⠀⠀⢠⣿⣿⣯⣷⠿⢞⣿⣛⠿⣴⣿⡟⢷
⡀⠘⣿⣧⡃⢹⣼⣇⢸⣿⣯⣩⣭⣭⣿⣿⠿⠛⠉⠉⠉⠙⠛⠻⢿⣿⣿⣾⡿⢿⣗⣎⢣⡸⡄⠹⣏⢿⣿⢿⣿⡹⢧⣝⡻⢿⣿⣷⣌⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⡼⡵⣣⣯⢞⠞⡱⢡⢃⡞⣾⠟⠁⠀⠀⠀⠘⠸⢻⣿⠿⠺⠁⠙⠋⠀⠀⠀⠀⠀⠂⠄⠀⠀⠀⢄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠐⠂⠀⠄⠂⠀⠀⠀⡀⠀⠀⠀⠀⠈⠙⠒⠦⢷⣄⡀⠘⣇⢳⠿⣭⣓⡼⠭⣽⣒⣒⠒⣺⣍⣉⠂⠀⠀⠀⠀⠐⢒⡚⣛⣿⣟⣛⣛⠯⢭⣓⠒⠤⣈⠛⠶⣝⡆⠀⠀⠀⠀⣼⣿⣻⡏⠁⠀⠀⣼⣿⣿⠶⣤⣶⣿⠟⣻⣷⣌⠻⣿⣎
⡇⠀⠹⣿⣷⡄⠻⣿⡄⠻⣷⠶⢿⣿⡟⠁⣀⠤⡤⠤⢤⣀⠀⣀⠀⠈⠛⢿⣿⣷⣬⡙⢧⡁⠹⣦⣈⢮⡈⠑⠙⠳⢤⣐⣉⡽⣿⣿⣿⣿⣿⣧⣽⣿⣿⣿⣿⣿⣿⣿⣿⣯⣾⢿⣿⣿⠟⡟⡷⣳⢋⡼⣱⢣⡞⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⢤⡴⣠⣰⠥⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠈⠀⠄⢀⣀⠀⠠⠤⠀⠠⠣⠢⡘⠆⠀⠠⠀⠀⠀⠀⠀⠀⠈⠙⠲⣌⣌⠣⠍⠒⢷⣱⣒⡦⠬⣩⠍⠉⠉⠐⣤⣐⠒⣋⣹⣉⣙⣲⣶⣖⡲⠬⣍⡒⢖⣛⠢⠤⣉⡀⠈⠑⠤⡀⠀⠀⠈⠻⣧⠀⠀⠀⣰⣿⣿⣿⣿⣶⣶⣶⡿⠿⣿⢟⠆⠘⣯
⡷⡀⠀⠹⣷⣿⣦⣌⠹⡄⠐⣾⣿⢏⢠⣾⡿⠛⢉⣭⣭⣉⡙⠪⣝⢦⣀⡑⢿⣿⣿⣿⣦⢻⣦⡙⣿⡷⢾⣿⡶⠶⠶⠶⠶⠟⣋⣩⡿⣾⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⡟⣽⣡⢏⠟⣿⣼⣽⣷⣗⡞⡕⣹⠃⣴⠃⠀⠀⠀⠀⠀⠀⠐⠃⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠽⠯⠴⢲⢎⡫⠅⠠⡀⠀⠀⠀⠀⣰⡠⠀⠀⠀⠀⠀⠀⠙⠂⠌⣀⠂⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⢀⠉⢻⣵⣤⣀⠤⠔⠢⢭⡒⠤⠀⣀⠀⠆⠬⣉⣙⢒⣂⡠⢬⢶⡝⠪⣑⠢⣌⡓⠤⣙⠢⡄⠈⠀⠀⠀⠈⢆⠀⠀⠀⡈⠂⠀⢠⣿⣿⣍⠻⢿⡯⣗⣷⣯⡹⣞⢻⣆⠀⢳
⡁⠱⡄⠀⣿⣿⡝⢾⣢⡹⡇⣾⢏⢠⣿⠋⣠⣾⣿⣿⣿⣿⣿⣶⣌⢣⢳⡵⡜⡻⣝⣿⣿⡖⠛⠉⣉⠀⠀⠀⠀⢀⣀⣀⣀⣤⣤⣶⣿⣿⠿⣿⣿⢏⣽⣿⣿⢟⣿⣋⣬⢟⠵⠋⣰⣿⣿⡟⠏⠾⠞⠊⠁⣼⠃⠀⠀⣀⢤⢖⣫⢆⡒⠒⠒⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢙⠋⡴⢾⣉⣈⠔⣩⡭⠽⠟⠒⣒⣒⣩⣤⢄⡀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠠⢷⢺⡆⢀⣽⡇⠈⠀⠉⠙⡛⠿⠶⣶⣮⣭⣛⣓⣚⣉⣛⣒⣦⡿⠽⠯⠽⠖⠛⠓⠚⠲⠽⠮⣵⣠⡙⠀⠀⠀⠀⠀⠀⠘⢄⠀⠸⡀⢰⣀⣿⣿⣏⡻⢿⣶⡶⢟⣩⣾⣿⠏⠳⣿⠀⠸
⢁⣠⠇⢢⣿⡽⣇⠀⠙⡷⣿⠏⢀⡾⣡⣾⣿⣿⡹⡿⡸⣻⣿⣿⣿⣧⣱⢧⠳⣽⣽⣿⣿⣓⠿⠿⠭⠿⠷⡟⢛⣛⣋⣉⣭⣽⣖⣚⣚⣩⣿⢟⣱⣿⣿⣯⣿⣻⡽⡥⠛⡡⣤⣾⣻⢘⣧⠟⠀⠀⠀⠀⠀⠁⠀⢠⢍⡴⠚⣋⡉⠥⠥⠒⢀⣀⣀⣀⣀⣤⡴⣂⣀⣠⢤⣤⠤⠒⠛⠁⠀⣀⣀⡬⠉⠉⣙⣛⣋⡛⣛⣩⡥⠴⣴⣊⣗⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡷⣤⠇⣸⢹⣧⠀⠀⢀⣀⣌⣀⣀⣠⡙⠛⠿⣿⣭⣭⣭⣭⣄⣀⠀⠀⣀⣀⢀⣀⣀⡀⠀⣀⠀⠈⠉⠓⠦⠄⠀⠀⠀⠀⠈⣆⠀⠅⣸⢿⣿⣿⣍⡻⢶⣦⡶⢫⣿⠏⢁⣴⡖⡌⠀⢸
⡿⠃⠀⢠⣿⢧⠿⠄⢀⣾⡏⢀⡞⣴⣿⣿⢣⢏⣼⣳⢱⢻⣿⣿⣿⣿⣿⣯⣧⣿⣻⣿⣿⢿⣿⣷⣶⣶⣾⣿⣻⡿⠭⠽⠿⠿⠿⠿⠿⢿⣿⢿⣿⣿⣿⢟⡽⡽⣻⣾⡝⠱⠃⡿⣼⡞⠉⠀⠀⠀⠀⠀⠀⠀⢀⣘⣋⣄⣩⠴⠒⣚⣫⡩⢵⣶⣾⠯⣭⣭⣯⣭⣿⣯⣛⣯⣭⣭⡶⠾⠭⠭⠉⢀⠠⠈⠀⠀⠖⠃⠉⢙⡷⠚⠒⠀⣏⡀⠂⠀⢂⡥⠄⠀⠀⠀⠀⠀⠀⠒⠦⠤⢄⣠⠋⡿⢀⡟⢸⡿⠀⣢⣿⣟⣓⢦⣴⡯⠄⠀⠠⡄⠢⣐⠢⠄⠰⢤⣙⣒⡤⢅⣀⠦⢗⠭⡩⠤⢀⣀⡀⣀⢄⠀⠀⠀⠀⠀⠀⢹⠀⠀⣣⣿⣿⣻⣝⣹⣿⠏⡜⠋⣠⣴⣮⣜⢿⡇⠀⠘
⡇⠀⣰⢿⡵⠋⣠⣶⣿⡟⠀⡼⣰⣿⣿⣿⡞⣵⣷⡇⢯⣿⣿⣿⡿⢿⢻⣿⣿⣷⣿⣿⡿⢰⡿⣻⡿⠋⣡⣠⣤⣴⣶⣶⢶⣶⣶⣶⠿⣋⣥⣿⣿⡟⣵⡿⣾⡵⣡⠏⠀⠀⠀⢸⣯⡱⣀⠀⠀⠀⠀⠀⢰⡪⠭⠥⠤⠭⣵⠚⣉⡭⠭⢿⠿⠿⣿⡿⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣟⡁⠄⠒⠀⠐⠂⠀⠀⠀⠀⣀⠔⠉⠴⠖⠚⢉⣩⣴⢾⡭⠷⢶⢶⡫⠤⢒⠤⢀⣀⢀⡉⣩⡿⢀⣿⡇⢰⢿⣻⢧⣎⣽⣿⠩⣉⡀⢚⣭⣵⢣⡻⢢⠔⠂⠢⠔⠭⠵⠒⢤⣙⣖⡒⠢⣶⠎⠙⠦⢄⣷⢤⠀⠀⠀⠀⢸⡞⣳⣿⣿⣿⡏⣽⣿⣿⣷⣷⠞⢉⣠⣴⣽⢾⡇⠀⢰
⡇⠀⠉⡟⠀⠻⢏⣿⣿⠁⢀⢻⣿⣿⣿⣿⣷⣷⣿⣷⣿⣿⣿⡿⣵⣏⢰⣻⣿⣿⣿⣿⢣⡟⣰⠋⣠⣾⡿⠟⠋⠉⠉⢉⣉⣥⠼⣒⣋⣽⣿⣿⢿⡰⣟⢽⣷⠷⠁⠀⠀⠀⠀⢸⣿⠓⢹⣾⢇⢦⣄⡀⠀⡽⣿⣚⣉⣩⣽⢦⡤⣐⠒⠚⢚⣛⣛⠩⣭⠭⠟⠓⠚⢻⡗⠿⣝⡻⠿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣷⣶⣶⣾⡭⠔⣊⣥⣴⠾⠿⣏⠁⠐⠒⢚⡩⠽⠝⠫⠭⠭⠯⠭⣶⡚⠶⢥⠆⣸⣿⠄⡛⡺⣳⣿⢢⣿⡟⠀⠀⢸⡇⠸⢿⢡⠧⡌⣍⣉⠭⠭⠿⢍⡉⢃⣤⣤⡬⠍⠉⠓⢢⠀⠀⠩⢛⢧⡀⠀⠀⡾⢿⢸⣿⣷⣮⣟⣶⣬⣍⣥⡤⢞⣵⡿⣋⢽⡾⠀⠀⢸
⠀⠀⢠⠇⢸⢣⣾⣿⡿⠀⣸⣿⣿⣿⡿⢿⢻⠋⢛⣧⠽⠏⢙⣃⣿⢀⣾⣿⣿⣿⣿⣿⠏⢀⡇⣾⣱⠏⠀⠀⠀⣠⡾⠯⠗⣴⣟⣽⣿⣿⣿⢿⡎⢷⣻⡾⠁⠀⠀⠀⠀⠀⠀⠈⠁⠁⣼⢻⢮⢧⣳⡘⡄⢹⣿⣿⡷⢲⡛⣿⣿⣅⡒⠢⠤⠤⠖⢊⡡⠴⢚⣉⠢⠄⣙⠺⢦⣍⣓⠦⣌⡙⢿⣿⣿⣿⣿⣿⣿⣿⣶⣷⣺⣛⣫⣵⣒⣛⣋⣭⣑⣶⡾⠭⠭⢦⣐⣖⣒⡩⡍⠙⢒⠪⢭⠆⣼⣿⠃⡰⡵⡷⣣⡿⢿⣿⠃⣁⣀⣾⡇⠀⢸⠌⠷⡵⠢⡄⠬⠭⢭⠛⠛⢋⡂⠈⠑⣒⣀⡈⠉⠀⠀⠀⠀⠑⣾⢦⠀⡏⢹⣾⣿⣯⣭⣙⣻⣻⣯⣵⡾⠛⣅⡵⣧⠟⠁⠀⣠⠏
⠀⠀⠸⠀⠘⣸⢻⣿⡇⠀⣿⡿⢹⡟⢡⡯⢋⡴⢋⣠⠖⣻⣿⣷⣿⣿⣿⣿⣯⣿⣿⣿⠀⢸⢰⣧⠏⠀⠀⣠⣶⣧⣴⣶⣿⡿⣿⣿⣿⣿⣳⡺⣿⡿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣮⠈⠳⣥⣇⠘⠦⢻⣿⣿⣟⢶⡘⢿⣷⣍⣙⣓⣉⡙⢦⣖⣛⣹⣦⣭⣥⣼⣿⣶⣶⣿⣿⣾⣛⣛⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣭⣿⣿⣷⣶⣦⣍⡛⢒⣴⣲⣯⡴⣧⣾⡿⢃⡼⣽⡿⡵⡿⣷⣿⣿⠠⠀⢰⣿⡇⣇⢸⡄⠀⡙⠉⣗⡒⣒⣒⣒⣉⣳⡾⢧⡰⢄⡀⠀⠀⠀⠀⠀⠘⠣⡜⢬⢧⣗⣸⣿⣿⣻⣿⣿⣿⣿⣿⣿⡞⣋⡵⠚⠁⠀⢠⠜⠁⠀
⡶⠀⠀⠈⢰⣿⢸⣿⡇⢸⣿⡇⣼⢀⠎⣠⠏⣰⢋⣵⣿⣿⣿⢿⣿⣯⣽⣿⢸⣻⣿⣿⡆⢸⣿⣿⠀⢀⣼⡏⣴⢶⣿⣿⡏⣽⣿⢿⣿⣿⣏⣇⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⣄⣀⣉⡛⠶⣄⡻⡟⠉⢧⣻⣤⡙⢿⣶⣶⣾⣾⣿⣿⣿⡿⠿⠟⠛⠏⠙⢋⣉⣉⣉⣭⣭⣭⡭⠭⠿⠿⢿⣻⣟⡻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣶⣾⣿⡟⣱⢋⡼⣋⢞⡽⣱⣃⣿⣿⢐⡿⢼⣿⡇⣿⠈⡇⠀⠁⢀⠛⠥⣥⣭⣕⣊⣣⣉⡒⠩⡒⠈⢢⣀⡀⣀⠀⠀⠀⠘⢾⢺⡏⣾⣿⣯⣿⣗⣶⣶⣷⣿⣿⣾⠏⠀⠀⢠⠜⠁⠀⠀⠀
⡇⠀⠀⠀⢸⡇⢸⣿⡇⢸⣿⡃⣧⠸⠰⢡⡞⣱⣿⣿⣿⢿⣏⣿⡿⣿⣿⣿⠈⡷⣿⡙⣿⡀⣿⣿⠀⢸⢻⡇⠸⣼⡇⣾⣸⣿⣿⣸⣿⢹⣻⠟⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⠶⠈⠉⠙⠻⣦⡹⣿⣦⡀⠣⣉⡛⠷⠶⡿⠟⢛⣉⣡⠴⣒⣖⣋⣩⣽⣯⣤⣴⣾⣾⣾⣶⣾⣿⣭⣭⣭⣖⣒⡮⢭⣛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣻⣟⣫⠾⡻⣋⡾⢗⣥⣾⠧⢽⣿⡟⢒⣒⠟⣿⣧⢻⣇⠹⡀⠠⡘⠂⠠⣌⡒⠖⢒⡓⠖⠯⣵⠬⣝⣒⠢⠽⠧⠵⣄⠀⠀⠈⢿⣷⣽⣿⣿⣿⡏⣹⠿⣯⡿⢋⡧⡆⠀⢰⡇⠀⠀⠀⠀⠀
⡿⡀⠀⣀⢸⡇⣿⣿⣇⠀⣿⠃⣇⠀⠀⡿⢰⣿⣿⣧⣿⣿⣿⣻⣿⣿⣿⣿⡍⡷⣿⣷⠈⢷⣘⢿⣇⢸⣧⣻⡄⣿⣧⣿⡿⣇⣿⣿⡿⣽⢯⠁⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⢿⣷⣦⣭⣭⣵⣶⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣮⣝⠾⣿⣿⣿⣿⣿⣟⡿⣿⣿⣿⣷⣿⣿⣿⣿⣛⣿⣭⡿⠿⢗⣛⣭⣵⣾⡿⠛⢁⣰⠋⠻⣿⢊⣵⣾⣿⣿⡎⢿⡆⢹⣆⢳⡀⠀⠀⠙⢯⢭⡉⠍⠓⢮⣍⠳⠮⢭⣑⠂⠀⠀⠳⡄⠀⠀⠙⢿⣿⣻⣿⣷⣿⣼⡿⢃⡺⣰⠇⠀⣽⠀⠀⠀⠀⠀⠀
⠇⢳⠀⠘⠈⣇⢹⣿⣿⠀⢹⡇⣿⠀⠀⡇⣿⣿⣿⣿⣿⣿⣟⢻⣾⣿⣿⣿⣿⣳⣸⣿⣧⠀⠻⣮⣳⠘⣿⣷⣿⣿⣿⣿⢧⡹⣿⣿⣷⡟⢾⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠲⠤⠤⠤⢤⣤⣄⠀⠀⠉⠛⢿⡋⡭⢵⣕⠦⣄⡈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣽⣻⢿⣿⡿⡿⣿⣻⣿⣿⣿⣿⡿⠿⠛⠁⠀⣠⣏⢷⢹⡀⢹⣿⣿⣿⡻⣯⣿⣎⢻⣄⠻⣯⡳⣄⠀⢄⠈⢢⣀⠀⠀⠀⠈⢣⠀⠀⠈⠙⠳⠦⠷⠬⢦⠀⠀⠈⢿⣟⣿⣖⣳⢴⣶⡏⡴⠋⠀⠠⡄⠀⠀⠀⠀⠀⠀
⠂⠈⢧⠀⢰⢿⡌⣷⣿⡆⠈⢷⢸⡇⠀⠇⣿⣿⣿⣿⡷⣟⢿⡿⣿⣿⣿⣿⣿⣷⣿⣾⣿⣷⣄⠈⢻⣷⣿⡏⠛⡿⢸⢠⣿⡻⣿⣿⣗⣿⠈⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⠉⠀⠀⠀⡉⠃⠀⠀⠀⠀⠙⢞⢌⢎⠲⣍⠻⣷⣦⣈⠛⢿⣿⣿⣷⣿⣿⣽⣽⢸⢿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣽⢾⣿⣿⣯⣿⣝⣻⣿⣿⣿⣿⣿⣿⠧⠀⢰⣀⣰⣿⣩⢯⡎⡞⡷⢈⡛⠛⢻⣿⣮⣝⣻⣷⣿⣷⣬⣿⣾⣿⣞⡧⣄⡙⠷⣦⣤⣀⠀⢧⣀⠐⠦⠤⢤⣤⣕⠚⠇⠀⢰⠘⣿⣿⣿⣿⣿⢋⡴⠃⠀⠀⡸⠃⠀⠀⠀⠀⠀⠀
⠀⠀⠈⢻⡾⠘⡿⠿⣿⣿⡀⠘⣯⣿⡀⠀⢻⣿⠻⣾⣿⣝⢿⣿⣿⣿⡿⠋⠀⢙⢿⣿⣿⣿⣿⣷⣼⡿⠉⠁⠀⠃⣾⢻⣞⢷⢿⣿⡿⢿⣿⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⢦⢀⠀⠀⠀⠠⡈⠫⣙⣶⢌⠓⢬⡱⢏⡷⢦⣌⡙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡟⣟⢿⢻⣭⠻⣷⣌⢿⡿⣿⣻⣿⣻⣟⣿⡟⣿⣿⠀⠀⠀⢿⣿⣿⢣⣏⢟⣷⠇⣠⣶⣿⣿⣿⣿⣽⣽⣭⣭⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣷⣿⣿⣝⠲⠶⠶⣬⣽⣢⠀⠈⠀⠻⠿⠿⠛⠋⠉⠀⠀⣀⠔⠁⠀⠀⠀⠀⠀⠀⠀
⠁⠀⠀⠀⢸⠀⢸⣶⢸⣿⣇⠀⠸⣿⣇⡀⠸⣿⠀⠸⣿⡾⣏⣿⣿⣿⠇⠀⠀⠈⢷⡹⣿⣿⣿⣿⣿⡀⠀⢀⣾⣿⣿⣿⡸⣎⣿⣿⣷⢸⣿⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠸⣿⡀⠀⠀⠀⠈⢆⠈⠉⢇⡈⠶⣈⢷⣉⠱⢎⣹⣷⣀⡉⠿⢿⣿⣿⣿⣿⣿⣿⡿⠿⠉⠁⠀⠀⠀⠹⢸⡎⢿⣿⣿⣿⣿⡎⣷⣹⣿⣹⡏⣿⣿⢹⠹⠀⠁⠀⠀⠀⠈⠁⢿⡸⣸⠇⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣆⡀⠀⠾⠿⢷⡀⠀⠀⠀⢀⢀⣀⣀⡶⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⣸⡆⢸⣿⠟⣿⣿⣆⠀⠙⣿⣧⠀⢻⣧⠀⢹⢿⣝⣾⣿⣿⠀⠀⠀⠀⠀⠙⢮⣻⣿⣶⡿⢉⣴⠿⢳⣿⣿⢃⡷⣝⢾⣿⣿⣯⡏⣿⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠂⠀⠀⠳⣝⢦⡀⠀⢄⠀⠑⣌⡲⢍⡲⢬⡓⠮⣝⣓⡚⠽⠛⠻⢷⣶⣦⣤⣤⣴⣶⣶⣷⣟⡿⢛⣽⣿⣿⡿⢀⣿⣾⣧⣿⣿⡟⡇⡟⢷⣹⣿⣿⣿⡟⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠋⣴⣿⣿⣿⣿⣿⣿⢿⣟⣿⢻⣟⣻⣛⣛⣛⡻⢯⣛⡿⢿⣿⣷⣮⣓⠰⡜⣏⠻⣟⠿⣿⣿⣷⣶⠒⠒⠽⠀⡐⡝⣋⠿⠟⡛⣉⡵⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢃⠀⣰⠀⡿⣰⢿⣿⣿⣧⠀⠘⣿⡄⠀⠻⣷⡈⡳⣻⣻⣿⣿⡀⠀⠀⠀⠀⢰⠦⣽⣿⣿⢠⠞⣡⣾⣿⡿⣡⠞⢇⡪⡱⣿⣿⣏⣧⡹⣽⣮⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢀⡀⢨⡎⠙⠢⡈⢣⡀⠪⣌⠳⣍⡳⣮⣛⡲⢯⣭⣽⣛⣿⣯⣤⣖⣛⣛⣿⢿⡿⢞⣩⣶⣿⣿⣿⠟⣱⣾⣷⣿⣿⣿⣟⡗⣷⡟⢸⢿⣿⡇⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠈⣿⣿⣿⣿⠿⣟⣛⣭⠶⠶⣚⣶⣲⣶⣶⠬⠽⣗⣒⣛⠶⣭⣛⢿⣿⣷⡜⣾⣧⠈⢦⠘⡏⠻⣿⢓⡿⠀⠀⢻⠦⠬⠽⠓⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣿⠀⣷⠯⡽⡽⣿⣿⣷⠀⠈⢻⣆⠀⠹⣷⣌⠫⣧⣿⣿⣿⣦⣄⠀⠀⢌⡹⣞⣾⣿⣾⡆⣼⣿⣿⣻⠁⠀⠀⠁⢙⣾⣿⣿⣾⣇⠹⡟⣟⢷⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡉⡑⣄⠱⢌⠢⡘⢦⠙⠦⣌⠳⣦⣙⠲⢭⣛⡻⠶⠶⠿⠶⢾⣛⣟⠽⢛⣥⣾⣷⣿⣿⡿⣿⢟⡵⣻⣿⣿⣿⣿⣿⠟⠈⡀⡝⢹⣯⣣⣇⠇⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⢻⣿⣿⣿⣿⣯⣽⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣉⠒⠫⣛⢯⡻⣿⣌⢻⡇⢸⠀⣿⠀⣿⢠⠃⠀⢈⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠄⠀⠀⠀⠀⣿⠂⣿⢱⣿⠣⠅⣿⣿⣧⠀⠈⣾⣦⠀⠘⢿⣷⣮⣍⣻⠿⣿⣿⣷⣑⢤⡹⣼⣿⡿⠋⠋⡇⢸⢸⡇⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⡙⣷⣸⣹⡟⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣜⢮⡳⣌⠳⣜⢢⡱⣕⢌⠳⣦⣽⣛⡳⢮⣭⣭⣽⣻⣿⣿⣷⢾⢿⣿⣿⣿⣿⠟⣫⠾⣗⡩⣞⡵⣵⣳⣿⡿⠋⠀⠀⡼⡱⠋⡿⣼⡜⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⢸⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡈⠢⣻⡜⣿⡄⢳⢸⢿⣟⢠⡿⠋⠀⢠⠞⠀⠀⠀⠨⡩⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⡿⠠⠝⣿⠡⠵⢊⠙⣿⣿⡀⠀⠘⢟⠧⠀⠀⠉⠙⠛⠿⢿⣶⣿⣿⡿⢷⣿⣿⢟⡅⠀⠀⡇⠏⣾⣷⠘⠀⠀⣾⣿⢋⣼⢟⣿⣿⣿⣿⣷⣻⣽⣼⣗⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠻⠶⠦⠽⢵⡝⣞⢦⡑⢤⡙⢮⣙⡧⠶⣖⣒⠶⠶⡶⣲⣿⣿⡿⢿⣝⡡⣯⢞⣩⣭⠶⣫⢞⣿⡿⠋⠀⠀⠀⡼⣱⠃⢸⢏⡏⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠰⣿⣟⠻⢿⣿⣿⣷⣿⣻⣼⡿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣦⠈⢇⠸⠃⠀⠘⣿⣧⠞⠁⣠⡴⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣄⢸⠇⠈⠀⢹⣿⣜⠩⣔⢾⣿⡇⠀⠀⠀⠀⠀⠢⠭⣖⠦⣔⡂⠌⠛⢿⠁⢸⣿⣿⠋⣠⠆⠀⠀⣼⣳⣿⣆⢀⠐⡷⢿⠘⣿⣏⣿⣿⣿⣿⣿⣿⣮⣿⣿⢯⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⠺⢧⡙⢦⡹⢦⣉⡽⣟⣶⣮⣙⣻⣾⣿⣻⣯⣞⣵⡾⣫⣿⠿⣫⢕⣮⡿⠟⠉⠀⠀⠀⠀⢸⢱⠃⢠⣿⣎⢸⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⢸⣿⣿⣷⣦⣌⠙⢿⣿⣿⣷⣿⣽⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣷⣼⡀⠀⠀⣼⠟⠁⣠⢾⣻⠿⠒⣲⠂⠀⠀⣀⡤⠤⠤⠒⠒⡲⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣿⠏⠀⠀⠀⠀⠙⢾⣜⢇⢻⣿⣷⢄⠀⠀⠀⠀⠀⠀⢎⢷⣦⣭⣓⠀⠸⡄⢺⣿⠟⢀⡇⠀⣀⠾⣳⡿⣻⣿⡟⠀⢳⢸⡄⡿⣧⣿⣯⠿⡛⣿⣿⣿⣿⣽⣮⣻⣽⢗⢦⡀⣀⣀⠀⠐⢦⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠂⠙⣶⣽⣳⣲⣯⣿⣿⣿⣟⣯⢷⣫⢝⣻⡿⣫⢞⡱⣟⣯⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⡾⡔⣻⣷⡇⡟⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⢸⣿⡻⣝⢿⣿⣿⣦⣌⡟⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⡿⢿⡇⠛⠷⣀⡾⠃⠀⣰⠛⡺⠁⢀⡞⠁⠀⠀⢰⠇⠀⠀⢀⡔⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢰⡶⠋⠀⠀⠀⠀⠀⢷⠀⠙⢮⡗⣿⣿⣿⠀⠀⠀⠀⠀⠀⢈⡲⢽⠿⠯⠍⢰⣿⡟⣁⠴⢛⠇⠀⢀⡴⠋⡴⢋⡼⠃⢠⣿⣼⢿⢀⡿⣵⢫⢳⡹⡌⢻⢿⣿⣿⣿⣿⣿⣯⡟⢎⠻⢍⡳⣌⠢⣑⢄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠪⠽⠿⠷⠿⠟⠛⠍⢂⡭⢚⡽⠫⠾⡑⢪⡭⢉⡠⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢻⢣⣿⣻⢼⡇⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⣼⣿⠹⡜⢿⣿⣿⣝⢿⣿⣦⣌⡹⠻⠿⣿⠿⠿⠛⠛⡋⠉⠁⠀⣾⣿⣽⣛⡋⠁⠀⡼⠁⠀⡇⢀⠞⠀⠀⠀⢀⢏⠀⣠⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣶⡏⠀⢠⠄⠀⠀⠀⠀⢘⢷⣤⣌⣻⣬⣿⣿⢿⣿⢿⣶⣤⠀⠂⠀⠀⠠⠤⢴⣻⣿⠋⢁⡴⠁⠀⡰⠋⠔⢋⡴⠋⣀⣴⣿⣾⠃⢠⡞⣽⣳⠑⢣⢝⣎⢦⡑⢙⠻⣾⣿⣿⣿⣿⣮⡳⣦⣝⠢⣝⠦⡟⠮⡻⡳⣕⢦⣢⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⣾⠵⣾⡯⣞⢭⣲⠬⣡⠖⢉⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠘⢱⣻⣯⣻⡇⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⣿⣧⡙⢮⣿⣯⡻⣮⡻⣿⣿⣿⣿⣶⣦⣭⣭⣭⡥⠤⠀⣠⣾⣿⣹⡏⠉⠀⢀⡞⠀⠀⠀⠙⠉⠀⠀⢀⠔⢁⣴⣞⣥⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⠀⠀⡾⠀⠀⠀⠀⢀⣸⣹⣯⣟⣻⣿⣿⣿⣎⠻⣷⣭⡟⠂⡄⠀⠀⠀⠓⢾⣿⣿⡃⠀⠀⢀⡞⠀⢀⣴⠁⢀⡞⣸⣿⠟⠁⢀⡿⣼⣿⢸⢠⡎⣳⣮⡓⠮⣳⡀⢨⠻⣟⣻⡿⢿⣿⡶⣬⣛⠶⢽⣚⠧⣝⠮⠦⣕⠷⡹⣖⢔⢦⡹⣄⣠⢄⣀⣀⡀⠀⣀⣠⡤⣗⡾⢿⣿⢯⡗⢶⢻⠍⣡⢻⠴⢦⡾⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⠙⢯⡟⡇⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⢸⣿⣿⣷⡝⣆⠻⣿⣿⣎⡿⣮⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢋⡎⣿⣿⠇⠀⢀⡞⠀⠀⠀⠀⠀⠀⡠⠞⠁⣠⣾⡿⠋⣷⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣏⠀⢰⡇⠸⠳⣤⣠⡫⣵⡴⠒⢚⣏⣿⣿⣿⣿⡌⠘⢿⣭⣛⠯⠭⠭⢭⣉⣿⣿⡿⠀⠀⢠⡟⠀⢠⣾⣿⡦⣾⡃⣿⡟⠀⠀⠘⢠⣿⣿⢸⡏⢳⣱⡑⣽⡑⢬⢽⡢⢄⡉⣌⣉⠒⠬⣙⠳⢭⣿⣿⣿⣿⣾⣝⣒⠦⢭⣙⢮⢮⣣⡻⣝⡞⢦⠻⣶⠯⣓⣮⣗⢽⣶⢯⡖⢶⣻⢬⠚⠁⠙⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢹⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⣾⠇⢻⣿⣿⢮⣛⡻⣿⣿⣿⣶⣽⡲⠥⣭⣯⡽⠿⠿⠉⠁⠀⣼⣷⡿⢸⠀⠀⣿⠃⠀⠀⠀⠀⡠⠊⠀⣠⣾⡿⠋⢀⣔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡧⠀⢸⠇⠀⠀⠀⠛⠛⠛⢛⣿⡿⢟⡯⣋⣽⣿⣿⣦⣈⢷⣾⢿⣽⣖⣲⣿⣿⣿⠖⠃⡠⠋⣀⣴⠟⣫⣾⠁⠸⣿⠹⣴⡶⡖⢠⠏⣹⣿⣿⣇⣾⣗⣿⣨⠻⣌⢷⡙⡶⢔⣷⣷⣿⠳⣬⣍⡲⢍⠻⢿⣿⣿⣿⣿⣿⣷⣮⣍⠳⣍⢷⠹⡌⠢⠵⠄⠙⠚⠿⡒⠍⠃⠈⠋⠉⠉⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⣢⣾⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⢸⣸⡇⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⣸⡟⡄⠀⠻⣿⣷⣜⣿⣟⢿⣿⣿⣒⣏⣏⣙⣉⣩⣤⡴⠖⠃⡼⣿⣽⡞⡾⠀⠀⣿⠀⠀⠀⢀⡜⠀⠀⣴⡿⠃⢀⣔⡷⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⢴
⣇⠀⣘⢆⡀⠀⠀⠀⠀⠀⠸⢧⣶⡋⢌⣿⣿⣻⣿⣿⣿⣷⣮⣟⣿⣾⣿⣿⡟⠁⠀⠀⠀⠈⠛⢶⣾⣿⠟⠀⠀⡿⢀⡟⢹⠃⣡⠞⠝⣿⣿⡿⣿⣿⣿⢿⣿⣽⣡⠇⣸⢢⠿⡹⣻⣻⢦⣷⡽⣆⠌⣁⢻⡿⣿⢿⣿⡻⣿⣿⣷⡈⢷⠣⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢮⣿⡼⡼⢬⣿⡼⣣⣧⡦⠀⠀⠀⠀⠀⠈⠙⠁⠀⠀⠀⠀⠀⠀⠰⢸⢰⠀⡼⢡⡿⠼⣠⣤⠀⠈⢻⣿⣞⡿⣿⣾⢯⣭⣍⣉⣉⣉⣉⣀⣀⡤⣾⣿⢳⣽⢹⡗⠀⠀⢻⠀⠀⢀⡜⠀⢀⣼⡟⢀⣴⠟⠁⢀⡇⠀⠀⠀⠀⠀⠀⠀⢀⡤⠐⠈⠀⣠⠊
⣧⡀⠘⣆⠙⠲⠤⢤⣤⣄⠀⢺⣿⡯⣾⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢀⠤⠂⢀⡁⢰⣾⣦⣤⡤⠀⠀⠀⣤⣼⠀⢼⠞⢁⡜⢸⣿⣿⣿⡿⠋⠀⠘⣰⢹⡜⡤⣿⣏⣷⡝⠢⢩⠃⢽⢿⡲⣌⠢⢄⡍⠌⣷⡟⠏⡞⢭⠻⣷⢰⣤⣤⣷⣶⣶⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣸⣟⣍⣑⣧⡼⠟⠋⠙⢯⣯⣧⣄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠈⠀⢣⠟⣱⡟⣵⣡⢇⡷⡄⠹⣧⡹⢶⣭⣓⡒⠒⠛⠛⢋⣩⠿⣫⡴⢻⣿⢿⣿⡘⠽⠄⠀⠈⣷⠀⢼⠁⢀⣾⠻⢷⠟⠁⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⢀⠌⠀⠀⣠⠞⠁⠀
⡇⢣⠀⣯⡳⣤⡀⠄⠀⠈⠑⡼⣿⣿⣧⣿⣾⢹⣿⣿⢿⣿⣿⣿⠃⡴⣿⢰⠇⠀⢀⡤⣖⣶⣭⣭⡖⠃⠀⢀⡼⢣⠟⢠⠏⣠⣾⠇⣸⣫⡿⠋⠀⢸⠕⡃⣼⣻⠿⣴⣽⣿⣿⣧⣎⣌⡃⡌⠈⢷⡆⠳⣦⢭⡑⡘⢟⠈⠕⡭⡕⢼⠯⣿⣿⣿⢻⢸⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⣴⣿⣿⣿⠿⠛⠉⠀⠀⠀⠀⠀⠙⢿⢟⣗⣿⣿⡕⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢰⠇⣾⣳⣛⠎⣱⣑⡀⠙⢿⣮⡻⣭⣍⣛⣛⣍⣥⢳⣫⠟⢁⣴⣿⣽⣿⣳⡄⠀⠀⠀⡿⠳⡏⢀⠎⠀⢐⠏⡀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⣠⠞⠁⠀⠀⠀
⡇⢸⡇⢧⢿⣌⠻⣷⣄⠀⠠⠀⣽⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⡜⠀⡟⣿⠀⡀⢸⣫⣙⠶⠖⠋⠀⠀⠀⠉⣠⠏⣠⠋⣴⠿⢋⡴⠛⠁⠀⠀⡠⠊⠈⢀⢇⡇⣼⣿⣿⣯⢀⣿⡿⣞⣶⠃⢰⠀⣨⢗⢳⣾⡟⢳⢸⠠⡸⣮⣻⡝⡇⣿⣿⢿⣼⠘⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⢿⣫⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣽⣟⠏⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣼⣞⣽⣝⢮⡺⡑⢆⡹⣄⠀⣍⡛⠶⢿⣿⣟⣭⠾⠛⣠⢶⣿⣿⣿⠾⣷⣗⠃⠀⠀⢻⣇⠎⠋⠁⠀⠀⣸⣴⡏⠀⢸⠀⠀⠀⠀⠀⠀⠀⡠⠊⣠⠞⠁⠀⠀⠀⠀⠀
⡇⠘⡇⢻⡜⢿⣽⣿⡟⣦⠀⠀⢹⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⠇⢰⣿⣿⣰⠷⠋⠉⠁⣀⠀⠀⠀⢀⣶⣫⣵⡞⠁⠉⠁⡰⠋⠀⠀⠀⠀⠈⠀⠀⠀⡾⡺⠃⣿⢷⠛⢟⣼⣿⣷⢿⣿⣱⡏⣴⢣⣐⣾⠃⣇⢼⠈⣾⢣⠿⢉⣧⣅⣽⣻⡸⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣞⢓⣤⣾⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡞⢿⠵⡑⠽⣍⠘⠰⡈⢷⡙⣌⢠⢀⠀⠀⣀⣴⡾⣻⡽⣿⡟⠁⠀⠈⠈⠀⠀⠀⣸⠃⠀⠀⣀⠤⢴⣤⣽⡇⠀⣸⠀⠀⠀⠀⢀⠤⠊⢀⡜⠁⠀⠀⠀⠀⠀⠀⠀
⡇⠀⠹⡄⠹⢎⡿⣿⣿⢻⣆⠀⣼⢿⣇⣽⡿⡾⣿⣿⣿⣿⠏⣿⣀⣸⢸⣿⣏⠀⠀⠀⠀⠀⠁⠀⠀⢠⡭⢟⡩⣰⠀⢀⠔⠁⢀⠀⠀⠀⣠⠶⠶⢀⣘⣙⣀⠘⡘⠞⠶⢚⡿⠉⣟⣾⣿⣿⣾⣿⣷⠏⡞⢸⣼⢸⠀⡇⣪⠩⣏⣿⢼⣺⢠⣔⣦⠀⢀⠀⠆⠀⠀⠀⠀⠀⠀⢀⣀⣴⡞⢍⣮⣶⣿⣿⣿⣿⣿⠀⠀⠀⠀⢀⣤⣤⣤⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡜⡾⢷⢅⡸⣖⠠⠉⠄⣱⡘⢮⣤⣙⣫⠿⡸⣞⣵⠿⠋⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⣠⠊⠁⣴⡾⠋⣿⢷⠖⠁⠀⢀⡠⠒⠁⠀⢠⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠃⠂⠀⢸⣅⠀⠛⢿⠀⢸⣣⣇⢹⡏⣿⣙⣿⣿⣿⣿⣿⢏⣼⣿⡏⣻⣼⡿⠛⠃⠀⠀⠀⠀⠀⠀⠀⠴⠞⣭⠞⣡⣖⣁⣤⡔⠁⠀⠀⢈⣠⡶⢟⣿⠿⠛⣛⣻⣦⣤⡾⠟⢁⠎⠀⣟⣿⢿⣿⢫⢧⢧⢃⣿⣿⠸⠰⠁⣧⢸⣿⡏⡿⣽⢸⡧⠟⠀⠀⢀⣀⣀⣠⣄⡀⣰⣿⡿⢿⣥⣿⣿⣿⣿⣿⣿⢿⣿⣟⢀⠀⠀⢀⣼⣿⣿⣿⣷⣯⣯⣛⢷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣼⣇⠜⡘⢎⣦⡀⣘⡂⢗⡄⠈⠻⠿⠿⠾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠠⡼⠁⠀⠀⠀⢀⠾⠁⣀⠤⠴⠖⠉⠀⠀⠀⣠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡄⠀⠀⢰⠈⢣⡀⠂⠱⢼⣿⢹⠄⢻⣿⣧⠿⣿⣿⣿⣿⣾⣻⣿⢠⣿⡿⠁⢀⣴⢶⠶⠖⠶⠲⠒⠂⢠⣛⣥⡾⢿⡏⠀⡸⠁⣠⣴⣴⡿⢋⣴⢟⣥⡾⢿⣋⣩⣤⣤⣽⣯⣋⠀⠀⠹⢨⣿⣿⠟⢸⡘⣮⠟⢁⡀⠀⢠⡧⣾⣸⢸⢣⡏⡚⢀⣀⣀⢀⣾⠿⡽⣫⠛⢞⣭⣽⣿⣿⣿⣿⠿⠿⠿⠽⠛⣉⣛⣿⡭⢳⣶⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⡀⢤⣤⡀⠀⠀⠀⠀⠀⡀⠄⣠⠖⠀⣀⢔⠀⢸⣿⣿⣿⡷⡉⣜⣹⢟⡑⠎⠒⢄⢤⣀⣀⡀⠆⠀⠀⠀⠀⠄⠀⣤⡇⠀⠀⣸⠏⢸⠃⠀⠀⠀⣴⣫⣤⠞⠁⠀⠀⠀⠀⠀⢀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡅⠀⠀⢐⠀⠀⢳⠄⠀⠦⡋⠳⣐⢶⣽⣿⣿⣽⡿⣿⡯⣿⢻⣿⣿⠟⠀⠀⠙⣓⣬⣾⡾⠿⣿⣿⡷⠚⠂⠀⢀⣿⠀⠈⣠⣾⣯⣾⡟⠀⠊⠁⠚⠋⠀⠉⠉⠀⣀⠠⠤⠤⠬⣍⠢⣤⡟⣸⣿⡀⡸⠛⢡⠀⣼⢀⢠⠇⢀⣶⠁⡏⡼⣠⡱⡟⡞⣹⢟⣟⡾⣴⣧⣾⣿⣿⡿⢟⢻⣽⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣦⣍⠻⠿⣿⣻⣿⣿⣿⣷⡝⣿⣿⡋⠻⣾⡽⣾⠦⣀⣄⣀⣤⣤⣠⣕⡥⠞⠋⡠⠀⡟⢸⣿⣿⣿⡹⣾⢣⡜⠒⣂⠋⢆⣴⣐⠎⠀⠀⠀⠀⠀⢀⣔⡞⣼⠃⠀⢸⡟⢠⡏⠀⠀⣠⣾⣶⠟⠁⣠⣴⣶⡶⠀⠀⣠⠛⠀⠀⠀⠀⠀⢠⠤⠤⡤⠤⠤⢤⠤
⠧⠀⠠⢺⠆⢰⠈⡇⠀⠸⣿⠶⣿⣷⣿⣾⣿⣿⣿⡿⠰⣿⣺⣿⠃⠀⣰⠆⢰⣿⡿⢫⡴⠀⠙⣿⡿⣿⣿⣿⣿⢿⠉⠛⠛⣉⣩⣾⣧⡄⠀⠀⠀⠀⠀⠀⠀⣠⡴⢶⣶⣶⣶⣤⣉⢉⣤⣿⡏⠀⠀⠀⣾⣰⠅⣰⠿⣧⣮⠃⣰⢳⢁⣷⣹⣽⣱⣯⣿⣶⣿⠿⣟⣻⣯⣭⣷⠾⠿⠿⠶⠿⢿⣿⣯⣥⣭⣿⣾⣿⣿⣿⣿⣷⣮⣭⣙⡛⠿⢿⣿⣆⠽⣗⠀⠙⡷⡙⢾⣿⣭⣿⠿⠿⢿⡧⠶⣚⠍⠀⣰⠇⢈⣿⣿⡾⣭⣿⡟⠀⡄⢈⡤⠁⠀⠀⠀⠀⠀⣀⣤⣖⠃⢃⡼⠃⠀⣠⠏⢀⠟⠀⣠⢾⡽⠟⠁⣠⡾⠟⠋⠁⢀⡴⠞⠁⠀⠀⠀⠀⠀⠀⢸⠀⠰⣧⣤⠵⠴⠜
⠀⡀⠀⡸⠀⢸⠀⢻⠀⠀⢹⡆⢈⡙⣻⡿⣿⣿⣿⡇⢸⣿⣿⡇⢠⢤⡏⠀⡺⠏⢀⣿⣁⠀⠀⠈⢻⡿⣿⣿⣾⡞⠀⠸⠛⠶⢎⢻⡄⠀⢀⠀⠀⠀⠀⠀⠚⣥⣾⠟⣉⣴⡶⢾⣿⣿⣿⣿⡇⠀⠀⣸⣧⣿⣸⢏⣾⢛⣮⢶⠇⡨⣼⣷⣿⣾⣿⣿⡿⠽⠗⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠉⠉⠛⠛⠿⣿⡿⢿⣿⣿⣿⣿⣿⣷⣮⣝⢧⡙⢷⣄⢍⡱⣄⠙⢿⣿⣿⣿⡷⣒⣫⣡⣴⡞⠏⠊⣼⣿⣿⣝⡚⢊⣄⠍⠤⠊⠀⠀⠀⠀⠀⠀⣼⡿⡝⢆⣴⠟⠀⢀⡴⠁⠀⠘⠒⡾⠟⠋⣀⠴⠛⣉⣤⣴⠒⠛⣯⠴⢻⠇⠀⢀⣀⣀⠀⢠⠏⠀⠀⠈⡯⠀⠀⠀
⡎⢀⡔⠁⠀⠐⠀⠀⢣⠀⠀⠻⢦⣭⣭⣿⣿⣿⢿⡇⣾⢿⣿⠀⣿⢸⣃⡐⠀⠀⠸⠉⠹⣧⠀⠀⢸⢣⡿⢹⡟⠁⠀⠀⠀⠀⠀⣿⣧⡀⠈⠀⠀⠀⠀⢠⣿⣋⣴⡾⠋⠙⠿⣮⣷⣀⣝⣿⡇⠀⢠⡟⣼⣳⣏⣜⣴⣮⣳⢏⣾⣿⣿⣿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠈⠹⣦⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣆⡙⢷⣿⣿⣿⣦⣬⣽⣿⣿⠿⠋⢁⣤⣶⣶⡿⢿⣿⣿⡿⣙⠲⠍⢹⣦⡀⠀⠀⠀⠀⣠⣾⣟⣯⡾⠋⠁⢀⡴⠋⠀⠀⠀⠀⠀⠓⠒⠛⠒⠚⠉⠉⣁⠤⠒⢉⣠⣔⣋⠀⡀⣯⣠⠏⣠⠏⢠⠔⠒⠒⠁⠀⠀⠀
⡷⠋⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠀⠀⠀⣰⣿⠏⡼⢁⡇⢸⣿⣄⠟⠛⢻⠇⠀⠀⠀⢀⣠⢽⡶⡫⣿⡿⢡⣿⠀⠀⠀⢠⠃⢀⠐⠓⠉⠀⢀⣰⣶⡶⠀⣾⣿⣿⡟⠁⠀⠀⠀⠈⠉⠛⠿⣿⡆⣠⡿⣸⢣⡿⢿⠾⣳⣩⣾⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠃⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠈⠛⠯⢟⣿⣿⣿⣿⣿⣶⣬⣉⣉⡙⣉⣉⣉⣤⣴⣶⣿⡿⡛⠍⡂⢸⣿⣿⣟⠀⠟⢍⢣⣨⠇⠀⠀⣠⣾⠿⠛⠋⠁⠀⣀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⣴⣿⠿⠫⣭⣝⡇⢈⡤⠖⠁⢠⠇⠀⠀⠀⠀⠀⠀⠀
⠇⠀⠀⡀⠀⠀⠀⠀⠀⢀⣼⡦⠤⣤⣾⣿⠏⣰⢃⣼⠇⢸⡿⣿⡷⢀⡟⠐⠀⠀⣰⠟⢁⡞⢀⣽⠋⡰⢻⡇⠀⢸⡄⣯⠀⠀⠀⠀⢀⡴⠋⠁⣠⠆⢰⠁⣿⡿⠀⠀⠀⠀⠀⠀⠀⠱⣄⠈⢻⣿⡦⡣⣏⣴⢋⣼⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⢠⠎⠀⠀⠀⣠⠏⠀⠐⣤⠤⡀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣴⡐⠀⢻⣿⣞⡯⡡⠀⡻⠫⠀⢀⣼⡟⠁⠀⠀⢀⡠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⣼⠟⠁⠀⠀⠀⢹⡷⡏⠀⢀⠴⠃⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⡀⠀⠀⠀⠀⠀⠀⡯⠿⡗⣲⢛⣿⣯⣼⣿⡟⠃⣠⡿⢠⣿⡏⣾⣶⠗⠀⡸⠋⢠⡟⣠⢟⣵⠞⢀⡞⣷⢄⠘⠀⣷⠀⣦⣀⣠⠊⠀⣠⡾⠃⣠⠃⣼⣿⠃⠀⣰⠃⠀⠀⢸⡀⡀⠘⢦⠀⠹⣿⣿⣿⣾⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⢠⡟⠀⠀⠀⣰⠏⠀⠀⣠⠏⢸⠇⠀⣰⠀⠀⠀⠹⣿⣿⡿⣿⣿⣿⡻⣯⣟⣷⣿⣿⣿⣿⣿⠿⠿⠷⣦⣻⣿⣗⣍⡍⠄⠈⣑⣾⠏⠀⠀⢀⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠊⠀⢀⢴⣁⢀⣀⡠⣤⣔⡸⠃⠉⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠰⣟⡫⠛⣥⣾⣿⣿⢻⡟⠀⣼⠟⠀⣸⣿⣿⡿⠁⢀⠞⠀⢠⣟⠾⠓⠉⡼⠂⠉⣸⣿⣿⡄⠀⣼⣾⣿⡿⢁⣴⠞⢋⣤⣾⠃⣰⢿⡯⠀⢀⡏⠀⠀⠀⢹⠂⡇⠀⠈⠷⣄⡘⢿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡞⠀⠀⢀⡄⠀⠀⣰⡿⠀⢀⣿⠁⠀⠀⡰⠓⣴⣿⠎⠁⢠⡟⠀⢰⠇⠀⠀⢰⡖⣿⣿⣿⣯⣿⣿⣷⠃⠈⠉⠛⢿⡍⠹⡍⢷⠀⠀⢺⠉⠻⣿⣶⠵⠂⠠⣹⡏⠀⢠⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⣉⣇⠴⠚⢁⡠⠤⠚⠁⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⣀⣠⠾⠏⠀⢀⣿⣿⡿⠁⢸⡇⢸⡏⠀⢠⣿⣿⠏⠀⢠⠏⠀⣠⠏⠁⢀⣠⠎⠀⢀⣴⡿⠋⣿⡇⠀⣾⣿⡿⢠⢏⣵⣾⣿⡿⢁⣴⢋⣾⣧⠀⢸⡃⢰⠀⠀⢸⡀⣣⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⢀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⠃⠀⢠⡟⠀⢀⣼⡿⠁⢀⣾⠏⢀⣠⠞⢠⣾⡿⠃⠀⢠⠏⠀⡰⡋⠀⠀⠀⣿⣏⣼⣿⠘⣿⣏⠹⣿⠀⠀⠀⠀⠀⢳⠀⢣⢸⠀⠀⠘⡇⠀⠙⢿⣧⡄⠸⣿⠁⠀⢹⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢋⡾⠋⢁⠤⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠋⠀⡇⠀⠀⠀⠀⠀⠀⠀⠐
⣀⣀⣠⠴⠚⠋⠁⠀⠀⢀⣴⣿⡿⠋⠀⢀⡼⣷⢈⣖⣀⣾⣿⠃⠀⢠⠋⠀⠀⠋⢀⡴⢱⡿⢀⣴⠾⠋⢀⣼⡿⠃⡴⢻⣿⡷⣣⣾⣿⡿⢋⣴⠟⢡⡿⣿⠻⣆⢸⡇⢸⣇⠀⠈⠫⠉⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⡴⠁⠀⠀⠀⣠⣾⣿⣿⣿⡿⠁⣠⣼⣿⣵⣾⢿⣿⣡⠴⢿⣩⣶⠟⣁⣴⣿⠟⠁⢀⡴⠋⣀⡴⢋⡠⣪⠏⢀⢿⣟⡿⣿⠀⢹⣿⠀⢹⡇⠀⠀⠀⠀⢸⡇⢸⣾⡄⠀⢸⡇⠀⠀⠈⢿⣿⡄⢸⡇⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⣠⠋⡠⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢴⠚⠉⢀⣠⠤⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠋⠁⠀⠀⠀⠀⣀⣤⣶⣿⣿⠟⠁⢠⠖⠋⣸⣿⡄⠀⣾⣿⡇⢀⡇⡏⠀⠀⠀⢀⡞⢀⣾⡵⠋⠀⠀⣴⣿⡫⠴⢚⢥⣿⡟⢀⡿⣾⠏⣴⠟⠁⣠⠟⠁⣿⡀⢻⢸⡇⠘⣿⣧⣄⠀⠀⠀⠀⠀⣠⠎⠀⠀⠀⠀⠀⢀⣴⠋⠀⠀⢀⡾⠀⠀⠀⣠⣾⣿⣿⣿⡿⠋⣠⣾⣿⣿⣿⣫⣴⣿⣭⣴⡾⠛⣉⣤⣾⣿⡿⠁⢀⣴⠟⣁⠾⣣⡶⢫⡾⠃⡄⢠⣾⣾⡇⣿⢠⠌⣿⠀⢸⡇⠀⠀⢸⡇⢸⡇⠘⢿⡇⠀⣻⠀⠀⠀⠀⠀⢿⣿⡄⢻⡄⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⢸⣁⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠤⠤⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⢴
⠀⠀⣀⣤⣶⢿⣿⣿⣿⠿⠁⢀⡔⠁⠠⢡⠂⣸⣿⢀⣿⣿⡇⠀⣯⡇⠀⡄⠀⠈⠀⠘⠻⠖⠀⠀⠀⠀⣀⣤⡶⢟⡿⠟⢡⢈⣷⣏⣾⠋⣠⠞⠁⠀⠀⠸⣷⡀⢸⣇⠀⠈⠙⠿⢿⣶⣶⣶⠟⠃⠀⠀⠀⢀⣠⣶⡿⠁⠀⠀⣠⡿⠇⠀⣠⣾⣿⣿⣿⣿⡿⠷⡿⠿⣿⣿⣿⣿⡿⢋⣾⢟⡡⠔⢛⣫⣿⠟⠁⣠⢴⣛⡥⠖⣩⡾⢋⣴⠟⢠⢞⡼⢛⣼⣿⡇⣿⠈⣧⢸⡇⠘⣿⠀⠀⠸⡇⢸⡇⠀⢸⣿⠀⢿⠀⠀⠀⠀⠀⠈⣿⡌⣏⣷⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⠤⠚⠉⢀⡴⠛
⣶⣿⣿⣟⣽⣿⣿⡿⠋⠀⣠⠋⠀⢀⡴⣱⠔⢩⣿⡾⣿⢸⡇⠀⠸⣇⢸⣇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠉⠉⠀⣰⡟⠈⣿⣾⠃⡴⠋⠀⠀⠀⠠⠀⣿⣿⣄⢻⡄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⣫⣾⡿⠁⠀⠀⣴⣯⢎⣠⣞⣭⣾⣿⣿⣿⣴⣷⣾⣿⣿⣿⣿⣿⢿⣷⣯⣽⣭⣶⣾⣟⣋⣤⣶⣿⣿⣿⣶⣗⣻⣧⣞⣯⣧⠞⢵⢟⣯⣿⣿⣿⣷⣻⣆⢿⣯⣿⡀⢻⣧⡀⠀⢧⢸⣿⢆⠈⣿⣇⢸⡇⠀⠀⠀⠀⠀⢸⣏⢸⣸⡇⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠁⢀⠀⠀⠀⢀⣴⠏⠀⠀
⢿⣵⢏⣿⣿⡿⠋⠀⢠⠞⠡⠀⣠⢋⠚⢁⡁⠚⢿⣯⢿⢸⡇⠀⠀⢿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⣼⠟⠀⠠⣿⠏⠜⠁⠀⠀⠀⠰⠃⢸⢿⣽⣿⣿⣧⠘⣦⣤⣴⠶⠶⠶⣞⣛⣥⣴⣿⣿⠏⠀⠀⣠⣾⠫⣠⡿⢋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⢿⣿⣿⣟⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣟⣿⣿⣽⣿⣯⣬⣾⣾⣿⣟⣿⡿⢿⢿⣾⡻⡦⣽⣿⣷⣄⠹⣿⣦⣾⡨⣿⡞⣦⡘⢿⣇⢿⡄⠀⢣⡀⠀⠀⣿⢐⡇⣿⠀⠀⣹⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⡴⠋⠀⣨⠚⠋⠙⠦⣈⢹⠇⡰⠉⠉
⡿⣫⣿⡿⠋⠀⢀⡴⠋⠄⢀⡜⠉⣠⠐⠂⠂⡊⠎⣿⡽⣿⣇⠀⢢⡟⢿⣿⢿⡇⢢⠀⠀⠀⠀⠀⠀⢸⣿⠟⢃⡼⠀⡀⠀⣠⡟⠀⡄⠀⢀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣷⣌⠻⣿⣿⣿⣿⣿⣿⣿⠿⠛⠁⠀⣠⣾⢿⡴⠛⣫⣵⣿⣿⣿⣿⣿⣿⣟⣿⣯⣾⣷⣿⣿⢿⣿⣯⣿⣿⣿⣿⡿⣽⣹⣿⡏⣿⡜⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣶⣾⣶⣿⣿⣿⣿⣿⣷⣾⣷⣽⣟⡿⢭⣩⣷⡹⣷⡊⠻⣮⡻⣯⢻⡄⠈⣷⠀⠀⢹⢰⢧⣿⠀⠀⣹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠉⠁⣠⠏⠀⢀⠾⣠⠤⠊⠀⠀⠀⠀⠀⠈⠙⠋⠁⠀⠀
⣾⣿⠛⠀⠀⣰⡟⣁⠂⡤⢋⠔⡺⠉⠀⡂⠂⠠⢕⢹⣷⣿⢿⢀⡏⠀⣾⢻⡞⣧⢸⡄⠀⣄⠀⠀⠀⠀⠉⠀⣾⠃⡾⣿⢸⠋⠀⢰⡧⣷⣬⡀⠀⢘⠟⠻⢿⣟⣿⣿⣿⣿⣿⣿⣦⣍⡉⣉⣉⣉⣀⣀⣤⣴⠾⠛⣉⣦⣶⣿⣿⣿⣿⣿⣿⡯⡳⣩⣾⢟⣿⣿⠿⣿⣿⣿⢿⠿⣿⣿⣿⣯⣿⣿⣿⣿⢿⣿⢯⣯⢻⣵⣿⣹⣽⣿⣿⣯⣿⣿⣿⣯⡿⢿⣿⣿⣿⣯⢿⣿⣿⣿⣿⣿⣿⣦⡈⢿⣧⠹⣿⣶⣌⠻⣾⣧⢻⡄⠘⣧⠀⢸⣦⢻⣿⠀⢀⣹⠇⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠋⠀⠀⢀⡤⠚⠁⠀⡠⠃⡰⠃⠀⠀⠀⠀⣤⠤⠤⡆⠀⠀⠀⠀⠀
⡟⠁⠀⢠⡾⢫⡤⢯⢴⡕⣡⠜⠀⠁⠀⢀⢔⠕⣁⣽⣿⡿⠎⡾⠀⣼⠃⣸⡇⡟⢸⣇⠀⢻⡄⠀⠀⣤⣀⢰⣧⠸⣿⢻⣾⡇⢹⣼⣿⣽⣿⠇⢰⡟⠀⠀⣰⢹⢻⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣬⣭⣭⣤⣶⣾⣿⣿⣿⣿⣿⡿⣿⡿⣷⠋⣨⢞⡭⠞⢋⠺⢐⡾⣹⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣾⣼⣸⣸⡿⡾⣿⣟⣿⣚⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⡿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⡄⢻⣇⢿⣾⣿⣷⣎⢿⢸⣿⡀⢸⣧⢸⡟⣮⡇⠀⢈⣿⡷⡄⠀⠀⣯⠀⢧⠀⠀⠀⠀⠀⠀⢀⡔⠁⣀⣀⠤⠒⠉⠀⠀⣠⠎⢀⡴⠁⠀⠀⠀⠀⠀⠯⠤⠤⢷⠀⠀⠀⠀⠀
⠀⢀⡴⣻⣗⡈⢠⣯⡎⠱⠋⡠⠀⠀⠀⠢⠄⠚⣹⣽⣿⡝⠐⠁⣰⠃⢰⠟⡜⢡⡾⣿⡄⠈⠳⣄⠀⠙⣿⣾⡿⣧⢻⣼⣿⣇⠸⣷⢻⡮⠋⢡⠟⢠⠀⢠⡇⡇⢻⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢏⣾⡿⣽⢃⣾⠟⢁⡀⣸⡇⢭⠏⣴⣿⢿⠟⢋⡽⠋⣀⣴⠿⣻⣽⡿⠿⢿⣿⣿⣿⣿⣿⣾⣾⣿⣿⣿⣿⣿⣭⣯⣷⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣖⢻⡘⣏⣿⣿⣿⢸⣿⣿⡇⠀⢹⠘⣧⢟⡇⠀⠈⣿⣧⠃⠀⠀⢭⠀⢸⡀⠀⠀⠀⠀⠀⣸⠔⢉⡽⠁⠀⠀⠀⠀⠸⠤⠔⠋⠀⠀⠀⠀⠀⠀⠀⢀⣠⠜⢛⠇⠀⠀⠀⠀
⠀⣾⠗⡹⠾⣠⣞⡟⢀⣲⣖⡥⠀⠉⠁⣴⢶⢛⣿⣿⠓⡜⠀⢠⡏⠀⣇⡞⡴⡿⢹⣿⣿⣄⠀⠀⢻⣆⠘⣿⠀⣿⣼⣿⣿⣿⠀⣿⡆⠗⢠⡞⢠⡏⠀⣼⠁⣤⣾⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣾⣿⣽⡇⣾⣧⣽⣶⣾⡿⢠⣯⡾⢋⡤⣢⣾⡟⢁⡾⠋⠑⢉⣡⣴⠶⣛⡛⣛⣿⡿⠿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⠿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣌⣷⣿⣿⣿⣿⠛⣿⣿⡇⠀⣾⠀⣿⣰⣇⠀⠀⢸⣏⠀⠀⠀⢸⠀⢸⡇⠀⠀⠀⠀⡞⢁⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠒⢉⡠⠔⠉⠀⠀⠀⠀⠀
⠰⢁⣴⡏⡰⠙⣿⣤⢎⡋⠜⢀⡤⠖⢉⠷⠳⡽⣿⡟⢂⣇⠀⡿⠀⢀⡟⣼⣿⡇⢸⢿⣿⡿⣧⠀⣼⢿⠆⡿⢤⣿⡾⠁⠀⠈⠁⠘⠁⠀⠈⢀⠾⠀⢀⡟⠀⢽⡔⢱⣿⡿⣿⣿⣟⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⡿⠛⣿⣧⡟⣹⣿⣿⡿⣧⡿⢋⡴⠋⣺⣻⠏⣢⡟⢁⣤⡾⢋⣵⠾⢠⣛⣿⣿⣭⣓⣒⡤⢹⣻⢶⣿⣿⣿⣿⣿⣿⣿⣶⣿⠿⣿⢿⣯⡿⣻⣷⣿⣿⣿⣿⣿⣿⣿⣿⣯⢿⢹⣿⣿⣿⣥⣾⣿⣇⠀⢸⠀⠘⣇⡿⠀⠀⠀⠻⢄⡀⠀⢘⣖⡸⠃⠀⠀⠀⠀⢉⣡⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡔⢲⣿⡗⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀
⡶⡰⣽⢰⠇⡸⢳⠃⣎⢐⣦⠋⠀⠀⠀⣠⡾⠀⣿⣳⢸⣇⢸⡇⣸⡿⠁⡏⣿⡇⡏⢀⣿⡇⣿⣰⣳⣾⢿⣏⣾⢯⠇⠀⠀⠀⠀⠀⠀⠀⡰⠃⢀⡴⢹⡇⠀⣸⣧⠛⢹⣇⣾⣿⣷⡏⣿⣾⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⡿⢶⣾⡿⢻⣿⣿⣿⣿⣷⡟⣡⠎⠀⡴⣷⠏⢰⡟⣠⡿⣋⡴⢫⡀⣤⢸⣿⣿⣋⣭⣭⣍⣛⠛⠶⣝⠽⣎⣿⣿⠿⣼⠳⢵⡜⢷⡺⣟⣛⢿⣯⣎⢿⣿⣿⣿⣿⣿⣿⣿⣿⡾⣼⣿⡟⢸⣿⣿⣿⣿⣄⠘⣇⠀⠈⠛⢦⣄⠀⠀⠀⠈⠑⢄⣲⡏⣧⠀⠀⠀⡴⠋⠀⣀⠇⠀⠀⠀⠀⠀⠀⠀⢀⠴⠊⣅⠤⠖⠻⠛⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡁⢡⡇⣎⡼⢡⡏⣸⠃⡼⠁⠀⠀⣰⡿⡽⠃⢸⡇⢻⡀⣿⠘⣇⢸⣿⠀⣇⣿⣿⡇⠀⢿⡗⡟⣿⣿⣿⣿⡿⣳⠏⠀⣠⠀⠀⠀⠀⢀⣴⠁⢀⡾⡇⢸⡇⠀⠿⣿⠀⠘⢻⣿⣿⣼⠀⡟⢸⣿⣿⡟⣿⣿⣿⣿⢿⣿⣿⡇⠸⣿⣧⣿⡃⣿⣿⣿⠏⣰⠃⠀⡜⢰⣿⠀⣿⣱⣿⣿⣿⢫⣿⡇⣿⡄⡿⠛⠉⠀⠀⠀⠉⠙⠦⡈⢳⣽⢸⡜⠆⠝⡼⠅⠹⡔⠲⡭⢟⡼⠯⣛⣗⣻⣿⣿⣿⣿⣿⣿⡿⣰⣿⣿⡇⠀⣿⢟⣮⣿⣿⣷⣬⣵⣦⣤⠤⠬⠝⠢⢄⠀⠀⠀⠱⡇⠀⠀⠀⠀⠑⠒⠈⠀⠀⠀⠀⠀⠀⠀⠀⣰⣁⠴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢁⡞⣜⡸⠁⠞⠀⠇⠴⢀⡠⣔⣿⡻⢏⣤⡶⣿⢿⣺⡿⢻⡆⠙⠷⣿⣧⡹⣎⣿⣿⠀⢾⣇⡇⣿⣿⢿⣟⣾⣷⠃⢰⡟⠀⠀⣴⢄⣮⠃⠀⡾⠁⣿⡘⣧⠀⠀⣿⠀⠀⣾⣿⣼⣛⣶⡷⣾⠁⡟⢹⣿⢿⣿⣫⣿⠏⣾⠇⠀⠉⣇⢻⡇⢻⣿⡟⣰⠃⠀⡜⢀⣿⣿⢀⠇⣿⣿⣿⢿⢸⣏⣧⠿⠋⠁⠀⠀⢀⣴⠂⢰⣶⡦⣈⣶⣿⠀⣇⢰⠔⡊⠵⡢⡜⡆⠭⢝⣲⠭⢳⠺⣧⣿⣿⣿⣿⣿⣏⣿⣭⣾⢿⣧⡀⠹⣷⣮⣙⣊⣉⣩⣥⠴⠶⠶⣶⣶⣄⠀⢃⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠈⢠⠀⠀⠀⠀⠀⣠⠞⣉⡵⢞⣫⡵⢟⣻⡼⣇⣿⢋⣿⣆⡀⠹⣷⡽⣼⣿⣹⡇⠸⣿⡆⣿⣽⣼⢹⣿⡏⠀⢸⣣⠀⢸⠇⠀⡏⠀⣸⠃⠀⡇⣧⠀⢠⣄⢻⡇⢠⣿⣿⠋⣹⠃⢱⡿⢸⠀⢸⡟⢸⣿⡿⠻⣼⡟⠀⠀⠀⠈⠀⣿⠀⣿⠃⠀⠀⢰⠁⢸⣿⠞⠀⠀⠿⢹⣿⠇⠀⠉⠀⠀⠀⠀⠀⠰⡋⠀⠀⣠⠞⠉⠁⡰⢃⡼⡋⢅⠑⣊⢅⣢⣵⣾⢻⡵⣒⡫⠔⠱⡘⠽⣿⣿⣿⣿⣿⣿⣿⣶⣿⢻⣿⣶⣬⣭⣭⣉⣤⣤⣤⣤⣤⣤⣤⣈⡉⠂⠀⣇⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢀⡖⠒⢂⠚⠉⠉⠲⡄⠀⠀⠀⠀⣀⠔⠉⠉⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⢚⣩⠖⣋⡥⠶⣋⡽⢷⣌⣈⣹⣿⣿⡉⢹⣿⣿⣿⣽⣟⣿⡀⢻⣿⣾⣿⣿⣿⣿⡇⠀⡐⠋⠀⡾⠀⢰⡇⢠⠏⠀⡼⡄⢻⣧⡏⣿⡺⣿⣹⣿⣿⢲⠏⠀⢻⡏⠀⠀⠈⣧⠸⣿⠃⢸⡏⠀⠀⠀⠀⣴⠀⢸⣠⣿⣧⠀⠀⢸⠀⢸⡇⢀⡔⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠂⢀⡀⠀⢀⡴⠁⠀⢠⢞⣵⢟⢗⢩⣐⢧⣽⡿⠿⣷⡾⣷⣮⣖⡊⢔⡳⢔⢭⡺⣿⣿⣿⣿⣿⣿⣿⣿⡿⣾⡿⢿⡿⢿⣿⣿⠿⣿⣿⢿⣿⣿⣿⣿⣧⠀⠛⠆⢀⢀⣇⠀⠀⠀⠀⠀⠀⠀⠈⠓⠢⠤⠤⠤⠤⠞⠁⠀⠀⣠⠞⠁⠀⢀⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⠈⣡⠞⣉⡴⢛⣭⠴⣋⡥⢖⣫⡿⣿⢯⢷⣿⢧⢸⣏⣿⠀⢹⣇⡿⣷⡄⠻⣿⣿⣿⣿⣿⣇⠰⡇⠀⢸⡇⠀⢸⠇⣼⠀⣼⠃⣧⢸⢸⣧⢷⣁⣹⣿⢻⡏⠿⠀⠀⠀⠁⠀⠀⠀⠙⠀⡟⠀⣸⣷⢄⠀⠀⠀⠀⠀⢸⣿⣿⣿⡅⠐⢸⡦⠜⠅⡏⠀⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⣠⠋⠀⢠⡿⢡⠆⢠⢯⡟⡵⢎⢅⣺⣿⠟⠁⣠⠊⠀⠀⠈⠙⠭⡻⣷⣌⢖⣙⣎⣿⢿⣿⣿⣿⣿⣿⣿⣿⣯⡯⡛⠒⠦⣄⣠⣄⠄⠔⣪⡔⠙⢾⢿⡹⢀⠀⢠⣾⠕⠿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⡠⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌
⠀⠀⠀⠀⠀⣀⡡⢚⡵⣚⡥⠞⣩⠴⢋⡥⠖⣫⡵⢚⣿⡼⣾⣟⣾⣾⡿⢡⡄⢸⢽⣎⠻⡿⣦⠘⢿⣿⣿⣿⣿⡄⢧⠀⢸⡅⣼⢿⡀⣏⠀⢿⡄⣿⡀⢸⣏⠀⢘⣿⣿⣷⡷⡶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢠⣿⣾⣻⡆⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠈⠁⣐⠸⠀⠀⠀⠀⣹⡀⠀⣸⢡⡇⠀⣸⠃⠀⠀⣾⠃⣿⠀⢸⡿⢀⣿⡄⣿⠟⠁⣠⣾⣿⡧⠀⠀⠀⢀⡀⠀⠈⠻⣿⡙⣿⢹⡿⣿⣿⣿⣿⣿⣝⢿⣿⣿⣮⣖⣄⣔⣹⣭⡳⣶⡑⢭⡽⠟⣃⣣⠎⣰⣟⠁⠀⠀⠀⠑⢄⡀⠀⠀⢀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⡗⠊⠀⠀⠀⠀⠀⢠⠤⢄⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⣠⡬⢚⡥⢞⣩⠔⣋⡴⢚⣩⠶⣋⡵⢞⣭⠿⣿⣿⣼⢋⢿⡇⢸⠃⣼⣸⡟⠀⡿⠹⣧⢸⣿⠃⣹⠛⣿⣼⡄⢸⣷⠹⢸⣇⢸⡄⠘⣧⢸⣇⡾⠙⡆⣿⣿⣿⣟⠟⣟⡃⢻⡂⠀⢀⠀⠀⠀⠀⠀⠛⠛⠙⠊⠀⠀⠀⠀⠀⣼⣿⡿⢿⡇⠀⠀⠀⣿⠀⠀⠀⠀⢸⡇⡗⠀⡇⢸⠃⠀⣿⢸⠀⠀⣿⠀⢿⡄⢸⡇⢸⡙⣿⣿⠀⢰⣿⡏⢻⣿⡄⠀⠀⢠⣷⠀⠀⠀⠹⣧⠘⡄⣿⢽⣿⣿⣿⣿⣿⣷⣬⣛⣛⢿⣿⣷⣯⣿⣿⣿⠿⣿⣭⡶⠟⣯⣾⠟⠉⠳⣤⡀⠀⠀⠀⠈⠉⠉⠕⣀⡀⠀⠀⠀⠀⠑⠒⠤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠤⣑⣒⣠⠤⠒⠁
⡇⠀⠀⠀⠀⠆⢉⣰⠏⣱⠏⣱⡾⢏⣷⠿⣱⡾⢏⣱⡾⣿⣿⣿⠈⡸⣇⢸⡀⢿⣇⣏⢸⡇⠀⣿⢈⡇⠀⠀⠀⢹⣿⣿⡸⡿⡀⣸⣿⠀⣿⠀⠸⣷⣿⣇⠀⣿⣿⣿⣿⣿⣸⣿⣷⢸⠇⠀⣸⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⢹⡏⡇⢸⡇⠀⠀⡀⣏⠀⠀⠀⢀⣷⠀⡇⠀⣇⢸⡀⠀⠿⢸⡆⠀⣿⠀⠸⡇⠸⡇⢸⢇⠸⣿⠀⠈⢿⣷⢸⣿⡇⡆⢸⢸⣿⣶⠀⠀⠀⢿⡆⢇⢿⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡉⠉⠹⢿⣿⣶⣶⣰⣶⣿⡿⠁⠀⠀⠰⣈⡹⣷⣆⡀⠀⠀⣰⣿⠿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠈⠉⠶⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡇⠀⢀⠀⠂⠊⣣⠴⣫⡵⢛⣡⠞⣫⠴⣛⣥⠞⣫⡵⣛⣽⡼⣿⡀⢇⢿⡀⣷⡘⣿⣧⢸⡇⢸⣿⡜⢀⡜⠀⠠⡿⠘⣿⣿⣿⡇⡏⣿⡇⢸⡀⠀⣽⣿⣿⣷⡿⣿⢹⣿⡥⣿⣿⣿⣸⢤⣴⣟⡿⠀⠀⠠⠀⠀⠀⠀⢀⣰⣶⡾⠋⢠⠟⣼⠁⣾⡇⠀⡜⢠⣿⡆⠀⢀⣿⠟⠀⣷⠀⢻⡀⠁⠀⠀⢸⡇⠄⢻⡇⠀⢣⠀⣿⠈⣎⢧⠹⣧⡀⠀⣿⣎⢿⣇⢹⠸⣆⢿⣿⠀⠀⠀⠘⣧⢸⢸⡏⣿⣿⣿⣿⣿⡿⣿⣿⢿⡟⣿⣟⠀⢰⠀⠹⣿⣿⣿⣿⠏⠀⠀⠐⠢⢤⡀⠈⠉⠛⠛⢿⣿⣿⣷⠀⠈⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⢤⣀⣀⡀⠀⠀⠀⢀⡀⠀⠀⠀
⣿⠀⠀⢁⡤⢊⠥⢛⣡⠖⣫⠴⣋⡵⢞⣩⠶⣫⡵⢞⣫⡷⢿⣿⣷⡌⢿⣧⠘⡿⣌⠻⣾⣧⢸⡏⢳⡏⢀⠄⣼⢃⣰⠿⣿⣿⣿⣇⣿⣧⢸⣇⡀⣿⠻⡛⢼⡇⣿⢿⣿⣼⣿⣿⣿⡽⣼⣿⣿⢇⡴⢂⡴⠂⠀⣠⡴⢛⣿⠋⠀⣰⠏⣰⠏⣸⣿⠁⣼⣵⣿⢸⡇⢰⣿⣿⣷⡆⢿⡀⠈⢣⠀⠀⠀⠀⠛⣀⠈⢿⡀⠈⡆⢸⡄⢻⡜⡆⢻⣶⠐⣿⣿⣦⢻⡎⣇⢻⣽⣿⣧⠀⡀⠀⢿⡀⢾⣷⣿⣷⢿⢿⣿⣿⣿⣿⢸⣧⡅⠸⣇⠀⠇⠀⣿⣿⣿⣏⣠⣀⠐⢶⣦⣄⡈⠑⠄⠀⠀⢈⣿⣿⣿⡄⠀⠈⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠻⠼⣀⠀⠀
⣿⣇⠀⠞⠐⣠⠴⣋⡴⣚⡵⢚⣩⠖⣫⠵⣛⡵⢞⣭⠿⣾⣻⣫⣿⣿⣦⠻⣧⠘⢿⣧⡙⢿⣯⣇⡏⢀⡾⣸⡏⢸⣿⠀⣧⣿⣿⣷⣯⣿⣎⣾⡯⡏⠀⣿⢼⣿⣿⢽⣿⣼⣿⣿⣿⡿⣸⣿⡯⢋⡵⠋⢀⣠⡾⢋⣴⣿⠋⢀⣾⠃⣴⡟⣰⡿⠁⣴⣿⣿⡇⢸⠇⢸⣿⡿⣿⣄⣸⣧⠀⡀⠐⣄⠀⠀⠀⢹⣷⡀⢳⡀⠘⠀⣷⠸⣧⣿⠘⣯⢰⣿⢻⣿⣧⢿⣸⠈⡿⣻⣿⣧⢻⠀⢸⡇⣸⣿⣅⠛⢿⡷⣿⣿⣿⣿⢸⣿⣷⣦⠙⢆⢰⠀⣿⣿⣿⣿⣿⣿⣷⡄⠉⠻⢿⣦⠀⠀⣠⣾⡿⠉⣿⣧⠀⠀⠸⣿⠀⡀⠀⠐⣄⠀⠀⠀⠀⠀⠒⠦⣄⣀⠀⠀⠀⠀⠀⠀⠉⠲
⢿⣿⡄⠄⠈⣡⢞⣥⢞⣫⠶⣫⠴⣫⡵⣞⣽⠖⣫⡵⣟⣭⣽⣯⣿⣿⣿⣷⣌⢧⡀⠻⣿⣷⣽⣿⡇⡼⣷⣿⣇⣸⡏⢀⣿⣿⣿⣿⣿⣿⣿⢻⡇⡇⠀⣿⠉⠀⠹⠹⠿⠛⠛⣿⡿⢠⣿⣿⡤⠊⡔⢊⠋⣠⠶⢟⣿⠃⣠⣻⠃⣼⠏⣰⡟⢁⡾⣿⣿⡟⢀⡟⠀⣾⠋⢻⡟⣿⣛⣿⡆⣷⠀⢻⣇⠀⢀⠀⠹⣿⡀⢳⡄⣂⣹⣶⣿⣿⣼⡏⢸⣿⣿⣿⣿⣸⣽⡇⢹⣏⣿⣿⣼⡇⢸⣧⣿⣿⡏⠐⡈⢿⣯⡻⣿⣿⡄⢿⡼⣧⠓⣌⢻⠏⠹⣿⣿⣿⡿⣿⡀⠀⠀⠀⠀⠹⣠⣾⡿⠋⠀⢰⣿⣿⡆⠀⠀⠹⣮⠱⣄⠀⠘⢧⡀⠀⠀⠀⠀⠀⠀⠉⠛⠷⣶⣤⣀⠀⠀⠀
⠀⢻⣷⣠⡞⠲⣫⠴⣋⠵⣋⡵⢛⡥⢞⣩⠶⣋⡵⢛⣭⣒⣽⣶⣿⣾⣿⣿⣿⣷⣾⡂⠙⢿⣿⣿⣼⣽⣿⣿⣿⣿⠀⣼⢻⣿⣿⡿⣿⢻⣿⢹⠇⣿⠐⣿⠀⢐⣶⠀⠀⠀⠀⢿⣻⣿⣿⠟⣠⡾⣷⢋⣝⠇⢀⣾⠃⣰⠃⡟⢰⡏⢠⡿⠀⣾⢣⣿⣿⣴⠏⢀⣸⠀⡇⢸⡇⢸⡿⣿⣷⢹⣇⠘⣿⠀⢸⡄⠀⢹⣇⠸⣧⢙⣼⣹⣿⣿⡟⠁⣸⣿⣿⣿⣿⣿⣿⡇⠀⠉⣿⣿⡇⠓⠘⣿⣿⣽⣇⠀⠀⣼⣿⣿⡝⢉⣓⠈⢳⣝⢧⣹⠏⠀⠀⢿⣿⣿⣷⢿⡟⠃⠀⠀⢀⣴⣿⠋⠀⠀⣠⣿⠻⣿⣿⡄⠀⠀⢹⡇⠹⣷⣄⠀⠻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣷⣦⡀
⡆⠀⢻⣿⡽⣫⡽⢛⡥⢞⣥⢖⣫⠔⣫⡴⣛⡥⢞⡏⣩⡿⢏⣽⣿⢿⣿⣿⣿⣿⣿⣷⣤⡀⠙⢿⣿⣿⣿⢯⠃⡏⢰⡟⢸⠛⣿⡇⣿⣼⡏⢸⢠⣿⡇⢸⡆⠐⠿⠀⠀⠀⠀⠸⣿⡿⣵⣾⣿⣿⢃⣾⡟⣠⣿⠇⢰⣿⠀⣧⣾⠁⢸⡇⢰⣿⣾⣿⣿⠏⣰⢣⣿⠀⢳⠈⡷⢸⡇⢹⣿⢘⣿⡄⢿⣧⣸⡇⠀⠀⣿⠀⣿⡸⣷⣿⣿⠏⠀⠀⡟⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⡷⠀⠀⣿⣧⠹⣏⡀⠀⣿⣷⠘⢿⣤⠼⣆⠀⢹⡷⢽⡇⢀⠀⢸⣿⣿⣿⣏⠉⠉⣠⣾⣿⣿⠃⠀⢠⣾⠟⠁⠀⣿⣿⣷⡀⠀⠀⣿⠀⢹⣿⡀⠀⠹⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿
⣷⡀⠀⠹⣿⣠⢞⣩⠖⣫⠶⣫⡴⣛⡵⢞⡿⢚⣥⢞⣫⠞⣫⡵⣟⣯⡿⣿⣿⢿⣿⣿⣿⢿⣷⣦⣹⣟⢁⡿⠀⠁⣸⠇⣾⢘⣿⢣⣿⣿⢀⣏⣾⣿⣷⠀⣏⠀⠄⠀⠀⠀⢰⡀⠘⣿⢿⣿⣿⣇⣾⣿⣷⣿⣿⠀⣾⣿⠀⣿⣿⠀⢸⡇⢸⣿⣿⢿⠃⠀⣿⣾⣿⣿⣾⣶⠃⣼⠇⣸⣿⣼⡿⡇⢸⡗⣹⠃⠀⠀⢹⠀⣿⣿⣿⡿⠁⠀⠀⢰⣿⡿⣿⣿⣿⡿⣿⣿⠀⢰⣿⣿⡇⠀⢀⡿⣿⣰⠇⡇⠀⣿⣿⠀⠸⣷⣶⣿⠀⢀⡇⠸⣷⢸⠀⢸⣿⣿⣿⣅⢄⡜⠀⣿⣿⠃⠀⣰⡟⠁⠀⠀⢠⣿⣿⣿⣧⠀⢠⠘⡆⠈⣿⣧⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢿⣷⡀⠀⠘⢿⣄⠳⢈⡵⢚⣵⢞⡭⢚⣥⡾⣫⠴⣫⡵⣛⡵⢞⣭⢿⡾⣯⣿⣿⣿⣿⣿⢻⣿⢿⣿⣿⣿⡀⠀⣰⣿⠀⣿⡘⣏⣸⣻⣷⣾⣿⣿⣿⣿⠀⠀⢰⣶⡆⠀⠀⠈⢧⠀⣿⣼⡿⢛⣿⣿⣿⡏⠀⡿⠀⢻⣿⡄⠘⣿⡇⠈⣷⠈⣿⠁⣿⣾⠀⣿⣿⣿⣿⣿⡟⢰⡏⢠⣿⣿⣿⠀⡇⣾⢀⡟⠀⠀⠀⣿⠀⣿⣿⣿⠃⠀⠀⠀⠸⢋⣼⣿⣿⣿⠁⣿⡇⠀⣼⣿⣿⢣⢆⣼⡿⣼⣿⠀⡇⠀⣿⣷⠀⠀⣿⠎⠁⢀⠸⣁⢸⠇⣾⠀⡀⣿⣿⣿⠫⣛⠁⢰⣿⠇⠀⣰⡟⠀⠀⢀⣴⡿⠋⣿⣿⣿⡆⠈⡆⢹⡀⠸⣿⡀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠻⣷⡀⠀⠈⢿⣆⠫⡴⣫⡵⣫⡴⣛⡵⢋⡵⢛⣥⠞⣫⠴⣋⢶⡳⢟⣍⣽⣿⣿⣿⣿⣄⣿⢸⣿⣿⣿⡜⢸⢻⣿⠀⢹⣧⣿⢃⣿⣿⣿⣿⣿⣿⡏⢀⢀⠈⠉⠀⠀⠀⠀⢸⠀⣿⣿⣷⣾⡿⢿⣿⣿⣿⣿⣦⡀⠻⣷⡀⠘⢿⣆⠘⣇⣿⣀⣿⣿⠀⣿⢿⣿⣿⡟⣠⡟⣰⡿⠛⣹⡟⠸⠁⠃⣸⠁⠀⠀⣰⠇⣸⣿⣿⣿⡀⠀⢀⠀⢠⣾⣿⣿⣿⠇⣸⡟⠀⣰⣿⣿⠏⣈⣾⠳⣷⣸⡏⢀⠇⠀⣿⡇⠀⠀⣿⠀⠀⠂⣰⢏⣿⢰⡟⠀⢹⣿⣿⣧⡞⠁⢆⣾⡟⠀⢰⡟⠀⠀⣠⡿⠋⠀⣠⠛⣿⣿⣷⠀⠸⡄⢧⠀⢹⣷⠀⢻⡀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⡄⠀
⡆⠀⠙⣷⡄⠀⠀⠻⣷⣹⣥⠞⣩⢞⣩⢞⣧⡾⣫⣥⠞⣭⠾⡳⣫⣶⢟⢟⣽⢾⢿⣿⣿⣷⠼⣄⣿⣿⣿⡇⢘⡎⢿⡆⠀⢹⠧⣽⣿⠟⡉⠀⣿⠋⣹⣿⣿⡯⣳⣿⠀⠀⡋⠽⣠⠏⠀⠉⡿⠁⡼⢟⣿⣿⣿⣿⣿⣦⠘⢿⣤⠀⠹⣧⢹⣼⣿⣿⣿⠀⡇⢸⣿⠏⣰⣿⡾⢋⣠⡶⠛⠁⠀⠀⢠⠏⠀⠀⣰⠏⣠⣏⡾⣽⣿⢇⠀⣿⣀⣾⣿⣿⣿⠏⣰⡟⠀⣴⣿⣛⠀⣴⢻⡏⠀⠉⢻⠂⢀⡀⢀⣿⠁⠀⠀⣿⠀⢀⣴⡟⡼⣣⡟⠀⢠⣿⣿⣿⡗⠉⣤⣿⡿⠁⢠⡿⠁⠀⠀⠀⠀⢀⣼⠏⠀⠘⣿⣿⣇⠀⢳⠈⠀⠈⣿⣇⠈⢷⡀⠀⠀⠀⢻⣷⣄⡀⢢⡀⠘⡄
⣷⡄⠀⠈⢻⣆⠀⠀⠙⣷⡝⢯⠢⣫⣶⢓⣕⠾⣋⠶⣛⡵⡯⡭⢺⡕⣱⡿⣹⣾⣿⢿⣿⣿⣧⡙⣿⣿⣿⡇⢸⣹⣎⢿⣀⡎⠀⣿⡟⠀⡇⣼⠧⣾⢿⣿⡿⣼⣿⡇⠀⣾⢁⣴⠋⠀⠀⢸⠃⣸⠷⠛⣿⣿⣿⣿⣿⣿⠘⡌⠧⣷⠀⢻⢸⣿⣿⣿⡿⠀⣧⣾⡟⣰⣿⣏⣴⣿⠋⠀⠀⠀⠀⢀⠎⠀⢀⣾⠋⡰⣝⣾⢧⣿⡇⢸⠀⣿⢰⣿⣧⣿⡏⢠⠏⢀⣾⡟⠣⢄⣾⠃⣼⣧⣘⢘⠏⠀⡼⡇⠸⣿⠂⠀⠀⣿⠀⢸⢻⣻⣾⠟⢀⣴⣿⣿⣿⠛⡀⠁⣿⣿⠃⢠⡾⠃⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀⠸⣿⣿⡄⠈⣇⠀⣆⢹⣿⡄⠘⣧⠀⠀⠀⠘⣿⣿⣿⣾⣷⡀⠹
⣿⣿⣄⠀⠀⠹⣷⡀⠀⠈⢿⣎⢿⣥⡶⣟⡵⢞⡭⢞⣥⡔⣫⢖⡵⣟⡽⣯⡿⣫⡼⣿⣿⣿⣿⣧⣿⡿⣿⣧⢸⡇⠹⣦⢻⣧⠀⣻⡇⠀⣽⣿⢸⢭⣿⣿⣻⣿⡟⠆⠀⣽⠟⡃⠀⠀⡼⠙⠀⠀⠰⣺⣿⣿⣿⣿⣿⣿⠀⣿⠀⣿⠀⣟⣾⣽⣿⣿⡇⢀⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⢠⡎⠀⣰⡿⢁⣾⣫⣿⣿⣿⣿⣿⣿⡄⠈⢸⣿⡿⢿⠁⠀⣠⣿⡿⢀⡗⣾⠃⣼⣿⡷⠃⡞⠀⢰⠇⡇⢀⡇⠐⠋⠀⣿⡀⢸⣿⠟⢁⣴⣿⣿⣿⣿⡿⡀⠜⣘⣿⠇⢠⡿⠁⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⡀⠀⢻⣿⣷⠀⠸⡆⢸⡈⣿⣷⠀⠸⣇⠀⠀⠀⢿⢻⣿⣿⣿⣿⣄
⠀⠻⣿⣦⡀⠀⠈⠻⣄⠀⠀⠻⣷⡻⣿⣹⡿⣫⢞⣵⢵⣚⣷⣫⣞⣽⡾⡛⣲⢿⡿⣫⣿⣿⣿⣿⢹⡇⢹⡿⢸⣧⠀⠹⣧⢻⡀⣯⢿⡄⢿⣿⣮⡏⢸⣷⣿⠏⣸⠀⣼⠇⢰⡇⠀⢸⠃⠘⠁⢀⣾⠟⢡⣿⣿⣿⣿⣿⡆⣿⢠⣟⣼⣿⠏⣿⣿⣿⠁⢸⣦⣼⣿⣿⣿⠋⠀⠀⢀⡴⠁⣠⠏⣠⡾⢋⣴⣏⡿⢻⡟⣿⣿⣿⣿⣿⣿⡄⢸⣿⡿⣿⠀⢠⣿⣿⠃⢸⢱⠇⢰⣿⣿⣉⡼⠀⢠⣏⣸⢣⡞⠀⢀⣤⢤⠟⡇⢸⣿⡐⣿⣿⣿⣿⣿⣿⠫⡘⢦⣾⡏⠀⠜⠁⠀⠀⣠⠀⢠⣿⠀⠰⠀⠀⠀⠀⠀⠘⣿⣿⡆⠀⢻⠀⣧⢹⣿⣇⠀⢻⡄⠀⠀⢸⡟⣿⡇⠙⠻⢿
⠀⠀⠘⢿⣿⣆⠀⠀⠙⢷⡀⠀⠘⢿⣿⡻⣲⣿⣟⣵⢿⣺⣾⣷⣿⢏⡵⣺⢕⢟⡽⣞⢻⣿⣿⣿⠘⣧⢸⡇⢸⢿⣦⡀⠹⣷⣣⣸⡌⢿⣌⢿⣷⠁⠸⣿⡏⢰⡝⢠⡏⠀⢸⡇⠀⣼⠂⠀⢰⣿⠃⠀⣾⣿⣿⣿⢋⣿⢿⣿⣿⣿⣿⠏⣼⣯⣿⡏⠀⣸⣿⣿⣿⡟⠁⠀⠀⢠⡞⠁⣴⢫⡾⢛⣴⡿⣻⣽⢾⡟⢸⣿⣿⣿⣿⣿⣿⡇⢸⣿⣷⣇⠀⢸⣿⡟⠀⠀⡽⠀⣾⣿⣇⣾⣽⣴⠟⣰⣯⣿⠇⢰⡟⣸⠎⣰⡏⢸⣿⣇⠈⢿⣿⣿⣿⣿⣿⣮⣿⡟⠀⠀⢠⠀⠀⢰⣟⠀⣺⡷⢹⡯⠿⠀⠀⠀⠀⠀⣿⣿⣷⠀⠘⣇⢸⡄⢿⣿⡄⠈⣷⠀⠀⠘⣧⢼⣧⠀⠀⠀
⠀⠀⠀⠀⠙⢿⣷⣄⠀⠀⠙⢦⡀⠀⠙⠿⣿⣷⣿⣷⣿⣽⣿⡫⣵⡿⣽⡧⣕⣯⣮⡶⣫⠿⣿⣿⣆⠹⣿⣿⡌⠄⢻⣷⣄⠹⣷⣵⣿⡌⢿⣾⣿⡀⠀⣿⢠⠇⣷⣾⡇⢸⠘⣧⠀⣿⠀⣠⢿⡇⠀⣰⣿⣿⣿⠃⣼⣧⣼⣿⣿⣿⣫⣾⣿⣿⡿⠀⢠⡿⢸⢏⡿⠀⠀⠀⣰⠏⢀⣾⡿⣫⣵⣿⢻⡏⣿⠻⠇⣇⣼⣿⣿⣟⣿⣿⣿⠃⣼⣿⣟⡿⢀⣿⣿⡇⠀⠀⠁⢠⣿⣿⠾⣿⣿⣏⣶⣿⡿⢋⣴⣟⣴⢏⣴⠟⢀⣿⡇⣿⠀⠈⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⣿⠀⢀⣿⡇⠀⠿⠃⠘⠁⠀⠀⠀⠀⠀⢸⣿⣿⣿⡆⠀⢻⠀⣧⠈⢿⣷⡀⠸⡇⠀⠀⣿⣘⣿⡄⠀⠀
⣄⠰⠂⠀⠀⠀⠙⢿⣷⣄⠀⠀⠙⢶⣄⡀⠈⠻⣷⣿⣿⣷⣷⣾⣿⣿⣿⣿⣿⣷⢿⡾⣡⠾⣯⣿⣿⣦⡙⢿⣿⣮⡀⢿⣿⣷⡘⢿⡿⣿⣆⡹⣿⣧⠀⣿⣾⠀⢻⣿⣿⠸⡀⠘⣄⣿⣧⡇⠘⡇⠀⢸⣿⣿⡇⢸⣿⢿⣿⣿⣟⣵⣿⣿⠟⠉⣀⣴⣿⠃⡿⢸⠇⠀⠀⣸⠏⢀⣾⣯⠞⣋⣾⣿⣼⠿⠋⠀⣴⣿⣿⣿⡟⣼⡿⢹⡿⢰⣿⣿⣿⢃⣾⢯⡿⠁⠀⠀⠀⣼⣿⣿⣾⣿⣿⣿⣿⣯⣴⠟⡡⣿⣿⣿⡗⢾⠁⣿⡇⡏⠀⡀⢸⣿⣿⣿⣿⡏⠀⠀⢀⣴⡿⠀⢸⣿⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⢸⣿⣿⣿⣷⠀⠸⡇⢸⡆⠘⢿⣷⡀⢿⡀⠀⢸⣏⢻⣇⠀⠀
⠹⣷⠰⣦⢄⠀⠀⡀⠙⢿⣷⣄⠀⠀⠈⠛⢶⣤⡈⠻⢿⣷⣿⣿⣿⣿⣿⣿⣿⢷⣏⡾⣡⡾⢗⣿⣿⣿⣿⣶⣍⠻⣷⢹⣿⣿⣿⣾⣷⠘⣿⣿⣾⣿⣧⢿⣿⠀⢸⡟⣻⡄⠃⠀⢹⣿⠘⣇⠀⢿⠀⢸⣻⣯⠀⣿⣻⣾⣿⣿⣿⣿⠟⡡⣴⣿⣿⣿⡟⢸⡇⢸⠀⠀⣼⣿⠀⢸⡟⡏⣠⢹⠁⠧⠟⠀⠀⢰⣏⣿⣿⢻⣼⡿⢡⣿⢡⣿⣿⣿⣣⡾⠛⣾⠃⠀⠀⡀⢠⡟⡿⣿⣯⣿⡿⣿⣿⣿⡷⢊⡼⣿⣿⣿⡇⢸⠀⣿⢣⡿⠀⣹⣧⣿⣿⣿⡟⠀⠀⢀⣿⡹⠁⠀⢀⣿⠀⠀⠀⡴⠲⣶⣯⣸⡿⣿⣍⢸⣿⣿⣿⣿⣆⠀⢿⠀⣷⠀⠘⣿⣷⡘⣧⠀⠀⢿⡜⣿⡄⢠
⡄⠈⠀⢹⠝⢷⡀⠀⠀⠀⠈⠛⢷⣦⣀⠀⠀⠈⠛⠷⣦⣈⠙⠻⢿⣿⣿⣿⣿⣿⣟⣾⣷⣿⣷⣿⢽⣿⣿⣿⣿⣟⣿⢸⡟⠻⣿⣿⣿⣇⠘⣿⣿⣿⡸⡏⣿⡄⠀⣿⣯⡇⠀⣼⣸⣿⡆⢿⠀⢸⡄⣿⣿⣇⠀⢻⣷⡿⣾⡿⣿⠿⡾⢹⡿⣿⣿⣿⡇⢸⡇⢸⡆⣼⢻⡇⠀⢸⣿⣺⡏⡀⠀⠀⣠⣦⠀⣿⣹⣿⣵⣿⠟⢠⡿⣣⣿⣿⡿⢛⡉⢌⡹⠃⢀⢔⣾⠉⣾⢛⠀⠈⢻⡿⣇⣿⣿⢏⣴⣿⣵⣿⢽⣋⣴⡟⢰⡿⣼⠇⢰⢧⠟⣿⣿⣿⡁⠀⣖⣼⠇⣴⠁⠀⡾⠋⠀⢀⡾⠁⢰⣫⣿⢥⣾⣯⡧⣾⣿⣿⣿⣿⣿⡆⢸⡇⢸⡆⠀⠸⣿⣷⣿⡄⠀⠈⣿⣽⡟⣼
⠁⢄⠀⠺⡇⠘⢧⠀⠀⠈⠷⣤⡀⠉⠛⠷⣶⣤⣀⡀⠈⠙⠻⠶⣦⣬⣉⡛⠻⠿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⡇⢹⠸⣇⣢⠚⣿⣿⣿⡄⠚⣿⣿⡇⢻⣿⣿⣄⣿⣿⢿⡀⣿⣿⣿⣷⠘⡇⠸⣧⣿⣽⡿⠃⠀⠹⣧⣿⡇⣿⠁⠁⢸⣧⢹⣿⣿⣿⡘⡇⢸⣷⣿⣾⡿⠇⢸⣿⣻⣿⡇⠀⣰⢽⡏⢰⣿⣿⣿⠟⢁⣴⣿⣿⣿⡿⠥⠶⠛⠋⠉⡀⠴⣫⡿⢅⣼⣿⣾⠇⠀⠈⣿⣿⣿⡿⢋⣩⣴⠶⣶⠿⠿⢋⣴⢿⣿⠏⢠⠃⡼⢠⣿⣿⣿⠟⠁⣾⡿⣤⠃⠀⠀⠀⠀⢀⣾⠁⠀⠎⣿⢔⢞⠣⠀⡐⣿⡟⡿⣿⣿⣿⣿⠀⣿⠀⣷⠀⠀⢻⣿⣿⡇⠀⠀⠸⣿⠀⢻
⣇⠈⢷⡀⠀⠀⠀⠀⠀⠘⢿⣮⠛⠷⣦⣄⣀⠉⠙⠻⠷⣶⣤⣄⣀⠈⠉⠛⠳⢶⣄⡉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣧⠘⡄⢿⣄⠳⣌⠟⢝⣷⡡⡽⣿⣷⠘⣿⣿⣧⣹⢿⣾⣧⣿⣿⣿⣿⣇⠱⢸⡿⣽⡟⠁⡰⡷⠀⣿⣿⡇⠀⠀⠀⠀⢻⣆⢿⣿⣿⣷⣷⠀⢿⣿⣿⣇⣧⢸⣿⣿⡟⢠⣻⡇⡦⢁⣾⡿⠟⡡⣾⡿⠛⠉⠀⢀⣀⣠⣤⡶⠞⠋⣡⠾⠋⣠⣾⣿⣿⢯⠂⣤⡆⣿⣿⣯⣾⠟⠓⠒⡓⠷⠿⠿⠛⢡⣿⠏⢠⢃⡼⠁⣼⣿⣿⡏⠀⢀⣾⠗⠃⠀⠀⠀⠀⢠⣾⡇⠀⠀⢠⡯⠀⠋⠒⣀⠥⣿⣿⣳⢹⣿⣿⣿⡄⢹⡇⢸⡆⠀⠈⣿⣿⡧⠀⠀⠀⢻⡆⢸
⣿⣷⣌⢻⣆⠀⠀⠀⠀⠀⠀⠀⠹⣤⡀⠉⠛⠿⣷⣦⣤⣀⣈⣉⣙⠛⡿⠶⣦⣤⣄⡉⠓⢄⠙⢷⣦⣄⠉⠛⢿⣿⣧⣿⣄⠛⢶⣌⣛⠾⣼⣷⠙⣿⢿⡄⢿⣿⣿⣌⣿⣿⣿⣿⣿⣟⣸⣿⢀⣾⣾⠏⠀⡴⢁⡞⢸⣿⣿⣱⠀⢀⣀⢠⡀⢻⣿⣿⣿⡟⢻⣇⠈⢿⣿⡇⣿⡜⣿⡟⢠⣷⣿⣢⣿⣿⠭⠔⠋⡴⠋⠀⣠⣴⡾⢿⣟⣏⣁⡤⠔⠊⣁⣴⣾⠟⢁⣿⢿⠃⣼⢱⣧⣿⣿⡟⢁⣴⡾⡟⠟⣻⣿⣿⣤⡿⠋⡠⢃⡞⠀⣼⣿⣿⡟⠀⠀⣾⡟⠀⢠⠆⠀⠀⢠⣿⣿⣀⠀⠀⢸⡇⠀⠀⠘⣭⣴⣿⡷⣽⣋⣿⣿⣿⡇⠼⣷⠈⣷⠀⠀⠸⣿⣷⠀⠀⠀⢸⡇⢸
⠈⠻⣿⣷⡽⣧⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⠤⠀⠀⠉⢿⡿⣿⣯⣛⢻⣿⣶⣶⡮⡯⣝⣳⢶⣕⢄⠹⣧⡀⣴⣤⣩⡿⣿⣿⣷⣦⣎⣙⠻⣿⣿⣆⢹⣿⣧⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢨⣿⠇⢠⣾⢣⣿⠁⣿⣾⣿⣹⡆⣾⣹⡞⡵⣄⠹⣿⣿⣇⢸⣿⣧⡈⢿⣷⢸⣿⠏⣰⣿⣿⣿⣿⣿⠃⢀⡠⠎⢀⣴⠟⣩⡶⠟⢛⣉⣤⣤⣴⣶⣿⡿⠛⢁⣴⣿⣫⡎⣼⠇⣼⣿⣿⣟⣰⣿⣫⢂⣴⠞⣵⡿⠟⢋⡠⠚⡡⠋⢀⣾⣿⣿⡟⠀⢀⣼⡟⠀⢠⡏⠀⣿⢧⣿⣿⠧⠀⠄⠀⣿⠀⠀⣠⠞⢋⣿⣿⣧⣯⣿⣿⣿⣿⣧⠀⣿⡄⢿⡤⡄⠀⢻⣿⣷⡄⠀⠀⠇⣸
⡆⠀⠘⢿⣿⣿⣧⡀⠀⠀⠀⠀⠘⣦⡀⢀⡀⠀⠀⠀⠀⠉⠳⢯⣟⣿⣾⣼⣹⢓⡶⢶⣶⣾⣾⣿⣆⠘⢷⡨⣛⠻⢿⣾⣝⡻⢿⣿⣿⣿⣿⣿⠈⡄⢿⣶⠂⢿⣿⡟⣿⣿⣿⣿⣸⡋⣿⣏⣿⡿⢀⣿⣤⣿⣯⠀⣿⣼⣿⣾⣷⣿⣼⡇⣷⢹⣷⣹⣿⣿⣮⣝⠿⣷⡌⢻⣾⠋⣔⣻⣿⣿⣿⣿⣿⡾⠋⢀⣴⣿⣷⣿⣋⣴⡿⠿⢛⣻⣿⢽⣻⣱⣴⣾⣿⣿⣿⣾⣣⣿⢰⣿⡟⣿⣭⡿⢨⢿⣿⡏⣸⣷⣷⣾⣷⣶⠞⢀⣴⣿⣿⣿⡟⠁⢀⣾⡟⠀⣠⠏⠀⢀⣧⣾⣿⣿⣀⠀⠀⣸⡏⠀⠾⣷⢞⣹⣿⣿⡟⣿⣹⣿⣿⣿⣿⠉⣿⡇⢸⣇⡁⢀⠀⣿⣿⣧⠀⠀⠀⣿
⠃⠀⠀⠀⠙⢿⣿⣷⣄⡢⣄⡀⠀⠈⢳⡌⢻⣷⣦⣄⣀⡀⠀⠀⢈⣻⣿⣿⣿⣿⣷⣿⣴⣻⣯⣷⣟⣧⠘⠷⡹⣷⣦⣬⣛⠛⠂⠉⠻⢿⣿⣿⣿⣵⠌⣿⣷⣜⣿⣧⣿⣿⣻⣟⣺⣷⣿⣿⣿⣿⣼⣿⣹⣮⣻⣶⣽⣿⡘⣯⣿⣿⣿⡇⣿⣾⡏⣻⣿⣿⣿⣿⣷⣽⣿⣖⢁⠞⣰⣿⣿⣿⣿⡿⠋⢀⣴⢾⢿⢛⣉⡽⠟⣁⣴⣾⡟⣫⣼⣾⣿⣿⣿⣿⣿⣿⢻⣿⢸⡇⢸⣿⠇⣿⣿⠃⣿⣸⣿⢠⣟⣡⣤⣼⣥⣾⣾⣿⣿⣿⡿⠋⠀⣠⣿⠏⢀⡴⠃⠀⢀⡎⣽⣿⣿⠋⠋⠀⣠⡿⠁⠀⠀⠙⣾⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣀⣸⣿⠸⣿⡳⢄⠀⢹⣿⣿⡄⡀⠀⢸

⠀⢀⡆⡄⠀⢰⠰⠀⠀⢈⠀⠸⡆⡀⢠⣽⠒⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢴⣶⣿⠭⠕⠋⠁⠬⢍⣐⣊⢻⠻⣿⣦⡀⠀⠀⠀⠀⠈⠁⠀⢀⡠⢊⠉⣠⠎⠸⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢸⣧⠳⣎⠲⣦⠄⠀⠡⡈⢻⠀⣼⠇⠀⠀⠈⣰⠃⠀⠸⣀⠀⢹⠑⠀⠙⠁⢄⠘⠆⠀⣠⣲⣿⠿⠿⠿⢿⣿⣿⡟⠋⠁⢀⡀⠀⠀⢀⡀⠤⣼⣿⠀⣇⢉⢹⣿⣗⣒⣛⣉⣠⣴⣞⠋⠐⣁⣴⢇⠄⠀⠀⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠒⢦⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⢻⡄⢿⢧⢹⣤⣽⡄⠁⠸⢸⠃⠀⠀⠀⠀⠁⠀⠀⠀⣿⡄⡄⠓⣄⠀⠀⡄⢠⣤⡴⣿⡏⠀⣴⣶⣶⣶⣾⡏⢀⣴⢾⠋⠀⠄⢊⠅⠀⠀⠙⣿⣇⣸⣄⠢⡻⣿⣿⣿⣿⣿⣯⡴⢶⠟⣹⣿⠂⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀