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. ⠠⠀⠐⠤⡸⠤⠒⢒⣶⣾⣶⣶⣶⣶⣾⣶⣤⣤⣐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠈⡀⣰⣴⣾⣿⣷⣶⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣵⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠊⠀⣠⣴⣻⣿⢟⣿⣿⣿⣿⣿⣿⣿⣥⣾⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢀⡼⠋⣰⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⢀⣼⣿⡻⢿⣿⣿⣿⡿⠿⠿⠿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⠁⢰⣿⣿⣿⠏⠎⠙⢮⣩⣥⣾⣿⣿⣿⢿⣷⣿⠿⠋⣼⣿⣷⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⢐⣿⣿⣿⡟⠈⢠⣭⡏⠺⠉⠽⠛⢛⣫⡵⡟⢍⡀⢰⣿⣿⣿⣿⣿⣿⣿⣼⠻⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣨⣷⣾⣿⣿⠟⠉⠀⠀⠩⠋⠁⠀⠀⠀⠈⢉⣲⣀⡀⠀⠈⣾⣿⣿⣿⣿⣿⣿⣿⣿⣦⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⡿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢈⡱⡄⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⠟⠋⣡⣼⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⣶⣾⠿⡀⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠟⠁⠀⣰⣿⣿⣿⣿⡇⠀⠀⠀⡄⠀⠀⠀⢀⠀⠀⠀⠐⠀⠊⠫⢰⣣⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠁⠀⠀⢀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠘⠀⠀⠀⠀⠐⠢⣤⣤⣤⣤⣶⣿⠿⠋⠚⠻⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⣼⣿⣿⣿⢹⣿⣿⣇⠀⢀⣤⡶⠿⠟⠛⠲⠦⣄⡀⠀⠀⠀⠀⣀⢰⠒⠀⣼⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⡇⣿⣿⡇⢸⣿⣿⣿⣶⡟⠩⠀⢀⣀⠀⠀⠀⠀⠈⣒⣦⣀⣀⣀⣀⣀⣰⣿⣿⣿⣿⣿⠛⠛⠛⠿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀ ⠀ ⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠃⢻⣿⣷⡀⠙⡿⠟⠉⠀⡩⠈⢈⢆⠂⠀⠀⡴⠊⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠈⣿⠀⠀⠀⠀⠀⠉⠻⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣆⠀⠀⠈⠀⠙⢿⣿⣦⠆⠈⠀⠔⠁⠂⠀⢁⠱⡈⢺⠛⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠀⢹⠀⠀⠀⠀⠀⠀⠀⠈⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⢿⣷⣄⣀⠀⡀⠤⣈⠁⠀⠂⠀⠀⠀⠀⠀⠀⠈⠅⠸⣖⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠁⢈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⡎⠊⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠀⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠉⢀⡀⠀⡐⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠥⠅⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠘⡑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⠀⠀⠀⡀⠐⠈⠀⠀⢀⠘⠄⠌⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⣠⢇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠌⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣂⠀⠈⡠⣺⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠄⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⢟⠣⡠⠑⢹⣇⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣬⠛⠂⢤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⢈⠃⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢐⣆⣉⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠈⠙⠳⢦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⠀⠠⠀⠀⡀⣥⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣸⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠉⠛⠶⠦⢤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⡄⠀⠀⠀⠀⡤⠂⠁⠁⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⡈⢿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠙⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢶⣄⡀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢠⣦⣾⠿⠛⠃⢂⡂⢀⠑⠈⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠁⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⡍⠡⢄⡙⢿⣿⣿⣿⣧⡹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠂⠀⠈⠙⢶⡄⠀⠀
⠀⠀⠀⠀⢀⣴⣶⣏⣉⠁⠀⠀⣔⡐⣠⠈⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠘⠉⠁⠀⠂⠀⠀⡀⠹⣿⣿⡏⠠⠁⠀⠈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡲⢄⡀⠀⠀⠀⠂⠀⠀⠀⠈⠲⡄
⠀⠀⢀⣀⣮⠗⠡⠀⢈⣁⡈⢀⠀⡀⠀⢀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⣤⡀⠀⠀⠀⠠⠀⠹⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠙⠲⣄⠀⠀⠄⠀⠀⠀⠀⠙
⠀⠀⣨⡯⡉⠐⡀⠄⠀⠀⠁⠀⠠⠁⡐⠀⠆⠁⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢑⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⢿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠈⠳⢤⣐⠀⠀⠀⠀⠀
⠀⡰⠙⢁⠂⠀⠀⠀⠀⡠⠀⡠⠀⢠⢂⠈⠀⠀⠀⠀⠀⠀⠀⢀⠠⠂⠀⠠⠀⠀⢠⠆⠀⠀⣤⣀⠀⠄⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡈⠻⣷⡄⠀⠙⣷⡄⠀⠀⠀
⠠⠀⠀⠀⠀⠃⠀⠀⠈⠀⠠⠠⠊⢁⠂⠀⠀⠀⠀⠀⠀⠄⠀⢤⢍⡁⠀⢀⠒⢰⡀⠀⢄⢀⡀⣄⢌⣠⡆⠻⢂⠈⡀⠀⢀⠀⡁⣀⣨⠉⠐⠀⡄⣘⠀⣿⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠙⢷⣄⠀⡁⠹⢆⠀⣀
⡆⠀⠃⠀⠀⠀⠀⠀⠀⡀⠈⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠠⠀⠀⢐⠈⠁⠐⠎⡰⠠⠨⣷⣿⣟⣵⣦⣤⡨⡢⣴⣃⡖⠟⠙⠋⠙⢃⢶⠌⠀⣸⡏⠀⢸⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⡄⠀⠸⣿⣷⡃⠀⠘⣿⡋
⢀⣀⠀⠀⠀⠀⠀⠀⠘⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡄⠂⢀⠀⠀⠉⢖⠂⠀⠄⠒⠢⣨⡟⣻⠿⣭⡙⢮⢘⠻⠾⣮⡀⢀⢔⠕⠁⠀⠀⡟⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣷⠘⣿⣿⣿⣿⣿⡇⠀⠀⠹⣿⣳⡀⠀⠘⣧
⣼⣿⣶⣶⣶⣿⣿⣵⡶⣦⡀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠙⢂⠀⡀⡀⠀⠃⠎⠕⣐⠉⠁⠉⠃⢐⠠⠈⠻⣤⣅⢀⢀⠠⡺⠄⠁⠀⢀⣴⠞⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⢹⡆⠈⢻⣿⣿⣿⣷⠀⠀⠀⢹⣷⠑⡀⠀⢹
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠐⠀⠄⠀⠈⠈⢀⡀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠉⠃⠘⠊⡎⢕⠊⢀⣀⡤⠶⠛⠁⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡟⢸⡇⠀⠀⢿⣿⣿⡏⠀⠀⠀⠀⣿⡀⠁⠀⠸
⣤⣿⠿⠟⠛⠛⣻⡟⠋⠅⠈⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠁⠐⠁⠈⠁⠀⠀⠁⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠐⢀⢈⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⢟⠃⢸⡇⠀⠀⠈⢻⣿⡇⠀⠀⠀⠀⢸⠃⢸⣀⠀
⠀⠀⠀⠀⠀⢀⠏⠀⠠⠀⡠⢠⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠘⢄⢄⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠂⠄⠀⠀⢀⣼⣿⣿⣿⣿⠟⣼⠀⢸⡇⠀⠀⠀⠀⢿⣿⠀⠀⠀⠀⣼⠀⠀⡇⠀
⠀⠀⠀⠀⠠⠀⠀⠀⠀⣰⣿⣻⠀⠀⠀⠀⠀⠀⠀⢀⠡⠁⠀⠀⠀⠀⠀⠀⠀⠉⠂⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠁⠠⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⢐⣴⣿⣿⣿⡿⡿⠋⣰⠏⠀⢸⡇⠀⠀⠀⠀⠘⣿⠀⠀⠀⢰⠃⠀⠀⡇⠀
⢥⣂⢄⠀⠊⠤⠀⢀⣾⡿⠍⢸⠀⠀⠀⠀⠀⠀⠀⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠄⢀⠈⠢⠀⠀⠀⠐⠄⠀⠀⠈⠰⠤⠤⢬⣶⣾⣿⣿⣿⣿⡿⠉⢀⡼⠃⠀⠀⣼⠁⠀⠀⠀⠀⢀⡟⠀⣠⠞⠁⠀⠀⢸⠃⠀
⠀⠈⠁⠀⠀⠉⡲⡠⠋⠈⠠⢹⠀⠀⠀⠀⠀⠀⡨⠁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠒⠠⢁⡀⠀⠠⡀⠀⠀⠀⠀⠀⠁⠉⠉⠉⠉⠀⣀⡶⠋⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⣸⠓⠛⠁⠀⠀⠀⠀⠌⠀⠀
⠀⠁⠀⠀⠠⠊⠉⠐⠺⠤⣗⣸⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⠂⠆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠠⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢠⣡⠄⡀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⣘⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠄⡀⠀⠀⠈⠀⠐⡀⠀⠀⠀⠄⠒⡀⠀⠐⠀⠁⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢀⣿⣿⣿⣷⣦⣖⣠⣄⡸⠀⠀⠀⠀⠠⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢀⠁⢡⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠠⡀⠀⠀⠀⠀⠀⡀⢀⢄⠀⠀⠀⠨⠢⡀⠀⠀⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠠⠁⠀⠉⠛⠻⢿⡿⠿⣻⠃⠀⠀⠀⠆⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠂⣰⡿⠛⣍⣳⣤⣾⠇⠀⠀⠀⠠⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡟⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠂⠀⠀⠻⢥⡿⠿⠿⢟⢻⠀⠀⠀⠀⠀⠡⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠟⠀⠀⠀⠀⠠⠢⠀⠄⠀⠀⠀⠀⠀⠂⠰⠀⠀⠀⠀⠉⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢸⠀⠀⠀⠄⠐⠀⡠⠐⠁⠃⠀⠀⠀⠀⠀⠀⠁⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠰⣻⣶⣦⣤⡄⠀⠀⠀⠀⠘⠛⠋⠀⠀⠀⠀⡠⠂⠀⠀⠀⠀⠀⠀⠁⠀⢁⠀⠄⠀⠀⠀⠀⠀⠀⠄⠀⠁⠀⢄⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠠⠈⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡁⠀⠀⠀⠐⢻⣿⣿⣟⣄⠀⠀⠀⠄⠀⠀⠀⠀⠀⠈⠄⠐⢄⠀⠀⠀⠀⠀⠀⠀⠀⠁⠨⡄⠀⠀⠀⠀⠁⢀⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠈⠀⠀⠐⠀⠀⠀⢀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠐⢀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⡀⠀⠀⠙⣿⣿⣿⣿⠆⠀⠌⠄⠀⠀⠀⠠⠂⠀⠀⠠⠀⠑⠀⠀⠀⠐⠄⠀⠄⡀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠸⠊⠀⠀⠀⠀⠄⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠁⡀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠈⢂⠀⢠⠘⠛⠏⢙⠔⠁⠀⠈⠢⠀⠘⠀⠀⠀⢀⠠⠐⠂⠂⢂⠀⠀⠀⠀⡀⠄⠒⠂⠒⠨⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠄⠁⠀⠀⠀⠀⠀⠀⢸⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠨⠠⢤⡌⠀⠀⠀⠀⠀⠀⠀⠪⠤⠤⠂⠐⠄⠀⠀⠀⠄⠀⠀⡠⠀⠈⠄⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢀⠁⠃⠀⣀⠀⠀⠀⠀⠀⠘⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠑⢄⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠁⣀⠔⢡⠐⢁⠀⠀⢂⠀⠀⠀⣘⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠘⡀⠀⠀⠀⠔⠐⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⡱⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⡄⡀⠀⠂⠀⠀⠄⢀⠄⠀⠄⠂⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠈⠆⡠⢐⠀⠘⠀⠘⠑⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠌⠀⢈⡀⠀⠁⠀⡇⡄⠀⠀⠁⠊⠤⠄⠀⠀⠀⠀⠀⠀⠤⠄⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠘⠈⠈⠀⢀⠀⠀⠀⠀⠅⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀