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