Sad Text Art

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

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠠⠔⠂⠐⠀⠉⠈⠁⠉⠉⠉⠀⠐⠐⠂⠄⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠔⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠂⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠡⡀⠀⠀⠀ ⠀⠀⢀⠌⠀⠀⠀⠀⠀⠀⢀⣠⡶⠿⠛⠁⠀⢀⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢆⠀⠀⠉⠻⠷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀ ⠀⢀⠄⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⣀⠠⠒⠁⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠁⠢⠄⡀⠀⠀⠉⠉⠀⠐⠀⠀⠀⠀⠀⠰⡀⠀ ⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⢒⣨⣴⣤⣄⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢀⣠⣤⣬⣅⡢⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀ ⠰⠁⠀⠀⠀⠀⠀⠀⡴⠊⠀⣰⡿⠋⢻⣿⣿⠣⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢺⣿⣿⠋⠙⣷⡄⠈⠓⣄⠀⠀⠀⠀⠀⠀⠈⠆ ⠐⠀⠀⠀⠀⠀⠀⡞⠀⠀⢀⢹⣽⣶⣾⣿⣿⣦⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢠⣼⣿⣿⣷⣾⣽⣠⠀⠀⠈⠇⠀⠀⠀⠀⠀⠀⠁ ⠆⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⡾⠸⣿⣿⡿⢿⣿⠁⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠸⣿⡿⢿⣿⣿⠉⡟⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⢸ ⡃⠀⠀⠀⠀⠀⠈⢇⠀⠀⠀⠐⢤⣹⣯⣷⡾⠃⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠹⢷⣮⣽⣁⡴⠁⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⢸ ⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⠂⠄⠀⠉⠉⠁⡠⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣀⠉⠉⠁⡀⠠⠐⠀⠈⠀⠀⠀⠀⠀⠀⠀⠸ ⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠄⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡐⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄ ⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆ ⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀ ⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⢄⠠⣀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀ ⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠒⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠐⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀ ⠀⠀⠀⠀⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠊⠀⠀⠀⠀⠀⠀⢀⡠⣄⣠⢠⣀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠉⠒⠄⠃⠒⠈⠉⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠢⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠐⠢⠄⠤⠀⣀⣀⣀⣀⣀⣀⠠⠄⠤⠔⠂⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢀⣤⣶⠶⠿⠿⠿⢶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⠾⠿⠿⠷⢶⣦⣄⠀⠀⠀ ⠀⣴⡿⠋⠀⠀⠀⠀⠀⠀⠈⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠋⠀⠀⠀⠀⠀⠀⠈⠙⢷⣄⠀ ⢸⡟⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠈⣿⣄⣤⣤⣤⣶⣶⣶⣶⣶⣶⣤⣤⣤⣀⡀⠀⣿⠃⠀⠀⠀⠀⠀⠀⣀⣤⣤⣬⣿⡆ ⣾⡿⢟⢛⠛⡛⠿⣷⣤⢀⣠⣶⠿⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠻⢿⣦⣄⡀⠀⠀⣠⣾⠟⡩⠑⡌⣹⣿ ⢹⣷⠈⢆⠱⣈⠒⣬⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣶⣴⣿⠃⡜⢠⠓⠤⣹⡿ ⠘⢿⣎⢢⠱⢤⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣜⢄⠣⢌⣳⡿⠃ ⠀⠈⠻⣷⣮⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣷⣾⠿⠋⠀⠀ ⠀⠀⠀⢀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡀⠀⠀⠀ ⠀⠀⠀⣸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⠀⠀⠀ ⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀ ⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀ ⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣦⡀⠀⠀⠀⣼⡇⠀⠀ ⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡷⠀⠀⠀⡀⠤⠀⠐⠠⠄⡀⠀⠀⠸⣿⣿⣿⡇⠀⠀⠀⣿⡇⠀⠀ ⠀⠀⠀⠸⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡿⣿⡇⠀⡐⠀⠀⢠⣿⣿⣷⠀⠈⠢⠀⠀⠈⠉⠉⠀⠀⠀⢠⣿⠀⠀⠀ ⠀⠀⠀⠀⠘⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣧⣼⡗⠀⠀⠀⠀⢨⣿⣿⣯⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⣠⣿⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠛⢷⣦⣀⡀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⢂⠀⢰⡿⠋⠈⠻⣷⠀⠠⠃⠀⠀⠀⢀⣠⣾⠟⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠷⢶⣤⣤⣄⣀⣀⣀⠀⠀⠀⠈⠐⠀⠀⠀⣂⣂⣀⣀⣠⣤⣴⠾⠟⠋⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⡿⠿⠛⠛⠛⠻⣿⣆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢰⣿⠛⠉⠉⠉⠙⠛⠿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠘⣿⡆⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣷⣦⣀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⢀⣴⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠛⠛⠛⠛⠿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣄⠀⠀⠀⠀⠀ ⠀⠀⠸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣦⠀⠀⠀⠀ ⠀⠀⢀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣷⡀⠀⠀ ⠀⠀⣸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⠀⠀ ⠀⢠⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡆⠀ ⠀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⠀ ⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀ ⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⣶⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇ ⠘⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇ ⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁ ⠀⢹⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠀ ⠀⠈⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠇⠀ ⠀⠀⠘⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣶⣶⣶⣶⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠏⠀⠀ ⠀⠀⠀⠈⢻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⡿⠋⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⠿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣶⡿⠟⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⣷⣶⣤⣤⣤⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣶⣶⣶⣶⡿⠿⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠢⣤⠶⣄⠀⢄⠄⣀⠠⣤⡀⠀⠀⠀⠀⠀⢀⣠⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠉⠀⠉⠁⠈⠀⠀⠈⠙⠿⣲⣦⠀⠄⠂⠵⠏⠒⠴⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣦⡀⠀⠀⠀⠀⠠⡀⠀⣾⠈⠘⢀⠀⠀⡀⠐⡄⠈⢣⣐⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⣈⣉⣁⡰⠶⠶⠂⠒⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⣴⡇⠙⢤⠀⢀⠀⠀⠻⢆⡏⠆⠀⢸⡇⠀⠙⣀⠈⠓⢤⣄⣉⠁⠒⠂⣒⣲⣲⣶⡎⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⠞⡇⠁⠀⠈⠃⠂⢠⠼⣠⠟⢰⠀⠀⣸⠃⠀⠀⠀⠀⠀⢀⠀⢏⡩⡭⢫⠄⣿⣯⡀⠈⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡼⠀⠡⠀⠀⠀⢀⢀⡬⠚⠁⣰⢏⣠⢞⢁⠀⣐⡤⣀⠤⠖⠲⠧⣙⢞⣣⢌⢰⡏⣷⣿⣯⣧⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠇⠀⠀⣀⡠⡰⠓⠁⠀⢀⣴⡷⡏⠉⢦⠆⢲⡍⡰⢡⣤⣶⡾⠿⣶⣵⣯⡦⠛⣧⡈⢿⣯⣾⣿⠶⣄⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⢠⠤⠓⠈⠁⠀⠀⠀⣰⣿⣿⣟⢿⣮⢁⡫⢑⠱⣱⣿⠋⠀⠀⠀⠀⠈⣻⣿⣦⡐⠈⠉⠙⠳⣶⣿⣎⠙⠛⡜⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠘⠓⢶⡦⠀⠀⠀⡠⡊⢰⠁⢠⣿⣷⡙⠷⡋⡴⣧⣿⠃⠀⠀⠀⠀⢀⠌⠀⠐⠋⠉⠔⡇⠀⠀⠀⠙⢿⣷⡐⢨⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠠⢒⠿⠌⢤⣶⡔⠁⠀⢸⡟⣿⣿⣻⡇⣿⠋⡰⣿⡧⠄⠒⠔⠤⠤⠂⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⢻⡝⢸⡆⢤⡀⠀⠀⠀⠀⠀ ⠀⠰⠅⠊⠘⣿⡏⠀⠀⠀⠘⢗⢿⣷⣿⣳⠋⠀⢡⢿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⠈⠀⠀⠈⠐⢄⠀⠀⠀ ⠀⠁⠀⠀⢀⠇⠸⡀⠀⠀⠀⡾⠶⣉⣾⠇⠀⠀⠀⠁⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠱⢇⠀⠀ ⠁⠀⠀⠀⠈⠀⠀⢡⠀⢠⠌⢛⢿⣿⡟⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢊⢿⡷⡦⠀⠀⠀⠀⠡⢂⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⡖⢋⡀⠈⠸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⢩⣘⣀⠁⠀⠊⢄⠀⠀⠀⢁⠄ ⠀⠀⠀⠀⠀⠀⠀⠈⡧⠶⣅⠀⠀⠹⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⢡⢸⠼⢡⣁⡉⠀⠀⠀⠐⡢⠀⠀⠈⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠈⠑⠠⠀⠀⠁⢈⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠘⡄⡀⡰⢼⡟⢊⡇⠬⠆⠀⠀⠀⠀⠀⣡⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⢄⠀⠀⠠⢤⠀⡂⠑⢅⢈⢂⣀⡀⡐⣨⣡⣠⡆⠇⡗⠜⢋⠢⢏⠏⠀⠀⠀⠀⠀⠀⠀⢰⠆⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠑⠤⠍⢖⠒⡒⠒⠚⢊⣔⠬⠇⠂⠁⠌⠀⠌⠚⠨⡀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠄⡈⢀⠄⠠⠄⢀⡤⠀⠀⣀⠠⠐⠈⠀⠀⠀⠀⠈⠂⡀⠀⠀⠀⠀⠈⠄⣿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠐⢄⠀⠀⠀⠀⠐⠀⠀⠀⠀⠈⠻⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢀⠂⠀⠀⠀⢀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡆⠀⠀⠀⠀⠈⠆⠀⠄⢪⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠁⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⡇⠀⠀⠈⠄⠀⠀⠇⠠⠁⠀⠀⢄⠀⢀⡀⠜⠀⠀⠀⠂⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠂⠠⠤⠐⡅⠀⠀⡀⠔⠀⡇⠀⠀⠀⠀⠠⠙⠀⠀⢀⠆⠀⠀⠀⠀⠀⠀⠀⠘⠈⠀⠀⠀⠀⠀⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠀⠀⠀⠀⠃⠀⠀⠒⠒⠁⠀⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
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