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⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣷⡄⢰⣿⣿⣿⡇⢠⣿⣿⣿⣿⣿⡇⠀⣸⣿⣿⣿⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦ ⠀⠀⠀⢠⣿⣿⣿⡟⢛⣿⣿⣿⡏⣼⣿⣿⣿⢀⣾⣿⣿⢿⣿⣿⡇⠀⣿⣿⣿⣿⡆⠀⣿⣿⣿⡟⢿⣿⣿⣿⠟⣿⣿⣿⡿⠛⢻⣿⣿⣿ ⠀⠀⠀⣼⣿⣿⡿⠀⠸⠿⠿⠿⢀⣿⣿⣿⡇⣼⣿⣿⡟⢸⣿⣿⡇⢸⣿⣿⣿⣿⣇⢰⣿⣿⣿⠀⣿⣿⣿⡿⢀⣿⣿⣿⣏⡀⠾⠿⠿⠇ ⠀⠀⢀⣿⣿⣿⠇⣤⣤⣤⣤⣤⣼⣿⣿⣿⢰⣿⣿⣿⠁⣿⣿⣿⡇⣾⣿⣿⣿⣿⣿⣾⣿⣿⡏⢰⣿⣿⣿⡇⠘⢿⣿⣿⣿⣿⣿⣶⡄⠀ ⠀⠀⣸⣿⣿⣿⢰⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣷⣶⣿⣿⣿⣇⣿⣿⣿⢹⣿⣿⣿⣿⣿⠃⣼⣿⣿⣿⠀⣄⣤⣨⡙⠛⣿⣿⣿⣿⠀ ⠀⠀⣿⣿⣿⡏⠈⣿⣿⣿⡟⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠘⣿⣿⣿⣿⣿⠀⣿⣿⣿⡏⢰⣿⣿⣿⠁⠀⣿⣿⣿⡏⠀ ⠀⢸⣿⣿⣿⣷⣴⣿⣿⣿⠃⣿⣿⣿⣿⣿⣿⣿⠃⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⢿⣿⣿⣿⡇⢸⣿⣿⣿⠇⣾⣿⣿⣿⣶⣾⣿⣿⣿⠁⠀ ⠀⠈⠻⠿⣿⣿⣿⢿⠿⠋⠰⠿⠿⠿⠿⠿⠿⠇⠀⠀⠸⠿⠿⠿⠿⠿⠿⠀⠀⠸⠿⠿⠿⠁⠾⠿⠿⠟⠀⠘⠿⠿⢿⣿⡿⢿⠟⠁⠀⠀ ⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠄⠀⠀ ⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀

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