Peter Eating a Donut Emojis & Text

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣊⣁⣀⠀⠀⠀⠀⠈⠑⠦⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠟⠉⠐⢄⠀⠉⢑⠶⠤⡤⠤⣤⠈⢦⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⠤⢼⠀⢰⠤⠼⡒⢲⠁⢀⡀⠘⠤⠧⠴⣾⣇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡜⠁⠀⠀⠑⡇⠀⠀⠀⠘⢄⡀⣀⠔⠀⠀⠀⠋⠙⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⡖⠈⠒⠒⠒⠀⠀⠀⣀⡄⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⠇⠀⠀⠀⠸⢍⣑⠒⠒⠒⠒⠂⠉⠁⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀ ⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⡔⠉⠀⠀⠀⠀⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢧⡀⢀⣀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠈⠁⠈⠑⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀ ⠀⠀⠀⠀⢰⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢹⢄⡀⠀ ⠀⠀⠀⡠⢿⡈⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠊⢀⡴⠁⠀⠈⠑ ⢀⠴⠋⠀⠀⠑⢄⠈⠑⠦⣀⠀⠀⠀⠀⢀⣀⠤⠔⠚⠉⠀⣀⠔⠉⠀⠀⠀⠀⠀ ⠁⠀⠀⠀⠀⠀⠈⠳⣄⡠⠼⢧⣀⡴⠯⣁⡀⠀⣀⠤⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢘⠁⢸⡾⠁⠀⠀⠀⠙⠉⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⣠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣶⣶⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⠛⠛⠛⠛⠛⢻⣯⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⢀⡼⣛⣦⠀⣠⣽⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡇⠸⣍⢋⣹⠀⠻⣍⣹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⢻⠋⠀⠀⡀⠉⠀⣀⣀⣸⠀⠘⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⢣⠏⠀⠀⠀⠉⠒⠦⠤⠭⣼⠆⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⡶⠟⠋⠉⠹⡿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣾⠏⠀⠀⠀⠀⠀⠹⡜⢦⡀⠀⠀⠀⣀⣀⠀⠀⠀⣀⣄⣀⣀⡼⠈⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⢀⡿⠃⠀⠀⠀⠀⠀⠀⠀⠘⠦⡙⠲⢄⡀⠀⠈⠉⠉⠉⢉⡟⡏⠁⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀ ⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠤⣈⡉⠒⢲⠶⠶⠻⡶⠁⠀⠸⡄⠀⣿⡇⠀⠀⠀⠀⠀ ⢸⣧⠄⠀⠐⠒⠶⠤⣄⡀⠀⠀⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⢤⣿⣷⠀⠀⠀⠀⠀ ⢸⡇⠀⠀⠀⠀⠀⠲⢤⡉⠳⣴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⢰⠃⢰⣿⣇⠀⠀⠀⠀⠀ ⢸⡇⠀⠀⠀⠀⠀⠀⠀⠉⠺⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⣠⠋⠀⠈⠻⣷⡀⠀⠀⠀⠀ ⢸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠁⠀⢠⠎⠀⠀⠀⠀⠀⠈⢷⡄⠀⠀⠀ ⠈⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣤⣀⡀⠀⠀⠀⠈⢿⣦⠀⠀ ⠀⠀⠀⠈⣽⣷⣶⣤⣤⣿⣦⠀⠀⠀⣄⢧⠀⣀⣤⣴⣶⣶⣶⣿⣼⣿⣿⣇⢰⣄⠀⠀⣾⡛⡇⠀ ⠀⠀⠀⠀⣻⣿⣿⠟⠹⣿⣿⣇⠈⣇⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣼⣶⣏⡵⠃⠀ ⠀⠀⠀⢰⣿⣿⡟⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣿⣿⣇⠀⠰⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀ ⠀⠀⠀⢸⣿⣿⡉⢀⡔⣿⣿⣯⣿⢸⢻⣿⡿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠀⠀⠀⠀ ⠀⠀⢠⣾⣿⣿⣧⢤⡼⠽⠛⠂⣻⣼⢻⣿⣿⣻⣿⣞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣒⡀⠀⠀ ⠀⠀⠀⠀⣿⣿⣷⠀⠀⢸⣾⢺⣿⡇⣿⣿⡇⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀ ⠀⠀⠀⠀⢿⣿⣿⣷⡀⢀⣭⣿⣟⣿⣿⡽⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠁ ⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⡅⣠⣾⣿⡿⢿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠿⠯⠟⠁⠼⠷⣿⣿⣿⣷⣟⣿⣶⣾⡿⢿⡿⣿⣿⣿⡿⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣟⣿⣿⡽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣵⣶⣤⣄⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠛⢻⣻⡛⠛⠛⣛⣛⡛⢹⣿⡿⠍⡧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣜⠁⠀⠙⡤⣎⠀⠀⠙⡍⠉⠀⠀⠀⠘⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⠖⠙⢄⠔⠒⠃⠹⣀⣀⠔⠁⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⠃⠀⠀⠘⣄⣀⣠⠄⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡘⠀⠀⠀⠘⠒⠀⠀⣴⣶⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⢿⡇⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⠀⠀⠀⠀⡠⠤⠤⠼⠿⠯⠤⠜⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀ ⠀⠀⠈⡇⠀⠀⠀⠙⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢄⠀⠀⠀ ⠀⠀⠀⣷⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⡠⠊⠈⠆⠀⠀⢧⡀⠀⣠⡀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢ ⡜⠁⠀⠀⠀⠀⠀⠀⠉⠉⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⢀⣤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⢤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡼⠋⠀⣀⠄⡂⠍⣀⣒⣒⠂⠀⠬⠤⠤⠬⠍⠉⠝⠲⣄⡀⠀⠀ ⠀⠀⠀⢀⡾⠁⠀⠊⢔⠕⠈⣀⣀⡀⠈⠆⠀⠀⠀⡍⠁⠀⠁⢂⠀⠈⣷⠀⠀ ⠀⠀⣠⣾⠥⠀⠀⣠⢠⣞⣿⣿⣿⣉⠳⣄⠀⠀⣀⣤⣶⣶⣶⡄⠀⠀⣘⢦⡀ ⢀⡞⡍⣠⠞⢋⡛⠶⠤⣤⠴⠚⠀⠈⠙⠁⠀⠀⢹⡏⠁⠀⣀⣠⠤⢤⡕⠱⣷ ⠘⡇⠇⣯⠤⢾⡙⠲⢤⣀⡀⠤⠀⢲⡖⣂⣀⠀⠀⢙⣶⣄⠈⠉⣸⡄⠠⣠⡿ ⠀⠹⣜⡪⠀⠈⢷⣦⣬⣏⠉⠛⠲⣮⣧⣁⣀⣀⠶⠞⢁⣀⣨⢶⢿⣧⠉⡼⠁ ⠀⠀⠈⢷⡀⠀⠀⠳⣌⡟⠻⠷⣶⣧⣀⣀⣹⣉⣉⣿⣉⣉⣇⣼⣾⣿⠀⡇⠀ ⠀⠀⠀⠈⢳⡄⠀⠀⠘⠳⣄⡀⡼⠈⠉⠛⡿⠿⠿⡿⠿⣿⢿⣿⣿⡇⠀⡇⠀ ⠀⠀⠀⠀⠀⠙⢦⣕⠠⣒⠌⡙⠓⠶⠤⣤⣧⣀⣸⣇⣴⣧⠾⠾⠋⠀⠀⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⣭⣒⠩⠖⢠⣤⠄⠀⠀⠀⠀⠀⠠⠔⠁⡰⠀⣧⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⢤⣀⣀⠉⠉⠀⠀⠀⠀⠀⠁⠀⣠⠏⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠒⠲⠶⠤⠴⠒⠚⠁⠀⠀

⠀⠀⠀⡔⠒⠖⣩⠿⢽⢿⠕⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⢰⠀⠀⢂⠡⠼⠊⠁⠈⠉⠉⠁⠐⢢⡀⠀ ⠀⠀⠘⡤⠤⠂⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣷⡄ ⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡏ ⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⠟⠀ ⠀⠀⠀⡔⠤⡀⠀⠀⠰⣶⠖⢰⠂⠀⠉⠀⠀⠀ ⠀⠀⡰⠉⠐⠠⠌⠉⠁⠠⡕⠺⡄⠀⠀⠀⠀⠀ ⠀⢰⠁⠀⠀⠀⠀⠀⠀⠸⠼⠀⢸⠀⠀⠀⠀⠀ ⠀⠘⡀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢰⢰⠀⠀⠀⠀ ⠀⠘⡦⠔⠤⠃⠀⠀⠀⠀⠀⠀⡟⠁⠀⠀⠀⠀ ⢠⣔⣉⠆⠀⠀⠀⠀⢄⠀⠀⠀⣇⠀⠀⠀⠀⠀ ⠀⠀⠀⢰⠀⠀⠀⠀⢸⠆⠀⠀⢸⠀⠀⠀⠀⠀ ⠀⠀⠀⡆⠀⠀⠀⢀⠈⡢⠀⠀⢀⢕⠀⠀⠀⠀ ⠀⠀⠀⠑⠢⠄⣀⣀⣱⠸⠂⠀⠚⠉⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣿⣿⣿⣿⣶⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⣿⣿⣿⡿⠿⠿⠟⠛⠛⡛⠻⢷⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⠪⣿⣿⣷⣀⢠⠮⠭⠭⠴⣀⣀⡜⠒⢒⠒⠓⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠠⢁⣷⣿⡿⠁⠀⢁⠀⠐⠀⠀⡇⠀⠉⠀⠢⣀⡐⠀⠉⠐⠠⡀⠀⠀ ⠀⠀⠀⢀⠃⣴⣿⣿⡇⠀⠀⠀⠑⠠⠄⠪⠀⠀⠀⢀⡀⠈⠐⠀⢄⠀⠀⠐⡀⠀ ⠀⠀⠀⠘⢰⣿⣿⣿⡇⠀⠀⠀⡠⠄⡀⠈⠀⠈⠉⠀⠀⠉⢐⠒⠊⠀⠀⠀⢱⠀ ⠀⠀⠀⡆⢾⣿⣿⣿⣿⠀⠀⠀⣷⣤⣀⣾⣉⣉⡆⠈⠉⢃⡈⠂⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡇⠀⠈⠉⠉⠀⠀⠀⠀⠘⢟⠛⠿⣿⣿⣷⡶⠲⠬⠄⣀⠀⠀⠀⠀⠀⡆ ⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⠀⡇ ⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⢀⠀⠀⠀⢀⠂ ⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⡠⠂⠀ ⠀⠀⡜⠐⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⡠⠢⢀⣀⠠⡢⠊⠀⢠⣾ ⢠⠞⣧⡀⠈⠑⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⢀⠠⠐⠁⠀⢀⣴⠿⠋ ⠁⠀⣿⡷⠄⠀⠀⠈⠐⠠⡀⠀⠀⠀⠀⠀⢀⡀⠠⠒⠈⠀⠀⠀⢀⣴⡟⠁⠀⠀ ⠀⢸⣿⡇⠀⠢⠀⠀⡠⠒⠀⠑⠄⢰⠒⠪⡀⠀⢰⣤⣀⣸⣷⣶⣿⠏⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⢀⣴⠟⠉⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣀⢀⣾⠿⠻⢶⣄⠀⠀⣠⣶⡿⠶⣄⣠⣾⣿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢻⣿⣿⡿⣿⠿⣿⡿⢼⣿⣿⡿⣿⣎⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠉⠛⢛⣛⡉⠀⠀⠙⠛⠻⠛⠑⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣧⣤⣴⠿⠿⣷⣤⡤⠴⠖⠳⣄⣀⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣀⣟⠻⢦⣀⡀⠀⠀⠀⠀⣀⡈⠻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠉⡇⠀⠀⠛⠛⠛⠋⠉⠉⠀⠀⠀⠹⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⠀⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠈⠑⠪⠷⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣦⣼⠛⢦⣤⣄⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠢⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠲⠖⠛⠻⣿⡿⠛⠉⠉⠻⠷⣦⣽⠿⠿⠒⠚⠋⠉⠁⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣾⠛⠁⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⠀⠀⠀ ⠀⠀⠀⠀⣰⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀ ⠀⠀⠀⣰⣿⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣧⣄⠀⠀⠀⠀⠀⠀⢳⡀⠀ ⠀⠀⠀⣿⡾⢿⣀⢀⣀⣦⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⣫⣿⡿⠟⠻⠶⠀⠀⠀⠀⠀⢳⠀ ⠀⠀⢀⣿⣧⡾⣿⣿⣿⣿⣿⡷⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢿⣿⣧⠀⡀⠀⢀⣀⣀⢒⣤⣶⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⠀⡾⠁⠙⣿⡈⠉⠙⣿⣿⣷⣬⡛⢿⣶⣶⣴⣶⣶⣶⣤⣤⠤⠾⣿⣿⣿⡿⠿⣿⠿⢿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⣸⠃⠀⠀⢸⠃⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⠟⡉⠀⠀⠀⠈⠙⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⣿⠀⠀⢀⡏⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠛⠉⠁⠀⠀⠀⠀⠀⠉⠠⠿⠟⠻⠟⠋⠉⢿⣿⣦⡀⢰⡀⠀⠀⠀⠀⠀⠀⠁ ⢀⣿⡆⢀⡾⠀⠀⠀⠀⣾⠏⢿⣿⣿⣿⣯⣙⢷⡄⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣻⢿⣷⣀⣷⣄⠀⠀⠀⠀⢸⠀ ⢸⠃⠠⣼⠃⠀⠀⣠⣾⡟⠀⠈⢿⣿⡿⠿⣿⣿⡿⠿⠿⠿⠷⣄⠈⠿⠛⠻⠶⢶⣄⣀⣀⡠⠈⢛⡿⠃⠈⢿⣿⣿⡿⠀⠀⠀⠀⠀⡀ ⠟⠀⠀⢻⣶⣶⣾⣿⡟⠁⠀⠀⢸⣿⢅⠀⠈⣿⡇⠀⠀⠀⠀⠀⣷⠂⠀⠀⠀⠀⠐⠋⠉⠉⠀⢸⠁⠀⠀⠀⢻⣿⠛⠀⠀⠀⠀⢀⠇ ⠀⠀⠀⠀⠹⣿⣿⠋⠀⠀⠀⠀⢸⣧⠀⠰⡀⢸⣷⣤⣤⡄⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⢼⡇ ⠀⠀⠀⠀⠀⠙⢻⠄⠀⠀⠀⠀⣿⠉⠀⠀⠈⠓⢯⡉⠉⠉⢱⣶⠏⠙⠛⠚⠁⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⠀⠀⠀⠀⠀⠻⠄⠀⠀⠀⢀⣿⠀⢠⡄⠀⠀⠀⣁⠁⡀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⢀⣐⡟⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢠⡇

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠀⠀⠀⠀⠀⠀⠀⢠⢱⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⡸⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⣠⠤⣀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⢠⢶⢟⢻⣗⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⢠⠇⠈⠒⠊⠑⠚⠓⠒⠒⠦⣄⠀⠀⠀⠀⠀⠀ ⠀⣀⡤⣄⠀⢸⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣦⠀⠀⠀⠀⠀ ⡜⢁⣠⣶⠷⣼⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀ ⢳⡾⠋⣠⣤⣿⠀⠀⠀⠀⠀⠀⠸⡀⠀⡀⠀⠀⠀⠀⠀⠀⢻⡿⠋⢠⣴⡒⠲⡄ ⠀⠉⠓⠛⡿⡿⢢⡀⠀⣀⣀⡀⠀⠳⣄⢹⠿⣶⣶⠒⠒⠒⠋⡀⢀⣯⡈⢿⡆⢸ ⠀⠀⠀⠀⢻⡵⢻⠑⠐⠓⠒⢮⠀⠀⠈⠩⣛⣒⣾⡀⢀⣠⣿⣽⣟⡿⠧⠼⠟⠃ ⠀⠀⠀⠀⠀⠳⣙⢷⡄⠀⠀⢸⠀⠀⠀⠀⠀⠀⢣⢏⢩⡾⠗⢈⡼⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⢻⡒⠒⠶⠥⠋⠀⠀⠀⠀⠀⠀⠻⣦⠴⠚⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣯⠖⠁⠒⢤⠀⠀⠀⠀⠀⠀⢈⣼⡆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⣿⣇⣀⣀⣀⠠⠜⡟⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⡃⠀⠀⠀⢸⠁⠀⡟⠀⠀⠀⠰⢇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣅⣆⣀⣀⡼⠀⠀⠳⣄⣀⣀⣆⣾⠃⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠸⣶⣦⣄⣀⣀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⣾⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⠿⠿⢿⠟⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⣹⣿⣿⣿⣿⣫⠝⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠶⠾⣤⡀⠀⠀⠀⢠⣤⠶⠶⠶⣤⡀⢀⣸⣿⣿⣿⠇⠛⢠⡏⠙⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀⠈⢻⣆⣀⣴⠏⠀⠀⠀⠀⠈⢻⡏⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣷⠆⠀⠀⠀⠀⢀⡏⠉⣿⡶⠀⠀⠀⠀⠀⢈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠋⢳⣄⢀⡤⠞⠛⠛⠓⠀⠘⣦⡀⠀⠀⠀⣀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣰⠟⠀⠀⠀⠀⠈⣿⠁⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣰⠇⠀⠀⠀⠀⠀⠀⢻⣄⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⢀⡀⠉⠛⠶⠾⠟⠋⠁⠀⠀⠀⣀⣴⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠘⠓⠲⠶⠶⠶⠶⠶⢶⣶⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⠟⠉⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡴⠶⠶⠶⠶⠿⠿⠿⣿⣤⣤⣴⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⢀⣬⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣼⣷⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀ ⠀⠀⠀⢀⡴⠋⠁⢹⡆⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⠀ ⠀⠀⣠⠞⠁⠀⠀⠈⠿⠀⠀⠀⠀⠀⠙⢧⣀⡀⠀⢀⣠⣿⣄⠀⠀⠀⠀⣠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇ ⢀⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠋⠉⠀⠙⠻⠶⠶⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⢸⣦⡀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣏⠻⣶⣤⡶⢾⡿⠁⠀⢠⣄⡀⢀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀ ⠀⠀⣀⣼⠷⠀⠀⠁⢀⣿⠃⠀⠀⢀⣿⣿⣿⣇⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠴⣾⣯⣅⣀⠀⠀⠀⠈⢻⣦⡀⠒⠻⠿⣿⡿⠿⠓⠂⠀⠀⢂⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠉⢻⡇⣤⣾⣿⣷⣿⣿⣤⠀⠀⣿⠁⠀⠀⠀⢀⣴⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠸⣿⡿⠏⠀⢀⠀⠀⠿⣶⣤⣤⣤⣄⣀⣴⣿⡿⢻⣿⡆⠂⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠟⠁⠀⢀⣼⠀⠀⠀⠹⣿⣟⠿⠿⠿⡿⠋⠀⠘⣿⣇⠀⠄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢳⣶⣶⣿⣿⣇⣀⠀⠀⠙⣿⣆⠀⠀⠀⠀⠀⠀⠛⠿⣿⣦⣤⣀⠀⠀ ⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⠿⠋⠁⠀⣹⣿⠳⠀⠀⠀⠀⠀⠀⢀⣠⣽⣿⡿⠟⠃ ⠀⠀⠀⠈⠀⢰⠿⠛⠻⢿⡇⠀⠀⠀⣰⣿⠏⠀⠀⢀⠀⠀⠁⣾⣿⠟⠋⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⣰⣿⣿⣾⣿⠿⢿⣷⣀⢀⣿⡇⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠋⠉⠁⠀⠀⠀⠀⠙⢿⣿⣿⠇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀ 𐙚 -`♡´-˙✧˖°📷 ༘ ⋆｡˚˙✧˖°📷 ༘ ⋆｡˚˚˖𓍢ִ໋🌷͙֒✧˚.🎀༘⋆˚‧｡⋆🌻⋆｡‧˚⛷🧚‍♀️🛖

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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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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠚⠛⠛⠛⠳⢦⣄⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠛⠷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⣠⠀⠀⣀⠀⠀⠀⠀⠀⢀⣠⣄⠀⢀⠀⠀⠀⠀⠙⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠀⠀⠀⠀⠀⠀⢸⢿⠖⡿⠿⠖⠚⠹⡿⠶⡏⠁⠘⠷⣼⡷⣤⣶⣄⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠰⡗⠒⠒⠶⠒⠶⠤⣷⠀⠀⢰⣇⣀⣀⣉⠉⠉⢿⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠳⣀⠀⠀⠀⠀⡰⠃⠀⠀⠀⢻⡀⠙⠉⠉⠙⣾⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⣰⣦⠀⡇⠀⠀⠀⠈⠙⠒⠒⠋⠀⠀⠀⠀⠀⠀⢳⣄⣀⣠⠜⢷⡀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⡏⠈⠛⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢷⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠈⣇⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠦⣤⠴⠞⠁⠀⠀⠀⠀⠀⠀⢸⡄⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣦⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⡀⠀⠀⠀⠀⠀⠀⣀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠴⠚⠛⣧⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⠶⠛⣉⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⣲⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣸⡇⠀⠀⠙⠛⢦⡀⠀⠀⠀⠙⢦⡀⠀⠘⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠉⣉⣉⡇⠀⠀⠀⠀⠀⠀⠀⠀⣸⢁⣿⡟⢦⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⠟⠳⢦⣄⠀⠀⠀⠙⣦⠀⠀⠀⠀⠙⢶⣤⣿⠙⠦⣄⡀⠀⠀⠀⠀⠀⠀⢰⡆⠀⠀⡀⠀⠈⡇⠀⠀⠀⠀⠀⠀⣠⢾⣏⣾⡞⠀⠀⠙⢷⡀⠀⠀⠀⠀ ⠀⠀⢀⡴⠃⠀⠀⢀⣽⠂⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⠈⠻⢤⡀⠀⠙⠳⢦⣄⡀⠀⠀⠀⠛⠶⠚⠙⠳⠚⠁⠀⠀⢀⣠⠴⠊⠁⢾⡿⠋⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀ ⠀⣰⠟⠁⠀⣠⡴⢻⡏⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠉⠳⢤⣀⠀⠈⠉⠛⠲⠦⣤⣤⣀⣀⠀⠀⠀⢠⠖⠋⠁⠀⢀⡴⠊⠁⠀⠀⠀⠀⠀⠈⠳⣤⡀⠀⠀ ⠀⠻⡶⠶⠛⠁⠀⡿⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢤⣄⣀⡀⠀⠀⠈⠉⢳⡀⠀⣏⣀⣠⠴⠚⠉⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠹⣿⣦⡀ ⢀⡼⠁⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠓⠒⠒⠶⢷⣼⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠹⣍⡷ ⣾⠃⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⢿⠄

⠀⠀⠀⠀⠀⣠⣤⣶⣶⣿⣿⣿⣿⣶⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⡻⠿⠿⠿⠿⠿⠛⠛⠿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢰⣿⣿⣿⣿⡏⠀⠈⠛⠛⢿⣓⡀⠀⠀⠀⠀⠰⠶⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣇⠀⠀⠀⣴⠿⠋⠁⠀⠀⠀⠀⠀⠀⣀⣉⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⡄⠀⠀⠀⣠⠴⠒⠲⢄⠀⠀⢠⡎⠁⠀⠀⠙⡄⠀⠀⠀⠀⠀⠀ ⠘⣿⣿⣿⣿⣿⣿⡀⠀⢰⠃⠀⣠⠀⠀⢣⠀⠘⣇⠀⠘⠂⠀⡇⠀⠀⠀⠀⠀⠀ ⠀⢹⣿⣿⣿⣿⣿⣇⠀⠘⣆⠀⠀⠀⢠⠏⠀⠀⠈⠢⣤⡤⠚⠑⢄⠀⠀⠀⠀⠀ ⠀⠀⢻⣿⣿⠟⡛⠏⠀⠀⠈⠙⠒⠚⠁⠀⡀⠀⠀⠀⠈⠳⡄⠀⠈⢦⠀⠀⠀⠀ ⠀⠀⠘⣿⣿⣦⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⡤⣄⡀⠀⢀⡟⠀⠀⠀⢇⠀⠀⠀ ⠀⠀⠀⢻⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣽⣿⣯⣀⠀⠀⠀⢸⡄⠀⠀ ⠀⠀⠀⠈⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠿⣿⣿⡇⠀⠀⠀⡇⠀⠀ ⠀⠀⠀⠀⠈⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣛⣋⣁⣀⣈⠆⠀⠀⠀⢸⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢖⣂⣈⣹⡀⠀⠀⠀⡸⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠋⠀⠀⢠⠇⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣼⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣶⣦⣀⠀ ⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣟⢶⡶⠤⠤⠤⠤⢤⠀⠀⠀⣠⣀⣠⣾⣿⣿⣿⣷ ⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠉⠲⣄⡀⠀⠈⠓⠒⠚⢁⡜⢿⣿⣿⣿⣿⣿ ⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠉⠓⠲⢤⣤⣴⡋⠀⢸⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⢀⣀⣀⣴⣾⣿⣿⣿⣷⣶⣶⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀ ⠀⠀⣸⣿⣿⣿⡿⠟⠛⠋⠉⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀ ⣀⣶⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀ ⢻⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀ ⠈⠻⣿⣿⠀⠄⠀⠶⠒⡄⠀⡀⠒⠒⠶⠶⢖⡂⠤⡀⠈⣿⣿⣿⣿⣿⣿⣿⡶⠂ ⠀⠀⡄⢉⡖⠉⠀⠈⢢⡧⠤⡇⢠⠊⠉⠉⠑⡄⠀⡇⠀⢿⣿⣿⣿⣿⣿⣿⣷⡆ ⠀⠀⠀⡠⢫⠀⠀⠀⡸⠁⠀⣇⢸⠁⠀⠉⠁⡗⠂⣇⣠⡟⢉⠛⣿⣿⣿⣿⠟⠁ ⠀⠀⠘⡇⠠⠭⠤⠼⢅⣀⡠⠤⠵⢑⣒⣐⣊⣀⢠⠋⠉⢠⠓⢢⣿⡟⠋⠁⠀⠀ ⠀⠀⠀⠸⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣶⣿⠟⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⡇⠀⠈⢢⡭⠯⠭⠵⠶⣤⡀⠀⠀⠀⠀⠀⡰⣿⣿⣿⣄⠀⠀⠀⠀⠀ ⠀⠀⢀⡤⠾⢄⠀⠀⠙⠒⠒⠒⠈⠁⠀⠀⠀⠀⢀⠜⠀⡹⠿⣛⠓⠂⠀⠀⠀⠀ ⠀⣠⠋⠀⠘⡀⠠⡀⠰⢄⣀⣀⠀⠀⣀⣀⡀⠔⠁⢀⠜⠁⠀⠀⠉⠲⢄⠀⠀⠀ ⠰⠃⠀⠀⠀⠐⠄⡠⠟⠒⢲⡄⠒⠉⠀⠀⢀⠠⠒⠁⠀⠀⠀⠀⠀⠀⠈⠳⡀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣶⣶⣶⣿⣿⣿⣿⣿⣷⣶⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠟⠛⠛⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠉⠁⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠛⢿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⣠⡶⠛⠉⠁⠀⠉⠙⠳⣄⠀⠀⠀⠀⢠⡞⠁⠀⠀⠈⢿⣿⣿⠿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣰⠏⠀⠀⠀⢀⣴⣶⣄⠀⠈⢳⡀⠀⢀⡿⠀⣴⠞⠳⢦⣼⣿⣿⣇⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣰⣤⣤⠶⠛⠁⣾⠏⢳⡄⠀⢷⡀⢸⡇⣼⠃⠀⠀⠻⠛⢹⣿⣿⣧⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠉⢻⡇⠀⠀⠀⠀⠀⠀⢿⡀⠸⣿⠙⠳⣿⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡇⠀⠸⣧⣤⣤⠶⠶⠶⠶⣿⠇⠀⡿⠀⠀⠈⠻⣟⠛⠉⠙⣻⠏⢻⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢻⡀⠀⠹⣧⡀⠀⠀⢀⣴⠟⠀⣸⠇⠀⠀⠀⠀⢹⣦⣴⠾⠋⠀⠈⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠳⣄⠀⠈⠙⠛⠛⠋⠁⠀⣰⠟⠀⠀⠀⠀⣠⣾⣧⣀⣀⣀⣤⠾⢻⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠙⠳⣤⣀⣀⣀⣀⣴⠞⠋⠀⠀⠀⠀⣰⠟⠀⠀⠉⠉⠉⠁⠀⠈⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠿⢛⣷⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣷⠛⠁⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⢀⣤⣾⣉⢻ ⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⢸⡇⠈⢳⣤⣴⣟⠭⢹⡆⡾ ⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠷⣦⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⠿⠃⠀⠀⠀⠀⠀⢀⣾⠇⠀⢸⡟⠉⢻⡄⢸⡟⠁ ⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡄⠀⠀⠀⠘⠻⠶⣶⣟⣠⣤⣴⣾⣿⠿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠸⠃⠀⢀⣧⡟⠀⠀ ⠀⠀⠀⠀⠀⠀⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⣰⠏⠉⣿⣿⣿⡿⠁⢀⣿⠙⣧⠀⠀⠀⠀⠀⢀⣠⠞⠁⢀⡶⠞⠀⠀⠀⣸⡟⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣶⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⢛⣷⣽⣷⣄⡀⠀⠀⢀⣀⣠⡿⠀⠀⠹⠿⠋⠀⠀⠾⠃⢀⣿⣷⣶⡶⠶⠛⠉⠀⠀⠀⠘⠁⠀⠀⠀⢠⡟⠀⠀⠀⠀ ⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿⠿⠏⠀⠴⠟⠁⠀⠉⠉⠛⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⢹⠿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡆⠁⠀⠀⠀⠀⠘⡀⠀⠀⢀⠀⠀⠀⡀⠀⠠⢇⣀⢂⠀⠀⠀⠀⠐⠀⣠⠂⠀⠀ ⡇⠀⠀⠀⠒⠛⢡⠃⠀⠀⠀⡄⠀⠀⠁⠀⠀⡇⠀⠀⠀⠀⠀⢣⡀⠀⠀⠀⠀⠁ ⢧⠀⠀⠀⢀⣀⡾⠀⠀⠀⠀⠀⠀⢀⢀⡀⠀⠇⠀⠀⡀⠀⠀⠀⣽⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠁⠀⣇⣀⠀⢃⣀⠴⠄⠈⠁⣇⠀⠤⠤⠤⠃⣀⣀⣀⠿⠀⠀⠔⠀⠀ ⠈⠃⠒⠒⠀⠀⠀⠀⠀⠈⠀⢠⠀⠀⠀⡄⠀⠀⠀⠀⡔⠁⠀⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡌⠀⠀⢀⠤⠤⡤⠀⠀⠀⠃⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢇⠀⠀⠑⠧⠀⠀⡀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠓⠤⣀⣀⣀⠤⠉⠓⠒⠂⠀⠀⠸⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠴⠒⠒⠦⣤⠤⠒⠇⠒⠠⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣴⣿⡿⠁⠀⢀⣰⣄⡀⠑⠢⣀⠀⠀⠀⠈⠓⢄⠀⠀⠀⠀⠀⠀ ⢀⡴⠛⠛⠛⢻⣿⣿⡇⠀⢰⣏⠀⠀⠉⠢⢀⠀⠙⠲⠤⢤⣀⣀⠱⠤⣀⠀⠀⠀ ⢸⠀⢋⢽⠀⠈⣿⣿⡇⠀⢹⠉⠒⠦⣄⡀⢀⡏⠀⠀⢲⠤⠤⠴⠒⢷⠀⡷⠀⠀ ⢻⠀⠈⢈⣦⠴⠛⠉⠀⠈⠉⠉⠉⠑⠢⢾⣋⣀⢀⣀⡿⣆⡀⠀⠀⠈⣗⡁⠀⠀ ⠸⢄⡔⠋⠀⠀⠀⣀⢠⡤⠤⠀⣀⠀⠀⠘⠀⠲⡄⠀⣳⠤⣌⣉⠒⣶⠋⠉⠳⡄ ⠀⢸⠔⠀⣠⠔⠉⠀⢠⠛⡄⠀⠀⠈⠓⢄⠀⠀⢸⠉⠁⠙⠋⠈⠉⠓⢎⠉⠀⢹ ⢰⠃⡠⢾⠉⡇⠀⠀⡸⠀⠹⡀⠀⠀⠀⡞⡇⠒⠒⢲⡒⠒⠒⢤⡀⠀⠀⢣⢀⡜ ⡏⠀⡇⡞⠀⢣⠀⢀⠇⠀⠀⢇⠀⢀⠜⠀⢱⠀⢠⠏⡇⠀⠀⡼⡏⢆⠀⣸⠏⠀ ⢣⠀⠑⢧⣀⡈⣧⣎⠀⠀⢀⣸⣴⣋⠀⠀⢸⡠⠋⠀⢀⢀⠜⠀⡇⠈⡆⢹⠀⠀ ⠈⠓⠦⣤⣤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠓⠂⠤⢼⡊⠀⠀⡇⣠⠇⠈⡇⠀ ⠀⠀⠀⠀⠘⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⠐⠤⣟⣁⠇⢰⠃⠀ ⠀⠀⠀⠀⠀⠈⠻⢦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⠶⠤⠤⠴⠋⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠓⠒⠲⠶⠤⣤⣤⠤⠶⠚⠁⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣤⣄⡀⠀⠀⠀⢀⣠⣾⣷⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣾⠟⠉⠉⠉⠉⠉⠉⠛⠿⣟⡛⠉⠁⠈⠉⠉⠉⠉⠉⠙⠛⠶⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⡟⠁⠀⠀⠀⠀⢀⣀⡀⠀⠀⠈⠛⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⢀⣀⣤⣽⡿⣦⣄⠀⠀⠀⠉⠻⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⣶⣿⠿⠿⠿⢶⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣴⡟⠉⠉⠀⠀⠀⠙⠳⣤⡀⠀⠀⠀⠉⠛⠿⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠙⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣠⡾⠋⠁⢀⣀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⠃⠀⠀⢰⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠙⠲⣤⣀⣀⠀⠀⠈⠉⠛⠛⠿⠶⠶⠦⠤⠴⠶⠿⠿⠷⢶⣦⡀⠀⠀⠀⠀⠀ ⢀⣿⠇⠀⠾⠟⠙⣷⠀⠀⠀⠸⣿⣿⣿⣿⣿⠀⠀⠀⢸⡟⠛⠻⢶⣤⣀⠀⠀⠀⠀⠀⠀⠈⣿⠉⠁⠀⠀⠀⢠⣤⣀⠀⠀⢀⣀⣠⣤⣶⣶⣶⡄⠉⣿⡆⠀⠀⠀⠀ ⢸⡏⠀⠀⠀⣴⠟⢿⡇⠀⠀⠀⣿⣿⣿⣿⡟⠀⠀⠀⢘⣧⡀⠀⠀⠈⠙⠻⠷⣦⣤⣀⡀⣠⡿⠀⠀⠀⠀⠀⣠⡿⠟⠛⠿⠿⠛⠋⠁⠀⠹⣷⡀⠀⣿⡇⠀⠀⠀⠀ ⢸⣇⠀⠀⠀⠿⠀⢸⡇⠀⢀⣠⣿⣿⠿⠟⠃⠀⠐⠋⠉⠉⠙⠛⠛⠶⠶⣦⣄⣀⣉⣹⣿⠟⠁⠀⠀⠀⠀⢰⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⣶⠟⠀⠀⠀⠀⠀ ⢸⣿⠀⠀⠀⠀⠀⣸⣷⡾⠟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⢩⡶⢶⣦⣄⣀⣠⣤⣼⣿⠿⢿⣤⣄⣀⠀⠀⠀⠀⠀⠈⣿⣧⣀⣀⠀⠀⠀⠀ ⠸⣿⡄⠀⢀⣴⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⢠⣦⣍⠉⠉⠀⠈⢿⣦⣀⠀⠉⠙⠛⠳⢶⣦⣄⣼⣿⠋⠙⠛⢿⣦⠀⠀ ⠀⠙⠷⣶⡿⠁⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠶⢶⣿⡖⠲⠶⠶⠦⢤⣄⣀⡀⠀⠀⠀⠈⠉⠀⠀⠙⣷⡀⠀⢀⣬⣝⡛⠛⣷⣶⣤⣄⣀⣈⣽⡿⠁⢀⣀⣀⠀⠙⣷⡄ ⠀⠀⢀⣿⠃⣀⠀⠀⠀⠀⣀⣴⠞⠋⠁⠀⠀⢸⡟⣷⡀⠀⠀⠀⠀⠀⠉⠛⠷⣄⠀⠀⠀⠀⠀⠀⠘⣿⠷⠛⠉⠉⠙⢷⣾⠋⠉⠉⠛⠻⢿⣤⣴⠛⠿⠟⠁⠀⢸⣿ ⠀⠀⢸⣿⠟⠁⠀⠀⣠⣾⡏⠁⠀⠀⠀⠀⠀⣸⠇⠘⣷⡀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣦⡀⠀⠀⠀⠀⠿⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⣿ ⠀⣰⡿⠁⠀⢀⣴⣿⡟⢹⡇⠀⠀⠀⠀⠀⠀⣿⠀⠀⠸⣷⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠦⣤⣀⣀⣀⣤⣤⡤⠤⠤⠤⢤⣤⣀⡀⠀⠀⠀⠀⠀⠈⢿⡄⠀⠀⢰⡿ ⢰⣿⠁⠀⣠⡞⢡⣿⠀⠘⣷⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⢹⣇⠀⠀⠀⠀⠀⠀⢠⡟⠀⣿⡀⠈⠉⠉⠁⢠⣿⣇⠀⠀⠀⠀⠈⠉⣿⣦⡀⠀⠀⠀⠀⠘⣿⠀⣠⣿⠃ ⣾⡇⠀⢀⡿⠀⢸⡏⠀⠀⢿⡄⠀⠀⠀⢀⣿⠁⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⢠⡿⠁⠀⢸⡇⠀⠀⠀⠀⣾⠋⣿⠀⠀⠀⠀⠀⢠⣿⣯⠙⣄⠀⠀⠀⠀⢻⡿⠟⠁⠀ ⣿⡇⠀⠘⣇⠀⣾⡇⠀⠀⠘⣷⠀⠀⠀⣼⠏⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⣰⠟⠀⠀⠀⠸⣷⠀⠀⢀⣼⠇⠀⢻⡄⠀⠀⠀⢀⣾⠋⣿⠀⠘⣆⠀⠀⢠⣾⡇⠀⠀⠀ ⣿⡇⠀⠀⢻⣄⣿⡇⠀⠀⠀⢹⣧⠀⣰⡟⠀⠀⠀⠀⠀⠀⠀⣿⡀⣠⡾⠋⠀⠀⠀⠀⠀⣿⠀⢀⣾⠃⠀⠀⢸⡇⠀⠀⢀⡾⠁⠀⢿⠀⠀⢹⡆⠀⢸⣿⡇⠀⠀⠀ ⠸⣿⡀⠀⠀⠉⠛⠷⣤⣄⣀⣀⣹⣿⣿⣄⣀⣀⣀⣀⣀⣀⣠⣸⣿⣏⣀⣀⣀⣀⣀⠀⠀⣿⣶⠟⠁⠀⠀⠀⢸⡇⠀⣠⡟⠁⠀⠀⢸⡇⠀⠀⣿⠀⠈⣿⡇⠀⠀⠀ ⠀⠙⢿⣦⣄⡀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠛⠛⠿⠿⣦⣤⣀⠀⠀⢸⣿⣼⠋⠀⠀⠀⠀⢸⡇⠀⠀⣽⡇⠀⢸⣧⠀⠀⠀ ⠀⠀⠀⠉⠛⠿⢿⣷⣶⣶⠶⠖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠿⣿⣁⠀⠀⠀⠀⠀⣼⡇⣠⡾⢻⡇⠀⢸⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⣤⣀⢀⣿⡾⠋⠀⣼⠇⠀⢸⡿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣤⣀⠀⠉⠻⢿⣤⣀⣼⠏⠀⢀⣾⠇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠳⣦⣄⣀⠀⠀⠀⢀⣰⣿⠏⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣷⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠛⠛⠛⠿⠿⠿⠛⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠻⠿⠶⣶⣶⣶⣦⣤⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣶⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠿⠿⢿⣷⣾⡿⠿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⠖⠋⠉⠒⠒⠦⠴⠒⠛⠓⠲⢤⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣴⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⣴⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀ ⠀⠀⣼⣿⣿⣿⠋⠀⠀⠀⠀⠀⢀⣀⠀⠀⢠⠟⠣⣄⠀⠀⠰⡄⠀⠘⣧⠀⠀⠀ ⠀⣰⣿⣿⣿⡇⠀⠀⣴⡆⠀⠀⣼⣿⣆⡴⠋⠀⠀⠈⠓⠦⣠⠗⢄⠀⠘⣇⠀⠀ ⠀⣿⣿⣿⣿⡇⠀⣼⣿⡇⢀⡾⢹⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⢹⡀⠀ ⢸⣿⣿⣿⣿⣧⣾⣿⣿⡷⠋⢀⣀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠂⡇⠀⡇⠀ ⣼⣿⣿⣿⣿⣿⣿⡟⠉⠀⠀⢀⡠⠤⠤⣄⠀⠀⠀⠀⠀⢀⡤⠒⠒⠢⣼⢀⡇⠀ ⣿⣿⣿⣿⣿⣿⢿⡇⠀⠀⡰⠁⠀⠀⠀⠀⠱⡄⠀⠀⠀⡞⠂⠀⠐⠒⠚⡏⠀⠀ ⣿⣿⣿⣿⣿⡇⣸⠇⠀⠀⡇⠀⠀⠴⠀⠀⠀⡁⠀⠀⠀⢇⠀⠈⠁⠀⠀⡼⢄⠀ ⣿⣿⡿⠟⠛⢿⠟⠀⠀⠀⠘⢄⠀⠀⠀⠀⡰⠃⠀⠀⠱⣌⠢⠤⠠⠤⠊⠱⣸⠀ ⢸⣿⡇⠀⠂⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⡩⠀⠀⠀⠀⠀⠈⠓⢥⡒⠂⠀⠀⢹⡀ ⠘⣿⣿⢦⣧⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⣧ ⠀⢻⣿⣌⠛⣀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣀⣀⣀⡀⠀⠀⠀⠀⡟⠀⠀⠀⢹ ⠀⠈⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠿⠻⣿⣿⣿⣶⣶⡿⢣⡀⠀⠀⡘ ⠀⠀⠸⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⣼⣧⣴⣶⣾⠿⠋⠉⠛⠿⣿⣷⠇⠀⢀⡇ ⠀⠀⠀⠘⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠒⠢⡀⠀⡀⡼⠀ ⠀⠀⠀⠀⠈⠉⠙⠻⣷⣄⠀⡀⠀⠀⠀⠀⠀⡠⠖⠒⠒⠲⢦⡤⠴⠁⢀⡼⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠣⡀⠀⠀⠀⠀⠘⠥⠤⠄⠒⠒⠚⠓⡆⢠⠞⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀⠀⠀⠀⡀⠀⠀⠀⣠⠚⡕⠉⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⣧⠀⠀⠀⠀⠓⠀⠀⠀⠁⡼⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣧⠀⠉⠲⠤⣀⠀⠀⠀⠀⠀⣸⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣷⣤⡀⠀⠀⢉⡶⠤⣀⡾⠖⠿⢤⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣴⠿⠟⠋⠀⠀⠀⠀⠙⠻⢶⡤⠋⠀⠀⠈⢣⠀⠀⠀⠉⠓⠦⣄⠀

⠀⠀⠀⠀⠀⠀⠀⣠⡤⠶⠒⠛⠛⠉⠉⠛⠒⠒⠲⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⣶⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢄⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⣾⠟⠁⣠⠆⠀⠀⣀⠴⢶⠆⠀⣀⣀⣀⠤⡶⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀ ⠀⢰⣿⣿⢀⠞⡟⠀⡠⠊⠁⢠⣇⠔⠋⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢣⡀⠀⠀ ⠀⢸⠏⠘⠋⠀⣇⠞⠁⠀⠀⠘⠡⠤⠤⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀ ⠀⣼⣘⣉⣉⠀⠉⠀⠀⠀⠀⢀⡠⠤⠤⣄⡀⠀⠀⠙⣄⠀⠀⠀⠀⠀⠀⢸⡀⠀ ⢠⠋⠁⠀⠀⠉⢢⡄⠀⠀⡴⠁⠀⠀⠀⠀⠙⡆⠀⠀⠘⡆⠀⠀⠀⠀⠀⠘⡇⠀ ⢻⡀⠀⠀⠀⠀⡿⠀⠀⠀⢷⡀⠀⠀⠀⠀⢸⠇⠀⠀⠀⢹⢀⠤⠤⡀⠀⠀⡇⠀ ⠀⡟⠒⠤⠤⣾⠃⠀⠀⠀⠀⢙⡒⠒⠒⠒⠁⠀⠀⠀⠀⠘⠋⠠⠂⡿⠀⠀⡇⠀ ⢀⡇⠀⠙⢉⡇⠀⠀⠀⠀⠀⠀⠈⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⢰⠚⠁⠀⢸⠁⠀ ⣸⠀⠀⠀⠸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⡜⠀⠀ ⡟⠀⠀⠀⠀⠈⠑⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣸⠇⠀⠀ ⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⢠⡏⠀⠀⠀ ⢸⡀⠀⠀⠀⣆⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢇⡀⣿⠀⠀⠀⠀ ⠈⢧⠀⠀⠀⠀⠈⣉⣽⣿⣿⡿⠓⢦⠀⠀⠀⠀⠀⠀⠀⢀⣿⠾⢿⠃⠀⠀⠀⠀ ⠀⠈⢆⠀⠀⠀⠘⠤⠄⠀⠀⠉⠁⠈⠀⠀⠀⠀⠀⠀⠀⣸⣃⣀⣀⣀⣀⣀⣀⡀ ⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣿⠋⠁⠀⠀⠉⠙⠻ ⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣇⠹⣧⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣧⡀⠀⠀⢀⠀⠀⠀⠀⠀⢀⡠⠊⠁⠀⢀⡴⣿⠀⢻⣧⠀⠀⠀⠀⠀ ⠀⠀⠀⣾⣿⠿⣿⠒⢻⢿⡒⠒⠒⠚⠉⠀⠀⣀⠔⠉⠀⣿⠀⠀⣿⡆⠀⠀⠀⠀ ⠀⠀⢰⣿⠇⠀⡿⠀⠘⡆⠈⠙⢲⣶⣶⠈⠉⠀⠀⠀⣰⡇⠀⠀⡸⠃⠀⠀⠀⠀

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⠀⠀⠀⢀⠠⠒⢀⣬⠏⠉⠁⢲⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⠊⠀⠀⠀⠘⠉⠀⠀⠀⢸⡏⠀⠈⠒⠒⠒⠀⠄⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀ ⢠⠁⠀⠀⠀⠘⡈⠀⠀⠀⢀⢀⠔⠈⢀⡀⠤⠒⣒⣒⡄⠀⠀⠟⠉⠉⠐⣄⡀⠀ ⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁⡠⠊⠁⠀⠀⠀⠠⠠⡅⠀⠀⠀⠀⠀⠠⡾⣿⡆ ⡇⠀⠀⠀⠀⠈⠢⡀⠀⢀⠁⠀⠀⠀⠀⣠⣦⣴⠾⠋⡁⠀⢀⣴⣶⢠⢹⢗⣿⣿ ⢃⠀⠻⠂⠀⠀⠀⠈⠄⠸⠀⣸⠇⣀⣠⣿⣟⣀⠀⡇⠀⠀⠘⣿⡏⡄⢩⣏⢸⣿ ⠈⢷⣿⠀⠀⠀⢀⣀⠘⡄⠙⢿⣷⣿⡿⠋⢈⡟⠀⢘⠀⡠⢄⠏⠣⠢⢼⣿⣿⠏ ⣀⣼⣿⣇⣀⠀⠈⢿⠀⡁⠀⠀⢀⣀⣠⡶⠀⠃⠀⣀⣉⡀⠀⠀⣀⣀⣼⡿⠁⠀ ⣿⣿⣿⣿⣿⣧⣴⣆⣠⡇⣰⣦⣾⣿⣿⣧⡴⠿⠛⠋⠀⠀⣀⡀⣲⣂⢸⡇⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣶⣆⣠⣷⣾⣯⣭⣻⣿⣿⠃⠀⠀ ⠀⠀⠉⠉⠉⠉⠁⠉⠛⠛⠉⠀⠀⠀⠀⠈⠛⠿⠿⠿⠿⣿⣿⠿⠿⠛⠁⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠖⠒⠋⠉⠙⡗⠲⡦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⠔⠛⢤⠜⠀⢰⠒⡄⠀⠙⠋⠁⠀⠑⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠘⠒⠃⢀⣀⣀⣀⣠⣯⣹⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⠃⡏⣱⠀⠀⣀⡤⠖⠚⠉⠉⠀⠀⠀⠀⣠⣶⡷⣄⠀⠀⠀⠀⠀ ⣠⢴⠒⠤⢄⡹⠀⠈⣡⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⠉⡠⣌⣦⡄⠀⠀⠀ ⠣⡼⠀⠀⡞⣇⡤⠾⡅⠀⠀⠀⠀⠀⣀⠀⠀⠀⣰⡿⠁⡜⠋⠀⠀⢀⣣⠀⠀⠀ ⠀⠈⡲⠖⠛⣼⠀⠀⢹⠀⢠⡜⠋⠉⠙⠙⢦⣼⠟⠀⢸⡵⠚⠉⢉⡉⢻⡀⠀⠀ ⠀⡼⢁⡀⢠⣿⡆⠀⢸⣰⣿⣾⣿⣿⣿⣿⣿⣿⠀⠀⠻⡏⠉⠉⣉⠉⠉⡇⠀⠀ ⠀⠳⣉⡹⣏⠠⢹⡀⢸⠉⢿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠘⣦⠀⠀⢀⣴⠃⠀⠀ ⠀⠉⠉⠀⣸⣶⠺⡇⡾⡆⠀⠙⠿⣿⣿⠿⣋⠀⠀⠀⠀⠀⠘⡗⠚⢉⣼⠀⠀⠀ ⠀⠀⠀⢰⠃⢻⡀⢷⢧⠀⠀⠀⠀⠐⠒⠊⠁⠀⠀⠀⠀⠀⠀⢻⡿⠍⢸⡇⠀⠀ ⠀⠀⠀⡞⠀⢸⡇⠈⠺⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣸⠃⠀⠀ ⠀⠀⢰⠇⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠉⠀⠀⠀⠀⣸⠀⢠⠃⠀⠀⠀ ⠀⠀⢸⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⢀⠞⠀⠉⠒⢦⡀⠀⢀⠏⢀⡏⠀⠀⠀⠀ ⠀⠀⠸⡖⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⡞⠀⠐⠄⠘⠀⠈⣻⠁⠀⢸⠀⠀⠀⠀⠀ ⠀⠀⠀⢱⣴⡄⠀⠀⠈⢧⠀⠀⠀⢠⡇⢀⣤⣼⣶⣷⣺⠁⠀⠀⢸⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠁⠙⠾⠢⡶⣼⣧⠀⠀⠀⣷⣿⣿⣿⣿⣿⠀⢠⢤⠀⠈⠧⣄⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⠀⡀⠀⣿⠛⠻⣿⡿⣽⠓⠺⠍⠓⠀⠀⡠⠙⣆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢸⠀⢡⠀⠈⠓⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠁ ⠀⠀⠀⠀⠀⠀⠀⣰⠛⠃⠀⢣⠀⠱⣈⠀⠀⠀⠀⢠⠀⠀⠀⠈⢢⠀⢀⡜⠁⠀ ⠀⠀⠀⠀⠀⠀⣠⣿⡀⠀⠀⠀⠱⣄⠉⠣⣄⠀⠈⠀⠀⠀⠀⢀⡸⢻⣥⣤⣀⠀ ⠀⠀⠀⠀⢀⣼⣿⣿⣿⣦⡀⠀⠀⠈⠑⠤⣤⢭⡖⠒⠒⣶⣾⣋⣀⣼⣿⣿⣿⣦ ⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⣠⢾⠀⣗⠢⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⢠⣾⣯⣍⡒⠒⠒⠒⣒⣒⠒⠤⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡈⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠑⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣈⣦⡀⠀⠀⠀⠀⠀ ⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⣭⣵⣶⣶⣶⣶⣶⣶⣶⣤⣽⡄⠀⠀⠀⠀ ⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠛⠛⠋⠉⠉⠉⣉⣽⣿⣿⣏⡀⠀⠀⠀ ⣰⣿⣿⣿⣿⣿⣿⣿⣿⠁⣠⣴⣿⡿⢿⣿⣶⣄⣀⣠⣾⣿⣋⣉⣙⣻⣿⣄⠄⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⠿⠓⠒⠒⠺⠿⣿⡿⠿⣿⠁⠀⠀⠀⠉⢹⣿⠉⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣿⡟⠀⠈⢣⠀⠀⠀⢀⣾⣿⡄⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⡏⢿⣷⣄⣀⣀⣠⣾⡿⠃⠀⠀⠀⠳⣶⣾⡿⣿⣿⣝⡄ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠙⠻⠿⠿⠟⠋⠀⠀⠀⠀⠀⠀⣸⠂⠀⢸⣿⣿⣷ ⣾⣿⣿⣿⣿⣿⣿⣿⢇⣇⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⠒⠚⠉⠀⠀⠀⢸⣿⣿⡿ ⣿⣿⣿⣿⣿⣿⣿⣿⣆⢸⡀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⠀⠀⠀⠀⣼⣿⣿⠃ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣷⡷⣄⠀⠀⠀⠲⣾⣿⣻⠛⣿⣹⠄⠀⣠⣾⣿⣿⠏⠀ ⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣦⣤⡀⠈⠛⠿⠟⢁⣠⣴⣿⣿⡿⠟⠁⠀⠀ ⠀⠀⠈⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠘⣿⣿⣏⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣷⣤⣀⣀⢠⠜⢱⣿⣿⣷⣤⡀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠶⠶⠖⠚⠓⠓⠒⠶⠶⢤⣄⣀⣀⡤⠶⠚⠛⠛⠛⠷⢶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠀⡤⠀⠀⠀⠀⠀⣠⡶⠛⠛⠳⣶⣄⠀⣠⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡴⠟⢁⣤⡞⠀⠀⠀⠀⢠⡾⠋⠀⠀⠀⠀⠀⠹⡟⠉⠀⠀⠀⠉⠻⣦⠀⠀⢺⡄⠀⢰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⢦⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢩⡟⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⢸⡻⣦⠀⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠛⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣼⣇⠈⠳⣮⣻⣝⠲⠶⠤⠤⠴⠖⠚⢿⣅⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⢻⣧⣀⠀⢀⣤⡾⠋⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡄⠀⠀⠉⠛⣷⠀⠀⠀⠀⠀⠀⠀⠹⢷⣄⡀⢀⣠⣾⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⣷⡉⠉⠉⠁⠀⠀⠀⠀⠀⠀⢀⣿⢠⠖⠒⠒⠒⠒⠒⠒⠒⠒⠲⣄⠀⠀⠀⠀⠀⡴⠒⠒⣒⠒⠛⠒⠒⠒⠒⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⢩⡟⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⡿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⢸⠀⠀⠀⣠⡶⠛⠉⠉⠛⢦⣿⠀⠀⠀⠀⠀⣧⡶⠛⠉⠉⠛⢦⡄⠀⠀⠸⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⢁⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠸⣷⡹⣷⡀⠀⠀⠀⠀⠀⣠⣾⠿⢶⣼⣀⠀⣰⠏⠀⠀⠀⠀⠀⠈⣿⣠⠴⠶⢤⣄⣟⠀⠀⠀⠀⠀⠀⢻⣄⠀⣠⣧⡿⠷⣦⡀⠀⠀⠀⠀⠀⢠⡿⢣⡾⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠹⣿⣮⣷⣄⠀⠀⠀⣴⠏⠸⣄⠀⢹⠈⠙⢿⡖⠛⠻⣶⡖⠒⢙⡟⠀⠀⠀⠀⠈⢿⠉⠙⢿⣶⠒⠒⢺⡟⠉⢹⠇⠀⣸⠈⢹⡆⠀⠀⠀⣰⣿⡿⣿⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⣧⡙⠻⢷⣄⠀⣿⠀⢸⣹⠀⢸⡄⠀⠈⢷⣄⠀⠀⢀⣤⠎⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⣠⡟⠀⠀⣸⠀⢸⣯⠇⠀⡇⢀⣠⠾⠛⢩⡾⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢶⣤⣀⠙⢻⣦⣀⣙⣄⠀⠉⠉⠉⠉⠛⠛⠛⠻⣄⡀⠀⠀⠀⠀⠀⠀⠀⣀⣼⠟⠛⠛⠋⠉⠉⠉⠉⠀⣀⣇⣠⡾⠃⠀⣀⣴⡾⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⡿⠋⢸⡏⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⢀⡿⠉⠙⠷⣄⣀⣠⠞⠋⠉⣧⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⣹⡆⠙⣿⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠈⠛⠶⣾⠁⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠘⡷⠖⠋⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⡄⠀⠀⢿⡄⠀⠀⠀⠀⠀⡼⠋⠀⠀⣀⣤⠤⢤⣀⡤⠤⣄⡀⠀⠀⠹⣆⠀⠀⠀⠀⠀⢸⡇⠀⠀⡄⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⢷⠀⢠⡾⢷⠀⠀⠀⠀⣼⠁⢀⣴⡋⠥⠤⣀⣀⣀⣀⡀⠤⠬⣳⣦⡀⠸⣆⠀⠀⠀⢠⡟⣷⡀⢠⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠁⠘⣧⡞⠀⢼⣧⠀⠀⢠⠇⠚⠉⠳⠦⣄⣀⣀⣀⣀⣀⣀⣀⡠⠴⠚⠉⠣⢻⠀⠀⠀⣿⠀⠈⣧⡾⠁⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡷⠾⠛⣿⡀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⢰⡟⠷⣦⣬⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠟⠋⠁⠀⠀⢀⡾⠻⣦⣀⠀⠀⠀⠀⠀⠀⢤⡀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⣀⣴⢿⡀⠀⠀⠈⠙⠻⢶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠾⠛⠁⠀⠀⠀⠀⠀⠀⣼⠁⠀⠈⠙⠛⠛⠶⣶⣀⠀⠀⠙⠛⠒⠛⠁⠀⠀⣘⡷⠞⠛⠛⠉⠀⠀⢷⡀⠀⠀⠀⠀⠀⠈⠛⠿⣦⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣤⣿⡋⠀⠀⠀⠀⠀⢀⡔⠀⠀⢀⡇⢀⣀⣤⠤⠴⠶⠶⠤⣽⣻⡶⢤⣤⣤⣤⡤⣶⣛⣭⠶⠦⠤⠤⣤⣀⡀⠈⡇⠀⠀⠠⣄⠀⠀⠀⠀⠈⠙⣿⣦⡀⠀⠀⠀⠀ ⠀⠀⠀⣠⣶⠟⠁⠀⠙⢦⡀⠀⢀⡴⠋⠀⠀⠀⠘⡷⠛⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⠦⣼⢻⢧⠞⠉⠀⠀⠀⠀⠀⠀⠀⠈⠛⢶⡇⠀⠀⠀⠘⢦⡀⠀⠀⣠⠞⠁⠈⠻⣷⣄⠀⠀ ⠀⣠⣾⣫⡅⠀⠀⠀⠀⠀⠙⣤⡞⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠻⣤⠞⠁⠀⠀⠀⠀⠈⢛⣷⣄ ⣾⠋⠀⠉⠻⣦⡀⠀⠀⢀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⡀⠀⠀⠀⣠⡾⠋⠉⠙ ⠀⠀⠀⠀⠀⠈⠻⣆⢀⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡄⣠⡾⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢘⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⡠⢤⠤⠤⠤⠤⡤⢠⡼⢿⡏⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣼⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠑⠚⠒⠢⠴⠤⠔⠒⠰⢦⣷⠴⠤⢀⠀⢀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡲⠖⠲⢌⡭⠭⣅⠒⢤⠤⢤⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣏⣏⣙⣛⡟⠒⠶⢺⡇⠀⠀⠀⠱⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⡴⠊⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠔⠊⠀⡄⠀⠀⠀⡇⠀⠀⠀ ⠀⠀⠀⢀⣾⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⢀⡇⠀⠀⠀ ⠀⠀⢀⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⡇⠀⠀⠀⠀ ⠀⠀⠸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀ ⠀⠀⠀⠻⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⢏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⠒⠒⠢⠤⠤⢤⠤⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀⣀⣷⠀⠀⠀⠀ ⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣶⣶⣤⣤⣤⣤⣤⣤⣶⣿⣿⠿⢆⠀⠀⠀ ⠀⢫⣉⣛⣻⣷⣶⣤⠀⠀⢀⠴⠋⠉⢻⠿⠿⠿⠿⠿⠿⠟⠛⠉⠀⠀⠈⡆⠀⠀ ⠀⢴⢻⡿⠷⢾⣋⣀⠤⠚⠁⡆⠀⠠⣿⣿⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢸⠀⠀ ⢀⣸⠛⠤⡤⠀⠀⠀⠀⠀⣸⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠘⡀⠀ ⠣⣀⣹⣏⣉⣁⠀⣀⣀⣀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡇⠀ ⠛⠭⣅⣙⣅⠈⠉⠉⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠘⡅⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⠀⠀⠀⣇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⣘⠦⠬⢶⠋⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣁⣉⡢ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣔⠁⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠸⣟⢠⠃⠀⠀⠀⣜⠄⢀⡄⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠒⠒⠻⠦⣸⣀⣀⣀⣀⠤⠤⠔⠃⠀⠀⠀⠀

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⣠⣤⣶⣶⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡄⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀ ⣿⣿⣿⣿⠿⠟⠃⣾⣿⣶⣄⣾⣿⣄⣸⣿⣷⣁⣤⣁⣶⣶⡆⢰⣿⣿⣤⣾⣿⠇ ⣿⣿⣿⣧⣤⡄⢠⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⡇⠀⠻⣿⣿⡿⠃⠀ ⢹⣿⣿⣿⠛⠃⢸⣿⡿⣿⣿⣾⣿⡟⠟⣿⣿⢸⣿⣿⢿⣿⣷⣶⠀⣿⣿⡇⠀⠀ ⠸⣿⣿⣿⠀⠀⠸⠿⠇⠸⠛⠉⠛⠁⠀⠘⠛⠈⠉⠉⠾⠿⠿⠛⠀⠛⠛⠋⠀⠀ ⠀⠉⠉⠉⠀⠀⣠⣴⣶⣶⣶⣤⣤⡆⠀⣤⣤⣴⣶⣄⢠⣶⣦⠄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣼⣿⣿⠟⠛⠛⢻⣿⣷⣀⣿⣿⡿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢻⣿⣿⣀⣛⣿⡿⣿⣿⣿⣿⡿⠁⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠻⠿⣿⣿⡿⠇⠈⠉⠛⠉⠀⠀⠘⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⢀⣀⠠⠐⠒⠂⠀⠉⠐⠀⠒⠢⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡤⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠀⠀⠀⠀⠀⠀ ⡴⠒⢧⣄⠀⠀⠀⠀⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈⢄⠀⠀⠀⠀ ⠐⠤⠀⠙⢿⣦⣐⣀⣴⣀⣀⣂⣀⠀⠀⠀⠀⠀⠀⡠⠐⠋⠄⠀⠀⠀⠄⠀⠀⠀ ⠀⠀⢣⠀⠀⠙⣿⣿⣿⣿⣿⡿⠛⢻⣶⣶⣶⣦⣴⣴⣾⣤⣤⣥⣀⠀⣾⢴⠀⠀ ⠀⠀⠀⠑⠀⠀⣻⣿⣿⣿⣯⣤⣴⣿⠁⠀⠃⠙⣿⣿⣿⣿⣿⠟⢙⣿⠏⠁⠀⠀ ⠀⠀⠀⠀⠀⠘⠀⢼⣿⣿⣿⠿⠛⠁⠈⠐⠂⠀⠹⣿⣿⣿⣷⣶⣿⠏⠀⢄⡀⠀ ⠀⠀⠀⠀⠀⣴⢀⢀⣗⣠⣀⣀⠀⠀⠀⠀⠀⠀⠀⢈⠙⠿⠿⠟⢫⣾⣿⣿⣧⢵ ⠀⠀⠀⠀⠀⢸⣷⣿⣿⣿⣿⣿⣿⣇⡔⠂⠂⢼⣿⣿⣦⣠⡤⢂⡹⠿⠛⠋⠉⠚ ⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⡇⠀⠐⡆⢸⣿⣿⣿⣿⣷⣼⣂⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⠀⠠⠇⢸⣿⣿⠙⠉⣏⡻⣏⣁⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣧⣤⠤⠤⣼⣿⣿⠀⠀⠁⠙⠛⠙⠁⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣶⣾⣶⣿⣶⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣾⣿⠿⠟⠿⠛⠛⠛⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⢿⣿⣿⣿⣿⣿⣄⠀⠀⠀ ⠀⠀⠀⠀⠘⣿⠃⠤⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡄⠀⠀ ⠀⠀⠀⠀⠀⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⡄⠀⠀ ⠀⠀⠀⠀⢀⠤⠀⠄⠀⠀⠀⠀⢀⣀⢄⣀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⠇⠀⠀ ⠀⠀⠀⠀⠛⢒⠒⠒⡂⠀⠀⢰⠧⠤⠤⠤⢷⠀⠀⠀⠸⠿⠿⣿⣿⣿⡿⠀⠀⠀ ⠀⠀⠀⠀⡧⣀⡔⠉⠀⠀⠀⠸⡀⠘⠀⠀⡸⠀⠀⠀⠀⠀⠂⣸⣿⣿⡇⠀⠀⠀ ⠀⠀⢀⠎⠐⢸⠀⠀⠀⠀⠀⠀⠈⠒⠒⠊⠀⠀⠀⠀⠀⠀⠘⠿⣿⡿⠀⠀⠀⠀ ⠀⠀⡎⠀⢀⣼⣦⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀ ⠀⠀⠁⠀⣾⣿⣿⠿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀ ⠀⠀⡀⠀⠈⢁⠀⠀⠀⠉⠙⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀ ⠀⠀⣇⠀⠀⠈⠒⢲⣶⣶⡾⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⢆⠀⠀⡤⠼⠿⠿⠥⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⢸⠀⠀⠀⠀⠀⠀ ⠠⠤⠀⣰⡷⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠟⠛⠶⠦⣤⣀⡀ ⠀⠀⠀⡏⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠉⠙ ⠀⠀⠀⢳⡀⠈⠉⠉⠒⠒⠊⠀⠀⠀⠀⠀⠀⠀⠀⡠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⡦⠠⠂⠒⠒⠂⢤⡆⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠠⢄⡊⡁⠀⠀⠀⡄⠀⠀⠀⠈⢆⠀⠀ ⣀⣎⠐⢄⠀⠀⠀⠀⠀⠀⠀⣇⡀⠠⠐⠀⠂⣀⡀⠀⢣⡈⠒⠁⠀⠀⠀⢸⠀⠀ ⠤⣈⢱⠐⣢⠀⠀⠀⠀⠀⠀⠂⡀⠐⡀⢀⠔⠒⠢⡀⠉⠀⠀⠀⠠⠀⢀⣘⠀⠀ ⢭⣙⠛⢡⠀⡆⠀⠀⠀⠀⠘⣄⣀⠤⠃⠀⠀⠃⠀⠰⠀⡀⠊⠀⠀⠀⠀⣠⠀⠀ ⠀⠀⢧⡀⠀⢠⠀⠀⠀⠀⠀⡏⠀⠀⣀⢌⠢⡤⠐⠁⠀⠐⣉⢇⡀⠤⠚⠁⠀⠀ ⠀⠀⠀⠙⠶⡀⠑⡤⡀⠀⢸⠀⠀⢰⠀⠀⠢⢀⣀⣀⠀⠀⢣⣉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⠓⣤⠃⠈⠢⡘⠤⠤⠚⠀⢢⣖⣺⢿⠋⠀⠄⠘⡈⠓⠄⠀⠀⠀⠀ ⠀⠀⠀⠀⢋⠈⠁⠀⠀⡠⠊⠉⠱⠾⠷⢾⠟⠛⠁⠀⡸⠀⠀⡇⠀⠀⠀⠢⣀⠀ ⠀⠀⠀⠀⠀⠓⢄⠀⠀⡇⠀⡀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⡠⠁⠀⠀⠀⠀⠀⠑ ⠀⠀⠀⠀⠀⠀⠀⠀⣄⠈⠒⠣⢀⠀⠀⠀⣀⠤⠎⠉⠉⠁⢀⠀⠀⠀⢄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠀⠀⠀⠉⠉⠁⠀⠀⡇⠀⠀⠀⢸⠀⠀⠀⠀⠑⢄⡀

⠀⠀⠀⢀⣠⣴⠶⠛⣛⣿⣷⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⡿⣉⣤⣶⣿⣿⣿⣿⣿⣿⡿⠖⣒⣶⣀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣿⣰⣿⣿⣿⣿⣿⣿⣿⣿⡟⣠⠞⠉⠀⠀⠛⠙⠓⢤⣤⣀⠀⠀⠀⠀⠀⠀ ⠀⢀⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣾⠋⠀⠀⠀⠀⠀⠀⠀⠈⠀⠙⢦⣀⠀⠀⠀⠀ ⢀⡿⢻⣿⣿⣭⣥⣴⣾⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⢀⡴⠆⠀⠀⠈⢧⡀⠀⠀ ⠈⠻⣮⣭⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⡀⣠⡾⠿⠶⢾⣠⡄⠀⠉⢹⣆⡀ ⣠⠼⠀⠈⡝⠀⠀⠀⠘⠄⠀⠀⠀⠀⠀⠀⠀⣽⠃⠀⢀⣀⣀⣘⡖⠀⠀⠀⠴⣹ ⢯⡂⠀⠀⡏⠉⠙⠉⠉⠹⠀⠀⡠⠀⠀⠀⠀⢾⡉⠉⠉⠁⠀⠀⣯⡁⠀⢀⠖⠁ ⠀⠙⣄⠀⠑⢄⣀⣀⡠⠂⠀⠀⠓⠀⠀⡀⠀⠋⠷⣤⣀⣀⡠⠞⠂⠀⣠⠊⠀⠀ ⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠈⠙⠋⠉⠀⠀⠀⠀⠋⠘⠀⠁⠀⣠⠞⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠑⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⡟⢲⠶⡦⠤⠤⠶⡖⢲⠛⠉⠉⢣⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⢹⢸⣤⣇⠀⠀⢀⣷⣾⠐⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡏⢸⠚⠛⠋⠉⠉⠉⠛⠛⠳⢇⣀⣀⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠏⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣍⣁⡁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⢺⠉⠑⠢⢄⣀⡠⠔⠒⠒⠒⢺⡏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⡀⠀⠀⣇⠀⠀⠀⠀⣀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣹⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠿⠿⠿⢿⣿⣿⣿⡿⠿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⣠⣴⣶⣶⣿⣿⣿⣷⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⣿⣿⣿⣿⣿⣿⠿⠿⠟⠛⠛⠛⠛⠛⢻⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣼⣿⣿⣿⣿⣿⡏⡔⠊⠉⡉⠢⡀⠀⡔⢁⡈⢿⣟⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⢤⡔⠊⠟⢢⠱⣠⣷⠁⠘⠛⣿⣾⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⢷⠀⡤⠤⠶⢺⠀⡇⠈⢲⠒⣲⠻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⣼⣿⣿⣿⣿⣿⣿⡈⢆⠈⠒⠒⢁⡜⠀⠀⡰⢍⣁⠤⢿⣿⡀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⡇⠀⠉⠒⠒⠉⠀⢀⣸⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀ ⢻⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⢠⣿⠟⠀⠀⠀⢀⣾⣿⠇⠀⠀⣀⠀⢀⣠⣲ ⠘⢿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⣿⡿⡀⠀⢀⣠⣾⡿⠋⠀⠀⢸⠀⢱⠻⣀⠎ ⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⠟⠂⠀⠈⡹⢳⣾⡟⢹⢿⠀⠀⠀⡠⠂⡤⠀⢠⠏⠀ ⠀⠀⢠⣿⣿⣿⣿⠏⡩⠛⠳⠤⠤⠖⠃⠈⠉⠀⠁⢼⡷⠊⠁⠀⠀⠀⢀⠎⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠂⠉⠉⠉⠉⠑⠒⠠⢄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⠊⢁⣀⣀⡀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀ ⠀⠀⠀⠀⠀⠀⢸⣾⡟⠁⠉⠐⢄⠀⠀⠀⠉⠉⠒⠢⢄⣀⠀⠀⠀⠀⠀⠀⢱⠀ ⠀⠀⠀⠀⠀⣰⣿⣏⣄⣒⡒⠢⡀⢣⠀⠀⢀⠔⠊⠉⠙⠲⢝⠢⣄⠀⠀⠀⠈⠀ ⠀⠀⠀⠀⣴⣿⠏⡏⠀⠀⠈⠱⠇⢸⣀⡠⠁⣠⣒⠒⠢⡀⠈⢂⣿⣷⣦⡀⠀⡇ ⠀⠀⢠⢮⣿⠇⠀⢯⠉⠉⠓⣢⠟⠁⠀⠇⢰⠁⠀⠈⠙⢾⡄⢸⣿⣿⣿⣿⣦⢱ ⠀⢠⣻⣿⠃⠘⢄⠀⠑⠒⢺⠁⠀⠀⠘⡀⠸⡉⠉⠐⠢⡼⠀⢸⣿⣿⣿⣿⣿⡊ ⠀⣿⣿⡟⠀⠀⠈⠑⠂⠀⠒⢣⠀⠀⠀⢡⠀⠙⠂⠀⠊⠀⣠⢻⣹⣿⣿⣿⣿⡇ ⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣀⠁⠀⠀⠀⠑⠦⢀⡀⠠⠒⠁⡘⣿⣿⣿⣿⣿⡇ ⠘⣿⣿⣿⡀⠀⠀⠀⠀⠀⠸⣀⣈⠒⣄⣀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇ ⠀⠘⢿⣿⣿⣄⠀⠀⠀⠀⢠⠺⠤⠤⡶⠃⠀⠀⠀⠀⠀⠀⢸⣼⣿⣿⣿⣿⣿⡇ ⠀⠀⠀⠙⢿⣿⣷⣄⡀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⡇ ⠀⠀⠀⠀⠀⠈⠙⠻⠿⡗⠂⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⡟⠀ ⠀⠀⠀⠀⠀⢀⣠⠄⡖⠂⠀⠀⠀⠀⠀⠻⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀ ⠀⠀⠀⡠⠒⠁⠘⡄⠐⠤⣀⡀⠀⣀⠠⠊⢀⣾⣝⡫⡉⠉⠉⠉⠁⠀⠀⠀⠀⠀ ⠀⢀⠎⠀⠀⠀⠀⠈⣢⣄⣀⣈⣁⣀⡠⠔⠋⠀⠙⣿⣮⢢⠀⠀⠀⠀⠀⠀⠀⠀ ⡔⣉⡉⠑⠢⡤⠊⠁⠀⠉⠓⢦⡤⠔⠒⠉⠉⠙⠲⣾⣿⣷⢣⠀⠀⠀⠀⠀⠀⠀ ⡙⠀⠈⠑⢲⣁⡀⠀⠀⠀⠀⠀⠙⠢⡀⠀⠀⡄⠑⡌⣆⡈⠙⠄⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀⠀⠀⠀⠈⠢⣀⢘⣄⠏⠀⠈⢱⠆⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀ ⠘⡄⠀⠀⠀⠀⠀⠀⣀⣽⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢹⠀⠐⡀⠀⠀⡗⠀⠘⡄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⣸⠤⢄⣑⠆⠚⠀⠀⠀⠘⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⢀⠃⠃⠀⠀⠀⠀⠀⠈ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⠈⠀⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⠔⠊⠉⠉⠉⠙⠻⣿⣶⣶⣦⣤⣀⡉⠉⢡⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡐⠁⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣷⡄⢇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡰⠀⠀⢀⣀⠠⠤⠄⠀⠒⠒⠒⠛⣻⠛⠛⠿⠿⢿⡘⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⣀⠧⠒⣈⡁⠠⠤⢴⠖⣒⣒⣒⣢⠉⠈⡆⠀⢰⢒⢦⠈⢣⠀⠀⠀⠀⠀ ⢀⣤⡮⣴⡪⠭⡐⠓⡀⠀⠸⠀⠀⠘⠀⢠⠀⠀⡇⡆⢸⠁⡸⠀⠈⡀⠀⠀⠀⠀ ⠘⠂⠩⢣⠀⠀⠀⠔⠀⠀⠀⠑⠤⠤⠔⠋⠀⢠⡗⡇⡄⢸⠀⠀⠀⢃⠀⠀⠀⠀ ⠀⢠⢁⠆⠉⠒⢺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡵⠀⢸⠀⠀⠀⠸⠀⠀⠀⠀ ⠀⠇⡈⠀⠀⠀⠈⢄⡀⠀⢀⠜⠀⠀⠀⠀⠀⠀⠈⠀⠀⢸⠀⠀⠀⠀⡆⠀⠀⠀ ⠸⠀⠇⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢇⠀⠀⢇⡀⠀⠀ ⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠜⢸⠀⠀⢀⣶⣿⣷ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠊⠀⢸⠀⠀⢸⢸⣿⣿ ⡇⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠈⢸⣿⣿ ⢰⠀⠇⠀⠀⠀⠀⠀⠀⡠⠀⠀⢀⣠⣶⡆⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡄⣼⣿⣿ ⠀⢆⠸⡀⠀⠀⠀⠀⠀⠑⠒⢲⣿⣿⢿⠇⠀⠀⠀⠀⠀⠀⢀⠃⠀⣰⣧⣿⣿⣿ ⠀⠈⢄⢣⠀⠀⠀⠀⠀⢠⠒⠚⠻⠓⠊⠀⠀⠀⠀⠀⢀⣴⣟⣠⣾⣿⣿⣿⣿⣿ ⠀⠀⠈⣆⢢⣀⠀⠀⠀⢰⠉⠀⢀⠀⠀⡰⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⢰⣱⣿⣿⣷⣶⣤⣤⣑⣒⣁⣩⣭⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⢀⢣⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⣸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⣷⡄⠀⠀⠀⠀⣀⣀⣀⣀⣤⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀ ⠀⠀⠀⣿⣿⣿⡶⠖⠒⠏⠉⠁⠈⠀⠀⠠⠋⠉⠉⢒⡤⢤⣄⠀⠀⠀⢀⣴⡇⠀ ⠀⠀⠀⣻⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢉⡢⢤⣶⣿⣿⠇⠀ ⣀⣤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣙⣿⡿⠀⠀ ⢏⡀⠀⠀⠀⠀⣑⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⠀⠀ ⠀⢹⠀⠀⢠⢮⣀⡀⠙⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠉⢷⠀ ⠀⠀⢣⠀⡏⠑⠂⠬⣑⡇⠀⠀⠀⠀⠀⠀⠀⠀⡨⠝⠋⠭⡉⠀⠀⠀⠀⠀⠙⡆ ⠀⠀⠀⠱⣘⠄⣀⣀⠔⠁⠀⠀⡔⠀⠀⠀⠀⣜⣲⠦⠤⠤⢜⡄⠀⠀⠀⠀⢐⢳ ⠀⠀⠀⠀⠈⠢⢄⠀⠀⠀⢀⡄⠈⠀⠀⠀⠀⢣⠀⠉⠉⠓⠲⠁⠀⠀⣀⠔⠒⠊ ⠀⠀⠀⠀⠀⠀⠀⠙⠲⠤⣀⠈⠋⠉⠉⠀⠀⠀⠑⠒⠐⠊⢁⡠⠔⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⢉⢟⣷⣖⢶⢤⠤⡤⠤⢶⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡇⠑⣽⢨⠉⠉⠉⠀⢀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡱⠶⣛⠶⢏⠭⡖⢲⡶⠖⠚⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠈⠁⠈⠉⠉⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⢄⠀⠀⠀⠀⠀⡜⠻⢿⣆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣇⡀⠀⠀⢸⠀⠀⠀⠀⠀⡄⠀⣾⠇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠈⠉⡖⠊⠑⠒⠤⠤⠤⡇⠀⠙⢷⣾⣆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠒⠚⠦⢄⣀⣀⣀⣀⠠⠃⠀⠀⠈⠛⠛⠓⠆⠀⠀⠀

⠀⠀⠀⠀⠀⠀⢀⣴⠾⢶⣶⣶⣾⣿⣿⣿⣷⠶⠶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣴⡟⣡⢄⡀⠈⠙⠛⠛⠉⠀⠀⢀⡀⠈⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⡏⡜⠁⠀⠉⠒⢶⠀⢠⠴⠒⠋⠉⠑⡄⢹⣿⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⣀⣤⣤⣸⣇⣧⠶⠦⠾⣆⡼⠀⢿⣀⣀⣀⣤⠀⣸⢀⣿⣿⣷⡀⠀⠀⠀⠀⠀ ⣼⠟⢩⠝⠋⠉⠉⠉⣖⠊⠉⠀⠀⢨⣦⣤⠤⠭⣽⣃⣼⣿⣿⣿⣿⣄⠀⠀⠀⠀ ⣿⣠⠃⠀⠀⠀⠀⠀⠀⠑⠴⠚⠓⠊⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⠿⠛⠛⠻⣶⡄ ⢸⣿⠀⠀⠀⣀⡤⠴⡖⠒⠒⢲⠲⠤⣄⡀⠀⠀⠀⠀⠀⠀⠘⣇⠔⠫⡉⠁⠈⣿ ⠸⣿⡄⢠⢚⢷⠀⡰⠹⡄⢠⠟⡇⠀⣸⡌⠑⢄⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⣰⡟ ⠀⣿⠠⣷⣸⠈⢦⠇⠀⠷⠃⠀⣧⠜⠁⡇⢀⣴⣳⠀⠀⠀⠀⣸⣦⣤⣶⠾⠋⠀ ⠀⢿⣄⠳⠿⠤⠒⠒⠛⠛⠛⠒⠢⠤⣀⠗⠁⢸⣇⠇⢰⢀⣰⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠉⠛⠶⠶⣦⡀⠀⠀⠀⠀⠀⠀⠀⡉⠒⠚⠋⣠⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠷⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⡟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣶⣿⣿⣿⣿⣿⣶⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⡿⠟⠛⠉⢀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣾⣿⠿⠋⠁⢀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣴⣶⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⣿⡿⠃⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⢁⣠⣴⣿⣿⣧⣀⣀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣾⣿⠁⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⢀⣴⣿⠟⠋⠉⠀⠀⠉⣹⡿⠻⠿⣿⣇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⣿⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⣰⣿⠟⠁⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠉⠙⢻⣷⣶⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣡⣾⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠈⠻⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⢩⣿⣿⣿⣿⣵⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣼⣿⣿⣿⣿⣿⣿⠿⠟⠛⠉⠉⢀⣀⣤⣾⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠄⠀⠀⠀⠀⠈⠻⣿⡇⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⠋⠉⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠙⣷⣄⠀⠀⠀⠀⠀ ⠀⠸⣿⣷⣄⡙⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣏⣁⣀⣰⣿⠀⠀⠀⠀⠀⠀⠉⠉⠻⣷⣦⠀⠀⠀ ⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡀⣴⣿⡿⠟⠛⠛⠛⠛⠻⢿⣤⣶⡷⠀⠀⠀⠀⠀⠀⢻⣷⣦⣤⡀ ⠀⠀⢀⣾⠃⠀⠉⠉⢋⡿⠉⠁⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⡿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣤⣴⡄⠀⠀⠀⠀⠈⢀⣴⢻⣷ ⣠⣶⠾⠏⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⢶⣿⠃⠀⢀⣀⣀⣀⣀⣀⣀⣠⣤⣼⣿⣁⣀⠀⠀⠀⠀⠀⠛⠉⢢⡟ ⣿⠛⣦⠀⠀⠀⠀⠀⡿⠿⠿⠛⠿⢷⠖⠒⠒⠒⠛⣧⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⢀⣤⣿⠛⠛⠛⠛⠛⠛⠛⠉⠀⠀⠀⠀⣿⠟⠛⠀⠀⠀⠀⠀⣤⡴⠟⠁ ⠘⢷⣤⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢠⠟⠀⠀⠀⠀⠀⠀⠀⠈⠉⣻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⢷⡦⠀⠀⠀⠀⣼⠟⠀⠀⠀ ⠀⠀⠙⣷⡀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⢀⡼⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠟⢻⣆⡀⠀⠀⠀⠀⠀⠀⠀⣠⢿⣦⠀⠀⠀⠀⢀⣼⠏⠀⠀⠀⠀ ⠀⠀⠀⠈⢻⣦⡀⠀⠀⠈⠳⣦⣤⣀⣠⣤⡶⠋⠀⠀⠀⠀⠀⠀⣀⠉⠀⠀⠀⠀⣰⠀⠀⠀⠀⠀⠿⠋⢻⣶⣦⣤⣤⣴⣶⠟⠿⡄⠉⠀⠀⠀⣠⡾⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠼⠷⠶⣶⠲⠞⠛⠁⠀⠀⠀⠀⠀⠀⠀⠿⠃⠈⣿⠁⠀⠻⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⢷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡾⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡶⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣶⣦⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣶⡶⠾⠟⠛⠋⠙⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠁⡀⣿⠉⠉⢹⠟⠛⠛⠛⠛⠋⠙⣿⠉⠈⣿⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⣼⠀⣿⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣿⣀⣠⡏⠀⢦⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⢀⡟⠀⣿⣿⣿⣿⣄⣀⣀⣀⣀⣀⣠⣿⣿⣿⣿⠀⠈⡇⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⣇⣰⣿⣿⣿⡿⠋⠛⠛⠛⠋⠉⠙⢿⣿⣿⠿⣧⣄⣸⡀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⢸⡿⠁⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠉⠻⣇⣀⣀⣀⣤⣽⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠳⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠉⠉⠉⠁⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⢸⣇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢷⣾⣆⡆⢰⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢼⣿⠉⠛⠻⢶⣄⡀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⡶⠶⠦⣤⣤⣽⡟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠈⠙⠶⣤⣤⣤⠴⠚⠋⠉⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣤⣄⣀⣀⣀⣀⣀⣀⣻⣀⣀⡀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⡟⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠛⠛⠛⠛⠋⠛⠿⠿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣟⣛⡛⠛⠶⢦⣄⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣦⣀⣈⣉⣉⣁⣀⣀⣀⣀⣀⣀⣈⣉⣉⠉⠛⠛⠳⠶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⡀⠀⠉⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠘⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠈⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠹⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣼⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠛⠛⠋⣉⣉⣉⣁⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣄⣀⡈⠙⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠛⠛⠛⢻⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠛⠉⢉⣉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠁⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⠿⠟⠛⠻⠿⣿⣿⣿⣷⡄⠀⣀⠀⠀⠀ ⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⢠⣾⣿⣿⣿⣿⠿⠿⠿⠿⣿⣿⣿⣿⣷⣄⣠⣤⣤⣾⣿⣿⣿⣏⣤⣤⣤⣤⣤⣴⣾⣿⣿⣿⣿⣶⠏⣀⡀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣰⣿⣿⣿⣿⣋⣤⣤⣤⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠉⠉⠀⠀⠀⠀⠀⠘⠿⠙⣿⣿⣿⡛⠉⠀⠀ ⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠉⠉⠉⠀⠀⠀⠀⠸⠿⢻⣿⣿⣿⡏⠉⠛⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡇⠀⠀⠀⠙⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡁⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⠇⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⡿⣷⡀⠀⠀ ⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⡏⢻⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠈⢿⣶⣦⣤⣶⣾⣿⣿⣿⣿⣿⣷⡜⢷⡀⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢻⡇⠀⠹⣿⣿⣿⣷⣦⣤⣀⣀⣠⣴⣾⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⠿⠛⢻⣿⣿⣿⣿⡜⣷⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣧⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣄⠀⠀⠀⠈⣿⣿⣿⣿⣷⣽⡇ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠾⠃⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣤⣴⠶⠟⠋⠁⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡇⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⡟ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⡿⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⠃⠀ ⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⣾⣿⣿⣿⣿⡿⠿⣿⡟⠉⢻⡄⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⠏⠀⠀ ⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡙⣷⣄⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣄⣿⡇⠀⣼⣿⣤⡼⠇⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀ ⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣝⣷⣦⣀⡀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣷⣶⠟⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀ ⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⠀⠀⠀⠀⠉⠙⠛⠋⠁⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡿⢿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⣀⣼⠏⢰⣷⣽⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣤⢠⡾⠛⠁⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⣶⣾⣿⣿⣿⣶⣶⣶⣶⣶⣦⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠿⣿⣿⣿⣿⣿⣿⣦⣌⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠉⠙⠻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠈⠙⠻⠿⣿⣿⣿⣿⣿⡶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⣶⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣶⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠻⠿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠻⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠾⠿⠿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⠶⠶⠶⣦⣄⡀⠀⠀⠀⠀⠀⢀⡾⠋⠀⠀⠀⠀⠀⠀⠙⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⣴⠟⠉⠀⠀⠀⠀⠀⠙⢿⣆⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣀⡀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⣼⡏⠀⠀⠀⢀⣀⠀⠀⠀⠀⢻⡆⠀⠀⠀⠸⣧⠀⠀⠀⠀⠻⠃⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⣿⡇⠀⠀⠀⠻⠟⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠹⣧⡀⠀⠀⠀⠀⠀⠀⣰⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠸⣧⡀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⠀⠀⠀⠀⠙⠿⣦⣀⣀⣠⣴⡾⠋⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠙⢷⣤⣀⡀⠀⢀⣀⣴⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣍⠁⠀⠀⠀⠀⠙⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⡿⠛⠛⠻⢿⠇⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠈⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⡇⠶⢶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡆⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠛⠷⢶⣶⣤⣴⠾⠋⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣾⣿⣷⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⠟⠉⠀⠀⠉⣿⡛⠛⠋⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣛⣛⣉⣀⡀⠀⠀⠀⠀⣨⡿⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣯⣉⣉⣉⡙⠛⠛⠛⢻⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢯⣍⣁⡀⢀⣀⣈⣿⣄⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠁⣸⡇⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠋⠀⠀⠀⠀⠀⢀⣼⠏⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣤⣀⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣷⣦⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣶⣄ ⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣌⠻⣿⣿⠻⠿⠿⠿⠶⠶⠶⠶⠶⢿⣷⡀⠀⠀⠀⠀⠀⣰⣷⣤⣤⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠙⢷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⣤⣤⣴⡾⠟⠀⢈⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠉⠻⢷⣦⣄⡀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⣠⡾⠋⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠈⠙⠻⢷⣦⣄⣀⠀⠀⠀⠀⢀⣤⡾⠋⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠉⠙⢛⣿⣿⣿⣿⣿⣄⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠠⡂⠍⠲⢶⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠂⢾⢄⡄⡅⡄⠠⠄⠀⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⣀⣀⠃⠀⠰⠖⣒⠢⢀⣿⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⢐⠟⠐⠃⡠⠃⢠⡀⠀⠈⠻⡿⠃⡒⠂⠀⠀⠀⠀ ⠀⣠⣴⣶⣶⣶⣦⣄⡀⠀⠘⡘⠒⠠⡄⠘⠀⡅⣰⡀⠀⠀⠳⠁⠁⠀⠇⠀⠀⠀ ⣴⣿⣿⡿⠟⠛⠿⣿⣿⡆⠀⣼⣿⣿⣷⣕⠔⢂⠠⡇⠀⠀⠔⠀⠀⠊⠀⠀⠀⠀ ⢿⡿⠋⠀⠀⠀⠀⢈⣿⣿⢀⣿⣿⣿⣿⣿⣷⣁⣈⣠⡀⠈⠀⠀⡖⠋⢄⠱⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢘⣿⣷⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⢀⡀⠊⠀⠀⠀⠀ ⠀⠀⢀⣴⣶⣶⣶⣼⣿⣿⣿⠃⠀⠹⣿⣿⣿⣿⣿⣿⣿⣷⣦⣬⣶⣀⣠⣷⡆⠀ ⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠘⢿⣿⣿⣿⡿⡿⢿⣿⣿⣿⡿⠿⠏⠀⠀ ⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠈⢿⡿⠇⠀⠀⠀⠙⠇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⢀⣾⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⢊⠀⠀⠉⠋⠉⠥⠬⠭⠛⠛⠓⠚⠛⠛⠇⠓⠀⠠⠀⡘⡄⠀⠀⠈⠠⡀⠀ ⠀⠈⠂⠤⠣⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⡒⢂⠀⠒⠄⠀⠀⠀⠈⠂ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣀⡀⠄

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