Little Mermaid Text Art

Copy & Paste Little Mermaid Text Art Emojis & Symbols

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

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣤⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡄⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣇⠀⠀⠀⢸⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠠⠴⠆⠀⠀⠀⠘⣿⣿⠀⣤⠀⣼⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈⣿⣿⠀⣄⠀⢻⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣰⣷⠀⠀⠀⠀⣿⣿⢠⣿⠀⢸⣿⣿⡇⠀⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣧⡀⠰⡆⣿⣿⣾⣿⣧⣸⣿⣿⡇⠀⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⢰⣇⣿⣿⣿⣿⣿⣿⣿⣿⡇⢀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⠃⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢼⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣼⣿⣧⣤⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣟⠀⠀⠀⣠⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⣟⠀⠀⠀ ⠀⣴⣿⣄⠀⢴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⢰⣿⡄⠀⠀ ⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣶⠆ ⢻⣿⣿⣿⣿⣿⣿⣿⠟⠉⠉⠀⠉⠙⢿⣿⣿⣿⣿⡿⠋⠉⠀⠈⠉⠻⣿⣿⣿⣿⣿⣿⣿⡿⠀ ⢸⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⠀⠀ ⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀ ⢸⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⡇⠀ ⣸⣿⣿⣿⣿⣿⣿⣿⣷⣶⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣶⣾⣿⣿⣿⣿⣿⣿⣿⡇⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀ ⣿⣿⣿⣿⡿⠿⠿⠿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⠀ ⠀⠉⠉⠁⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠉⠉⠉⠁⠀
N   O     O      o      o       o      o      。     。    .    .     .     .
⠀⠀⠀⢠⣾⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣰⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣄⣀⣀⣤⣤⣶⣾⣿⣿⣿⡷ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀ ⣿⣿⣿⡇⠀⡾⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀ ⣿⣿⣿⣧⡀⠁⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⢹⠉⠙⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⠀⣀⣼⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠀⠤⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⠿⠋⢃⠈⠢⡁⠒⠄⡀⠈⠁⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⠟⠁⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠈⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣾⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡀⠀⠠⣷⢀⢸⣿⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⠀⠀⣿⢸⢸⣿⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⢰⣿⡧⢠⣿⣿⣾⣿⡇⡆⠀⠀⠀⠀ ⠀⠀⠀⢸⣿⡇⣾⣿⣿⣿⣿⣏⣿⡀⠀⠀⠀ ⢀⣇⢀⣾⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⡆⣸⠀ ⢿⣿⣿⣿⠿⠛⠻⣿⣿⣿⠟⠛⠿⣿⣷⣿⣷ ⢸⣿⣿⠃⠀⠀⠀⠸⠿⠇⠀⠀⠀⢸⣿⣿⡇ ⣿⣿⣿⣧⣤⡀⠀⠀⠀⠀⠀⢀⣤⣼⣿⣿⣧ ⣿⣿⡿⢿⣿⡀⠀⠀⠀⠀⠀⢸⣿⣿⢿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀
⠀ ⠀ (\__/) (•ㅅ•) Don’t talk to _ノヽ ノ\_ me or my son `/ `/ ⌒Y⌒ Y ヽ ever again. (  (三ヽ人  /  | | ノ⌒\  ̄ ̄ヽ ノ ヽ___>、__/ |( 王 ノ〈 (\__/) /ミ`ー―彡\ (•ㅅ•) / ╰ ╯ \ / \>
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⣄⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣶⣦⡀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀ ⠀⠀⠀⣰⣾⣿⣿⣿⣷⣆⠀⠀⢀⣿⣿⣿⣷⡀⠀⢸⣿⣿⣇⣀⣽⣿⣿⡇⠀⠀ ⠀⠀⢸⣿⣿⡿⠛⣿⣿⣿⠆⠀⣸⣿⡟⠻⣿⣷⡀⠘⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀ ⠀⠀⢸⣿⣿⣇⠀⠀⠉⠁⠀⠀⣿⣿⣷⣶⣿⣿⣷⡀⢿⣿⣿⡟⠉⠀⠀⠀⠀⠀ ⠀⠀⠸⣿⣿⣿⠀⠀⣤⣦⣄⢸⣿⣿⣿⣿⣿⣿⣿⣷⣸⣿⣿⣧⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢿⣿⣿⣷⣾⣿⣿⡿⣿⣿⣿⠇⠀⠀⠻⢿⠿⠁⠛⢟⣃⣀⡀⣀⣀⠀⡀ ⠀⠀⠀⠈⠻⢿⣿⣿⠿⠟⠁⣈⣉⣭⣤⣤⣶⣶⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⣀⣀⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⠿⠿⠛ ⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠛⠛⠋⠉⠉⠀⠀⠀⠀⡀⡀⠀⠀⠀ ⠸⣿⣿⣿⣿⣿⠿⠟⠛⠋⠉⠁⠀⠀⣀⣀⣠⣤⣴⣶⣶⣾⣿⣿⣿⣿⣿⣷⠀⠀ ⠀⠈⠉⠉⠀⠀⠀⠀⣠⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠛⠋⠉⠉⠉⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⠻⠿⠟⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣶⣶⣿⣷⣆⠀⠀⠀⠀ ⠀⠀⠀⢀⣤⣤⣶⣶⣾⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⡆⠀⠀⠀ ⠀⢀⣴⣿⣿⣿⣿⣿⣿⡿⠛⠉⠉⠀⠀⠀⣿⣿⣿⣿⣷⠀⠀⠀ ⣠⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⢤⣶⣾⠿⢿⣿⣿⣿⣿⣇⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠈⠉⠀⠀⠀⣿⣿⣿⣿⣿⡆⠀ ⢸⣿⣿⣿⣏⣿⣿⣿⣿⣿⣷⠀⠀⢠⣤⣶⣿⣿⣿⣿⣿⣿⣿⡀ ⠀⢿⣿⣿⣿⡸⣿⣿⣿⣿⣿⣇⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣧ ⠀⠸⣿⣿⣿⣷⢹⣿⣿⣿⣿⣿⣄⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⢻⣿⣿⣿⡇⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠘⣿⣿⣿⣿⠘⠻⠿⢛⣛⣭⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⢹⣿⣿⠏⠀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋ ⠀⠀⠀⠈⣿⠏⠀⣰⣿⣿⣿⣿⣿⣿⠿⠟⠛⠋⠉⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⡿⠿⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
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⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣠⣤⣶⣶ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢰⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⣀⣾⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⡏⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿ ⣿⣿⣿⣿⣿⣿⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠁⠀⣿ ⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠙⠿⠿⠿⠻⠿⠿⠟⠿⠛⠉⠀⠀⠀⠀⠀⣸⣿ ⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣴⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⢰⣹⡆⠀⠀⠀⠀⠀⠀⣭⣷⠀⠀⠀⠸⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠉⠀⠀⠤⠄⠀⠀⠀⠉⠁⠀⠀⠀⠀⢿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⢾⣿⣷⠀⠀⠀⠀⡠⠤⢄⠀⠀⠀⠠⣿⣿⣷⠀⢸⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⡀⠉⠀⠀⠀⠀⠀⢄⠀⢀⠀⠀⠀⠀⠉⠉⠁⠀⠀⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⡿⠉⠄⠄⠄⠄⠈⠙⠿⠟⠛⠉⠉⠉⠄⠄⠄⠈⠉⠉⠉⠛⠛⠻⢿⣿⣿⣿⣿⣿ ⠁⠄⠄⠄⢀⡴⣋⣵⣮⠇⡀⠄⠄⠄⠄⠄⠄⢀⠄⠄⠄⡀⠄⠄⠄⠈⠛⠿⠋⠉ ⠄⠄⠄⢠⣯⣾⣿⡿⣳⡟⣰⣿⣠⣂⡀⢀⠄⢸⡄⠄⢀⣈⢆⣱⣤⡀⢄⠄⠄⠄ ⠄⠄⠄⣼⣿⣿⡟⣹⡿⣸⣿⢳⣿⣿⣿⣿⣴⣾⢻⣆⣿⣿⣯⢿⣿⣿⣷⣧⣀⣤ ⠄⠄⣼⡟⣿⠏⢀⣿⣇⣿⣏⣿⣿⣿⣿⣿⣿⣿⢸⡇⣿⣿⣿⣟⣿⣿⣿⣿⣏⠋ ⡆⣸⡟⣼⣯⠏⣾⣿⢸⣿⢸⣿⣿⣿⣿⣿⣿⡟⠸⠁⢹⡿⣿⣿⢻⣿⣿⣿⣿⠄ ⡇⡟⣸⢟⣫⡅⣶⢆⡶⡆⣿⣿⣿⣿⣿⢿⣛⠃⠰⠆⠈⠁⠈⠙⠈⠻⣿⢹⡏⠄ ⣧⣱⡷⣱⠿⠟⠛⠼⣇⠇⣿⣿⣿⣿⣿⣿⠃⣰⣿⣿⡆⠄⠄⠄⠄⠄⠉⠈⠄⠄ ⡏⡟⢑⠃⡠⠂⠄⠄⠈⣾⢻⣿⣿⡿⡹⡳⠋⠉⠁⠉⠙⠄⢀⠄⠄⠄⠄⠄⠂⠄ ⡇⠁⢈⢰⡇⠄⠄⡙⠂⣿⣿⣿⣿⣱⣿⡗⠄⠄⠄⢀⡀⠄⠈⢰⠄⠄⠄⠐⠄⠄ ⠄⠄⠘⣿⣧⠴⣄⣡⢄⣿⣿⣿⣷⣿⣿⡇⢀⠄⠤⠈⠁⣠⣠⣸⢠⠄⠄⠄⠄⠄ ⢀⠄⠄⣿⣿⣷⣬⣵⣿⣿⣿⣿⣿⣿⣿⣷⣟⢷⡶⢗⡰⣿⣿⠇⠘⠄⠄⠄⠄⠄ ⣿⠄⠄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⡟⢀⠃⠄⢸⡄⠁⣸ ⣿⠄⠄⠘⢿⣿⣿⣿⣿⣿⣿⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢄⡆⠄⢀⣪⡆⠄⣿ ⡟⠄⠄⠄⠄⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣟⣻⣩⣾⣃⣴⣿⣿⡇⠸⢾
⠀⠀⡤⠒⠊⠉⠉⠒⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠾⠙⠛⢿⢿⠿⡿⢷⠼⠷⡄⠀⠀⠀⠀⠀ ⢠⠎⠀⠀⠀⠀⠀⠀⢸⠷⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠿⠿⠿⠿⠏⠾⡋⡡⠼⠿⠿⠿⡦⡴⠖⠒⠒ ⠃⠀⠀⠀⢀⠤⠶⠴⠿⠿⠿⠶⠶⡆⠀⠀⠤⠴⠶⠚⠛⠉⠉⡩⠟⠛⠉⠉⠙⢟⠻⠿⠶⠾⠿⠿⠿⠿⡗⠴⠿⠟⡼⢿⠿⡇⡇⠀⠀⠀ ⠀⠀⠀⢀⠾⠿⠿⠿⠿⠿⠿⠿⠿⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠈⠉⠓⠀⢄⠉⠻⢿⠿⠿⠷⠄⠿⠿⠇⠀⠀⠀ ⠀⠀⠀⠼⠿⠿⠿⠿⠿⠿⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⢄⢻⠿⠿⠿⠿⠿⠿⠿⠿⠿ ⠀⠀⠀⢻⠿⠿⠿⠿⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢇⠈⠻⠿⠿⠿⠿⠿⠿ ⠀⠀⢠⠿⠿⠿⠿⡿⠁⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠀⠈⢿⠿⠿⠿⠿ ⠀⠀⠿⠿⠿⠿⡟⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠆⠀⢻⠿⠿⠿ ⠀⠿⠿⠿⠿⡿⠀⠀⠀⢀⠤⡴⠶⢲⠞⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠛⠛⠓⠶⠦⠤⠀⠀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠘⠆⠀⢿⠿⠿ ⠀⢸⠿⠿⠿⠇⢰⠀⠈⠁⠀⢀⡴⠋⠀⢸⠀⠀⠀⠀⠀⠀⠸⠀⠀⢀⠀⠈⠄⠀⠀⠀⠀⠈⠉⠂⢳⡀⠀⠀⠀⠀⠀⠀⠀⠸⡄⢸⠿⠿ ⠀⠀⠻⠿⠿⠀⢸⠸⠀⠀⠠⠏⠀⠀⠀⠈⠇⠀⠀⠀⠀⠀⠀⡷⡀⠘⡄⠀⢘⢦⡀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠿⠿ ⠀⢀⡴⠉⠿⠀⠘⡏⠀⠼⠃⠀⠀⠀⠀⠀⠹⠆⠀⠀⠀⠀⠀⡇⠻⠄⠘⠤⡈⢧⠈⠢⠄⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⠀⢠⠀⠧⠿⠿ ⢀⡾⠁⠀⡇⠀⠀⠇⠼⡧⠴⠶⠶⢤⠤⠄⠀⠹⠄⠀⠀⠀⠀⢳⠀⠈⠳⢨⠻⠿⢦⠄⠙⢟⡲⢤⠄⡀⠀⠘⢦⡀⠀⠀⠀⠀⠇⢹⠿⠿ ⠼⠁⠀⢸⡇⠀⠀⢏⠀⠀⠀⠀⠸⠿⢟⠉⠳⡄⠈⠣⡀⠀⠀⠈⠦⠤⠤⠤⠤⠭⠳⡈⠙⠢⢽⠦⠄⡏⠉⠒⠒⠉⠆⠀⠀⠀⢸⡼⠿⠿ ⠳⢦⠄⠸⠇⠀⠀⠠⠟⠀⠀⠀⠀⠉⠛⠛⠉⠀⠀⠀⠈⠳⢦⠀⠹⠄⠀⠀⡀⠴⠾⠿⠿⠦⠀⠀⠸⠇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠿⠙ ⢀⡞⠁⢹⠀⠀⠰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠁⠉⠉⠛⠢⠤⠄⡼⠇⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠿⠀ ⠏⠀⠀⢸⡇⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠿⠀ ⠦⠀⡀⢸⡇⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠞⢀⠴⡆⠀⠀⠀⠀⠀⠀⠀⠀⠿⡇⠿⢷ ⠁⠈⠙⠿⡇⠀⠻⡄⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠠⠴⠚⠡⠴⠋⠸⠃⠀⠀⠀⠀⠀⠀⠀⠸⠿⡇⡿⠻ ⠀⢀⡼⢁⠿⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠙⠲⠤⠤⠤⠖⠋⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⢠⠿⠼⠿⡇⠀ ⠠⡞⠁⢸⠿⡄⠀⠀⠀⠙⠶⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠾⠿⠁⠀⠀⠀⠀⢀⠀⢀⡾⠿⠿⠿⠦⡀ ⠹⠁⠀⢸⠟⠇⠀⠀⠀⠀⠀⡄⠉⢳⠦⠤⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠴⠾⠿⠿⠿⠇⠀⠀⠀⠀⠠⠎⢀⠾⠷⠹⠯⡟⠿⠿ ⠇⠀⠀⡾⠀⢻⡄⠀⠀⠀⠀⠿⡄⢸⠿⠿⠿⠿⠿⠿⠷⠶⠆⠀⠀⠀⠻⠿⠿⠿⠿⠿⠿⠿⠏⠀⠀⠀⠀⡴⠋⠠⠾⠿⠿⠿⠿⡅⠀⠀ ⠀⠀⠼⠁⠀⠀⢷⠀⠀⠀⠀⢹⠷⠸⠿⠿⠿⠿⠿⠿⠿⠿⠷⠤⠾⠿⠿⠿⠿⠿⠿⠿⠿⠋⠀⠀⠀⠠⠞⢁⠴⠿⠿⠿⠧⡿⠀⢻⠦⠀ ⠠⠞⠁⠀⠀⠀⠈⢣⡀⠀⠀⠘⠿⠿⠿⠿⠿⠿⠿⠿⡿⠛⠏⠿⠿⠿⠿⠿⠿⠿⠿⠟⠁⠀⢀⠠⡾⢋⠴⠿⠿⠿⠿⠿⡿⠁⠀⠀⠙⠷
⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜🟦🟦🟦⬜🟦🟦⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜🟦🟦🟦🟦🟦🟦🟦⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬜⬜🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬜🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦⬜⬜⬜⬜ 🟦🟦🟦⬜⬜⬜⬜🟦🟦🟨🟦🟦🟦🟨🟨🟦🟨🟦⬜⬜⬜⬜⬜⬜ ⬜🟦🟦🟦⬜⬜🟦🟦🟨🟦🟦🟦🟨🟨🟨🟨🟨🟨⬜⬜⬜⬜⬜⬜ ⬜🟦🟦🟦🟦🟦🟨🟦🟨🟦🟦🟨🟨🟨🟨🟨🟨🟨🟨⬜⬜⬜⬜⬜ ⬜🟦🟦🟦🟨🟦🟨🟦🟨🟦🟦🟨🟨🟧🟨🟨🟨🟨🟨⬜⬜⬜⬜⬜ ⬜🟦🟦🟦🟨🟦🟨🟦🟨🟦🟦🟨🟧🟨🟧🟨🟨🟧🟨⬜⬜⬜⬜⬜ ⬜🟦🟦🟦🟨🟧🟨🟦🟨🟦🟦🟨🟧🟨🟨🟨🟨🟨🟧⬜⬜⬜⬜⬜ 🟦🟦🟦⬜⬜🟧🟧🟨🟨🟨🟦🟨🟨⬜⬜🟨⬜⬜🟨⬜🟦🟦🟦⬜ ⬜⬜⬜⬜⬜⬜🟧🟧🟨🟨🟨🟨🟨⬜🟦🟨⬜🟦🟨🟦🟦🟦🟦🟦 ⬜⬜⬜⬜⬜🟦🟦🟦🟦🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟦🟦🟦🟦 ⬜⬜⬜🟦🟦🟦🟦🟦🟧🟧🟨🟨🟨🟥🟨🟨🟨🟨🟨🟨⬜⬜⬜⬜ ⬜⬜⬜🟦🟦🟦🟦⬜🟧🟧🟧🟧🟨🟨🟥🟥🟨🟨🟧🟧⬜⬜⬜⬜ ⬜⬜⬜🟦🟦🟦⬜⬜⬜🟧🟧🟧🟨🟨🟥🟥🟨🟧🟧⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜🟧🟧🟨🟨🟨🟨⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜🟨🟨🟨⬜⬜⬜⬜⬜⬜⬜⬜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠊⠀⠀⠀⢀⠀⣀⠈⠒⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠊⠁⠀⠀⠀⠈⠁⠈⠉⠉⠁⠀⠀⠈⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⣠⣾⢶⣶⣶⣯⡢⡀⠀⠀⠀⠈⠓⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⣠⣾⣿⡇⡏⠉⣾⣿⡻⢮⡀⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⠫⠉⢭⣾⣿⣾⡄⠙⢦⣄⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⠀⢀⣠⡾⢟⣛⣯⠥⠤⠀⠒⠒⠒⠒⠶⠦⠭⣝⣒⡚⠷⣤⡀⠀⢠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢾⡵⣞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣶⡿⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡷⢜⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣶⠿⢋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠂⠀⢸⠋⠉⠁⢒⠒⠚⢻⠒⠉⠉⠉⢡⡇⠀⠀⢨⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠇⢰⠀⡆⣀⣀⣀⡀⠁⡕⠘⡆⢀⣀⣄⣀⡣⠀⠀⠈⡄⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠜⢀⠈⡦⢾⠛⣻⣿⣿⠁⠙⠀⢩⢙⣿⣯⡏⠻⢲⠀⢠⠉⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠎⠀⣿⠘⠀⠻⠙⠃⠀⠀⠀⠀⠎⠛⠙⠀⢀⣼⠀⠈⠂⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⣸⠀⠀⠀⠀⡏⢢⠀⠀⠀⠀⠀⠀⠀⠀⠪⣂⠀⢀⢾⢿⠀⠀⠀⠀⣇⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⠀⠀⠀⡀⣿⣤⣷⣀⠀⠀⠀⠀⠀⠀⠀⠈⢀⣰⣇⣸⠀⠀⠀⠀⢹⣯⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⣻⣿⣿⠀⡆⠀⡇⣿⠇⠈⠙⣿⡖⠤⣀⣀⡠⠴⣾⠛⠉⠀⡾⢰⠀⠁⠀⣾⣿⣟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠚⢋⣿⣿⢀⢰⠀⣷⠸⠀⠀⣰⢻⣟⠲⠤⠤⢴⣞⡿⢳⠀⠀⣙⣼⠀⡇⣴⣿⣿⡟⠓⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠠⠾⠿⣿⣿⣾⣄⠸⣶⠀⢠⣏⠈⢿⣷⠀⠀⢽⣿⠇⠘⣇⠀⢡⣃⣴⣷⣿⣿⡿⠿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⣻⣿⠿⣿⣿⣿⣆⣸⣿⡦⣄⠉⠀⠀⢉⣀⡴⣾⣿⣠⣟⣿⣿⡿⠿⣟⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠙⣔⢍⡛⠧⣀⡈⠉⠭⠷⠦⣄⠀⣹⣿⠴⠿⠯⠭⠍⠀⠉⠉⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠈⡗⠪⣑⠢⣍⠓⠦⣄⡀⠀⠁⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⠀⡹⠀⠀⠉⠒⢍⠒⢤⣉⠛⠲⢦⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢀⠇⠀⠀⠀⠀⠀⠑⢆⠈⠙⠒⠶⣤⣈⡉⠙⠛⠲⠶⢶⣤⣤⣀⣀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠀⠀⠉⠙⠓⠶⢦⣤⣀⡀⠈⠉⠉⠙⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠓⠲⠦⣾⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⣤⣈⣣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⡴⠁⠐⠆⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠰⡍⠑⠒⠒⢶⡏⠀⣀⣧⣼⣇⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢠⠇⡇⠀⠀⠀⠀⠻⢹⢿⣻⣿⣿⠟⡟⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⡞⠀⡇⠀⠀⠀⠀⠀⢨⣷⣆⠐⣶⠿⡇⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠃⠀⠃⠀⠀⠀⠀⠀⠘⡗⠒⠒⠒⠒⠁⠀⠈⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⢶⣤⡀⠀ ⢀⣤⣤⣤⣀⣤⡴⣤⣤⣴⠶⢶⡌⠉⢻⣎⢻⡄ ⣿⠁⠀⠈⠀⠀⠀⠀⠈⠁⠀⢨⡿⠀⠀⣿⠈⣷ ⠘⢷⣤⡀⠷⣦⡀⠀⣼⠏⢰⡟⠁⠀⢠⡿⢀⣿ ⠀⠀⠈⢿⡄⠈⠻⠿⠋⣠⡾⠿⠿⠿⠛⠁⣸⠇ ⠀⣠⣴⠟⣁⡀⠲⠶⠟⠋⢀⣴⠆⠀⠀⢰⡟⠀ ⢼⣯⣴⣾⠟⣡⡶⠻⠿⢶⣾⠇⠀⠀⣰⡟⠀⠀ ⠈⠉⠸⠷⠾⠋⠀⢠⡶⠞⠋⢀⣠⡾⠋⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠉⠀⠀⠀⠀⠀
⣿⠟⣽⣿⣿⣿⣿⣿⢣⠟⠋⡜⠄⢸⣿⣿⡟⣬⢁⠠⠁⣤⠄⢰⠄⠇⢻⢸ ⢏⣾⣿⣿⣿⠿⣟⢁⡴⡀⡜⣠⣶⢸⣿⣿⢃⡇⠂⢁⣶⣦⣅⠈⠇⠄⢸⢸ ⣹⣿⣿⣿⡗⣾⡟⡜⣵⠃⣴⣿⣿⢸⣿⣿⢸⠘⢰⣿⣿⣿⣿⡀⢱⠄⠨⢸ ⣿⣿⣿⣿⡇⣿⢁⣾⣿⣾⣿⣿⣿⣿⣸⣿⡎⠐⠒⠚⠛⠛⠿⢧⠄⠄⢠⣼ ⣿⣿⣿⣿⠃⠿⢸⡿⠭⠭⢽⣿⣿⣿⢂⣿⠃⣤⠄⠄⠄⠄⠄⠄⠄⠄⣿⡾ ⣼⠏⣿⡏⠄⠄⢠⣤⣶⣶⣾⣿⣿⣟⣾⣾⣼⣿⠒⠄⠄⠄⡠⣴⡄⢠⣿⣵ ⣳⠄⣿⠄⠄⢣⠸⣹⣿⡟⣻⣿⣿⣿⣿⣿⣿⡿⡻⡖⠦⢤⣔⣯⡅⣼⡿⣹ ⡿⣼⢸⠄⠄⣷⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣕⡜⡌⡝⡸⠙⣼⠟⢱⠏ ⡇⣿⣧⡰⡄⣿⣿⣿⣿⡿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣋⣪⣥⢠⠏⠄ ⣧⢻⣿⣷⣧⢻⣿⣿⣿⡇⠄⢀⣀⣀⡙⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠂⠄⠄ ⢹⣼⣿⣿⣿⣧⡻⣿⣿⣇⣴⣿⣿⣿⣷⢸⣿⣿⣿⣿⣿⣿⣿⣿⣰⠄⠄⠄ ⣼⡟⡟⣿⢸⣿⣿⣝⢿⣿⣾⣿⣿⣿⢟⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠄⡀⡀ ⣿⢰⣿⢹⢸⣿⣿⣿⣷⣝⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠉⠄⠄⣸⢰⡇ ⣿⣾⣹⣏⢸⣿⣿⣿⣿⣿⣷⣍⡻⣛⣛⣛⡉⠁⠄⠄⠄⠄⠄⠄⢀⢇⡏⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣤⣶⣶⣶⣶⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⡇⣿⣷⣿⣿⣿⣿⣿⣿⣯⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⣿⣿⣿⣇⣿⣀⠸⡟⢹⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢡⣿⣿⣿⡇⠝⠋⠀⠀⠀⢿⢿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢸⠸⣿⣿⣇⠀⠀⠀⠀⠀⠀⠊⣽⣿⣿⣿⠁⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣷⣄⠀⠀⠀⢠⣴⣿⣿⣿⠋⣠⡏⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠾⣿⣟⡻⠉⠀⠀⠀⠈⢿⠋⣿⡿⠚⠋⠁⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣾⣿⣿⡄⠀⣳⡶⡦⡀⣿⣿⣷⣶⣤⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡆⠀⡇⡿⠉⣺⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣯⠽⢲⠇⠣⠐⠚⢻⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡐⣾⡏⣷⠀⠀⣼⣷⡧⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⣿⣿⣮⠳⣿⣇⢈⣿⠟⣬⣿⣿⣿⣿⣿⡦⢄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢄⣾⣿⣿⣿⣿⣿⣿⣿⣷⣜⢿⣼⢏⣾⣿⣿⣿⢻⣿⣝⣿⣦⡑⢄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣶⣷⣿⣿⠃⠘⣿⣿⣿⣿⣿⣿⣿⡷⣥⣿⣿⣿⣿⣿⠀⠹⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣇⣤⣾⣿⣿⡿⠻⡏⠀⠀⠸⣿⣿⣿⣿⣿⣿⣮⣾⣿⣿⣿⣿⡇⠀⠀⠙⣿⣿⡿⡇⠀⠀⠀⠀⠀ ⠀⠀⢀⡴⣫⣿⣿⣿⠋⠀⠀⡇⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢘⣿⣿⣟⢦⡸⠀⠀⠀ ⠀⡰⠋⣴⣿⣟⣿⠃⠀⠀⠀⠈⠀⠀⣸⣿⣿⣿⣿⣿⣿⣇⣽⣿⣿⣿⣿⣇⠀⠀⠀⠁⠸⣿⢻⣦⠉⢆⠀⠀ ⢠⠇⡔⣿⠏⠏⠙⠆⠀⠀⠀⠀⢀⣜⣛⡻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡀⠀⠀⠀⠀⡇⡇⠹⣷⡈⡄⠀ ⠀⡸⣴⡏⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⡇⡇⠀⢻⡿⡇⠀ ⠀⣿⣿⣆⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⣰⠿⠤⠒⡛⢹⣿⠄ ⠀⣿⣷⡆⠁⠀⠀⠀⠀⢠⣿⣿⠟⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠻⢷⡀⠀⠀⠀⠀⠀⣸⣿⠀ ⠀⠈⠿⢿⣄⠀⠀⠀⢞⠌⡹⠁⠀⠀⢻⡇⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⢳⠀⠀⠁⠀⠀⠀⠀⢠⣿⡏⠀ ⠀⠀⠀⠈⠂⠀⠀⠀⠈⣿⠁⠀⠀⠀⡇⠁⠀⠘⢿⣿⣿⠿⠟⠋⠛⠛⠛⠀⢸⠀⠀⡀⠂⠀⠀⠐⠛⠉⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠕⣠⡄⣰⡇⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⢀⣸⠠⡪⠊⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢫⣽⡋⠭⠶⠮⢽⣿⣆⠀⠀⠀⠀⢠⣿⣓⣽⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⢹⣶⣦⣾⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠄⠄⢿⣇⠄⠄⠘⣆⢀⣼⣿⣿⣿⣿⢿⡿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣟⢧⡲⣿⢷⢦⡀ ⠄⠄⠈⣿⠄⠄⠄⢙⢞⢿⣿⢹⢿⣦⢏⣱⢿⠘⣿⣝⠹⢿⣿⡽⣿⣿⣏⣆⢿⣿⡞⠁ ⠄⠄⠄⢻⡀⠄⠄⠈⣾⡸⡏⢸⡾⣴⣿⣿⣶⣼⣎⢵⢀⡛⣿⣷⡙⡻⢻⡴⠨⠨⠖⠃ ⠄⠄⠄⠈⣧⢀⡴⠊⢹⠁⡇⠈⢣⣿⣿⣿⣿⣦⣿⣷⣜⡳⣝⢧⢃⢣⣼⢁⠘⠆⠄⠄ ⠄⠄⠄⠄⢹⡇⠄⣠⠔⠚⣅⠄⢰⣶⣦⣭⣿⣿⣿⡿⠟⠿⣷⡧⠄⣘⣟⣸⠄⠄⠄⠄ ⠄⠄⠄⠄⠄⢷⠎⠄⠄⠄⣼⣦⠻⣿⣿⡟⠛⠻⢿⣿⣿⣿⡾⢱⣿⡏⠸⡏⠄⠄⠄⠄ ⠄⠄⠄⠄⠄⠸⡄⠄⡄⠄⣿⢧⢗⠌⠻⣇⠿⠿⣸⣿⣿⡟⡐⣿⠟⢰⣇⠇⠄⠄⠄⠄ ⠄⠄⠄⠄⠄⣠⡆⠄⠃⢠⠏⣤⢀⢢⡰⣭⣛⡉⠩⠭⡅⣾⢳⡴⡀⢸⣿⡆⠄⠄⠄⠄ ⠄⠄⠄⢀⣶⡟⣽⠼⢀⡕⢀⠘⠸⢮⡳⡻⡍⡷⡆⠤⠤⠭⢸⢳⣷⢸⡟⣷⠄⠄⠄⠄ ⠄⠄⣴⣿⢫⢞⣵⢏⡞⠄⢸⠄⣛⣗⠩⠄⣰⣚⠒⠂⣀⡀⢸⢸⣿⣧⠇⡼⣧⠄⠄⠄ ⢠⣾⢟⡴⢫⡾⣱⢟⠄⠄⢸⠄⢈⡓⡮⡦⡬⠽⡠⠄⠔⠄⢸⠈⣿⣿⡄⣷⢹⣆⠄⠄ ⡿⢁⠞⢀⣿⢣⠇⣿⠄⠄⠸⢀⢳⢣⣗⣿⡇⡔⠄⠔⠄⠄⢠⠄⠹⣿⣷⡝⣧⢻⣆
⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀ ⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀ ⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀ ⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢀⣀⣀⣀⡀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇ ⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡻⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀ ⠀⠀⠀⠙⠛⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠟⠋⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣋⢹⣿⡄⢸⢛⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡟⠸⣿⡇⠀⢸⠀⢸⢹⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⡟⠁⠀⠀⠀⠸⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡟⣻⣿⠀⠀⠇⠀⠀⠀⠀⠈⠀⠙⣿⡿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⡿⠃⠙⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁⠻⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣴⠄⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⣴⡾⠛⠋⠉⠀⠀⠀⠀⢸⣿⣷⠀⠛⢷⣦⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⡾⠋⠁⠀⠀⠀⠀⠀⢸⣧⣤⣼⣿⣿⠀⠀⠀⠈⠙⢷⣄⠀⠀⠀⠀ ⠀⠀⢠⣾⠋⠀⠀⠀⢀⣷⠀⣸⡀⣼⣿⣿⣿⣿⣿⡀⣾⡀⠀⡄⠀⠙⣷⡄⠀⠀ ⠀⢰⡿⠁⠀⢀⠀⠀⢸⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠸⠇⠀⠀⠈⢿⡆⠀ ⢠⣿⠁⠀⠀⣿⡀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡄⠀⠀⠈⣿⡄ ⣸⡇⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⠆⠀⠀⢸⣇ ⣿⡇⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⢸⣿ ⠛⠃⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠃⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠃⠀⠀⠘⠛
⠀⠀⠀⡠⠄⠒⠒⠲⠖⡢⢄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⠊⠀⠀⠀⠀⠀⠀⠀⠑⠕⡄⠁⠂⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠧⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠑⠝⢅⠐⠢⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠰⠙⠒⠒⠒⠒⠀⠩⠉⠀⠂⢵⡀⡀⠈⢆⢢⠀⠘⡀⢀⣀⣤⡴⡶⠂ ⠀⠀⠀⡆⠤⡄⠀⠀⠀⣀⠀⠈⠀⠀⡀⠰⣡⠀⠈⡀⣆⠤⣋⠝⠛⡶⠊⠀⠀ ⠀⢠⠄⢿⣶⠇⠀⢠⠊⡀⠹⡄⠀⢀⠃⠀⢡⢣⣀⡇⢸⢊⡀⠔⠈⠀⠀⠀⠀ ⠰⠛⡄⠀⠙⢄⠀⢿⣺⣿⡞⠀⠀⢸⠀⠀⠀⡆⢋⡇⠸⡜⠀⠀⠀⠀⠀⠀⠀ ⢣⠘⡈⠢⠀⠜⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡇⠈⡅⡶⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⡆⠸⡢⣀⣀⣀⣰⡀⠀⠀⠀⠀⠘⣉⠐⡄⡇⠀⢙⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠘⣄⠫⣉⠩⠋⠁⠈⠀⠀⠀⡀⠀⠀⡰⢡⠁⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠫⢐⣀⣀⣀⡀⠤⠄⣒⠡⠭⣥⡐⠁⠀⣠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡰⠉⢲⢹⡀⢀⣠⣃⠑⡄⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⠔⠇⠀⢨⠒⢢⠞⠁⠀⡇⠈⠐⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢇⡼⠀⡠⡇⠀⡆⠀⠀⠀⡇⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢰⠁⡠⢰⠛⢸⠘⠀⠀⢸⠀⠀⠀⣠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠘⠾⠊⠁⠀⠀⢇⠀⠀⢘⠐⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄⣀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢋⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠏⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢹⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣁⡀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠊⠀⢀⡎⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠉⠉⠈⠙⢮⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠚⠁⠀⠀⠀⣼⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣆⣀⡀⠀⠀⢀⣿⡆⠀⠀⠀⠀⠀⠀⣀⠴⠚⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡿⠶⠖⠚⠉⠁⠀⠈⠙⢶⣾⣿⠁⠀⠀⠀⢀⡤⠊⠁⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⣿⠁⣠⡀⠀⠀⢀⣦⣴⠀⠀⠘⡿⢿⠀⠀⣠⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⡧⣿⣿⡄⢠⢾⡿⠯⢆⠀⢠⣹⣿⢀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣷⣟⡋⠉⢽⣷⠊⢣⣿⢿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠺⡗⠀⠈⠉⠀⣶⠏⣸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡬⢤⠖⢀⡼⡿⢲⣧⡗⠒⠢⡄⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡭⠛⠻⠁⠀⠿⣟⡽⡇⠀⠀⠘⡆⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣠⠆⠀⠀⠀⠀⠈⢧⢻⠀⠀⠀⢱⣀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠹⡶⠛⠑⣶⠀⠀⣸⡜⠀⣀⠤⡞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠻⡀⠀⠀⠀⡏⠀⠀⣿⠋⠉⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣀⣿⣄⠀⢰⠁⠀⣸⡃⠉⠓⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⢾⣧⣀⣭⣿⠗⠻⠄⢀⠇⠳⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣶⣿⣅⡠⠾⠚⢿⣿⣍⣄⣀⣀⡞⠀⠀⠀⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡿⡏⠀⠀⣀⠀⠀⠀⠈⠉⣿⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢰⠃⣷⠀⠀⠈⠑⣄⠀⠀⠀⠙⣇⣠⡖⠀⠀⢨⡯⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡇⠀⠸⡄⠀⠀⠀⢸⠦⠤⣀⣀⠘⠁⠉⣲⣄⡜⠁⠈⠙⡦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣾⠀⠀⠀⢳⠀⠀⠀⢀⣇⠴⠁⢈⣉⠿⢭⣁⠉⠓⠒⠒⠋⠁⠉⠻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢰⠇⠀⠀⢀⠞⣇⠀⠀⢸⠀⠀⡔⠁⠀⠀⠀⠀⢱⡀⢀⠴⢦⣄⣤⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡞⠀⠀⡰⠫⣰⣹⡀⠀⣸⣤⠤⣵⠤⠤⠔⠒⠒⠚⢳⣖⡦⠝⣋⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢰⠃⢀⠜⠁⠀⠳⢔⣷⠀⢹⠤⠤⢿⡄⠀⠀⠀⠀⠀⠈⢻⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣀⣠⡇⠀⣿⡀⠀⠀⠀⠀⠈⡆⠈⣿⢍⢹⠃⠀⠀⠀⠀⠀⠀⠘⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡟⠁⠀⢱⡞⣹⠃⠀⠀⠀⢠⠖⠉⠲⡇⡼⡏⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⢀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣵⠤⢤⡪⠊⠁⠀⢰⣶⣞⠽⣄⣀⣠⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣼⣗⣦⢿⣟⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠉⠉⠉⠀⠀⠀⠀⠈⠙⠉⠉⢽⡯⢷⣋⣈⣙⠒⠦⠤⠤⠤⠤⠖⠛⠻⠽⠿⠽⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠤⣿⣿⣿⣷⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣻⣿⡷⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⬜⬜⬜⬜⬜⬜⬜🟫🟫🟫🟫🟫🟫🟫⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜🟫🟫🟥🟥🟥🟥🟥🟥🟥🟫🟫🟫⬜⬜⬜⬜⬜⬜⬜ ⬜🟫🟫🟫🟫🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟫⬜⬜⬜⬜⬜⬜ 🟫🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟫⬜⬜⬜⬜⬜ 🟫🟥🟥🟫🟫🟫🟫🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟫⬜⬜⬜⬜⬜ 🟫🟥🟥🟫🟫🟫🟫🟫🟫🟫🟫🟫🟫🟫🟫🟥🟫🟫🟥🟫⬜⬜⬜⬜ ⬜🟫🟫🟥🟥🟥🏻🏻🏻🏻🏻🏻🏻🏻🏻🟫🟥🟥🟥🟫⬜⬜⬜⬜ ⬜⬜⬜🟫🟥🟥🏻🟦⬜🏻🏻🏻⬜🟦🏻🟫🟥🟥🟥🟫⬜⬜⬜⬜ ⬜⬜⬜🟫🟥🟥🏻🟦🟦🏻🏻🏻🟦🟦🏻🟥🟥🟥🟥🟫⬜⬜⬜⬜ ⬜⬜⬜🟫🟥🟥🏻🏻🏻🏻🏻🏻🏻🏻🏻🟫🟥🟥🟫⬜⬜⬜⬜⬜ ⬜⬜🟫🟥🟥🟥🏻🏻🏻🏻🏻🏻🏻🏻🏻🟫🟥🟥🟥🟫⬜⬜⬜⬜ ⬜⬜🟫🟥🟥🟥🟥🏻🏻🏻🏻🏻🏻🏻🟫🟥🟥🟥🟥🟥🟫⬜⬜⬜ ⬜⬜🟫🟥🟥🟥🟥🟥🟥🏻🏻🏻🟫🟫🟥🟥🟥🟥🟥🟥🟫🟫⬜⬜ ⬜⬜🟫🟥🟥🟥🏻🏻🏻🏻🏻🏻🏻🏻🏻🟥🟥🟥🟥🟥🟥🟫⬜⬜ ⬜🟫🟥🟥🟥🏻🏻🟦🟦🏻🏻🟦🟦🏻🏻🏻🟥🟥🟥🟥🟥🟫⬜⬜ ⬜🟫🟥🟥🏻🏻🟦🟪🟪🟦🟦🟪🟪🟦🏻🏻🟥🟥🟥🟥🟥🟫⬜⬜ ⬜⬜🟫🟥🏻🏻🟦🟪🟪🟦🟦🟪🟪🟦🏻🏻🟥🟥🟥🟥🟫⬜⬜⬜ ⬜⬜⬜🟫🏻🏻🏻🟦🟦🏻🏻🟦🟦🏻🏻🏻🟥🟥🟫🟫⬜⬜⬜⬜ ⬜⬜⬜🏻🏻🏻🟫🟫🏻🏻🏻🏻🏻🟫🏻🏻🏻🟫⬜⬜⬜⬜⬜⬜ ⬜⬜⬜🏻🏻⬜🟩🟩🏻🏻🏻🏻🏻🟩🟩🏻🏻⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜🟩🟩🟩🟩🟩🏻🟩🟩🟩🟩🟩⬜⬜🟩🟩⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜🟩🟩🟩🟩🟩🟩🟩🟩🟩⬜⬜🟩🟩🟩🟩⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜🟩🟩🟩🟩🟩🟩🟩⬜⬜⬜🟩🟩🟩🟩🟩🟩⬜ ⬜⬜⬜⬜⬜⬜⬜🟩🟩🟩🟩🟩🟩🟩⬜⬜⬜🟩🟩🟩🟩🟩🟩🟩 ⬜⬜⬜⬜⬜⬜⬜🟩🟩🟩🟩🟩🟩🟩⬜⬜⬜⬜🟩🟩🟩🟩🟩🟩 ⬜⬜⬜⬜⬜⬜⬜🟩🟩🟩🟩🟩🟩🟩⬜🟩🟩🟩🟩🟩🟩🟩🟩🟩 ⬜⬜⬜⬜⬜⬜⬜🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬜🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬜🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬜⬜🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜🟩🟩🟩🟩🟩🟩🟩🟩⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜🟩🟩🟩⬜⬜⬜⬜⬜⬜⬜
⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢆⠈⢱⣄⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠺⡉⠙⠀⡰⠃⢠⢁⣦⠀⣠⢺⡏⢒⡤⢚⡟⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠹⡄⡡⠂⠳⡄⠿⠊⠈⠂⠓⠈⠈⠂⠯⠔⡗⢒⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠉⡇⠀⠈⣇⠃⠀⠈⠐⠢⡀⠲⢄⠀⠀⠐⢟⣀⡇⢀⡄⢰⠲⠀⠀⠀⠀ ⠀⠀⠀⠀⢰⠀⠀⠈⡧⡀⠀⠀⠀⠘⠶⠂⠉⠒⠂⠀⠀⣱⠟⣇⠂⢀⠉⠀⠉⡱ ⠀⠀⠀⠀⠀⢳⠀⢠⠓⢝⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢇⡰⠁⢱⠐⢀⠀⠢⡀ ⠀⠀⠀⠀⠀⠀⠳⡆⠀⠀⠑⠨⣑⠢⠤⠤⠤⠤⢔⣲⠉⠉⠀⢀⠜⠒⠈⠀⠒⠁ ⠀⠀⠀⠀⠀⠀⢸⢄⠀⠀⠀⠀⠀⠈⢩⣿⣯⠝⠁⢸⠀⣠⠔⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢹⢄⠑⠢⢄⡀⣀⡠⠾⠿⠟⠀⢀⣼⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⠀⠉⠐⠰⣀⡀⠈⡇⠀⠈⠉⣁⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⡌⠉⠉⠉⠉⠁⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⠒⠱⡀⠀⠀⠀⡇⠀⠀⠀⠀⡠⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⠃⠀⠀⠀⠉⠁⢈⠭⡁⠀⠀⠉⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠑⠒⠒⠒⠒⠋⠁⠀⠈⠑⠲⠤⠤⠤⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣾⣿⣿⡿⠟⠛⠛⠛⠛⠛⠻⠿⣿⣿⣿⣿⣿⣷⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣿⣿⣿⣿⣿⣶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣼⡿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢻⣿⡟⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⢿⣼⡟⢻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⠆⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢈⣻⣷⣾⣿⡇⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⢻⣿⣿⣿⡿⢋⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⠙⢿⣿⡇⠀⠀⠀⠈⢻⣿⣷⣶⣄⣠⠀⠀⠀⣀⣠⣾⣿⣿⡯⠉⠁⠀⠀⠀⢻⣿⣿⡿⠛⢿⡆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣟⠀⠘⢾⡿⠀⠀⠀⢀⣠⣤⣶⣿⣿⣿⠟⠀⠀⣿⣿⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀⢸⣿⣯⠀⣶⡆⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⠈⠀⣼⠃⠀⠀⠘⠋⠁⣈⣹⣿⣿⠏⠀⠀⠀⣿⣿⣏⠀⣈⣁⣈⡝⠻⠿⡆⠀⠰⣿⣏⠈⣿⢷⡟⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠰⡇⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢸⣽⣿⣆⠀⠀⠀⠀⠀⠀⠁⠀⢸⣿⣿⡆⣏⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢱⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢿⣿⡄⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⣿⣿⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⠀⠀⣸⡄⠀⠀⠀⠀⠀⢀⡞⠁⣤⣤⣀⣠⣤⣀⣄⣸⣿⣦⡀⠀⠀⠀⠀⠀⢸⣿⣄⠟⣼⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠷⠶⠻⡇⠀⠀⠀⠀⠀⠟⠀⠀⠀⠀⠉⠙⠿⠿⣿⠉⢀⡿⣷⡀⢸⣇⢰⠀⠸⣿⣡⡾⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠐⠛⠀⠀⠁⠀⠀⢰⡟⢷⢸⣿⢀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⣼⡿⠓⠶⠒⠛⠛⠉⠙⠛⠻⠻⠿⣿⡇⠀⢸⡟⠀⠀⣠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡇⠒⠀⠀⠀⠈⠀⠀⠀⠀⠀⣶⠶⠶⠶⠶⠀⢀⣿⠁⢠⡾⠁⠀⣰⣿⠉⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡷⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠿⠃⢀⣴⡟⢹⡄⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢁⡆⠀⠐⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠒⠀⠀⣠⣴⣿⡟⣰⡿⣡⡄⠈⢣⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⣠⡤⠖⠒⠋⠁⠀⠘⣷⠀⠀⠀⠙⠦⣄⣀⣀⣀⣀⣀⣤⣶⣿⣦⣤⣴⣶⣿⡿⢋⣼⠟⢁⣿⠁⣠⣤⡉⠀⠀⠀⠀⠀⠀ ⣠⠤⠔⠒⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠉⠻⣿⣿⣿⣯⣥⣤⣤⣶⣿⣿⡿⠋⣠⡿⠁⠀⠀⠁⠲⢈⣿⣿⣷⣤⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠤⡄⠀⠀⠀⠀⠉⡻⢿⣧⣿⣿⡟⢋⣤⡾⠋⠀⠀⠀⠀⠘⠛⢺⣿⣿⣿⣿⣿⣷⣤⣤ ⡀⠀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣈⣳⣦⣤⣤⣿⣿⣿⠟⢋⣡⣶⣿⠋⢀⠀⠀⠀⡀⠀⠀⢀⡌⠘⣿⣿⣿⣿⣿⣿⣿
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⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⡇⢀⢀⠍⠙⢿⡟⢿⣿⣿⣿⣿⣿⣿⣿⣿ ⠹⣿⣿⣿⣿⣿⣿⣿⠁⠈⢀⡤⢲⣾⣗⠲⣿⣿⣿⣿⣿⣿⣟⠻ ⡀⢙⣿⣿⣿⣿⣿⣿⢀⠰⠁⢰⣾⣿⣿⡇⢀⣿⣿⣿⣿⣿⣿⡄ ⣇⢀⢀⠙⠷⣍⠛⠛⢀⢀⢀⢀⠙⠋⠉⢀⢀⢸⣿⣿⣿⣿⣿⣷ ⡙⠆⢀⣀⠤⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢸⣿⣿⣿⣿⣿⣿ ⣷⣖⠋⠁⢀⢀⢀⢀⢀⢀⣀⣀⣄⢀⢀⢀⢀⢸⠏⣿⣿⣿⢿⣿ ⣿⣷⡀⢀⢀⢀⢀⢀⡒⠉⠉⢀⢀⢀⢀⢀⢀⢈⣴⣿⣿⡿⢀⡿ ⣿⣿⣷⣄⢀⢀⢀⢀⠐⠄⢀⢀⢀⠈⢀⣀⣴⣿⣿⣿⡿⠁⢀⣡ ⠻⣿⣿⣿⣿⣆⠢⣤⣄⢀⢀⣀⠠⢴⣾⣿⣿⡿⢋⠟⢡⣿⣿⣿ ⢀⠘⠿⣿⣿⣿⣦⣹⣿⣀⣀⣀⣀⠘⠛⠋⠁⡀⣄⣴⣿⣿⣿⣿ ⢀⢀⢀⠈⠛⣽⣿⣿⣿⣿⣿⣿⠁⢀⢀⢀⣡⣾⣿⣿⣿⡟⣹⣿ ⢀⢀⢀⢀⢰⣿⣿⣿⣿⣿⣿⣿⣦⣤⣶⣿⡿⢛⢿⡇⠟⠰⣿⣿ ⢀⢀⢀⢀⣿⣿⣿⡿⢉⣭⢭⠏⣿⡿⢸⡏⣼⣿⢴⡇⢸⣿⣶⣿ ⢀⢀⢀⢰⣿⣿⣿⢃⣶⣶⡏⠸⠟⣱⣿⣧⣛⣣⢾⣿⣿⣿⣿⣿ ⢀⢀⢀⣾⣿⣿⣿⣾⣿⣿⠟⢻⡿⡉⣷⣬⡛⣵⣿⣿⣿⣿⣿⣿ ⢀⢀⣸⣿⣿⣿⣿⣿⣿⡿⢰⠘⣰⣇⣿⣿⣰⣿⣿⣿⣿⣿⣿⣿ ⢀⢀⠘⢿⣿⣿⣿⣿⣿⡷⢺⣿⠟⣩⣭⣽⣇⠲⠶⣿⣿⣿⣿⣿ ⢀⠐⢀⣾⣿⣿⣿⣿⠟⢐⡈⣿⣷⣶⠎⣹⡟⠟⣛⣸⣿⣿⣿⣿ ⠠⢀⣼⣿⣿⣿⣿⣯⣼⣿⣷⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠄⠄⠄⣰⣿⠄⠄⠄⠄⠄⢠⠄⠄⢀⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄ ⠄⠄⢰⣿⠿⠄⡀⠄⠄⠄⠘⣷⡀⠄⠢⣄⠄⠄⠄⠄⠄⠄⠄⣠⠖⠁⠄⠄⠄⠄ ⠄⣤⢸⣿⣿⣆⠣⠄⠄⠄⠄⠸⣿⣦⡀⠙⢶⣦⣄⡀⠄⡠⠞⠁⢀⡴⠄⠄⠄⠄ ⢰⣿⣎⣿⣿⣿⣦⣀⠄⠄⠄⠄⠹⣿⣿⣦⢄⡙⠻⠿⠷⠶⠤⢐⣋⣀⠄⠄⠄⠄ ⢸⣿⠛⠛⠻⠿⢿⣿⣧⢤⣤⣄⣠⡘⣿⣿⣿⡟⠿⠛⠂⠈⠉⠛⢿⣿⠄⠄⠄⠄ ⠄⡇⢰⣿⣇⡀⠄⠄⣝⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⡄⠄⠈⠄⣷⢠⡆⠄⠄⠄⠄ ⢹⣿⣼⣿⣯⢁⣤⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣴⠶⣲⣵⠟⠄⠄⠄⠄⠸ ⠄⢿⣿⣿⣿⣷⣮⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣟⣡⡴⠄⠄⠄⠄⠁ ⠄⠰⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⡀⠄⠄⠄⠄ ⠄⠄⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣶⡞⠄⠄⠄⠄⠄ ⠄⠄⠐⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠄⠄⠄⠄⠄⠄ ⠄⠄⠄⠈⠻⣿⣿⣿⣿⣿⣿⣯⣿⣯⣿⣾⣿⣿⣿⣿⣿⡿⠋⠄⠄⠄⠄⠄⠄⠄ ⠄⠄⠄⠄⠄⠄⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣵⠄⠄⠄⠄⠄⠄⠄⠄⠄ ⠄⠄⠄⠄⠄⠄⠄⢀⣿⣯⣟⣿⣿⣿⡿⣟⣯⣷⣿⣿⡏⣤⠄⠄⠄⠄⠄⠄⠄⠄ ⠄⠄⠄⠄⠄⠄⠄⣞⢸⣿⣿⣿⣾⣷⣿⣿⣿⣿⣿⣿⣇⣿⡆⠄⠄⠄⠄⠄⠄⠄
⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⣀⡀⠀⠀ ⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡶⠶⠚⣱⣿⠁⠀⠀ ⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀ ⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⡀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢠⡇ ⠠⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠁⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷ ⠈⣿⣿⣿⣿⣿⣿⣿⢁⡀⠤⠤⠄⠤⠤⠐⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⣿⣿⣿⣿⢹⣿⡇⠀⠠⠒⠉⢯⣿⡉⠀⠀⣽⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏ ⣾⣿⣿⣿⣿⡜⣙⠂⠀⠈⠒⠀⠀⡭⠇⠀⠸⠣⠄⠀⠚⠹⣿⣿⣿⣿⣿⡿⠟⠀ ⣿⣿⣿⣿⣿⣷⣄⣠⡀⠀⠀⠀⠀⠀⠀⠀⠘⠄⠀⠀⠀⠀⢹⣿⣿⣿⣦⡀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠘⠒⠂⣊⣀⣀⠀⠀⣼⣿⣿⣿⣿⣷⡄⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⠡⡀⠀⠀⠀⠒⠚⠛⠛⠛⠋⣠⣾⣿⣿⣿⣿⣿⣿⣿⡄ ⣿⣿⣿⣿⣿⠿⠛⠋⠁⢃⠈⠂⢄⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⠟⠉⠀⠀⠀⠀⠀⠈⡄⠀⠀⠈⠒⠠⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣘⡀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠚⠉⠉⠉⠉⠉⠑⠒⠤⣄⣀⡀⠤⣤⡤⠼⠓⠶⡦⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⣼⠋⢧⣀⠀⠀⠘⡯⠏⢳⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⠬⠷⢤⣈⡙⠓⠒⠓⠒⠛⣀⡷⠈⠙⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠉⠛⢖⡚⠉⠉⠀⠘⢦⡀⠀⠀⠙⠢⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠑⡄⠀⠀⠀⠈⢦⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⠀⠐⢢⡤⠤⣄⣀⠤⢤⠴⠒⠉⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣄⠀⠀⠀⠘⡄⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⠀⢠⠋⠀⢠⡇⠈⠳⣄⢷⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⢦⠀⠀⠀⠸⡀⠀⠀⠀⠘⡆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⢠⠇⠀⢘⣿⣥⣀⣀⠈⠛⠀⠀⠀⠀⠀⠙⣄⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠈⢆⠀⠀⠀⢇⠀⠀⠀⠀⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⣸⠀⠀⠀⣟⡟⢻⣮⣧⠀⠀⠀⠀⠀⢀⡤⠼⢧⡀⠀⠀⠀⠀⠀⠙⢄⠀⠀⠘⡄⠀⠀⢸⡆⠀⠀⠀⡵⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⡼⣿⣾⣟⣿⡟⠀⠀⠀⠀⠀⠈⠓⠒⠚⠛⣄⠀⠀⠀⠀⠀⠈⠳⣄⠀⢻⠀⠀⢸⡇⠀⠀⠀⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⠞⠀⠹⠿⣿⠋⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣮⣵⣄⠀⠀⠀⠀⠀⠀⠑⢼⡇⠀⢸⠀⠀⠀⢠⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⢀⡠⠞⠉⠀⠀⠀⠀⠀⠀⢀⡾⠋⠀⣰⣚⣿⣯⣯⢙⣦⡀⠀⠀⠀⠀⠀⠙⠢⣼⠀⠀⠀⡼⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡴⢻⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡅⠀⢸⢹⣯⣿⣿⡟⠋⡇⠘⢢⡀⠀⠀⠀⠀⠀⠘⢦⡀⣸⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣰⡏⠀⢸⠀⡤⡌⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⠼⠾⠿⠟⠛⠀⠀⣧⠀⠀⠉⠢⡀⠀⠀⠀⠀⠀⠙⢧⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣯⠀⠀⢸⠀⡷⣬⡙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠙⢆⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⠲⡀⢸⢸⠀⠳⠬⣒⣝⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡬⡇⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⢾⠀⠳⢤⡠⠤⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠊⠁⠀⢱⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠘⡆⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠞⢁⣴⠖⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠸⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⡤⢤⣀⣀⣀⣀⡠⠤⠤⠤⠖⠒⠉⢰⠋⢰⠁⡎⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠹⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠸⡀⠘⢆⢇⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⢀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⢀⣽⡀⠀⠀⠀⠀⠀⠀⠀⠙⢲⣬⣉⠃⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣰⠃⢸⠁⠀⠀⠀⠀⠀⢀⡠⠖⠋⢀⣀⣹⠛⠒⠒⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠔⠚⢉⡇⢠⠃⠀⠀⠀⠀⡠⠚⠁⠀⢀⠔⠉⠀⠘⢆⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⠔⠉⠀⠀⠀⠀⣸⠀⢸⠀⠀⣠⠔⠋⠀⠀⢀⠔⠁⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⣿⢠⡈⠋⠉⣀⣀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⠀⠀⡀⠀⠀⠀⠀⢿⠸⣉⣉⠽⢋⡠⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⣀⠤⠚⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡏⠀⢠⠃⠀⠀⠀⠀⠈⠳⠴⠒⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡠⠤⠤⠒⢺⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⡠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⣠⠟⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⠴⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡗⠉⠀⠀⠀⠈⠓⢄⡀⠀⠀⠀⠀⠀ ⠀⡠⠚⠁⠀⠹⡄⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠙⢆⠀⠀⠀⠀ ⡞⠀⠀⠀⠀⠀⠹⡄⡠⢋⣀⠤⠤⠔⠒⠒⠒⠢⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠀⠀⠀ ⢇⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠀⠀⠀⠀⠀⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀ ⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢵⣠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⣀⠤⠖⠒⠚⠓⠒⠲⢿⣓⠒⢤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢌⡻⣍⠑⠒⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⡑⠄⠀⠀⠉⠻⢶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣧⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠀⠀⠀⠀⠱⣌⠻⡉⠉⠒⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⡦⣄⣀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⡀⠙⢦⠀⠀⠀⠀⠈⢆⠘⢆⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣸⠁⠁⠀⠉⠉⠉⠉⠉⠁⠀⠤⠦⢤⡀⠀⠈⠑⢦⢷⡀⢀⠀⠀⠈⢆⠈⢆⠀⠀⠈⣇⠀⠀⣀⣤⣴⣖⡾⢿⡿⠋ ⠀⠀⠀⠀⢀⡇⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠀⠀⠀⢸⠀⠱⡌⡄⠀⠀⠘⡆⠘⡆⠀⢀⡼⠖⢋⣿⣿⣯⢥⠴⠋⠀⠀ ⠀⠀⠀⠀⠈⣧⡞⠉⢧⠀⠀⠀⠀⢀⡠⠤⢤⡀⠀⠀⠀⠀⠀⡼⠀⠀⢹⡽⡄⠀⠀⢳⠀⢹⡴⢋⡠⠔⠉⠀⣀⠼⠋⠀⠀⠀⠀ ⠀⠀⢠⠴⠶⣿⣶⣶⡟⠀⠀⠀⢠⠏⠀⠀⠀⢹⡄⠀⠀⠀⢠⠇⠀⠀⠈⢷⠹⣄⣀⣸⡄⠸⡗⠉⢀⣀⠤⠊⠁⠀⠀⠀⠀⠀⠀ ⠀⣴⢿⠀⠀⠈⠻⢿⡀⠀⠀⢰⡏⢰⣾⣿⣆⡸⠁⠀⠀⠀⢸⠀⠀⠀⠀⠘⡆⢻⡟⢻⡇⠀⡏⢹⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡼⠁⠈⢣⡀⠀⠀⠀⠙⡆⠀⠘⢷⣸⣿⣿⣿⠃⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⢧⠀⢣⣸⠀⢸⢃⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢷⠀⠻⡀⠙⢄⡀⠀⣠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⢸⠀⠀⣟⠀⣸⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠸⡆⠀⠱⡄⠀⠉⠉⠁⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣄⣀⣀⠀⠀⢸⠀⠀⢸⣤⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢹⡀⠀⢻⠲⢄⣀⡀⣀⣀⣀⣸⣆⠀⠀⠀⠀⠀⠀⠀⠀⢈⣀⣀⠈⢳⠀⣼⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢳⡀⠘⡗⠘⠟⠛⢛⡿⠟⠉⠈⠃⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⢁⡼⢀⡇⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠻⣦⡈⠒⠒⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣤⣀⣀⣀⡤⠞⠁⡜⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠙⢮⣁⡀⠀⠀⠀⠀⢀⣀⣀⣀⡤⠴⢲⠟⠦⠤⢬⣤⠤⠒⠊⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢈⡽⢯⣉⡽⢻⠁⠀⠀⠀⠀⡞⠳⣄⠀⠀⠈⠉⠒⠒⠒⠒⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⢻⠀⠻⣄⣀⣠⢤⣾⡷⣄⠈⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⣿⠀⠀⠀⢈⡧⠤⢤⣄⡴⠋⠁⠀⠘⡆⠀⠈⠳⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢰⠋⢀⡇⠀⠀⢀⡾⠀⠀⢠⠏⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠈⠉⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣀⡾⠃⠀⣠⠞⣇⠀⢀⣾⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣽⠁⠀⠈⣀⣴⡿⣄⣸⠙⣆⠀⠀⠀⢰⡾⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡇⢀⡤⢊⡡⠊⠀⠀⢹⡆⠈⠀⠀⠀⢸⡇⠀⠀⠀⠀⣠⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠿⡷⠶⠋⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⢸⡋⠒⠒⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⣄⣠⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⠿⠟⠛⠉⠉⠉⠀⠀⠀⠀⠀⠉⠉⠉⠛⠻⠿⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⠿⠛⠉⢀⣠⣤⣶⣶⣿⣿⣿⣿⣿⣿⣟⣛⡛⠲⣶⣤⣄⡀⠉⠛⠿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠁⣠⣴⣾⣿⢿⣿⣿⡿⠛⢉⠉⢁⡔⠉⠉⢛⡷⠀⠈⣿⣿⣿⣷⣦⣄⠈⠙⢿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣴⡿⠋⢀⣴⣾⣿⣿⣿⣿⡷⢸⠋⠀⠀⠀⢠⡟⠀⠀⠘⢁⣠⡤⣴⣿⣿⡿⣿⣿⣿⣷⣦⡀⠙⢿⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣰⡿⠋⠀⣴⣿⣿⣿⣿⣿⣿⠟⢡⡇⠀⠀⡆⠀⣾⠀⠀⠆⠀⠀⢀⣀⣀⠈⠙⠛⢀⣿⣿⣿⣿⣿⣦⡀⠙⢿⣦⠀⠀⠀⠀⠀ ⠀⠀⠀⣼⡟⠁⢠⣾⣿⣿⡿⢿⣿⠏⡏⠀⠸⣇⠀⠀⢧⡀⠻⣄⠀⡆⢀⡔⠋⢁⡀⠈⠑⠒⠉⠻⣿⣿⢿⣿⣿⣷⡄⠈⢻⣷⡀⠀⠀⠀ ⠀⠀⣼⡟⠀⣰⣿⣿⡟⢻⢘⣸⣿⠀⠻⣄⡀⠙⠓⣶⣤⣭⣑⢮⢡⣧⣾⣄⡀⠀⠘⡆⠀⢀⠄⠀⣿⣧⡓⢙⢻⣿⣿⣆⠀⢻⣷⡀⠀⠀ ⠀⣸⡿⠀⢰⣿⣿⣿⡇⢟⣡⣾⣿⢷⣤⣈⣉⣭⡿⠋⠀⠀⠀⠉⠛⠁⠀⠀⠹⡀⢰⠓⠒⠋⠀⣠⣿⣷⣬⡻⢸⣿⣿⣿⡆⠀⢻⣧⠀⠀ ⢠⣿⠃⢀⣿⢋⠭⡙⠳⣛⣙⢻⣿⠀⠋⠉⠋⠇⠤⠤⢄⣀⠀⠀⠀⠀⠀⣀⡴⣇⠸⣦⡄⠀⠈⢹⣿⡿⣋⣙⠊⢋⠭⡝⣿⡀⠈⣿⡆⠀ ⣼⡟⠀⣸⣿⢸⣐⡂⠸⢄⡼⢸⣿⣷⡆⣀⢬⣤⣶⣶⣶⡌⠁⠀⠀⠀⠉⣡⣶⣾⣯⣁⢷⣄⠐⣿⣿⣇⢻⡐⠇⠈⣂⡟⣼⣇⠀⢹⣷⠀ ⣿⡇⠀⣿⣿⣎⢿⠀⡿⢋⣴⣿⣿⣿⡟⢏⢸⡈⢆⠿⡿⠛⡄⠀⠀⠀⡘⠻⢿⢇⠜⢸⠘⠇⢀⣿⣿⣿⣦⣍⢻⡀⡿⣡⣿⣿⠀⢸⣿⠀ ⣿⡇⠀⣿⡿⣛⠢⠀⢀⣭⣍⠻⣿⣿⣷⡈⠲⡇⠀⠉⠉⠁⠀⠀⠀⠀⠀⠉⠉⠁⠀⡼⠊⢠⣾⣿⣿⡟⣩⣭⡁⠀⢐⣛⠻⣿⠀⠈⣿⡇ ⣿⡇⠀⣿⢸⡛⣿⠀⣿⠁⣽⠂⣿⣿⣿⣿⣧⠹⣄⠀⠀⠀⠀⠒⠒⠂⠀⠀⠀⠀⡴⠃⠙⣿⣿⣿⣿⡀⢿⠀⣿⠀⣿⢋⡇⣿⠀⢸⣿⠃ ⢿⡇⠀⢻⣷⣵⣿⡇⢻⣷⣶⣾⣿⠿⢿⣿⣿⠀⠈⠢⣄⠀⠑⠶⣶⠶⠂⠀⣠⠞⠀⠀⢄⣿⡿⠿⢿⣿⣶⣾⡟⢰⣿⣷⣾⡿⠀⢸⣿⠀ ⢸⣿⠀⠸⣿⣿⣿⣷⢰⣝⡻⠏⠴⠟⣸⣿⣿⣧⣄⠀⠈⣷⣤⣀⠀⣀⣠⣾⠁⠀⠀⠀⠈⣿⣧⡘⠶⠙⢟⣫⡞⣸⣿⣿⣿⠇⠀⣾⡏⠀ ⠀⢿⣇⠀⢻⣿⠟⣛⢘⡻⠏⠰⣿⣿⣿⣿⣿⣿⣿⣿⣶⡿⠛⠉⠉⠉⠻⣿⡀⠀⠀⠀⠀⢼⣿⣿⣿⠷⠸⢛⡃⣛⡛⣿⡟⠀⣸⣿⠁⠀ ⠀⠘⣿⣆⠀⢻⣌⣩⣾⣿⣿⡘⢶⣌⢻⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⣸⣿⣿⠋⠀⠀⠀⢻⢡⡶⢃⣾⣿⣷⣬⣥⡞⠀⢠⣿⠇⠀⠀ ⠀⠀⠘⣿⣆⠀⠻⣿⣿⣿⣿⣿⣦⡤⠾⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⣴⡟⠙⡇⠀⠀⠀⠀⣼⣦⣴⣿⣿⣿⣿⣿⡟⠀⣠⣿⠏⠀⠀⠀ ⠀⠀⠀⠈⢿⣦⡀⠙⢿⣿⣿⣿⣿⣷⣶⣄⠀⠀⠀⠀⠀⠈⠉⠙⠲⢚⣿⠀⠀⠀⠀⠀⣠⣼⣿⣿⣿⣿⣿⣿⡿⠋⠀⣴⣿⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠻⣷⣄⠀⠙⢿⠉⠉⠉⠛⢿⣷⣄⠀⠀⠀⠀⠀⠀⢸⡟⠛⠃⠀⠀⠀⠀⣿⣿⠟⠋⠉⠀⠈⠋⠀⣠⣾⠟⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⡀⠀⠀⠀⠀⠀⠈⠻⣷⣤⣄⣀⣀⣀⣸⣇⠀⠀⠀⣀⣠⡾⠛⠁⠀⠀⠀⠀⢀⣠⣾⠿⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣦⣄⡀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠿⠿⣿⡂⠀⠀⠈⣿⡇⠀⠀⠀⢀⣠⣴⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣷⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠙⣷⡤⠶⠞⢻⡿⢿⣶⣾⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⠿⣷⣶⣶⣶⣶⣶⣿⣿⣶⠶⠛⠀⠀⠹⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠙⠷⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠳⠶⠶⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⢀⣤⣤⣄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄ ⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⣴⣤⣤⣤⣴⣾⣿⣿⣿⣿⡄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄ ⠄⠄⠄⠄⠄⠄⠄⠄⠠⠾⢿⣿⣿⠟⠋⠁⠤⣬⣽⣿⡇⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄ ⠄⠄⠄⠄⠄⠄⠄⠄⡄⠄⠄⢀⣽⣦⡎⠁⠒⠒⢻⣿⣿⣄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄ ⠄⠄⠄⠄⠄⠄⠄⢀⣧⡀⢀⣾⣿⣿⣧⣦⣴⣾⣿⣿⣿⣿⣧⠄⠄⣠⣴⣆⠄⠄⠄⠄ ⠄⠄⠄⠄⠄⠄⠄⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⡻⣿⣿⣿⣿⣧⢸⣿⣿⣿⠄⠄⠄⠄ ⠄⠄⠄⠄⠄⠄⠘⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⣿⣿⣿⣿⣝⣿⡟⠄⠄⠄⠄ ⠄⠄⠄⠄⠄⠄⠄⠸⣄⢺⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠄⠄⠄⠄⠄ ⠄⠄⠄⠄⠄⠄⠄⠄⢿⠄⡀⠄⣸⣿⡿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠄⠄⠄⠄⠄ ⠄⠄⠄⠄⠄⠄⠄⠄⠸⡆⠄⣀⣛⣫⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠄⠄⠄⠄⠄ ⠄⠄⠄⠄⠄⠄⠄⠄⠄⠇⠄⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠄⠄⠄⠄⠄ ⠄⠄⠄⠄⠄⠄⠄⠄⠄⠐⠄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠄⠄⠄⠄⠄ ⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠄⠄⠄⠄⠄ ⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠄⠄⠄⠄⠄ ⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠄⠄⠄⠄⠄ ⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠈⠿⠽⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠄⠄⠄⠄⠄⠄ ⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⢸⣿⣿⣿⡿⠟⠛⠉⠄⠄⠄⠄⠄⠄⠄⠄
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠠⠄⠤⠐⠚⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠢⠤⣀⠀⠀⠀ ⠀⠀⠀⠀⢀⠤⣖⣶⣭⣷⣼⣄⠁⠀⠀⠀⠀⠀⠀⢐⣫⣭⣴⣶⣦⢄⠀⠀⠀⠀ ⠀⠀⠀⣪⣿⣿⣿⠿⢿⣿⣿⠻⣄⠀⠀⠀⠀⠀⢀⣼⠿⠿⢿⣿⣿⣿⣧⡀⠀⠀ ⠀⠀⣩⣿⣿⡟⣿⣠⣼⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⣤⣼⣿⣿⠻⣿⣿⠀⠀ ⠀⢀⣿⣿⡟⠀⠹⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⠏⠀⢹⣿⡄⠀ ⠀⠈⢿⣿⡃⠀⠀⠀⠉⢁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⠈⠀⠀⠀⢰⠟⡇⠀ ⠀⠀⠀⠉⠗⠖⠀⠊⠉⠉⠁⠀⠀⠀⠀⠀⠀⠰⠀⠀⠈⠙⠛⠒⠀⠐⠆⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣒⣢⣤⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣝⠿⣿⣿⣿⣿⣿⠿⣻⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣈⡭⠭⣭⠴⠚⠁⠀⠀⠀⠀⠀⠀⠀
▕╮╭┻┻╮╭┻┻╮╭▕╮╲ ▕╯┃╭╮┃┃╭╮┃╰▕╯╭▏ ▕╭┻┻┻┛┗┻┻┛ ╰▏ ▕╰━━━┓┈┈┈╭╮▕╭╮▏ ▕╭╮╰┳┳┳┳╯╰╯▕╰╯▏ ▕╰╯┈┗┛┗┛┈╭╮▕╮┈▏
_ _ (_) | | _ ___ | | _____ _ __ | |/ _ \| |/ / _ \ '__| | | (_) | < __/ | | |\___/|_|\_\___|_| _/ | |__/
▒▒▒▒▒▒▒▒▒▒ 0% █▒▒▒▒▒▒▒▒▒ 10% ██▒▒▒▒▒▒▒▒ 20% ███▒▒▒▒▒▒▒ 30% ████▒▒▒▒▒▒ 40% █████▒▒▒▒▒ 50% ██████▒▒▒▒ 60% ███████▒▒▒ 70% ████████▒▒ 80% █████████▒ 90% ██████████ 100%
⢻⣕⢯⢿⣯⡷⣹⣿⣿⣦⠹⣿⡆⢿⣿⡄⡆⢿⣿⣷⣿⣇⣿⣿⣿⣿⣸⣿⣿⣿⣿⡟⣰⠟⠛⠻⢿⣴⣿⠏⣴⣿⣟⣾⠟⢀⣵⣿⣿⣿ ⢷⣝⢷⣱⣟⣿⠋⣌⢿⣿⣷⡹⣿⣬⣿⠿⠿⣛⣛⣉⣭⣭⣭⣭⣭⣭⣝⣛⡻⠿⢿⣴⡟⠀⠀⠀⢸⡿⢣⣾⣿⠟⠛⠙⠛⠛⢷⣿⣿⣿ ⠙⠻⣷⣏⣿⢣⠁⢻⣷⡙⡿⢟⣫⣥⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣬⡇⠀⠀⠀⣾⣵⣿⡟⠀⠀⣴⣶⣦⠀⠀⠙⣯⣵ ⣿⣿⣍⣿⢣⠉⠀⠶⣿⣷⠐⣿⣿⣿⡿⣿⣿⣿⣿⣿⣻⣿⣿⠿⢿⣛⣛⣭⣭⣭⣶⣶⡇⠀⠀⣸⣧⣭⣽⣇⠀⠀⢸⣿⣿⠁⠀⠀⣿⣿ ⡙⠿⣿⠇⠆⠀⢀⣾⣾⡝⠇⢿⣿⡿⣕⣪⣿⡿⢟⣛⣭⣵⣶⣿⣿⣿⣿⣿⡿⠿⠿⢻⡇⠀⢠⡟⠀⠀⠀⠈⡳⠶⣳⠞⠁⠀⠀⣰⣿⡿ ⣿⣷⡿⠀⠀⠀⢸⣿⣿⣿⢮⣿⣷⡿⢟⣫⣵⣾⣿⣿⣿⣿⠿⠟⠛⠉⠁⠀⠀⠀⠀⢸⡇⠀⣾⡀⠀⠀⠀⠀⡀⡼⠁⠀⣀⣴⡾⣟⡭⠖ ⠿⣿⡇⠀⠀⠀⣿⣿⡿⢏⡾⢟⣥⣶⣿⡯⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠤⠶⠂⠘⣴⠞⠂⠸⣯⢈⠄⡀⠎⡐⣸⠇⠀⣼⣵⡟⢻⣡⣴⣾ ⣬⣿⢰⣀⣀⣤⣾⠶⠞⣭⣾⣿⣿⣿⠟⠋⠁⠀⠀⢀⠀⠀⠀⠩⠁⠀⠞⣈⣷⠐⣯⠀⠀⠀⣽⠂⣾⣿⣦⣴⠛⠁⠘⣯⠻⣿⣿⣿⣿⣿ ⢾⡇⣾⣿⠟⢩⣾⣿⣿⠇⢬⠛⠋⠀⠀⠀⢠⣤⠄⠀⠀⠀⣿⡶⡤⠀⢀⠻⢿⠀⢸⠳⠶⠞⣷⡀⠛⠿⠿⣯⡀⠀⠀⡼⢷⡹⣿⣟⣛⣩ ⣿⢸⣿⠟⠀⠀⠨⣶⠷⠀⡈⠃⢀⡀⠠⠚⣿⣿⠁⡀⢠⠀⠨⠁⠄⠀⠨⠈⠂⠀⢸⡌⠀⡀⣿⣧⠀⠁⠀⢎⡛⠛⠛⠡⠀⢳⠹⣿⣿⣟ ⣿⠘⣡⣾⡀⡀⠀⣁⣀⣤⣑⠀⠈⠁⠈⠊⠂⠀⠀⣇⣿⠀⠀⣀⣀⣀⣤⣤⣤⣤⣼⣥⣤⣥⠿⢿⠆⠀⠁⠁⠈⠀⠀⠀⠀⠀⠃⢻⣿⣿ ⢣⣾⣿⡿⠋⢀⡘⠻⠟⠛⠁⠀⠀⣀⡤⣀⣤⣶⣶⣬⣙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣫⣾⣿⣿⣿⣿⣮⡻⣶⡆⠀⠀⢠⣇⠀⢸⣿⣿ ⣿⠿⢁⠀⠀⢸⠀⣀⡀⠠⢰⢰⣿⣟⣾⣿⣿⣿⣿⣿⡿⠷⡽⣿⣿⣿⣿⣿⣿⣿⡏⣼⣿⣿⣿⣿⣿⡟⠋⠙⢸⡇⠀⢰⢸⣿⠀⢸⡿⠾ ⠁⠀⢸⠀⠀⣸⠀⠃⠀⠀⣿⡎⣿⢸⣿⣿⣿⣿⣿⣟⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡇⢿⣿⣿⣿⣿⣿⣇⠀⠀⣠⡇⠀⠘⣇⢿⠀⢸⡿⣿ ⠀⠀⠸⡀⠀⣿⠓⡇⢘⠿⠹⡿⡸⡼⣿⣿⣿⣿⣿⣿⣶⣤⣖⣿⣿⣿⣿⣿⣿⣿⣿⡘⢿⣿⣿⣿⣿⣿⣿⣟⣼⣇⠀⠀⠈⠪⡠⣿⣿⣿ ⠀⠈⠀⢇⠀⢻⠀⡀⠈⢇⠀⠐⠱⡑⣌⡻⣿⣿⣿⣿⠿⣫⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣝⣛⣛⣛⣻⣵⣿⣿⣿⣶⠲⠂⣆⢦⣤⣉⣻ ⠁⠀⠀⠘⡄⢸⠀⠠⠀⡐⠘⢀⣀⣌⣌⣿⣷⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢸⡘⣿⣿⣿ ⠀⠀⠀⠀⠐⠘⡄⠀⠀⠠⠅⡈⠉⢩⠉⠉⣤⣙⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠈⡇⣿⠛⠿ ⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⡀⠀⠀⢡⠁⢌⢻⣿⣿⣿⣿⢏⣦⣭⣭⣮⣭⡁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⡇⢸⡷⢦ ⠀⢀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠁⢀⠀⠀⠂⠔⢡⠹⣿⣿⣿⢺⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⠿⢛⠁⠀⠀⠀⠀⠀⠀⡇⣼⣛⠷ ⢀⠄⠀⣼⣄⣀⣀⡀⠰⡄⠀⠀⠀⡠⠀⠀⣁⠡⠂⢻⣿⣿⣦⣍⡻⠿⠿⢟⣡⣿⡿⠿⠿⢛⣛⣭⣶⣾⠃⠀⠀⠀⠀⠀⠀⠀⡇⣿⢿⣿ ⠘⠀⢰⣿⣿⣿⣿⣿⣄⣿⡄⠀⠀⢃⠀⠀⠸⢤⠈⡀⢭⣩⣭⣭⣭⣉⠭⣶⢠⣶⢶⢄⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡶⢰⣿⣷⣎ ⣶⣤⣼⡿⣟⣽⣿⣿⣿⣿⣧⣤⣤⣤⡤⠀⣀⡁⠐⠀⢠⣙⠛⠛⠟⠛⠫⢦⠞⣩⣽⣮⡻⣿⣶⣮⣭⣛⣛⣛⢿⣿⣿⢋⣶⣶⣎⢿⣿⣿ ⣾⣛⢇⣫⣿⣿⢫⣶⣶⡝⣿⢟⣋⣥⣶⣿⣿⣿⣿⣿⣿⡟⢸⣿⣿⢟⣧⣬⢱⣮⣝⣿⣿⡸⣿⣿⣿⣿⣿⣿⡎⣛⠟⡨⢹⠻⣋⣾⣿⣯ ⠀⣱⣾⣿⣿⡿⡘⠿⠿⡣⠁⠿⢻⣿⣿⣿⣿⣿⣿⣿⠏⡀⢺⣿⢱⣿⣿⡟⣄⠻⣿⣷⡹⣧⠹⣿⣿⣿⣿⣿⡇⣿⠺⣥⡰⣵⣟⣮⠻⣿
., . _,'f----.._ |\ ,-'"//_\ | ,' |,_ ,--. / /,-. ,'`. (_ | 0 0|__ "`-. ,-._ʘ,--'_ `. _.,-` `"' __/ .,'` j,-' `-.__.,--'
⢰⡟⣡⡟⣱⣿⡿⠡⢛⣋⣥⣴⣌⢿⣿⣿⣿⣿⣷⣌⠻⢿⣿⣿⣿⣿⣿⣿ ⠏⢼⡿⣰⡿⠿⠡⠿⠿⢯⣉⠿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣦⣍⠻⢿⣿⣿⣿ ⣼⣷⢠⠀⠀⢠⣴⡖⠀⠀⠈⠻⣿⡿⣿⣿⣿⣿⣿⣛⣯⣝⣻⣿⣶⣿⣿⣿ ⣿⡇⣿⡷⠂⠈⡉⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣍⡤⣤⣤⣤⡀⠀⠉⠛⠿ ⣿⢸⣿⡅⣠⣬⣥⣤⣴⣴⣿⣿⢿⣿⣿⣿⣿⣿⣟⡭⡄⣀⣉⡀⠀⠀⠀⠀ ⡟⣿⣿⢰⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣶⣦⣈⠀⠀⠀⢀⣶ ⡧⣿⡇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣾⣿ ⡇⣿⠃⣿⣿⣿⣿⣿⠛⠛⢫⣿⣿⣻⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿ ⡇⣿⠘⡇⢻⣿⣿⣿⡆⠀⠀⠀⠀⠈⠉⠙⠻⠏⠛⠻⣿⣿⣿⣿⣿⣭⡾⢁ ⡇⣿⠀⠘⢿⣿⣿⣿⣧⢠⣤⠀⡤⢀⣠⣀⣀⠀⠀⣼⣿⣿⣿⣿⣿⠟⣁⠉ ⣧⢻⠀⡄⠀⠹⣿⣿⣿⡸⣿⣾⡆⣿⣿⣿⠿⣡⣾⣿⣿⣿⣿⡿⠋⠐⢡⣶ ⣿⡘⠈⣷⠀⠀⠈⠻⣿⣷⣎⠐⠿⢟⣋⣤⣾⣿⣿⣿⡿⠟⣩⠖⢠⡬⠈⠀ ⣿⣧⠁⢻⡇⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⠿⠟⠋⠁⢀⠈⢀⡴⠈⠁⠀⠀ ⠻⣿⣆⠘⣿⠀⠀⣀⡁⠀⠈⠙⠛⠋⠉⠀⠀⠀⠀⡀⠤⠚⠁⠄⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢀⣴⣄⣴⣗⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣯⣽⣿⣿⣿⣿⣿⡻⢻⣿⣾⣧⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣶⣾⣿⣿⣿⣿⣶⣾⣿⢿⣿⣷⣶⣿⣽⣿⣿⣿⡿⣾⣯⣶⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣟⠻⣝⢿⣿⣿⣿⣿⠿⣷⢿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣽⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡻⣿⣷⣾⣷⣽⣿⣿⢿⡿⡾⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⡿⢛⣻⡿⠿⠙⠉⠉⠉⠉⠀⠀⠀⠀⠈⠉⠁⠁⠀⠈⠈⠀⠁⠁⠈⢾⡟⢻⣿⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣬⣿⣷⣾⣿⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣾⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠰⢿⣿⣿⣏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⢫⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣍⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡽⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣯⡿⠀⠀⣀⣠⣄⣀⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⢠⣻⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⢿⣿⡇⠀⠚⠛⠉⠀⠈⠙⠛⠻⡍⠁⠀⠀⠀⠘⣿⠿⠟⠛⠛⠉⠉⠻⣇⠀⣿⢿⡿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣦⢻⡇⠀⠀⠀⣠⣾⣿⣭⣽⣗⠈⠆⠀⠀⠰⠿⣥⣶⣯⣿⣭⣷⡆⠀⠘⠂⢸⣞⡗⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣎⠀⠀⠀⠀⠉⠙⠋⢉⣩⠽⠀⠀⠀⠀⢸⠀⠉⢡⣼⡟⠛⠩⠃⠀⠀⠀⢸⣿⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡏⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢹⣸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠟⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣈⣹⡧⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠹⡄⢲⡄⠀⠀⠀⠀⠀⠀⢸⡆⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢻⠇⠀⠀⠀⣠⠴⠃⠀⣸⣦⣤⣀⡀⠀⣀⣽⡚⣁⣀⠠⣄⠀⠀⠀⢸⡿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡄⠀⠀⢸⣡⣴⣶⠊⠁⠹⠀⠉⣉⠛⠋⠉⠙⢦⣭⣷⣮⠇⢰⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢉⣿⡀⠀⠈⠉⠙⠻⠿⣷⢶⣶⣶⣾⣷⣿⠭⣿⠟⡿⠁⠉⠀⡾⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁⢀⡞⠈⣷⡀⠀⠀⠀⠀⠀⠈⡙⠲⠶⠶⠶⠖⠋⣡⠞⠀⠀⠀⠘⢀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡴⣿⠀⠀⢸⠃⠀⣇⠳⡄⡀⠀⠀⠀⠀⠈⠙⠛⠓⠓⠂⠀⠀⠀⠀⠀⠀⢀⣾⡟⠛⠿⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡴⠞⠋⢰⡏⠀⠀⢸⠀⠀⢻⠀⠹⣟⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢀⡼⣿⣇⠀⠀⠘⣟⠻⠷⣦⣄⡀⠀⠀⠀⠀⠀ ⢀⣤⠖⠉⠀⠀⠀⢸⡇⠀⠀⢸⡇⠀⠘⣧⠀⠈⠘⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠗⠋⠀⡿⢹⡀⠀⠀⢻⡄⠀⠀⠉⠛⠳⣶⣤⣄⠀ ⠈⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠈⢧⠀⠀⠈⢧⡀⠀⠈⠛⠶⣶⣶⣦⣤⣶⣶⡶⠞⠋⠀⠀⠀⣸⠃⢸⡇⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠈⠛⠃ ⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠸⡀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠈⣷⠀⠀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠙⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⢹⠀⠀⠀⠀⠹⡞⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠈⠓⢤⣀⠀⠀⢀⣀⣤⠶⠋⠁⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⡽⠾⠯⣭⣤⠤⠤⢤⣤⣄⠀⠀⢸⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠸⣄⣀⣠⣤⠶⠶⠒⠋⠻⣄⠀⠀⢶⣿⠃⠀⠀⠀⠀⠉⠻⣶⡏⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⠀⠀⠀⠈⠉⠀⠀⠹⢧⡀⠀⠀⠀⢈⡟⠒⠲⣯⠀⠀⠀⠀⠀⠀⣠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠻⠂⠀⠀⢛⠃⠀⠀⠙⠁⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢀⣤⣶⣶⣦⣄⠀⠀⠀⠀⠀⢀⣤⣶⣶⣤⣄⠀⠀ ⠀⣴⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣷⡄ ⢰⣿⣿⣿⣿⣿⣿⣿⣧⣤⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣷ ⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡍⣿⣿⣿⣿⣿⣿⣿⣿⠏ ⠀⠀⠉⠙⢩⣿⣿⣿⣿⣿⠸⠇⢿⣿⣿⣿⣯⠛⠉⠁⠀ ⠀⠀⠀⠀⢸⣿⣿⣿⡏⠹⠀⠁⠈⣿⣿⣿⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠸⣿⣿⠻⠃⠀⠀⠀⠀⠙⠻⣿⡿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠹⣿⠀⠀⠀⠀⠀⠀⠀⠐⡿⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
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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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