Ginko Biloba Emojis & Text

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