Ghibli Dot Art

Copy & Paste Ghibli Dot Art Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣦⣄⡀⢀⣀⣤⣤⣄ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣆⠀⠀⠀⠀⠀⠀⢀⣄⠙⢿⣿⣟⣿⣿⣿⣿⣿⠇ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡀⠀⠀⠀⠀⢀⣿⣿⡇⠀⠈⢹⡏⠉⠉⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⢸⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣷⣶⣶⣶⣷⣾⣿⣿⡀⠀⠀⢸⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠋⢉⠙⣿⣿⣿⣿⣿⠟⠛⢦⡀⣼⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠐⢒⣾⣿⣿⣷⡀⠛⢀⣿⣿⣿⣭⣿⣈⠛⣸⣧⣿⠤⠤⠀⠀⠀⠀ ⠀⠀⠀⠠⠤⠒⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠤⠤⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠁⠀⠀⠀⠀⠈⠙⠻⣆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⡿⠋⢀⣠⣄⠀⠀⠶⠿⠦⠀⠰⠶⠹⣧⠀⠀⠀⠀ ⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠚⠉⠉⠀⠀⠀⠀⠀⣀⡀⠀⢀⣇⠀⠀⠀⠀ ⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠠⠾⠛⠂⠀⠘⠉⠉⠀⠉⢹⠀⠀⠀⠀ ⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀ ⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀ ⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠀⠀⠀⠀⠀ ⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠃⠀⠀⠀⠀⠀ ⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⣀⠀⠀⠀⢀⣠⣴⣿⠏⠀⠀⠀⠀⠀⠀ ⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠉⠉⠉⠉⠉⠉⠙⠛⠿⠿⠿⠿⠟⠛⠿⠿⠿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠃⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡿⠛⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡟⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠏⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠁⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡿⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣇⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡆⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⢀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣦⡀⠀⠀⣿⣤⠤⠴⠶⠶⠒⠒⠒⠒⠒⠶⠶⠤⣤⣼⣿⣿⠇⠀⣶⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣽⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠀⣤⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠃⢀⠠⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠐⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠤⣤⣀⣀⣀⡀⠀⠀⣠⣿⣿⣿⣿⠊⠀⠰⢿⠿⠀⢢⠀⠀⠀⠠⠤⠤⣄⣀⣀⠀⠄⠀⠀⠀⢠⠋⢿⣿⠆⠈⢢⠀⠘⣧⡀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠉⠉⠙⠛⣿⣿⣿⣿⣿⠏⠢⣀⠀⠀⣀⡠⠊⠀⠀⠀⠀⠀⠉⠛⠛⠉⠁⠀⠀⠀⠀⠸⣄⠀⠀⠀⢀⠜⠀⣠⡼⢷⠒⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠉⠙⠛⠒⠒⠒⠲⠶⣶⣿⣿⣿⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠠⠤⠼⢷⡤⠤⠤⠤⠤⠤⠤⠤⠤⠀⠀ ⠀⠀⠀⠀⠀⢀⣀⣀⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠺⢷⡶⠶⠦⣤⣤⣄⣀⠀⠀⠀ ⠀⠒⠛⠛⠉⠉⢉⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⣀⣤⣶⠶⠖⠛⠋⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠓⠲⠦⢤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠀⠀⠀⠀⠀ ⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣯⡤⠖⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠳⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀ ⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⢀⣀⣠⣤⣀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠈⠛⢦⣄⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄⠀ ⣾⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⢠⣶⣿⠿⠿⠿⠿⢷⠀⠀⠀⠀⠾⠿⠿⠛⠉⠉⠙⠛⠿⣷⠀⠀⠀⣠⣶⡿⠿⠟⠿⣿⣷⡀⠀⠀⠙⢷⣄⠀⠀⡄⠀⠀⠀⠀⢻⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠈⠁⠀⠁⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⡄⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡇⠀⠀⠀⠀⠀⠀⢰⣿⣿⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣯⣤⣤⣤⣀⣀⣸⣿⣿⣿⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡏⢠⡦⠈⣿⣿⣿⣿⣿⣿⠟⠛⢻⣷⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣦⣤⣾⣿⣿⣿⣿⣿⣿⠀⠿⢀⣿⣷⠄⠀⠀⠀ ⢠⣄⠀⠀⠀⣼⣿⡆⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⡇⠀⠀⠀ ⢸⣿⣷⣄⢀⣿⣿⣿⠀⠀⠀⢀⣿⣿⣿⠿⠋⠉⠁⠀⠀⠈⠉⠉⠻⢿⣿⣿⣿⣿⣿⣷⠀⠀⠀ ⠀⣿⣿⠿⣿⣿⡿⣛⢷⠀⠀⢸⣿⣿⠏⢀⣤⣄⠀⣠⣤⡄⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣦⣄⠀ ⠀⣿⣇⣀⣽⣿⣷⣤⣾⣧⠀⠘⣿⠏⠀⠛⠋⠙⠀⠛⠙⠛⠀⠾⠿⣷⢸⣿⣿⣿⣿⣿⣿⣿⡇ ⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡿⣿⣿⣿⣿⣿⡇ ⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⠁ ⠀⢻⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡿⠋⠀⠀ ⠀⠀⠉⠛⠛⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠘⠻⢲⠦⠤⠤⠀⠀⠀⠀⣤⢴⡿⠟⠁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡆⠀⠀⢀⣶⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇⣀⣀⣼⣿⠆⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⡟⡝⣿⣿⣿⠿⢯⠀⠀⠀ ⣀⠀⢀⣆⠀⠀⣰⣿⣷⣶⣿⣿⣿⣭⣼⣇⠀⠀ ⢹⣷⣼⡿⡄⢰⣿⠟⣁⠀⣀⠈⠙⣿⣿⣿⣀⠀ ⢸⣦⣿⣷⣷⠈⡏⠈⠉⠈⠉⠈⠓⢿⣿⣿⣿⡇ ⢸⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠟⠀ ⠀⠉⠉⠉⠀⠀⠀⠈⠁⠀⠀⠀⠀⠈⠁⠀⠀⠀
pls note the ai inflicts emotional damage (ᵕ—ᴗ—)
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⠀⠀⠀⠀⣶⣄⠀⠀⠀⠀⠀⠀⢀⣶⡆⠀⠀⠀ ⠀⠀⠀⢸⣿⣿⡆⠀⠀⠀⠀⢀⣾⣿⡇⠀⠀⠀ ⠀⠀⠀⠘⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀ ⠀⠀⠀⠀⢿⣿⣿⣤⣤⣤⣤⣼⣿⡿⠃⠀⠀⠀ ⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀ ⠀⠀⢠⣿⡃⣦⢹⣿⣟⣙⣿⣿⠰⡀⣿⣇⠀⠀ ⠠⠬⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⡭⠤ ⠀⣼⣿⣿⣿⣿⠿⠛⠛⠛⠛⠻⢿⣿⣿⣿⣿⡀ ⢰⣿⣿⣿⠋⠀⠀⠀⢀⣀⠀⠀⠀⠉⢿⣿⣿⣧ ⢸⣿⣿⠃⠜⠛⠂⠀⠋⠉⠃⠐⠛⠻⠄⢿⣿⣿ ⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿ ⠘⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡏ ⠀⠈⠻⠿⣤⣀⡀⠀⠀⠀⠀⠀⣀⣠⠾⠟⠋⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣴⠛⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⢸⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡇⠀⡘⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⣿⣦⠀⠗⠒⠒⠒⠒⠒⠒⠼⢿⠀⡖⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣴⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠠⠤⣀⣠⣾⣿⠀⠸⠃⠀⠀⠀⢤⣤⠄⠀⢀⠲⠆⠀⠈⢄⡀⠠⠀⠀⠀⠀ ⠀⠒⠒⠂⠰⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠬⣦⠤⠤⠤⠀⠀ ⠀⠀⠒⠒⣾⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢉⡉⠁⠀⠀ ⠀⠀⣠⣾⣿⣿⡿⠃⣀⡤⠤⠒⠒⠒⠂⠀⠀⠐⠆⢀⡀⠀⠀⠀⠀⠀⠑⠄⠀⠀ ⠀⣼⣿⣿⣿⡿⠃⣉⣀⡀⠀⠀⢀⣤⣶⣤⡀⠀⠀⠀⣀⣉⠑⠦⡀⠀⠀⠈⠢⡀ ⠘⠛⠛⠛⠛⠀⠚⠋⠉⠙⠀⠀⠉⠉⠀⠈⠙⠀⠐⠛⠉⠙⠃⠀⠘⠂⠐⠀⠀⠃
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠛⠋⠉⠉⠉⠛⠛⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⢀⣠⡤⠶⠚⠛⠉⠉⠉⠉⠀⠀⠀⠀⠀⠉⠉⠉⠛⠛⠿⢶⣤⣀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⡿⠟⠋⠀⠀⠀⠀⠀⠀⠄⠒⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢦⣄⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣏⣀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣄⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⠄⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣦⣤⣤⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⠈⢻⣿⣿⣿⣿⣿⠋⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⡿⢿⣿⣿⣷⡄⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢻⣿⣿⣿⣇⠀⢀⢆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⢿⣿⣿⣿⡄⠹⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⢻⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⢸⣿⣿⣿⣷⠀⢻⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣿⡄⢸⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣸⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠈⠿⠿⠟⠛⠛⠛⠻⠇⠀⠀⠀⠀⣾⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣄⠀⠀⠚⣡⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⠃⢸⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⢠⣶⠶⣶⣄⠀⠀⠀⠀⠀⠀⠀⣤⣶⠶⣦⡈⢻⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⣿⣷⣤⣿⣿⠀⠀⠀⠀⠀⠀⢸⣿⣷⣤⣿⡇⠀⠙⢿⡿⠀⣾⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠘⠻⠿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠛⠁⠀⠀⢠⣤⡄⠛⢿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠁⠀⠘⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣶⣶⣶⣶⣶⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⡿⢁⣠⣄⣀⢻⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢰⣿⣿⡿⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣡⣤⣌⣿⣿⣿⡀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣠⣴⡇⠀⣿⣿⣟⣠⣴⣤⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠃⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣈⠙⠛⠿⠿⢿⣿⣿⣿⠿⠿⠿⠛⠋⣁⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣤⣤⣤⣤⣤⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
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⠀⠀⠀⠀⠀⠀⢀⣴⠾⠟⠻⢷⣦⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣰⡿⢁⠀⠀⠀⢠⠙⣷⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⣿⠇⠾⠀⠀⠀⠸⠃⢹⣧⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣼⣿⠀⣛⠂⠀⠀⠘⠛⢸⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⣿⡇⢰⠀⠀⠀⢰⡆⣾⣿⡄⠀⠀⠀⠀ ⠀⠀⠀⢸⣿⣿⣧⠘⠀⠀⠀⠀⠁⣿⣿⡇⠀⠀⠀⠀ ⠀⠀⠀⣾⣿⣿⣿⣆⠐⢛⡛⠂⣼⣿⣿⣧⠀⠀⠀⠀ ⠀⠀⢰⣿⣿⣿⣿⣿⣶⣤⣴⣾⣿⣿⣿⣿⣇⠀⠀⠀ ⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀ ⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀ ⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⠀⠀⠀⣀⣀⣀⠀⠀⠸⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣾⣿⡟⠁⡠⢄⠙⢿⣿⣿⣿⠿⠿⠿⣿⣿⣿⡿⠁⣠⠤⡈⢻⣿⣧⠀⠀⠀⠀⠀⠀⠀ ⣀⣀⣀⠀⠀⠀⣾⣿⣿⣇⠘⠿⠾⠁⣼⣿⣿⣿⣦⣤⣴⣿⣿⣿⣇⠀⠿⠶⠃⣸⣿⣿⣇⠀⠀⠀⣀⣀⡀ ⠀⠀⠈⠉⠉⢻⣿⣿⣿⣿⣶⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣴⣾⣿⣿⣿⣿⡏⠉⠉⠀⠀⠀ ⠀⠒⠒⠒⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡓⠒⠒⠒⠀ ⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀ ⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀ ⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀ ⠀⠀⣾⣿⣿⣿⣿⣿⡿⠁⠀⣀⡀⠀⠀⠀⠀⠀⣠⣤⣄⠀⠀⠀⠀⠀⢀⡀⠀⠘⢿⣿⣿⣿⣿⣿⣇⠀⠀ ⠀⢀⣿⣿⣿⣿⣿⡟⠀⢀⣾⡿⢿⣦⡀⠀⢠⡾⠛⠛⠛⢷⡄⠀⣠⣾⠿⣿⣷⡀⠈⣿⣿⣿⣿⣿⣿⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⠃⠀⠛⠃⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠙⠓⠀⢸⣿⣿⣿⣿⣿⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⠀⠀ ⠀⠘⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⠀⠀ ⠀⠀⢻⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡏⠀⠀ ⠀⠀⠈⢿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⡟⠀⠀⠀ ⠀⠀⠀⠈⠻⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⡿⠏⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⠶⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣴⠾⠿⠛⠛⠉⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⠿⠋⠁⠀⢀⡀⠤⠤⠐⠒⠒⠒⠲⠤⢄⣀⠀⠈⢿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣋⣁⣀⣀⣀⣈⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⠘⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⢻⣿⣿⡿⠘⣿⣿⣿⣿⣿⣷⣶⣶⣦⣤⣤⣤⣤⡤⣶⡜⢿⣿⣿⣿⣿ ⣿⣿⣿⡿⠀⢹⣿⣧⣴⣿⣿⣿⣿⣿⠃⠈⢿⣿⣿⣿⣿⠃⠀⢿⣿⡌⣿⣿⣿⣿ ⣿⣿⣿⠁⠀⡀⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠘⡿⠿⠿⠿⠀⠀⣼⣿⡇⢸⣿⣿⣿ ⣿⣿⣿⣦⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣀⣤⡀⠀⠀⠀⣀⣌⢻⣿⡇⣼⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠻⠾⠇⠀⠀⠀⠿⠾⠃⠙⡃⢿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⢀⣀⣀⣀⣀⣀⠀⠀⠀⠁⢀⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⣠⣾⣿⣿⢛⡛⣿⣿⣿⣦⠀⢠⣾⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⡀⢰⣿⣋⣙⣿⣿⣿⣿⣷⣶⣿⡇⢸⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⣼⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⡛⠿⢿⣿⣿⣿⠿⠟⣫⣾⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢀⣀⠤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣠⣼⣿⣿⣿⣾⣿⠀⠀⣷⡄⠀⣀⣀⣀⡀⣴⠇⠀⠀⠀⠀⠀ ⢠⣿⣿⣿⣿⢿⣿⣁⠀⠀⣨⣿⣉⣿⠯⠽⣯⣻⣦⡀⣀⣴⣾⡧ ⠈⡿⠿⠟⠋⣵⣽⣿⣷⣶⣿⣧⣄⣀⡀⣀⣀⣤⣾⣿⣿⣿⣿⡇ ⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⡿⠛⠉⢉⣁⠀⢀⣀⠉⠙⢿⣿⣿⠁ ⠀⠀⠀⠀⠀⠀⠈⢻⣿⡏⠀⠊⢁⣌⠀⠤⠤⠀⠠⡀⠀⢻⠃⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣷⣄⠀⠀⠀⠀⠀⠀⢀⣴⠏⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣦⣤⣤⣴⣾⠋⠁⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⣶⢶⣟⣛⣻⣭⣥⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⣱⡿⣫⣷⣿⣷⣶⣿⣽⣛⢿⡀⠀⠀⢸⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣠⣾⢟⣿⣶⣕⣽⡿⣿⣿⣿⣿⣿⡿⠂⠀⠀⠈⢿⣿⣿⡆⠀⣀⣀⣤⣤⣤⣤⣤⣀⣀⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀ ⢠⣿⣿⣾⣿⣿⣿⣮⡻⣾⣿⣿⣿⠟⠀⠀⠀⠀⠀⠈⢉⣿⡿⢛⡛⣿⣿⡿⠿⠿⢿⣿⡋⢝⢣⣄⠀⠀⠀⠀⡀⠀⣠⣴⡾⢜⡠ ⣿⢻⣿⡟⣿⣿⣿⣿⡿⣌⢹⣿⣯⣤⣀⠀⠐⠀⠀⣤⣿⣿⣷⣤⣴⡿⠿⠿⠟⠛⠿⠿⠷⢶⣾⣿⣷⣄⠁⢤⣴⣿⣿⣿⣿⣾⠊ ⣇⣿⣿⣿⣻⣿⣿⡿⠗⠻⠆⢹⣿⣿⣿⣿⣶⣄⣲⣿⣿⣭⡉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⣠⣾⣿⣶⣿⣿⣿⣿⣿⣿⣿⠀ ⠀⡿⠿⠿⠯⠟⠁⠀⠀⢻⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣄⣀⣀⣀⣀⣠⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠿⣿⣿⣿⣿⣿⣿⣿⠇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⣀⠀⠀⠀⣠⣶⣦⡀⠀⠀⣠⠶⣄⠀⠀⣀⡀⠙⢿⣿⣿⣿⡿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⡟⠁⠀⡴⠛⠓⠀⠐⠉⠀⠀⠀⣀⡀⠀⠀⠈⠀⠀⠉⠉⠀⠈⢿⣿⡿⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⡟⠀⠀⠀⠀⠀⠀⣴⠶⢤⠀⠠⠞⠛⠛⠣⠀⠀⠴⠳⣄⠀⢀⡀⠘⣿⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠁⠀⠼⠛⠓⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠂⣿⣧⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡏⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡟⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠏⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣷⣦⣄⣀⠀⠀⠀⠀⣀⣠⣴⣾⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣙⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣋⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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

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