Squirtle Emojis & Text

Copy & Paste Squirtle Emojis & Symbols

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