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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀
⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀ ⠀⠀⠀⣽⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣿⠀⠀⠀⠀ ⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀ ⠀⠀⠀⣿⠀⢰⣶⣶⣶⡆⠀⠀⠀⢰⣶⣶⣶⡆⠀⣿⠀⠀⠀⠀ ⠀⠀⠀⣿⠀⢸⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⠀⠀⠀⠀ ⠀⠀⠀⣿⠀⠈⠉⠉⠉⠁⣶⣶⣶⠈⠉⠉⠉⠁⠀⣿⠀⠀⠀⠀ ⠀⠀⠀⣼⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⠀⠀⠀⠀ ⠀⠀⠀⢹⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⠀⠀⠀⠀ ⠀⠀⠀⢸⠇⠀⠀⣸⠿⣏⣉⣉⣉⣹⡿⣇⡀⠀⢸⣛⡀⠀⠀⠀ ⠀⠀⠀⠈⢩⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢩⠍⠉⠉⠁⡇⠀⠀⠀ ⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⡇⠀⠀⠀ ⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⡇⠀⠀⠀ ⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⡇⠀⠀⠀ ⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⡇⠀⠀⠀ ⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⡇⠀⠀⠀ ⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⡁⠀⠀⠀ ⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⣦⣀⢀⠀ ⠀⠀⠀⢀⣼⠇⣤⣀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⣠⡴⢫⠇ ⣤⣖⠚⠉⠀⠀⠈⠉⢛⡲⢦⣤⣀⠀⠀⣸⠀⢀⡴⣾⠁⠀⢸⠀ ⣯⠉⠛⠶⣤⣀⡠⠾⠛⠁⠀⠀⠉⠛⢓⣩⠾⠋⠀⣿⠀⠀⢸⠀ ⣿⠀⠀⠀⠀⢯⠙⠳⢦⣤⣀⠀⢠⡴⠛⢱⣂⠀⠀⣿⠀⠀⢛⡄ ⡿⠀⠀⠀⠀⢸⠀⠀⠀⠀⠉⣛⠉⠀⠀⢸⣿⣿⣷⣶⢀⣴⠟⠀ ⣿⣶⣤⡀⠀⢸⠀⠀⠀⠀⠀⣿⠀⠀⠀⢿⡛⠿⣿⣿⠟⠁⠀⠀ ⠹⣿⣿⣿⣷⣮⣄⡀⠀⠀⠀⣿⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠉⠻⢿⣿⣿⣿⣷⣦⣄⡻⠀⠀⢀⡼⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣿⢀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
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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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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣤⡶⠁⣠⣴⣾⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣴⣿⣿⣴⣿⠿⠋⣁⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣰⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⣠⣾⣿⡿⠟⠋⠉⠀⣀⣀⣀⣨⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⣤⣤⣴⠂ ⠈⠉⠁⠀⠀⣀⣴⣾⣿⣿⡿⠟⠛⠉⠉⠉⠉⠉⠛⠻⠿⠿⠿⠿⠿⠿⠟⠋⠁⠀ ⠀⠀⠀⢀⣴⣿⣿⣿⡿⠁⠀⢀⣀⣤⣤⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣾⣿⣿⣿⡿⠁⢀⣴⣿⠋⠉⠉⠉⠉⠛⣿⣿⣶⣤⣤⣤⣤⣶⠖⠀⠀⠀ ⠀⠀⢸⣿⣿⣿⣿⡇⢀⣿⣿⣇⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀ ⠀⠀⠸⣿⣿⣿⣿⡇⠈⢿⣿⣿⠇⠀⠀⠀⠀⠀⢠⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢿⣿⣿⣿⣷⡀⠀⠉⠉⠀⠀⠀⠀⠀⢀⣾⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠙⢿⣿⣿⣷⣄⡀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣋⣠⡤⠄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀ ⢾⣿⣿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⣀⣴⣶⣿⣿⣿⣿⡇ ⠈⢿⣿⣿⣿⡛⠛⠈⠳⣄⠂⠀⠀⠀⠀⠀⣠⠞⠉⠛⢻⣿⣿⣿⡟⠀ ⠀⠸⣿⣿⣿⠥⠀⠀⠀⠈⢢⠀⠀⠀⠀⡜⠁⠀⠀⠀⢸⣿⣿⣿⠁⠀ ⠀⠀⣿⣿⣯⠭⠤⠀⠀⠀⠀⠃⣰⡄⠌⠀⠀⠀⠀⠨⢭⣿⣿⣿⠀⠀ ⠀⠀⠹⢿⣿⣈⣀⣀⠀⠀⠠⢴⣿⣿⡦⠀⠀⠀⣀⣈⣱⣿⠿⠃⠀⠀ ⠀⠀⠀⢠⣾⣿⡟⠁⠀⠀⠀⠀⣿⣏⠀⠀⠀⠀⠘⣻⣿⣶⠀⠀⠀⠀ ⠀⠀⠀⢸⣿⣿⢂⠀⠀⠀⠀⠘⢸⡇⠆⠀⠀⠀⢀⠰⣿⣿⠀⠀⠀⠀ ⠀⠀⠀⠈⣿⣷⣿⣆⡀⠀⠀⠁⠈⠀⠠⠀⠀⢀⣶⣿⣿⠏⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⣿⣿⣿⣷⣴⡜⠀⠀⠀⠀⣦⣤⣾⣿⣿⡏⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡿⠛⠿⠿⠛⠁⠀⠀⠀⠀⠘⠿⠿⠿⠿⢧⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀ ⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡴⣆⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⣼⣿⡗⠀⠀⠀⠀ ⠀⠀⠀⣠⠟⠀⠘⠷⠶⠶⠶⠾⠉⢳⡄⠀⠀⠀⠀⠀⣧⣿⠀⠀⠀⠀⠀ ⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣤⣤⣤⣤⣤⣿⢿⣄⠀⠀⠀⠀ ⠀⠀⡇⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠙⣷⡴⠶⣦ ⠀⠀⢱⡀⠀⠉⠉⠀⠀⠀⠀⠛⠃⠀⢠⡟⠂⠀⠀⢀⣀⣠⣤⠿⠞⠛⠋ ⣠⠾⠋⠙⣶⣤⣤⣤⣤⣤⣀⣠⣤⣾⣿⠴⠶⠚⠋⠉⠁⠀⠀⠀⠀⠀⠀ ⠛⠒⠛⠉⠉⠀⠀⠀⣴⠟⣣⡴⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣶⣦⠀⠀ ⠀⠀⣠⣤⣤⣄⣀⣾⣿⠟⠛⠻⢿⣷⠀ ⢰⣿⡿⠛⠙⠻⣿⣿⠁⠀⠀⠀⣶⢿⡇ ⢿⣿⣇⠀⠀⠀⠈⠏⠀⠀⠀ text here ⠀⠻⣿⣷⣦⣤⣀⠀⠀⠀⠀⣾⡿⠃⠀ ⠀⠀⠀⠀⠉⠉⠻⣿⣄⣴⣿⠟⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⡿⠟⠁⠀⠀⠀⠀
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⠀⣠⣶⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠹⢿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡏⢀⣀⡀⠀⠀⠀⠀⠀ ⠀⠀⣠⣤⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣟⣋⣼⣽⣾⣽⣦⡀⠀⠀⠀ ⢀⣼⣿⣷⣾⡽⡄⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⣿⣿⣿⡿⢿⣟⣽⣾⣿⣿⣦⠀⠀ ⣸⣿⣿⣾⣿⣿⣮⣤⣤⣤⣤⡀⠀⠀⠻⣿⡯⠽⠿⠛⠛⠉⠉⢿⣿⣿⣿⣿⣷⡀ ⣿⣿⢻⣿⣿⣿⣛⡿⠿⠟⠛⠁⣀⣠⣤⣤⣶⣶⣶⣶⣷⣶⠀⠀⠻⣿⣿⣿⣿⣇ ⢻⣿⡆⢿⣿⣿⣿⣿⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠀⣠⣶⣿⣿⣿⣿⡟ ⠈⠛⠃⠈⢿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠋⠉⠁⠀⠀⠀⠀⣠⣾⣿⣿⣿⠟⠋⠁⠀ ⠀⠀⠀⠀⠀⠙⢿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⠟⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣼⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠻⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢀⣠⠤⣶⣶⣤⣀⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠟⢦⣤⡄⠒⠋⠁⠀⠀⢻⡝⢧⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⢿⡏⠀⢀⡀⠀⠀⠀⠀⠀⢷⢸⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠘⠃⠀⠀⠀⠀⠀⣸⣸⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⠁⠉⢳⣴⢻⣽⣟⢦⠘⠃⠀⠀⠀⠀⠀⠀⠀⢀⡿⠃⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠋⠐⠉⠙⣿⢿⡇⠀⠀⣀⡀⠀⠀⢀⡴⣿⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢾⣄⠀⠀⠀⠀⠀⣰⠟⣽⠁⠀⣀⠓⠃⠀⢠⡞⣱⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣾⣿⣧⣦⣤⣤⡔⢋⠈⠁⠀⠀⠀⠀⠀⠀⠏⡼⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠀⠀⠀⢸⣻⣿⣿⣯⠟⠋⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣞⣳⠀⠀⠀⠀⠀⠙⠛⠉⠀⠀⠀⢠⡀⢠⡄⠀⢀⡾⡯⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣡⡾⢋⡼⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠉⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⣸⢸⢠⡆⠀⠀⠀⠀⠀⠰⠞⠁⠰⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⡽⠛⠘⢿⣥⣤⣤⣤⣀⠀⠤⠠⢤⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣠⠶⣿⡛⠁⠀⠉⠉⠉⠙⣿⣦⢠⣰⠚⣋⣉⣁⣀⣤⠤⣶⣫⡤⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⠓⠚⠿⠯⠭⠭⠭⠤⠼⠏⢹⢾⠿⠿⠟⠓⠒⠚⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⢸⣼⠀⠀⠀⠸⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡄⢠⡏⠀⠘⣿⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡞⣤⠏⠀⠀⠀⡿⠀⠀⠀⢴⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣾⡾⠃⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣸⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⡶⡦⢤⣀⡴⠋⣥⣍⡻⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⢿⠀⠠⣶⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⣥⣾⣷⣷⣶⡝⠂⠈⠀⠘⠓⢻⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⠘⣆⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢸⣸⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⣔⢸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠘⣆⠹⣆⠀⢠⡆⠀⢀⡀⠈⠁⠀⢸⠐⣿⣿⡀⠀⠀⠀⠀⢀⢠⣶⣟⠟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⠫⢘⢧⣼⣷⣂⡈⠉⠀⢀⣀⡌⢧⠻⣿⣷⡀⠀⠀⠀⠨⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⢉⣿⡟⠿⠥⣶⣟⣉⣁⣠⡤⠴⠖⠙⠟⣴⣀⠀⣽⡿⣳⠇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡴⠃⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠦⢤⣈⣨⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⬛⬛ ⬛⬛ ⬛⬛ ⬛⬛ ⬛⬛ ⬛⬛⬛⬛ ⬛ ⬛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠶⢦⣤⠶⠶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠁⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⣄⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠉⠛⠃⣠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠉⠙⢳⣄⢀⡾⠁⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠙⢿⡇⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⡀⠀⠀⠹⣦⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣄⠀⠀⠈⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠋⠛⢧⡀⠀⠀⠘⢷⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⠾⣧⡀⠀⠀⠹⣦⠀⠀⠈⢿⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⠀⠀⠈⠻⣄⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⡟⠉⠛⢷⣄⠀⠀⠈⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠀⠀⠉⠃⠀⠀⠀⠀⠀⠀⠀⣴⠏⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⣤⣤⣤⡤⠶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⣠⠤⠔⠒⠒⠒⠒⠒⠢⠤⢤⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⠴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⣄⠀⠀⠀(Ignore for z00phile rights, Like for YIPPEE) ⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠦⠀ ⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧ ⠀⡇⠀⠀⠀⢀⡶⠛⣿⣷⡄⠀⠀⠀⣰⣿⠛⢿⣷⡄⠀⠀⠘⣿⠀ ⠀⡇⠀⠀⠀⢸⣷⣶⣿⣿⡇⠀⠀⠀⢻⣿⣶⣿⣿⣿⠀⠀⠀⢸⠀ ⠀⡇⠀⠀⠀⠈⠛⠻⠿⠟⠁⠀⠀⠀⠈⠛⠻⠿⠛⠁⠀⠀⠀⢸⠀ ⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠁ ⠀⠀⠈⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣚⡁⠀⠀ ⠀⠀⠀⠀⠈⠙⠒⢢⡤⠤⠤⠤⠤⠤⠖⠒⠒⠋⠉⠉⠈⢙⢨⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹ ⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⣤⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⢠⣿⠀⠀⠀⢸⠀⠀⣿⠀⠀⠀⣸ ⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⢸⠘⡆⠀⠀⢸⣀⡰⠋⣆⠀⣠⠇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠤⠤⠼⠀⠘⠤⠴⠃⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⢶⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⣸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⠀⣰⡿⠁⠀⠀⠀⣀⣀⣤⣤⣤⣶⡶⠿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⢠⣿⠁⣠⣴⠾⠟⠋⠉⠉⠉⠀⠀⠀⣰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⣾⣷⡿⠋⠁⠀⠀⢀⣠⡄⠀⢀⣤⣾⣏⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⣿⡟⠀⠀⠀⢀⣴⠟⠉⠀⣠⣾⣿⠟⠋⠉⠉⠉⠉⠉⠛⠛⠛⠿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⣶⠿⠛⠛⠿⢿⣿⡇⠀⢹⡇⠀⠀⢠⡾⠁⠀⣠⡾⠋⠉⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣷⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⣴⡿⠋⠁⣀⣠⣤⣤⣤⣼⣷⡀⠈⣿⠀⢀⣾⠁⣀⣴⣿⣀⣀⡀⠀⠀⠻⣆⠀⠀⠀⠈⠉⣉⣷⠀⠀⠀⠀⠈⠻⣷⡄⠀⠀⠀ ⠘⠿⢿⣯⡁⠀⠀⠈⠉⠁⠀⠀⠀⠉⢻⣷⣄⣹⣧⣼⣿⠟⠋⠉⠉⠉⠉⠙⠻⠶⠄⠹⣧⡀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠘⢿⣆⠀⠀ ⠀⠀⠀⠙⠿⣶⣤⣄⣀⣀⣠⣤⣶⣶⡿⠋⠙⣿⠋⠉⠙⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⠀⠀⠀⠀⠀⠀⢤⡀⠀⠀⠀⠈⣿⣆⠀ ⠀⠀⠀⠀⠀⢈⣽⡿⠋⠉⠉⠀⣸⠏⠀⠀⣰⠏⠀⠀⠀⢸⣇⠀⢀⣠⡴⠞⠛⠛⠛⠛⢶⣤⣸⡇⠀⠀⠀⠀⢀⣴⠇⠀⠀⠀⠀⠘⣿⡀ ⠀⠀⠀⠀⢀⣾⠏⠀⠀⡄⠀⢀⡟⠀⠀⠀⣿⡀⠀⠀⠀⣸⡟⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇ ⠀⠀⠀⢠⣿⠋⠀⠀⡞⠀⡤⢸⡇⠀⠀⠀⠉⠀⠀⠀⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧ ⠀⠀⠀⣾⠇⠀⠀⠀⠙⠋⠀⠀⣿⠀⠀⠀⠀⠀⣠⡾⠃⠀⠀⠀⠀⠀⢰⣄⡶⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⠀⠀⢀⠀⠀⠀⠸⣿ ⠀⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣀⣴⠟⠋⢠⡀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠲⠚⠁⠀⠈⠷⠞⠀⠀⠀⠀⣿ ⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣾⠛⠁⠀⠀⠀⠓⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿ ⠀⠀⣿⡇⠀⠀⢀⡀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟ ⠀⠀⣿⡇⠀⠀⢸⡤⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠖⠀⠀⠀⠀⠀⣄⠀⣠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇ ⠀⠀⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⣄⡰⠀⠀⠀⣿⠃ ⠀⠀⠘⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⣠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⢠⣿⠀ ⠀⠀⠀⢻⣧⠀⠀⢧⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠀ ⠀⠀⠀⠈⢿⣆⠀⠈⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠚⠁⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⡄⢠⡄⠀⠀⣿⡇⠀ ⠀⠀⠀⠀⠈⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⡆⠀⠀⠀⠀⠀⠀⠀⠒⠚⠁⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⣿⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⠀⢦⣀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⠆⠀⠀⠀⠀⠀⠀⢨⣿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⠀⠀⠀⠀⠀⢀⡀⠀⢲⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⢀⡀⠀⠀⠀⢸⣿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣦⣤⡀⠀⠀⠙⠦⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⠀⠀⠦⡼⠇⠀⠀⠀⣾⡏⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢷⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠲⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡟⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠻⠿⠿⠿⠶⣶⣶⣶⣶⣤⣤⣄⣀⣀⠀⠀⠀⠀⠀⣀⣠⣴⡿⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠛⠛⠿⠟⠿⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀
🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩 🟩⬛⬛🟩🟩🟩🟩⬛⬛🟩 🟩⬛⬛🟩🟩🟩🟩⬛⬛🟩 🟩🟩🟩🟩⬛⬛🟩🟩🟩🟩 🟩🟩⬛⬛⬛⬛⬛⬛🟩🟩 🟩🟩⬛⬛🟩🟩⬛⬛🟩🟩 🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢤⠤⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⣀⣀⡜⠻⠿⢾⣷⠹⠀⠀⠀⠀⣀⣤⣤⡀⠀⠀⠀⠀ ⠀⠀⠀⢠⡎⠁⠀⠀⠃⠀⠀⠀⠉⠀⠀⠀⡠⠞⠛⠛⠻⢽⠀⠀⠀⠀ ⠀⠀⠀⠸⣷⡀⠀⢀⠀⢂⠀⡀⠀⠀⠀⠜⠀⠀⠀⠀⡀⠸⠀⠤⢄⠀ ⠀⠀⠀⠀⠙⣗⣄⠀⠠⡀⢢⠃⠀⢸⠌⠀⡠⢊⠀⠊⠀⠀⠀⠀⠀⡇ ⠀⠀⠀⣀⣀⣈⣲⣕⣦⡈⠢⣻⡀⡎⢀⣴⡢⠑⠂⠁⠀⠀⠀⠀⡠⠃ ⠀⣴⠿⠽⠏⠀⠀⠀⠈⠉⢒⣺⣷⣗⣉⣁⣀⣀⣀⠀⠠⠤⠐⠈⠀⠀ ⢸⠀⠀⠀⠀⠀⠀⠀⢀⠠⡖⠁⣿⢳⡬⡁⠒⠒⠤⢄⡀⠀⠀⠀⠀⠀ ⠈⢦⡀⠀⠀⡀⠄⠂⠁⠊⠀⢰⣯⡏⠎⢌⠑⠀⠀⠀⠈⠑⢄⠀⠀⠀ ⠀⠀⠉⡻⠀⠀⠀⠀⠀⠀⣲⡟⡟⠀⠀⠀⠢⡀⠀⠀⠀⠀⢸⠀⠀⠀ ⠀⠀⠀⢧⣤⡄⡀⠀⢀⡔⣽⠃⢧⡄⠀⠀⠀⠰⣀⠀⠀⣀⠞⠀⠀⠀ ⠀⠀⠀⠈⠳⠬⠥⠔⠋⡜⡌⠀⠘⣿⣦⣀⠀⡀⡇⠉⠉⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⠜⡰⠀⠀⠀⠈⠛⠯⠥⠒⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡠⠊⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣛⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⣿⣯⣿⣿⣿⣯⣽⣿⣛⡒⡶⠶⠤⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠟⠉⠛⠉⠉⠁⠉⠈⠉⠙⠉⠉⠉⠉⠀⠀⠉⠉⠑⠒⠲⠦⠤⣄⣀⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⡽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣯⣿⣤⣀⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⡞⣸⠃⠀⠀⠀⠀⠀⠀⣴⡟⠑⠒⠚⠡⠼⠧⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⡼⢡⡇⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⢹⠃⢠⠤⠤⢤⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠈⡽⣿⣿⣿⣿⠟ ⠀⠀⠀⠀⠀⠀⣰⢃⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢣⣿⣿⣿⡏⠀ ⠀⠀⠀⠀⠀⢠⠇⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⣿⣿⣿⣿⠁⠀ ⠀⠀⠀⠀⢀⠏⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⣸⣿⣿⣿⠇⠀⠀ ⠀⠀⠀⠀⡞⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⠏⠀⠀⠀ ⠀⠀⠀⣼⢡⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⣿⣿⣟⣿⡅⠀⠀⠀ ⠀⠀⢰⠃⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⡏⠀⠀⠀⠀ ⠀⢀⠏⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⣠⣤⣤⣼⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀ ⠀⡞⣰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡾⢿⣿⣿⣿⡿⢡⣿⣿⣿⣏⡭⠇⠀⠀⠀⠀⠀ ⣼⢁⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣾⣿⣾⣿⣋⣥⣾⣿⣿⣭⣾⢋⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀ ⣿⣿⣷⣦⣤⣤⣶⣦⣤⣤⣤⣤⣤⣴⣿⣿⣿⡿⣿⡿⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀ ⢹⣿⡟⠛⠻⠿⢿⣿⣿⣿⣿⣿⣛⠻⠿⠬⣥⣏⣡⠚⠽⢻⢿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀ ⠀⢻⣷⡀⠀⠀⠀⠠⣌⣉⠉⠛⠛⠻⣿⣶⣶⣤⣍⣉⣛⠒⠺⠷⢦⣘⣛⣿⣷⣟⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠙⠿⢷⣶⣤⣄⣀⠈⢉⣑⣲⣶⣬⣍⠙⢿⣿⣿⣿⠿⠷⣶⡶⣤⣤⣭⣤⣿⢿⣿⣿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠷⣶⣿⣭⣟⣻⡉⠓⢾⣻⣿⣿⠷⠒⠦⠀⠀⢨⣿⣿⣟⣿⣶⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠿⢿⡞⢿⣷⣄⣀⣠⣤⣾⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⠈⣿⣿⠛⠛⠯⠿⠿⠿⠿⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡁⢰⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⢡⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⢀⣀⠀⠀⠀ ⠀⣿⣁⢈⠉⠉⣉⣉⡧⠀⠀⣼⠋⠁⠀⠘⠢⡾⠋⠉⠉⢳⠀ ⠐⠛⢻⣯⠀⢠⠋⠉⠀⠀⢸⣷⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡇ ⠀⠀⢸⡿⠀⢸⠀⠀⠀⠀⠘⣿⡆⠀⠀⠀⠀⠀⠀⠀⢀⠜⠀ ⢴⣯⣉⣁⣀⡈⠒⠒⡀⠀⠀⠈⠻⣧⡀⠀⠀⠀⢀⡠⠊⠀⠀ ⠈⠉⠉⠉⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⠉⠢⡠⠒⠁⠀⠀⠀⠀ ⢰⣖⠒⡀⠀⢠⣴⠒⡂⢀⣀⣀⡀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠙⣦⠈⢄⡾⠃⡜⣴⠟⢉⢥⡈⢢⢶⣯⢀⠁⠀⢰⡯⠉⡇ ⠀⠀⠈⢿⡬⢁⠌⢠⡿⠁⠆⠈⡇⢸⣿⣇⢸⠀⠀⢸⡇⠀⡇ ⠀⠀⠀⢸⡯⢻⠀⢸⡇⠀⡀⢸⠇⢸⣿⠃⢈⠀⠀⣿⡀⠀⡇ ⠀⠀⠀⣾⠁⠘⠀⢸⣧⠀⠈⠁⢀⠎⣿⠀⢺⠀⣰⡿⠀⢠⠁ ⠀⠀⠀⠛⠒⠃⠀⠈⠛⠳⠶⠖⠋⠀⢿⣄⡀⠉⠁⠀⡠⠋⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣴⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⢛⣛⣩⣭⣴⣶⣾⣿⠏⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⠿⠿⠟⠛⠛⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣉⣉⠛⠻⠀⣿⣿⣿⡿⠟⣛⣋⣭⣥⣶⣶⣄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠔⠚⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⣶⣾⣿⣿⣿⣿⣿⣷⠀⢸⣿⣿⣿⠃⠟⣛⣋⣭⡭⢹⣿⣿⡆ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣶⣶⠀⠀⠀⢀⣀⣠⣤⣴⣶⣾⠇⠀⢀⣿⣿⣿⡟⠉⠁⠀⢈⣿⣿⣿⠇⢀⣿⣿⣿⣿⣿⣿⣿⠿⠿⣣⣿⣿⣿⣷ ⠀⠀⠀⠀⠀⣀⣀⣠⣤⣄⠀⠀⠀⠀⠀⣼⣿⣿⣿⠇⠀⣿⣿⣿⣿⠛⠛⠛⠉⠁⠀⠀⣼⣿⣿⣿⢀⣀⣀⣤⣾⣿⠿⠋⠀⣼⣿⣿⣿⠋⠁⣰⣶⣾⣿⣿⣿⣿⣿⡇ ⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣆⠀⠀⠀⢠⣿⣿⣿⡿⠀⢰⣿⣿⣿⠇⠀⢀⣀⣠⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⡏⠁⠀⠀⢠⣿⣿⣿⠇⠀⣠⣿⣿⣿⣿⣿⣿⣿⡟⠀ ⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⣾⣿⣿⣿⠃⠀⣾⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⣾⣿⣿⡟⠀⠈⢿⣿⣿⣿⣄⠀⠀⣾⣿⣿⡟⢀⣴⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀ ⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣧⣸⣿⣿⣿⡏⠀⢸⣿⣿⣿⠋⠁⠀⠀⠀⠀⠀⢸⣿⣿⣿⠁⠀⠀⠘⣿⣿⣿⣿⡿⢸⠿⠿⠟⣓⣸⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀ ⠀⠀⢠⣿⣿⣿⣿⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⠁⢀⣿⣿⣿⡟⠀⠀⢀⣀⣀⣤⢂⣿⣿⣿⣏⠀⠀⠀⠀⠈⠛⠉⠉⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀ ⠀⠀⣾⣿⣿⣿⠇⠀⠀⢻⣿⣿⣿⣿⣿⣿⠇⠀⣼⣿⣿⣿⣷⣿⣿⣿⣿⡿⠏⠘⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⣿⣿⣿⡟⠀⠀⠀⠀⠻⣿⣿⣿⣿⡿⠀⠠⠿⠿⠟⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠹⣿⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣾⣿⣿⣿⣿⣿⠿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣸⣿⣿⣿⡿⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣠⣤⣤⣶⣶⣾⣿⣿⣿⣿⣿⠿⠟⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⠿⠿⠿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠛⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⠀⢠⣿⡟⠀⣿⣿⣿⣿⣷⢰⣿⣿⣿⣿⣿⢰⣿⣿⣿⣷⣦⠀⠀⠀⢸⣿⡗⢾⣿⣿⣿⣿⣿⠀ ⠀⣿⡿⢠⣿⡏⠀⢀⣿⡇⠀⠀⠀⢸⣿⡇⠀⠀⠀⢠⣿⡇⠀⢹⣿⡇⠀⠀⢸⣿⡇⠀⠀⣽⣿⠀⠀⠀ ⢀⣿⣧⣿⡏⠀⠀⢸⣿⣧⣤⣤⠀⢸⣿⣧⣤⣤⡀⢸⣿⣇⠀⣼⣿⠁⠀⠀⢸⣿⡇⠀⠀⣿⣿⠀⠀⠀ ⢸⣿⣿⣿⣷⠀⠀⢸⣿⠛⠛⠛⠀⢸⣿⡟⠛⠛⠀⢸⣿⡿⠿⠿⠋⠀⠀⠀⢸⣿⠃⠀⠀⣿⣿⠀⠀⠀ ⢸⣿⡇⢹⣿⡆⠀⣼⣿⠀⠀⠀⠀⣸⣿⣧⣴⣾⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⣸⣿⠀⠀⢸⣿⣿⠀⠀⠀ ⣽⣿⡇⠀⢻⣿⡜⣿⣿⣿⣿⣿⠏⣽⡿⠛⠉⠁⠀⠀⠈⠙⠻⢿⣆⠀⠀⠀⣿⣿⠀⠀⢸⣿⣇⠀⠀⠀ ⡶⠚⠒⠒⠒⠚⠓⠒⠓⠚⠛⠛⢺⡟⠁⢐⠉⠀⠀⠀⠐⠒⠀⠺⣿⡒⠒⠒⠒⠒⠒⠒⠚⠒⠒⠒⡆⠀ ⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡷⠛⠻⢿⠀⠀⠀⠛⠛⠲⣆⣹⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠟⢿⠿⠃⠀⠠⣴⣷⣆⢀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀ ⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣟⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⠛⠛⣇⠀⠀⠤⢄⡠⠴⠀⠀⠀⣸⠻⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡆⠀⠀⠀⠀⠀⠀⠀⣟⡀⠙⠶⣤⠸⣤⣤⡤⢤⣤⢤⣤⣤⢠⣿⠀⠀⣼⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⢀⡴⠛⠁⠻⣷⣄⡈⠳⣷⣌⠻⠭⠭⠽⠋⣠⡾⠃⢠⣾⠃⠀⠉⠙⢦⡀⠀⠀⠀⠀⡄⠀ ⣷⠦⣄⡀⣰⠋⠀⠀⠀⠀⠀⢭⠻⣶⢌⡙⠶⣄⣀⣀⠴⢉⣀⡴⡿⠃⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⡇⠀ ⣿⣄⠀⠙⢧⣀⡀⠀⠀⠀⠀⠀⢣⡈⢳⡬⠷⠤⠿⠷⠯⠽⠋⠸⠃⠀⠀⠀⠀⣰⠶⠚⢳⡞⠉⢙⣷⠀ ⢿⠈⠳⣄⠐⠁⠉⠙⠒⢦⡀⠀⠈⢧⠠⡝⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⢀⣀⣴⠚⠋⣿⠀ ⢸⠀⢠⠈⠓⣆⠀⠀⢠⡀⢈⣦⣄⢸⠀⠹⡄⠀⠠⡄⠀⠀⠀⠀⠀⣠⡞⢉⣕⣲⠞⠉⠀⢸⠀⠀⢻⠀ ⢸⠀⣸⠀⠀⠸⡆⠀⠈⠻⣤⣤⣬⣿⣦⠀⢻⡀⠀⠹⡄⠀⠀⠀⢀⣿⡿⣦⢀⠴⢀⡏⠀⣿⠀⠀⢸⡇ ⠸⡇⡿⠀⠤⡴⣿⣟⠶⣄⠀⢳⠙⢦⡘⣇⠀⠃⠀⠀⠻⡄⠀⠀⡼⠉⣿⡏⢸⠀⣸⣇⣸⡃⡇⠀⢸⠁ ⠀⣧⡇⠀⠀⣸⠿⣿⣷⣼⣷⣜⢧⡀⢻⢸⠀⠀⠀⠀⠀⠀⠀⣼⡇⣼⢻⣿⣿⣿⣿⡿⠟⢳⣷⠀⢸⡆ ⠠⠿⢁⣴⡾⠅⠀⢙⠛⣿⣿⡟⢿⣝⣺⡏⢀⠀⡀⣀⡀⠀⢀⢹⢧⠏⣸⢂⠉⠉⠁⠀⡀⠠⠷⡤⢼⠇ ⠀⣴⣿⡿⣿⣷⣤⢹⣿⡇⢻⣿⣿⡏⠉⢁⣿⣿⡏⠹⣿⣿⣿⣿⣶⣤⢻⣿⡇⠀⠀⠀⣿⣿⣿⣿⣿⠁ ⠀⣿⣿⠀⠸⠿⠇⢸⣿⡇⢸⣿⣿⣿⠀⢸⣿⣿⡇⣼⣿⡇⠀⢸⣿⣿⢸⣿⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀ ⠀⠹⣿⣷⣄⠀⠀⢸⣿⠃⢸⣿⢽⣿⠀⣾⣯⣿⡇⢿⣿⣗⣀⣸⣿⠇⣾⣿⠀⠀⠀⠀⣿⣿⣤⣤⡄⠀ ⠀⠀⠈⠻⣿⣧⡄⢸⣿⠀⢸⣿⢸⣿⣶⣿⢿⣿⡇⢸⣿⡿⠿⠿⠋⠀⣿⣿⠀⠀⠀⠀⣿⡟⠛⠛⠃⠀ ⢰⣶⡖⠀⢹⣿⡇⣿⣿⠀⢸⣿⠸⣿⣿⡟⢻⣿⡁⢸⣿⡇⠀⠀⠀⠀⣿⣿⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀ ⠀⢿⣿⣶⣿⠟⠀⣿⣿⠀⢸⣿⠀⢸⣿⠇⢸⣿⠆⢸⣿⡇⠀⠀⠀⠀⣿⣿⣶⣶⡶⢺⣿⣷⣾⣷⠀⠀
🟩🟩🟩🟩🟩🟩🟩🟩 🟩🟩🟩🟩🟩🟩🟩🟩 🟩⬛⬛🟩🟩⬛⬛🟩 🟩⬛⬛🟩🟩⬛⬛🟩 🟩🟩🟩⬛⬛🟩🟩🟩 🟩🟩⬛⬛⬛⬛🟩🟩 🟩🟩⬛⬛⬛⬛🟩🟩 🟩🟩⬛🟩🟩⬛🟩🟩
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⣤⠟⡇⠀⠀⠀⠀⠀⠀⣠⣶⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣀⣼⣿⡃⠀⠀⢀⡾⡃⠀⣿⠀⠀⠀⠀⢠⡼⠋⢸⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠹⠟⠋⠁⣰⡟⣠⡇⠀⢻⡀⠀⢀⣴⠏⢀⡀⠘⣷⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣰⠟⣶⣿⡇⠠⠸⣧⣠⠟⠁⢀⣾⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀ ⠐⣧⡀⠀⠀⠀⣸⠏⢾⠿⣿⡇⠀⠀⠙⠃⠀⢠⣾⣿⡇⠀⣿⡆⠀⠀⢀⣀⠀⠀ ⠀⠀⠙⢦⣀⡾⢿⣶⣮⣅⡀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠅⠀⢹⣇⣠⠶⠛⠛⠀⠀ ⠀⢠⣄⣀⣹⡇⠘⣿⣿⣿⠿⠆⠀⠒⢻⣾⣶⣶⣤⡀⠀⣠⣼⡟⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣸⣧⠀⠀⠀⠀⠰⡆⠀⠀⠈⠿⣿⡿⡟⠻⠞⢯⣼⣇⣀⠀⠀⠀⠀⠀ ⠀⠠⡾⠛⠁⠘⠷⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠁⠀⠉⠛⠶⣤⣀⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⣿⣶⣶⣶⣶⣶⣶⠶⠛⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠙⠛⠛⠛⢻⣇⠀⠀⠀⠀⠉⠳⣦⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⡆⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⡇⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⢸⠇⠀⠀⠀⣷⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⣤⠴⠞⠛⠛⡆⠀⠀⠀⢸⣆⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣾⣋⢀⣀⣠⣴⣾⠇⠀⠀⣰⠟⠙⠶⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠉⠉⢁⡴⠋⠀⠀⣠⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣤⣤⡴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣴⠟⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢻⡆⠀⠙⣧⠀⠀⠀⠀⠀⠀⢀⣀⣠⡶⠖⠲⢶⣄⠀⠀⠀⠀⠀⠀⣀⣠⣤⣀⡀ ⠈⢿⡄⠀⠸⣇⢀⣤⣤⣤⡞⠋⠉⢻⡇⠀⠀⣤⢻⣆⠀⠀⣠⡴⠟⠉⠁⠀⠈⣿ ⠀⠀⢻⡄⠀⢹⣿⠁⠀⠘⣧⠀⠀⠸⣧⠀⠀⢹⢀⣻⣤⠾⠋⠀⠀⠀⣀⣤⡴⠟ ⠀⠀⠈⣿⡀⠀⢻⡆⠀⠀⣿⠀⠀⠀⣿⠀⠀⢸⠈⠉⠀⠀⠀⢀⣴⠟⠉⠀⠀⠀ ⠀⠀⠀⢸⣇⠀⠀⣷⠀⠀⢸⡆⠀⠀⢹⡆⠀⢸⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢿⡀⠀⠸⡇⠀⠈⣷⠀⠀⠸⣧⣀⣼⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠸⣇⠀⠀⢿⡀⠀⣹⣦⣄⣴⠏⠉⠁⠀⠀⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢿⡄⠀⠈⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⢷⣄⣠⣤⠀⠰⠶⣶⣤⣶⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢻⡏⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢠⣾⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣰⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣄⣀⣀⣤⣤⣶⣾⣿⣿⣿⡷ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀ ⣿⣿⣿⡇⠀⡾⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀ ⣿⣿⣿⣧⡀⠁⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⢹⠉⠙⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⠀⣀⣼⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠀⠤⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⠿⠋⢃⠈⠢⡁⠒⠄⡀⠈⠁⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⠟⠁⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠈⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
🟩🟩🟩🟩🟩🟩🟩🟩 🟩🟩🟩🟩🟩🟩🟩🟩 🟩⬛⬛🟩🟩⬛⬛🟩 🟩⬛⬛🟩🟩⬛⬛🟩 🟩🟩🟩⬛⬛🟩🟩🟩 🟩🟩⬛⬛⬛⬛🟩🟩 🟩🟩⬛⬛⬛⬛🟩🟩 🟩🟩⬛🟩🟩⬛🟩🟩
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⠢⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⠖⠋⠀⠀⠀⣀⣹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⢠⣶⡞⢁⣸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⢁⣠⠞⢻⡁⢻⣷⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⠤⢄⣘⣿⢬⣛⡷⢋⣈⣉⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢰⡇⠀⠀⠙⠿⠀⢀⠿⠋⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⡃⠀⢰⠀⠀⠀⡁⠀⡀⠀⠘⣆⠈⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⣼⡦⠠⠤⣈⡆⢃⡤⠒⠙⡆⠀⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⠇⠀⡇⢷⣄⣀⡠⠟⠛⠢⠤⠞⡟⠦⡀⠙⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡞⢀⠀⠀⠀⠳⡄⠀⠀⠠⡀⠀⠀⠘⠉⠙⠦⣀⠀⠉⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡇⠀⢠⠀⠀⠀⠈⠓⢄⠀⠁⠀⠀⠀⠒⠂⠀⣾⠋⠉⠒⠢⢍⣙⡒⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡇⠀⡜⠀⠀⠀⠀⠀⠀⠱⡀⢀⡀⠁⠀⢀⡼⡇⠀⠀⠀⠀⠀⣏⠙⠯⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡇⢠⠇⠀⠀⠀⠀⠀⠀⠀⢱⣀⣽⠶⠾⠛⠒⠛⠒⠒⠒⠤⠤⣸⡍⠀⠀⠉⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣀⣀⣀⠇⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣙⠢⣀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠉⠙⠛⠥⠰⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⠤⠤⠤⠤⠴⠒⠚⠉⠙⠢⣀⠀⠈⠑⠢⢄⡀⠈⠳⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠒⠒⠒⠚⠑⠢⢌⡓⠤⠤⠤⠤⣀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⠠⠤⣼⠇
⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⠞⠉⠀⡀⠄⡒⠈⠭⠭⠥⠈⠐⣚⣛⠛⠛⠛⡲⢦⣀⠀⠀⠀ ⠀⠀⠀⣰⠃⠀⠔⡨⡢⠑⠈⠉⠁⠉⠄⠀⠀⠀⡲⠀⠀⠐⢄⠀⠈⢷⠀⠀ ⠠⣤⣿⣛⡛⠛⣻⢿⣛⣟⡻⣿⣿⣿⣿⣿⣿⣿⣟⣿⣛⢿⣿⣿⣿⡟⢦⡀ ⡴⠛⢡⡶⠒⡖⠦⢭⣿⣮⣱⣎⣿⣿⡿⠏⠀⠙⡿⠷⠿⣾⢿⣿⢭⡞⡐⣷ ⡇⠀⢺⠠⢾⡟⠲⢤⣀⡀⠠⠤⠄⡖⢂⣀⠀⠀⠙⣦⣄⠉⠉⢰⡄⠠⢃⣿ ⠹⣎⡪⠀⠀⢷⡦⣄⣯⡉⠓⠲⣤⣵⣉⣀⡀⠶⠞⠁⣀⣨⣴⢿⣷⠈⣰⠃ ⠀⠈⢳⡀⠀⠀⠻⣌⡟⠛⠷⣶⣧⣄⣀⣹⣏⣉⣻⣉⣉⣧⣸⣷⣿⠀⣿⠀ ⠀⠀⠀⠳⣄⠀⠀⠈⠳⢤⡀⣸⠉⠉⠛⡿⠻⠿⡿⠿⣿⢿⡿⣿⡟⠀⣿⠀ ⠀⠀⠀⠀⠈⠳⣅⡪⢔⡠⢉⡛⠲⠦⠤⠧⣤⣤⣧⡴⠧⠾⠖⠛⠀⠀⣿⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣅⡒⠡⠶⠀⣠⡤⠤⠤⠤⠤⠤⠐⢁⠠⠀⢸⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣤⣄⣀⡀⠀⠉⠉⠉⠉⠀⢀⣠⠏⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠓⠒⠒⠒⠚⠉⠁⠀⠀
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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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