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⠀⠀⠀⠀⠀⢀⣤⣶⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣴⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣸⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣠⣾⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣽⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢰⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⣷⡀⣀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠈⢿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠹⣿⣿⣿⡟⠉⠉⠙⢿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢿⣿⣿⡀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣷⣄⣀⣠⣿⡿⠉⠙⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣿⠿⣧⡀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⠁⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠿⠿⠋⡀⠀⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⡀⠀⢀⣄⡈⠙⠻⠟⢁⣠⣈⠙⢁⣠⣶⣤⣾⣿⣦⣴⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⢷⣤⣾⣿⣿⣷⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣿⣿⣷⠀ ⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⣿⣿⣿⣿⣿⣿⠿⠟⠛⠛⠉⠉⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⠿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣧⠀⢀⣴⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⠀⣿⣿⡇⠈⣿⣿⣿⣿⣿⣿⣿⡀⢾⣿⣿⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣤⣿⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⡇⢨⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠾⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠻⠿⠿⠯⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠈⠉⠀⠀⠙⠋⠁⠈⠛⠋⠈⠛⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⬜⬜⬜⬜⬜⬛⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬛⬛⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬛🏻⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬛🏻⬛⬜⬜⬜⬜⬜⬛⬛⬜⬜⬜⬜⬜ ⬜⬜⬜⬛🏻🏻⬛⬜⬜⬛⬛⬛⬛⬛⬜⬜⬜⬜ ⬜⬜⬛🏻🏻🏻🏻⬛⬛🏻🏻🏻⬛⬛⬜⬜⬜⬜ ⬜⬛🏻🏻🏻🏻🏻🏻🏻🏻🏻⬛⬛⬛⬜⬜⬜⬜ ⬛🏻🏽🏽🏻🏻🏽🏽🏻🏻🟨⬛⬜⬛⬜⬛⬜⬜ ⬛🏻🏽🏽🏻🏻🏽🏽🏻🏻🏻⬛⬜⬜⬛🟫⬛⬜ ⬛🟥🏻🏻🏻🏻🏻🏻🟥🏻🏻🟨⬛⬜⬛🟫🟫⬛ ⬛🏻🏻🏽🏻🏽🏻🏽🏻🏻🟨🟨⬛⬛🟫🟫⬛⬜ ⬜⬛🏻🏻🏽🏻🏽🏻🏻🏻🟨⬛⬛⬛🟫⬛⬜⬜ ⬜⬜⬛🏻🏻🏻🏻🏻🟨🟨⬛⬜⬛🟫⬛⬜⬜⬜ ⬜⬜⬜⬛🏻⬛🏻⬛🟨🟨⬛⬜⬛🟫🟫⬛⬜⬜ ⬜⬜⬜⬛🏻⬛🏻⬛🟨⬛⬜⬜⬜⬛🟫🟫⬛⬜ ⬜⬜⬜⬛🏻🏻🏻🏻🏻🟨⬛⬛⬜⬛🟫⬛⬜⬜ ⬜⬜⬛🏻🏻🏻🏻🏻🏻🏻🟨⬛⬛🟫⬛⬜⬜⬜ ⬜⬜⬛🏻🏻🏻🏻🏻🏻🟨🟨⬛🟫⬛⬜⬜⬜⬜ ⬜⬛⬜⬛🏻⬛🏻⬛🟨⬛🟨🟨⬛⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬛⬜⬛⬜⬛⬜⬛⬜⬜⬜⬜⬜⬜⬜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡀⣶⢦⡀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣟⣁⣷⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠠⠀⡄⢀⣿⢿⣦⡄⡲⣍⣦⣠⢄⡀⠀⠀⠀⠀⠀⠄⠀⠄⣤⣀⣰⣿⣿⣲⠃⠈⠙⣿⣄⣀⣠⡤⠒⠙⣾⣿⡁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠛⠀⢹⣶⣿⣿⠿⠗⠻⠿⣌⣿⣣⣀⣠⢄⡿⣚⣴⣿⣿⣿⣿⣿⣿⡇⠀⠀⣧⢸⣿⡿⠋⠀⡠⠀⣸⠟⢁⢄⠀⠀⢠ ⠀⠀⢀⣠⣾⣧⣤⣤⣿⣿⣿⣿⠶⠀⠀⠈⡎⠀⡞⠻⣿⣿⣿⣿⣿⡿⠙⠱⡿⠟⣿⠀⠀⠀⠙⣼⠏⠀⡠⢊⢔⡵⠁⠀⢸⢱⣀⣿⣿ ⠀⢠⣾⣿⠟⠛⣿⢟⡻⠿⣿⠿⠀⠀⢠⣤⡇⠀⠁⢇⢻⣿⣿⣿⣿⣿⡦⠛⣶⡿⠻⡀⠀⠀⢀⠛⠂⢔⢳⡿⠛⢗⣠⠘⢾⣿⣿⣏⣉ ⠀⠈⠙⠓⠒⠒⣇⠀⠘⠢⡀⠉⠒⢾⣿⣿⡇⢀⠆⠘⢸⣿⣿⡿⠏⣠⢥⣦⠏⠀⠀⢣⡤⡊⠎⠀⠀⠈⢯⣠⣾⣾⣿⣿⣿⡛⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⣨⣦⡀⠀⠈⠁⠁⠀⠉⠏⠉⠉⠀⠠⣸⠾⣼⣦⣾⣿⡟⢯⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⢰⣽⣿⣿⣿⣦⣀⠀⠀⠀⢀⣀⡀⠀⡀⣠⣌⣷⣿⡿⣾⢯⣾⣿⡟⣾⣇⠤⢄⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣏⡁ ⠀⠀⠀⠈⢙⣿⡿⡿⠿⣿⠃⠀⠀⠀⣿⣿⠇⢠⢈⠿⣿⣽⣿⣿⣿⣯⣿⣿⣁⠀⣅⠀⢨⠀⠀⠀⠀⠀⠀⠸⣿⠿⠿⠿⠉⠉⠉⠐⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⡇⠀⠀⢾⣿⠧⡠⠒⡻⠢⠊⣿⣿⣷⣿⣿⣟⣿⣿⣦⡬⠭⠥⠄⠀⠀⠀⠀⠀⠀⢳⣤⣤⣤⠀⠀⠀⠀⡴ ⠀⠐⠒⠒⢉⡭⠽⠲⡄⠀⠈⠢⣄⡀⠀⠀⣀⠤⣂⣠⠔⠃⠉⠛⠛⠻⣿⠉⠀⠀⠀⠀⠀⢀⡀⠀⠀⣀⣠⣤⣤⣝⣆⠀⠀⡴⠉⠁⠀ ⣴⠢⠤⠄⢸⣄⣀⡀⠉⠉⢣⠀⠀⡨⠛⠙⠫⢍⠹⡄⠀⠀⠀⠀⠀⠀⠘⢷⣤⣀⣴⣀⣴⠾⠄⣴⠾⠟⠛⠉⠉⠉⠉⢯⠉⣀⡴⠒⠒ ⠘⣅⠙⠛⢉⡠⠽⣿⠒⡆⠀⢩⠞⠀⠀⠀⡀⣀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⣿⣧⡀⡽⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣧⠠⠤⠃⠀ ⠀⣌⣦⠿⠷⠶⣿⣿⡤⠤⠴⠃⠀⠀⠀⠀⠁⠉⠀⠀⢸⣀⡀⠄⡀⠀⢀⣸⣻⠻⡟⠀⠀⠑⠀⠀⠘⠶⢶⣶⣾⣿⠿⠟⢹⠀⠧⠀⠀ ⠀⠻⣧⠮⢛⠅⡹⠿⢿⣶⢂⡀⣀⠀⡠⡀⢠⣴⠀⠀⣀⣧⣉⣑⣀⡐⣆⠉⠀⣺⠀⢀⠰⠀⣶⠀⠀⠀⠀⠀⠀⠀⢀⢠⣾⣽⣷⠀⠀ ⠀⠀⡻⣻⡎⣺⣔⠜⣤⠿⠻⡛⢷⠾⣿⣿⣯⣴⣾⠾⣿⡟⠛⠿⠳⡟⠃⢣⢰⠈⢦⡨⣏⢪⢟⣄⠀⠀⠀⠀⣄⣤⣽⣿⣾⣝⢿⠆⠀ ⠀⠀⠀⠀⠀⠈⠛⡇⡈⠁⠀⠘⠄⠀⢭⠟⠻⠏⢃⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠎⠙⠿⠟⣿⡏⠀⠉⠉⠑⠃⠻⢿⣿⣿⢿⠊⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠳⢽⣇⡠⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠄⣠⡏⠙⡈⠲⠀⢲⡒⠤⠄⣛⠿⣾⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⣸⣔⣀⡧⠌⠀⣀⢻⣿⣶⠁⠀⠈⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⢄⠐⠀⠀⠀⠀⠀⡀⠀⠐⠀⠀⠀⢰⢹⠛⠋⠀⣠⠶⢶⢿⢿⠛⠀⠀⠂⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣀⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡃ ⠀⠀⠀⠀⢀⣾⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈ ⠀⠀⠀⡠⢶⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠄ ⠀⠀⢸⠛⠉⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠄⠠⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡘⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠉⠀⠀⠀⣾⣿⣦⡀⠀⠀⠀⢴⠀ ⠀⠀⡇⠀⠀⠀⢡⠄⠀⠀⣀⣀⣀⣠⠊⠀⠀⠀⠀⡠⠎⠀⠀⠓⠚⠀⠀⠀⠀⠀ ⠀⠀⢃⠀⠀⠀⠀⠗⠚⠉⠉⠀⠈⠁⠀⠀⠀⢀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀ ⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣄⠲⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠀ ⠀⠀⠀⠃⠀⠀⢠⣤⡀⠀⠀⠀⠀⣿⣿⣿⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⢀⡜⠀⠀ ⠀⠀⠀⡆⠀⠀⣿⣿⡇⠀⠀⠀⠀⠈⠛⠉⣴⣆⢹⡄⠀⠀⠀⠀⠀⡐⠉⠀⠀⠀ ⠀⠀⠀⣇⢰⡧⣉⡉⠀⠀⢀⡀⠀⣀⣀⣠⣿⡷⢠⡇⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢻⠘⠃⠈⠻⢦⠞⠋⠙⠺⠋⠉⠉⠉⢡⠟⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠳⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⠀⠀⠁⠀⠀⠀⠀⠀⣀⣀⠀ ⠀⠀⠀⠀⠀⠀⠈⠁⢲⡄⠀⠀⠀⠀⠀⠀⠘⡆⢤⢃⠀⣀⣤⣴⣶⣿⣿⣿⣿⡇ ⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⠀⠀⠀⠀⠀⠀⢿⣾⢤⣷⣿⣿⣿⣿⣿⣿⣿⣿⠃ ⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⣾⠀⠀⣶⠀⠀⠀⢸⣷⣷⣿⣿⣿⠛⠉⠉⠉⠉⠁⠀ ⠀⠀⢀⣀⡰⠏⠀⠀⠀⠀⠉⠀⠈⠋⠀⠀⠀⠘⣿⣿⣿⠛⠋⠀⠀⠀⠀⠀⠀⠀ ⠰⣮⣉⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠉⠻⠥⠤⢤⣶⢄⠀⢀⣠⣄⠀⠀⢠⣶⣤⣄⠈⠑⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠈⠋⠁⠠⠁⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠟⠛⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠁⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⠄⠈⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠔⣡⣤⣠⣶⣿⡇⠀⠀⠀⠀⠀⠀⢢⠀⠠⠄⠐⠒⠲⣶⣤⠀⠀⠀ ⠀⠀⠀⠀⠀⣸⣿⣿⡛⠛⠛⠁⠀⠀⠀⣠⣶⣶⡄⠁⠀⠀⠀⠀⣾⣿⣿⣷⡀⠀ ⠀⠀⠀⠀⠀⢃⠉⢸⡇⠀⠀⠀⠀⠀⠀⣿⣿⣿⠇⠀⢀⡠⠐⠈⠀⠈⠙⢿⣿⣆ ⠀⠀⠀⠀⠀⠈⢆⠈⠛⠛⢻⣄⡀⠀⢀⣩⣏⠁⠀⠰⠁⠀⠀⠀⢀⡀⠀⠀⠉⠋ ⠀⠀⠀⠀⠀⠀⠀⠢⢀⠀⠈⠉⢻⣤⣿⣿⣿⠃⠠⠁⠀⣀⣴⣾⣿⣿⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠄⣀⡘⣛⣛⡁⠔⠁⣠⣾⣿⣿⣿⣿⣿⠇⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⣼⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠆⠀⠀⢀⡄⠀⢠⠀⠀⠈⠄⠀⠀⣹⣿⣟⠋⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠐⠀⠀⠀⠸⡇⠀⠸⠇⠀⠀⠈⡄⢾⣿⡿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢋⣭⣍⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⠋⠉⠙⠋⠄⠂⠙⠛⠒⠤⠺⠷⠂⠠⠄⠙⠿⠏⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣀⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣾⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⣾⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⠛⠉⢹⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠄⠠⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡘⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠉⠀⠀⠀⣾⣿⣦⡀⠀⠀⠀⠀⠀ ⠀⠀⡇⠀⠀⠀⢡⠄⠀⠀⣀⣀⣀⣠⠊⠀⠀⠀⠀⡠⠞⠛⠛⠛⠛⠀⠀⠀⠀⠀ ⠀⠀⢃⠀⠀⠀⠀⠗⠚⠉⠉⠀⠈⠁⠀⠀⠀⢀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣄⠲⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠃⠀⠀⢠⣤⡀⠀⠀⠀⠀⣿⣿⣿⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡆⠀⠀⣿⣿⡇⠀⠀⠀⠀⠈⠛⠉⣴⣆⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣇⢰⡧⣉⡉⠀⠀⢀⡀⠀⣀⣀⣠⣿⡷⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢻⠘⠃⠈⠻⢦⠞⠋⠙⠺⠋⠉⠉⠉⢡⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠳⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀ ⠀⠀⠀⠀⠀⠀⠈⠁⢲⡄⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⣀⣤⣴⣶⣿⣿⣿⣿⡇ ⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃ ⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⣾⠀⠀⣶⠀⠀⠀⢸⣦⣴⣿⣿⣿⠛⠉⠉⠉⠉⠁⠀ ⠀⠀⢀⣀⡰⠏⠀⠀⠀⠀⠉⠀⠈⠋⠀⠀⠀⠘⣿⣿⣿⠛⠋⠀⠀⠀⠀⠀⠀⠀ ⠰⣮⣉⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠉⠻⠥⠤⢤⣶⢄⠀⢀⣠⣄⠀⠀⢠⣶⣤⣄⠈⠑⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠈⠋⠁⠠⠁⠀⠈⠁⠀⠀⠀⠀⠀⠀
⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠙⢿⣿⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣰⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣶⣶⣶⡄ ⣠⣾⣿⣿⣿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣶⣿⣿⣿⡟⠛⠛⠁⠀ ⠘⠻⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀ ⠀⠀⣿⣿⣿⣿⣿⡟⠉⠛⠶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠛⠛⠻⣿⣿⣿⣿⡟⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⡏⠛⠛⠋⠀⠀⠀⠀⠀⠈⠛⣦⣄⣀⣀⣀⣀⡀⠀⠀⣀⡴⠟⠁⠀⠀⠀⢻⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠻⣆⠀⠀⠀⠀⠀⣠⣴⠾⠛⠋⠉⠉⠀⠈⠉⠉⠛⢿⣏⠀⠀⠀⠀⠀⠀⠀⠙⣻⠇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢹⣆⠀⢀⣴⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢻⣦⡾⢋⣴⡶⣶⡄⠀⠀⠀⠀⠀⣠⣶⣶⣿⣶⣤⣄⠀⠀⠀⠀⠀⢀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣸⡟⠀⣾⣿⣿⣿⡇⠀⠀⠀⠀⣼⣿⣿⣶⣿⣿⣿⣿⡆⠀⠀⠀⠀⣼⠃⠀⣀⣤⡴⣾⠶⣄⠀⠀⠀ ⠀⠀⠀⠀⢰⡟⠀⠀⠹⢿⣿⠿⠁⠀⠀⠀⠀⢿⣿⣿⠿⠟⣹⣿⡿⠁⠀⠀⠀⣼⣷⡶⠿⠋⠁⠀⣸⣧⠙⢧⠀⠀ ⠀⠀⠀⠀⣾⡇⢀⠁⠠⣶⡄⡠⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⠿⠛⠁⠀⠄⢠⣴⣏⡡⠔⠀⢀⠀⠚⠻⢿⣄⠘⡇⠀ ⠀⠀⠀⠀⢻⣇⠀⠀⠀⠘⢷⣤⡾⢧⣀⣀⢀⣀⣤⣶⠦⠀⠀⠀⣺⠷⠄⢹⣿⡩⠀⠐⠈⣀⡠⠄⠀⠀⢻⣦⡟⠀ ⠀⠀⠀⠀⠀⠙⠷⣤⡀⠀⠀⠉⠀⠀⠋⠉⠟⠋⠉⠐⠀⠀⠠⡪⡔⣐⣴⠟⠁⠀⠒⠊⠉⣀⣠⣤⡶⠟⠛⠉⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢶⣤⣀⡀⠀⠀⠀⠀⠀⠀⢀⣠⣥⣷⣾⠛⠁⢀⣀⣠⣴⠶⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣸⠟⠁⠀⠀⠈⠉⣻⡿⠛⠉⢹⡇⡏⠀⢸⣿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀⢸⡇⠅⡇⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⣴⣷⠀⠀⣴⣦⠀⠈⠻⣦⣰⠗⠀⢣⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣼⡃⢠⣀⠘⠛⠀⠀⠻⠛⠀⠀⠀⠘⣿⣠⡴⠾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡀⢀⣤⡾⠃⢈⣏⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠠⠶⠿⣷⣶⣶⣾⣯⡅⠀⠀⠀⠀⣠⣦⣤⣤⣄⣀⡀⠈⠻⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⠿⣦⡀⣠⡾⠻⢿⣿⣿⣿⣿⣿⣿⡟⠾⠿⠷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡼⠿⠛⠉⠁⠀⠀⠈⠻⠋⠀⠀⠀⠀⠉⠙⠛⠿⢿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
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