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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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⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀ ⢾⣿⣿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⣀⣴⣶⣿⣿⣿⣿⡇ ⠈⢿⣿⣿⣿⡛⠛⠈⠳⣄⠂⠀⠀⠀⠀⠀⣠⠞⠉⠛⢻⣿⣿⣿⡟⠀ ⠀⠸⣿⣿⣿⠥⠀⠀⠀⠈⢢⠀⠀⠀⠀⡜⠁⠀⠀⠀⢸⣿⣿⣿⠁⠀ ⠀⠀⣿⣿⣯⠭⠤⠀⠀⠀⠀⠃⣰⡄⠌⠀⠀⠀⠀⠨⢭⣿⣿⣿⠀⠀ ⠀⠀⠹⢿⣿⣈⣀⣀⠀⠀⠠⢴⣿⣿⡦⠀⠀⠀⣀⣈⣱⣿⠿⠃⠀⠀ ⠀⠀⠀⢠⣾⣿⡟⠁⠀⠀⠀⠀⣿⣏⠀⠀⠀⠀⠘⣻⣿⣶⠀⠀⠀⠀ ⠀⠀⠀⢸⣿⣿⢂⠀⠀⠀⠀⠘⢸⡇⠆⠀⠀⠀⢀⠰⣿⣿⠀⠀⠀⠀ ⠀⠀⠀⠈⣿⣷⣿⣆⡀⠀⠀⠁⠈⠀⠠⠀⠀⢀⣶⣿⣿⠏⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⣿⣿⣿⣷⣴⡜⠀⠀⠀⠀⣦⣤⣾⣿⣿⡏⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡿⠛⠿⠿⠛⠁⠀⠀⠀⠀⠘⠿⠿⠿⠿⢧⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀ ⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⢀⣠⠤⠔⠒⠒⠒⠒⠒⠢⠤⢤⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⠴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⣄⠀⠀⠀(Ignore for z00phile rights, Like for YIPPEE) ⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠦⠀ ⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧ ⠀⡇⠀⠀⠀⢀⡶⠛⣿⣷⡄⠀⠀⠀⣰⣿⠛⢿⣷⡄⠀⠀⠘⣿⠀ ⠀⡇⠀⠀⠀⢸⣷⣶⣿⣿⡇⠀⠀⠀⢻⣿⣶⣿⣿⣿⠀⠀⠀⢸⠀ ⠀⡇⠀⠀⠀⠈⠛⠻⠿⠟⠁⠀⠀⠀⠈⠛⠻⠿⠛⠁⠀⠀⠀⢸⠀ ⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠁ ⠀⠀⠈⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣚⡁⠀⠀ ⠀⠀⠀⠀⠈⠙⠒⢢⡤⠤⠤⠤⠤⠤⠖⠒⠒⠋⠉⠉⠈⢙⢨⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹ ⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⣤⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⢠⣿⠀⠀⠀⢸⠀⠀⣿⠀⠀⠀⣸ ⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⢸⠘⡆⠀⠀⢸⣀⡰⠋⣆⠀⣠⠇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠤⠤⠼⠀⠘⠤⠴⠃⠀⠀⠀⠈⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣶⣦⠀⠀ ⠀⠀⣠⣤⣤⣄⣀⣾⣿⠟⠛⠻⢿⣷⠀ ⢰⣿⡿⠛⠙⠻⣿⣿⠁⠀⠀⠀⣶⢿⡇ ⢿⣿⣇⠀⠀⠀⠈⠏⠀⠀⠀ text here ⠀⠻⣿⣷⣦⣤⣀⠀⠀⠀⠀⣾⡿⠃⠀ ⠀⠀⠀⠀⠉⠉⠻⣿⣄⣴⣿⠟⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⡿⠟⠁⠀⠀⠀⠀

⠀⣠⣶⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠹⢿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡏⢀⣀⡀⠀⠀⠀⠀⠀ ⠀⠀⣠⣤⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣟⣋⣼⣽⣾⣽⣦⡀⠀⠀⠀ ⢀⣼⣿⣷⣾⡽⡄⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⣿⣿⣿⡿⢿⣟⣽⣾⣿⣿⣦⠀⠀ ⣸⣿⣿⣾⣿⣿⣮⣤⣤⣤⣤⡀⠀⠀⠻⣿⡯⠽⠿⠛⠛⠉⠉⢿⣿⣿⣿⣿⣷⡀ ⣿⣿⢻⣿⣿⣿⣛⡿⠿⠟⠛⠁⣀⣠⣤⣤⣶⣶⣶⣶⣷⣶⠀⠀⠻⣿⣿⣿⣿⣇ ⢻⣿⡆⢿⣿⣿⣿⣿⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠀⣠⣶⣿⣿⣿⣿⡟ ⠈⠛⠃⠈⢿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠋⠉⠁⠀⠀⠀⠀⣠⣾⣿⣿⣿⠟⠋⠁⠀ ⠀⠀⠀⠀⠀⠙⢿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⠟⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣼⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠻⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡴⣆⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⣼⣿⡗⠀⠀⠀⠀ ⠀⠀⠀⣠⠟⠀⠘⠷⠶⠶⠶⠾⠉⢳⡄⠀⠀⠀⠀⠀⣧⣿⠀⠀⠀⠀⠀ ⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣤⣤⣤⣤⣤⣿⢿⣄⠀⠀⠀⠀ ⠀⠀⡇⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠙⣷⡴⠶⣦ ⠀⠀⢱⡀⠀⠉⠉⠀⠀⠀⠀⠛⠃⠀⢠⡟⠂⠀⠀⢀⣀⣠⣤⠿⠞⠛⠋ ⣠⠾⠋⠙⣶⣤⣤⣤⣤⣤⣀⣠⣤⣾⣿⠴⠶⠚⠋⠉⠁⠀⠀⠀⠀⠀⠀ ⠛⠒⠛⠉⠉⠀⠀⠀⣴⠟⣣⡴⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢀⣠⠤⣶⣶⣤⣀⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠟⢦⣤⡄⠒⠋⠁⠀⠀⢻⡝⢧⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⢿⡏⠀⢀⡀⠀⠀⠀⠀⠀⢷⢸⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠘⠃⠀⠀⠀⠀⠀⣸⣸⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⠁⠉⢳⣴⢻⣽⣟⢦⠘⠃⠀⠀⠀⠀⠀⠀⠀⢀⡿⠃⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠋⠐⠉⠙⣿⢿⡇⠀⠀⣀⡀⠀⠀⢀⡴⣿⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢾⣄⠀⠀⠀⠀⠀⣰⠟⣽⠁⠀⣀⠓⠃⠀⢠⡞⣱⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣾⣿⣧⣦⣤⣤⡔⢋⠈⠁⠀⠀⠀⠀⠀⠀⠏⡼⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠀⠀⠀⢸⣻⣿⣿⣯⠟⠋⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣞⣳⠀⠀⠀⠀⠀⠙⠛⠉⠀⠀⠀⢠⡀⢠⡄⠀⢀⡾⡯⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣡⡾⢋⡼⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠉⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⣸⢸⢠⡆⠀⠀⠀⠀⠀⠰⠞⠁⠰⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⡽⠛⠘⢿⣥⣤⣤⣤⣀⠀⠤⠠⢤⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣠⠶⣿⡛⠁⠀⠉⠉⠉⠙⣿⣦⢠⣰⠚⣋⣉⣁⣀⣤⠤⣶⣫⡤⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⠓⠚⠿⠯⠭⠭⠭⠤⠼⠏⢹⢾⠿⠿⠟⠓⠒⠚⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⢸⣼⠀⠀⠀⠸⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡄⢠⡏⠀⠘⣿⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡞⣤⠏⠀⠀⠀⡿⠀⠀⠀⢴⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣾⡾⠃⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣸⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⡶⡦⢤⣀⡴⠋⣥⣍⡻⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⢿⠀⠠⣶⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⣥⣾⣷⣷⣶⡝⠂⠈⠀⠘⠓⢻⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⠘⣆⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢸⣸⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⣔⢸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠘⣆⠹⣆⠀⢠⡆⠀⢀⡀⠈⠁⠀⢸⠐⣿⣿⡀⠀⠀⠀⠀⢀⢠⣶⣟⠟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⠫⢘⢧⣼⣷⣂⡈⠉⠀⢀⣀⡌⢧⠻⣿⣷⡀⠀⠀⠀⠨⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⢉⣿⡟⠿⠥⣶⣟⣉⣁⣠⡤⠴⠖⠙⠟⣴⣀⠀⣽⡿⣳⠇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡴⠃⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠦⢤⣈⣨⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⢀⣀⠀⠀⠀ ⠀⣿⣁⢈⠉⠉⣉⣉⡧⠀⠀⣼⠋⠁⠀⠘⠢⡾⠋⠉⠉⢳⠀ ⠐⠛⢻⣯⠀⢠⠋⠉⠀⠀⢸⣷⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡇ ⠀⠀⢸⡿⠀⢸⠀⠀⠀⠀⠘⣿⡆⠀⠀⠀⠀⠀⠀⠀⢀⠜⠀ ⢴⣯⣉⣁⣀⡈⠒⠒⡀⠀⠀⠈⠻⣧⡀⠀⠀⠀⢀⡠⠊⠀⠀ ⠈⠉⠉⠉⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⠉⠢⡠⠒⠁⠀⠀⠀⠀ ⢰⣖⠒⡀⠀⢠⣴⠒⡂⢀⣀⣀⡀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠙⣦⠈⢄⡾⠃⡜⣴⠟⢉⢥⡈⢢⢶⣯⢀⠁⠀⢰⡯⠉⡇ ⠀⠀⠈⢿⡬⢁⠌⢠⡿⠁⠆⠈⡇⢸⣿⣇⢸⠀⠀⢸⡇⠀⡇ ⠀⠀⠀⢸⡯⢻⠀⢸⡇⠀⡀⢸⠇⢸⣿⠃⢈⠀⠀⣿⡀⠀⡇ ⠀⠀⠀⣾⠁⠘⠀⢸⣧⠀⠈⠁⢀⠎⣿⠀⢺⠀⣰⡿⠀⢠⠁ ⠀⠀⠀⠛⠒⠃⠀⠈⠛⠳⠶⠖⠋⠀⢿⣄⡀⠉⠁⠀⡠⠋⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⣤⠟⡇⠀⠀⠀⠀⠀⠀⣠⣶⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣀⣼⣿⡃⠀⠀⢀⡾⡃⠀⣿⠀⠀⠀⠀⢠⡼⠋⢸⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠹⠟⠋⠁⣰⡟⣠⡇⠀⢻⡀⠀⢀⣴⠏⢀⡀⠘⣷⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣰⠟⣶⣿⡇⠠⠸⣧⣠⠟⠁⢀⣾⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀ ⠐⣧⡀⠀⠀⠀⣸⠏⢾⠿⣿⡇⠀⠀⠙⠃⠀⢠⣾⣿⡇⠀⣿⡆⠀⠀⢀⣀⠀⠀ ⠀⠀⠙⢦⣀⡾⢿⣶⣮⣅⡀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠅⠀⢹⣇⣠⠶⠛⠛⠀⠀ ⠀⢠⣄⣀⣹⡇⠘⣿⣿⣿⠿⠆⠀⠒⢻⣾⣶⣶⣤⡀⠀⣠⣼⡟⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣸⣧⠀⠀⠀⠀⠰⡆⠀⠀⠈⠿⣿⡿⡟⠻⠞⢯⣼⣇⣀⠀⠀⠀⠀⠀ ⠀⠠⡾⠛⠁⠘⠷⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠁⠀⠉⠛⠶⣤⣀⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⣿⣶⣶⣶⣶⣶⣶⠶⠛⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠙⠛⠛⠛⢻⣇⠀⠀⠀⠀⠉⠳⣦⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⡆⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⡇⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⢸⠇⠀⠀⠀⣷⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⣤⠴⠞⠛⠛⡆⠀⠀⠀⢸⣆⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣾⣋⢀⣀⣠⣴⣾⠇⠀⠀⣰⠟⠙⠶⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠉⠉⢁⡴⠋⠀⠀⣠⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣤⣤⡴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⣀⣤⣄⠀⠀⠀⠀⠀ ⠀⠀⢀⣤⣤⣄⣀⠀⣀⣀⣤⣤⡞⠉⠉⢳⡟⠉⠀⠹⣇⠀⠀⠀⠀ ⠀⠀⣾⠁⠀⠀⠉⠉⠉⠉⠀⣼⠀⢸⣿⡟⠋⠳⣶⡚⠛⢷⠀⠀⠀ ⠀⠀⢿⣀⠀⠀⠀⠀⠀⠀⠀⠸⢦⣤⡽⢧⣀⣠⣿⡿⢀⡿⠀⠀⠀ ⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠶⠚⣧⠀⠀⠀ ⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠖⢻⠛⠉⠁ ⠤⠴⣷⠖⠀⠀⢰⣦⠀⠀⠀⠀⡀⠀⠀⠀⠸⠟⠀⠀⠐⣾⠒⠒⠀ ⠀⣠⠼⣖⠂⠀⠈⠁⠀⠀⠀⠻⠬⣇⡀⠀⠀⠀⠀⠀⣲⠷⢤⡄⠀ ⠀⠀⢀⡼⠿⣥⣀⣀⣀⣖⣛⠙⠓⠧⢯⣀⣀⣠⣴⠞⠁⠀⠀⠀⠀ ⠀⠀⠉⠀⢀⡟⠁⠀⢹⡦⠿⠤⠴⣆⠀⣸⡏⠀⠈⣷⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣨⣇⠀⠀⢸⣯⢔⡞⢝⡉⢻⣿⠀⠀⢀⣿⡀⠀⠀⠀⠀ ⠀⠀⠀⢰⠃⠈⠓⠒⣿⠰⠓⠫⡯⠱⣢⣨⠟⠚⠋⠈⢳⠀⠀⠀⠀ ⠀⠀⠀⢸⡀⠀⠀⠀⠸⣆⡈⢃⣩⣶⡟⠁⠀⠀⠀⠀⣸⠀⠀⠀⠀ ⠀⠀⠀⠈⢷⡀⠀⠀⢀⣼⠿⠿⠿⠶⣷⡀⠀⠀⢀⣴⠏⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠉⠛⠚⠋⠀⠀⠀⠀⠀⠀⠙⠓⠚⠋⠁⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠻⠟⢛⣛⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣳ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⣉⡄⠀⣀⡀⠨⣙⣏⣉⣽⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡿⣿⢿⣿⣿⣿⡿⣟⣿⣯⣿⣷⣿⢾⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣒⡛⢫⠤⣠⢤⣤⣤⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣻⣯⣿⢿⣿⢯⣿⣯⣿⣿⣻⣞⡷⣿⣽⣻⡽ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢮⣭⣉⡓⠺⠊⢉⠓⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡽⣿⣻⢿⡿⣯⢿⣷⢯⡷⣯⣟⠷⣯⡗⡿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⣩⣿⣿⢿⣷⣄⡙⢮⠭⡁⢠⣬⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣽⣯⢿⣽⡿⣾⣻⣽⣳⣞⣟⡧⣟⡽ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⡴⠹⢿⣿⣀⣿⣿⣯⣍⢛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣾⡿⣯⣿⡽⣟⡾⣵⢫⣾⡱⢯⡜ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⢀⣞⣰⣀⣾⡷⠘⣿⣿⣟⣩⠙⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣻⢷⣟⣿⢯⡷⣏⡟⣶⡹⢇⡞ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⣰⢯⣾⣿⣿⡿⠁⠀⠀⠼⢿⣿⠥⢤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣟⡾⣟⣯⢿⡼⣹⢶⡹⢣⠞ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣴⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠘⠺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⢿⡽⣯⣟⢾⡱⣏⠵⣋⠎ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢬⡙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣽⣳⢯⣏⡗⣎⠳⡌⠆ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣷⢻⡗⣮⡝⣬⢳⠉⡎ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡿⣯⢷⣫⢗⡭⢎⢧⡙ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣶⡆⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⣀⢛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣟⣯⣟⣧⡟⡼⣉⢆⠣ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠹⣿⢿⡟⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡂⠭⢊⠻⡹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣷⣻⣞⡽⣲⢍⡎⢇ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⢻⠆⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢡⠒⠐⢀⠀⠠⠐⡆⢯⡹⡹⢛⡯⢭⡹⣿⣿⣿⣿⣿⣿⣿⡿⣾⢯⣷⣻⣜⡳⢎⡜⠦ ⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠻⢷⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⡄⠠⢎⢦⡹⢄⡄⣌⣩⣝⠾⣡⢃⠡⠃⡘⢧⠿⣽⣻⣿⣿⣿⣿⣿⣽⣿⣟⣷⣻⡼⣝⢮⡙⡖ ⣿⣿⣿⣿⣿⣿⣿⠃⣾⣷⣄⣀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢉⣩⣁⣳⣶⣦⣤⣤⣈⣥⢛⡞⣶⣿⣜⣫⢝⣶⣫⢞⣡⣀⣒⣀⡴⣨⡽⣎⣿⣿⣿⣿⣿⣿⣿⣿⢾⣯⢷⣻⡜⣮⢱⢣ ⣿⣿⣿⣿⣿⣿⣿⡇⣿⢻⠇⠛⢧⠀⠀⠁⠀⠀⠀⠾⠛⣉⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣿⣯⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣯⣿⢾⣯⢷⣻⣼⢣⢧ ⣿⣿⣿⣿⣿⣿⣿⣿⡌⣿⠀⣶⣿⠃⠀⠂⠀⠀⢰⣶⡾⠟⠫⣈⢿⡿⠟⣨⣿⣿⣿⢿⡆⠀⠈⣿⣿⣿⣿⣿⡟⢹⣯⣿⡟⢻⣿⣿⣿⣿⣿⣿⣿⣿⡏⢸⣿⢯⣿⢯⡿⣟⡾⣏⣞ ⣿⣿⣿⣿⣿⣿⣿⣿⣷⠸⡀⢿⡃⠀⠀⠁⠀⠀⠀⠀⠀⠀⣀⣉⣛⠶⣿⣿⣿⣿⠟⣿⠃⠀⢠⣿⣿⡏⢿⣯⣭⠷⣭⣭⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣃⣿⣿⣯⣟⣯⡿⣽⣻⢞⡵ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠱⡈⠹⡄⠀⡁⠀⠀⠀⠀⠀⠈⠙⠋⣙⣹⣿⣿⡿⠋⠀⠀⠀⠀⢺⣿⣿⣿⣆⢻⣿⣻⣶⣷⣿⣿⣿⡿⣟⣿⣿⣿⣿⣿⣿⣿⣟⣾⢯⡿⣽⡷⣯⢿⣹ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⢲⡾⠀⡂⠀⠀⠀⠀⠀⠀⠀⠀⠜⡹⠟⠉⠀⣀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣞⡽⢿⣿⡿⢿⡟⢶⣡⣿⣿⣿⣿⣿⣿⣿⣳⣯⢿⣯⣟⣷⣻⣽⡳⣏ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⡀⣀⡆⡇⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⢀⣠⣾⣿⠀⠀⠀⠀⢠⣿⣿⣿⣿⡏⠱⠂⠄⣙⢣⣟⣮⣿⣿⣿⣿⣿⣿⣿⣟⣷⣻⣟⡾⣽⣞⡷⣯⡽⣳ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠏⠀⠀⠀⠀⢈⣿⣿⣿⣿⣍⠣⡉⠴⣌⢷⣾⣻⣿⣿⣿⣿⣿⣿⡿⣞⣯⢷⣯⡟⣷⣫⡽⢶⡻⣵ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⡑⢺⡿⢏⢀⣠⣀⠀⣦⣀⢻⣿⣿⣿⣿⣣⣝⡳⣎⣿⣽⣿⣿⣿⣿⣿⣿⣟⣿⡽⣯⣟⢶⡻⣵⢣⡟⣯⢳⢧ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠁⢰⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣟⢢⣏⣷⢿⣭⣻⢷⣿⣿⣿⣿⣽⣾⣳⣟⣷⣫⢯⡷⣭⢳⡝⣮⢛⡼ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠷⣞⡿⣎⡶⣿⣿⣿⣿⣿⣿⣞⡷⣟⣾⡳⣏⡷⣹⢎⡷⣙⢦⣋⠖ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣺⣽⢳⢏⣾⣿⣿⣿⡍⣉⣛⣻⡿⢿⣾⣽⣝⣳⣝⢮⠳⣍⠶⣉⠞ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⣧⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⡿⠿⠾⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣞⢿⣺⣿⣿⣿⣿⣿⡉⢿⣿⡙⠲⣤⣈⡙⠻⠮⣽⣙⡌⢣⠱⣊ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⢸⣆⠠⡀⠀⠀⠀⠀⠘⠉⠁⠀⠀⢀⣠⣶⣿⢿⡛⣴⣿⣻⢻⡽⣷⢯⣞⣿⣿⣷⣿⣿⣿⣿⣿⣿⣡⡄⠀⢢⠉⠱⣄⠀⠉⠈⠐⠃⠄ ⣿⣿⣿⣿⢿⣻⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⢀⠹⣄⠙⣄⡀⠀⠀⠜⢢⠳⣾⣿⣿⣿⣿⣿⣷⣯⡷⢭⡷⣯⢿⣯⣿⢾⣯⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆⠀⠀⠉⠢⠈⢦⡀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⢱⡙⢧⡈⠻⣦⣄⠘⠀⠠⠀⠈⠁⠀⠀⠀⠀⠀⢌⢧⡻⡽⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣷⡄⠀⠀⠃⠈⣷⡀⠀⠀⠀ ⣿⣿⣧⣿⣿⣧⣿⠟⠀⠀⠀⣠⠀⠀⢀⣠⠀⠀⢿⠛⠻⢤⡘⠻⣤⡀⠀⠀⠀⠀⢀⣀⣠⣤⡼⣼⢧⣿⣻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⣿⡄⠀⠀⢀⠸⡇⠀⠀⠀ ⣿⣷⡿⣿⣽⠟⠁⠀⣠⡏⢰⡇⠀⠀⢸⣿⠀⠀⠘⣧⠤⠄⠙⢶⣌⠛⢶⣤⣶⣶⣿⣾⣿⣯⣟⣯⣿⢷⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣳⢯⣿⡄⠘⠤⢂⠙⢦⡀⠀ ⣟⡾⣽⠟⠁⠀⠀⢠⡿⠀⣾⡇⠀⠀⠹⢿⣀⣤⡀⠙⢆⡰⣳⣦⣈⡛⣶⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣟⣿⣿⣿⣿⣿⣿⣷⢫⣞⢿⡃⠄⢂⠀⢣⢳⡀ ⣯⡟⠃⠀⡰⠀⠀⣿⠃⢸⣿⡇⢀⠀⡀⠀⠈⠻⢿⣷⣮⠵⣹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣻⣷⣿⣿⣟⡿⣷⣿⠿⣝⡷⣎⠲⣅⠀⠀⠈⠀⠡⢓ ⠋⠀⣀⠔⠁⠀⢀⡇⠀⣾⣿⡄⠈⣆⠘⡀⠀⠀⠀⠹⢿⣿⣿⣟⣯⣙⣌⣙⡻⢿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⣿⢯⣟⣿⣿⡿⣿⡽⣾⣽⣻⣿⡹⣌⢳⣍⡒⠈⠄⠀⠀⠀⠀⠈ ⠀⠀⠀⠠⣆⠀⢸⠀⢠⠿⣿⡇⠀⢸⣧⠑⢦⠀⠁⠀⠀⢈⠛⢿⣿⣽⣶⣯⣽⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣯⣿⣻⣞⡷⣿⢯⣟⣷⢳⣿⣯⡕⢎⠲⡡⠌⠐⠠⡀⠀⢀⠀⠀ ⠀⠀⠀⠀⠈⢆⡇⠠⠊⠀⣿⡇⠀⠀⣿⡷⣄⠳⣤⠀⢠⠀⠀⠀⠘⠻⠿⣿⢿⡿⠟⢉⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⢷⣟⣾⢿⣽⡻⢾⡭⣟⣿⡗⢮⡡⠂⠑⣂⠀⡲⢱⠀⠄⡁⠀ ⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⣿⣷⠀⠀⢸⡷⠜⢧⡈⠂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡾⡽⢧⠿⣜⣿⡟⢢⠑⡤⠘⢤⠣⢌⢣⠘⠠⠀⠂ ⣾⣦⡀⠀⠀⠀⠀⢙⣦⠀⣿⣿⠀⠀⠀⠀⠆⠐⠛⣦⣄⠠⣄⠀⠰⠀⠀⠀⠀⠀⡐⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⢯⡿⣷⣿⣻⠯⣷⣎⡿⡍⢦⡙⠴⡁⠎⣇⠫⢄⠊⢀⠁⠀ ⠀⠀⠉⠲⣭⣯⣿⣾⣿⣷⣽⣿⡀⠀⠀⠀⠁⠀⣨⡇⠸⣷⣄⠁⠄⠀⠀⠀⠀⠀⢠⣿⣿⣿⡿⣟⢿⣿⣿⣿⣿⣿⣿⡣⢿⡱⢎⡝⠻⠶⣾⡽⣙⠦⡙⠤⠃⢘⠀⢳⡈⡐⠀⠀⠀ ⠀⠀⠀⠀⡿⢿⣿⣿⣿⣿⣿⣿⣇⢠⠐⡁⢰⣿⠿⡷⠀⠹⡙⣶⣄⡀⠀⢠⡄⢀⣾⡿⣟⢣⠟⡼⢫⣿⢿⣿⣿⣿⡿⣿⣷⣏⠂⢜⡱⣌⡄⢣⣝⠂⡉⠒⡁⠀⠀⠂⠐⠈⠀⠠⠀

⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⠞⠉⠀⡀⠄⡒⠈⠭⠭⠥⠈⠐⣚⣛⠛⠛⠛⡲⢦⣀⠀⠀⠀ ⠀⠀⠀⣰⠃⠀⠔⡨⡢⠑⠈⠉⠁⠉⠄⠀⠀⠀⡲⠀⠀⠐⢄⠀⠈⢷⠀⠀ ⠠⣤⣿⣛⡛⠛⣻⢿⣛⣟⡻⣿⣿⣿⣿⣿⣿⣿⣟⣿⣛⢿⣿⣿⣿⡟⢦⡀ ⡴⠛⢡⡶⠒⡖⠦⢭⣿⣮⣱⣎⣿⣿⡿⠏⠀⠙⡿⠷⠿⣾⢿⣿⢭⡞⡐⣷ ⡇⠀⢺⠠⢾⡟⠲⢤⣀⡀⠠⠤⠄⡖⢂⣀⠀⠀⠙⣦⣄⠉⠉⢰⡄⠠⢃⣿ ⠹⣎⡪⠀⠀⢷⡦⣄⣯⡉⠓⠲⣤⣵⣉⣀⡀⠶⠞⠁⣀⣨⣴⢿⣷⠈⣰⠃ ⠀⠈⢳⡀⠀⠀⠻⣌⡟⠛⠷⣶⣧⣄⣀⣹⣏⣉⣻⣉⣉⣧⣸⣷⣿⠀⣿⠀ ⠀⠀⠀⠳⣄⠀⠀⠈⠳⢤⡀⣸⠉⠉⠛⡿⠻⠿⡿⠿⣿⢿⡿⣿⡟⠀⣿⠀ ⠀⠀⠀⠀⠈⠳⣅⡪⢔⡠⢉⡛⠲⠦⠤⠧⣤⣤⣧⡴⠧⠾⠖⠛⠀⠀⣿⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣅⡒⠡⠶⠀⣠⡤⠤⠤⠤⠤⠤⠐⢁⠠⠀⢸⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣤⣄⣀⡀⠀⠉⠉⠉⠉⠀⢀⣠⠏⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠓⠒⠒⠒⠚⠉⠁⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢔⣒⠂⣀⣂⣤⣄⣀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣴⣿⠋⢠⣟⣼⣷⠼⣞⣽⢏⣿⣆⠱⣄ ⠀⠀⠀⠀⠀⠀⠀⠹⣿⡀⣆⠛⠢⠐⡍⡉⣾⣾⣽⣟⡰⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⢈⢿⣿⣦⠀⠤⢶⣿⠿⢋⣴⡏⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⣺⡙⢻⣿⣿⣧⣽⣉⣁⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⣷⡔⡉⣩⢋⡋⠩⠯⡟⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⣘⣶⣁⢙⢐⣄⡴⠪⠓⠁⠉⠃ ⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⢻⣿⣿⣿⣿⠻⣧⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠫⣿⠉⠻⣇⠘⠓⠂⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠇⣿⠂⠁⠀⠀⠀⠀⠀⠀ ⠀⢶⣾⣿⣿⣿⣿⣿⣶⣄⠀⢐⢝⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣧⠈⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠙⠻⢿⣿⣿⠿⢛⣄⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠘⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⠂⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠉⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠉⠉⠙⢲⠋⠁⠀⠘⡷⡄⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⡴⠒⠢⡄⠀⠀ ⠀⠀⠀⠀⣠⠋⠁⠀⠙⢾⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠁⠀⠀⠀⠀⡰⠃⠀⠀⠀⠱⡜⠀⠀⠀⢸⠀⠀ ⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⣀⡞⠁⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠘⠈⠀⠀⠀⡎⠀⠀ ⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⣠⠤⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣠⡤⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠹⡀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀ ⠀⠀⠀⠀⠀⠑⣄⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢠⠏⠀⠀⠀⠈⢣⠀⢀⠖⠉⠀⠈⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⡤⠒⣄⠀⠀⠀⠀⠈⠳⢄⠀⠀⣠⠞⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠲⠤⣄⡀⣀⡔⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣷⠃⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⢠⠖⠒⢼⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡅⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⡼⠀⠀⠀⠀⡾⠋⠉⠛⠳⣄⣴⠃⠀⠀⠀⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⢀⡠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠁⠀⠀⠀⢀⡇ ⠀⠀⠀⠀⠀⠀⠀⡞⠉⠙⢾⠇⠀⣿⡄⠀⠀⠀⠀⠀⠀⠈⠳⣀⠔⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⢀⠏⠀ ⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⣧⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⣄⠀⠀⠀⢀⡴⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀⠀⡠⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠮⣲⠾⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠓⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣶⢦⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⢪⣯⢦⡈⠑⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⢣⢧⢧⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⣇⠀⡇⠀⠀⠀⠉⠉⠙⠒⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⣯⢆⢷⡀⠀⠀⠀⠀⠀⣸⡤⣄⣹⣊⡁⠀⠀⠀⠀⠀⠀⠀⠀⠑⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣷⡀⠀⠀⢠⣤⠿⣶⣿⣿⣶⣭⣭⣍⣓⠖⠦⣤⣀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⣷⣿⣯⣡⡇⠀⠀⠀⣸⠋⠉⠉⣻⡗⠛⠛⠫⠿⢿⣖⣢⣬⣉⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣶⣋⡭⢿⣿⣷⣼⠇⠀⠀⢿⠀⢀⡠⠋⢇⠀⠀⠀⠀⢀⡏⠙⠒⢻⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣀⠴⠚⠉⢈⣥⠴⠚⣻⣿⠁⠀⠀⠀⠀⣽⠉⣄⣀⡈⠓⠤⣀⣠⠞⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣼⡥⠴⠒⠉⢁⣠⣴⠿⣯⠁⢣⣀⣀⣠⣤⣿⠀⠀⠙⠃⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢻⣤⣤⢖⡯⠛⠉⠀⠀⠈⢳⣰⣇⣠⡏⢀⣼⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣟⡀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀ ⠀⢹⡋⠁⠀⠀⠀⠀⢰⡦⢾⠋⠀⣿⠀⠻⣅⢻⠭⢿⣷⡖⢲⣶⣒⣿⣿⣿⣧⣭⣿⡿⠷⠒⣋⣿⣿⣿⡿⠟⠛⢳⠀⠀⠀ ⠀⠀⠹⣆⠀⠀⠀⠀⠀⢷⠸⡄⠀⣿⣀⠀⠸⡿⡆⢠⠿⣾⣾⣳⠀⢹⣯⣿⣿⣿⣧⣴⡲⠯⠛⠋⠉⠀⠀⠀⠀⠈⡆⠀⠀ ⠀⠀⠀⠈⢣⡀⠀⠀⠀⠘⣇⣧⠀⡟⠿⢍⣻⣇⣳⡞⢸⣿⣿⣿⣄⣿⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀ ⠀⠀⠀⠀⠀⠑⣄⠀⠀⠀⠸⡼⡀⡷⣾⣿⣧⡬⣿⡟⠛⠹⣿⣿⡟⢽⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡆⠀ ⠀⠀⠀⠀⠀⠀⠈⠳⠤⠤⠴⠟⠻⡇⣏⢸⠉⡇⢽⡇⢰⣖⣿⣧⠀⢸⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠚⢉⡠⢷⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡇⠙⠻⠼⠀⣿⡇⢸⠉⡏⢹⠀⢸⠀⢸⣦⡤⡤⠤⠤⠖⠚⠉⢉⣉⠤⠖⠊⠁⠀⢸⡆ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⡟⡇⠸⢤⣧⡼⠀⢼⠀⠀⡏⠚⠚⠓⠲⠚⢹⡏⠉⠁⠀⠀⠀⠀⠀⢸⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⠙⠒⠤⣄⣟⡇⠀⠀⠀⠀⠀⣿⠀⠀⡇⠀⠀⠀⠀⠀⢺⠃⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣉⠒⢤⣀⠈⠑⠲⣤⣀⠀⠀⡿⠀⠀⡇⠀⠀⠀⠀⠀⢸⡃⠀⠀⠀⠀⠀⠀⠀⢹⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠙⠒⢬⣯⢽⠲⠤⢌⣉⠒⡿⠖⢺⣇⠀⠀⠀⠀⠀⢼⡇⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠈⠉⠉⠉⠒⠦⢄⣉⢑⢚⡿⠋⠉⠙⠒⠒⠤⣾⠀⣀⡀⡀⠀⠀⠀⢀⡿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠈⠉⠁⠙⠲⢤⣄⡀⠀⢠⠃⠀⠈⠉⠉⠙⠛⠛⣯⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡇⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡙⠛⠒⠢⠤⢤⣀⣀⠀⠀⢸⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⢸⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣷⡀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⠉⢦⣦⣀⡠⢀⣀⣼⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢌⡿⠶⠞⠋⣁⣤⡷⣄⡀⠀⠀⠀⠀⠀⠀⢀⡴⣫⢾⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠚⠉⠀⠀⠙⠢⣈⠑⠦⣀⠀⣀⣔⢽⡫⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠦⣀⣉⣡⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡴⠶⠚⠛⠛⡿⠿⣿⠛⢶⠛⠓⠶⢦⣄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠛⠉⠀⣀⣀⣴⡶⠾⢤⣚⠉⢣⡈⠳⡀⠀⠀⠹⡆ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠶⠛⠉⠀⠀⠀⡏⠉⢁⡤⢟⠀⡖⢦⡈⠓⠤⠵⠀⡇⠀⠀⠀⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡴⠶⠛⠋⠉⠀⠀⣀⠤⠴⡽⠋⠁⠚⣅⠀⠸⡀⢳⠀⠉⠒⠤⠔⡞⠉⠒⠉⢱⣏ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡴⠶⠚⠋⢉⣀⠀⠀⣀⣠⣎⣁⠚⣁⡤⠖⡁⢸⠉⢦⡈⠳⠤⠃⡸⠀⢀⡴⠒⠴⡥⠒⠒⢦⢀⡿ ⠀⠀⠀⠀⠀⠀⢀⣠⣤⠶⠛⠋⠉⠀⠀⣀⣀⣰⠋⠀⠉⠉⢠⠏⢁⣀⠙⢧⡀⠀⡇⠈⡇⠀⠙⠒⠤⢲⠗⠒⠚⢀⠖⠋⠀⠀⠀⢸⡟⠀ ⠀⠀⠀⠀⣴⠞⠋⠁⠀⡰⠓⢦⠤⠒⠚⠀⡸⠋⡉⠓⣖⠉⠹⡀⢸⠀⠱⢄⡈⠉⣡⠜⠓⠤⡤⠒⣒⣋⣀⠞⠁⠀⠀⠀⠀⠀⠀⣾⠃⠀ ⠀⠀⢀⣼⣧⣀⡞⣉⣉⣡⠞⢉⡉⠳⡊⠉⡇⢸⠉⢦⠈⢦⣀⡇⢸⠄⠀⠀⠉⣹⠃⢀⡠⠤⠤⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃⠀⠀ ⠀⢀⣼⠷⢧⡀⠹⡄⠀⢸⠀⡎⠹⡄⠱⡄⡇⢸⣇⡀⠓⢤⣀⣠⣞⠀⡰⢋⣀⣁⡠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠀⠀⠀⠀ ⢰⠟⠁⠀⠀⠙⡄⠘⣄⡸⠀⡇⠀⠙⢤⣈⣠⡾⠉⠈⠉⠒⠊⢀⣀⣉⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠋⠁⠀⠀⠀⠀⠀ ⣿⠀⣆⡀⠀⠀⠘⠦⣀⣀⣴⠥⠤⠄⠠⠔⠚⠁⡰⠚⠒⠤⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⢿⡀⡜⠃⠀⢠⠖⠲⠤⠞⡡⠤⣀⣀⡴⠊⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⢳⣌⡀⠀⠈⢆⣠⠒⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡴⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠙⠛⢲⣏⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠴⠞⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠙⣷⣤⣀⣀⣀⣀⣀⣀⣀⣠⣤⠴⠶⠚⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠟⠛⠛⠿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠋⠀⠀⠀⠀⢸⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠀⠀⠀⠀⠀⠰⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠨⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠈⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⢐⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⠠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡇⠀⠀⠀⠀⠀⢰⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⡿⠿⢿⣿⣿⠃⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠋⠀⠀⠀⠹⣿⠀⠀⠀⠀⠀⠀⢸⣿⣷⣶⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣼⣿⠃⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠈⣿⠛⠉⠉⠙⢿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣼⣿⡿⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢹⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣴⣿⠿⣿⠇⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠘⣿⠛⠲⢦⣤⠀⠀⠀⠀⠀ ⠀⠀⣰⣿⠟⠁⠀⣿⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠹⣧⡀⠀⠀⠀ ⢀⣼⠟⠅⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠸⠟⠁⠀⠀⠀⠀⠀⠑⠿⠃⠀⠀⠀⠀⠀⢹⣇⠀⠀⠀⠹⣧⠀⠀⠀ ⣾⠏⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⢽⣧⠀⠀ ⣿⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⠀⠀⠀⣿⣆⠀ ⣿⣆⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀ ⠹⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇ ⠀⠈⢻⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠇ ⠀⠀⠀⠙⢿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡟⠀ ⠀⠀⠀⠀⠀⠙⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠟⠁⠀ ⠀⠀⠀⠀⠀⠀⠈⠹⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠋⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠏⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣶⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣶⣶⣿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠖⠚⠉⠉⠀⠀⠀⠀⠉⠉⠙⠒⠤⣄⡀⠀⠀⣀⣠⣤⣀⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢯⡀⠀⠀⠀⠉⠳⣄⠀ ⠀⠀⣀⠤⠔⠒⠒⠒⠦⢤⣀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣄⠀⠀⠀⠀⠀⣴⢶⣄⠀⠀⠀⠉⢢⡀⠀⠀⠀⠘⡆ ⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠈⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⢹⣧⠀⠀⠀⠀⣿⠀⢹⣇⠀⠀⠀⠀⠙⢦⠀⠀⠀⣧ ⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣦⣼⣿⡇⠀⠀⠀⢿⣿⣿⣿⡄⠀⠀⠀⠀⠈⢳⡀⢀⡟ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡿⠿⠿⣿⠀⠀⠀⠘⣿⡛⣟⣧⠀⠀⠀⠀⠀⠀⢳⠞⠀ ⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡄⢴⡿⠀⠀⠀⠀⠘⣿⣷⡏⠀⢀⡠⠤⣄⠀⠀⣇⠀ ⠀⢳⡀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⣠⠄⠀⠀⠀⠀⠀⠈⠛⠛⠁⣀⡤⠤⠤⠤⢌⣉⠀⠀⢠⡀⠀⠀⡱⠀⢸⡄ ⠀⠀⠙⠦⣀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠸⣅⠀⠀⢀⡀⠀⠀⠀⢀⠴⠋⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠈⠉⠉⠀⠀⢘⣧ ⠀⠀⠀⠀⠈⠙⢲⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⣰⣋⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⢐⣿ ⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠉⠙⠒⢤⣀⠀⠀⠈⣇⠀⠀⠀⠀⠀⣿ ⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⢸⠀⠀⠀⠀⢠⡏ ⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠘⣧⠀⠀⠀⣸⠀ ⠀⠀⠀⠀⠀⠀⠀⡟⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⢰⠏⠀⠀⢠⠇⠀ ⠀⠀⠀⠀⠀⠀⢸⠁⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⣸⠀⠀⢀⠏⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⠀⠀⠘⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⣣⠃⠀⣠⠏⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⡱⠋⢀⡴⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠈⠣⣄⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⢀⣀⡤⠖⢋⡠⠞⢁⡴⠋⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠈⠙⠢⣄⡀⠀⠀⠀⠀⠈⠙⠯⠭⢉⠡⠤⠴⠒⣉⠴⠚⠁⠀⢰⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⠖⠲⠤⠤⠤⠤⠤⠤⢶⡖⠚⠉⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠤⠤⠤⠤⠔⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢤⡀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠑⠒⠒⠋⠂⠐⠒⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⢀⣀⠀⠀⠀ ⢰⣶⣾⣿⣶⡦⠀⠀⠀⠀⠀⠈⠀⠀⠈⠐⡤⠊⠀⠀⠈⠑⡀ ⠀⣿⣿⣿⡏⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰ ⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎ ⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀ ⢠⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠐⠢⡀⠀⡀⠔⠁⠀⠀⠀ ⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠊⠀⠀⠀⠀⠀⠀ ⠹⣿⣆⣰⣿⡟⠙⢿⣷⣼⠟⠁⠀⠈⣿⡟⣻⣷⠀⣿⣿⣙⠿ ⢠⡟⣿⠏⣿⡇⠀⠀⣿⣇⠀⠀⠀⠀⣿⣟⢹⣿⡆⣿⣿⠻⠀ ⠙⠋⠈⠈⠛⠋⠀⠈⠛⠋⠀⠀⠀⠈⠛⠙⠛⠉⠈⠛⠋⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠈⠠⣻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠥⣤⢟⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⣺⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⠚⠛⠻⠯⢽⡿⣯⢭⣧⢤⣤⢴⣿⣶⣶⣶⣤⡶⢿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠚⢾⡟⠉⠹⡿⠿⣿⠞⠛⣶⣿⣿⡿⣿⡾⣦⣼⠧⣬⣽⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠚⢁⡔⠋⠳⣴⠃⡈⠭⠭⠍⠭⠭⠽⠿⢅⣏⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡩⠿⠲⠶⠟⠺⡝⠤⠤⢄⡴⠋⠙⠛⠋⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⠋⡁⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⢿⣀⣀⣀⣀⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠤⣶⣶⠖⠖⠚⠛⠓⢦⠀⠀⠀⠀⠀⡴⠋⠀⠠⣿⣻⣷⠀⠀⠀⠀⠀⢸⣿⣧⣠⠤⢌⡏⠉⠉⢉⣟⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣀⡤⠴⠿⠯⠤⣟⡁⠀⠀⠀⠀⠀⠀⠱⣄⢀⣠⡞⠁⠀⠀⠀⠙⠚⠁⠀⠀⠀⠀⢀⣼⣿⣿⠈⠀⣀⣏⠉⠉⠉⢁⣀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣠⣾⠉⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠂⠄⠀⠤⠤⠜⠛⣁⡽⠒⢲⣤⣤⣤⡤⣤⣤⣶⣶⣶⣿⣿⡿⢈⣿⡏⠉⢳⠒⠋⠙⣏⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⡁⣉⣷⣷⣟⣉⣉⣽⡉⠑⢾⡀⠀⠀⠀⠀⠀⣀⡤⠞⢡⢴⡾⠛⠁⢠⣯⣿⡁⠀⠀⠀⠈⠙⢻⠇⣞⠉⣽⡄⠀⢧⠀⠀⠘⣆⢀⣹⣄⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠉⢁⣨⣿⣿⣶⣦⡄⠙⣄⠀⢧⣀⣠⠔⢚⣭⣤⣼⣾⠋⡟⠀⠀⠀⠀⠙⣿⢿⣢⢄⣀⠀⠀⣸⢀⣿⢷⣯⣷⠀⠈⣧⠴⠒⣋⣁⣤⣤⣮⣿⣿⣟⣷⠄⠀⠀⠀⠀⠀⠀ ⠀⢰⠋⠛⠻⢿⣿⣿⣿⣿⣦⡘⣤⣖⣭⡶⠞⠋⠀⠉⠛⠛⣶⣇⠀⠀⠀⠀⢠⣿⣼⡟⣽⣾⣭⡶⡇⢸⣧⣤⡟⢿⣧⠀⣸⣦⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀ ⠀⢿⠀⠀⠀⠀⠈⢉⡻⠻⢿⣿⢛⡟⣟⠀⠠⢤⢤⡶⣾⣾⢉⡘⢷⣶⣶⢶⣿⣿⣟⣾⣿⣿⠟⢹⠁⣟⣿⣿⣿⡿⡿⣿⠉⢿⣿⣿⡿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀ ⠀⣼⣿⡶⢤⣀⠀⢸⣄⠀⢀⡼⠿⣧⢹⣦⣤⣼⣿⣤⣷⣿⣯⣿⣦⠉⠛⠿⡿⢫⣾⣿⡿⠁⢠⡟⢠⣿⣿⣿⣿⣿⣿⣿⣇⠀⣿⠁⠀⣀⣀⣀⡀⠙⢿⣿⣿⣿⣿⣿⣷⡄⠀ ⢰⣿⣿⠀⠀⠀⠉⠲⢭⣀⢸⣀⠀⠈⠻⣽⣏⣹⣿⠏⠀⠀⠹⣟⠛⠲⠤⡀⠘⣾⣿⠏⢀⣴⣿⠇⢸⣿⣿⣿⣿⣿⣿⣿⡿⣆⣘⡶⣯⣝⠏⢻⣿⣷⣤⣹⣿⣿⣿⣿⣿⣷⡀ ⠐⣿⣿⡦⣄⡀⠀⠀⢰⠏⠀⠀⠙⣆⠀⠘⢧⣰⠁⠀⠀⠀⠐⢻⡆⠀⢀⠇⢀⡟⢁⣠⣾⣿⡿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣆⢸⡑⡄⠈⣻⣿⣆⠬⢿⣿⣿⣻⣿⣿⣿⣿⣿⡇ ⠀⣿⣿⣡⠹⡽⣷⣤⣾⠿⠀⢀⠉⠉⠣⣄⡀⠈⠉⠉⠉⠉⠉⠉⠓⣖⠋⠤⣼⣀⡼⣷⡿⠛⢣⢠⠟⢻⠉⣹⣿⣿⣿⣿⠀⢸⣧⣿⡠⢬⣹⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠘⣿⣿⣆⠙⢾⣿⣯⣿⣶⣾⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢯⠷⠒⣶⠘⢷⣋⡃⠀⢼⣾⣤⣶⣶⠋⣿⣿⣿⣿⣠⣬⣿⣿⠇⢸⡟⣿⣿⠬⣷⡿⣍⣿⣿⣿⣿⣿⣿ ⠀⠀⠹⣿⣿⣷⣄⣈⣉⣉⣽⣿⣿⣿⣿⣿⡿⠯⣉⣛⡓⠒⠶⠶⠶⢾⠶⠾⢿⣷⣤⣍⡙⣲⣺⣿⣿⣿⣿⠟⠋⢿⣿⣿⣆⢳⠸⢿⣿⣷⢿⡿⠿⢈⡿⣷⠏⣿⣿⣿⣿⣿⡿ ⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠉⠉⠉⠉⠉⠛⠛⠒⠒⠚⠛⠲⠖⠛⠉⠉⠛⠋⠉⠀⠀⠘⣿⣿⣿⣆⠐⢤⣉⣻⣞⣄⣴⣿⡿⠃⣸⣿⣿⣿⣿⣿⠇ ⠀⠀⠀⠀⠀⠙⠛⠿⠿⣿⣿⠿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣷⣄⠉⠉⠉⠉⠈⠁⣠⣼⣿⣿⣿⣿⣿⡟⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⡿⠿⠛⠛⠉⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⢠⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡇⠀⢱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⡇⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⢋⠟⠉⠇⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠸⡇⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⢁⠔⠁⠀⡜⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢰⡇⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⠀⡰⠃⠀⠀⣰⣡⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠘⡇⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⢠⠞⠁⢀⠌⠀⠀⠀⣰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢱⠀⠀⠀⠘⡆⠀⠀⠀⡀⠔⠃⠀⢀⠞⠀⠀⣠⢞⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡎⠀⠀⣀⣀⣹⣄⠔⠉⠀⠀⠀⢠⠏⢀⡤⣪⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⡷⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⢠⠷⣶⠟⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⠤⠤⠤⠄⠤⠤⠤⠤⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡀⠀⠸⡇⠀⢀⣀⡠⠤⠒⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢄⠀⠀⠀⠀⠀⠀ ⠀⣰⡿⠀⠀⠀⠀⠀⠀⢀⣾⣿⡿⠁⠀⠀⠹⡉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀ ⢠⣿⠁⠀⠀⠀⠀⠀⠀⠈⠁⠉⠀⠀⠀⠀⠀⡇⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀⠀ ⡿⠈⢣⡴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡗⠀⠀⠈⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀ ⠿⣆⢈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⠀⠀⠀⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀ ⠀⠈⠙⠻⢷⠆⠀⠒⠂⠀⠀⠀⠒⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀ ⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀ ⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀ ⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀ ⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⢱⡀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠑⢦⡀⠀⠀⠀⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⢠⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣽⡖⠲⠤⠵⢤⣀⡀⠀⠀⠀⠀⠀⣼⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠧⠶⠋⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢼⣁⣀⣤⡾⠋⠀⠀⠀⠀⢀⡞⠁⠙⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠁⠀⠀⠀⠀⢀⡰⠋⠀⣀⠀⠀⠙⠲⠤⡄⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣁⡰⠀⠀⢀⣠⠴⠛⢄⡰⠊⠀⠀⠀⢀⡀⠀⠀⠠⠤⠀⠀⠤⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠈⠁⡀⠀⠀⠀⠑⠢⠤⠔⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⢀⣠⣴⡖⠒⠒⢶⡒⠒⢤⡴⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣾⣋⠀⠄⢀⣉⡦⠴⠓⠒⠲⠇⠀⡿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡾⢁⡤⠒⠒⣶⠋⠀⠀⠀⠀⠀⠀⣴⠁⣇⠀⠀⢀⡀⣠⠖⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⢸⠀⠀⢠⠇⢀⡴⣤⣄⠀⠀⠀⠀⢸⠸⡀⢠⢋⡟⠁⡼⣁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢱⠘⡄⠀⠈⡇⠘⣟⢸⣏⢳⣶⣦⠀⡞⠀⣧⣏⣈⢀⡼⠋⢁⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠳⡘⢄⣀⡼⠀⠹⢿⣿⡿⠀⢀⡜⠀⢸⣿⠃⣼⡊⢀⣔⡁⠀⢀⡤⠔⠒⠒⠒⠶⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠹⣎⠻⡳⠴⠀⣀⠀⣤⢶⠎⠀⣠⡿⡏⠐⢁⠟⣁⣤⣿⣚⡁⠤⠤⠄⣀⠀⠀⠀⠙⢦⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⢷⡜⢄⠀⡹⠀⡶⠃⣠⢞⠟⢰⠃⢰⣟⡿⢨⣽⡯⠔⠒⠒⢤⡀⠀⠙⢢⡀⠀⠈⣇⠀⠀⠀⠀⠀⠀ ⠀⣴⡶⢦⢈⢿⠈⣄⡇⡼⢁⠞⡱⠃⠀⡎⠀⢉⣥⡀⠋⣀⡇⠀⠀⠀⠀⠱⡀⠀⠀⢱⠀⠀⢸⡀⠀⠀⠀⠀⠀ ⠀⢿⡳⠤⠊⢸⢀⡝⢠⡷⢃⠜⠀⠀⡜⡀⠀⢧⠈⠛⠲⢽⠇⠀⠀⠀⠀⠀⡇⠀⠀⢠⠇⠀⡞⡇⠀⠀⠀⠀⠀ ⠀⠀⠉⠒⠒⠛⠉⠀⢸⠃⡌⠀⠀⡜⠀⣷⠒⠺⡷⢄⠀⠚⢢⠀⠀⠀⠀⢠⠇⠀⠀⡞⢀⡜⢸⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⡇⠀⢸⡇⠤⣼⠀⠀⠘⡌⢣⠀⠀⢧⠀⠀⢀⡞⠀⢀⠌⡠⠊⠀⡞⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡀⣓⡾⠛⡆⠀⠀⢣⠀⡇⠀⠘⡄⢠⠎⠀⣠⣣⠊⠀⣠⠞⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢃⠏⠀⠀⢀⠇⠀⠀⡇⢀⠇⠀⠀⣧⡏⠀⣰⡟⢡⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡏⠀⠀⠀⣼⠀⠀⢸⣤⠞⠀⠀⢀⡿⡄⢠⠻⡅⠈⠓⠒⠒⠒⣒⣺⣯⣑⢲⣄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠈⠓⠳⠽⠦⠤⠒⠊⠁⠀⠀⠀⠀⠙⣿⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⠉⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⠴⠴⣤⣤⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣤⡾⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⢶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠟⠋⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⠶⢦⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣼⡟⠁⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣷⣦⠀⠀⠀⠀⠀⠀⢰⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⡾⠋⠀⠀⠀⠀⣀⣤⡴⠏⠀⠀⠀⠀⠀⣾⣿⢿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⣇⠀⡃⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⣰⡿⠁⢀⣀⣤⠾⠟⠛⣿⠀⠀⠀⢀⠀⠀⠀⣿⠁⢀⣿⣿⣿⡇⠀⠹⣿⠀⠀⠀⠀⠀⠈⠛⠁⠀⠹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡀⠀⠀⠀⠀ ⢠⡶⠚⠿⣶⠾⠛⠉⠀⠀⠀⢸⡇⠀⠀⣠⣾⢷⣤⡀⠈⠷⣿⣿⣿⣿⣿⣶⡾⠋⠀⠀⣀⣠⣄⣀⠀⠀⠀⠀⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀⠀ ⢸⡀⠀⢀⣿⠀⠀⠀⠀⠀⠀⢸⣷⠀⣼⣿⡄⠀⠈⠙⠳⢦⣄⣛⠿⣧⣿⣧⣤⠶⠞⠛⠉⠀⠈⠉⠛⢶⣄⠀⠀⠙⠓⠶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀ ⠈⠙⠒⠛⠁⠀⠀⠀⠀⠀⠀⠘⣿⣠⡏⢘⣧⣀⣀⣀⡆⠀⠈⠙⠛⠛⠋⠉⡷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡄⠀⠀⠀⠀⠉⣹⡿⠶⣦⣤⣀⣀⣀⡽⠓⢶⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⢹⣿⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠛⢹⣷⣶⣤⣤⣀⣀⡀⠀⠀⠈⢻⡄⠀⠀⠀⣠⡿⠀⠀⠀⠀⠉⠉⢻⡀⠠⣠⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡄⠀⠻⢿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⠟⠂⠀⠀⠀⢸⡇⠀⢀⣴⡟⠁⠀⠀⠀⠀⠀⠀⠈⠙⠚⠋⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣦⣀⠀⠀⠀⠀⠀⢰⣟⣲⠆⠀⠀⠀⠈⠛⠿⠿⠋⠀⠀⠀⠀⢠⡿⢁⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣭⡿⠿⣦⣄⣀⠀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⡶⢿⣋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣹⢿⣥⣄⣀⣀⠉⠙⠛⠿⠶⢶⣶⣶⣶⣶⣶⣶⣶⠶⠾⠿⠛⠋⠉⠀⠀⠀⠙⢷⡤⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠈⠉⢹⡇⠀⠀⠀⠀⣀⣴⣦⣄⡀⠀⠀⠀⠀⠀⢸⡟⠛⠛⠛⠉⠉⠉⠻⣤⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣇⣠⡴⠶⠛⠉⠁⠀⠉⠻⢶⣄⡀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⠉⢻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣤⠼⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣤⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡴⠒⠲⠦⣄⣀⣀⣠⣤⣤⠎⠉⠉⢦⠶⠛⠉⢳⠀⠀⠀⠀ ⠀⠀⠀⢰⠇⠀⠀⠀⠈⠉⠀⠀⠀⡏⠀⣴⢲⠼⠶⢄⣀⣼⣇⠀⠀⠀ ⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⢇⡀⢘⣯⠀⠀⢸⠶⡀⠀⡇⠀⠀ ⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠈⠑⠒⣏⠉⢀⡜⠀⠀⠀ ⠀⠀⠀⣯⣤⣴⣶⡶⠒⣲⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣯⣭⣿⠀⠀⠀ ⠐⠒⠚⣿⣿⣿⡏⠀⠺⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠉⠁ ⠀⠀⠤⢿⣿⣿⣡⣴⣾⣿⣿⡿⣕⣲⢿⣿⣿⣿⣿⣿⣿⣿⡟⠒⠂⠀ ⠀⠀⠀⣠⠿⣿⡛⠿⠿⠛⠋⠀⠀⠀⠀⠙⠛⠿⠿⠛⣻⡿⠷⢄⠀⠀ ⠀⠀⠈⠁⠀⠈⠙⠲⠦⣤⣄⣀⣀⣀⣀⣀⣠⣤⠴⠞⠉⠀⠀⠀⠀⠀

⣀⠀⢻⣿⣿⣿⣦⠘⢶⣄⣀⡀⠘⣷⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠺⠥⢄⣀⠀⠀⠀⣀⣠⣤⣶⣾⣿⣿⣿⣟⣁⣀⣤ ⠙⠿⣿⣿⣿⣛⠛⠳⢤⣈⣂⠈⠑⠞⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣍⡹⠶⢤⡀⠈⠙⡒⠆⠀⠀⠈⣉⠛⠛⢿⣿⣿⣿⣿⡿ ⣶⣿⣿⡿⠟⠋⠁⠀⠐⠒⢬⣭⠵⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠋⠁⠀⠀⠀⠘⢷⡀⠈⠳⠦⣄⠀⠽⣿⣿⣿⣿⡿⠟⠋⠀ ⢿⣿⣿⣿⣿⣯⠄⠐⣺⣽⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠙⣄⠀⡄⠤⣵⣦⠀⠉⣙⠛⠒⠀⠀⠀ ⠀⠈⣩⣿⣿⡵⢒⣽⢶⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠇⠀⠀⠀⠀⠀⣀⠔⠀⠘⢦⠘⡆⠈⠛⠷⡄⠹⣯⡓⠤⣀⠀ ⣴⣾⣿⣿⣿⣿⠟⠡⡿⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣤⣶⣶⣶⡶⠞⠁⠀⠀⠀⠀⢣⡄⠀⠀⠀⡈⠂⠈⠻⣦⡀⠀ ⠀⠀⠀⠀⣠⣧⠄⢀⡇⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⠿⠿⠛⠛⠉⠀⠀⠀⠀⢀⠄⠀⢸⠃⠀⠀⠀⠙⣦⣤⣤⣬⣽⡦ ⠀⠀⠀⠈⠉⠀⣼⢨⣇⣀⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⣾⡿⠋⠁⣀⣤⣶⠶⠶⠶⠶⠶⡶⠊⠁⠀⠀⠸⠀⠀⡆⠀⠘⡎⢙⡋⡁⠰⣄ ⠀⠀⠀⠀⠀⠀⣿⢸⡏⠻⠿⣿⣿⢿⣆⠀⠀⠀⠀⠀⡸⢋⣠⢃⣾⡿⠓⠒⠦⣄⠀⠀⢸⠃⠀⠀⠀⢠⠃⠀⢠⡇⠀⠀⡷⠋⠙⠢⡀⠈ ⠀⠈⠀⠀⠀⠀⣿⠀⣿⣄⡴⠛⠿⣶⣿⣧⡀⠀⠀⠀⠁⣾⠃⡾⠛⣰⣿⣿⡆⡎⡆⢀⠎⠀⠀⢀⡴⠃⠀⠀⣾⡇⠀⠀⡇⡀⠀⠀⢹⠀ ⠀⠀⠀⠀⠀⡴⠃⣠⣿⣿⡆⠠⣶⣦⠸⣿⣧⠀⠀⠀⠀⠀⠈⡇⠈⢮⡻⠛⠃⢁⡠⠋⠀⢀⡤⠊⠀⠀⢀⣼⣿⡇⠀⠀⡇⠉⣀⠀⢸⠀ ⠀⠀⠠⠀⠈⠀⠰⡟⢸⣿⠱⡀⠻⠟⠀⢸⣿⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠉⠉⠡⠤⣤⡚⠁⠀⠀⠀⣠⠞⠁⡇⣼⠀⠀⢹⠀⠘⠀⣸⠀ ⠄⠀⠀⠀⠀⠀⠀⠀⢻⣯⡆⠈⠉⠀⠀⡸⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⢉⠏⠀⣸⠃⣹⠀⠀⣏⠄⠀⠀⠅⠀ ⠁⠀⠀⠀⠀⠀⠀⠀⢠⡏⡇⠀⠀⠀⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⣰⠋⠀⣿⠀⠀⡟⢆⢀⠞⠀⠀ ⠀⠀⠀⠀⠀⣰⠒⣠⡞⠁⣿⠀⠀⠀⠀⢻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⣰⠃⢀⠀⡏⠀⢸⢃⡼⢳⡀⠀⠀ ⠸⠗⠀⠀⢘⣥⣾⣫⠔⡸⢻⣇⠀⠀⠀⠀⣈⠤⠀⠀⠀⠀⠀⠀⠀⠀⣰⠀⠀⠀⠀⠀⠀⢀⣼⢇⣾⠇⠀⣼⠀⡇⣄⣼⠀⠀⠘⣇⠀⠀ ⠀⠀⠀⠠⠿⣿⣿⢋⠀⠃⡼⠙⣄⠀⠀⠀⢳⣤⣴⣶⣶⣶⣾⣿⣿⡿⠁⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⢀⢰⣿⡄⣧⣿⡿⠀⠀⠀⢻⠀⠀ ⠀⠀⠀⢀⣴⣿⣷⡟⠀⣼⠁⡕⢹⣦⠀⠀⠀⠙⣟⠉⠉⠉⢉⡽⠋⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣵⣏⣸⣿⣿⡇⣿⣿⣷⣄⠀⠀⠀⠀⠀ ⠀⠀⢀⣾⣿⣿⣿⠁⣾⣿⡆⢃⣼⣌⠳⣄⠀⠀⠈⠑⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡟⠁⠈⣿⣿⣿⣿⣿⣿⡟⢿⣿⣷⣄⠀⠀⠀ ⠀⠀⢸⣿⠿⢻⣿⣰⣿⣿⣇⣾⣿⣿⡇⠈⢳⣄⠀⠀⠀⠈⠑⠀⠀⠀⠀⠀⣀⡤⠞⠉⢿⢀⠀⢀⣿⣿⡁⢸⣿⣿⠀⢀⢷⠀⠈⠀⠀⠀ ⠴⠶⠿⠷⠄⢼⣿⡿⢿⣿⣿⣿⣿⢿⡇⣠⢸⡏⡱⢄⡀⠀⠀⢀⣀⣤⡶⠟⠉⠀⣀⣀⣠⠏⢀⡼⠋⢺⠁⢸⡟⢿⠀⠆⠈⣇⠀⠀⠀⠰ ⡀⠀⠀⠀⡐⠸⡿⠗⠋⣿⣿⡿⠀⣿⣿⠇⢸⡏⣧⠤⠭⠿⠟⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⡆⠁⠈⠱⣇⠀⠸⡆⠀⠀⠀ ⠀⠀⠀⠀⠙⢦⣁⠀⣸⢟⣽⠁⣰⢻⡇⢠⠏⠀⣿⣤⠀⠀⠀⠀⠀⣤⡤⣤⣶⣶⣴⣶⣾⣿⣿⣿⣿⣇⣼⡇⠀⣸⢀⣿⡄⠀⣿⠀⠀⠀ ⠀⠀⠀⠀⠐⣋⣭⣿⣿⣿⠏⣴⡇⢀⡇⣎⣠⠞⢻⣿⠄⠀⠀⠀⠀⠹⣶⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢰⣿⣾⣿⣇⣰⢹⠀⡄⠀ ⠀⠀⠀⣠⣿⡿⢿⣿⣿⣏⣼⣿⡇⢸⡷⠋⠀⢀⣤⣿⡄⠀⠀⠀⠀⣿⣏⣹⣿⢛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣴⣿⣿⣿⣿⣿⣿⣿⠀⠙⠆

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠧⠤⢾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⡀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠃⠀⠀⢿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠃⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡿⠙⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣠⡶⠤⠿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⡿⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢲⣤⠮⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⣾⡿⣫⢾⡟⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⣩⠞⣫⡾⣡⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠞⣉⡴⠋⣡⡾⢋⡾⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⣁⡴⠞⠉⣠⠞⢁⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠈⠻⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⠇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠖⠋⠁⣠⠴⠚⠉⢀⡰⠞⠁⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠙⢷⣦⡀⣀⣠⣤⡶⠶⠛⠋⠉⣹⠇⠀⠀⠀⣀⣠⡤⠖⠒⠋⠉⠀⣠⡴⠒⠉⠀⢀⣠⠖⠋⢀⡤⠎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠉⠛⠉⠉⠀⠀⠀⠀⠀⢠⡟⠒⠊⠉⠉⠁⠀⠀⣀⣤⠔⠚⠉⠁⠀⢀⣠⠖⠋⠁⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠁⢀⣠⣤⠤⠒⠚⠉⠁⠀⠀⠀⣀⠴⠚⠉⠀⠀⣠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⣴⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠉⠁⠀⠀⠀⠀⠀⣀⣠⠴⠒⠉⠁⠀⠀⣀⠴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣀⣴⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⣀⣀⡤⠴⠒⠋⠉⠀⠀⠀⢀⣠⠴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣠⣴⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣞⠉⠉⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠛⠿⠷⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠀⠀⠀⢀⣠⠴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣄⠀⠀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠙⠻⠶⢤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡖⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⠈⠻⡛⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣇⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠈⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⢿⣥⡀⠀⡈⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⢠⡾⠋⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⡾⠉⠙⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣷⠀⠀⠀⢀⣴⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢰⡄⠀⠀⠀⡀⠀⠀⠀⠀⠘⣧⣰⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⠙⠶⠶⣿⠋⠀⠀⠀⠀⠀⢹⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢶⣄⠀⠀⠀⣀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣤⣿⡋⠀⠀⠀⣯⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠙⠷⠞⠛⣹⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀ ⠀⠉⠙⣇⣰⠓⠚⠻⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠟⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠶⣾⡇⠀⠀⠀ ⠀⠀⠀⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠿⣤⣤⡀⠀⠀⠀⠀⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠻⢯⡄⢠⣽⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⣼⠟⠒⠒⠛⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠏⠉⠉⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⡃⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⣤⣄⣴⣶⣿⣿⣶⣶⣦⣤⣤⣤⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣶⣀⣶⣆⣶⣦ ⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿ ⢀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠈⠛⠛⢿⣿⣿⣿⣿⣿⠛⡟⠛⢿⡿⠛⠛⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣿⣿⣿⣿⣿⣧⣀⣀⣀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣼⣿⣿⣿⣿⣿⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣼⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠉⠙⠛⠿⠿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢤⠤⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⣀⣀⡜⠻⠿⢾⣷⠹⠀⠀⠀⠀⣀⣤⣤⡀⠀⠀⠀⠀ ⠀⠀⠀⢠⡎⠁⠀⠀⠃⠀⠀⠀⠉⠀⠀⠀⡠⠞⠛⠛⠻⢽⠀⠀⠀⠀ ⠀⠀⠀⠸⣷⡀⠀⢀⠀⢂⠀⡀⠀⠀⠀⠜⠀⠀⠀⠀⡀⠸⠀⠤⢄⠀ ⠀⠀⠀⠀⠙⣗⣄⠀⠠⡀⢢⠃⠀⢸⠌⠀⡠⢊⠀⠊⠀⠀⠀⠀⠀⡇ ⠀⠀⠀⣀⣀⣈⣲⣕⣦⡈⠢⣻⡀⡎⢀⣴⡢⠑⠂⠁⠀⠀⠀⠀⡠⠃ ⠀⣴⠿⠽⠏⠀⠀⠀⠈⠉⢒⣺⣷⣗⣉⣁⣀⣀⣀⠀⠠⠤⠐⠈⠀⠀ ⢸⠀⠀⠀⠀⠀⠀⠀⢀⠠⡖⠁⣿⢳⡬⡁⠒⠒⠤⢄⡀⠀⠀⠀⠀⠀ ⠈⢦⡀⠀⠀⡀⠄⠂⠁⠊⠀⢰⣯⡏⠎⢌⠑⠀⠀⠀⠈⠑⢄⠀⠀⠀ ⠀⠀⠉⡻⠀⠀⠀⠀⠀⠀⣲⡟⡟⠀⠀⠀⠢⡀⠀⠀⠀⠀⢸⠀⠀⠀ ⠀⠀⠀⢧⣤⡄⡀⠀⢀⡔⣽⠃⢧⡄⠀⠀⠀⠰⣀⠀⠀⣀⠞⠀⠀⠀ ⠀⠀⠀⠈⠳⠬⠥⠔⠋⡜⡌⠀⠘⣿⣦⣀⠀⡀⡇⠉⠉⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⠜⡰⠀⠀⠀⠈⠛⠯⠥⠒⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡠⠊⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣛⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣷⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⡀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⠟⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⡏⠀⠀⢀⣾⡯⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣇⠀⠀⠸⠿⠁⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠁⠀⢀⣾⡇⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠸⠟⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠣⢄⡈⠉⠓⠒⠦⠤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⠁⠙⠦⡀⠈⠑⠦⣄⡀⠀⠀⠀⠉⠉⠐⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⡿⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠀⠀⠈⣧⠀⠀⠈⠣⡀⠀⠀⠉⠓⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠈⠉⠙⠛⠋⠛⠛⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠸⣆⠀⠀⠀⠈⠢⡀⠀⠀⠀⠈⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⢀⡴⠋⠉⢉⠍⣉⡉⠉⠉⠉⠓⠲⠶⠤⣄⠀⠀⠀ ⠀⠀⢀⠎⠀⠪⠾⢊⣁⣀⡀⠄⠀⠀⡌⠉⠁⠄⠀⢳⠀⠀ ⠀⣰⠟⣢⣤⣐⠘⠛⣻⠻⠭⠇⠀⢤⡶⠟⠛⠂⠀⢌⢷⡀ ⢸⢈⢸⠠⡶⠬⣉⡉⠁⠀⣠⢄⡀⠀⠳⣄⠑⠚⣏⠁⣪⠇ ⠀⢯⡊⠀⠹⡦⣼⣍⠛⢲⠯⢭⣁⣲⣚⣁⣬⢾⢿⠈⡜⠀ ⠀⠀⠙⡄⠀⠘⢾⡉⠙⡟⠶⢶⣿⣶⣿⣶⣿⣾⣿⠀⡇⠀ ⠀⠀⠀⠙⢦⣤⡠⡙⠲⠧⠀⣠⣇⣨⣏⣽⡹⠽⠏⠀⡇⠀ ⠀⠀⠀⠀⠀⠈⠙⠦⢕⡋⠶⠄⣤⠤⠤⠤⠤⠂⡠⠀⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠦⠤⣄⣀⣀⣀⣠⠔⠁⠀

⠀⠀⠀⠀⢀⣠⣴⣶⣶⣶⣶⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣼⡿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⣿⣿⢿⠿⡿⢿⠿⠿⣛⠿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠸⣿⣿⠁⢰⣷⠀⠀⠘⠿⠆⠸⠛⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠸⣿⠀⠤⠕⠀⠀⠀⠐⠂⠀⣠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⢦⡀⠀⠀⠀⠀⠀⣠⡾⣿⢦⣴⢱⡎⡑⣦⣲⡤⢤⣄⠀ ⠀⠀⠀⠀⣿⡀⣿⣶⣶⡖⠂⢹⣿⣧⠀⠀⠠⠀⠈⠉⣁⠀⠀⠀⢸⠀ ⠀⠀⠀⠀⣾⡅⣿⣿⣿⣿⣿⣶⣷⣾⠀⠀⢠⡏⠹⠸⣀⡇⠀⠀⠈⠀ ⠀⠀⠀⢀⣿⡏⢰⢻⠟⠉⠉⢹⠛⣦⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⡌⢿⡇⠀⡦⠴⠀⠀⡌⠈⢸⠀⠀⠀⢀⡧⠔⠣⠀⠀⠀⠀⠀ ⠀⠀⢠⠃⠘⣿⠀⢠⠀⠆⠐⣀⠠⠼⣠⢔⠮⠋⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠎⠀⠀⠉⡂⠔⠱⠚⠈⠀⠀⠀⢨⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀ ⠀⡘⠀⢀⠄⠋⠀⠀⠐⡐⠤⠀⣤⡀⠚⠒⠒⠒⠀⠀⠀⠀⠉⠉⠉⠀ ⢠⠡⠊⠁⠀⠀⠀⠀⠀⠈⠙⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⣀⠴⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠃⠤⠤⠤⠄⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⢠⣞⣛⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣴⠟⠉⢸⣿⣷⡈⠛⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣰⡞⠛⢿⡇⠀⠀⣰⣟⣿⣾⢶⡄⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⡶⠶⠶⠶⠶⠤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢿⡀⢀⣼⣧⡀⠀⠻⠏⠁⠉⠛⠁⠀⡟⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠟⠋⠁⠀⣀⣤⣤⣤⣤⣄⣀⠈⠙⠻⢶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⣻⡿⠗⠀⠉⣳⣄⠀⠀⠀⠀⠀⣼⡥⠟⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣋⣀⡶⢶⣶⡿⢋⣡⠴⠖⠶⢤⣍⠳⣦⠀⠀⠈⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⡾⠁⠀⠀⠀⢸⡏⠙⢷⡤⠤⠴⣞⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠲⠦⣼⣥⣿⠏⣠⣟⣷⡄⠀⠀⠀⠘⢷⡌⢳⣠⣤⡶⠶⠿⠷⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣸⡇⠀⠀⠀⠀⠀⠛⣶⠾⣧⣀⢀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⠛⠓⢶⣯⣿⡏⢠⡿⣿⣿⠃⠀⠀⠀⠀⠘⣿⠀⠋⣁⡤⠖⠒⠲⢶⣌⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡾⠁⠳⣄⠀⠀⠀⠀⢠⡟⠀⠉⢹⣏⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀⠀⠉⣿⣇⠸⣟⠛⠋⠀⠀⠀⠀⠀⢠⣿⠀⣼⡛⣦⠀⠀⠀⠀⢹⣷⡘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠻⢦⡴⠏⢹⡓⠒⢺⡏⠙⢷⡴⣏⡉⠛⢦⣄⡀⠀⠀⠀⠀⢠⣾⠁⠀⠀⠀⠀⠀⠘⣿⡄⠹⣆⠀⠀⠀⠀⠀⣠⡾⠃⢸⠿⣿⡿⠀⠀⠀⠀⠀⣿⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⣧⣀⣠⡷⠀⠀⠀⠈⠙⢦⣄⠈⠙⠳⢦⣄⣰⡋⠘⣦⠀⠀⠀⠀⠀⠀⠘⠿⣦⣌⠙⠒⠶⠶⠚⢋⣠⡄⠸⡟⠉⠁⠀⠀⠀⠀⢀⣿⠃⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⣤⣀⠀⣸⢻⡄⠈⢧⡀⠀⠀⠀⢸⣻⣦⣄⠈⠙⠛⠒⠒⠛⠉⠙⣿⣄⠹⣦⡀⠀⠀⠀⣠⡾⢋⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣷⡏⠀⠻⡄⠈⢳⡀⠀⠀⢸⣏⠳⣬⣷⢦⣄⠀⠀⠀⠀⠀⠈⠻⢷⣄⡉⠙⠛⢉⣁⣴⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠹⣆⢀⣳⣤⣀⠀⠹⣦⡀⠈⠓⠮⢿⡦⣤⣀⡀⠀⠀⠀⠈⠉⠉⠉⠉⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⢀⡿⣿⣽⡿⠈⠛⠦⣄⡙⠲⢤⣄⣀⠉⠛⣻⣽⠇⠀⠀⠀⠀⠀⠀⣸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠛⠶⣄⣀⣠⡟⠀⠈⠋⠀⠀⣠⣀⠀⠉⠛⠲⢤⣍⣉⡉⠉⠀⠀⠀⠀⠀⠀⠀⣠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⢀⣽⠋⠀⠀⠀⠀⠀⡾⠃⠈⠙⠲⢤⣀⡀⠀⡈⠉⠉⣳⣶⡤⠶⠒⠛⢉⣹⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠛⠋⠁⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⢉⡽⠃⠀⠀⣿⣧⣿⠤⠖⠛⠉⠉⠻⢦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⣀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠲⠦⢤⣤⠴⠛⠁⠀⠀⠀⢠⡟⠀⠀⠀⣴⠶⠶⣤⣀⠀⠉⠛⠲⠦⣤⣀⣀⠀⠀⣀⡤⣄⣀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⠿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣟⠀⠀⠀⣼⠇⠀⠀⠀⠉⠛⠳⠦⣤⣄⣀⢉⡿⢻⠋⠋⣀⡼⠉ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠉⠛⠶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠈⠉⠙⢻⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⠷⠾⣄⣠⣿⣶⠞ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠳⠦⢴⡞⠋⠉⠙⠛⠻⣶⣤⣤⣀⡀⠀⠀⠀⠀⠻⢤⣤⡶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠧⠤⠶⠋⠀⠀⠀⠀⠀⠀⢹⡀⢈⣉⣉⣛⣿⣷⣶⠖⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣛⣻⠽⠟⠓⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣽⣿⠖⠒⠚⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡔⠒⠒⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢧⠿⣶⢤⣀⠀⠀⠀⠀⠀⡿⠀⢠⣆⠘⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⣷⠈⠻⣦⠑⢲⣤⣤⣠⡇⠀⣿⣿⡆⠈⣿⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠸⡦⠀⠙⢳⡾⠃⠀⣸⣷⣄⢹⣿⠃⠀⢸⣿⡘⢦⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢱⢀⠔⠋⠀⣠⣾⠃⠀⠉⠺⠃⠀⠀⠀⠘⡇⠀⠙⡦⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣏⠞⢹⢠⠋⠉⠁⠀⡀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⢼⣦⣀⠀⠀⠀ ⠀⠀⠀⢨⡏⠀⡞⢸⡔⢐⡆⠀⠈⠲⣤⠀⠀⠀⠀⠀⢹⡄⠀⠀⠹⣿⠓⠀⠀ ⠀⠀⠀⢘⣷⣤⠇⢸⠁⢒⡶⠦⡶⢤⡈⠑⠀⠀⠀⠀⠘⡇⠀⠀⠀⢸⡄⠀⠈ ⠀⠀⠀⠘⣿⠏⠀⠀⣳⠟⠛⠋⠀⠀⣿⠓⠶⢤⠀⠀⠀⠙⠀⠀⠀⠈⡅⠀⠀ ⠀⠀⠀⡠⠃⠀⠀⢀⡳⠴⣄⣵⡆⢶⣿⡄⠀⣸⠀⠀⠀⠀⡀⠀⠀⠀⡇⠀⠀ ⠀⠀⡔⢁⡄⠀⠀⠁⠀⠀⠀⠀⠀⠈⠛⠻⢲⣿⠀⠀⠀⠀⠆⠀⠀⢀⠃⠀⠀ ⣠⠊⡠⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⢿⡇⠀⠀⠀⢰⠀⠀⠀⢸⠁⠀⠀ ⢷⣾⣿⡿⠁⠀⠀⠀⠀⡠⠎⣀⡴⠏⠁⠀⠀⠇⠀⠀⢀⡌⠀⠀⠀⠀⠀⠀⠀ ⠀⠙⠿⣁⣀⣀⣤⣴⠞⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠉⠙⣏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢹⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠸⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠒⣢⣵⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠚⠉⠀⠀⣸⣿⣉⠃⠑⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣀⣀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠤⠤⠖⠒⠺⠛⠛⣿⠀⢀⣠⣤⣛⣛⠻⣷⡄⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠚⠉⠁⠀⠀⠀⠀⠀⠈⠀⠀⡏⠙⣿⣯⠉⠛⣫⣤⣿⣷⠃⣸⢧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠈⢿⣿⣾⣷⣶⡿⠛⢰⠇⠀⠀⠙⠲⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⢀⣠⠄⠀⠀ ⣷⠀⣿⣇⢀⣠⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠘⣿⡿⠋⠁⠀⢠⠟⠀⠀⠀⠀⠀⠀⢉⠲⢤⡀⠀⠀⠀⢠⣤⣼⡗⠊⠉⠀⠀⠀⠀ ⣿⣄⠸⠿⠟⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠘⣽⡀⠀⠀⣀⣀⣠⣤⣤⣴⣶⣶⣤⣼⣇⠀⠀⢠⠏⠀⠀⠀⢠⡾⠀⠀⠀⠀⠀⠀⠀⠀⢙⣦⣙⢦⡀⣶⣿⣿⣏⡀⠀⠀⠀⠀⠀⠀ ⠉⢁⣶⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⡴⠞⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠒⠶⠤⣄⣼⣇⣀⠀⠀⠀⠀⠀⠀⢸⡳⠈⣯⢳⣷⣯⢿⢹⣿⠇⠀⠀⠀⠀⠀⠀ ⢀⣾⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣔⣮⣿⣤⣤⣶⣶⣶⣶⣶⣶⣶⣶⣤⣤⣤⣤⣤⣀⣀⠀⠀⠀⠀⠈⠉⠛⠻⣶⣶⣶⢋⣷⣞⢳⡏⡿⢰⣿⣿⠹⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⠉⠛⣹⣷⣠⣤⡀⠀⠀⠀⠀⠀⢶⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣀⡀⠀⠀⠽⣡⡴⣶⣿⠰⢤⠀⢹⣿⠟⢾⣁⠁⠀⠀⠀⠀⠀⠀⠀ ⡿⠿⠛⣿⡋⠉⠀⢶⣦⠀⠀⠀⠀⠙⠿⣿⣿⣻⡏⠀⠀⢰⠟⠀⠀⣠⠟⣏⡇⠀⠀⠀⠈⢉⠙⠛⠛⠻⠿⢿⣿⣿⣿⣶⣤⣀⠙⠛⠙⢿⡙⣛⣿⢿⣄⣯⠿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⡧⠀⢤⣬⣿⣿⢿⣿⠆⠀⠀⣸⣷⣿⠁⠀⢀⡏⠀⣨⢾⣅⠀⠸⡇⠀⠀⠀⠀⠘⣧⠀⠀⠰⣆⠀⠈⢻⠛⢿⣿⣿⣿⣶⣤⡈⣿⣧⣴⡆⢿⣷⠲⠶⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣷⡄⠈⠉⠈⢿⣦⠀⠀⢀⣴⣿⡟⡿⠀⠀⣼⡵⠊⠁⠀⠈⠉⢻⡟⠁⠀⠀⠀⢸⡏⣧⣀⣠⣼⣶⠖⠈⡇⠈⣿⠈⠉⠻⣿⣿⣿⣷⣌⣻⣘⢿⣧⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢻⣷⡀⠀⠀⠀⠁⢀⡴⠋⠋⢸⢿⡇⠀⢠⣿⣦⣤⣤⣤⣤⡀⠈⣧⠀⠰⡄⠀⢸⡇⠈⢯⣹⠀⠘⣧⠀⢹⡄⢸⡀⠀⠀⣿⡏⢿⣿⣿⣿⣟⣿⣝⠻⣦⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⣧⠠⣀⣀⠴⣫⠀⢀⣠⣾⢸⡇⠀⢻⢿⡁⠀⣼⣿⡿⣿⡷⣾⡄⠀⢹⡄⢸⡇⠤⣬⣿⣄⣀⡈⢳⡀⢷⣸⠀⠀⢰⣿⡇⢸⡿⠿⠿⠿⠛⢿⣿⠿⠃⠀⠀⠀⠀⠀ ⡀⠀⣀⣠⣤⠘⣛⣤⠀⠉⠉⣩⣿⡿⢻⡯⢸⡇⠀⢸⠀⢁⡀⢿⣧⣀⣾⡇⠀⢻⡀⢸⡛⢾⡇⠛⣿⣿⢿⣿⡿⢿⣿⣿⣿⠀⠀⣼⣸⡟⠘⣧⠀⠀⠀⠀⠸⣿⣷⣄⡀⠀⠀⠀⠀ ⠇⠀⠹⣿⣿⡆⢹⣿⣤⣴⢞⣽⡿⠁⣼⣷⠈⣿⠀⢸⠀⠀⠀⠈⠛⠛⠛⠁⠀⠀⠻⣮⣧⠈⠓⠀⣿⣤⣬⣿⡇⠀⡽⢟⡿⠀⢠⠇⣿⢷⣄⠘⣦⡀⠀⠀⠀⠘⣿⣍⢻⣶⣤⡀⠀ ⠀⠀⠀⢹⣿⣿⡦⠟⢉⣡⣿⣟⡁⣼⡟⢸⣦⠛⣧⡈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠄⠀⠀⠙⠿⠿⠟⠀⠄⢀⣾⠁⢀⡾⢠⣿⣔⣯⠹⣍⣉⠀⠀⠀⠀⠸⣿⣷⣿⣿⣿⣦ ⠀⠀⠀⠀⠉⠀⠀⣠⣿⣿⠟⠌⣸⣿⡇⠈⣿⠀⡟⣷⣿⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡏⣠⣟⣁⣿⠁⢠⡙⣷⠀⠈⣧⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿ ⡄⠀⠀⠀⠀⠀⣰⣽⣻⠋⠀⢰⣿⣿⠃⠀⡟⠀⣧⣿⣿⣧⡀⠀⠀⠀⠀⢸⠏⠉⠒⠒⠒⡆⠀⠀⠀⠀⠀⠀⢠⣿⣿⣾⠋⡋⢹⡻⣤⣤⣧⠙⣶⣶⠿⣄⣠⣄⠀⠀⠙⣿⡿⠟⠋ ⣿⠀⠀⠀⠀⣼⣿⠃⠁⢀⣴⣿⣿⣿⠀⠀⡇⠀⢹⣿⣿⢹⣿⣦⣄⠀⠀⠈⠷⣀⣀⣀⠼⠁⠀⠀⠀⢀⣠⠖⠉⠉⢿⣿⣰⣧⣶⣿⡘⠿⠛⠀⠿⣏⣠⠏⠀⣸⠀⠀⠀⠀⠀⠀⠀ ⠟⠀⠀⠀⡼⣽⡟⠉⢻⣿⠀⠀⢻⣿⠀⠀⡇⠀⢸⣿⠃⠘⣿⣿⣯⢹⣦⣄⠀⠀⠀⠀⢀⣀⣠⡴⠚⠋⠀⠀⠀⠀⠸⣿⠁⢸⣽⣿⡅⠀⠀⠀⠀⢠⣿⣧⣞⡻⡇⠀⠀⠀⠀⠀⠀ ⣄⣴⣤⡞⠛⣏⢸⡀⠀⢯⡇⣶⣾⠋⠙⢾⡇⠀⢸⡏⠀⢀⣿⢿⣿⡇⠈⠻⣝⠒⠖⠚⣉⡡⠴⠟⣆⡀⠀⠀⠀⠀⠀⢻⣤⠞⣿⢏⣷⠢⢍⡉⠉⠁⠉⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀ ⣿⡿⡞⢣⠀⡸⡆⢷⣿⡿⠛⠿⢿⠀⠀⢸⡇⠀⠸⣯⣭⣭⣾⣿⡏⠁⠀⠀⠘⣦⡴⠋⠀⠀⠀⠀⣿⣽⣲⠤⢀⣀⠀⠘⡿⣆⠠⠊⠙⡆⠀⠉⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀ ⡟⢠⡇⠸⢿⣿⣧⠈⠉⠁⠀⠀⢸⣶⣶⡟⣧⠀⠀⣿⣿⣿⣿⣿⣿⡀⠀⠠⠤⣿⣄⣤⡀⠀⢀⣤⣿⣿⣿⣿⣶⣾⢽⣖⡗⢩⠛⢦⣄⡀⠀⠀⠀⠀⠀⣀⣀⡤⢿⣿⣭⣽⣿⣿⣽ ⣶⣿⠀⠀⠀⠉⠁⠀⠀⠀⠀⢀⢸⣿⣿⣆⣿⠀⠀⢸⣿⣿⣿⣿⣿⣷⡀⣀⡼⢻⠈⠉⢁⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⠀⠀⠀⠉⣿⣿⡍⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⡿⢋ ⣿⡏⠀⠀⠀⠀⠀⠀⣤⠖⠋⠁⢸⡀⠿⠏⣿⡆⠀⠀⣿⣿⣿⣿⣿⣿⣿⡄⠀⠈⢷⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⡇⢸⠀⠀⣠⣾⣿⣿⣿⡄⠀⠀⠀⢀⣀⣤⣿⣋⣥⣾⣿ ⣿⠆⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⢀⣹⡶⠖⠋⠘⣆⠀⠹⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⣷⢸⠀⠀⣿⣿⣿⣿⣿⣷⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠁⠀⠐⠲⠶⠒⠚⣳⣶⣶⢶⡞⠋⢹⡄⠀⠀⠀⠸⣧⡀⠹⣿⡿⠟⢋⣵⠋⠹⡝⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⣿⢸⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⢀⣼⣿⣿⡟⣼⠁⢀⢈⣇⠀⠀⠀⠀⢹⡿⠓⣿⡶⣺⡯⠙⠖⢶⣻⡦⣝⢿⣿⣿⣿⣿⣿⣿⣿⠻⠦⣤⣀⡿⢀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣀⠀⠀⠀⢀⣾⢫⣿⣿⣷⠟⢀⣭⣿⣿⣀⡀⠀⠀⠀⢿⡘⠧⣭⣭⠤⣴⡆⢠⣹⠷⡎⢷⠙⢿⣿⣿⣿⠟⠁⠤⣲⣶⣿⣇⣼⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛ ⣒⣙⣛⣓⣿⣿⣿⣿⣿⣯⣾⢟⣻⣿⣿⣯⡳⣄⠀⠀⠈⢧⡀⠀⢸⠀⣿⡇⢸⠏⠛⠓⠚⠃⠀⠻⠿⠁⠀⣴⡿⣿⠃⠀⣿⢻⠀⠀⠀⠀⣸⡿⢟⣿⡿⢿⣿⣿⣿⡿⠿⠛⠁⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡿⢿⠟⣿⣿⠈⠳⣝⡷⢦⣤⣈⣷⡀⢸⡆⠿⣡⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⣱⠃⠀⢰⠏⡾⠀⠀⠀⢠⣯⣧⣸⡜⢿⣄⡙⢿⣿⣷⡀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣯⡟⠀⠀⠈⠙⠇⣠⣴⣭⣭⡀⣻⠞⠁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣻⠃⠀⡰⠋⠀⡇⠀⠀⢠⣾⣿⣿⣿⣿⣷⣾⣿⣦⣉⠛⠷⣄⡀⠀⠀ ⣿⣿⢿⣟⠟⣻⣿⣿⣿⣿⡯⣿⣿⣿⡇⠀⠀⠀⠀⠸⣯⣄⣀⣨⣽⣿⠛⠛⠛⢿⣧⠀⠀⠀⠀⠀⢀⡼⣫⠃⠀⠀⠀⠀⣠⡇⢀⡴⢻⣿⣿⣿⣯⡧⣿⣿⣿⣿⣿⣿⣦⣬⣟⣂⣀

⠀⠀⠀⣿⣇⣾⣾⣟⣦⣄⠀⠀⠀⠀⠀⢀⣠⣾⣵⣾⣶⣶⣶⣶⣶⣶⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⣿⡟⠺⡟⣧⣏⠓⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣏⢹⡏⠗⢴⡈⣿⣿⣯⣭⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣇⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⣏⡏⠻⣬⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⢯⡷⢄⣸⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠋⠛⠛⢿⣿⣭⣽⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⣤⢷⢈⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀ ⠀⠀⠀⠸⡿⣟⣼⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⡏⠹⣇⠀⠀⠀⠀⠀⠀⢹⡿⣿⣿⣿⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢫⡸⢿⣿⣿⣞⣿⣿⣷⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⡇⠘⣿⣿⠉⠑⠻⣄⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⢧⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⢻⡇⢿⣿⢿⡇⠀⠘⣿⡀⠀⠀⠈⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⡾⣿⠟⠻⢿⣿⣿⣿⣿⣿⡟⠀⠀⠈⣧⣤⣿⣴⣿⣶⣤⡸⡇⠀⠀⠀⠀⠀⠀⠀⠓⢄⣿⢿⣿⣿⡃⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⣼⣿⠗⢞⠙⣆⣹⣿⣿⣿⣿⠀⠀⠀⠹⣏⢹⠁⠀⢠⣼⠻⠟⠄⠀⠀⢀⡠⠔⠂⠀⠀⢀⣿⡟⣿⣿⣿⣷⡀⠀⠀⠀ ⠀⠀⠀⣿⠿⣻⡀⡿⢋⠈⣿⣿⣿⣿⣿⠀⠀⠀⠀⠈⠙⠓⠦⢼⡋⠀⠀⠀⠀⠀⢈⣠⠤⢥⣤⡄⣸⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀ ⠀⠀⢀⣿⠿⠛⠧⡈⠢⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣔⢒⣾⡏⣷⣿⣿⣿⣿⣿⣿⣿⢻⠀⠀⠀ ⠀⣠⠟⠁⠀⠀⠀⢑⣾⣿⣿⣿⣯⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣟⠶⣿⣿⠋⣿⡿⣿⣿⠃⠀⠀⠀⠀ ⠀⠁⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠰⣖⠢⠤⣀⠀⠀⠀⠀⠀⣸⣿⣿⣷⣿⠡⠿⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⢿⡿⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⠚⠃⠀⠀⠀⣠⣿⣿⣿⣿⣿⡆⠀⠀⣀⡤⠄⠤⠄ ⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣇⠞⡇⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⣿⣿⣿⣿⣿⣿⣇⡰⠉⠀⢀⣀⣀⣀ ⠀⠀⠀⠀⠀⢸⡟⣿⡿⠟⠉⠁⠀⠀⡇⠀⠀⠀⢈⣲⣄⡀⠀⠀⠀⠀⠀⠀⢀⣠⠖⠁⠀⣽⣿⣿⣿⣿⣿⠏⢀⠴⠊⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠒⠉⡉⠉⠏⣁⣤⣤⣼⣷⣦⣤⣀⣤⣾⣅⣈⡇⢀⡼⣿⡿⠿⢿⢿⢏⡴⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣶⣿⣿⣿⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢀⣠⣅⠀⠀⣸⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⠀⠈⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣀⠤⣿⣿⣿⣿⣀⣧⣀⣿⣿⣿⡿⠟⠉⢈⢁⣈⣉⠙⠻⣿⣿⡟⠋⠁⠀⠀⣀⣤⣴⠶⡶⣶⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⢰⠋⠈⠉⣠⣾⣿⣿⣛⣿⣿⣿⣿⣿⣿⣯⡄⢠⣚⣻⣿⣐⣲⠭⡒⢤⡙⡇⠀⠀⡰⢚⡽⠚⠏⢉⣵⠘⠈⡀⠀ ⠀⠀⢀⠔⠂⣹⠇⠀⢀⣾⣿⣿⣿⣿⣿⡇⠀⠈⣿⣿⣿⣿⡁⠘⣿⠀⠀⠀⠈⠙⠢⡑⢈⢳⡀⡜⡴⠁⠀⠄⡧⢄⠀⠀⠀⡇⠀ ⢀⡀⢀⠔⢋⡜⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⡁⠀⢻⢧⠀⠀⠀⢰⠀⠈⢢⣱⣿⡽⠁⠀⠉⠐⣀⡄⢠⢠⢤⠅⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⠴⠶⠶⢶⣶⣒⣒⣒⢒⣲⣖⠒⠒⠲⠶⠾⠶⢶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⣴⠿⣻⣭⣭⣭⣀⣀⣀⡀⣀⣀⣤⡤⠖⠒⠢⠤⣬⣉⠓⠦⣄⡀⠀⠀⠉⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⡾⠋⠁⠀⢁⡠⠴⠒⠦⢤⡉⠉⠁⠀⠀⠀⣶⠒⠒⠒⠒⠚⠿⣇⡠⢉⡲⣄⠀⠀⠹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣾⠁⠀⠀⢰⠋⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠃⠀⢀⣀⣀⣀⡀⠈⠙⠻⢧⠈⠀⠀⠀⠹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣴⠟⠀⠀⠀⡀⣠⣶⠶⣶⣤⣤⡿⠀⠀⠀⠀⢀⣴⠾⠛⢙⣿⣿⣿⡟⢶⣄⢀⣀⠀⠀⣀⣀⣹⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣰⡿⢣⣖⡏⠉⠉⠉⠛⠛⠛⠛⠿⢿⣷⡶⠖⠀⠀⠸⣧⣴⠾⠛⠻⣏⡙⠛⠛⠋⠘⢛⣳⣿⣿⣿⡉⠻⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠐⣿⠁⢰⢿⡿⠟⠳⣶⣄⣠⡆⠀⠀⠀⣿⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠙⠻⢶⣶⣶⠾⠛⢉⣾⡀⠉⢿⡆⢹⡟⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢿⡄⠸⣄⠀⢸⡟⠉⠛⠉⠀⢀⣴⡾⠋⠀⠀⠀⠀⠠⢶⣦⣤⣄⣀⡀⠀⠀⠀⢀⣠⣴⠿⢻⣧⣄⣈⣿⢸⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠘⣷⡀⢸⠀⣿⣿⣄⠀⠠⠞⠛⠻⣦⡀⠀⡀⠴⠾⠿⣦⣼⠇⠀⢀⣀⣤⣶⠾⡿⠉⠀⣠⣾⠇⠉⢿⠏⣼⣇⡿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠘⣷⠀⢰⣿⡟⣿⠷⣦⣄⣀⣀⣈⣛⣻⠁⣀⣠⣤⣴⡿⣶⡟⠋⠉⠁⢀⣼⣧⣴⢾⣿⠏⠀⠀⠀⣛⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢻⠀⢸⣿⣧⣿⠀⢸⡏⠉⠛⢻⡟⠛⠋⢻⡉⠉⠀⠀⣸⣷⣤⣴⣾⠿⢿⡏⢠⣾⠃⠀⠀⠀⢠⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⠀⠸⣿⣿⣿⣿⣿⣿⣷⣶⣾⣷⣶⣾⣿⣿⣶⣶⣿⠿⣿⡋⠉⠀⠀⢘⣷⠟⠁⠀⠀⠀⢠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⠀⠀⣿⡙⣟⢿⡿⢿⣿⠿⠿⣿⠿⠟⠛⣿⠋⠁⠀⠀⠸⣧⠀⣠⣶⠟⠉⠀⠀⠀⠀⣠⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣾⠀⠀⠘⢿⣿⣈⣷⣀⣿⣄⠀⣿⡀⠀⠀⣿⡀⢀⣀⣠⣤⡿⠟⠋⣀⡤⠂⣤⡆⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⠀⢀⠀⢤⡈⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⢉⣀⠤⠖⣋⠵⠒⣩⣴⠿⠻⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡇⠀⠘⣆⠀⠙⠢⠤⣀⣀⣀⡸⠟⠛⠛⠛⠓⢲⣤⣬⠋⠁⠀⣈⣤⡶⠟⠋⠁⠀⢀⣼⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⡀⠀⠈⠙⠒⠒⠒⠒⠂⠐⠒⠒⠂⠉⠉⠉⠉⠀⣀⣤⡶⠟⠋⣁⣤⣄⣤⣤⣾⣏⣉⣿⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠘⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⠶⠶⠟⠋⠁⠀⠀⣼⠏⢈⣽⡿⠋⠉⠉⢉⣿⡟⠻⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠙⠛⠷⠶⠶⠶⠾⠟⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⣠⣾⠯⠾⠟⠁⠀⠀⠀⠀⣾⣿⡇⠀⠀⠙⠿⣦⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠈⠙⢷⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠹⣷⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠆ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠈⣩⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣠⣴⠶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣤⡞⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠙⠓⠒⠒⠒⠤⢤⣠⣄⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠒⠢⠤⢄⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢉⠃⠀⠀⠀⢠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⡾⠀⠀⡀⠀⠀⣴⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠃⠀⠀⠀⢸⠃⣠⠞⣰⢀⠎⢸⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⢀⡠⢶⣿⡏⠀⠀⠀⢀⣿⠞⠁⢠⡿⡇⠀⢸⢀⣼⠀⢸⡆⠀⠀⢲⣦⠀⠀⠀⠀⠀⢢⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡴⢀⠎⠀⠀⢀⡠⠒⣩⣶⣿⣿⠃⡀⠀⠀⠈⢁⠀⠀⠈⣼⠃⠀⢸⠃⢈⣦⣿⣷⡀⠀⠈⢿⡆⠀⠀⠀⣤⠀⠑⡄⠀⠀⠀⠀ ⠀⠀⢠⠞⢀⠎⠀⣠⠔⢉⣤⣾⣿⣿⣿⣿⢠⠁⠀⢀⣰⠃⠀⢠⣾⣿⡀⠀⠀⠀⣼⣿⣿⣿⣷⣼⡀⠘⣿⠀⠀⠀⣿⡆⠀⠈⢿⣦⠀⠀ ⢀⣴⠏⢠⣾⠟⠋⣠⠔⠉⠀⠹⢿⣿⣿⣷⡟⠀⢀⣾⠇⣰⣾⣿⣿⣿⠁⠀⢀⣾⣿⣿⣿⣿⣿⣿⠷⣄⠸⡇⢀⢀⠇⣹⡀⠀⠀⠉⠓⣄ ⢫⠏⢠⠎⠀⣠⣾⣿⡇⠀⠀⠀⠀⢻⣿⣿⠇⢀⣾⢏⣾⣿⣿⣿⣿⣇⡀⣧⣾⣿⣿⣿⣿⡿⠋⠁⠀⠈⠢⣣⢘⡾⠀⢤⣷⠀⠀⠀⠀⢹ ⣮⡴⢁⡴⢻⣿⣿⣿⣿⣆⠀⠀⠀⠈⠫⠿⠀⡞⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢻⣯⢏⡆⠀⠀⠀⠀⠙⢿⣃⣠⣾⣿⣧⣄⢀⠀⣿ ⣹⣵⠏⢀⣿⣿⣿⣿⣿⣿⣧⣀⡀⠀⠀⢰⣼⡔⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠉⠉⠀⠀⢀⠀⠀⣤⣴⣾⣿⣿⣿⡿⠛⠎⢢⡟ ⢹⡟⢀⣾⣿⣿⣿⣿⡈⠛⢿⣿⣿⣶⣶⣿⣿⣿⡿⢿⡿⡿⠿⠿⣿⡿⣿⣷⣮⣤⣀⣠⣀⣤⣷⣶⣾⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⣸⠀⣁ ⡸⠀⣼⣿⣿⣿⣿⣿⣇⠀⠀⠈⠛⠿⠿⠿⠯⠀⠀⢠⣿⠃⠀⠈⠁⠀⠀⠉⠛⠿⠿⠿⠿⠟⠛⠋⣹⠿⠛⠛⠉⠁⠀⠀⠔⠀⣰⣟⡿⠁ ⠇⠀⣻⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠠⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⢿⠃⠀ ⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⠤⣶⣶⡦⠀⠀⠀⠀⡔⠀⠀⠸⠀⣠ ⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⢀⡀⢀⣀⣀⣁⣀⣀⠀⠀⠤⠤⠔⠒⠒⠚⠉⠛⠁⠀⢀⣼⣿⡿⠀⠀⠀⢀⣾⡀⠀⣀⣠⣾⣧ ⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠈⢻⣿⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣶⣶⣿⠋⣾⡿⠁⠀⢀⣴⣿⣿⣿⣿⠿⠛⢋⣁ ⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠙⣿⡓⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇⢈⠟⠁⢠⣴⡿⠿⢛⣉⣥⣤⣶⡿⠿⢿ ⠤⠤⣀⣀⠀⠀⠀⠈⢻⡿⣿⣿⣿⣿⣿⣿⣷⣄⠈⢣⡙⠛⢿⣿⣿⣿⣿⣿⣿⠿⠟⠋⠁⢀⣠⣿⣶⣾⣿⣾⣿⣿⣿⣿⣿⡿⣿⣷⣄⣸ ⠀⠀⠀⠀⠉⠑⠒⠲⠤⣿⡄⠙⢿⣿⣿⣿⣿⣷⣷⠴⠻⢦⣀⡨⠭⣉⣉⣉⣀⣤⣴⣶⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⣿⠿⠿⠿⠿⠿⠿ ⢰⡶⢷⣶⣷⣄⣀⠀⠀⠘⠋⢳⣿⡿⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠟⠋⣁⡤⢶⣆⣼⣿⣿⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣀⡀⠀⠀⢀⣠⠖⠒⠒⠒⠒⠒⠒⠒⠒⠦⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡞⠉⠀⡠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⣶⣶⣾⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⠟⣡⠋⡼⠁⠀⠀⠀⣼⡇⠀⢀⠈⠳⣦⣄⠀⠀⠙⢿⣿⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠃⡴⠁⣼⠁⠀⠀⠀⣼⣿⣷⠀⠈⣇⠀⠈⢻⠀⢐⡆⠀⢻⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⡇⠀⣿⡀⠀⠀⢰⣿⣿⡇⠀⣀⣿⡄⢀⣾⠀⢸⡇⠀⢺⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⢠⣿⣄⣿⣿⣤⠀⠀⣿⣿⢀⣠⣿⢻⣿⡿⢿⣦⣾⣇⣀⣾⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣶⣼⣿⣿⣿⣧⡙⢷⣾⣿⣿⣿⡿⠃⣼⡿⠒⣻⡿⣿⣷⣿⠟⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣧⣬⣽⣿⣿⣿⣿⣿⣻⣶⣿⣿⣿⣿⠧⢤⣿⡟⣧⠀⣿⣷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⠇⣿⡈⠁⣞⢻⣿⡟⠋⠈⠛⠉⠉⣟⣿⣿⣀⢙⣿⣧⡇⠀⢹⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠰⠾⣿⣿⠟⠁⠀⢹⣧⠈⠻⠿⠛⠀⠀⡄⠀⠀⠀⠙⠛⠛⠁⣸⣿⣿⣷⠀⡘⣿⣿⣿⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⢋⡏⠀⠀⡴⢿⣿⣦⠀⠀⠀⠀⠀⢑⣀⣀⣠⣤⠀⠀⢰⡿⡏⣿⢟⠂⢻⡘⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⠴⠛⠚⡟⢠⠊⢁⣾⠀⢹⣧⡀⠀⠘⢯⣥⣒⣲⡶⠃⢀⣴⣿⡇⠁⠘⣾⣷⡘⣷⣿⣿⣍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡜⠁⠀⠀⠀⣧⠎⠀⡾⣿⠀⠸⡟⢿⠓⢤⡀⠀⠛⠁⢀⡴⢋⣿⣿⣷⠀⠀⣧⣿⣿⠉⠛⠛⠻⢦⣤⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡞⠀⠀⠀⠀⣠⡇⠀⢀⣇⠙⣄⠀⡟⠻⣆⠀⠙⢷⡶⠖⠋⠀⡞⣿⠃⠟⣧⢀⣼⠀⠛⠀⠀⠀⠀⠀⠈⠻⣦⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣇⡠⠔⠊⠉⠉⠃⠘⢏⠈⢦⣈⡄⣇⠀⠈⢳⡀⠀⣄⠀⠀⣸⠁⠀⠀⠀⣿⣾⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀ ⠀⠀⣠⠚⠁⠀⠀⠀⠀⠀⢸⠀⠀⢣⠀⢹⠁⡟⠓⠤⢄⣷⠀⠸⠀⣰⣇⣀⣀⣠⣾⠿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠲⢦⣄⠀⠀ ⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⣸⡄⠀⢸⢀⣼⠞⢓⣀⡐⢦⣈⣙⣒⣛⣋⣤⡴⢂⣘⣁⣀⣀⣀⣀⡀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄ ⠈⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⠴⠶⠶⠶⠶⠶⠶⠶⠶⢤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣤⠶⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠶⣤⡀⠀⠀⠀⠀⠀ ⠀⠀⢀⡴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⡄⠀⠀⠀ ⠀⣰⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⠀⠀ ⢰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠀ ⣿⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⢹⡄ ⡏⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇ ⣿⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⢸⡇ ⢹⡆⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⣾⠀ ⠈⢷⡀⢸⡇⠀⢀⣠⣤⣶⣶⣶⣤⡀⠀⠀⠀⠀⠀⢀⣠⣶⣶⣶⣶⣤⣄⠀⠀⣿⠀⣼⠃⠀ ⠀⠈⢷⣼⠃⠀⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⡾⠃⠀⠀ ⠀⠀⠈⣿⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⠃⠀⢸⡇⠀⠀⠀ ⠀⠀⠀⣿⠀⠀⠘⢿⣿⣿⣿⣿⡿⠃⠀⢠⠀⣄⠀⠀⠙⢿⣿⣿⣿⡿⠏⠀⠀⢘⡇⠀⠀⠀ ⠀⠀⠀⢻⡄⠀⠀⠀⠈⠉⠉⠀⠀⠀⣴⣿⠀⣿⣷⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⢸⡇⠀⠀⠀ ⠀⠀⠀⠈⠻⣄⡀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠀⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⣟⠳⣦⡀⠀⠀⠀⠸⣿⡿⠀⢻⣿⡟⠀⠀⠀⠀⣤⡾⢻⡏⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⡄⢻⠻⣆⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⢀⡾⢻⠁⢸⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⡇⠀⡆⢹⠒⡦⢤⠤⡤⢤⢤⡤⣤⠤⡔⡿⢁⡇⠀⡿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⡇⠀⢣⢸⠦⣧⣼⣀⡇⢸⢀⣇⣸⣠⡷⢇⢸⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣷⠀⠈⠺⣄⣇⢸⠉⡏⢹⠉⡏⢹⢀⣧⠾⠋⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠻⣆⠀⠀⠀⠈⠉⠙⠓⠚⠚⠋⠉⠁⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⠦⣤⣤⣤⡤⠶⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣶⣶⣤⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣴⣿⡿⠛⠋⠉⠉⠙⠛⢿⣿⣦⡀⠀⠀⠀ ⠀⠀⢠⣿⡿⠁⣠⣾⣿⣿⣿⣿⣷⣄⠈⢿⣿⡄⠀⠀ ⠀⠀⣾⡿⠁⣼⣿⣿⣿⣿⣿⣿⣿⣿⣧⠈⢿⣷⠀⠀ ⠀⠀⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣸⣿⠀⠀ ⠀⠀⢻⣿⡄⠙⣿⣿⣿⣿⣿⣿⣿⣿⠋⢠⣿⡟⠀⠀ ⠀⠀⠈⢻⣿⣄⠈⠻⠿⢿⡿⠿⠟⠁⣠⣿⡟⠁⠀⠀ ⠀⠀⠀⠀⠙⠿⣿⣶⣦⣼⣧⣴⣶⣿⠿⠋⠀⠀⠀⠀ ⢀⣤⣤⣤⣤⡄⠀⢿⣿⣿⣿⣿⡿⠀⢠⣤⣤⣤⣤⡀ ⢸⣿⣿⣿⣿⣧⣤⣼⣿⣿⣿⣿⣧⣤⣼⣿⣿⣿⣿⡇ ⢸⣿⣿⣿⣿⡏⠉⠙⣿⣿⣿⣿⠋⠉⢹⣿⣿⣿⣿⡇ ⢸⣿⣿⣿⣿⡇⠀⠀⠈⠛⠛⠁⠀⠀⢸⣿⣿⣿⣿⡇ ⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇ ⠀⢿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡿⠀ ⠀⠘⠿⠿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⠿⠃⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⣦⢀⣴⣿⣿⣿⣿⣦⡀⣴⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀ ⠀⠀⠀⢀⣾⣿⣿⣿⣿⠟⠻⣿⣿⣿⣿⣷⡀⠀⠀⠀ ⠀⠀⢀⣾⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣷⡀⠀⠀ ⠀⠀⣸⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⠀ ⠀⠀⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⠀⠀ ⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀ ⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀ ⠀⣰⣿⡿⢿⣿⡿⠿⠿⣿⣿⠿⠿⢿⣿⡿⢿⣷⣄⠀ ⣼⣿⠏⠀⢸⣿⠇⠀⠀⣿⣿⠀⠀⢸⣿⡇⠀⠹⣿⣧ ⣿⣿⠀⠀⢸⣿⡀⠀⠀⣿⣿⠀⠀⢠⣿⡇⠀⢀⣿⣿ ⠘⣿⣧⠀⠈⢿⡷⠀⠀⣿⣿⠀⠀⢾⡿⠁⠀⣾⡿⠃ ⠀⠈⠁⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠉⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⣶⣶⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠋⠛⠻⢿⣿⠿⠿⡿⡆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⡸⠀⡄⠂⠤⠙⣷⣶⣾⣧⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⡷⠇⠀⢄⠀⣰⠃⠙⣿⣿⡿⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⠰⠄⠲⠭⠀⠀⠀⡿⠗⠀⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠓⠦⠇⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠀⠀⠀⠀⠔⠒⠒⠒⠛⢲⠀⠑⢤⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⣤⡎⡟⢠⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⢸⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡀⢴⣿⣿⣿⣿⣿⡼⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠛⡗⠢⡀⠀⠀⠀ ⠀⠀⡠⠊⠀⠸⣿⣿⠿⣿⠇⢿⣮⡑⠒⠤⠤⠔⠊⠒⠦⣴⠁⠀⠸⠀⠈⣦⡀⠀ ⠀⡰⠁⠀⠀⠀⠙⠁⠀⠈⠦⠜⠻⢿⣦⣄⠀⠀⠀⠀⡠⣫⠊⠉⠒⣧⡄⣿⣷⡀ ⢰⣿⣷⣀⣤⣠⣾⣦⣄⠀⠀⠠⣤⣤⣙⠁⡉⠢⣄⣜⠀⠁⠀⠀⢠⣿⣿⣿⣿⣇ ⣾⣿⣿⣿⣿⡿⠿⣿⣟⢰⠀⠀⢿⣿⣿⣿⣿⣠⣾⣼⣿⣴⣦⠀⣹⣿⣿⡏⠟⢸

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠤⠤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠚⠉⠉⠀⢀⢤⡄⢸⣿⣿⣿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢴⠉⣠⠚⠁⠀⠀⢀⠊⣼⠇⠈⣷⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⡰⣥⠞⠁⠀⠀⠀⠀⠂⣰⡟⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⡰⡻⠋⠀⠀⣼⠀⣠⠀⣰⠏⠀⠀⡀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⣰⡿⠁⠀⣀⣼⠇⣴⠁⢰⠏⣸⠀⠀⠁⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⢀⢀⡟⠀⠀⡴⣹⣟⣼⠏⢀⡜⡰⠻⢸⠀⣸⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡇⢘⡼⠀⡀⡰⢁⣿⠏⡏⣠⢞⠜⠁⠀⣿⡆⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠘⡇⠀⣷⠃⡼⡏⣸⣴⠟⠓⠒⠤⢄⣿⣧⣸⣿⣿⠃⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠁⠀⡏⢰⣀⣶⡟⢲⣶⠲⠶⣶⡄⠈⢸⣿⡿⠏⣉⠉⢻⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⢰⠀⢁⣴⣧⠇⠉⠒⠓⠒⠒⠀⠁⠀⠈⣿⠃⢻⡟⠓⠚⠛⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢷⣸⣸⣧⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠘⢆⡈⠁⠒⠒⢚⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣻⢹⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠙⠊⠉⠓⠊⢀⣿⣿⣿⡏⠙⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣄⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡿⠿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⢻⣷⣾⣆⠀⠀⠀⠀⠀⠀⠴⣶⣶⡦⠀⠀⠀⠀⠀⢀⡼⣟⣡⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠙⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠮⠤⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⠉⢻⣿⣦⣄⡀⠀⠀⠀⠀⢀⣠⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠛⢄⡀⢻⣿⣿⣿⣷⣶⣶⠟⠛⠉⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡤⠤⣶⣶⣦⣀⣀⣰⠃⠀⠀⠈⠛⠯⣝⠫⠿⠋⠁⠀⠀⢰⣷⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣀⠤⣾⣛⣉⡉⠑⢦⡈⢻⡿⢷⣶⣿⡄⠀⠀⠀⠀⠀⠈⣵⣤⣤⡖⠒⠉⠁⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢰⠏⠀⢢⡀⠀⠀⠈⢦⠀⠱⡀⠹⣿⡇⠹⢷⠀⠀⠀⠀⢠⣾⣿⣿⡟⠳⡀⠀⠀⠀⣿⣯⣙⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠠⠔⢚⠏⠀⠐⠤⣽⣷⣾⡄⠀⡇⠀⡝⠀⣿⣿⡀⠈⣇⠀⠀⣰⠋⣿⣿⣿⡷⡴⠛⢄⠀⢰⡏⠻⢿⣿⣗⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡠⠋⠀⠀⠀⠀⣿⣿⣿⣷⠈⡁⢰⣇⢫⣿⣿⡇⠀⠸⡀⡼⠻⣦⣽⣿⣿⣶⠇⠀⠈⠣⡈⡇⠀⠈⠫⠛⠿⠿⣿⣶⣤⣀⡀⠀⠀⠀ ⠜⠁⠀⠀⠀⠀⢸⠟⠛⢻⣀⣿⣷⣾⣿⣿⣿⣿⡇⠀⠀⠙⠁⠀⠈⣹⣿⣏⠹⡀⠀⠀⠁⠙⠇⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠦⡀⠀ ⠀⠀⠀⠀⠀⢀⣿⣷⡄⣠⠟⠁⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⠀⠀⠀⢹⣷⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡄⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠱⡀⢿⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⢱⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⢀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⢄⠙⣦⡀⠀⢳⣸⣇⠀⠀⠀⢀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡇⣸⣷⡀⠘⣄⠀⠀⠀⢹⣄⠀⠀⠈⢣⡀⠀⢳⣤⡀⠀⠀⠀⠀⠀⠈⠣⣘⢿⣦⠀⢿⣿⠀⠀⠀⢸⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⣰⡿⠉⢿⣆⠘⣧⡀⠀⠈⣿⣿⣦⡀⠀⠹⣦⠈⢧⡉⠲⢤⣀⡀⠀⠀⠀⠘⢿⣿⣷⣼⣿⠀⠀⠀⢸⠀ ⠀⢸⠀⠀⠀⠀⠀⡀⣠⣾⣿⣷⡿⡁⠀⠀⢿⣷⣌⣿⣦⡀⠸⡝⠻⣿⣷⣤⣘⣷⣾⣿⢦⣄⠀⠉⠙⠒⢲⣤⠴⢿⣿⣿⣿⠀⠀⠀⢸⠀ ⠀⢸⡆⠀⠀⠀⠀⣴⣿⣿⣿⣿⠷⠀⣄⡀⠀⠙⠻⢿⣿⣿⣦⣱⠀⠈⡙⠿⣯⣙⠛⢿⣦⠈⠓⢦⣤⣾⣋⣠⡴⠂⠀⣨⠛⢦⣄⡀⣈⠀ ⢰⢀⡇⠀⠀⠀⠀⣿⣿⣿⣷⣶⣶⣶⣶⣾⣷⣦⣄⡀⠙⠻⢿⣿⣷⡀⠈⠙⠂⠉⠛⠻⣿⣷⣶⣿⣿⣿⣿⣿⣷⣶⣿⣻⡶⠚⠛⠛⠛⣧ ⠾⣾⠁⡀⠀⠀⠀⢹⣿⣿⡉⠀⠁⠀⡜⠛⠛⠿⣿⣿⡿⣶⡖⠛⠛⠿⠂⠀⠀⢤⣶⢿⣿⡿⠟⠛⠳⡄⠀⠈⠉⣹⣿⢿⠃⠀⠀⢀⡀⢹ ⠀⢿⠀⡇⠀⠀⠀⣼⠀⠹⢧⡀⠀⠸⡀⠀⠲⠂⣸⠀⠙⠊⠃⠀⠀⠀⠀⠀⠀⠈⠠⠏⢿⠀⠴⠆⠀⢱⠀⠀⢠⡿⠓⡾⠀⠀⠀⣸⠇⣸ ⠀⢸⡇⠸⡀⠀⠀⢹⡄⠀⠀⠿⠦⣀⠑⢄⣀⡠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠧⢄⢀⡴⠃⣀⠔⠋⠀⠀⠃⠰⠀⢀⠏⢠⠟ ⠀⠀⣿⡄⢣⠀⠀⠸⣷⡀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢀⠇⠀⡜⣠⠟⠀ ⠀⢳⢾⣿⣤⡂⢀⠀⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⡜⠀⢰⡿⠃⠀⠀ ⣷⣶⣾⣿⣿⣷⠐⡀⢹⡏⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⣰⠃⢀⡿⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣇⢱⠈⣿⡚⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢠⡟⢀⣾⣿⠇⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⡈⣧⢻⣧⢈⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠁⣾⠁⡾⠻⣿⣷⣶⣶⣶ ⣿⣿⣿⣿⣿⣿⣿⢱⡸⣾⣿⣇⠘⢦⡀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⠀⠀⠀⠀⠀⣠⢿⡏⣼⡇⣼⠃⠀⠙⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⠿⠛⠉⠱⣿⣿⣿⡆⠀⠙⢦⡀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⣠⠞⠁⣸⣿⣿⣿⠏⠒⢄⠀⠈⠻⣿⣿ ⣿⣿⣿⣿⠃⣄⡀⠀⠀⠹⣿⣿⣿⡀⠀⠀⠙⠷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠟⠁⠀⢰⣿⣿⣿⠏⠀⠀⠀⠑⢄⠀⠙⣿ ⣿⣿⣿⣿⢰⡏⢳⡀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⣹⡟⠳⣦⣀⠀⠀⠀⠀⠀⠀⣀⡴⠞⢹⣿⡀⠀⠀⣿⣿⣿⡏⠀⠀⠀⣴⢷⠈⣆⣀⣸ ⣿⣿⣿⣿⣾⡃⠈⣧⠀⠀⠀⣿⣿⣿⣧⣀⣤⡾⠿⣧⠀⠀⠉⠛⠶⣤⣤⡴⠞⠉⠀⠀⣸⠋⠙⢦⣠⣿⣿⣿⡇⠀⠀⢰⠇⠘⣇⢹⣿⣿ ⣿⣿⣿⣿⣿⣶⣾⣿⡆⠀⠀⢿⣿⣿⣿⣿⠋⢀⡀⣿⡄⠀⠀⣀⣀⣐⠹⠆⠀⠀⠀⠀⣿⠀⠀⠈⢿⣿⣿⣿⡇⠀⠀⣾⣶⣶⣿⡘⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⢸⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣷⣦⣄⣿⣿⣿⣿⣿⠀⢠⣿⣿⣿⣿⣇⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⢘⣿⣿⣿⢿⣯⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣼⣿⣿⣿⣿⣿⣼⣿ ⣿⣿⣿⣯⣏⣿⣟⣿⣫⣿⣿⣿⣿⣿⣇⣺⣿⣟⠿⣏⣭⣟⣭⣿⢻⣿⣿⣿⣿⣿⣛⣟⣹⣿⣿⡻⣿⣿⣽⣿⣿⣿⣟⣿⣿⣾⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⣿⠿⢄⡀⠀⠻⡄⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠹⠀⠀⠉⠑⠲⠽⣄⡀⠙⢿⣿⣿⣿⣿⠟⠉⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⠤⣦⡤⠤⠤⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠖⠛⠉⠀⠀⠀⠀⢂⠀⠀⠀⢀⡀⠀⠉⠛⠲⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠋⣡⠖⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠻⣄⠀⠀⡷⢄⠉⠳⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠋⠀⣠⠞⠁⠀⠀⠀⠀⠀⢠⠂⠀⠀⢰⠀⠀⠀⠀⠸⡄⠀⠙⢎⠳⣄⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠉⠀⢠⣾⠟⠀⠀⣰⠀⠀⠀⠀⢸⠀⠀⠀⠈⡆⠀⠀⠀⠀⠹⡄⠀⠈⢷⠈⢷⡀⠀⠙⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⢀⣴⢋⡞⠀⠀⢠⠇⠀⠀⠀⠀⡇⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⢻⣆⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠃⠀⢠⣿⠃⣼⠁⠀⠀⣾⠀⠀⡀⠀⢠⡇⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠙⣦⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠠⣿⠃⢠⠇⠀⠀⢰⡇⠀⣸⢇⣄⢸⣇⠀⠸⣤⠀⢸⢡⠀⠀⠀⠀⠂⣼⠀⠆⣠⣶⡄⠀⠘⣇⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⢰⠏⠀⡼⠀⣀⠀⣼⢠⢀⡟⢸⢟⣸⡇⠀⠀⠁⠀⢸⣸⠀⠀⠀⠀⠀⠉⠁⠀⠈⠻⣽⡀⠀⠘⡄⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⡟⠀⢸⣇⣼⣽⡎⣿⣿⠼⠛⠉⠉⢸⡇⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠰⠀⠀⠀⠈⣇⠀⠀⢻⠀⢀⡈⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⢰⠇⠀⣾⠋⠁⠀⢸⡏⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⣆⠀⠀⠀⢸⠀⠀⠈⡆⠀⠹⣞⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠇⠀⠀⠀⣾⠀⢀⡇⠀⠀⠀⣿⡇⠀⠀⠀⠀⢀⣘⣇⣤⠤⠤⠖⠒⠛⠛⠛⣛⣿⠿⠿⠿⠛⢛⣓⠲⢶⡇⠀⠀⢹⡀⠀⢈⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠀⢀⠀⠀⡟⠀⢸⠃⠀⠀⠀⣿⡇⢀⣤⠴⠾⠯⠭⣄⠀⠀⠀⠀⠀⠀⠀⡞⢉⣤⣶⣶⣶⣾⠿⠿⢶⣾⣿⠀⠀⢸⣷⠀⠸⣄⠘⢧⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡴⢟⣼⠃⢠⡏⠀⢠⡇⠀⣿⠀⠀⢀⣤⣿⣿⣭⣥⣶⣶⣲⢤⣘⠀⠀⠀⠀⠀⠀⠀⣽⣿⢿⢫⣏⢻⡄⠀⠀⣼⡟⢹⡀⠀⡀⣿⣇⠀⢿⡷⣄⠙⢦⡀⠀⠀⠀⠀ ⠀⠀⠀⣠⣴⣫⠶⢋⡏⠀⡼⠀⢠⢸⠀⠀⣿⣴⣾⡟⠉⠉⠉⠉⣽⡋⣏⢻⠿⠿⠀⠀⠀⠀⠀⠀⠀⠙⠡⣼⣷⣿⣿⡶⠶⠾⠋⠀⠸⡇⢀⡇⣿⣸⡆⢸⡟⠘⣷⢤⡙⠲⣄⠀⠀ ⣀⣤⣾⠿⠋⠀⢀⡾⠀⢠⡇⠀⡏⢸⠀⠀⠀⢸⡟⠻⢧⣄⣀⣤⣽⣷⡾⠿⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣇⠸⣧⢻⢧⣳⠀⢷⡀⠘⣦⠉⠓⠬⣝⡦ ⠟⠋⠁⠀⠀⠀⡼⠁⣰⢿⠀⢸⠁⢸⠀⢻⠀⢼⡃⠀⠀⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠇⢸⠈⢻⣠⢸⢳⣄⠈⢧⠀⠀⠀⠉ ⠀⠀⠀⠀⠀⣴⠃⣴⠋⢸⠀⣸⠀⢸⠀⢸⡇⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠀⠀⣼⡀⠀⡿⢾⠈⣿⣦⠈⢳⡄⠀⠀ ⠀⠀⠀⠀⣼⣣⡾⠃⠀⣸⠀⡇⠀⢸⠀⢸⡃⢹⡿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣤⣤⡀⠀⠀⠀⠀⠀⢀⣿⣹⠇⠀⣿⣇⠀⣇⣼⡆⢸⣎⣷⣄⠙⢦⠀ ⠀⠀⢀⣾⡷⣿⠃⠀⣰⣿⢰⡇⠀⣸⡇⠈⠁⢸⡿⣷⡄⠀⠀⠀⠀⠀⠀⠀⢠⣴⡖⢋⣭⣭⣽⣿⣶⣶⣶⠼⠿⠁⠀⠀⠀⠀⢀⣾⣿⣿⢀⠀⡿⠸⣆⡟⣿⢱⡀⣿⡞⣆⠱⢮⡳ ⠀⣰⠿⠋⢠⠏⠀⣴⡟⢹⢸⡇⢀⡟⣷⠀⢀⠘⣷⣤⣹⣄⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⢻⣿⢸⢠⣷⠀⠉⣧⡿⡿⣇⡈⢿⡜⣆⠀⠙ ⠞⠁⠀⠀⡜⠀⣸⡿⠁⢸⢸⡇⡾⠀⣿⡀⠈⡆⢻⣹⠏⣿⡷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⡟⣿⣿⣾⠀⢹⣸⢸⡙⣆⠀⣿⡇⢳⢹⠻⡜⡿⣜⢷⡀ ⠀⠀⠀⢠⡇⣰⡿⢣⢧⡟⣼⡟⠁⢰⠋⡇⠀⣧⢸⡏⠀⣿⣷⣾⡽⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣯⡄⡇⣿⡉⣿⡇⢸⣿⣿⡿⣼⣆⣿⣇⠸⡯⠀⢹⣷⠘⢦⡃ ⠀⠀⠀⣾⢠⡿⢁⡼⢸⢃⣇⣇⠀⠸⡄⢹⡄⢻⣇⣇⠀⣹⡇⣿⣹⠘⣷⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣷⣷⢿⡇⢸⣷⢸⣿⣿⣷⠀⢹⡄⣿⣆⢹⡀⠀⣿⡄⠀⠙ ⠀⠀⠀⣿⣾⠶⠁⡇⣼⢾⢸⣿⢷⡀⢻⣀⣿⣸⡿⣸⡄⠀⣇⡏⢸⣧⢻⣿⣧⠀⠉⠛⠻⠿⠿⣿⡟⠻⠿⠛⢸⣿⠏⣱⡟⢸⠀⢸⠘⣿⣿⣇⣿⣀⣘⢷⣸⡘⢧⠻⡄⠸⡇⠀⠀ ⠀⣠⣾⣿⠇⠀⣸⡇⡏⢸⠀⣿⡄⢣⠈⣧⣿⢧⡃⢻⣳⣸⢽⣤⢸⣿⣸⣧⣛⠷⢤⣄⣀⠀⠀⠀⠀⢀⣀⣴⣞⣷⣿⣿⠁⣾⠀⢸⣄⣿⡏⢻⣿⢻⡏⢻⣿⣷⡌⠳⣝⢦⡇⠀⠀ ⠟⠋⠁⣿⠀⣰⠛⡇⣷⢻⡀⣿⢷⠈⣇⣿⣿⣈⣧⡼⣿⣿⣾⣾⢸⣿⣿⣿⣿⣿⣶⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⡟⢰⣿⡀⠸⣿⣿⣶⣬⡈⢺⡇⢸⣿⠹⣷⠀⠈⠳⣗⣦⣀ ⠀⠀⠀⣿⢘⣥⣾⣿⢸⠋⣇⢸⠀⠀⣻⣿⣿⣿⣿⢣⣾⣿⣿⣿⡌⣿⣿⣿⣿⣿⣿⡇⣾⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⢁⣿⣿⣧⠀⣿⣿⣶⣬⣿⢿⣄⣸⡏⠀⠘⣆⠀⠀⠈⠙⠻ ⠠⣤⠤⠿⠋⠉⠁⠈⣿⡇⠘⣏⣷⣾⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣏⣾⣿⣿⣿⣇⠸⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠙⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣠⣾⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣦⢻⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠁⠀⢸⣿⣿⣿⣿⣿⠀⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣷⢒⢿⢿⣕⣏⢹⣿⣿⢧⠿⠛⠒⠈⠉⢉⣤⡾⠟⢋⡗⠄⣒⣩⣤⣶⣾ ⣿⣿⣿⣿⣯⡋⠻⣿⡿⡌⣟⣩⠞⠰⣰⣀⠤⠖⠋⢁⠤⢒⣥⣶⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⡿⣶⢦⠭⠿⠿⠥⠀⠀⠀⠀⣀⠤⣊⣵⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⠿⠛⠁⠀⠀⠀⠁⠀⠀⠀⠀⢀⡠⠔⣪⠔⠉⠻⡽⠋⠙⢿⣿⣿⣿⣿⣿⣿⣿ ⠀⢂⠀⠀⠀⠀⠀⣀⠠⠦⢐⣪⣥⣶⡿⢿⠀⠀⠀⠈⠐⣤⣀⡙⠻⣿⣿⣿⣿⣿ ⠒⣒⣒⣒⣀⣭⣥⣶⣶⣿⣿⣿⣿⣿⢇⢸⢀⡤⠖⡂⠀⢹⢸⠀⣿⠛⢻⢻⣿⣿ ⠁⠠⣿⣿⣿⡝⣿⡟⣻⠻⢿⣻⡯⠘⠜⣼⠀⣴⣒⡛⡟⢿⠈⢸⢨⡀⠸⡎⡏⠉ ⠀⣸⣿⣿⣿⣿⣿⠸⣰⠙⠊⠐⠀⠀⠀⠘⠀⠀⠂⠑⠋⣆⠀⣬⡞⣇⠀⡇⢱⠀ ⢀⣿⡟⢸⣿⡿⠘⣇⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⢰⠃⢣⢹⡀⢱⠈⡆ ⣾⡿⠁⣼⣿⠇⠀⠘⢆⢩⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡝⢠⢻⠀⠈⡆⢇⠈⡆⢘ ⢠⠃⢀⢿⡟⠀⠀⠀⠈⢣⣻⣶⡤⢀⠀⠀⡀⢤⣶⣟⡔⢹⡼⠀⠀⠸⡈⢆⠡⠀ ⠊⢀⠎⡜⠀⠀⠀⠀⣠⣿⣿⣿⣿⣶⡬⢣⣶⣿⣿⣿⣿⣞⠃⠀⠀⠀⠱⡈⠆⠀ ⢀⠎⡜⠀⠀⠀⠀⠀⣿⣿⣿⣿⣇⠀⠈⠁⠀⣸⣿⣿⣿⣿⡀⠀⠀⠀⠀⠱⡈⠄ ⠌⡘⠀⠀⠀⣀⠤⠚⠛⢿⣿⣿⣿⣷⡄⢠⣾⣿⣿⣿⣿⠛⠓⠠⣄⠀⠀⠀⠱⠈ ⠠⠁⠀⡰⠋⠀⠀⠀⠀⠀⠀⢉⠹⣿⣏⢹⣿⡿⣉⠀⠀⠀⠀⠀⠀⠉⢆⠀⠀⢡

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⣀⣀⣠⠤⢤⡞⠓⢤⡀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠦⣌⣙⠦⢤⣀⣴⢿⣋⣽⡇⠀⠀⠙⢦⡀⠙⣦⠤⣤⣶⡮⢥⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⠤⢬⣭⣭⣤⣖⡿⠋⠀⠘⢢⡀⢀⡴⢻⠛⠻⢷⡖⠒⠺⠖⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣴⠶⠶⠒⠶⢦⣄⠀⠀⠀⠀⠀⠀⣠⠴⠒⠉⠉⠀⠀⠉⠻⣦⣀⣠⠤⣥⣸⡁⡇⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣇⠀⠀⠀⣠⣶⣿⣷⡀⠀⠀⢠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢽⠀⠈⠻⡷⣧⡀⢀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣤⠾⢿⣦⡀⠸⣿⠟⠛⠛⠛⢦⣀⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⡀⠀⣳⠘⢿⡷⢏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⡇⠀⠀⠙⢿⣄⠻⢷⣤⣤⣀⡴⠟⠉⢙⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣛⡆⠀⠱⡀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠸⣧⡤⠴⣞⣋⣻⣷⡄⠀⠀⠀⠀⣀⠴⠋⣡⠿⣄⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠙⣿⣧⠹⣄⠀⠱⡄⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⣶⡿⠿⠿⣅⡈⠛⠷⣤⣠⠞⠁⣠⠞⠁⠀⠹⣦⡀⠀⠀⠀⢀⣠⣾⢿⡇⠀⠁⢻⣧⠹⡄⠀⢹⣄⠽⠶⠖⠒⣲⣶⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣾⡿⠋⢀⠀⠀⠀⡙⣦⡴⠋⢀⣤⢚⣡⢴⡶⣄⠀⠈⠙⠲⠶⠶⠿⢿⠉⢸⠀⠀⠀⠀⢿⣦⠹⡖⠉⠀⠀⠀⢠⣾⣋⡈⠉⠉⠙⠲⢤⡀⠀⠀⠀⠀⠀ ⠀⣾⡟⠀⡴⠋⢠⡖⣢⠽⢋⠀⠀⣾⢟⡯⣖⢵⣻⡘⣠⡾⣯⡙⢦⡤⡀⣼⠀⡜⠀⠀⠀⠠⠸⣿⣧⡹⡄⠀⢀⣠⠛⣉⣉⣛⣲⣤⣀⠀⠀⠙⢶⡄⠀⠀⠀ ⢸⣿⠁⣼⣀⡀⣸⠟⢁⡴⡿⣆⠀⢹⣦⣹⣿⣿⣶⢿⣅⣾⣿⣟⡆⣹⡘⡏⠀⡇⠀⠀⠀⠀⢷⠇⢘⣧⠹⡟⢉⠶⠋⠁⠀⠀⠀⠉⠻⣧⠀⠀⠀⢻⣆⠀⠀ ⣼⣿⢰⡇⣧⠟⢁⣴⣯⣤⣷⣿⣦⡀⢿⠉⠀⠀⠉⢳⣎⡿⠛⡿⢿⡃⢱⠇⢰⠁⠀⠀⠀⠀⣾⢠⣾⣿⣇⠹⡇⠀⢢⡀⠐⠀⠀⠐⢦⠈⢷⡀⠀⠀⢻⡆⠀ ⣿⣧⢸⡇⣇⣀⣘⣉⣉⣭⠭⠽⣿⠖⣇⠀⠀⠀⠀⠀⢻⣹⠏⠉⢦⡑⢾⡀⢸⠀⠀⠀⠀⢠⣿⣿⣷⡏⢹⡆⠹⣄⡼⠥⣤⡀⢢⡀⠀⢳⡘⣧⠀⠀⠈⣿⡄ ⢸⣿⠈⡇⠱⣌⣿⡥⠞⠁⡴⠂⣿⠀⠸⣦⡀⠀⠀⠀⣼⠟⢀⠀⠀⠹⣄⣙⠛⠒⠒⠂⠀⠀⢸⣿⢻⡇⢸⣿⡦⠈⠛⣦⠈⢳⡀⢱⠀⠀⡇⣿⡄⠀⠀⣿⡇ ⠘⣿⣇⢿⡀⠀⡖⠒⢲⢰⠁⢠⡟⠀⢀⣿⢉⡷⣾⠉⠀⠀⠸⣄⣠⠇⡏⠈⣿⠉⠁⠀⠀⠴⢻⣿⢸⡇⢸⢹⡀⠀⠀⡼⠀⣸⠃⡸⠁⠀⡇⣿⠇⠀⠀⣿⡇ ⠀⠹⣿⣆⢳⡀⠙⠳⠼⠀⢠⣿⠃⢀⣾⠏⠸⣄⣈⣓⡢⠶⠴⠾⠓⠋⢁⣠⣿⣚⣉⣉⣠⠔⠋⣿⣟⣷⠘⣆⠑⠒⠺⣥⠴⠯⠜⠓⠀⡼⢁⣿⠀⠀⠀⣿⡇ ⠀⠀⠹⣿⣧⣝⠶⠤⢤⣾⡿⠃⣠⣾⠏⠀⠀⣿⠋⠉⠙⠻⣿⠛⠛⠛⠛⠁⠀⠈⠉⠉⠀⠀⠀⢹⣿⣿⣦⠘⣆⠀⠀⠙⠲⠤⠤⠴⠚⢁⣼⠃⠀⠀⢸⡿⠁ ⠀⠀⠀⠈⠻⢿⣿⣿⣿⣯⣼⣿⠟⠁⠀⠀⠀⣿⡀⠀⠀⠀⠹⣿⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣷⣌⠳⣄⡀⠀⠀⠀⢀⣤⣾⠃⠀⠀⢠⣿⠃⠀ ⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⢸⣷⣳⡄⠀⠀⠀⠻⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⠿⣿⣶⣭⣭⣽⣿⡿⠛⠁⠀⢀⣴⣿⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣷⣯⣄⡉⠭⠍⠀⠀⢀⣠⣴⡿⠟⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⠿⠿⠿⠿⠿⠛⠉⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠟⠛⠛⠛⠶⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠉⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣾⣷⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣾⠟⢉⣀⣀⡈⠃⠀⠀⠒⣉⣀⡀⠈⢻⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡏⠀⣴⣶⣿⣿⣷⠂⠀⣾⣿⣿⣿⣆⢠⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⠀⠻⠿⢿⡿⠃⣰⣆⠙⣿⡿⠿⠋⠸⣧⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠈⠀⠠⣿⠿⠀⠀⣀⣀⣀⠀⣿⣦⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣼⣿⣶⣾⣿⣿⡟⢀⠀⠀⠀⢀⢀⢻⣿⣿⣿⣿⢻⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣇⢸⡇⠻⢿⣿⠇⡜⢸⠀⡇⢸⠘⣼⣿⠿⠉⠙⣿⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⣾⣿⣦⠀⣿⣷⣷⣾⣤⣷⣾⣿⣿⢋⣴⣶⣶⣿⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⠞⠙⠻⣿⣿⣷⣿⣿⣿⠿⠿⠻⠟⠋⠀⣼⣿⣿⡿⣻⣿⣦⡀⠀⠀⠀ ⠀⢀⡼⢿⡦⣠⣴⢿⣿⣿⣿⣏⣿⣤⠀⠀⢰⡔⣶⣾⣿⠏⠀⠀⠀⣿⣿⣄⠀⠀ ⠀⡾⢡⣏⢰⣯⠃⣼⣿⡿⢿⡟⢿⡋⠀⠀⢸⣽⣿⣿⡿⣇⠀⠀⠀⢈⡿⡿⣆⠀ ⢸⡿⠿⠏⢰⠇⢸⡿⠋⠀⠀⣿⡟⠀⠀⠀⠈⡟⠀⠉⠳⣿⣿⠆⠀⢿⣙⡇⣿⡄ ⣿⠀⠀⠀⢸⢰⣿⠁⠀⠀⠀⢸⣧⣤⠀⠀⡼⡇⠀⠀⠀⢹⣾⠀⠀⠈⢻⡇⢹⡇ ⣿⣿⣷⠀⢸⣸⣿⠀⠀⠀⠀⠀⢷⣿⠀⠀⠳⡇⠀⠀⠀⢸⡟⠀⠀⠀⡸⠀⢼⡇ ⢿⣟⠋⠀⢸⡿⣿⠀⠀⠀⠀⠀⠘⣿⢲⣦⠀⢹⡀⠀⠀⡼⠀⣤⣤⣴⠃⢠⣾⠇ ⠸⡏⣿⠆⠘⢷⣼⣷⣄⠀⠀⠀⠀⠹⣿⡇⠀⠘⢵⣤⡾⢁⡤⣡⠞⠁⠀⣸⠟⠀ ⠀⠹⣧⠀⢀⣀⠀⠸⣯⣽⣷⣦⣄⡀⢻⣷⣦⣄⣤⠙⣷⡼⠞⠁⣀⢄⣾⠏⠀⠀ ⠀⠀⠈⠻⣟⠙⢧⣀⣀⠀⠘⢳⣾⣿⣿⣿⣿⣮⡻⣤⡌⠛⢶⣵⣵⡿⠁⠀⠀⠀ ⠀⠀⠀⠀⠈⠳⢶⣤⣿⣦⠖⡉⠕⠊⢉⣿⣿⣿⣷⣾⣧⣖⣦⠙⢿⣄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣸⠟⠠⠈⠀⢀⣰⣿⣿⣿⣿⣿⣟⢿⣿⣿⣠⡴⢮⢳⣄⠀⠀ ⠀⠀⠀⠀⠀⠀⣼⡫⠂⠀⠀⠀⣶⡿⣿⣿⣿⠁⠘⢿⣆⠙⣿⣿⣅⢺⡇⠛⢷⡄ ⠀⠀⠀⠀⠀⢰⣿⠁⠀⠀⠀⣼⠏⠀⠈⢿⣿⠀⠀⢀⣿⠀⢸⣿⢿⣿⣷⢺⡆⣿ ⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢰⣿⠀⠀⠀⠈⣏⢻⡇⢷⣾⡇⢸⣿⠃⠘⢿⣼⣧⣿ ⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⢉⢿⣆⠀⠀⠀⣿⡟⠀⠀⢹⣷⣿⡏⠀⠀⢽⣿⣿⠏ ⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⠀⠸⢻⢿⣶⣶⣿⢻⡆⢀⣼⣿⠏⠀⠀⣠⣹⣿⠋⠀ ⠀⠀⠀⠀⠀⠀⠀⠻⣷⣀⣀⠀⠈⠈⠘⣿⡇⡿⠃⣸⢸⣿⢀⣠⣦⡿⠛⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠶⣤⣴⣾⣿⣠⡇⠐⣇⣿⣿⠿⠛⠉⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣿⠁⠀⠀⣹⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣧⡀⠀⣀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢧⡟⠁⣾⢻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠞⠃⢠⣆⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡄⠀⡀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⣼⠋⣸⢹⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣷⠿⠀⢫⣾⠁⠀⠀⠀⡠⠚⢉⣉⠓⣦⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢰⡟⠀⠀⢀⣼⢱⣿⣾⣿⣷⣼⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣆⠀⢠⣾⠇⠀⣼⡥⢃⣾⣿⣿⣿⡟⠈⠻⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⡿⠂⢸⣸⠀⢰⣏⠔⠛⠛⢻⣿⣿⣧⢠⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡇⠀⠘⢿⡆⠸⣇⠀⠀⠀⠀⠈⠉⠉⣩⠇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⣦⡄⠸⣷⡀⢹⣷⠄⠀⠀⢠⣤⠾⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡍⠳⠤⠾⠿⠛⠁⠀⠀⣨⡿⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⠀⠀⠀⢀⠀⢤⡾⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⣴⣴⣶⠶⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠋⢀⣿⣿⡿⣿⠿⣟⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣟⣿⠿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠁⠀⣸⠛⢹⣿⣯⡀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⢸⣿⣷⣄⠙⠻⣷⣄⠀⠀⠀⣀⣠⠤⣶⣶⣶⣶⢶⣛⡷⠶⠶⢿⣀⠀⠸⣿⣇⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠋⢸⣿⣿⣿⣷⣄⢙⣿⣦⣖⣿⠿⠛⠋⠉⠉⠉⠙⢿⣏⠛⠛⠛⠛⠶⣯⣿⣛⠿⣾⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⢸⡟⠻⠙⢿⣿⣿⣿⡿⠛⠷⣤⡀⠀⠀⠀⠀⣄⣀⣽⣷⣦⠤⠴⠶⠿⣿⡿⢿⣟⠿⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠸⣇⠀⢠⣾⣷⠟⠁⠀⠀⡘⣿⣿⣤⡶⠾⠛⠛⠋⠉⠉⢻⣦⣤⣄⣀⠀⠱⣄⠙⢧⡀⠈⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡀⣹⡾⣿⡟⠁⠀⢀⣴⣴⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣷⣶⣵⣄⣀⠸⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣟⣾⡟⠀⢠⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠘⢿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣷⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣧⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠞⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⣻⣿⣿⣿⡇⠙⣿⣿⣿⣿⣿⣷⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⢠⣿⣿⢁⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢹⣿⣿⣿⣿⣿⣿⣿⡏⠉⠉⢻⣿⣿⠇⠀⠘⣿⣿⣿⣿⣿⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠒⠀⠀⠈⠓⠉⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⡏⠈⠀⢿⣿⣿⣿⣿⣿⡿⠀⠀⠀⢀⡿⠿⠀⠀⠀⢸⣿⣿⣿⣿⠈⣿⠀⣶⠚⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿⢐⣿⣿⠏⣿⡃⠀⠀⢸⣿⣿⣿⣿⣿⠃⠀⡠⣶⣯⣤⣦⣀⣀⠀⢸⠁⣿⣿⡏⠀⢹⠀⠉⠙⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠃⣼⠿⠟⠸⣃⣹⣿⣷⣿⣿⠋⠉⠋⠁⠀⠈⣾⣿⣻⣟⣿⠙⠛⣿⣦⡄⣿⣿⣇⣀⣘⠴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠃⠘⢃⣴⣾⡿⠿⣿⣻⠻⠯⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠁⠀⢀⣿⡿⣻⡉⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡆⣰⣿⠋⠉⣧⠴⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢒⠒⠒⠋⢹⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⠛⠓⠒⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣾⡍⢹⣿⣷⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣯⣷⢻⣇⣠⡴⠛⠁⠀⠀⠀⠀⠀⠀⢀⣠⠴⠖⣉⣉⣉⡉⣷⣶⣾⡀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣯⣿⣄⠴⠂⠀⠀⠀⢀⢀⣠⣔⣋⣴⣾⣿⣿⣿⣿⣿⣿⣿⡿⠗⠛⠛⠓⠒⠾⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣷⡖⠀⠀⠀⠀⣿⡿⣿⣿⣿⣿⠟⠛⠿⠿⠟⠉⠻⣿⣠⠤⣲⠶⠞⠁⠀⠈⠻⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⣠⡤⠚⠉⠀⣈⣿⡙⢿⣶⣄⠀⠀⠀⠀⠀⡿⢠⡊⢁⡴⠋⠀⠀⠀⠀⠈⠻⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠁⠀⠒⠖⠛⠛⡟⠒⠒⠲⠻⣆⠀⠀⠀⣠⡇⢀⡷⢋⠆⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠒⠒⣧⠀⠀⠀⠀⠹⢷⡶⠾⠋⢀⡼⢷⠋⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⠟⠋⡽⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⢧⣤⣄⣀⣠⠤⠤⢴⡟⠁⠀⠘⢲⡾⣏⣽⣦⡀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣷⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⡆⠈⡄⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⣰⡾⠋⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⡼⠃⠀⠀⠱⣝⣶⣤⣄⠄⠀⠀⠀⠈⢻⣿⣿⣿⡀⠀⠀⠀ ⠀⠀⠀⠀⢹⡀⠀⠦⣄⡀⠀⠀⣿⣿⣿⣿⠇⢀⡜⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣷⡀⠀⠀⠀⠀⠀⢰⡇⠀⠀⢀⡞⠁⠀⠀⠀⠀⢿⠸⣿⣿⣷⠀⠀⠀⠀⠀⠹⣿⣿⣷⠀⠀⠀ ⠀⠀⠀⠀⠀⠻⡀⠀⠀⠙⡄⢰⣿⣿⣿⡿⠀⢸⡇⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠈⠇⠂⣠⠏⠀⠀⠀⠀⠀⠀⢸⡄⣿⣿⣿⣧⠀⠀⠀⠀⠀⠙⣿⣿⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠲⠦⣀⢀⣾⣿⣿⣿⡇⠀⢸⠁⠀⠀⠀⠀⣠⡾⠉⠸⣿⣿⣿⣿⣿⣿⠦⣄⡀⠀⠀⢀⡶⠃⠀⠀⠀⠀⠀⠀⠀⠘⣇⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠈⢿⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⣿⡇⠀⡜⠀⠀⠀⠀⠀⢸⢡⠃⠀⢻⣿⣿⣿⣿⣿⣇⠀⠙⠂⠐⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠈⠇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⠇⢀⡇⠀⠀⠀⠀⠀⢸⢸⠀⠀⣸⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⠀⡼⠀⠀⠀⠀⠀⠀⢸⢸⠀⢠⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⡏⣰⠃⠀⠀⠀⠀⠀⠀⠘⡾⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠟⡟⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣱⠇⠀⠀⠀⠀⠀⠀⠀⠀⡇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠏⠀⣿⢸⡄⠀⠀⠀⠀⠀⠀⠀⠠ ⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⣰⣿⣌⠇⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⣀⡤⠾⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠒⠠⢀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡴⠚⢁⣀⣀⣀⣀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀⠁⠢⡀⠀⠀⠀⠀ ⠀⠀⢀⡴⢋⡠⠚⠁⠀⠀⠈⠻⠓⢄⠀⠀⢀⡏⠀⠀⠀⠀⠿⠷⢄⠈⠢⡀⠀⠀ ⠀⣠⠋⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠐⠄⠀ ⣸⠃⠀⠀⠳⣄⡀⣠⠖⠛⠓⠒⠊⠀⠀⠀⠀⠙⠒⠊⠉⠑⠦⠠⠊⠀⠀⠀⠈⡄ ⡇⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢳ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣄⠀⣀⣀⣤⣄⣀⣼⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠟⡏⠀⡇⠀⢸⠈⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⡇⠀⡇⠀⢸⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⢇⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠇⠀⠁⠀⠈⠀⠀⡇⡔⢲⠀⠀⠀⠀⠀⠀⠀⡼ ⠈⡄⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠀⡘⠀⠀⠀⠀⠀⠀⣰⠃ ⠀⠈⢄⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⠀⠀⠀⢀⡾⠃⠀ ⠀⠀⠈⠢⡀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⢀⡞⠁⠀⠀ ⠀⠀⠀⠀⠈⠢⢀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⡠⠁⠀⠀⣀⡤⠖⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⠒⠦⣄⣈⣂⣤⣄⣀⣤⣊⣀⣠⠴⠛⠉⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠶⠚⢋⠉⡉⠉⠉⡁⢈⠀⠄⠈⠉⠉⠓⠚⠖⠳⠶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⢉⠠⠐⠈⠄⣂⣠⣥⣦⣴⠶⠾⠶⠷⢾⣄⡡⠈⠄⢂⠠⠈⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡐⢂⠰⠁⠌⠘⠛⠿⠶⠶⠶⠶⠖⠛⠋⡉⠉⢁⠰⢈⠂⠐⡈⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠛⢦⣐⣀⠂⠡⢈⠐⡀⠂⠄⠠⡀⠄⡐⢀⠂⠄⣁⣂⣐⣠⣨⣴⠾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠻⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⣿⣿⣍⣷⣶⠦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄⣤⣶⡿⠿⠛⠋⢉⠉⡈⠄⡁⠠⡀⠄⠠⢀⣡⣬⣭⣿⣭⣿⣿⣿⡷⣯⣝⣶⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣯⡁⠠⠐⡠⠒⢀⠂⡁⢂⠡⢁⠐⣨⣶⣿⣿⣿⡿⠟⠿⢿⣿⣿⣿⣿⣝⢿⣮⡳⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⣾⣿⣿⡿⠉⠻⣿⣷⣆⠁⠰⢀⠂⡐⠄⠂⠄⣢⣿⣿⣿⣿⣿⣿⣇⠀⠀⣸⣿⣿⣿⣿⣿⣷⡜⢿⣞⡆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣴⣿⣿⣿⠿⠿⠶⣾⣿⣿⣿⡆⢁⠂⠡⠐⡈⢐⣸⣿⢻⣿⡿⠛⠉⠉⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣎⢻⣷⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⣯⡿⠋⠀⠀⠀⠀⠹⣿⣿⣿⣿⡀⠌⢂⠡⠠⣱⣿⠃⠈⠃⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠹⣷⠀⠀⠀⠀⠀ ⠀⢀⣿⡿⠁⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⠐⡈⠄⢒⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡟⠉⠙⢻⣿⣿⣿⣿⡆⢹⣧⠀⠀⠀⠀ ⠀⢸⣿⡇⠀⠀⢀⠀⣠⣴⣿⡿⠿⢿⣿⡇⡐⡈⠄⢫⡗⠀⠀⠀⠀⠀⠀⣀⣠⣶⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⣷⠀⢻⡆⠀⠀⠀ ⣠⡿⣿⠀⠀⠙⣿⣿⣿⣿⡿⠁⠀⠀⢻⡧⢀⠱⢈⣿⠇⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⣠⣿⣿⣿⣿⣿⡇⢸⡗⠀⠀⠀ ⢹⣇⡿⠀⠀⠄⢻⣿⣿⣿⣇⠀⠈⢀⣾⡗⠠⢁⠂⣽⡆⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢠⡟⠀⠀⠀ ⢘⡷⣟⠀⠀⠀⠀⢿⡿⠛⢻⣿⣾⣿⣿⣯⠐⢀⠂⡽⣧⠀⠀⠀⠀⠀⠈⢿⣿⡿⠛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢂⡟⠀⠀⠀ ⣸⣟⣯⠀⠀⠂⠀⠈⢰⣴⡿⠋⣿⣿⣿⣿⡀⢂⠐⡘⢻⡄⠀⠀⠀⠀⠀⠈⢿⣁⣴⣿⣿⠁⣻⡿⠹⣿⣿⣿⣿⣿⣿⠇⣽⡏⠀⠀⠀ ⠀⣿⣿⡀⠀⠁⠀⠀⠘⣿⠁⣰⠏⣸⣿⣿⠃⠄⠂⠄⡉⢿⡄⠀⠀⠀⠀⠀⠀⢿⣿⣿⠇⢠⣿⡇⢐⣿⣿⣿⣿⣿⡏⢲⣿⠀⠀⠀⠀ ⠀⠸⣿⣧⠀⠀⠀⠀⠀⠸⣷⣿⣀⣿⣿⡟⣸⡆⢹⣦⢰⣶⠻⣦⠀⠀⠀⠀⠀⠈⢿⣿⣶⣾⣿⣷⣾⣿⣿⣿⣿⡟⢤⣿⠁⠀⠀⠀⠀ ⠀⠀⢹⣿⣷⣤⣀⣀⠀⡀⢻⣿⣿⣿⠟⢀⠘⢿⣾⡿⢷⡿⠀⡘⢷⣦⡀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⠿⠋⢠⣿⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠹⣿⣟⠛⡿⢿⣿⡿⣟⡋⠁⠄⢂⠌⡀⠄⡐⠀⠄⡐⠠⠀⠌⠛⠻⣶⣦⣤⣬⣿⣿⡿⠿⠛⠋⠁⢄⣸⡿⡿⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⣿⣿⣜⢣⣿⢿⣶⡙⡆⠘⡀⢂⠐⠠⠠⢁⠒⠠⢁⠘⠄⣁⠲⡔⢮⣭⣭⢷⡜⣜⢳⡄⠡⢈⣴⣿⡿⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠻⣿⣧⣯⡛⢧⡙⠆⠡⠐⠠⠈⠄⡁⠂⠄⡁⠂⠌⡐⢠⢏⡝⣶⣿⡼⣿⡹⣌⡳⣌⣶⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⣿⣧⣁⠌⠠⢉⠠⠑⡈⠄⣁⠂⠄⣁⠂⠔⠈⢾⡸⣍⢮⡱⣇⣳⣭⣷⢿⡷⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠽⣿⣶⢦⣦⣔⣠⠐⠀⠌⡐⠀⠌⠠⢁⣂⣹⣼⣶⢷⣿⣻⠽⠚⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⠉⠈⠉⠙⠻⠻⠶⠷⠿⠾⢿⠟⣟⣯⢷⡛⣋⣉⣀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣾⣴⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⢛⡋⢉⠩⢀⠄⠤⡀⢄⠠⡈⠄⡉⠙⠛⠻⠿⢿⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣛⡏⢰⣿⢿⣦⠁⡘⢄⢊⡐⣁⠊⠔⡁⠎⡐⢩⡐⢡⠂⡐⢌⣟⠻⠿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣴⣾⣿⡏⣾⠛⢻⣿⡇⢠⣿⠂⡌⠂⢢⠐⢠⠉⠂⠁⡎⠐⢡⠈⡆⢡⠐⢸⣿⡄⠀⣿⠛⣿⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣴⣿⠟⣩⣿⠋⣠⣾⣿⣅⣾⠏⡐⠀⠎⢠⠃⢌⠂⣉⠒⡀⢃⠌⢒⠠⣁⠂⢂⠹⣷⣴⡿⢁⠘⠻⣿⣦⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⣾⡟⠣⠘⡸⣷⣾⠟⣀⡘⢻⢉⣰⣀⡉⠐⠂⢌⠢⠑⡄⢢⠑⡈⠔⡈⡐⠄⡘⢀⣦⣜⣻⣄⣂⣌⡐⢈⠻⣿⣦⡀⠀⠀⠀⠀ ⠀⠀⢠⣿⡟⠠⢁⢢⣱⣼⣿⣿⣿⡿⢿⠿⢿⠿⣿⣿⣷⣦⣀⠃⠌⡀⠆⡑⡈⡐⣄⣾⣾⡿⠟⢛⠻⠟⠻⠿⢿⣿⣶⣮⣿⣷⣄⠀⠀⠀ ⠀⢀⣿⡟⢠⣑⣾⣿⡿⢛⠛⡩⢁⡒⢌⠒⠤⠒⡄⢊⡙⠿⣿⣿⣆⣵⡄⡐⣴⣿⡿⢛⠡⣂⠍⢢⠃⣎⠱⢌⠢⢄⠩⡙⠻⣿⣿⣆⠀⠀ ⠀⣼⣿⢡⢶⣿⡿⢋⠔⡡⠎⡔⢣⠘⡄⢋⡌⠱⡘⢤⠘⡰⢈⢿⣿⣾⣷⣿⣿⢏⠰⡁⢖⡐⢊⠅⣊⠤⢃⠎⠢⢍⡒⢡⠃⡜⠻⣿⣧⠀ ⢀⣿⡟⣼⣿⡟⢠⠃⢎⠰⢡⠘⡄⢓⠌⡒⡌⡱⢌⢢⠩⢔⡡⢂⠽⣿⣿⣿⡿⢀⠣⠜⢢⠘⡄⢋⡔⢌⠲⢨⡑⠦⣘⢡⢊⠔⡡⠹⣿⣧ ⣼⣿⢯⣿⣟⠠⢃⠜⡈⢆⣅⣎⣰⠁⢎⠱⡐⠥⢊⡄⢓⠢⠆⡅⢊⢿⣿⣿⣿⡀⢃⠎⣄⣣⡘⠤⡘⢄⡋⠴⡀⠧⡐⠣⢌⢊⡅⢣⢹⣿ ⣸⣿⣾⣿⣇⠸⡀⢾⣸⣿⣿⣿⣿⣿⣆⠱⠸⠆⢇⠸⣀⠷⠸⣀⠏⣸⣿⣿⣿⡁⣾⣾⣿⣿⣿⣷⡎⠰⠈⠆⠱⠆⠉⠱⠈⠆⠈⠀⠈⣿ ⢹⣿⡞⣿⣧⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠄⠀⠀⠁⠀⢀⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢢⣿ ⠘⣿⣯⣹⣿⣶⣿⡿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠁⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⠿⠏⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣿ ⠀⢻⣿⡔⣻⣿⣿⣿⣾⡷⠿⠛⠏⠉⠀⠀⠀⠀⠀⠀⣀⣤⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣾⣿⢻⣿ ⠀⠘⣿⣿⡔⣎⠿⣿⣿⣿⣶⣦⣤⣤⣀⣠⣤⣤⣶⣾⣿⣿⣿⣿⡿⠋⠌⡁⠛⢟⣻⢿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣾⣾⣿⣿⣿⡿⣣⣿⠟ ⠀⠀⠸⣿⡷⣌⠳⣭⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣋⡾⢁⡘⠰⢠⠉⠄⡘⢯⡙⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⢿⢟⡱⣾⣿⠏⠀ ⠀⠀⠀⠹⣿⣮⠳⣌⣷⠃⠈⣿⣽⡛⠛⣻⡿⣩⢏⡝⢦⠫⠑⡀⢆⠰⢁⢂⠩⠐⡄⢂⠙⡘⢧⣿⡆⣨⣽⢿⣷⠀⣼⣋⢮⣷⣿⠋⠀⠀ ⠀⠀⠀⠀⠈⢿⣷⣄⣿⣃⢠⣿⠹⢷⡾⠟⢣⠓⢊⠘⡠⠑⠌⡰⢈⠂⡌⠰⢈⠡⠒⡈⠆⡐⠠⠘⠟⠟⢋⠚⠻⣿⣿⣽⣿⠛⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠻⣿⣿⢿⡿⠟⠠⢀⠠⢘⢀⡘⢀⠇⠠⠃⠜⠠⡀⠇⢠⠃⠜⡀⠇⢠⠃⡄⠣⠘⢠⠘⢠⠘⣿⣤⣿⡿⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⣌⡐⢁⠂⠅⠢⠌⡂⢌⠂⡍⠰⠁⠆⡉⢄⠊⠤⠁⠎⠤⡈⠤⠑⡈⢤⣈⣦⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣶⣬⣌⡄⠑⡈⠄⠊⠄⢃⠡⢊⠐⠌⣈⠂⣉⠰⢀⣢⣴⣱⣾⣿⠟⢻⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣯⣛⣿⢿⣿⣷⣾⣾⣴⣬⣴⣦⣥⣶⣶⣶⣾⣿⡿⠿⢻⣟⣩⣿⣷⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣻⡿⢏⢥⡻⢬⡍⢳⡘⢦⢣⢝⡢⡓⡜⠰⢂⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦⠀ ⡿⢏⡜⣲⡙⢦⡙⢧⡙⣎⠞⢦⠡⢁⠈⠀⠀⠄⠀⢈⠀⠈⢀⠈⠀⠈⠐⠈⠀⠁⡀⠁⠈⠀⠄⠁⠀⢁⠂⠄⠀⢀⠀⠀⠉⠲⣄⡀⠹⣧ ⡱⣩⢚⡥⣙⢦⡙⣦⡙⢦⡛⣬⢓⡆⣴⣤⣦⣴⣬⣦⣴⣤⣆⣤⣈⡀⠐⢀⣈⣴⣴⣶⣶⣶⣦⣤⣌⡀⠀⠠⠀⠠⠀⠈⠀⠄⡈⠧⣀⠈ ⣱⢣⢏⡖⣭⢒⡝⢦⣝⢣⠞⣴⣿⠿⣛⣿⣿⣿⣦⡄⠉⠉⠙⢻⣿⣿⣿⣿⠟⠋⠉⣨⣿⣿⣿⣏⠛⠿⣿⣶⣄⠀⠠⠁⠀⠄⡀⠀⠹⡄ ⢎⡳⢎⡜⢦⢫⢜⡣⢎⢧⣛⣿⠋⡀⢾⣿⣿⣿⣿⣿⣶⠀⠀⢀⣼⡿⢿⣾⠗⠀⣾⣿⣿⣿⣿⣿⣧⡀⠈⠛⣿⡧⠀⠀⠁⠐⡀⢁⠂⢜ ⡹⣜⢣⢞⡱⢎⢮⡱⣋⢦⡹⣿⣷⣈⠻⣿⣿⣿⣿⣿⠟⠀⢠⣿⣿⠀⡍⢿⣿⡄⠹⣿⣿⣿⣿⣿⡟⠋⠀⣰⣿⠗⠀⢈⠀⡐⠠⠀⠌⠰ ⠳⣌⢳⢪⡕⣎⠶⡱⣍⠶⡱⢻⣿⣧⣳⡰⠩⠿⠟⡁⢀⣠⣾⡿⡁⢆⠈⢆⡹⣿⣄⣩⠍⡛⠟⠉⠀⣀⣴⣿⠋⠀⡐⠀⠂⠀⠄⠡⠘⡠ ⡹⡌⢧⠳⡜⡜⢮⡱⢎⡳⣍⢣⠞⡽⢻⣿⣷⣷⢶⣶⣾⣿⡿⣵⢏⡶⣍⠶⣰⢹⣿⡙⢻⢷⣶⣶⡿⢿⠛⠁⢀⠠⢀⠠⠁⡈⠄⡁⠂⠁ ⡱⢎⢇⡻⣌⢳⢃⡞⡥⢳⢜⡣⡝⡼⣡⠂⣽⣿⣿⣿⣿⣿⣿⣽⣞⣳⣭⢳⣣⢿⣿⣿⣶⡆⠀⠀⠀⣀⠠⢀⠂⠀⠂⠀⠀⡐⠀⠄⠠⠁ ⡱⢎⢮⡱⢎⡣⢏⡲⣙⢬⡚⡴⣹⢒⠡⣼⣿⣿⣿⣿⣿⣿⣿⣿⡽⣟⣿⣿⣿⣿⣮⣟⣽⣿⣶⣀⠀⠀⠈⠀⠀⠐⠀⠀⠀⠄⡁⢈⠀⠄ ⡱⣋⠶⣱⢋⠶⣩⠖⣭⢢⢓⡱⢎⠢⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⢮⣿⣽⣾⣷⣿⣿⣿⡆⠀⠀⠀⠈⠀⠀⠀⠀⠒⣀⠂⡀⢀ ⡱⢣⡝⢦⣋⠞⣥⠺⣔⢣⡙⢦⢃⡱⢛⢿⡟⣿⡿⣿⠿⣿⣿⣿⣿⣾⣿⣿⡿⣿⢿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⢀⠠⠁⠄⢂⠐⠠ ⡱⢣⢎⡳⣌⢏⠶⣩⠖⣣⡙⢆⡇⢆⡉⢂⠉⠐⠡⠉⠊⡙⠿⣿⣿⡟⡿⠏⠓⠉⠋⠉⠋⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠠⠀⠂⠄⣈⠐ ⡱⣃⢮⠱⣎⠺⡜⣥⢛⡤⣙⠶⣘⢢⡑⢢⠈⠄⠐⡀⠄⠀⠁⠐⠀⢈⠀⡁⢀⠠⠄⠀⢀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠄⠂⡈⠐⠠⢈ ⡱⡜⣢⢛⡴⢫⡜⢦⡍⢶⣉⠶⡑⢦⡉⠆⡌⡐⠀⡐⠈⡐⠈⠄⡈⠄⡀⠐⡀⢀⠀⠁⠀⢀⠀⠁⠀⠀⡀⠀⠀⠁⠀⢀⠀⠄⠠⢁⠂⠄ ⡱⢥⢣⡍⣖⢣⠞⡱⢎⠧⡜⢎⡙⢦⡉⠖⡰⢀⠁⠠⠀⠄⡐⢀⠠⠀⡀⠁⡀⠄⠈⠐⡀⠀⠀⢀⠀⠀⠀⠀⠠⠀⠈⠄⠠⢀⠱⠀⡌⠐ ⢧⢋⠖⣱⢪⠱⣎⠵⣫⠜⣜⢣⡝⣢⠙⣆⠱⠀⠌⡀⠂⠄⡀⠄⠀⠂⢀⠁⠀⡐⠈⠀⠄⠐⠈⠀⠀⠈⠀⠀⠀⠄⠡⠈⠄⢂⠄⡃⠤⢁ ⢧⣋⠞⡥⢎⠳⣌⠳⢬⡙⣤⠳⡸⢄⠫⣄⠣⢉⡐⠠⠁⠠⢀⠂⠁⢂⠀⠌⠀⠄⠠⢁⠠⠈⠀⠄⡐⠀⠈⠀⠄⠈⠄⠡⣈⠢⡘⢠⠒⠠ ⣧⢻⡜⣱⢋⠶⣌⡹⣂⠗⡢⢝⡰⢋⡱⢄⠃⢆⠰⠁⠠⠁⢂⠐⠨⡀⢂⠄⠡⠈⡀⢂⠠⢈⠐⠀⠀⢁⠊⡐⡈⠌⡐⠡⣀⠑⡌⢂⠡⢃ ⣭⢳⣭⢣⢏⡞⡴⢣⡕⣫⢱⣊⡔⢣⢰⡈⣔⣨⡐⣌⢠⠐⡀⠌⡀⠡⠀⠂⠄⠁⠀⢀⠠⠀⠀⠁⠈⠀⠀⠁⠌⠢⢅⠣⢄⠣⡘⡌⡑⢢ ⣯⣗⣮⣛⣮⣽⡹⣧⢻⣜⣧⡟⡾⣏⢷⡻⡜⢧⡛⠾⡹⢏⠿⣳⠯⣷⢳⣳⢎⣶⢣⣖⡦⣖⢦⡌⡔⣈⡐⢀⠀⡐⠈⢘⢢⢣⠱⣌⠱⣂ ⣟⣮⢷⣻⣞⣷⣻⣽⣻⣞⣶⣝⢦⣉⢦⡑⣌⢂⠌⡐⠡⢈⠂⡅⡘⢀⠃⠌⠊⠔⡉⠌⠃⠍⠂⡙⠘⠠⢉⠃⠎⡐⢈⡤⣓⢎⡳⣌⠳⣌ ⣿⡽⣯⣷⢿⣞⣯⣷⡿⣯⣿⡾⣿⣽⡾⣽⢾⡽⣮⣵⢻⣬⢳⡜⣜⣣⠻⣜⡛⢶⡱⢎⡖⣦⡱⣤⢲⡰⣆⣜⣲⣜⡳⣞⡭⡞⡵⣎⡟⡼ ⣿⣿⢯⣿⣻⣯⣿⢷⣿⣟⣷⡿⣟⣾⣟⣿⢯⣿⣳⣯⣟⡾⣧⣟⡾⣖⣟⣶⣹⢧⣛⣮⡽⡶⣝⣮⠷⣝⣮⡽⢶⡭⣷⡹⣞⡽⣳⡝⣾⡹ ⣿⣻⡿⣯⣿⣻⣽⣿⣳⡿⣯⣿⣟⣿⢾⣻⡿⣽⣯⣷⣿⣻⣽⣯⣿⣽⣾⣳⣯⣿⣽⣾⣽⣻⣽⣞⡿⣽⡾⣽⢯⣟⣶⣻⡵⣏⡷⣹⠶⣽