⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⢦⡀⠐⡄⠀⠀⢳⡀⠘⢦⡀⠀⠀⢰⠀⠀⠀⠈⠛⢦⣄⣸⡇⠀⠀⠘⡄⠀⠘⠄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠈⡇⠙⢆⠘⠆⠀⠀⢳⣄⠀⠙⢦⠀⠀⡇⠀⠀⠀⠀⠀⢹⣿⣄⠀⠀⠀⢣⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⣸⠀⠀⡆⠀⠀⠀⠀⠀⢆⠀⠀⠀⠀⠀⠀⣇⠠⢼⢲⢯⠻⡉⢯⠉⠙⣏⠻⣖⠒⠧⣄⣸⠀⠀⠀⠀⠀⣾⠃⠹⣧⡀⠀⢸⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⡇⠀⡏⡇⠀⢳⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢹⡀⠸⡼⡆⠳⡹⡌⢣⠀⢱⠑⢌⠢⡀⠐⡌⡇⠀⠀⠀⣼⠇⠀⠀⠈⢻⡄⠸⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢰⣥⣧⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⡇⡇⠀⠙⣜⣎⢆⠈⡆⠀⠱⣝⢆⠘⢣⠀⠀⣰⠏⠀⠀⠐⠀⠀⠙⣆⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⢀⡴⠊⢹⢠⣸⡄⡆⣧⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢱⠀⡇⡇⠀⠀⠈⢾⣞⠀⢇⠀⠀⠈⢮⢣⣸⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢀⡼⡏⢠⠀⢸⢸⠈⣷⡀⢻⢇⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⢸⢸⠀⡇⠃⣀⣤⢖⣒⣾⣦⣺⣒⠀⠀⠀⠳⡹⣷⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⡀⠀⠸⡀⣠⠋⢸⢧⠈⠀⢸⠘⠀⠘⣧⡘⡌⢆⠀⠀⣀⠀⠀⠘⡆⠀⠀⡏⢸⢸⢰⢊⣵⣾⡿⠿⣷⣲⣾⣿⣿⣦⣄⠀⠱⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⡄⠀⡷⢹⠀⢸⠈⣆⠄⠸⡇⠀⠀⠹⡷⡱⡈⣧⡀⠘⡄⠀⠀⢱⠀⢠⢃⢾⣸⢸⣿⢟⡉⡰⠺⣯⣿⣿⣿⣿⣿⢿⣧⡀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⣇⢡⠀⢹⠈⡆⢸⢸⠘⣆⠀⣇⡠⠤⣒⣛⣛⣷⡙⢷⣄⠸⡄⠀⠀⡇⡜⣸⢸⡇⡜⠃⠎⠀⣷⣶⣻⣿⣿⣿⣿⣿⣏⢿⣷⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣀⢸⢸⠘⡄⠀⢇⢇⠈⡏⡆⢘⣖⣿⣿⡿⣿⣛⣻⠿⠿⣄⠙⢷⣷⠀⠀⢰⢁⠇⣾⢁⠇⠀⠀⠀⣿⠿⠿⣿⣿⣿⠉⠁⢻⢸⡟⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⠘⡈⡇⢱⠀⠈⣞⠀⣇⢇⢪⣾⢟⣷⣟⣩⣽⣿⣷⡄⠈⠁⠀⠹⡄⢠⠇⡞⠠⠇⡿⠀⠀⠀⠀⢻⡄⠀⠙⠻⠛⠀⡠⢾⠘⠁⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⠀⠀⢹⡆⡇⠸⡌⢇⠀⠘⣆⠸⡈⣿⡏⣼⠁⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⣇⢎⡞⠀⠀⠰⠃⠀⠀⠀⠀⠈⢳⣄⠀⠀⠀⠀⡸⠃⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀ ⠀⣇⠀⢸⢳⢸⠀⢱⡈⢆⠀⣏⠣⣷⣿⡇⣿⣿⣿⣿⣿⣿⡏⠉⢻⠀⠀⠀⢫⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠒⠒⠉⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀ ⠀⠘⡄⠈⡏⣇⢇⠀⢳⡈⢆⢻⡄⠈⣿⣧⠸⣏⠁⠈⠻⠿⠃⠀⠼⠇⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⢀⢀⠀⠆⠄⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀ ⠀⠀⠘⡄⠸⣾⣞⡆⠸⡵⡌⠛⡝⣄⠈⠙⠳⠙⢦⣀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢠⠊⠐⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀ ⣶⣿⣿⣿⣦⢻⣿⣞⠀⢣⠘⢆⠱⡈⢦⠀⠀⠀⠀⠉⠓⠒⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀ ⡛⠉⠀⠛⠛⠳⣿⡏⠣⡈⢆⠈⠳⣵⡌⢣⠀⠀⠀⠀⠀⡀⢀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀ ⠀⠀⠀⠀⣀⡠⠬⡟⢄⡸⠪⣦⠀⠈⠻⢎⣧⠀⠀⣎⠞⠃⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡆⡄⢀⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡇⠀⠑⡆⢸⠓⠀⠀⢸⠈⣧⠘⠋⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⡔⠀⠀⠀⢸⢀⠃⢸⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⢱⠈⠀⠀⠀⢸⠀⡏⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⡟⠀⢰⠁⠀⠀⠀⡎⢸⢀⣧⢇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠈⠀⠀⠀⠀⢸⢸⠁⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢺⠁⢠⠇⢀⠇⠀⠀⠀⣸⡇⡘⣸⢹⢸⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠘⣾⠀⠀⠀⠈⠑⠢⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠚⠁⠀⢸⠀⡜⠀⡜⠀⠀⠀⡰⢻⠁⣷⠃⢸⡘⡆⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡇⢰⠀⠀⠀⠀⠀⠀⣟⠀⠀⠀⠀⠀⠀⢸⠀⠉⠉⠑⠒⠢⠤⠤⣄⣀⣀⡀⢀⣀⠤⠒⠉⠀⠀⠀⠀⠀⠈⣶⠁⢰⠁⠀⠀⡴⠁⡞⢠⠏⠀⠀⣇⢣⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢱⠸⡀⡆⠀⠀⠀⣠⢺⡄⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡏⢳⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠏⢠⠇⠀⢀⡜⡇⢰⢁⠎⠀⠀⣀⣸⡜⡆⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡸⡆⡇⢹⠀⠀⡰⢁⡟⡇⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⢻⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⢀⡎⠀⣠⠟⢲⣾⣏⣾⣿⣿⣿⠟⡽⠛⠛⠢⠤ ⠀⠀⠀⠀⠀⠀⠀⢰⠃⣵⢹⠸⣇⡰⢁⡿⠀⢱⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢀⡼⠚⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢀⠎⢀⠜⠁⣠⣿⣿⣾⣿⣿⣿⢃⡞⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⠇⣰⠁⢯⡆⡿⢡⡿⠁⠀⠀⢧⠀⠀⠀⠀⢸⢧⠀⠀⠀⠀⣀⠔⠉⢀⡴⠇⠀⠀⠀⠀⠀⠀⠀⠀⢀⡰⢡⣎⠔⠁⠀⣰⣿⣿⣿⣿⣿⣿⢃⡎⠀⠀⠀⡠⠀⠀ ⠀⠀⠀⠀⠀⢀⠏⣰⡏⠀⠈⡿⢡⡟⠣⡀⠀⠀⠈⢆⠀⢀⣤⣾⣾⣶⣾⠟⠋⠉⠑⢒⠾⠤⠤⠤⠤⠤⠤⠤⠤⠒⠊⣹⣵⠟⠁⠀⠀⢠⣿⣿⣿⣿⣿⣿⠃⡜⠀⠀⠀⡴⠁⠀⠀ ⠀⠀⠀⠀⢀⠎⣰⢻⠁⠀⡼⢡⡟⠙⡆⠙⠢⣀⠀⠈⢷⣿⣿⣿⣿⡟⠀⠀⠀⠀⣠⠾⠒⠊⠉⠉⠉⠉⠒⠤⣀⠀⠈⡽⠁⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⡏⡸⠀⠀⠀⡸⠁⠀⠀⠀ ⠀⠀⠀⢀⠎⡔⠉⠙⠢⣜⢠⡟⢱⢠⢿⣄⡴⢫⣷⡦⣄⡻⣿⣿⡿⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢱⠞⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡿⢀⠇⠀⠀⠀⠁⠀⠀⠀⠀ ⣀⣀⣀⠎⠀⣇⣀⡀⠀⠈⢻⠀⢸⡼⡰⠋⠂⣾⣿⣸⣿⣿⣿⣿⠃⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⠇⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡉⠀⡜⠀⡼⠈⠉⠛⢷⣄⠘⡄⠸⣿⠃⠀⢠⢻⣇⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀

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