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

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●┳┳┳┳┳┳┳● ┣/\_/\ _/\ ┃(・ω・)ω-*) ♡ ┃ノ  ̄`⊂⌒ ̄\ sleep well <3 ( ノ ● \ ● \ ┣┳┳┳┳┳┳┳┳┫ \_. ┣┻┻┻┻┻┻┻┻┫
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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢀⣠⠤⣶⣶⣤⣀⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠟⢦⣤⡄⠒⠋⠁⠀⠀⢻⡝⢧⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⢿⡏⠀⢀⡀⠀⠀⠀⠀⠀⢷⢸⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠘⠃⠀⠀⠀⠀⠀⣸⣸⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⠁⠉⢳⣴⢻⣽⣟⢦⠘⠃⠀⠀⠀⠀⠀⠀⠀⢀⡿⠃⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠋⠐⠉⠙⣿⢿⡇⠀⠀⣀⡀⠀⠀⢀⡴⣿⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢾⣄⠀⠀⠀⠀⠀⣰⠟⣽⠁⠀⣀⠓⠃⠀⢠⡞⣱⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣾⣿⣧⣦⣤⣤⡔⢋⠈⠁⠀⠀⠀⠀⠀⠀⠏⡼⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠀⠀⠀⢸⣻⣿⣿⣯⠟⠋⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣞⣳⠀⠀⠀⠀⠀⠙⠛⠉⠀⠀⠀⢠⡀⢠⡄⠀⢀⡾⡯⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣡⡾⢋⡼⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠉⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⣸⢸⢠⡆⠀⠀⠀⠀⠀⠰⠞⠁⠰⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⡽⠛⠘⢿⣥⣤⣤⣤⣀⠀⠤⠠⢤⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣠⠶⣿⡛⠁⠀⠉⠉⠉⠙⣿⣦⢠⣰⠚⣋⣉⣁⣀⣤⠤⣶⣫⡤⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⠓⠚⠿⠯⠭⠭⠭⠤⠼⠏⢹⢾⠿⠿⠟⠓⠒⠚⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⢸⣼⠀⠀⠀⠸⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡄⢠⡏⠀⠘⣿⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡞⣤⠏⠀⠀⠀⡿⠀⠀⠀⢴⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣾⡾⠃⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣸⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⡶⡦⢤⣀⡴⠋⣥⣍⡻⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⢿⠀⠠⣶⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⣥⣾⣷⣷⣶⡝⠂⠈⠀⠘⠓⢻⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⠘⣆⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢸⣸⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⣔⢸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠘⣆⠹⣆⠀⢠⡆⠀⢀⡀⠈⠁⠀⢸⠐⣿⣿⡀⠀⠀⠀⠀⢀⢠⣶⣟⠟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⠫⢘⢧⣼⣷⣂⡈⠉⠀⢀⣀⡌⢧⠻⣿⣷⡀⠀⠀⠀⠨⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⢉⣿⡟⠿⠥⣶⣟⣉⣁⣠⡤⠴⠖⠙⠟⣴⣀⠀⣽⡿⣳⠇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡴⠃⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠦⢤⣈⣨⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀ ⠐⠶⣿⣿⡿⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣿⣿⣇⡀⠀⠀⠀⠀ ⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⢿⣿⣿⡿⠟⠋⠉⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⣿⣿⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⡤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣿⣿⣿⣿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣶⣿⣿⣆⣀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡿⠉⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⣤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⢤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡼⠋⠀⣀⠄⡂⠍⣀⣒⣒⠂⠀⠬⠤⠤⠬⠍⠉⠝⠲⣄⡀⠀⠀ ⠀⠀⠀⢀⡾⠁⠀⠊⢔⠕⠈⣀⣀⡀⠈⠆⠀⠀⠀⡍⠁⠀⠁⢂⠀⠈⣷⠀⠀ ⠀⠀⣠⣾⠥⠀⠀⣠⢠⣞⣿⣿⣿⣉⠳⣄⠀⠀⣀⣤⣶⣶⣶⡄⠀⠀⣘⢦⡀ ⢀⡞⡍⣠⠞⢋⡛⠶⠤⣤⠴⠚⠀⠈⠙⠁⠀⠀⢹⡏⠁⠀⣀⣠⠤⢤⡕⠱⣷ ⠘⡇⠇⣯⠤⢾⡙⠲⢤⣀⡀⠤⠀⢲⡖⣂⣀⠀⠀⢙⣶⣄⠈⠉⣸⡄⠠⣠⡿ ⠀⠹⣜⡪⠀⠈⢷⣦⣬⣏⠉⠛⠲⣮⣧⣁⣀⣀⠶⠞⢁⣀⣨⢶⢿⣧⠉⡼⠁ ⠀⠀⠈⢷⡀⠀⠀⠳⣌⡟⠻⠷⣶⣧⣀⣀⣹⣉⣉⣿⣉⣉⣇⣼⣾⣿⠀⡇⠀ ⠀⠀⠀⠈⢳⡄⠀⠀⠘⠳⣄⡀⡼⠈⠉⠛⡿⠿⠿⡿⠿⣿⢿⣿⣿⡇⠀⡇⠀ ⠀⠀⠀⠀⠀⠙⢦⣕⠠⣒⠌⡙⠓⠶⠤⣤⣧⣀⣸⣇⣴⣧⠾⠾⠋⠀⠀⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⣭⣒⠩⠖⢠⣤⠄⠀⠀⠀⠀⠀⠠⠔⠁⡰⠀⣧⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⢤⣀⣀⠉⠉⠀⠀⠀⠀⠀⠁⠀⣠⠏⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠒⠲⠶⠤⠴⠒⠚⠁⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠉⠉⠻⣦⡀⠀⠀⠀⠀⠀⣴⠞⠛⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣤⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠈⣷⠀⠀⠀⢀⡾⠃⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢰⡇⠀⠹⢦⡤⢤⣄⡀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⣾⠁⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⡴⠞⠋⠀⠀⠀⠀⠀⢀⡾⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⢸⡇⠀⠀⠀⠀⠀⠀⠘⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⢧⣄⡀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⠇⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⣿⠀⠀⢀⣀⣀⣀⣱⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢿⣤⠶⠋⠀⠈⠉⠁⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠘⠳⠛⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠸⠃⠐⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠐⠀⠀⠂⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠇⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠂⠀⢀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠀⠀⠀⠀⠊⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡟⠋⠙⣧⠀⠀⣰⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠛⠻⡧⠀⠀⢻⣄⡀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠁⠀⠀⠘⠛⠳⢦⣀⠀⠀⠀⢀⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⡀⠀⣤⣤⣤⡄⠀⢹⡆⠀⠀⠀⣽⡷⣿⡋⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡁⠸⣇⡀⣀⡤⠀⢸⡇⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⢀⣠⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⠈⠛⠉⠀⣠⠞⠛⢳⡶⢤⣤⣤⣴⡶⠶⠶⠚⠛⢩⡿⢦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⢻⡁⠀⠀⠀⠙⠳⠶⠖⠛⠀⠀⠀⠀⣴⣋⣠⡾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⣰⣾⠁⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣌⠙⠳⢶⡶⠶⠶⠞⣫⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡞⢻⠄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠒⠛⠛⠶⠶⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠉⠉⠀⠈⠳⣤⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠂⠀⠀⠀⣤⠟⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⠤⠶⢤⣀⡿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀
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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣅⣁⢈⣭⣿⣷⣾⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⣴⣖⣦⣤⣲⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣯⡿⠟⠋⠉⠻⡟⢟⡽⣗⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⢞⢝⣍⢿⣹⡿⠳⣛⣋⣓⣩⣲⡤⡀⠀⠀⠀⠀⠀⣰⡿⣣⠟⠁⠀⠀⠀⠀⠀⠘⢑⡻⣟⡧⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠐⣿⣽⡿⣿⣟⡁⠀⠀⠀⠉⠉⢻⣟⠋⠝⢓⢤⣠⡴⣶⡿⣟⣭⣓⠖⠢⣤⣀⣀⣀⣬⡶⣻⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣹⣫⢿⡇⣃⠴⡀⣀⡠⠤⠶⠒⣺⠿⣟⢸⣯⣃⣳⡾⡲⠷⣮⣥⣼⣮⣤⣥⣾⣿⣿⣻⡿⢯⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢘⠣⣿⣿⣶⣾⣿⣷⣶⡂⢩⡭⢊⣽⣿⡿⠿⠿⢿⣦⣴⣙⠈⠙⠏⠉⠋⠉⠀⠩⠀⠂⠀⢀⣤⢤⣤⣤⣂⣅⠉⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⠀⠉⠉⠙⠟⡟⢛⠋⡵⣻⣿⠏⠀⠀⠀⠘⢿⢯⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⣀⠖⣫⠵⢏⣽⣿⣿⡧⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⣩⢅⡏⠀⠀⠀⠀⠀⠈⠫⣳⠄⢹⡆⠀⠀⠀⠀⣢⣴⣿⣿⣿⠟⠁⠈⢿⢿⡿⠄⠀ ⠀⠀⣰⣾⣏⣩⣉⠰⣄⠀⠀⠀⠀⣠⢖⣴⢟⠎⠀⠀⠀⠀⠀⠀⠀⠀⠉⠷⣾⣿⡀⠀⢠⣾⣿⣿⡿⠟⠁⠀⠀⠀⣸⣾⠣⠂⢀ ⠀⣰⡇⠈⠙⠤⣽⣿⣹⣷⣤⣈⣴⣩⡤⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⠛⠛⡫⠁⠀⠀⠀⣀⣴⣾⡿⠃⠁⠀⠘ ⢰⣿⣹⡄⠀⠀⠀⠉⠛⠻⠿⠛⠋⠉⠂⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⣀⡀⣤⡶⠁⢼⣿⠃⠀⠀⠀⠀ ⢹⡇⠂⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡁⡆⠡⣬⣧⣀⡜⠁⠀⠀⠀⠀⠀ ⠀⠱⡄⢂⠣⠀⣠⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⢶⠃⠙⠋⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠢⢀⣙⠿⣿⡿⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡾⡄⠀⠀⠀⣀⣀⠀⠀⠀⡄⠀ ⠀⠀⠀⠀⠀⠈⠑⠊⠁⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠺⢿⣿⣿⡶⡤⣕⡤⠀⠂⠀ ⠀⢀⠀⣤⠔⠆⢶⣶⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁⠄⠀⠀ ⠁⣠⡎⠀⣀⣠⡾⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠄⠀⠀⠀ ⠀⣿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀ ⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⋆౨ৎ˚⟡˖ ࣪⋆୨୧⋆⋆ ˚。⋆୨♡୧⋆ ˚。⋆
⡤⠒⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⢤ ⢣⡀⠀⠉⠲⢤⣀⡀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠖⠉⠀⢀⡜ ⢸⡉⠒⠄⠀⠀⠀⢉⡙⢢⠀⠀⡔⢋⡉⠀⠀⠀⠠⠒⢉⡇ ⠀⠉⢖⠒⠀⠀⠀⣇⠀⣸⠀⠀⣇⠀⣸⠀⠀⠀⠒⡲⠉⠀ ⠀⠀⠀⠉⠙⠫⠤⠚⠉⠀⠀⠀⠀⠉⠓⠤⠝⠋⠉⠀⠀⠀
⠀⣠⣶⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠹⢿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡏⢀⣀⡀⠀⠀⠀⠀⠀ ⠀⠀⣠⣤⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣟⣋⣼⣽⣾⣽⣦⡀⠀⠀⠀ ⢀⣼⣿⣷⣾⡽⡄⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⣿⣿⣿⡿⢿⣟⣽⣾⣿⣿⣦⠀⠀ ⣸⣿⣿⣾⣿⣿⣮⣤⣤⣤⣤⡀⠀⠀⠻⣿⡯⠽⠿⠛⠛⠉⠉⢿⣿⣿⣿⣿⣷⡀ ⣿⣿⢻⣿⣿⣿⣛⡿⠿⠟⠛⠁⣀⣠⣤⣤⣶⣶⣶⣶⣷⣶⠀⠀⠻⣿⣿⣿⣿⣇ ⢻⣿⡆⢿⣿⣿⣿⣿⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠀⣠⣶⣿⣿⣿⣿⡟ ⠈⠛⠃⠈⢿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠋⠉⠁⠀⠀⠀⠀⣠⣾⣿⣿⣿⠟⠋⠁⠀ ⠀⠀⠀⠀⠀⠙⢿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⠟⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣼⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠻⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢤⠤⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⣀⣀⡜⠻⠿⢾⣷⠹⠀⠀⠀⠀⣀⣤⣤⡀⠀⠀⠀⠀ ⠀⠀⠀⢠⡎⠁⠀⠀⠃⠀⠀⠀⠉⠀⠀⠀⡠⠞⠛⠛⠻⢽⠀⠀⠀⠀ ⠀⠀⠀⠸⣷⡀⠀⢀⠀⢂⠀⡀⠀⠀⠀⠜⠀⠀⠀⠀⡀⠸⠀⠤⢄⠀ ⠀⠀⠀⠀⠙⣗⣄⠀⠠⡀⢢⠃⠀⢸⠌⠀⡠⢊⠀⠊⠀⠀⠀⠀⠀⡇ ⠀⠀⠀⣀⣀⣈⣲⣕⣦⡈⠢⣻⡀⡎⢀⣴⡢⠑⠂⠁⠀⠀⠀⠀⡠⠃ ⠀⣴⠿⠽⠏⠀⠀⠀⠈⠉⢒⣺⣷⣗⣉⣁⣀⣀⣀⠀⠠⠤⠐⠈⠀⠀ ⢸⠀⠀⠀⠀⠀⠀⠀⢀⠠⡖⠁⣿⢳⡬⡁⠒⠒⠤⢄⡀⠀⠀⠀⠀⠀ ⠈⢦⡀⠀⠀⡀⠄⠂⠁⠊⠀⢰⣯⡏⠎⢌⠑⠀⠀⠀⠈⠑⢄⠀⠀⠀ ⠀⠀⠉⡻⠀⠀⠀⠀⠀⠀⣲⡟⡟⠀⠀⠀⠢⡀⠀⠀⠀⠀⢸⠀⠀⠀ ⠀⠀⠀⢧⣤⡄⡀⠀⢀⡔⣽⠃⢧⡄⠀⠀⠀⠰⣀⠀⠀⣀⠞⠀⠀⠀ ⠀⠀⠀⠈⠳⠬⠥⠔⠋⡜⡌⠀⠘⣿⣦⣀⠀⡀⡇⠉⠉⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⠜⡰⠀⠀⠀⠈⠛⠯⠥⠒⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡠⠊⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣛⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣴⣿⣿⠿⣟⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣏⡏⠀⠀⠀⢣⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣟⠧⠤⠤⠔⠋⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⣿⡀⢀⣶⠤⠒⠀⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢹⣧⠀⠀⠀⠀⠀⠈⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠈⢿⣆⣠⣤⣤⣤⣤⣴⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣾⢿⢿⠀⠀⠀⢀⣀⣀⠘⣿⠋⠁⠀⠙⢇⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣾⢇⡞⠘⣧⠀⢖⡭⠞⢛⡄⠘⣆⠀⠀⠀⠈⢧⠀⠀⠀⠙⢿⣄⠀⠀⠀⠀ ⠀⠀⣠⣿⣛⣥⠤⠤⢿⡄⠀⠀⠈⠉⠀⠀⠹⡄⠀⠀⠀⠈⢧⠀⠀⠀⠈⠻⣦⠀⠀⠀ ⠀⣼⡟⡱⠛⠙⠀⠀⠘⢷⡀⠀⠀⠀⠀⠀⠀⠹⡀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠹⣧⡀⠀ ⢸⡏⢠⠃⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠸⣷⡀ ⠸⣧⠘⡇⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⣿⠇ ⠀⣿⡄⢳⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠈⠆⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀ ⠀⢹⡇⠘⣇⠀⠀⠀⠀⠀⠀⠰⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⣼⡟⠀⠀ ⠀⢸⡇⠀⢹⡆⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢳⣼⠟⠀⠀⠀ ⠀⠸⣧⣀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⢃⠀⢀⣴⡿⠁⠀⠀⠀⠀ ⠀⠀⠈⠙⢷⣄⢳⡀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⣠⡿⠟⠛⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠻⢿⣷⣦⣄⣀⣀⣠⣤⠾⠷⣦⣤⣤⡶⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢸⣦⡀⠀⠀⠀⠀⢀⡄ ⠀⠀⠀⢸⣏⠻⣶⣤⡶⢾⡿⠁ ⠀⠀⣀⣼⠷⠀⠀⠁⢀⣿⠃⠀ ⠴⣾⣯⣅⣀⠀⠀⠀⠈⢻⣦⡀ ⠀⠀⠀⠉⢻⡇⣤⣾⣿⣷⣿⣿ ⠀⠀⠀⠀⠸⣿⡿⠏⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠟⠁⠀⠀⠀⠀⠀
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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡴⣆⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⣼⣿⡗⠀⠀⠀⠀ ⠀⠀⠀⣠⠟⠀⠘⠷⠶⠶⠶⠾⠉⢳⡄⠀⠀⠀⠀⠀⣧⣿⠀⠀⠀⠀⠀ ⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣤⣤⣤⣤⣤⣿⢿⣄⠀⠀⠀⠀ ⠀⠀⡇⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠙⣷⡴⠶⣦ ⠀⠀⢱⡀⠀⠉⠉⠀⠀⠀⠀⠛⠃⠀⢠⡟⠂⠀⠀⢀⣀⣠⣤⠿⠞⠛⠋ ⣠⠾⠋⠙⣶⣤⣤⣤⣤⣤⣀⣠⣤⣾⣿⠴⠶⠚⠋⠉⠁⠀⠀⠀⠀⠀⠀ ⠛⠒⠛⠉⠉⠀⠀⠀⣴⠟⣣⡴⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠤⢤⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⣀⠔⠒⢺⠻⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣳⡄⠀⠀⠀⠀⢀⣴⢳⣖⢁⡴⠂⢹⣉⣳⡀ ⠀⠀⠀⠀⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠉⣁⣈⣯⣛⡦⡤⠠⠔⠋⣠⠊⡸⠋⡠⢾⣹⡀⠀⢵ ⠀⠀⠀⢸⡟⠉⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢁⡴⠋⣀⣠⡷⠬⣉⡗⠒⢲⣾⣿⠔⢁⠜⢁⠜⠁⠀⠀⠀ ⠀⠀⠀⢸⠁⢀⣾⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⢰⢁⠎⡠⠊⢙⠿⠓⠒⠢⡯⣁⠒⠋⢁⡤⠋⡠⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠸⣦⣾⠏⠀⠀⠀⠀⠀⢸⢦⡀⠀⠀⠀⠀⠀⠀⠀⢸⠛⡎⡸⢰⢁⠔⢁⡤⠒⠉⠉⡗⠢⢍⣉⣁⡠⠚⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⣾⣿⠟⠒⠉⣉⣀⣈⣉⣹⣑⡗⠢⢤⣆⣀⠀⠀⠀⢸⡼⣹⠃⡇⡎⡠⠃⠀⠀⢾⣭⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣼⣿⠟⢹⡐⠊⢉⣀⠠⠤⠾⠿⠀⣉⣉⢺⠻⢷⢍⣹⣾⢟⡠⠊⣸⢰⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣾⡿⠁⣠⣾⣿⣿⣧⡄⠤⠐⠒⠒⠒⠤⣤⣨⣍⣛⠒⠤⠄⢀⠠⠔⢹⣯⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⠁⠰⡟⠉⢳⠊⢹⣷⠔⠒⠀⠉⠁⠐⠛⠛⠦⠬⣉⡑⠒⠠⠤⠔⢻⡰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⣧⡀⠳⢄⢸⡎⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⢒⣶⣾⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠙⠲⠤⠴⣗⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣀⡀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣿⣿⡿⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠙⡻⠤⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
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⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⢿⡿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⡼⣯⡿⣽⡷⣿⢿⡿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠐⣿⣽⣷⡟⣯⣿⣽⣯⣿⣽⠂⠀⢠⣶⣿⡟⣦⠀⣶⣶⣶⣶⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢻⣽⣾⣻⠏⠀⠈⣿⣞⠟⢀⣴⣿⣻⢾⣽⣟⡿⣯⢿⣽⢯⣷⠀⠀ ⠀⠀⠀⠀⠀⡀⠀⡀⢀⠻⣾⡽⣷⠀⠀⠸⣻⠀⣸⣟⠾⣽⣯⠷⣻⣽⣟⡿⣾⣻⢧⠀⠀ ⠀⠀⠀⢠⣾⣇⣀⢧⣨⣇⣏⡙⠯⣧⡄⠀⣟⠀⡿⠀⠀⠈⠀⠀⢀⣿⢾⣻⡷⣟⣿⠃⠀ ⠀⠀⠀⠘⢷⡏⠐⠊⠰⠃⠈⠛⢷⡷⣄⡀⠀⠀⡅⠀⢀⣠⣶⡿⠻⠏⢛⡓⠛⠋⠁⠀⠀ ⠀⠀⢀⣤⣦⣴⡶⣶⢶⣴⣤⣀⠀⠙⢟⡿⣦⠀⠀⠀⠛⣉⣴⡴⣞⡿⣟⣿⣻⣗⣦⠀⠀ ⠀⢀⣾⡿⣽⣯⢷⠛⠈⠉⠛⠛⠂⠀⠘⢷⣻⠀⠀⠀⠒⠛⠉⠁⢻⡷⣟⣯⡿⣽⢿⡄⠀ ⣠⣿⢯⣟⣷⣻⢿⣤⣤⡤⠤⠶⣶⠆⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠉⠙⢻⣽⣻⢯⣟⡿⡄ ⠙⠋⢿⣻⣞⣯⣿⣽⠚⢁⣤⡾⠁⠀⠀⠀⣾⠀⣿⣇⠀⠀⢰⣦⣀⣠⣼⢯⣟⡿⣽⣻⢿ ⠀⠀⠀⢿⣽⠳⠏⣠⡾⣟⣷⢿⣦⣤⠀⠀⢸⡄⢸⣯⢿⣶⣻⢾⣟⡿⣞⣿⣽⣻⢯⠿⠁ ⠀⠀⠀⠀⠀⠀⠀⣿⡽⣟⣾⣯⡷⣟⣧⣤⣿⣻⡀⠹⣟⣾⡽⣿⣞⡿⣯⠃⠉⠉⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠻⠻⢿⣧⣟⡿⣿⣻⢧⣟⣧⡇⠀⠘⠟⣿⣧⢿⠻⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣞⣿⣳⣿⣻⣽⢯⡇⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣾⣽⡾⠙⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢸⣦⡀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣏⠻⣶⣤⡶⢾⡿⠁⠀⢠⣄⡀⢀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀ ⠀⠀⣀⣼⠷⠀⠀⠁⢀⣿⠃⠀⠀⢀⣿⣿⣿⣇⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠴⣾⣯⣅⣀⠀⠀⠀⠈⢻⣦⡀⠒⠻⠿⣿⡿⠿⠓⠂⠀⠀⢂⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠉⢻⡇⣤⣾⣿⣷⣿⣿⣤⠀⠀⣿⠁⠀⠀⠀⢀⣴⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠸⣿⡿⠏⠀⢀⠀⠀⠿⣶⣤⣤⣤⣄⣀⣴⣿⡿⢻⣿⡆⠂⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠟⠁⠀⢀⣼⠀⠀⠀⠹⣿⣟⠿⠿⠿⡿⠋⠀⠘⣿⣇⠀⠄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢳⣶⣶⣿⣿⣇⣀⠀⠀⠙⣿⣆⠀⠀⠀⠀⠀⠀⠛⠿⣿⣦⣤⣀⠀⠀ ⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⠿⠋⠁⠀⣹⣿⠳⠀⠀⠀⠀⠀⠀⢀⣠⣽⣿⡿⠟⠃ ⠀⠀⠀⠈⠀⢰⠿⠛⠻⢿⡇⠀⠀⠀⣰⣿⠏⠀⠀⢀⠀⠀⠁⣾⣿⠟⠋⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⣰⣿⣿⣾⣿⠿⢿⣷⣀⢀⣿⡇⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠋⠉⠁⠀⠀⠀⠀⠙⢿⣿⣿⠇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀ 𐙚 -`♡´-˙✧˖°📷 ༘ ⋆。˚˙✧˖°📷 ༘ ⋆。˚˚˖𓍢ִ໋🌷͙֒✧˚.🎀༘⋆˚‧。⋆🌻⋆。‧˚⛷🧚‍♀️🛖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠋⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⠀⢀⣀⣀⣠⣤⣀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠟⠛⠛⠋⠉⠉⠛⣷⡄ ⠀⠀⠀⠀⠀⠀⠀⢠⣿⢀⣀⡤⣤⢤⡤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇ ⠀⠀⠀⠀⣀⣤⣶⠿⠛⠋⠁⠁⠀⠀⠀⠉⠛⣯⣳⡀⠀⠀⠀⠀⠀⠀⢠⡿⠃ ⠀⣠⣶⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡻⣿⠀⠀⠀⠀⠀⣠⡿⠃⠀ ⢸⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠉⢹⡆⠀⠀⢸⣿⠀⠀⠀⠀⢠⡿⠁⠀⠀ ⢸⣧⡀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠈⠀⠀⢀⣮⠏⠀⠀⠀⠀⠘⣷⡀⠀⠀ ⠀⠙⠿⣶⣤⣀⠀⠀⠀⠀⠈⠻⢦⣤⣤⣤⡶⠟⠁⠀⠀⠀⠀⠀⠀⠘⣷⡄⠀ ⠀⠀⠀⠀⠉⠛⠿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄ ⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣦⣤⣤⣄⣀⣀⣤⡿⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⣠⣾⠏⠀⠀⠀⠈⠉⠉⠙⠛⠉⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣄⠀⠀⣠⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣅⣀⢈⣩⣷⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⠴⣒⣤⣀⡲⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢾⣿⣯⡿⠟⠋⠈⠻⡛⠋⠹⣗⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⠊⢔⢉⢙⣹⡿⠳⣙⡊⣓⣉⣒⡤⡀⠀⠀⠀⠀⠀⣰⡟⣡⠟⠁⠀⠀⠀⠀⠀⠈⠑⠢⡍⡧⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠐⡇⠀⠻⣿⠟⠁⠀⠀⠀⠉⠉⠻⣟⠋⠙⠓⢤⣠⡴⣶⡿⣛⣉⣁⠒⠢⣄⣀⠀⣀⣤⡶⢺⣷⠇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠱⡀⢾⠁⠀⠀⠀⣀⡠⠤⠶⠒⣺⠿⣟⢠⣯⣃⣳⡾⠲⠷⣮⣥⣴⣮⣤⣤⣬⣿⣟⣻⡿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠢⣷⣦⣤⣾⣿⣷⣶⡂⢉⡤⢊⣥⣿⡿⠿⠿⢿⣦⣤⣀⠈⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⢀⡤⢤⣄⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠋⡴⣻⣿⠏⠀⠀⠀⠘⢿⢯⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⢀⢽⣿⣦⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⣡⢁⡏⠀⠀⠀⠀⠀⠈⠫⣳⠄⢹⡆⠀⠀⠀⠀⣠⣴⣿⣿⣿⠞⠁⠈⢿⢿⡷⠀⠀ ⠀⠀⣰⣾⣏⠩⡉⠰⣄⠀⠀⠀⠀⢠⢂⡴⢛⠎⠀⠀⠀⠀⠀⠀⠀⠀⠉⠷⣾⣿⡀⠀⢠⣾⣿⣿⡿⠟⠁⠀⠀⠀⣸⣾⠃⠀⢀ ⠀⣰⡇⠈⠙⠤⣽⣧⣹⣷⣤⣀⣴⣡⡤⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⠛⠛⠋⠁⠀⠀⠀⣀⣴⣾⡿⠁⠀⠀⠘ ⢰⣟⣹⡄⠀⠀⠀⠉⠛⠻⠿⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⢀⡖⠁⢸⣿⠃⠀⠀⠀⠀ ⢹⡇⠂⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡁⠀⠠⣬⣧⣀⡜⠁⠀⠀⠀⠀⠀ ⠀⠱⡄⠀⠣⠀⣠⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⢶⠃⠙⠋⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠢⢀⣙⠿⣿⡿⢿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡾⡄⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠑⠊⠁⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠺⢷⣽⣾⡶⠤⢕⡄⠀⠀⠀ ⠀⠀⠀⣠⠔⠂⢶⣶⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁⠀⠀⠀ ⠀⣠⡎⠀⣀⣠⡾⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀ ⠀⣿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
.  +⠀ ⠀ ⠀˚⠀ ⣴⠟⠉⠉⠛⢦⡀⢀⣴⠛⠉⠈⠙⠻⣄ ⠀⠀⣼⠃⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠹⣦ ⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿ ⠀⠀⠿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡆ ⠀⠀⠀⢻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃ ⠀⠀⠀⠀⠀⠻⢦⣄⠀⠀⠀⠀⠀⣠⡴⠛ ⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⣄⠶⠋ ⠀⠀⠀+. *
⠀⠀⠀⠀⠀⠀⠀⣀⡄⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀ ⠀⠀⠀⠀⠀⠀⠐⢿⠓⠀⢀⡴⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠹⡒⠤⣀⡀⠀⢀⡴⠋⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠱⡀⠀⠉⠑⠋⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀ ⠀⠀⠀⠀⢱⡄⠀⠀⠀⠀⠀⠉⠒⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀ ⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣈⠵⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀ ⢀⡤⠋⣀⣀⣀⣤⠀⠀⠀⢰⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀ ⠈⠉⠁⠀⠀⠀⠀⢧⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢐⣶⣆⠀⠀⢠⠈⢇⢰⠃⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣰⡄⠀⠀⠀⠀⠀⠀ ⠀⠈⠙⠀⠀⠀⣏⣧⠈⠟⠀⠀⠀⠀⠀⠀⠽⡿⠆⠀⠀⠀⢀⣿⣿⣦⣶⣶⠟⠀⠀ ⠀⠀⠀⠀⣀⣸⣿⣯⢧⠤⢤⣤⣴⠦⠀⠀⠀⠁⠀⠀⠛⠿⣿⣿⣿⣿⣿⡁⠀⠀⠀ ⠀⠙⠯⡻⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠰⣄⣠⡇⠀⠀⠀⠀⢸⣿⡿⠛⠛⠿⣆⠀⠀ ⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⠁⠀⠀⠀⣠⢿⣿⠟⠒⠀⠀⠀⠸⠊⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡾⣿⠿⠺⢝⡯⢧⠀⠀⠀⠀⠀⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢼⠓⠁⠀⠀⠀⠉⠺⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠈⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢟⡒⠒⠛⠁⠀⠘⠒⠒⢲⡶⠂⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡆⠀⠈⢢⠀⠀⠀⠀⡤⠚⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠉⠀⢠⠇⢀⡤⣀⠀⢳⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠊⠁⠀⠈⠳⣼⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⠀⣀⠀⠀⢀⣄⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⢾⣿⣟⠁⠀⠀⠺⡟⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⢉⠓⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠿⠿⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣾⣿⣶⣶⣤⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠘⢿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀ ⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠈⠻⣿⣿⣿⣿⣆⠀⠀⠀⢀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⣀⣤⣶⣶⣌⠻⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀ ⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⠁⣰⣿⣿⣿⣿⣿⣦⣙⢿⣿⣿⣿⠄⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣦⣹⣟⣫⣼⣿⣿⣶⣿⣿⣿⣿⣿⣿⣯⡉⠉⠉⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠐⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⡆⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⢻⣿⣿⣿⣿⣿⡇⠀⠀⠈⠉⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⣠⣴⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⡇⠀⠸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠹⢿⣿⣿⢿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢰⣶⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣧⣄⣐⣀⣀⣀⣀⣀⡀ ⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠁⠛⠛⠛⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁
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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢆⡴⢪⢁⣾⡅⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢀⣞⢰⣿⣡⣾⠟⡅⠀⠠⠂⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⣾⡈⠘⢟⠩⣣⠚⠀⡁⠂⣅⡜⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠱⣀⡇⡎⡘⣷⢠⡞⠀⠃⢀⡖⣧⣼⠋⡐⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢰⢸⡇⣃⠣⢹⡾⡀⠆⢇⣿⢣⠹⡣⠪⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡘⣏⢷⢎⠃⢸⡇⠃⡀⢸⡟⠄⢐⢎⣠⢗⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⢿⢿⣿⣿⣸⣸⣠⢇⡟⣔⠠⡢⢞⢕⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⡬⠂⢐⡭⠿⣴⠁⠀⢈⠣⣾⣱⢵⠾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢚⡤⣰⢿⣅⡀⣆⠢⣖⡃⢹⢇⡧⢏⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢨⢟⣣⣬⣷⣭⡉⣹⡀⢀⣼⣧⠀⠀⣸⣵⣿⠂⣜⠤⠶⣦⡀⠀⠀⠀⠀⠀ ⢠⠔⠈⢃⡤⡀⠠⢺⣿⣿⣿⣻⢾⣾⣍⣡⣿⢟⡀⢀⣼⣿⣿⣷⡿⠃⠈⠀⠈⠳⡀⠀⠀⠀⠀ ⡾⠁⠐⣚⣧⠎⢷⣿⣿⣿⣿⡙⠃⠙⠻⣿⠯⠛⣨⣿⣿⡿⣯⣿⡗⣡⡶⠟⠛⣿⣾⠀⠀⠀⠀ ⣶⣎⣝⣯⠆⡀⡸⣿⣿⣿⡿⣄⠀⠀⢀⠁⠀⡠⣲⣿⡿⣿⣿⣧⡿⠯⢑⡤⠂⠛⢟⠀⠀⠀⠀ ⣿⡅⣢⠇⠀⠈⠃⠈⢻⣿⣿⣳⣗⡤⠇⠀⢐⣿⣿⣿⣿⣿⣿⣿⡱⡌⠀⠀⣄⠀⠀⡱⡀⠀⠀ ⠸⠿⣟⢅⠀⠀⠰⢤⣲⣿⣿⣿⣮⣙⡳⡾⠊⣾⣿⣾⣿⣿⣿⣿⣷⣝⣦⡄⠋⠈⠆⠁⠵⢄⠀ ⠀⠐⠽⣶⣍⢦⡄⢘⣿⡿⢿⣷⣯⣭⣴⠴⣻⣿⣿⣿⣿⣿⣿⣿⣿⣮⣟⠆⠁⠀⠉⠂⢆⢸⠀ ⠀⠀⠈⠐⠹⡛⢞⡽⠋⠀⠀⣽⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢏⠃⠀⠀⠀⠁⠀⢻⠄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢿⣿⣿⣿⣿⣿⣿⡿⠟⡿⠏⠐⡅⠈⠓⠖⣂⠀⠀⢀⡸⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣷⠳⡽⣁⣠⠆⠀⠐⠠⠀⠘⣧⡴⠋⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣤⣰⣀⣰⢀⣡⠟⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣷⣿⣏⡏⠛⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⣿⣾⢿⣿⢶⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣔⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣽⣿⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣴⡷⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⡾⣟⣾⡇⢟⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡠⣢⣽⣶⣾⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢿⣻⣿⢯⡗⠻⡂⠀⠀⠀⠀⠀⠀⠀ ⢀⣮⣾⣿⣟⣿⣽⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡿⣿⣽⡿⣇⡘⡇⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⢯⣷⣿⣻⣯⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⣿⣿⣿⣷⡿⣟⣷⣿⣧⡏⣧⠀⠀⠀⠀⠀⠀⠀ ⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⢸⣿⣿⣿⣷⢿⣟⣿⣾⣿⡧⢧⠀⠀⠀⠀⠀⠀⠀ ⠀⢫⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠸⣿⣿⣿⣿⣟⣯⡷⢳⣿⣷⡏⣧⠀⠀⠀⠀⠀⠀ ⠀⠈⠫⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢻⣿⣿⣿⣷⣷⣶⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⢳⠀⠫⣿⣿⣿⣿⣿⠿⣯⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀ ⠀⠀⠀⠀⠰⢙⡻⢿⣿⣿⣿⣟⠽⢄⠀⢨⠒⡀⢎⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠈⠈⠁⠝⢿⣮⣧⡇⢢⢀⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢸⡟⡚⠁⣸⠟⠀⢸⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣵⠃⣠⠇⠀⠀⠀⠁⢊⢿⣿⣿⣿⣿⣿⣿⡿⠟⠻⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⢏⣰⡴⠋⠀⠀⠀⠀⠀⠀⠁⠒⠄⢻⣿⠛⣛⡄⠀⠀⢣⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠌⢻⣧⠒⢧⠀⠀⠈⡆⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡌⢿⣎⡜⡡⣠⡌⡆⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠱⠺⡿⡝⠋⠀⢱⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢹⡶⠀⠀⡀⢇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣷⡄⠀⠒⠈⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣷⣧⡁⣐⡀⡃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠨⡻⣷⡤⢄⠇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠵⠞⠀
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⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣀⠀⡞⠉⠉⢳⣤⠤⣤⠀⠀⠀ ⠀⠀⢰⡏⠈⠹⣷⡄⠀⡞⠁⠀⠘⡇⠀⠀ ⠀⠀⣘⣧⠀⠀⠘⢷⡀⠀⢀⣠⡾⢥⣄⠀ ⠀⢸⡏⠁⠀⠀⠀⣸⣿⡞⠋⠀⠁⠀⣬⠃ ⠀⠘⢿⣤⣶⡶⠛⠉⠘⣷⡀⠐⠁⣾⡅⠀ ⠀⠀⠀⢰⣿⠀⠀⣹⡄⣺⣿⣷⡔⣼⡇⠀ ⠀⢀⣠⡾⠛⠶⠾⠻⣿⣻⣿⠊⠉⠁⠀⠀ ⠛⠋⠁⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀
ο__________ο ∥ (\_(\___/) ∣ ∥ (〃(〃  )♡♡ ∣^︵︵`︵︵︵\ ( /    ︵ ︵\ \  ||‾‾‾‾‾‾‾‾‾‾‾‾|| \ , ||——————––||
⠀⠀⠀⢀⠤⠤⠠⠤⠤⠠⠤⠤⢀⡀⠤⣀⡀⠀⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡠⢋⢰⠀⢀⠀⠂⡄⢠⡀⡤⠀⢠⠀⡄⢀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀ ⢀⠜⠀⡃⠇⠃⠀⠅⢠⠊⠁⠀⠁⢤⠊⠁⠈⠙⠄⠀⢨⠀⠀⠀⠀⠀⣠⡄ ⠈⢆⠀⠉⠀⢠⠀⠀⢇⠀⠀⢿⣿⢸⢸⣿⡇⠀⡸⠀⠸⠀⠀⠀⣀⡌⡌⠁ ⠀⠘⡄⢸⡅⠀⠀⠀⠪⢄⢁⠤⠔⠉⠦⠄⠐⢈⡩⠀⢠⠀⠀⠸⠰⠏⡼⠀ ⠀⠀⠘⠀⢸⢹⢂⠀⠀⢸⠒⠤⡤⢠⣤⠭⡟⠀⠀⠀⡇⠀⠀⢀⠳⠉⠀⠀ ⠀⠀⠀⢱⡀⢉⢐⠀⠀⢸⣤⣤⣓⣚⣿⠀⠁⠀⠤⠃⡇⢄⢀⢢⠃⠀⠀⠀ ⠀⠀⠀⢠⠉⡄⠀⡆⠀⠀⠑⠠⠥⠽⠃⠀⠀⠀⠗⢸⣀⡿⠒⠁⠀⠀⠀⠀ ⠀⠀⠀⠠⡤⡔⠒⠂⠁⠢⠄⡒⡢⣤⠤⣀⠤⠐⠒⡎⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠇⡟⢻⡇⠲⠾⠟⠿⠿⣋⡿⠿⠻⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠆⢹⢲⡷⠤⠤⡆⠀⠐⢾⣒⣒⡶⠒⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⢧⠇⠁⢸⢙⠉⠀⠀⠀⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⢼⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣾⣾⣤⣄⠀⠀⢸⣿⣷⣲⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣾⠉⢳⣰⠋⠙⡆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀ ⡀⠘⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀ ⠙⠷⠋ ⣰⠟⠉⠙⢦⡀⢀⣾⡟⠉⠳⣆ ⣿⠀⠀⠀⠀⠛⠛⠁⠀⠀⠀⡿ ⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃ ⠙⢧⡀⠀⠀⠀ ⠀⢀⡴⠃⠀ ⠀⠀⠀⠙⠶⣄⣀⠴⠋⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡀⣰⡿⠛⠛⠿⢶⣦⣀⠀⢀⣀⣀⣀⣀⣠⡾⠋⠀⠀⠹⣷⣄⣤⣶⡶⠿⠿⣷⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⣿⠁⠀⠀⠀⠀⠈⠙⠛⠛⠋⠉⠉⢹⡟⠁⠀⠀⣀⣀⠘⣿⠉⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⣾⡋⣽⠿⠛⠿⢶⣤⣤⣤⣤⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣿⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⡀⠀⢈⣻⡏⠀⠀⠀⠀⣿⣀⠀⠈⠙⣷⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠙⢷⣄⣀⣀⣼⣏⣿⠀⠀⢀⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⣿⡉⠉⠁⢀⣠⣿⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠗⠾⠟⠋⢹⣷⠀⠀⠀⠀ ⢀⣤⣤⣤⣿⣤⣄⠀⠀⠀⠴⠚⠲⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡆⠀⠀⠀⠀⢀⣈⣿⣀⣀⡀⠀ ⠀⠀⠀⠈⣿⣠⣾⠟⠛⢷⡄⠀⠀⠀⠀⠀⠀⠀⡤⠶⢦⡀⠀⠀⠀⠀⠹⠯⠃⠀⠀⠀⠈⠉⢩⡿⠉⠉⠉⠁ ⠀⠀⣤⡶⠿⣿⣇⠀⠀⠸⣷⠀⠀⠀⠀⠀⠀⠀⠓⠶⠞⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣼⣯⣀⣀⠀⠀ ⠀⢰⣯⠀⠀⠈⠻⠀⠀⠀⣿⣶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁⠉⠉⠁⠀ ⠀⠀⠙⣷⣄⠀⠀⠀⠀⠀⢀⣀⣀⠙⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⡿⢷⣄⡀⠀⠀⠀ ⠀⠀⠀⠈⠙⣷⠀⠀⠀⣴⠟⠉⠉⠀⠀⣿⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣾⠟⠉⠀⠀⠈⠉⠀⠀⠀ ⠀⠀⠀⠀⠰⣿⠀⠀⠀⠙⢧⣤⡶⠟⢀⣿⠛⢟⡟⡯⠽⢶⡶⠾⢿⣻⣏⣹⡏⣁⡿⠀⠀⠀⠀⣸⠀⠀⠀⠀ ⠀⠀⡌⠀⡂⠹⣷⣄⠀⠀⠀⠀⠀⣠⣾⠏⠀⠀⠙⠛⠛⠋⠀⠀⢀⣽⠟⠛⠖⠛⠀⠀⡅⠀⠀⡌⡂⠀⠀⠀ ⠀⠀⡂⠀⠃⠀⠀⠙⠻⠷⠶⠿⠟⠋⠹⣷⣤⣀⡀⠄⣡⣀⣠⣴⡿⠁⠀⠀⠀⠀⠀⠀⡅⠀⠀⠆⠉⠀⠀⠀ ⠀⡀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣍⣉⣻⣏⣉⣡⠞⠁⠀⠀⠀⠀⠀⠀⡀⠃⠀⠀⠃⠀⢀⠒⠀ ⠀⠈⠂⠤⠤⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣀⡀⣀⡠⠋⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣠⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠘⣿⣿⣿⣿⠟⠁⠀⠀⠀⠹⣿⣿⣿⣿⣿⠟⠁⠀⠀⠹⣿⣿⣿⠇⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⢼⣿⠀⢿⣿⣿⣿⣿⠀⣾⣷⠀⠀⢿⣿⣿⣿⠀⠀⠀⠀ ⠀⠀⠀⢠⣿⣿⣿⣷⡀⠀⠀⠈⠋⢀⣿⣿⣿⣿⣿⡀⠙⠋⠀⢀⣾⣿⣿⡇⠀⠀⠀⠀ ⢀⣀⣀⣀⣿⣿⣿⣿⣿⣶⣶⣶⣶⣿⣿⣿⣿⣾⣿⣷⣦⣤⣴⣿⣿⣿⣿⣤⠤⢤⣤⡄ ⠈⠉⠉⢉⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⣀⣀⡀⠀ ⠐⠚⠋⠉⢀⣬⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣥⣀⡀⠈⠀⠈⠛ ⠀⠀⠴⠚⠉⠀⠀⠀⠉⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠋⠁⠀⠀⠀⠉⠛⠢⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠉⠉⠻⣦⡀⠀⠀⠀⠀⠀⣴⠞⠛⠻⣦⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠈⣷⠀⠀⠀⢀⡾⠃⠀⠀⠀⠘⣷⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⣾⠁⠀⠀⠀⠀⠀⢸⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⢸⡇⠀⠀⠀⠀⠀⠀⠘⡧⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⠇⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠘⠳⠛⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣤⠶⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠇⠂⠀ ⠀⠀⠀⢀⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢸⡄ ⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⢣ ⠀⠀⠀⢻⡀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰ ⠀⠀⠀⢨⡟⠋⠙⣧⠀⠀⣰⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⣿ ⢠⡞⠛⠻⡧⠀⠀⢻⣄⡀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠀⠀⠀⠀⢰⡏ ⠈⣷⠀⠀⠁⠀⠀⠘⠛⠳⢦⣀⠀⠀⠀⢀⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠃ ⠀⠙⢷⣄⡀⠀⣤⣤⣤⡄⠀⢹⡆⠀⠀⠀⣽⡷⣿⡋⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁⠀ ⠀⠀⠀⢿⡁⠸⣇⡀⣀⡤⠀⢸⡇⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⢀⣠⡼⠋⠀⠀⠀ ⠀⠀⠀⠘⢷⣄⠈⠛⠉⠀⣠⠞⠛⢳⡶⢤⣤⣤⣴⡶⠶⠶⠚⠛⢩⡿⢦⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⠉⠛⠛⠛⢻⡁⠀⠀⠀⠙⠳⠶⠖⠛⠀⠀⠀⠀⣴⣋⣠⡾⠇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⣰⣾⠁⠉⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣌⠙⠳⢶⡶⠶⠶⠞⣫⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠒⠛⠛⠶⠶⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠷⣿⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⣠⠀⠀⠀⠀⠀⠇⣷⢶⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠁⡝⢚⣷⢿⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣸⠀⠀⠁⠉⠈⠀⠀⡀⢦⠉⣄⠑⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠃⣼⣫⠛⣾⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠉⣭⣯⣹⣉⣉⣤⠤⣖⠻⡈⢦⠘⠀⠀⠉⠀⠀ ⠀⠀⠀⠀⠀⠇⣳⠴⢯⡴⢀⠀⠀⡄⠤⠢⠛⠈⠀⠀⠀⠀⡟⠚⠒⡀⣦⣷⠿⠤⣶⣛⢍⠤⠶⢰⠀⣆⠘⠋⣿⣴⠀ ⠀⠀⠀⠀⠀⣧⣸⠟⢠⠀⠀⠀⠀⠀⠀⠀⠀⣄⠣⠋⠴⣠⢀⠀⠀⠀⠀⠀⡀⢄⠶⠓⠉⣀⠀⠀⠀⠀⣄⢹⡇⢀⠀ ⠀⠀⠀⠀⠀⡏⠃⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡞⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢦⠙⠀⠀⠀⠀⡄⣷⠀⠀ ⠀⠀⠀⠀⠀⣿⡇⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠘⠀⠀⠀⠀⡄⢳⠀ ⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠹⠀⠀⠀⠀⡀⠹ ⠀⠀⠀⠀⠀⢸⡇⠈⠀⠀⠀⠀⠀⠀⠀⠃⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡟⠑⠀⠀⠀⠃⣾ ⠀⠀⠀⠀⠇⢀⡇⢸⠀⠀⠀⠀⠀⠀⠃⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡼⢀⣀⣳⣾⠓⣴⠀ ⠀⠀⠀⠀⡟⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡾⠀⠀⠀⠀⠀⡾⠀⠀ ⠀⠀⠀⠁⢸⠀⠀⡄⠸⠀⠀⠀⠀⠀⠀⠁⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡼⠀⠀⠀⠀⠀⡏⢠⠀⠀ ⠀⠀⠀⡾⠀⠀⠀⠀⣇⠘⠀⠀⠀⠀⠁⡿⣿⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡾⠀⠀⠀⠀⠀⠃⣰⠀⠀⠀ ⠀⠀⠇⢠⠀⠀⠀⠀⡇⣼⠹⠀⠀⠘⡿⣿⣿⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡼⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀ ⠀⡇⡾⠀⠀⠀⠀⠀⡇⢹⡀⢳⠀⠳⣿⣿⣿⣿⢿⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡼⠀⠀⠀⠀⠀⠀⡏⢠⠀⠀⠀⠀ ⠀⡇⢸⠀⠀⠀⠀⠀⡇⢸⠀⠀⢦⠛⣿⣿⣿⣿⣿⣿⢿⠻⠙⠉⠀⠀⠀⠀⠁⡼⠀⠀⠀⠀⠀⠀⠁⢸⠀⠀⠀⠀⠀ ⠀⡇⢀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⢧⠈⠀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣥⣼⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀ ⠀⡾⠀⠀⠀⠀⠀⠀⡇⢰⠀⠀⠀⠀⢷⠀⡶⣶⡠⣤⢦⡴⡷⣯⡿⠀⠁⡞⢀⠀⠀⠀⠀⠀⠀⡏⢠⠀⠀⠀⠀⠀⠀ ⡇⢸⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⡁⢸⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⡾⢀⠀⠀⠀⠀⠀⠀⠋⢰⠀⠀⠀⠀⠀⠀⠀ ⡇⢸⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠃⡴⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠋⣼⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢹⠀⠀⠀⠀⠀⠀⣧⠘⠀⠀⠋⣰⠀⠀⠀⠀⠀⠀⠁⣰⠀⠀⡇⢀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡇⠘⠀⠀⠀⠀⠀⡄⢹⠀⠞⢠⠀⠀⠀⠀⠀⠀⠁⡼⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⠀⠀⠀⠀⠀⠀⡇⡼⢀⠀⠀⠀⠀⠀⠀⠃⡰⠀⠀⠀⠇⢠⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣇⠈⠀⠀⠀⠀⠀⡄⠸⠀⠀⠀⠀⠀⠀⠎⣠⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⢼⠢⠓⠈⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⠀⠀⠀⠐⠀⠀⡆⠘⠀⠀⠀⠇⡼⠀⠀⠀⠀⠀⠇⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠘⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢰⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⢠⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢠⠀⠀⠀⠀⠀⠀⠋⠴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠆⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣰⠞⠛⠲⣦⣤⠤⠤⢴⠏⣦⣈⣷⣚⠉⠻⡄⠀⠀ ⠀⠀⠀⣿⣀⠀⠈⠁⠀⠀⠀⢾⡀⢻⡿⠉⠉⣷⡞⠻⣦⠀ ⠀⠀⢀⡿⠁⠀⠀⠀⠀⠀⠀⠈⠛⠛⠷⣤⣴⠿⠿⣠⡟⠀ ⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢦⡶⢻⡄⠀ ⠠⠤⡧⠤⠄⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⠀⠋⢹⡏⠁ ⠀⢀⣿⡤⠄⠘⠿⠁⠀⠠⣞⣻⠄⠀⠀⠻⠏⢀⡈⣽⠛⠃ ⠀⠀⢈⡷⣶⣃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠿⠛⠂⠀ ⠀⠀⠀⠀⠀⠉⠙⠛⠛⠓⠒⠒⠒⠚⠛⠛⠉⠁⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⠿⠿⣦⡀⠀⠀⠀⠀⠀⢀⣠⣴⠿⢷⣤⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⣾⠋⠁⠀⠀⠙⢿⣦⣤⣤⣤⣴⡿⠋⠁⠀⠀⠙⣿⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠐⠟⠁⠀⠀⠀⠀⠀⠈⠉⠁⠈⢩⠁⠀⠀⠀⠀⠀⠀⠻⠧⠀⣀⣀⣀ ⠀⠀⠀⠿⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⠟⠛⠛ ⠀⠀⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠿⠛ ⠀⣀⣀⡉⠙⠃⠀⣤⣦⠀⠀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣄⠀⢰⣦⠀⠀⠀⡀⠀⠀⠀ ⣼⠟⠛⢿⣇⠀⠀⠀⠀⠀⠀⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⢰⣿⠀⠀ ⣿⠀⠀⠘⠛⠛⠛⢷⣦⠀⠀⠀⢿⡆⠀⠀⠀⠀⠀⢠⡟⠀⠀⢀⣠⣴⠟⠁⠀⠀⠀ ⣿⠀⠀⠀⠀⠀⠀⠀⢻⣿⠦⠤⠄⣿⡄⠀⠀⠀⢰⣿⠃⠻⠿⠻⢿⣧⠀⠀⠀⠀⠀ ⣿⠀⠀⠀⠀⠀⢀⣀⣸⣿⠀⠀⠀⠸⣿⣄⠀⢠⣾⠏⠀⠀⣤⣤⡾⠟⠀⠀⠀⠀⠀ ⣿⣄⠀⠀⠀⠀⠀⢀⣾⣿⠀⠀⠀⠀⠀⠿⣶⣾⠟⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀ ⠘⠿⣿⣶⣶⣶⡿⠿⠛⣿⠀⠀⣤⣤⣤⣤⣶⣶⣾⠿⣷⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣤⣿⠋⠁⠀⠀⠀⠀⠀⠻⠷⠟⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢰⣿⡿⠗⠀⠠⠄⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⡜⠁⠀⠀⠀⠀⠀⠈⠑⢶⣶⡄ ⢀⣶⣦⣸⠀⢼⣟⡇⠀⠀⢀⣀⠀⠘⡿⠃ ⠀⢿⣿⣿⣄⠒⠀⠠⢶⡂⢫⣿⢇⢀⠃⠀ ⠀⠈⠻⣿⣿⣿⣶⣤⣀⣀⣀⣂⡠⠊⠀⠀ ⠀⠀⠀⠃⠀⠀⠉⠙⠛⠿⣿⣿⣧⠀⠀⠀ ⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡇⠀⠀ ⠀⠀⠀⣷⣄⡀⠀⠀⠀⢀⣴⡟⠿⠃⠀⠀ ⠀⠀⠀⢻⣿⣿⠉⠉⢹⣿⣿⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠉⠁⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀
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