⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⣼⠟⠉⠒⠄⢸⠀⠀⠀⠀⠀⠀⠀⣿⣿⣶⣿⣿⣿⣧⠈⢿ ⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⢿⣿⣿⣇⠀⠀⠀⠛⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠸⠿⣿⣿⣿⣿⣿⣇⠀⠈ ⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠸⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⣀⣀⣾⠀⠀⠀⠀⠀⠀⢸⠀⠀⣀⣀⣀⣀⡀⠀⢈⣿⣿⣿⣿⣿⡷⠀ ⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢻⣿⣿⣧⣤⣶⣶⣾⣿⣿⣿⣿⣿⣤⣤⣄⣤⣴⣶⣿⡿⠯⠛⠛⠛⢻⣿⣷⣾⡿⣟⣻⡿⣿⠇⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⡶⠶⠶⠤⢤⣤⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡿⠟⠉⠙⢀⡀⠈⠁⠀⡖⢀⣬⠉⢛⡮⣪⣾⣿⡁⠀⠀⣸ ⣿⣿⣿⣿⣿⣿⣿⣿⢷⣦⣄⣠⠀⢈⡈⠙⠿⢻⣿⣿⣿⣿⣿⣿⠟⠇⣴⣿⣕⢀⣠⠼⠏⠀⠀⠀⠀⣸⣿⠟⠑⢉⣾⣿⣿⣿⣿⣶⣴⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⡇⠙⠻⣿⣿⣶⣧⣤⣀⡀⠈⢉⣻⣿⢿⣑⣠⣿⣿⢻⠿⢁⠀⣀⠤⡀⣄⢖⣼⠋⢀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣶⣿⣿⣷⣿⣿⣿⡟⠰⠕⠃⠉⡐⠀⢠⣴⣿⠝⠀⣲⣫⣿⠟⠘⣿⣿⣿⣿⣿⣿⣻ ⠉⣛⣿⣮⣽⣿⣿⣿⣇⣠⣴⡾⠿⠟⠟⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠠⠔⠀⠀⠀⢁⣴⣿⣿⠏⠀⣄⣿⡿⣧⣶⣾⡟⢻⣿⣿⣿⣿⣿ ⠸⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠁⠀⠀⣤⠘⣻⣹⣿⣿⣿⣿⣿⣿⣿⡁⠱⠀⠀⣠⣶⣿⣿⣿⠃⢀⣲⣿⠟⣼⣿⣿⣸⣷⣹⣿⣿⣿⣿⣿ ⠀⠈⢉⣻⣿⠿⢯⣓⣦⣤⣷⣶⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⠋⣿⣯⠁⠀⢀⣼⣿⣿⣿⣿⠏⣀⣿⡿⠃⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣤⣾⣯⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣨⣿⣿⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⠿⠶⠋⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⡣⣸⣿⣿⠟⠁⠀⡴⠊⡼⢻⣿⠃⣸⣿⣿⢿⣿⣿⡟⠁ ⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠉⢻⠟⠟⠁⠀⠀⠀⠳⠞⠁⠀⠹⣦⣿⡇⢀⣿⣿⠟⠀⠀ ⠀⠀⠀⠘⢿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⡠⢊⣵⣿⠀⠀⢠⡤⠤⠀⠀⠀⠀⠀⠀⠹⣿⡇⣾⣿⠏⠀⠀⠀ ⣄⡀⠀⠀⠀⠈⠿⡟⠻⠿⣿⣿⣿⡟⣉⠻⣿⠿⢿⣿⣿⡿⠟⢉⡤⣊⣤⠿⢓⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣱⠟⠁⠀⠀⠀⠀ ⠀⠙⠓⢦⣄⡀⠀⡇⢀⣤⢶⣿⢏⡔⢙⣻⡏⡆⠈⡏⠁⣠⢔⣭⣶⡿⣿⣤⣾⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠾⠉⠁⠀⠀⣠⠴⠚⠉ ⠀⠀⠀⠀⠈⣙⡷⠟⠉⣠⣾⡿⠋⣠⡾⠿⠃⠽⣲⣿⣪⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⢀⣀⣠⡴⢶⣻⠽⠶⠶⢤⣤⣀⡞⠁⠀⠀⠀ ⠓⢦⣀⢀⡾⠉⠀⠀⡰⠃⢈⣽⣿⣿⣇⣀⣴⣾⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢉⣤⠞⠉⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⡹⣿ ⢀⣠⠽⣿⡁⠀⢀⡜⠁⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢻⠏⠀⠀⠀⠀⠀⢀⣠⠔⠂⠀⠀⣸⠞⠁ ⠁⠀⠰⡏⢷⡾⢁⣤⣰⣾⡿⠛⠛⠻⠿⣿⣿⣿⡿⠥⠤⣤⣾⠀⠈⢿⣿⣿⣿⣿⡿⣏⣰⢏⠏⠀⠀⠀⢀⣤⡶⠋⠀⠀⠀⠀⣼⠏⠀⠀ ⣀⣠⣴⣿⣷⣬⠻⢿⣿⡏⠀⢀⣠⡤⢀⣀⣁⣀⣀⣀⣠⠀⢨⡿⢀⡿⠋⣭⠟⠓⠉⢰⡏⢸⠀⠀⠀⠀⡞⠋⠥⠀⡀⠀⠀⠀⣿⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣾⣬⣿⣿⣿⣿⣿⠛⠉⠉⠉⠛⠛⢁⣈⣵⡞⠁⠀⠀⠀⢿⠁⠈⡆⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣤⣤ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⣠⢶⣿⣿⠿⠃⠀⠀⠀⣠⣴⣾⠟⠛⠛⠳⠦⢤⣄⣀⠸⡆⠀⠸⣄⡞⠀⠀⠀⠀⠀⠀⠀⠀⠘⠾⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣻⡵⠟⠉⠀⠀⠀⣠⠶⠋⣵⠋⠀⠀⠀⠀⠀⠀⠀⠀⣨⣿⡟⠀⣠⡿⣄⠀⡢⠂⢀⣀⣀⣀⣤⣤⣬⣿⣻⣿ ⣿⣿⣿⣿⣿⣿⡿⢛⣡⡾⠋⠀⠀⠀⢀⣴⠛⠁⢀⡼⠛⠛⠻⠷⢶⣦⣤⣀⡀⣴⣿⠋⠀⢾⡿⠊⢈⢾⣴⣿⣿⣒⡫⡟⠀⠀⠀⠀⠈⠉ ⡟⠛⠛⠛⠋⢉⡿⢫⠞⠁⠀⠀⠀⣠⠞⠁⠀⣰⠟⠀⠀⠀⠀⠀⠀⠀⠈⣉⣿⠿⠟⢂⣴⡟⢁⣔⣵⣿⣿⣿⡿⠀⢠⡇⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⢠⡟⢡⠏⠀⠀⠀⠀⣰⠏⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⣠⣴⠿⠋⠁⠀⠀⡸⠋⣠⣿⣿⣿⣿⣿⣿⡏⠀⢸⣥⣤⠴⡶⢴⠲⠲ ⣳⠤⣤⣀⣸⠀⡞⠀⠀⠀⠀⢀⡟⠀⠀⠀⡏⠀⠀⠀⠀⠀⣠⡾⠛⠁⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⢷⠛⣏⣿⡼⠤⠟⠚⠓⠛ ⡏⠙⠒⢶⢿⠀⡇⠀⠀⠀⠀⢸⡇⠀⠀⢸⠁⠀⠀⠀⢀⣼⠟⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⢳⣿⠜⠚⡏⠀⠀⠀⠀⠀⠀⠀ ⣷⣦⡀⢸⡜⡆⢳⡀⠀⠀⠀⠘⣷⡀⠀⢸⣆⠀⠀⢠⣻⠃⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⠇⣿⣿⠀⢀⣇⣤⣶⣶⣶⣶⣶⣾ ⣿⣿⣷⠈⣧⡹⣮⠣⡀⠀⠀⠀⠙⢷⣄⡀⠻⣆⠀⣿⠃⠀⠀⠀⣀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢠⡿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⠀⠈⢳⣌⣳⣌⡳⢤⣀⠀⠀⢙⣿⣶⣾⣷⣿⣶⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⡰⠋⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡟⠋⠁⠀⠀⠀⠈⠙⠛⠛⠛⠛⠛⢻⠛⢿⠻⣿⣿⣿⣿⣿⡿⡛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣁⣴⡾⠁⠀⠀⣊⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢸⣆⣨⡿⢿⡿⢿⣿⣿⡇⠙⢦⡰⠛⠋⠻⠿⠛⠛⠙⠿⣟⡀⠀⠀⣴⣿⣿⣿⣿⡟⠛⠻⢿⣿⣿⣿ ⣟⣶⢤⣄⣀⡀⢀⢀⣠⡴⠶⣶⠟⢠⣾⠿⡽⠋⠀⠀⠈⠙⢳⣶⣶⣯⣿⣶⣶⣶⣶⣶⣶⣶⣾⣿⣦⣨⣿⣿⣿⣿⣿⠁⠀⠀⠀⠈⢙⠻ ⡿⠉⠙⠓⠚⠿⠿⠻⠦⠤⠤⠟⢀⣾⣿⣿⠁⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣝⣿⣿⣿⣿⡏⠀⠀⠀⢀⢆⠔⢀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⢰⢝⣡⠔⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⢀⣠⣤⡶⣾⣻⣦⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣻⠁⠀⠀ ⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣷⡷⠺⣿⣿⣧⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣯⣾⠁⠀⠀⠀ ⣿⣷⣀⣀⣀⣤⣤⣤⣤⣴⣶⣶⠶⠛⢿⣿⣿⣻⡿⠿⠒⠒⠛⠾⠿⡾⢿⣟⠟⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣃⣨⣿⠃⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⢻⣿⣿⣿⣷⣦⣄⠈⠉⠐⢤⡀⠀⠉⠙⣺⡯⢯⣿⣭⣉⣉⣉⣏⣽⣾⣿⣿⣿⠁⠀⠀⠀⠀⠀ ⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡜⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠈⠀⠀⠀⠀⠀⠀⠘⠉⠋⠛⣿⣿⣿⣿⡿⣿⠇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠉⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠁⠀⠀⠀⠀⠀⠀⢀⡩⠿⠿⠟⣵⣃⣤⣤⣤⣤⠤⣤⣤ ⣶⣶⣶⣶⣦⣤⣤⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣀⣀⣀⣠⢚⡁⣀⣀⣀⣸⣿⠟⠋⠁⠀⠀⠀⠀⠀
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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣰⡏⠀⠀⢠⢛⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣜⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⠈⠙⠛⠿⣿⣿⣯⣅⡀⠀⣿⣿⣴⢏⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣟⣀⣀⣠⡏⢨⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⣻⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠻⣽⠁⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣠⠤⠤⣄⣀⣀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⠿⣿⣿⣭⣉⣻⣿⣿⣷⣤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠷⣶⣿⣭⣷⣾⣿⠏⣿⣿⢿⡽⢯⡿⣽⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣟⡿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡟⠁⠈⠉⢉⣣⣼⣿⣻⢎⣟⡷⣽⣚⢿⣿⣿⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡽⣞ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠏⠀⠀⣀⣴⣿⣿⣿⣏⣷⣫⣾⣵⣧⢿⣾⣼⣿⣷⡿⠋⠁⠀⠀⠀⠀⠀⠉⠉⠙⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣆⠀⠀⠀⠀⠀⢀⣠⠦⡢⣿⡟⠁⣠⣴⣾⣿⣿⣿⢿⣿⣯⠉⠁⠀⠀⠀⠀⠀⠈⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠈⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣀⠀⠀⠀⠉⠷⣄⠀⠀⠀⠀⠀⠀⣀⠜⣦⢻⣷⣶⣤⣂⣖⣲⣬⣷⠟⣉⣤⣿⣿⣿⣿⣿⣟⣯⣿⣟⣿⣷⡀⠀⠀⠀⠀⠀⠀⢰⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢦⣤⡒⠀⠈⠛⠶⣤⣤⣄⡳⣬⣻⣼⣻⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣻⣷⣿⣻⣽⡿⣯⡿⣷⡄⠀⠀⠀⠀⠀⠀⢿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠫⣟⣳⠶⣤⣤⣭⣭⣿⣷⣿⣾⣿⣿⣿⣿⣿⠉⠀⠀⠀⠀⢻⣿⠻⠷⡿⢿⠷⣿⣛⡿⠟⠱⣉⠘⣿⡄⡀⠀⠀⠀⠀⢸⡟⣿⣂⠀⠀⠀⠀⢀⣴⢳⠀⠀⠀⠀⡇⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠲⣶⣿⣿⣿⣿⣿⣿⢿⣻⣿⣧⠀⠀⠀⠀⠀⢯⡟⠳⠶⣤⡆⠠⠤⠀⠌⡑⢠⢃⠩⣿⠇⠀⠀⠀⠀⠀⠙⣬⢿⣶⣀⣤⡶⠛⣡⠏⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣯⣷⣿⣿⡿⣿⣿⣷⡀⠀⠀⢠⡾⢋⡑⢣⠐⡡⢃⠀⢤⣄⣀⣀⣀⣀⣿⠠⠀⠀⠀⠀⠀⠀⠈⢻⣿⣏⣁⣰⡚⠁⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣽⣾⣿⣿⣻⣿⣿⣆⢀⡟⢠⠡⠜⡠⣍⠰⢀⣶⠂⠀⠀⠈⠉⠁⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣯⢙⠉⢷⡀⠀⠀⣀⣀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣯⠿⠋⠛⠛⠛⠉⠈⠻⣧⠠⡉⢆⠡⢻⡆⠌⡟⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣼⠀⠘⣧⠖⣪⡷⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡟⠻ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⡱⠨⢌⡡⢻⣼⠛⢦⡀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣀⣤⢿⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⠡⠒⡄⢛⢿⣄⠀⠈⠓⠦⣀⠀⠀⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⣿⣓⠁⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⠀ 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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠈⠙⣦⡀⠀⠀⢀⣱⣼⠿⠷⢧⣄⠀⠀⣧⠒⡤⠙⢿⣿⡀⣧⣀⠴⠊⠁⠀⠀⠀⠀⠈⢻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⡐⢀⠂⢸⡯ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠨⢷⣴⠞⠋⠁⠀⠀⣠⣼⣟⣀⠀⢸⠆⠇⠜⡀⢿⡇⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦⠀⠀⠀⠀⠀⠀⠀⠀⡃⢀⠂⠌⢸⡯ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⢰⣏⢈⡦⠀⠀⠀⠀⠀⠀⠈⠉⢟⣾⣗⠨⢑⡈⢼⣷⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄⠀⠀⠀⠀⠀⠀⠀⡅⠂⡈⠐⢸⡯ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢹⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣧⠂⡌⡘⣿⡀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣇⠀⠀⠀⠀⠀⠀⠀⠆⡐⠠⢁⢸⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⡀⢹⣿⣧⡐⣁⢻⡇⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⡃⢀⠂⠄⢸⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠸⡆⠠⠀⠀⠀⠀⠀⠀⠀⠀⢹⣦⡈⢿⡿⣧⠄⢺⣷⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⡅⠠⢈⠐⢸⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⣿⡀⠈⠙⢿⣤⣿⣿⠀⢀⠀⢰⠀⢀⢰⡀⠀⠐⢻⡟⠀⠀⠀⠀⠀⠀⠀⡀⠂⠄⡈⢸⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⣿⣻⠿⣦⣄⣠⣽⢿⡿⠀⡞⠀⣿⠀⠈⠘⢹⣦⠀⠘⢿⡀⠀⠀⠀⠀⠀⢀⠄⡁⢂⠐⢸⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠘⣇⢠⠀⠀⣶⠀⠀⢸⡀⠀⣿⣿⠡⡐⢠⠂⢌⢺⣧⠘⣿⡀⠙⢿⡄⠀⢸⡏⢧⠀⠘⣧⠀⠀⠀⠀⠀⠐⠠⠐⠠⢈⢸⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⢀⡇⢸⣤⡀⢿⣤⠤⢸⣇⠀⠀⢿⡐⢨⠐⡌⠢⡘⣿⢧⠘⣧⠀⢀⣇⠀⠀⣧⠊⣇⠀⢸⡆⠀⠀⠀⠀⠘⢀⠁⠂⠄⢺⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠹⣶⢿⣇⠘⢻⣄⠀⢻⡄⠀⠸⣇⠢⡁⠆⡑⢄⢻⡟⡇⠘⡆⠀⢹⠀⠀⢻⡀⢻⠀⠀⣿⠀⠀⠀⠀⠘⡀⠌⡐⠈⣼⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠘⣯⢿⡄⠀⢿⡄⠀⢻⡄⠀⢿⡆⢡⠘⢄⠢⢼⣇⠹⡄⣿⠀⠸⡇⠀⠘⣇⢸⡆⢀⡿⠀⠀⠀⠀⡆⠐⠠⢀⠁⣾⠅ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠙⣮⣿⣄⠘⣷⠀⠘⣇⠀⢸⣷⢂⠩⣀⠒⡄⣿⡀⣳⣸⡄⠀⣷⠀⠀⣿⠈⠷⠞⠁⠀⠀⠀⠀⡇⢈⠐⡀⠂⣽⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠘⣯⡙⢦⣽⣇⠀⢻⠀⢸⣿⢀⠒⡄⢡⠂⣹⡇⠉⣿⡇⠀⢻⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢸⠁⠄⠂⠄⡁⣿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠈⢻⣄⣿⣿⡀⠸⣄⣼⠇⢻⠐⡌⢂⡜⢘⣷⠀⠹⣇⣀⣾⣀⡼⡿⠀⠀⠀⠀⠀⠀⠀⢸⠠⢈⠐⠠⠀⣿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠙⠉⠘⢧⣠⡞⠁⠀⢸⡆⡘⢠⠐⡌⢿⡄⠀⠈⠻⠟⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⣼⠀⠂⠌⠠⠁⣿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢇⣀⣀⣀⣀⣀⣀⣀⣄⢕⢀⣀⣀⣰⣷⣬⣴⣬⣴⣸⢷⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣧⣤⣥⣌⣤⣁⡾⠀
⣿⣶⢻⣿⡿⠂⣼⣿⣿⣭⣍⣽⣛⣟⣓⡙⠻⣟⢫⢖⣩⠭⢍⡓⠦⣄⠀⠀⠀⠀ ⣾⣿⡿⡏⣱⣿⣿⣿⣿⣿⣷⣽⣻⣧⣬⣿⣛⢯⣻⣫⡾⡴⣾⡎⢳⣌⠻⣤⡀⢀ ⣿⣿⡿⣾⣿⣻⣫⣿⣿⣿⣵⣟⣿⣿⠿⠛⠉⠉⠿⡞⣽⣾⠏⢧⣠⡏⠳⡝⡷⢿ ⣿⡿⢹⣷⣿⡿⣯⡿⣿⢯⣾⣟⡟⠁⠀⠀⠀⠀⢰⣳⡟⣻⢟⣹⣿⡧⢰⡿⣼⡜ ⣿⣣⣷⡷⡿⣿⣽⣿⣿⡟⣽⣛⣿⣦⡀⠀⠀⠀⣿⣿⣯⣯⣾⢹⣿⣽⣼⣹⣯⢧ ⣯⣿⣿⣿⣷⢷⣿⣿⡿⣰⠿⠁⠀⡏⠃⠀⠀⢸⣿⣿⣿⣿⡇⣼⣿⡿⣿⢿⣿⣼ ⢸⣯⣻⣿⡿⣿⣯⣿⣫⣘⠀⠀⠀⢸⠀⠀⠀⢸⢋⣿⣿⡿⡏⣷⣿⣯⣾⣿⡿⣿ ⣿⣧⢿⣻⣏⢹⣿⣿⢯⠙⠛⡶⣄⠀⠆⠀⠀⢸⢿⢸⡟⣿⡸⡿⣿⣯⣿⡟⣟⡟ ⠟⠸⣿⡇⡯⣿⣿⣼⢱⠀⠀⡇⠿⠓⠀⠀⠀⠘⡽⣼⠿⣧⣿⡿⣟⣿⡟⣿⣿⣇ ⣼⡆⢻⣿⣷⣿⣧⣻⣮⠉⡉⣉⠉⠁⠀⠀⠀⠀⢫⣿⣿⣫⣽⣿⣿⣿⢾⡿⡧⢾ ⣿⣿⡼⠸⣿⡏⣿⡏⡭⡀⠝⠋⠀⠀⠀⢠⡂⠀⠀⠻⡙⣿⡟⣿⢷⡇⣾⣷⣷⣧ ⣿⣿⡿⡶⡝⠿⠃⡄⣿⠈⣄⠀⠀⠠⣄⣀⣀⡀⠤⡄⠘⠿⡇⠫⣤⢭⣏⣹⣽⠷ ⣿⣵⣿⡿⡟⣷⡞⣧⡇⠀⠈⠤⡀⠀⡇⠀⠇⠀⠀⡨⠀⠀⡨⠞⠁⠀⠀⠀⠀⠀ ⣿⣿⡅⣿⢿⡯⣿⢼⣷⡂⣀⠀⠈⡏⠛⠢⠤⠴⠥⠒⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠻⡟⠈⠻⣯⣿⣿⣉⠉⠉⠁⡸⠀⣟⢦⡴⣛⠄⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
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