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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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⣿⣿⣿⣿⠏⠌⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⠀⠀⠸⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⠃⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⡿⠃⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⠃⠀⠀⣾⣿⣿⣿⣿⣿⣦⠀⠈⠻⣿⣿⣿⣿ ⣿⠀⠀⠀⣿⣿⣿⠟⠉⠉⠉⢃⣤⠀⠈⢿⣿⣿ ⣿⠀⠀⠀⢸⣿⡟⠀⠀⠀⠀⢹⣿⣧⠀⠀⠙⣿ ⣿⡆⠀⠀⠈⠻⡅⠀⠀⠀⠀⣸⣿⠿⠇⠀⠀⢸ ⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠔⠛⠁⠀⠀⠀⣠⣿ ⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿ ⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿ ⣿⣿⡇⠀We Go Jim ⣠⣿⣿⣿⣿⣿⣿ ⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿ ⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿ ⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿
⠀ (\ __ /) (UwU) _ノ ヽ ノ\_ / `/ ⌒Y⌒ Y  \ (  (三ヽ人  /   | | ノ⌒\  ̄ ̄ヽ  ノ ヽ___>、__/ |( 王 ノ〈 /ミ`ー―彡\ |╰ ╯ | | /\ | | / \ | | / \ |
⣿⣿⣿⣿⠏⠌⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⠀⠀⠸⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⠃⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⡿⠃⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⠃⠀⠀⣾⣿⣿⣿⣿⣿⣦⠀⠈⠻⣿⣿⣿⣿ ⣿⠀⠀⠀⣿⣿⣿⠟⠉⠉⠉⢃⣤⠀⠈⢿⣿⣿ ⣿⠀⠀⠀⢸⣿⡟⠀⠀⠀⠀⢹⣿⣧⠀⠀⠙⣿ ⣿⡆⠀⠀⠈⠻⡅⠀⠀⠀⠀⣸⣿⠿⠇⠀⠀⢸ ⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠔⠛⠁⠀⠀⠀⣠⣿ ⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿ ⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿ ⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿ ⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿ ⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿ ⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿
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⣿⣿⣿⣿⠏⠌⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⠀⠀⠸⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⠃⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⡿⠃⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⠃⠀⠀⣾⣿⣿⣿⣿⣿⣦⠀⠈⠻⣿⣿⣿⣿ ⣿⠀⠀⠀⣿⣿⣿⠟⠉⠉⠉⢃⣤⠀⠈⢿⣿⣿ ⣿⠀⠀⠀⢸⣿⡟⠀⠀⠀⠀⢹⣿⣧⠀⠀⠙⣿ ⣿⡆⠀⠀⠈⠻⡅⠀⠀⠀⠀⣸⣿⠿⠇⠀⠀⢸ ⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠔⠛⠁⠀⠀⠀⣠⣿ ⣿⣿⠀⠀⡆⠀⡀⠀⡆⡤⠤⠀⠀⠀⢀⣴⣿⣿ ⣿⣿⠃⠀⢳⠞⢣⡼⠀⡗⠒⠀⣠⣾⣿⣿⣿⣿ ⣿⣿⡇⠀⠀⠀⠀⠁⠀⠉⠉⣠⣿⣿⣿⣿⣿⣿ ⣿⣿⡇⠀⡴⠒⠆⠀⡖⢲⢰⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⠀⣇⣐⡖⠀⣇⣸⢸⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⠁⠀⡆⢰⠀⡴⣠⢷⠀⢹⣿⣿⣿⣿⣿⣿ ⣿⠟⢠⠀⡇⢸⢠⠃⠁⠘⡆⢠⣿⣿⣿⣿⣿⣿ ⡟⠁⠈⠉⠁⠈⠈⠀⠀⠀⠁⢸⣿⣿⣿⣿⣿⣿
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