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⡇⠀⣼⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣩⣽⣿⠿⠛⠛⠉⠀⠀⠀⠀⠀⢀⣾⣿⣿⡁⠀⠀⠀⢀⣠⣴⣶⣿⠿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠰⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⢰⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡿⠛⠛⠛⠛⠿⢾⣿⣿⣋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠟⠻⠷⡾⣿⢿⣷⣶⣶⣦⣄⡶⠛⠁⠀⠀⠀⠀⠀⠀⠀⠈⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣇⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡆⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢠⣾⣿⣇⣠⣤⣼⣇⠉⠀⣿⢻⣍⡉⠙⠛⠳⠿⢶⣦⡀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⠠⣤⣼⠿⣗⣶⣄⠀⠀⠀⠀⠀⢀⣤⣀⢀⠀⣠⣤⣼⣿⡏⠹⣿⣿⣄⠻⡄⠀⢻⣷⣿⣧⣀⣀⣽⣗⢠⣿⠁⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⠀⠀⠀⠀⠀⢀⣤⡶⠆⠀⠀⠀⠉⠁⠀⠀⠀⢠⡾⠛⠩⠙⢷⣄⠀⣀⣀⣿⣯⣽⣿⡟⢋⣄⡀⠈⠀⡀⢚⣛⣿⣿⣧⣤⣸⣿⣿⡿⠟⠛⠉⠉⢻⡇⠀⠀⠀⣠⣄⣴⣶⠷⠾⠿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣧⠀⠀⠀⢠⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⢾⣄⡀⠻⣦⡟⣷⣿⣿⣿⣏⠛⢷⣶⣦⣭⣽⣽⣿⣿⣏⠉⠁⠁⠀⠈⠉⠛⠛⠻⠀⢀⢀⣠⣾⡿⡷⠾⠟⠉⢻⡆⠀⠀⢀⣴⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣆⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣷⣹⣿⣄⠘⢿⡍⣿⡿⠋⠙⠷⣦⣈⡙⢻⡶⠆⠀⠉⠻⣿⣦⣤⣤⣀⡀⠀⠀⠀⠀⠸⣿⠿⠿⢐⠚⠳⣶⣀⣀⣠⣴⠾⠟⠋⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⠈⣧⢰⡄⡀⢀⣶⡿⣿⣸⣿⣶⣦⣀⢸⡏⡻⣿⣷⡈⠻⣿⣥⣄⡀⢰⣾⡿⢿⣿⣷⣤⣦⡈⢉⡉⡙⢧⣉⣭⡝⠻⠶⣦⣀⢀⣿⣟⣛⣾⣷⣶⣿⢻⣿⣿⣷⣦⣄⠀⠀⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣿⣶⣿⡜⠏⢷⢸⣟⡗⠺⣷⣿⠈⢿⣿⣿⣇⠙⠈⢻⣿⣄⠈⢷⡝⠻⠾⢿⣿⣆⣀⠀⠈⠉⠉⢉⡻⣿⡛⠛⠁⠻⠦⠄⠉⣉⣿⣉⣉⡉⠉⢛⡉⠉⠉⠈⠉⠉⠙⢻⣶⣄⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⠀⠀⠀⠀⠀⣰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⠿⠟⠛⠁⣧⠙⠀⠈⣿⠃⢾⣻⣿⠀⠸⣿⣿⡙⣷⣶⣿⡝⢻⣷⣈⡁⠀⠀⠀⠈⠛⠟⣧⣿⣶⣤⣬⣉⡈⠁⠀⠀⠀⢠⠀⢷⣦⡈⠉⠙⠛⠻⠎⠙⠿⢾⣿⣿⣶⣶⣾⣿⠾⠛⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⡏⢿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⠛⠻⣷⣦⡄⠀⠀⠀⠀⠀⠀⢸⣿⡀⠀⠀⢀⣾⣿⠟⠉⠉⠛⢿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣘⡧⠀⠸⣇⠘⠟⢻⡆⠀⠸⣿⣷⠚⣿⣿⡷⢶⣿⠋⣿⡘⠻⣾⣿⣦⣤⣄⣈⠃⢠⠉⠙⠛⠻⠶⣦⣤⣤⣶⣤⣬⣭⣀⣀⠀⠀⠄⠘⠛⢦⡄⠀⠀⠘⠿⠶⠦⠤⠴⠾⠿⢶⣶⣄⠀⠀⠀⠀⠀ ⡇⠘⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⣰⣿⡟⠁⠀⠀⠀⠀⠀⠈⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⣧⠀⠀⢿⣷⡀⠈⢿⡄⠀⣻⣿⡗⠈⠙⢷⣄⠿⣧⠘⣧⠀⢻⣿⠛⠻⣿⣿⡟⣾⣿⣶⣤⣀⠘⡶⣦⠈⢉⡛⠟⣻⡿⣿⡿⠷⣶⣶⣤⣤⣥⣤⣠⣴⣦⠤⢤⣶⣶⣦⣇⣠⣼⡟⠀⠀⠀⠀⠀ ⡇⠀⠙⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡄⠀⠈⣿⣱⣿⣾⣿⣦⣍⣹⣷⣜⢷⣄⠻⣷⠜⣧⢻⣖⠘⣿⣾⡇⠘⢿⣧⣙⠃⢶⣍⡙⠻⢿⣶⣤⡾⠁⣰⠟⢁⣿⠿⢶⡶⠿⠿⡭⠟⠋⠙⠊⠙⠓⠲⠶⠶⠶⠻⣿⣧⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠈⠻⣿⣦⣀⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣟⠷⣾⣿⣿⣿⣿⣿⣦⣀⣉⠛⠿⣿⣦⡻⢆⣽⡄⠹⣎⠻⣇⢹⣿⣿⣾⣾⣿⣿⣿⣦⣌⠛⠶⢄⣼⠋⠀⣴⠏⣰⣿⣿⣿⡿⠛⢿⣿⣶⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣆⠀⠀⠀⠀⠀ ⡇⠀⠀⣀⣀⣬⣿⣿⡿⠃⠀⠸⢿⣶⣦⣤⣤⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣾⣇⣠⣿⣀⢹⣧⠙⢿⣮⠻⣿⣿⣯⣿⣦⣈⠙⠿⣾⡟⠃⠀⣿⡀⢿⣞⣿⣿⣿⣿⣦⡘⢿⣿⣿⣿⣦⡾⠉⠀⠀⢀⣴⣿⢿⣿⣿⣷⡀⠲⠆⠉⠙⠿⣿⣿⣿⣿⣷⠶⠶⣦⣴⠾⠋⠹⣆⠀⠀⠀⠀ ⣧⣾⣿⠿⠛⠋⠉⠀⠀⠀⠀⠀⢸⣿⠀⠀⠉⠉⠙⠛⢻⣿⣿⣿⣿⣾⣷⣶⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⣤⣤⣤⣤⣤⣤⣤⣴⣶⣶⣿⡿⠿⣿⠟⢀⣻⣿⡿⢻⡇⢀⠙⢷⣤⡘⠻⢿⣿⣿⣿⣿⣿⣷⡀⠀⠶⠀⠀⣿⣧⢶⡉⢹⣿⣿⣿⣿⣿⣾⡻⣿⡿⠃⢀⡄⠀⣠⣿⣿⠁⠀⠘⠻⣿⣿⣷⣦⡀⠀⠀⠀⠈⠙⠻⢿⣷⣤⣿⡏⠀⠀⠀⢹⣆⠀⠀⠀ ⡇⠻⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡆⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⣿⣶⣿⡿⠋⠀⠀⣿⢸⡶⢶⣬⣿⣦⣄⡀⠉⣽⣿⠛⢿⣿⣦⣄⠀⣠⡟⢿⡈⢃⠀⢻⡿⣿⣿⣞⢿⣷⡿⠋⠀⠈⢁⣴⡿⢏⠻⣷⣤⢀⠀⣹⣿⣮⠹⠻⠿⣶⣤⣄⡀⠀⠀⠈⠙⠛⢿⣦⣤⣀⠀⢻⣆⠀⠀ ⡇⠀⠈⠙⠿⢷⣶⣤⣀⣀⣀⣀⠀⢿⣿⣆⡀⠀⠀⠀⠀⠀⠈⠛⠻⠿⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⢀⣼⣿⠿⠉⠀⠀⠀⠀⢸⡿⣷⠀⠀⠸⣇⠩⣯⠉⠻⣿⣦⡙⠟⣿⢿⣿⣿⣇⣸⡇⠹⠂⢸⣇⠘⢿⣿⣿⠏⠀⠀⠀⣰⣿⣿⠿⢿⣦⣿⠃⠈⠈⠛⠻⢿⣧⣠⣄⠀⠿⡝⣻⣿⣶⣦⣀⡀⠀⠈⠙⠻⠿⢷⣿⣦⠀ ⡇⠀⠀⠀⠀⠀⠀⠈⠉⠉⢹⣿⡆⣶⣏⠙⢻⡷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⢀⣴⣿⠟⠁⠀⠀⠀⠀⠀⠀⠘⣷⢹⣷⣄⣀⣙⣦⠹⣇⢀⡘⢿⣿⣦⡉⠛⣭⡛⣿⣿⡇⠀⠀⠀⢻⣦⣼⡿⠁⠀⠀⠀⣼⣿⠻⣿⣀⣠⣬⣿⣿⣷⣄⡀⠀⠀⠀⢹⣿⣶⣴⡾⠛⠛⠛⠿⢿⣿⣷⣦⣄⣀⠀⢀⣴⣿⡆ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⠙⣿⣷⣿⠟⢿⣿⣷⡀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣾⡛⠁⢰⣤⠘⣧⡘⠿⡧⠈⢻⣿⣿⣷⣌⠙⠻⡟⣷⠀⠀⢸⣿⣿⡟⠀⢀⡀⢀⣾⣟⣿⣖⠙⢿⣿⣿⣿⢀⣤⠈⠿⢷⣦⡶⢟⣛⣛⣛⣛⣃⣀⣀⣀⠀⣈⣙⣻⣿⣿⡿⠛⠛⠛⡇ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡄⠙⠻⣷⣤⣈⠉⠉⠁⠀⠀⠀⢸⣿⣇⠀⠀⠀⢻⣿⡿⠿⠷⠀⠀⠘⢿⣷⠀⠀⠀⠀⠀⠸⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣧⣤⣾⣿⣶⣾⣧⡈⠀⠀⠁⠻⣿⣽⣿⣿⠷⣦⣿⣀⣴⣿⣿⡟⠛⢠⡟⣡⣿⣿⣿⣧⡀⠓⣤⣿⣿⣿⣿⡿⠟⠛⠛⠛⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⣀⣴⡇ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⡀⣀⣴⣿⢿⣿⣶⣦⣤⣀⣀⠀⠙⠻⠿⠶⠾⠿⠟⠛⠻⠷⢶⣤⣴⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠏⠉⣛⠃⠀⠈⢿⣄⠀⠀⠆⠈⢻⣷⣿⣿⣶⣿⣿⣿⣿⠏⠀⠀⠟⣼⣯⣼⣿⣿⣿⣷⣀⣿⣿⣿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣴⡶⠾⠟⠛⠁⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⠋⢡⣾⡿⠃⠈⠉⠙⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣾⠛⠙⢷⡄⢀⠀⠙⣧⡀⠀⠀⠀⢻⣆⣈⣹⣿⡇⠀⠋⠀⠀⠀⣼⠟⠀⣀⣼⠿⠛⠋⠹⠉⠉⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣤⣴⡶⠶⠶⠟⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣶⣾⣿⠿⠶⣶⣼⣿⠈⠷⠀⣍⠻⣦⡀⠀⠀⣿⣬⣿⣿⠏⢀⡀⠀⠒⣼⣯⣴⣿⠟⠁⠀⠀⠀⣀⣀⣠⣤⣤⣶⠶⠶⠿⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠃⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣴⣶⡿⠿⠟⠛⠛⠉⠉⠀⠀⠀⠀⠈⠙⢿⣄⠀⠘⠝⠃⠈⠛⣷⣶⣿⠟⠋⠁⠀⠈⠻⣶⣾⣟⣫⣭⣥⠴⠶⠶⠟⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠋⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣿⠙⠁⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣼⣿⠿⠓⢀⣀⣈⣭⣤⣤⣶⡶⠿⠟⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⠟⠁⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡇⠀⠀⢸⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠋⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⠟⠁⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⣾⡿⠹⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⢰⣿⠛⠿⠷⠀⠀⠀⠀⠀⢀⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃⣠⣾⣆⣼⡿⠁⠀⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠸⣿⣄⠀⠀⠀⠀⢀⣠⣴⣾⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣾⠿⣿⡿⠟⠁⠀⠀⠈⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠙⢻⣷⠀⠀⠀⠛⢿⣿⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⣤⣤⣤⣶⡾⣿⣧⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠹⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⠀⠀⠀⠀⠀⠀⢀⣴⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡏⠀⠀⠀⠀⠀⢀⣴⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⣀⣀⣀⣀⣀⣠⣤⡄⠀⠀⠀⠀⠀⠀⠀⣸⣿⣶⣤⣤⣤⣶⣾⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ 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⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀