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