⠀⢿⣟⣻⣿⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣴⣾⣿⡿⢛⡻⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣧⠈⢱⠀⣰⣿⠛⠛⢿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⡧⠈⢸⠀⣿⣿⢿⣿⣿⣿⣷⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢿⣛⣹⡏⠀⢸⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⢀⣠⣤⣤⣶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣷⡄⢾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠁⣍⢿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣟⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⠿⢿⣿⣿⣿⣶⡾⢿⠿⠂⠻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣹⣿⣿⣿⣿⡉⣧⣢⡆⢀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠏⠉⠉⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣽⡿⣿⣷⡾⣟⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠽⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⣤⣦⣄⢀⣻⣿⣿⣿⡿⣩⣶⣟⢿⣿⣛⣀⣿⡿⣅⢰⣤⣄⡀⠀⠀⠀⠀ ⣲⣿⣿⡿⠉⢻⣿⣿⣿⣿⣦⣀⡙⠟⢛⣵⠿⣿⠿⠟⡿⣯⣾⣿⣵⣆⣄⡾⢽⠛⠛⢿⣿⠻⢿⡃⢀⠀⠀ ⠉⡿⣦⣄⡀⠀⠻⣿⣿⣿⣿⣯⣿⣿⡿⢃⣀⡤⢔⣻⣷⣿⡿⠋⣿⣿⣿⣯⣾⢤⢀⣸⢿⡇⠠⢀⡩⡂⠀ ⡑⠣⣹⣿⣿⣦⡀⢿⣿⢿⣿⠿⢿⣿⡾⢾⣿⣤⣽⡋⢑⣯⡀⢀⣿⢬⣧⠙⣻⣍⣁⡈⢻⣷⣴⣿⣿⠞⠀ ⠀⢠⡟⠈⣽⡟⣿⢳⡇⣷⣇⡬⠋⠇⠀⢘⢏⣽⣿⣿⡿⠿⢶⡾⢶⡾⠿⢿⡿⢿⣻⣿⣏⡏⡸⠻⣿⣇⠄ ⠀⢞⡀⡼⣱⠳⣥⢸⢿⣿⣿⡇⠀⠀⣀⢶⣿⣿⣿⣿⠀⠀⠀⠀⠀⣇⠀⣸⠁⠀⠙⣿⡾⠀⠀⠀⠈⢻⣿ ⠀⠀⡽⠁⠁⠂⢠⣟⣙⣿⣿⣿⣄⣠⣷⣿⣟⣿⢿⡿⠓⠀⠀⠀⠀⢻⠉⡏⠉⠉⠉⢹⢿⡀⠀⠀⢀⣼⣷ ⠀⠰⠁⠀⣠⢀⣾⣙⢿⢻⣿⣿⣿⣿⣿⣵⡈⢻⢸⡇⢣⠀⠀⠀⠀⠈⢟⠀⠀⠀⠀⠈⠈⣷⣦⣴⣿⣿⣿ ⠀⠀⠀⠰⠋⡟⠨⣹⡟⠀⠉⠙⣿⣿⣿⣍⠀⠸⣿⣇⣜⣄⣀⣀⣀⣾⣷⣷⠀⠀⠤⡄⢀⡏⠻⢿⣿⣿⣿ ⠀⠀⣠⢀⡼⢿⡖⣽⠁⠀⠀⠀⢳⣾⣿⣿⣆⡄⡇⠹⠘⣆⠀⠀⠀⠙⠿⠋⠀⠀⠔⠡⠊⢰⠀⠈⠉⠛⠋ ⠀⢰⠋⣹⢟⣂⠚⡇⠀⠀⠀⠀⢺⣿⣿⣿⣿⣲⢅⡀⠀⠪⠳⠀⠀⠀⠀⠀⠀⠀⡾⢃⡠⠔⡆⠀⠀⠀⠀ ⠠⣾⣽⠉⣯⣵⣿⠁⠀⠀⠀⠈⢀⢧⢿⣿⣿⢿⡇⠢⠍⠋⠉⠒⠒⠒⠒⠒⠋⠈⠀⠀⠀⠀⠇⠀⠀⠀⠀ ⣷⠿⣻⣷⣾⣽⣃⠀⠀⣀⣀⣀⣴⢾⣿⢛⣿⣞⠂⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡨⡄⠀⠀⠀ ⣿⣦⣤⡀⢩⡏⠿⣬⢿⣿⣿⡿⠬⠃⣆⠗⠙⣷⣷⣦⡄⣤⢀⣀⠀⠀⠀⣀⣀⣀⣤⣤⣔⡿⣪⡆⠀⠀⠀ ⣿⣿⡿⠈⠙⠁⠀⢈⣷⣿⣿⡇⠁⠀⠀⠀⠀⣿⣿⣿⣿⣮⢿⢿⣽⣞⣷⣿⣽⢷⣿⣿⣿⣽⣷⡇⠀⠀⠀ ⣿⣿⣧⠀⠀⠀⠀⢠⣾⣿⣿⣦⡄⠀⠀⠀⠀⣿⣿⢵⣿⡽⣿⣧⣻⣻⣞⣷⣿⣾⣱⣿⣾⣿⣷⠇⠀⠀⠀ ⣿⣿⣟⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣦⡀⠠⠀⣿⣿⢿⡇⠉⣻⣾⣿⣷⣻⣿⣿⣿⣿⣫⣿⣿⡏⠀⠀⠀⠀ ⣿⣿⣿⣞⣦⠀⣆⣹⣿⡇⠹⣿⣿⣿⣯⡂⢰⣿⣿⡖⠧⢄⠀⢻⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⠁⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣤⣼⣿⣿⣯⣶⣿⣿⣿⣿⣾⢸⣿⣿⣷⠀⠀⢴⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⡀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⡟⣿⣿⠃⣢⣾⣿⣿⣿⢿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⡀⠀⠄⢀⠀⠀⠠⡀⣄⠢⡅⠴⢠⠀⡰⠀⡀⠀⡄⡀⢄⠀⡄⡀⠀⠀⠀⠀⠤⢦⠤⣤⢤⣤⣤⣤⣴⣤⣦⣶⣶⣶⣶⣶⣷⣾⣾⣷⣶⣶⣶⣶⣶⣴⣤⣦⣤⣤⣄⢦⡤⢦⢤⠤⡀⠀⠀⠀⠀⣂⠐⢀⠠⡐⡀⠀⠀⢄⢢⡄⢤⡐⡠⠄⠠⣀⢀⠐⡠⢆⠠⠀⠀⠄⠀⠄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠒⠒⠐⡆⢰⢐⠂⣆⠒⠄⠠⠙⠦⡓⠾⠴⠓⣪⢔⠕⠀⢒⠰⡐⠆⠒⣐⡤⠗⣂⠄⢘⣹⣮⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣧⣏⡡⠀⠀⠒⠢⢴⡘⠂⠦⠑⠄⠃⠘⢮⠲⢌⠓⠒⠓⣪⠖⡵⠀⠀⢰⡠⢆⢸⠈⠍⠉⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⠀⠀⠀⠀⠳⡌⢸⠐⠠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣠⠖⠋⠉⣀⣬⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⣠⡀⠉⠙⠦⣅⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠼⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠋⢀⣠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⡀⠙⠲⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⡄⠀⠙⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⢠⣴⡿⠛⠩⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠈⠓⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⢀⣠⡾⠟⠉⠀⠄⢉⠳⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣦⡀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ 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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡞⠀⢰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣇⠊⢧⠀⠀⠀⠄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⠀⣼⠁⠰⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⣤⣤⣀⣤⣀⣤⣀⣀⣀⣀⣠⣀⣀⣘⣯⣆⣜⣦⣠⣀⣀⣄⣀⣀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⢠⠇⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⠿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠀⠀⠀⠀⠀⢠⣿⣿⢿⣻⣿⢿⡿⣟⣿⣯⣿⢿⣟⣿⡿⣿⣟⣿⣿⢿⣿⣿⢿⣿⣿⣿⣻⢿⣻⣟⡿⣿⣻⣟⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⠀⢀⡿⠀⣀⠐⠠⠤⢄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⡿⣟⣯⠷⠖⢎⢋⡙⠍⡙⢃⠒⠦⢭⣝⡻⢿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⣿⣿⣽⣻⣟⡾⣿⣽⣻⢷⣯⣟⣯⣿⣳⢿⣻⣾⣻⢾⣻⢷⣯⡿⣞⣿⡾⣟⣯⡿⣞⣿⣽⣻⢯⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣸⠇⠀⢀⡈⡙⠒⠶⠤⣍⣑⠒⠤⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⢟⡽⢊⡱⠀⠌⠈⠀⠀⠀⠄⠀⠄⠈⠀⠂⠄⡙⠢⢭⡻⢿⣿⣿⣧⡀⠀⠀⠀⠀⠀⣿⡷⣯⣷⣟⣿⣳⣯⣟⡿⣾⣽⣳⣯⣟⣿⣳⣯⣟⡿⣯⣿⢾⣽⣟⡷⣟⣯⡿⣽⣟⡷⣯⣟⣯⣾ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢠⡿⡀⠀⠀⠈⠉⠁⠉⠀⠀⠢⢍⣙⣒⠢⠬⢍⣒⡒⠤⢄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⢟⡵⣉⡴⠋⢁⡴⠂⠁⠀⣈⠠⠀⠌⠀⠁⠀⠁⠀⢀⠁⠂⢌⡫⡻⣿⣿⣿⣄⠀⠀⠀⠀⣿⡿⣽⡾⣽⡾⣯⣷⣻⣟⣷⢯⣟⣾⣽⡾⣯⣷⣻⣽⡷⣯⣿⣳⣯⢿⣻⣽⣻⣽⡾⣿⣽⣻⢮⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⡗⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠭⣉⣒⠢⠭⣑⡒⠦⢄⡀⠀⠀⠀⠀⢠⣿⣿⣿⢯⢫⢶⠋⢀⡴⡋⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠠⠀⠈⢎⠢⡀⠈⠵⡑⡞⢿⣿⣿⡆⠀⠀⠀⣿⡿⣽⣻⣽⣟⣷⢯⣷⢿⣾⣻⢯⣟⣾⣽⢷⣻⣽⣾⣻⣽⢾⣯⣟⡿⣽⣳⣿⣳⢿⣳⣯⣟⣟⣾ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⣼⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠉⠒⠦⣤⣄⣀⠀⢠⣿⣿⣿⢣⢣⣳⠃⣠⢋⠎⠀⠀⠀⠀⠀⢀⠸⣛⡎⠀⠀⠴⠋⠀⠀⠑⡝⣄⠀⠹⡌⡞⣿⣿⣿⡄⠀⠀⣿⡿⣽⣻⡾⣽⡾⣿⣽⣻⣞⣯⡿⣯⡷⣟⡿⣯⣷⢯⣷⣟⡿⣾⣽⣻⢯⣟⣾⡽⣟⣯⡷⣿⣝⣾ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣻⣿⣿⣏⡇⣆⢇⢰⢃⠆⠀⠀⢠⠊⠁⠀⠀⠧⠍⠸⠀⠉⠀⠐⢄⠀⠀⠘⡸⡄⠈⡷⠸⡸⣿⣿⣧⠂⠀⣿⡿⣯⣷⢿⣯⣟⣷⣯⡷⣿⣽⣻⢷⣟⡿⣽⡷⣯⣿⣳⣯⢿⡷⣯⣟⡿⣽⣯⣟⡿⣽⣻⢷⡯⣾ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⢸⢰⡙⡌⡞⡜⠀⠀⠀⢃⡀⠀⠀⠠⠁⠀⠀⠂⠀⠀⢀⡘⠂⠀⠀⢧⢻⢤⢳⡇⡇⣿⣿⣿⠀⠀⣿⣟⣷⣯⢿⡾⣽⣾⣳⡿⣽⡾⣯⣿⢾⣟⣯⢿⡷⣯⣷⣟⣯⣿⣽⢾⣟⡿⣾⣽⣻⢯⣟⣯⣷⣻ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⣇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⢸⠀⡇⡇⡇⡇⠀⠀⠰⠀⠀⠈⠰⡀⠀⠀⠀⢀⡶⠉⠀⠀⠀⢀⠁⠸⢸⢸⢸⡇⡇⢿⣿⣿⠀⠀⣿⡿⣾⣹⢿⣹⡿⣾⣹⢿⣹⡿⣷⣏⣿⣾⢿⣏⣿⣷⢿⣾⢿⣾⣹⡿⣾⡿⣷⣏⡿⣿⣹⢿⣶⢿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⢸⡀⡇⣇⠳⠀⠀⠀⠀⠀⣄⠀⠀⠙⠀⠀⢠⡎⠀⠀⠀⠀⠀⠀⢀⠀⠘⣼⣹⢀⡏⣾⣿⣿⠄⠀⣿⡿⣽⣯⢿⣯⣟⡿⣽⣻⢯⣿⣽⢾⣻⡾⣯⢿⡾⣽⢿⡾⣯⣷⢿⣽⢯⣿⣽⢾⡿⣽⣯⢿⡞⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡜⣧⠘⡸⡄⠀⠐⠠⠀⠈⡿⠂⠂⠀⠀⠀⡀⠀⠀⠀⠀⠀⢈⠐⠠⠀⢠⣇⠏⣸⢡⣿⣿⡟⠀⠀⣿⣟⣷⣻⣟⣾⣽⣻⢯⣟⣿⣳⣯⡿⣯⢿⣽⡿⣽⣟⣯⡿⣷⢯⣿⢾⣟⡷⣯⣿⣻⢷⣻⣯⣟⣽ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⢽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⡸⣆⠡⠱⡄⠈⠄⠁⠀⠀⠀⠀⠀⢐⢢⠀⠀⠀⠀⠀⠀⢠⠈⠄⢀⡞⡜⢠⠏⣼⣿⣿⠇⠀⠀⣿⣟⣾⣽⣾⣻⣞⡿⣯⢿⣞⣯⣷⣟⡿⣯⣷⣟⡿⣾⣽⣻⣽⢿⣽⣻⡾⣿⣽⣞⣯⣿⣻⢾⡽⣾ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣧⡙⣆⠡⠙⢄⠀⠁⢂⠐⡀⠀⠀⠀⢂⠀⠀⠠⠈⠄⠡⠀⠂⣠⢏⠞⣠⠏⣼⣿⣿⠏⠀⠀⠀⣿⣟⣾⣳⣯⡷⣟⣿⡽⣟⣯⡷⣟⣾⣟⡷⣟⣾⣟⣷⢯⣟⣾⣯⡷⣿⡽⣷⣻⣾⣻⢾⣽⣟⡿⣽ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠘⠀⢏⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣷⣌⠧⣄⠈⠓⢌⠀⠀⠐⠀⡀⠌⡀⢂⡀⠐⠁⠌⢐⡠⠞⠑⣁⡶⢃⣾⣿⣿⠟⠀⠀⠀⠀⣿⣻⡾⣽⣳⡿⣯⣷⢿⣻⣽⣻⢯⣷⣻⣟⣯⣷⢿⣾⣻⢯⣷⢯⣿⣳⡿⣯⣷⢿⡽⣯⣷⢿⣽⣻ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠘⡀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣷⣜⠒⡀⢀⠠⠀⠐⠀⠀⠀⠐⠀⠀⠐⠈⠀⠈⢀⣠⠖⣋⣴⣿⣿⡿⠋⠀⠀⠀⠀⠀⣿⡷⣟⣿⣽⣻⢷⣯⡿⣯⣷⢿⣻⡽⣷⢯⣟⣾⣟⣾⢯⡿⣯⢿⣳⡿⣽⡷⣯⣿⣻⣽⡾⣯⣷⣻ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢸⠀⢸⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣦⣅⡂⠡⠌⡀⠄⣀⠀⡐⢀⠂⠄⠈⢐⣋⣥⣾⣿⣿⡿⠏⠀⠀⠀⠀⠀⠀⠀⣿⣟⣯⣷⢯⣟⡿⣾⣽⢷⣯⡿⣯⣟⣯⡿⣯⣷⣻⡽⣿⣽⣻⢿⣽⣻⢷⣟⡿⣾⣽⣳⣿⣻⢾⣽ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢸⡀⠘⡄⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣴⣤⣤⣤⣤⣤⣶⣶⣿⣿⣿⣿⣿⣿⣯⡝⣦⠀⠀⠀⠀⠀⠀⠀⣿⣯⡷⣟⣯⡿⣽⡷⣯⣿⢾⣽⣷⣻⣽⣻⢷⣯⢿⣽⡷⣯⣟⣯⣷⢿⣻⡾⣟⣷⣯⣟⣾⣽⣻⢾ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢸⠀⠀⢳⠈⢘⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆⠳⢄⠀⠀⠀⠠⡀⠙⣷⣿⣻⣽⣻⣽⣻⢷⣯⢿⣞⣷⣯⡷⣿⣻⡾⣟⡷⣿⡽⣯⣷⢯⣿⣳⡿⣯⡷⣟⣾⣻⡾⣽⣻ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⡀⠈⢇⠘⡼⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡈⠳⡄⠀⠀⠈⠀⠈⠙⠛⠛⠛⠓⠛⠛⠚⠛⠛⠚⠓⠛⠛⠓⠛⠛⠛⠓⠛⠛⠚⠛⣷⠿⠛⣷⠟⠛⠓⡛⠻⡓⠛ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠘⣆⠙⡽⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠰⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠝⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⢣⠇⣼⠓⠀⠀⠀⢡⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠱⣹⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡐⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡄⠳⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⢧⠁⣴⠃⠀⠀⠀⠀⠠⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⢜⣆⠹⣜⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⠰⣘⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡲⢌⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣋⢣⡾⡃⠌⠀⠀⠀⠀⠀⠀⠀⠀ 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