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⣿⣻⢯⣟⡿⣽⣻⢯⣟⣯⣟⢿⣽⣻⢯⣟⣯⣟⣯⡿⣽⢯⣟⡿⣽⣻⢯⣟⡿⣽⣻⢯⣟⡿⣽⣻⢯⣟⡿⣽⣻⢯⣟⡿⣽⣻⢯⣟⣟⡿ ⣿⣽⣻⢾⣽⣳⢯⣟⡾⣳⠾⣻⢮⣟⡽⣞⡷⡾⠁⠀⠈⢿⡾⣽⣳⢯⣟⡾⣽⣳⢯⣟⡾⣽⣳⢯⣟⡾⣽⣳⢯⣟⡾⣽⣳⢯⣟⡾⣽⣻ ⣟⡾⣽⣻⢾⣽⣻⢾⡽⡏⠀⠈⠙⠺⡽⢋⣽⣠⠀⠀⠀⠘⣟⡷⣯⣟⡾⣽⣳⢯⣟⡾⣽⣳⢯⣟⡾⣽⣳⢯⣟⡾⣽⣳⢯⣟⡾⣽⣳⢯ ⣿⣽⣳⢯⣟⡾⣽⢯⣿⡁⠀⠀⠀⠊⠀⠀⠀⠁⠀⠀⠀⠀⢻⣽⣳⣾⣿⣷⣿⣿⣾⣿⣷⣿⣻⢾⣽⣳⢯⣟⡾⣽⣳⢯⣟⡾⣽⣳⢯⣟ ⣟⡾⣽⣻⢾⡽⣯⢷⢯⡇⠀⠀⠀⠀⠤⡀⠀⠀⠀⣀⣤⣀⣸⣷⣻⢟⡿⣿⣟⡿⣟⡿⣿⣳⢯⣟⡾⣽⣻⢾⣽⣳⢯⣟⡾⣽⣳⢯⣟⡾ ⣿⣽⣳⢯⡿⣽⣻⣞⡯⠟⠀⠀⢹⢹⣿⣿⠉⠀⣿⣿⡇⢈⠎⢳⣯⢿⣽⣳⢾⡽⣏⣿⣳⢯⣿⣻⣟⡷⣯⣟⡾⣽⣻⢾⣽⣳⢯⣟⡾⣽ ⣟⡾⣽⢯⣟⣷⡻⣾⣽⣳⠀⠀⠈⠪⠛⠋⠀⠀⠨⠏⡀⣬⣄⣿⣽⣻⢾⡽⣯⢿⡽⣾⣭⢷⣟⡷⣿⣽⣳⢯⣟⡷⣯⣟⡾⣽⣻⢾⣽⣳ ⡿⣽⣛⡾⣽⣶⣻⢷⡾⣽⣳⣦⣤⣘⣛⣀⣈⣭⣝⣡⣤⣾⡟⣷⣳⢯⣟⣳⢯⣷⣻⣧⣟⣿⢾⡽⣯⢿⡿⣿⢾⣽⣳⢯⣟⡷⣯⣟⣾⣳ ⣿⡷⣯⡿⠁⣿⣽⣳⣟⣷⣻⢞⡷⣯⠟⠓⣄⠀⠀⢀⢺⡗⠛⠓⢋⡙⠾⠽⠛⠾⣷⣻⢿⣭⠿⣽⣯⢿⣽⣻⣟⡾⣽⣻⢾⣽⣳⣟⡾⣵ ⣿⢿⡗⠀⠀⠻⣞⣧⣟⡾⣭⠿⣝⡿⡀⠀⠈⢆⠀⠀⠘⠴⡠⠶⠉⠀⠀⠀⠀⠀⠀⠀⠈⠉⢟⠳⢯⣟⡾⣵⣻⣾⢷⣯⣟⣾⣳⢯⣟⡷ ⣿⠘⠆⠀⠀⠀⠈⠉⠉⠙⠫⣿⠃⠀⠱⡀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⡈⠙⢷⣿⣿⣿⣷⣯⡶⣯⣟⡾⣽ ⣟⠀⠀⠀⠀⠀⠀⠀⢀⠔⠊⠁⠱⠀⠀⠳⡀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡌⠄⡙⢾⣿⣽⣾⣟⣷⣫⣟⡷ ⣿⡄⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⡇⠀⠀⢳⡀⠀⠙⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠐⢠⠊⢿⣻⣟⣿⣿⣳⢯⣟ ⣯⣟⣆⡀⠀⢀⠄⡇⠀⠀⠀⠀⠀⢰⠀⠀⠀⢱⡀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⡄⠌⡘⢷⣻⣿⣟⣯⣟⡾ ⣷⣻⢾⣽⣻⣦⣌⣷⡀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠣⡀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠰⢈⠐⡸⣿⣿⣿⣻⢾⡽ ⡿⣽⣫⣞⣷⣻⠾⣽⢧⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡆⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠄⢡⠊⡐⡐⣯⣟⣷⣯⣯⣟ ⣿⣳⣟⣾⣳⢯⡿⣽⢿⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠘⠖⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠁⡌⠰⠠⢁⠔⣿⣿⣿⣟⣷⣻ ⣟⡷⣞⡷⣯⢿⡽⣯⢿⡄⠀⠀⢀⢼⠀⠀⠀⠀⠀⠀⠀⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠃⠤⢁⠂⠥⢁⠢⢸⣿⣽⣿⣻⢾⡽ ⣿⡽⣏⡿⣽⢯⣟⡷⣯⢿⡅⡒⠌⢺⠀⠀⠀⠀⠀⠀⠀⢸⠈⠅⡒⠠⢀⠀⠀⡀⢀⠠⢀⠩⠐⣨⠌⡐⠨⡐⠌⡐⠰⢸⣷⣻⢞⡷⣯⣟ ⣟⡾⣽⣻⣭⣟⡾⣽⢯⣻⡽⡆⠌⢹⡑⢄⠀⠀⠀⠀⢀⠎⡈⠔⡠⢃⠂⡌⢡⠐⣁⠢⢁⢂⣵⣧⠂⡐⢡⠐⠌⡠⢱⣿⣳⢯⡿⣽⣳⢯ ⣿⣽⣳⣟⡾⣽⣻⡽⣯⢷⣻⡗⡊⠄⢻⡠⢉⠡⣀⠂⡄⢂⠔⠡⡐⠄⢊⠐⠤⢈⠄⠒⡈⠯⠔⢣⡔⢁⠂⢌⠂⣴⣿⣯⣟⣯⣟⡷⣯⣟ ⣟⡾⣵⢯⣟⡷⣯⡽⣯⣟⣳⣷⡐⢈⢸⣷⡀⢆⢀⠒⢠⠡⢈⠂⠔⣈⠂⢡⠒⡈⠄⠣⠐⡡⢌⡞⢁⠂⡉⢄⣾⣟⡷⣻⣞⡷⣾⣽⣳⢯ ⣿⡽⢯⣟⡾⣽⣳⣟⡷⣯⢷⣯⢷⣼⣦⡿⣿⣦⡂⠌⠄⡂⣁⠊⠔⡠⠘⡀⠆⢌⠰⢁⠡⡐⢘⠡⢂⣡⣾⣿⡿⣾⣽⣻⣯⣟⡷⣾⡽⣯ ⣯⣟⢿⡾⣽⣳⣟⡾⣽⢯⣟⣾⣻⠾⣵⣻⢷⣫⢿⣻⢶⣄⣄⡌⡐⠠⢁⠒⡈⠄⢢⣈⣔⣰⣬⣶⣿⣿⡿⣽⢯⡷⣯⣟⡷⣾⣽⣳⣟⣳ ⣿⣞⣯⢟⣷⡻⣾⢽⢯⣟⣾⢳⣯⢿⡽⢯⡿⡽⣯⢟⣯⣟⡾⣽⣻⢿⣿⣻⢿⢿⣯⢿⣹⢷⡯⣷⣻⢯⣟⡷⣯⢿⣵⣻⣞⣷⢻⣞⣽⣳

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣣⠦⣄⣀⠀⠀⠀⢀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⡖⣻⣴⠞⢃⠐⠠⢉⠛⠶⣶⠾⡗⢦⣍⠙⣶⣄⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠶⠟⠩⢄⠡⠐⠛⠠⡈⠄⡈⠒⡀⠂⠄⢈⡧⣧⠘⡏⡀⣿⢿⣿⡙⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⢋⠌⡡⠂⠌⠸⢀⠁⡐⠠⠀⢁⠀⠐⠈⢀⡇⣿⠀⡓⠠⣿⠢⠘⢻⣄⠹⡷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡧⠃⡌⠄⢃⠈⠐⠀⠂⠀⠄⠈⠀⠈⠀⠐⢸⠇⣿⠀⠄⢹⡟⠠⠁⠌⡻⣆⢻⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠿⡇⠌⡐⠈⠄⠂⠁⠈⠀⠀⠀⠀⠂⠀⠂⠀⡿⠀⡟⢠⠃⣸⠇⠠⠁⠠⢀⢻⣼⡟⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠑⡠⢁⠂⠄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢠⡗⢀⣇⡏⢀⣿⠀⠂⠌⠀⠄⢨⣇⡧⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠄⠣⠀⠄⠂⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⢸⠃⢸⡟⢀⣾⣣⣿⣦⢀⠡⢠⣽⣿⣧⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⣾⡇⠠⠁⡀⠂⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢀⡯⢀⡿⢁⣾⡟⠿⣿⡟⠆⠐⡘⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⣰⡶⠦⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ 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⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⠇⡐⠠⣰⠟⠀⢠⣿⣧⣿⠀⢠⠀⣸⠟⣾⣤⣛⠎⣞⣿⣶⣿⣿⡿⣯⣷⣿⡾⣿⣻⣽⡿⣟⣿⢿⣻⣿⢿⣽⣿⣻⣷⡿⣽⣯⣿⣻⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣯⣷⣿⣻⣟⣿⡿⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣼⣳⣿⢏⠠⣰⠾⠁⠀⠀⢸⣟⠛⡿⡆⢸⢀⣿⠿⡋⢧⣸⣾⣿⣿⣿⢿⣽⡿⣿⣽⣾⢿⣟⣿⣽⡿⣟⣿⣿⣻⣽⣿⣻⣾⣟⣷⣿⢿⣽⣷⡿⣯⣿⣯⣿⣟⣿⣿⣿⣿⣿⡿⣿⣽⣾⣟⣯⣿⣟⣷⣿⣽⢿⣻⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⡴⠿⠛⠋⡽⠒⠛⠁⠀⠀⠀⠀⣼⠁⠂⣧⢧⠘⣿⠇⠜⢠⣳⣿⣿⡿⣽⣿⣻⣯⣿⢿⣽⣾⣿⣻⣯⣷⣿⢿⣻⣾⣟⣿⣾⣟⣷⣿⣻⣾⣿⣻⣾⢿⣟⣷⣿⣳⣿⣟⣾⣷⢿⣾⣟⣿⣽⣾⣟⣯⣷⣿⣻⣾⣟⣿⢿⣳⣿⣻⣿⣿⣶⣄⠀⠠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⢴⣿⣶⣶⣿⡎⠆⣿⣷⣶⣾⣿⣿⣷⢿⣿⣳⣿⢯⣿⣟⣯⣷⣿⣻⣽⣷⡿⣿⣻⣷⣿⣻⣾⢿⣽⣾⣟⣷⣿⣻⣽⣿⣻⣿⢾⣟⣷⣿⣻⣾⣿⣻⣾⢿⣽⣾⣟⣯⣿⣾⣟⣷⣿⣻⡿⣿⣽⣟⣷⣿⣽⣿⣷⣄⠀⠳⣄⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣷⡀⢸⣿⣿⣿⣿⡷⣿⣟⣯⣿⣻⣿⣻⣾⢿⣽⣾⣟⣿⡾⣟⣿⣯⣷⣿⣻⣽⡿⣯⣷⣿⣻⣾⣟⣿⣾⢿⣽⣿⣻⣿⢾⣟⣷⣿⣻⣽⣿⣻⣾⣟⣯⣷⡿⣯⣿⣾⣟⣿⢿⣽⣾⢿⣾⣯⣷⡿⣿⣷⡄⠈⢦⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣯⣷⣿⣷⠃⢻⣿⣿⣿⣽⡿⣯⣿⣽⣿⣳⣿⣻⣿⢯⣷⡿⣯⣿⢿⣯⣷⣿⣳⣿⣯⣿⢿⣽⣾⣟⣷⣿⣻⣾⣿⣻⣾⣿⣽⣿⣿⣿⣾⣿⣿⣿⣿⣷⣿⣿⣽⡿⣟⣷⡿⣯⣿⢿⣯⣿⢿⣳⣿⣽⣿⣻⡿⣿⣦⡀⠳⡀⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⣠⣿⣿⣿⡿⣿⣾⣿⣿⣿⣧⢈⣿⣿⣷⣿⣻⣿⣽⣾⢿⣽⡿⣽⣿⣻⣯⣿⢿⣽⡿⣯⣷⣿⣻⣷⡿⣽⣿⢯⣷⣿⣻⣾⣟⣷⣿⣻⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢯⣿⡿⣽⣿⣻⣾⡿⣿⣽⣾⢿⣽⡿⣟⣿⣷⡀⠹⡄⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⣀⣴⣿⣿⣿⣿⡿⣽⡿⣿⣿⡷⣿⣿⣎⣿⣿⣾⢷⣿⣻⣾⣟⣿⣯⣿⣟⣷⡿⣯⣿⢿⣯⣿⢿⣽⣾⣟⣷⣿⢿⣽⡿⣯⣷⣿⣻⣾⣟⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⡿⣷⡿⣯⣿⢿⣽⣿⣻⣯⣿⢿⣯⣿⣷⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣼⠁⠀⣠⡴⠞⣻⡟⠸⣿⣿⣿⣟⣿⣽⣟⣿⣿⣿⣿⣿⣿⣿⣾⣿⣻⣽⣷⣿⣻⣾⣯⣿⢯⣿⣿⣽⡿⣯⣿⢿⣯⣷⡿⣿⣾⢿⣻⣿⢿⣽⣷⡿⣟⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⡿⣽⣿⣻⣿⣻⣾⢿⣽⣿⣻⣯⣿⣻⡇⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣧⠶⣛⠱⣈⣱⠏⠀⠀⣿⣿⣿⢯⣿⣞⡿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣻⣿⢾⣿⣽⣷⡿⣯⣿⢿⣾⢿⣽⡿⣯⣿⢿⣽⣿⣻⣽⡿⣿⣽⣿⣻⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⡁⢆⡘⢄⠢⡉⢍⠛⠿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣻⣽⣷⣿⣻⣿⣻⣾⢿⣽⣷⣿⡇⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⡑⠄⢃⣰⡏⠀⠀⠀⣽⣿⣿⣿⣻⣾⣟⣿⣽⣿⣿⣿⡟⣿⣿⣾⢿⣽⣿⣻⣾⣯⣿⢿⣽⡿⣯⣿⣟⣿⡿⣽⣿⣻⣾⣟⣯⣿⣿⣽⣾⣟⣷⣿⣿⣿⣿⣿⣿⡿⠋⠤⡉⠔⠂⢀⠂⠐⡈⢀⠉⠞⠶⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡿⣽⣷⣿⣻⡿⣿⣾⣿⡇⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢻⡇⠈⢀⡿⠀⠀⠀⢠⢟⣿⣿⣷⣿⣳⣿⣻⣾⣿⣿⣿⠒⣽⣿⣿⣿⣿⣾⣟⣷⡿⣯⣿⣟⣿⡿⣽⣾⣟⣿⡿⣽⡿⣷⣿⣻⣷⣿⣿⣾⣿⣿⣿⣿⣿⣿⡿⠋⠤⣉⠂⢁⠐⡈⠄⢈⠐⡀⠂⠄⢂⠈⢀⠀⠀⠉⠉⠙⠻⢿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⣷⠀⢸⡇⠀⠀⠀⣼⠸⣿⣿⣿⢾⣟⣷⣿⣿⢿⣿⠧⣉⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣽⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⢄⡁⠂⠀⡀⠀⢂⠠⠀⠂⠄⠐⡀⠂⠄⡈⠄⠠⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⡖⡟⡏⠀⠀⢠⡇⢰⣿⣿⣿⣻⣿⣿⢿⣽⣿⡿⢢⣹⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⢥⣠⡷⠛⠁⠐⡀⠀⠂⠀⠀⠂⠠⠀⡁⠐⢈⠀⡐⠈⠄⠠⢀⠀⠀⠀⠀⠀⠀⠀⠚⢻⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⣇⡗⠀⠀⣾⢀⣿⣿⣿⣷⢿⣳⣿⣯⣿⣿⡇⢣⣿⣿⠰⣉⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣛⣍⣴⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠁⢀⠀⠄⠀⠂⢀⠂⠐⢀⠂⠈⠄⡁⠂⠄⠀⠀⠀⠈⢙⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⢸⠓⣿⣿⣿⣿⣯⣿⣟⡷⣿⣿⣿⡇⣿⣿⣿⡵⡈⣞⣦⣿⠿⠟⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠭⣔⣼⠟⠋⠀⠀⠀⠀⢀⠀⠀⡀⠀⠈⠀⠀⠄⠈⢀⠀⡈⠀⠂⡀⠄⠀⠁⠀⢈⠐⠄⠨⠐⡈⠄⠠⠀⡀⠀⠻⣧⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⢉⢈⡿⣿⣿⣿⣽⣾⣿⣿⣿⣯⣿⣷⣿⣿⣿⠿⢛⠉⠄⠀⢀⠂⠁⠢⡐⢌⠩⡉⢍⠩⡉⢍⠩⡑⢂⠔⡌⢱⣼⠟⠁⠀⠠⠀⡐⠈⠠⠀⠐⠀⠀⠐⠀⠀⠂⠐⠀⠀⠂⠀⠐⠀⠀⠠⠐⠀⠁⠠⠀⠌⡐⠡⠐⡈⠄⠡⠐⢈⠰⣿⣦⠘⡉⠻⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⡜⣠⣞⡗⠻⣿⣿⣿⣿⣿⣿⣿⢿⣟⣿⣿⢟⠑⠨⠀⠌⠀⢈⠀⠄⡁⠂⠌⡀⠣⠜⡠⢃⠜⡠⢃⠜⡠⢊⢰⡿⠃⠠⠐⢈⠀⢂⠠⠀⡁⢀⠡⠀⠁⠈⠀⡀⠀⠠⠈⠀⠄⠁⠠⠈⠀⢁⠠⠈⠀⠁⠌⡀⠠⠁⠆⡐⡈⠄⡁⠂⠄⠻⣟⣷⠙⠾⠃⢻⡀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣾⣷⠏⣾⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣉⣦⣥⠷⠾⠴⠆⠠⡈⠔⡠⢁⠂⠐⡀⠠⠑⠀⢊⠐⠈⠀⠄⣂⡿⠁⠂⡁⠂⠄⠂⢀⠂⠠⠐⢀⠠⠐⠀⠐⠀⠀⡀⠁⠀⠂⠀⠂⠐⠀⠂⢀⠀⠐⠀⠂⠐⠀⢂⠁⡐⠀⠆⠂⠄⠡⢈⣶⣿⣹⣷⠾⢦⣼⣇⠈⢧⠀⠀⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣸⣿⠏⣸⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡟⡰⠋⡅⢂⢂⠀⠀⠀⠰⣷⣌⠰⢄⢊⠐⠠⢀⠂⢈⠠⠀⡁⠂⠄⣿⠃⠈⠄⡀⠡⠈⠄⠂⠠⠁⠀⠄⠠⠈⠀⠈⡀⠁⠀⡈⠀⡁⠄⠡⠀⠈⠄⠀⡈⠠⠁⠄⠈⠀⠄⠂⠄⡈⠄⠡⠘⠠⢀⠘⠛⠚⢻⣧⠀⢠⡾⡆⠈⠛⢦⡹⣄⠀⠀⠀⠀ ⠐⣶⡤⠤⠤⢴⣾⣿⠃⢠⣿⠀⠀⢸⣿⣿⣿⣿⣿⣿⣫⠟⠛⠛⠛⠿⠻⢾⠟⣻⣦⣥⣈⡻⣷⣄⠊⡜⣀⠂⡐⠀⡐⠀⠄⢀⠘⣼⠀⡈⠄⠐⡠⠁⢂⠈⠄⠐⢣⠀⡀⠁⡐⠀⠐⡀⢁⠀⡀⠐⡀⠐⢀⠂⡀⠂⢀⠀⠄⡀⢂⠀⠌⡐⢀⠀⡈⠄⡁⠂⠄⢂⠀⠄⠐⣿⣇⠀⢷⣿⣆⠀⠀⢳⠈⠳⡄⠀⠀ ⠀⠀⠉⠉⠉⠉⣰⠃⢀⣾⡷⠀⠀⣿⣿⣿⣿⡿⠋⠉⠁⠲⠶⣶⣶⣤⣤⣿⣴⠃⠀⠈⠙⠛⠿⣿⣢⠐⡤⢁⠄⠂⠠⠁⠂⡀⠂⠹⢿⠇⡐⠠⠐⣀⠂⢈⠐⠠⠀⢡⠀⠄⠠⢀⠀⠄⠀⠄⠠⠀⠄⠡⠀⠠⠀⠌⠀⠠⠀⠄⠠⠀⠂⠄⠠⠐⠀⠐⠠⠐⠈⡀⠄⠠⠀⠡⣿⡆⠀⣾⢹⡀⠀⠈⡇⠀⢹⠀⠀ ⠀⠀⠀⠀⠀⣼⠁⢀⣾⣿⣧⠀⢰⠃⢹⡿⠋⠀⠀⠠⠘⣤⣧⣽⣇⠀⠀⠉⠙⠛⠿⣷⣲⢤⡄⠈⣷⣎⡗⠨⢌⠁⠂⠄⡁⠠⠀⠄⡀⠠⠀⡁⠄⠀⠄⠢⠤⠤⣐⡀⢀⠀⠁⠀⡈⠄⡈⠐⠠⠀⠂⠐⠈⢀⠂⠐⢈⠀⡁⢀⠂⢈⠐⡀⢂⠀⡁⠈⠄⡈⠐⠠⠐⡀⢁⠀⢻⣧⠀⢹⠝⠛⢦⣀⢿⠀⠘⡇⠀ ⠀⠀⠀⠀⢰⠇⠀⡾⣽⢻⢹⡆⠀⣼⠟⠁⠀⠀⢠⠡⢉⠄⠂⢸⢛⠓⠶⣤⣄⣀⡀⠀⠈⠉⠓⠶⣼⣿⣏⠡⠌⠢⠁⠄⠠⠐⠈⠀⠄⠁⠀⠀⠐⠠⠀⠀⠀⠀⠀⢀⠉⠉⠘⠒⠤⣀⡀⠈⢀⠁⢂⠡⠐⠀⠄⠈⠄⠀⠄⠂⢀⠂⠄⠠⢀⠐⠀⡁⠄⡀⠁⢂⠐⠀⡀⠂⠤⣹⡆⠀⢠⢤⡄⠀⠈⢳⠀⠙⠆ ⠀⠀⠀⠀⠸⣆⠀⠼⣿⠀⠀⣹⡾⠁⠀⠀⠀⢐⡀⠒⡀⠀⠀⣾⠎⠀⠀⠀⠀⠉⠙⠓⠶⢦⣤⣀⡀⢹⣷⠈⡌⡑⠌⠠⠁⠌⢀⠀⡀⠈⠀⡀⠂⠀⠈⠀⠁⠈⠀⠀⠈⠐⠠⢀⠀⡀⠈⠓⠠⣄⠀⡀⠁⠂⠄⡁⠄⠈⡀⠌⠀⠄⠂⡐⢀⠀⢂⠀⢸⡇⠀⢂⠈⠄⠐⠈⡀⢻⣧⠀⣸⢾⡅⠀⠀⠈⡇⠀⠀ ⠀⠀⠀⠀⠀⠙⢳⣾⡿⣆⣼⠏⠀⠀⠀⠀⡐⠠⠈⠄⠐⠀⣰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢻⣿⡘⢠⠑⡈⠅⠌⡐⢀⠀⡀⠐⠀⠀⠀⠂⠀⠀⠂⠐⠀⠂⠀⠂⠀⠀⡐⠀⠂⠄⡀⠀⠁⠒⠤⡐⠀⠐⠈⠄⢀⠐⠈⡐⠀⠐⠀⠠⠀⠀⣿⠃⠌⠀⠂⠌⠠⢁⠐⣨⣿⢀⠟⠉⠙⠿⠂⠀⡇⠀⠀ ⠀⠀⠀⠀⠀⣠⣾⡝⠀⣸⠋⠀⠀⠀⠀⡐⡈⠄⡡⠈⠀⣠⣯⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⢢⠑⡌⢌⠰⣀⠂⠄⡐⠠⠀⢁⠀⠌⡀⠀⡁⠠⠀⠀⠁⠀⡈⢀⠀⠁⠄⢂⠀⠁⠄⠂⢀⠈⠃⡄⠀⠈⠄⢀⠂⠄⡁⠄⠈⠄⢂⣽⣯⠐⡀⠡⠈⠄⡁⢂⠂⢸⣿⠀⣴⣤⣶⡀⠀⣰⠇⠀⠀ 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⣳⣽⣞⢻⣷⣞⣻⣵⢿⣯⡷⣟⢯⣻⣷⡯⢷⣹⢿⣯⢿⢿⣻⣿⢿⣻⣽⡾⣟⣯⢟⣯⡽⡿⢯⡽⢿⣯⢳⣾⣟⢯⢽⣾⡻⣷⢟⣯⣞⣿ ⣳⣟⣳⣽⣾⡷⣟⣯⡷⢯⣽⡿⣿⣿⣶⣬⣰⣔⣈⢢⠄⡈⠒⢁⠠⡐⡌⣄⣄⢶⣻⢿⣫⢷⣻⣵⠾⣻⣾⣟⢯⣽⡾⣟⣳⣽⡾⢿⣟⣯ ⣯⡽⣾⡷⣟⣯⣻⣽⣾⡿⣿⣾⣡⢂⠡⢘⡐⠡⢁⠰⢌⠆⡀⠘⡠⠔⠊⣁⡂⠄⠌⡂⣦⣿⡿⣦⣼⢷⣯⢷⣯⡷⣟⣳⣽⡾⣟⢯⡽⣿ ⢯⣳⣽⣾⡷⣞⣻⡷⣟⣾⢄⡉⠂⢁⡞⢌⡡⠐⠣⠄⡈⠒⢡⠂⣈⠔⠂⢈⠡⢠⠒⢀⢆⡀⣷⢸⢈⡐⣷⣳⣟⣯⡽⣯⡷⣟⢯⣵⡾⣟ ⣟⣯⡷⣟⣯⣟⣯⣿⣴⠂⢌⠂⢁⡔⢣⠔⠯⡈⠒⠄⢈⠤⠐⢊⠄⡐⠡⠔⢂⡄⠂⣀⠡⢉⡠⢻⠄⡊⡗⣻⢷⣯⡽⣻⣽⡾⣟⣳⣽⣿ ⢯⣳⣽⡿⢯⣳⣿⢱⡠⠌⠐⢡⡐⠂⣧⣵⢂⢁⠢⣁⠐⢡⡌⠂⢃⡠⠔⡈⠎⢀⠀⠀⠀⠀⢄⡑⢹⠌⡆⡽⣻⢯⣽⡾⣟⣭⣻⣽⡾⣟ ⣟⣯⡷⢞⣻⣷⢸⠰⡐⠌⡐⠨⡐⠌⣨⠐⠩⢀⠠⢀⡀⠀⠀⢀⠠⡒⠅⠈⢸⠀⠀⠀⠀⠀⠀⠀⢺⠌⡒⡅⢿⣯⡷⣟⢯⣽⡿⣏⡽⣿ ⡽⢾⣻⣿⣽⣿⢸⠢⢁⠥⠂⢁⠤⠃⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢣⠀⠀⠀⠀⠀⠀⠀⢼⢀⠀⠀⡄⢿⣯⡽⢿⣯⡷⣞⡷⣟ ⣻⣷⣟⣿⣿⣿⠔⢁⠠⠰⡌⠁⠴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠖⠘⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢿⣽⡿⢯⣳⣾⣟⣳⣿ ⣟⣯⣯⣷⣟⣯⡐⡐⠊⢡⠄⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⡆⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢧⣽⠾⣻⣷⣞⣫⣽⡿ ⡽⢾⣻⣿⣿⣿⡸⠐⢈⠰⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡀⠣⠀⠀⠀⠀⢸⠀⠀⠀⠀⡀⣷⣌⣦⣻⣽⢾⣻⣷ ⡾⣟⣯⣟⣿⣻⢷⡘⠌⡄⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠸⠀⡀⢱⠀⠀⠀⢰⠀⠀⠀⠀⠀⡇⠄⢀⠀⡀⣆⣟⣯ ⣟⢯⣳⣿⣿⣟⣻⢿⠊⢠⠐⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠙⠀⡀⢳⠀⠀⡇⠀⠀⠀⠀⠏⢠⠀⠀⠀⠀⠀⡄⣿ ⡷⣟⣫⣷⣟⣾⣽⣿⢾⡙⠄⡌⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠘⠀⡀⠳⠀⠀⠱⠁⠊⠔⢀⠀⠀⠀⠀⠀⠀⠀⣟ ⣽⡾⣟⣯⡶⣯⣷⣿⣿⣿⢷⠙⡈⠢⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠘⠀⡀⠱⠀⠃⣿⠫⠙⠉⠉⠈⠀⠀⠀⠆⠘⣿ ⡷⣟⢯⣳⣾⣟⣯⢷⣾⣻⣵⡾⣟⢯⠳⢟⠉⠈⠀⠀⠀⠀⠀⠀⠀⠉⠶⡠⠴⠘⠀⠀⢆⠈⠀⡀⡿⣝⠿⣭⡾⣟⣧⣞⠻⠀⠀⡗⢿⣿ ⣵⡾⣟⣳⣽⢾⣻⣽⡾⣟⣻⣽⢿⣯⣽⠿⣭⢿⣻⣷⠾⠛⠽⠾⡙⢋⠓⠛⡗⢺⢀⠀⠀⣄⠓⠟⣯⡷⢞⣻⣷⣟⣳⣽⣿⠁⡿⣯⡷⣿ ⣳⣾⣟⣯⡷⣟⢯⣳⣽⢾⣿⡿⢿⣯⡽⢾⣿⣟⣧⣻⣷⢯⣳⣟⢯⣳⣷⡟⣾⣤⣡⣝⣭⣈⣀⣛⣘⣤⣦⣳⣽⡾⢷⣻⣶⣽⡾⣛⣽⡿ ⣳⣽⢾⣻⣽⡾⣟⣯⡷⣟⢯⣳⣽⣿⡷⣟⢷⣭⣾⡽⢿⣯⡽⢾⣻⣽⣿⣄⣬⡀⠏⠨⠀⠀⠋⠛⠪⠈⠀⠀⣳⣽⣾⡻⣷⣟⢯⣽⡾⣟ ⣽⡾⣟⢯⣳⣽⢾⣻⣽⡾⣟⣯⡷⣟⣻⣿⢯⣳⣿⣏⡽⢾⣳⣽⢿⣯⢳⠎⢈⡇⣿⣿⠀⠉⣿⣿⢹⢹⠀⠀⠟⡯⣞⣻⣽⡿⢯⣳⣽⣿ ⡾⣟⢯⣳⣽⡾⣟⢯⣳⣽⢾⣻⣽⡾⣟⢯⣳⣿⡿⣟⡿⣟⣿⡿⢟⣻⣷⣸⣀⣤⣀⠀⠀⠀⡀⠤⠀⠀⠀⠀⡇⢯⢷⣯⡽⢾⣻⣽⡾⣟ ⣟⢯⣳⣽⡾⣟⢯⣳⣽⡾⣟⢯⣳⣽⢾⣻⣿⣷⣿⣾⣿⣿⣷⣿⣾⣳⣽⢻⠀⠀⠀⠀⠁⠀⠀⠀⠊⠀⠀⠀⡁⣿⢯⣽⡾⣟⢯⣳⣽⣿ ⢯⣳⣽⡾⣟⢯⣳⣽⡾⣟⢯⣳⣽⡾⣟⢯⣳⣽⡾⣟⢯⣳⣽⡾⣟⣯⡷⣟⠘⠀⠀⠀⣠⣽⢋⡽⠺⠙⠈⠀⡏⡽⢾⣻⣽⢾⣻⣽⡾⣟ ⣻⣽⡾⣟⢯⣳⣽⡾⣟⢯⣳⣽⡾⣟⢯⣳⣽⡾⣟⢯⣳⣽⡾⣟⢯⣳⣽⡾⢿⠈⠀⠁⡾⡷⣞⡽⣟⢮⣻⠾⣳⡾⣟⢯⣳⣽⢾⣻⣽⣿ ⡿⣟⣟⢯⣻⣽⡿⣟⢯⣻⣽⡿⣟⢯⣻⣽⡿⣟⢯⣻⣽⡿⣟⢯⣻⣽⡿⣟⢯⣽⡿⣯⣟⣯⣟⢯⣻⣽⢿⣟⣯⣟⢯⣻⣽⡿⣟⢯⣻⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡿⣼⣱⢢⣙⡬⠓⢤⡘⠧⣂⡜⠣⢆⡙⢣⣤⠞⢏⢡⣷⢸⠁⡞⣝⢫⣠⡱⢌⠢⢌⠣⢄⠢⠐⢡⠠⠌⠡⢂⠄⠈⠠⢁⠤⡈⠐⠢⡀⠐⢂⠀⣰⣂⣤⢾⢛⡏⢊⡐⢸⡇⢻⠈⣏⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠟⣬⢣⡄⡘⢣⠐⣘⠣⣐⡘⢘⢢⡜⢃⢤⡙⠦⣌⠓⢡⣲⡜⢻⡿⣱⢢⠐⣈⠰⡘⢊⡄⠉⢂⢂⡐⠈⢂⠀⠒⠀⠐⠂⡀⠀⠐⠂⡀⠐⢀⡐⠂⢀⠂⠠⢀⠀⡄⣄⢷⠙⢸⡏⢠⠟⢰⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣸⢰⡈⠰⢌⡁⠡⠤⡉⢁⠤⠌⡌⠌⠡⢢⡌⠃⢡⣌⡘⡱⠧⣃⣿⣤⠂⢁⠤⢈⠡⠄⠈⢄⠀⠠⢈⠄⠀⠈⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠡⠀⠄⠀⢁⡀⠀⠈⠀⣄⣷⢿⡼⢀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⡼⢁⠄⠂⠄⠂⡀⠐⠠⠄⠂⡀⠂⠄⠀⡐⠂⢀⡑⢂⠡⢆⡌⡘⠰⣿⣱⠀⢂⠀⠐⠀⠐⠂⠀⡐⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⡀⠀⠀⣄⠳⠈⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠞⣠⠀⠀⠀⠀⢀⠀⠀⠀⡀⠀⠀⠀⢀⠀⢀⠌⡀⠄⠀⠰⢂⠡⢆⡌⡟⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⠘⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡼⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠄⠐⢂⡠⠔⢏⣷⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠙⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⢿⠀⠀⠀⠀⠀⠁⠂⠀⢂⡔⠃⣿⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠘⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠟⣶⣿⠛⠙⠉⠀⠀⠀⠈⠆⢀⠱⣇⢮⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢰⠀⠀⠀⠀⠀⠉⠋⠞⠶⠤⠤⣤⣤⣤⣤⣤⣤⠤⣦⠶⠛⠙⠉⡀⢃⠡⣿⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢸⠀⠀⠀ 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⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠏⣿⢱⢈⠠⢂⠄⠀⡈⠁⠠⢀⠠⠐⠠⠐⠠⠀⠐⠂⠀⠠⢀⠄⠀⠌⠀⡁⠀⠠⠀⠡⠀⠠⠐⠡⠄⠂⢀⠌⠀⠈⠰⠌⠄⡐⠡⡠⠔⡉⠡⢆⡈⠰⡘⡆⣷⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠠⠁⠋⠛⠾⠴⣤⣠⣀⣀⣄⣥⣽⢞⡠⢀⠀⠀ ⠀⠀⠀⠀⠀⣯⣛⢻⠧⠰⠀⠏⣼⡑⠢⡌⠐⢈⡀⠌⠀⡎⠁⢀⡀⠈⢂⡁⠀⢂⠀⢈⠂⢀⡈⠂⢀⠐⡈⠂⡀⠐⡀⠂⠀⢀⠠⠂⠁⢀⠐⠌⠂⠁⠄⠂⢁⡠⠐⣈⠔⠊⠠⢒⡌⠆⡈⢑⡤⣿⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠾⣤⣐⠢⢁⠀⠀⠀⠀⠀⠁⣾⣠⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠁⡈⣦⣼⣼⠀⠇⣽⣴⠈⠠⠔⠂⠁⢀⠂⠅⣿⠛⠈⢀⠐⠠⠐⠂⢀⠄⠈⠐⢀⠄⠀⠠⠌⠀⠌⠀⠠⢀⠄⠁⠀⠈⢀⠈⠀⠠⠐⠄⠀⠠⠌⠀⡈⠄⠃⢠⠌⡠⠜⡉⢂⢌⡑⠢⣇⣿⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⡾⣀⠐⢈⡱⠄⠈⠀⠀⠀⠀⠁⣼⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡄⣷⡏⠻⠇⠀⡏⣸⠌⠀⡰⠂⢁⠂⡀⠁⣿⣿⣿⠄⠀⠂⢀⡀⠐⠂⢀⠁⠢⡈⠀⠠⢀⠈⢀⠌⠂⢀⡀⠂⠀⠀⠀⠀⠀⢀⠐⠠⡀⠐⢀⠂⠄⠂⢁⠂⠄⠂⢂⠄⠐⢨⡔⠊⢡⡆⣿⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣿⣰⠀⢁⠆⡁⠄⠠⠀⠀⠀⠀⠃⣼⠀⠁⠛⠛⠚⠀⠀⠀ ⠀⠀⠇⣰⠀⡀⣶⣤⣴⠀⣿⢸⠂⢂⡁⠄⠈⠡⡀⠐⣯⣽⢂⠄⠈⠄⡁⠄⠂⢀⠄⠈⠀⡄⠃⠈⢀⠂⠄⠁⠀⢂⠄⠁⠀⢀⡈⠀⠁⠀⠀⠠⡁⠀⡀⠌⠀⢁⠀⠠⡐⠄⠂⣀⠰⢌⡌⠑⢢⡇⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣯⣠⠀⠈⡡⠄⡈⡐⠀⠀⠀⠀⠋⣸⠀⡝⣾⣠⠀⠀⠀⠀⠀ ⠀⠀⡇⠀⠂⠿⠙⠉⠟⢀⣿⣨⠐⢁⠠⠌⠂⠀⠌⠃⣿⠀⠀⠠⠀⠐⠀⡐⠈⠐⢀⠄⠈⠐⠀⡐⠤⠒⠁⠀⡀⠄⠂⠀⡐⠀⠀⠂⠀⠂⠀⠐⠂⠀⠀⠂⠀⠀⠀⠐⡀⠀⢀⡐⠌⠅⡈⠑⢠⡘⣿⢻⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⣰⠀⠐⠄⠈⠠⡐⠀⠀⠀⠀⠏⣼⣆⡿⣾⢳⠙⠀⠀⠀⠀⠀ ⠀⠀⡇⠈⠀⠀⡅⢾⣸⠀⣧⢻⡀⠈⠐⠄⠈⢂⠀⡇⢸⠀⢂⠀⢀⡐⠂⠄⠀⠌⡀⠈⠄⡁⠄⠂⠁⡀⠀⣄⠠⠓⠈⡀⠀⢀⠠⠐⠈⠀⠀⠈⠁⠀⠈⠀⠂⡀⠀⠈⡀⠀⢀⠌⠁⠠⠌⡑⡌⠈⣷⢹⡀⣀⣤⢦⠶⠓⠙⠉⠀⠀⠀⠀⠎⣾⠀⠀⡀⠒⡀⢐⠀⠀⠀⠁⡾⣹⠀⠀⣿⠼⠀⣆⠸⠀⠀⠀⠀ ⠆⠙⠀⢳⠈⠀⡄⢤⢠⠀⡆⣹⠤⠂⡀⠀⠐⢂⠁⡀⠄⡁⠀⠐⢀⠠⠄⠂⢀⠂⠄⠀⠄⠈⠄⠀⠐⠡⢂⠁⢀⠈⡀⣀⠤⠒⠘⠉⠉⢀⠀⠀⠀⠀⠀⠠⠐⠀⠀⠁⠄⠀⠈⠐⠠⠄⠁⠢⠌⠡⣏⣿⣼⠶⠓⠉⠈⠀⡀⣀⣄⣤⠶⠓⢛⢸⠂⠄⢉⠡⢠⠀⠀⠁⠟⣼⠀⡆⢹⢻⣽⡾⠀⠇⢰⠀⠀⠀⠀ ⠀⡇⠘⠀⢿⣀⢦⠛⠝⢹⠀⣧⢻⠀⢁⡀⠐⠠⠐⡈⠄⠈⡁⠀⢂⡀⠐⢈⠂⢀⡁⠀⢈⠐⠂⢀⠈⠐⠂⠀⠠⠐⡈⠄⡈⠀⠁⠀⢀⡀⣐⠤⠤⠢⠄⠀⠄⡁⠀⠠⡀⠄⠀⠠⡁⠄⠂⠁⢌⠨⡗⣎⣷⠈⡄⢤⣲⣷⠿⠛⠙⠉⠀⠀⣇⣽⣧⣤⠘⠠⠀⠀⠋⡿⢹⠃⢰⠀⣧⣿⣾⢀⠁⣼⠀⠀⠀⠀⠀ ⠀⠀⢹⠀⡇⠈⠀⡀⢹⣾⠀⡆⣿⠡⠀⠠⠄⡀⠈⠐⠠⠐⠀⠐⠠⠄⠂⠀⠠⠄⠀⠠⠀⠌⠀⠠⠀⠡⠄⠀⠠⠄⠀⠄⠀⢀⠠⠄⠀⢡⠀⠠⠐⢈⠂⣀⠐⠠⡐⠇⢿⠹⠂⡀⠂⠁⠠⠂⠄⢁⡤⠐⣢⣿⠿⠛⠙⠈⠀⠃⣴⣿⣤⣤⣶⣶⠶⠲⠁⠉⠋⡿⣿⣿⣿⣿⠀⠀⡷⣾⢀⠃⣰⠉⠉⠉⠉⠀⠀ ⠀⠀⡄⠳⠈⢳⠀⠀⣆⣿⢷⠀⣇⣿⠐⠄⠀⢂⠄⠂⡁⠄⡈⠀⢀⡐⠌⠀⢂⡀⠄⠀⢀⠂⡀⠂⢀⠐⡀⠐⡀⠀⢁⡀⠐⠀⡐⠁⡀⠀⢣⠐⠄⠈⢂⠁⡠⠐⠄⡈⠀⣼⠘⢀⠄⠀⡐⠀⡐⠂⣀⡜⠊⣄⣷⡻⣈⣥⣦⣻⠟⢾⠻⠿⠛⠛⠛⠟⣫⣿⣿⣿⣿⣿⣿⢸⠀⠀⣿⢠⠃⣿⣾⢴⠤⠤⡤⣶⠐ ⠀⠀⠀⠀⣄⡹⢦⠛⠈⡆⡾⢠⠀⣧⢻⠚⠛⠘⢀⠠⠘⠡⠄⡈⠄⠂⠄⠀⠈⠄⠁⠠⡈⠀⠄⠈⠀⠡⠄⡁⠀⡈⠀⠁⡀⠈⠀⠈⠠⠄⠀⠁⠠⠂⠄⠈⠡⡀⠄⠈⠃⣿⠄⠂⡁⠀⠠⢈⠂⢀⠠⠐⢊⢄⠰⣌⣷⠰⠀⠀⠀⢂⢂⡅⠋⡰⡟⣿⣿⣿⣿⣿⣿⣿⣿⢸⠀⡇⣸⠏⣿⣸⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣄⠀⠀⢧⠈⣇⣼⢦⠾⣷⣹⣿⣶⢈⠡⠄⠂⠆⠀⡐⠁⢂⠀⠐⠂⠀⠐⠀⢀⠂⠀⠐⠂⠀⠂⠀⠁⡀⠀⠀⠐⠀⠐⠠⢀⠐⠠⠂⢀⠂⠄⠂⡁⠂⠁⡿⣂⠄⠀⠈⠐⢊⠀⠑⠠⡀⠐⠂⢁⡠⠔⡈⠠⠆⠴⠾⠷⣥⣦⣉⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⠀⣾⠏⣷⣾⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⢻⠃⠾⠙⣷⣟⠻⠄⠂⡁⠄⡈⡐⠆⠁⠠⡀⠌⠁⠀⠈⠠⢁⠀⠈⠠⠁⠄⠀⠈⠠⠀⡀⠀⠈⠁⠀⠡⢀⡁⠀⠠⢂⠀⢈⠐⠠⠃⡿⢰⢊⡠⠜⢃⡠⠜⢃⡠⠜⠣⡀⠌⠂⡁⠄⠀⢈⠀⠌⠀⠨⠑⢟⣿⣿⣟⢿⣿⣿⣿⣿⣿⣿⣿⠻⡗⣞⣠⡜⢸⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣧⠻⡉⠘⣦⣿⠰⢈⠐⠡⠄⡈⠐⠡⡐⠌⠀⠠⠁⠀⠐⠠⠀⠀⠐⠀⠂⠀⠀⠐⠂⠀⠀⠐⠀⠀⠐⠀⠠⠈⡐⠀⠠⠀⠁⠟⣼⢱⡌⠔⢂⡑⠩⢍⡉⠩⢍⡉⠩⢌⡐⠢⠁⠂⢀⠀⠄⠉⢛⠿⣿⣿⣿⣷⣿⣯⣿⣿⣿⣾⣽⣿⣿⣿⡿⢈⢉⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⣧⠻⠀⡀⠀⠠⠄⡈⠐⠨⠄⠐⢈⠀⠁⠀⠄⡀⠂⠀⡈⠀⢀⠈⠄⠀⠀⠈⠀⡀⠀⠀⢀⠀⠀⠀⠀⠋⠟⣼⣔⠭⠛⠿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠻⠟⠿⣿⣦⣞⡈⡵⣿⣿⣿⡇⣿⣿⣿⡷⣟⣿⣯⣿⣿⣿⣿⠓⢸⠀⡇⢻⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⢙⠈⠀⠀⠀⠄⠂⡁⠄⠈⠂⢀⠐⠂⢀⠂⠀⠄⠀⢀⠁⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠁⠋⠟⣴⣍⣛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠿⣉⠰⣿⣿⢣⡇⣿⣿⣯⣿⣳⢿⣷⣿⣿⣿⢀⣾⠀⠀⡗⣇⢻⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⡿⣿⣿⣿⢻⠚⠀⠀⠀⠀⠀⠀⠀⢀⠠⠄⠈⡐⠀⢈⠐⡁⠀⠠⠂⠀⠀⠂⠀⡀⠐⠁⠛⡷⣠⢥⠛⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣹⢢⡿⣿⣽⢿⣿⣿⣻⣿⣿⣿⢰⡇⢠⠀⠀⡏⡟⡖⠘⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⣿⣿⣿⣿⣿⣿⣿⠿⠙⠈⠀⠀⠀⠀⠀⠀⠠⠄⡈⠄⠂⡀⠐⠄⠂⠀⠠⢂⠀⡀⠀⠂⡁⢄⠋⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣽⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣉⠧⣿⢿⣿⣿⣷⣟⢾⣿⣿⣿⠸⣼⠀⠀⠀⡇⢸⠀⣷⠈⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⢿⠻⠙⠉⠉⠀⠀⢀⠈⢂⠄⠂⡀⠐⢈⠄⡈⠐⢁⠂⣉⠤⠋⡿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣷⣻⣿⣷⡿⣽⡿⣿⣟⣾⣽⡿⣿⣟⣿⣯⡿⣷⣟⣾⣿⣿⣿⣿⣽⠒⣿⣿⣿⣾⣻⣿⣳⣿⣷⣿⣿⢟⢠⠀⠀⠀⡿⢀⠈⡇⢻⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡇⣿⣾⣿⡿⣻⣿⣷⣽⡿⣾⣿⣿⣿⣿⣿⣿⣿⣿⢿⠿⠶⠞⠉⢀⡈⠐⠂⢀⠂⠔⡉⠤⠋⡿⣿⣿⣿⣿⣿⣿⣷⣟⣾⣽⣿⣿⣯⣟⣾⣻⣿⣽⡿⣿⣟⣿⣯⡿⣽⢿⣿⣯⣾⣻⣿⣽⢿⣾⣿⣿⡟⣿⣿⣿⣽⣿⣟⣾⣻⣿⣿⣿⣽⠀⠀⠀⡏⣰⢃⠄⡑⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⡇⣿⣷⣽⢿⣾⣻⣿⣻⣿⣷⣽⣻⣿⣽⣿⣿⣿⣿⣿⣿⣿⠿⠛⢍⡉⠢⢄⡘⢆⡁⠛⡿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣻⣿⣽⣿⡿⣽⣻⣿⣽⢿⣿⣯⡿⣽⢿⣾⢿⣿⣯⡿⣷⣽⣿⢾⣿⣻⣿⣷⣿⣿⣿⣿⣿⣿⣿⡿⣞⣿⢯⣿⣿⣿⠀⠀⠏⣱⣈⠱⣛⠶⣧⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢻⠀⡇⣻⣿⣯⣻⣿⣽⢿⣾⣻⣿⣻⣿⣽⡿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣟⡿⣷⣽⢿⣿⣻⢿⣾⣿⡿⣷⣯⢿⣿⣯⡿⣽⣿⣿⢯⣿⣯⣾⣻⣿⣷⣽⣻⣿⣾⣿⣿⣿⣿⣿⣿⣿⣟⣽⣿⣟⣿⣿⣿⠸⡟⣻⠞⡴⣠⠀⠁⣼⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠹⠀⣷⣿⣯⢿⣿⣯⣻⣿⣽⢿⣿⣯⡿⣷⡿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣟⣾⣻⣿⣷⣯⡿⣽⢿⣿⣷⣟⣾⣽⢿⣿⣯⢿⣿⣯⡿⣷⣟⣿⣯⣿⣟⣾⣻⣿⢷⣾⣿⣿⣎⣿⣿⡷⣿⣿⡿⣽⡿⣿⣿⣿⣿⣴⣀⠀⠀⠀⠁⡼⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠹⡀⣷⣿⣟⡿⣽⢿⣾⣽⣿⡿⣾⣻⣿⣽⡿⣿⢯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣻⣿⣷⣟⣾⣻⣿⣷⢯⣿⣽⡿⣷⣻⣿⣷⣯⡿⣽⢿⣿⣯⣻⣿⣽⡿⣽⢿⣾⣽⣿⣻⣿⣷⣿⣿⢈⣧⣿⣿⣿⣾⣿⡿⣿⣿⣿⣠⠀⠀⠀⠀⠀⠁⡼⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠳⡀⠳⡀⣦⣿⡿⣻⣿⣽⣿⣳⢿⣿⣯⢿⣿⣯⡿⣷⣟⡿⣽⣿⣿⣷⣿⣿⣿⣿⣾⣿⣿⣿⣽⣿⣾⣻⣿⣾⣻⣿⣷⣟⣾⣽⢿⣿⣯⣿⣳⣿⣷⣯⢿⣿⣯⡿⣷⢯⣿⣻⣿⣳⣿⣽⣿⣯⡿⣽⣿⣿⣿⢻⠃⣷⣿⣷⣯⣿⣿⣿⣾⢀⠀⠀⠀⠀⠀⠀⡞⢀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⠙⢦⠈⡄⣷⣿⡿⣷⣯⣾⢿⣾⣽⢿⣿⣟⣾⣿⣯⡿⣷⣯⣟⣾⣻⣿⣽⣻⣿⣷⣟⢾⣿⣻⣿⣽⢿⣾⣿⣟⣾⣻⣿⣷⣯⡿⣽⣻⣿⣷⣯⣿⣟⡾⣿⣟⣾⣽⢿⣾⣻⣿⣻⣿⣯⣟⣿⡷⣿⣿⣿⣿⢸⡀⣷⣿⣿⣿⣿⣾⢀⠀⠀⠀⠀⠀⠀⡏⢠⠀⠀⠀⠀⠀⠀⠀ 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