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⡏⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠘⣯⣼⣿⠟⣿⣿⠟⠁⣸⠁⠒⠠⢀⡀⠀⠠⠈⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⡧⠖⠒⠒⠁⠉⠁⠀⠀⢻⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣧⠀⣴⡇⠀⢰⠀⠀⠀⢀⠀⡜⠀⠀⠹⡏⢁⣴⠛⠁⠀⢠⠇⠀⠀⠀⠀⠀⠜⠁⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣧⢹⣒⣒⠶⠶⢦⡤⠝⠛⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢹⠞⢠⡁⠀⢷⠀⠀⢀⠎⠸⠀⠀⠀⢀⣴⠋⠁⠀⠀⢀⠏⠈⠉⠀⠀⢀⣀⠀⠤⠐⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠸⡇⠀⠈⠆⢀⠇⠀⠁⠀⣼⢠⡞⡁⠀⠀⠀⢀⠏⠀⠀⠀⠚⠛⠂⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣀⠀⠀⢀⣀⣀⣀⣀⠠⠄⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠹⡄⠀⠈⠚⠂⠀⠀⣴⣿⡎⠀⠀⠀⠀⠀⡞⠀⠀⠐⠒⠐⠀⠀⠀⠀⠈⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠙⢄⠀⠀⠀⠀⠀⡇⠈⠀⠀⠀⠀⠀⠈⢳⠀⠀⠀⠀⢀⠀⠀⠤⠄⠒⠂⠨⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⠢⢤⣀⡀⢳⢀⣀⣠⠤⠤⠤⠤⠬⡇⠒⠈⠉⠀⠀⠀⠀⠀⠀⢀⠀⠘⣆⢀⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⠤⠂⠈⠙⠁⡀⠄⢂⠐⡀⠆⠐⣻⠀⠀⢀⡀⠄⠐⠂⠉⢀⣀⣀⣠⣼⣦⣤⣂⠐⠐⡈⠐⢂⠁⠒⠠⢁⠂⠌⢉⠑⢦⠀⣠⠤⠴⠾⢲⠶⠶⠤⠤⢤⣀⣀⠒⠀⠤⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠳⠤⣌⣌⣠⠁⡐⠈⠄⢂⠐⡈⠄⣹⡖⠀⣀⣠⣦⣶⣿⣿⣭⣽⣶⣷⣽⣶⣬⣭⡳⣥⠀⠡⠀⠌⠠⢁⠂⠌⡀⠂⠌⢀⣾⣥⣶⣶⣿⣿⢿⡿⣿⣿⣿⣿⣮⣽⣿⣶⣄⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠌⠐⡀⢂⠐⠠⢈⣷⣿⣿⣿⣟⡿⣽⣻⣿⣟⡷⣯⣟⣿⣿⣟⣿⣿⠇⠠⢁⠈⡐⠠⠈⠄⠠⢁⠂⣼⣿⣯⣷⣻⣿⣽⢯⣟⣷⣿⣟⣾⣽⣻⣟⡿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⣌⡐⢀⠂⡈⠐⡀⠻⣿⣿⣿⣾⣿⣿⣽⣯⣿⣟⣷⣿⣾⣿⣿⣿⡿⠀⡁⠂⡐⠠⠁⠌⠠⠁⠂⠄⡈⢿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣾⣷⣿⣾⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⠒⠃⠐⠤⠀⠙⠛⠿⠿⣿⣿⣿⣿⠿⠿⠟⠛⢋⠉⡀⠄⢂⠐⠠⠐⠠⠁⠌⠠⠁⠌⠠⠐⡀⠈⠉⠛⠛⠟⠻⠟⠟⠻⠛⠛⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠒⠐⠒⠂⠂⠂⠑⠀⠃⠈⠀⠃⠈⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢸⠂⠀⠀⠀⠘⣧⠀⠀⣟⠛⠲⢤⡀⠀⠀⣰⠏⠀⠀⠀⠀⠀⢹⡀ ⠀⡿⠀⠀⠀⠀⠀⠈⢷⡀⢻⡀⠀⠀⠙⢦⣰⠏⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⡇⠀⠀⠀⠀⠀⠀⢀⣻⠞⠛⠀⠀⠀⠀⠻⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⡇⠀⠀⠀⠀⠀⠀⠛⠓⠒⠓⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀ ⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⢀⡟⠀ ⠀⠘⣇⠀⠘⣿⠋⢹⠛⣿⡇⠀⠀⠀⠀⣿⣿⡇⠀⢳⠉⠀⣠⡾⠁⠀ ⣦⣤⣽⣆⢀⡇⠀⢸⡇⣾⡇⠀⠀⠀⠀⣿⣿⡷⠀⢸⡇⠐⠛⠛⣿⠀ ⠹⣦⠀⠀⠸⡇⠀⠸⣿⡿⠁⢀⡀⠀⠀⠿⠿⠃⠀⢸⠇⠀⢀⡾⠁⠀ ⠀⠈⡿⢠⢶⣡⡄⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⣴⣧⠆⠀⢻⡄⠀⠀ ⠀⢸⠃⠀⠘⠉⠀⠀⠀⠠⣄⡴⠲⠶⠴⠃⠀⠀⠀⠉⡀⠀⠀⢻⡄⠀ ⠀⠘⠒⠒⠻⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠞⠛⠒⠛⠋⠁⠀ ⠀⠀⠀⠀⠀⠀⠸⣟⠓⠒⠂⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⣦⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣼⣃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⣹⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⢰⠙⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠸⢹⠰⡀⠀⠀⡃⠑⢾⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣀⡀⠀⡆⠇⠀⠛⣄⠀⣇⣰⡿⣧⣤⣤⣬⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢹⠀⠸⠐⣧⣈⢸⣄⢈⣷⣿⣿⢃⣿⣫⣴⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⡄⠐⡁⠈⢆⠈⠉⠻⣿⡿⡛⠉⣀⣤⣤⣤⣭⣿⡓⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⠀⠐⡆⠈⢳⣶⣶⢯⠊⣠⣾⣿⣿⣿⣿⡍⠉⠳⢄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢆⠀⠑⠀⡀⠙⡿⠁⣾⣿⣿⣿⣿⠝⠒⠢⢄⠀⠀⠑⢤⡀⠀⠀⠀ ⠀⠀⠀⠐⣤⣈⣦⣀⣀⠀⢀⡧⢤⣿⣿⣿⣿⣀⠄⠀⠀⠀⣣⣷⣦⡀⠈⠢⡀⠀ ⠀⠀⠀⠀⢣⡈⠙⢣⡀⢨⠃⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣶⣶⣿⡆ ⠀⠀⢀⣐⣶⣛⠯⠖⠳⢼⠀⠀⠀⠀⡜⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀ ⠀⠀⠹⣁⠀⠀⣈⣩⠥⠀⠳⣦⠀⠀⣳⡿⢿⣿⣿⣿⣮⡻⢿⣿⣿⣿⣿⡫⣺⠀ ⠀⠀⠀⢈⣻⢛⡳⠤⠤⡾⣟⣒⠛⠯⡽⣍⠐⢌⡉⠙⠛⠛⠳⠬⠟⠋⠐⢊⠍⠀ ⠀⠀⡠⢐⡗⢁⡾⠋⣉⣬⠖⠒⠲⡤⠌⣂⠥⢀⡈⢣⡈⠀⠀⠀⠐⠪⢽⣋⠒⢄ ⡠⠊⠀⠛⠲⣿⡃⠜⡯⣴⢺⡛⠲⣵⢄⡀⠨⠁⠒⠒⠈⠀⠀⠀⠀⣀⣀⣉⡹⠂ ⠀⠀⠀⠀⠀⠘⡿⠀⢀⢿⢸⡇⠀⠀⠑⠪⡍⠒⠂⠀⠀⠀⠀⣠⠤⠐⠒⢾⡿⡂
⠀⠀⠈⢶⡀⠀⠉⠓⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⢀⡴⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠲⣤⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢳⠀⠀⠀⠀⠈⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠉⡿⢀⡔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠖⠛⠋⠉⠉⠉⠉⠙⠒⠦⣄⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⣦⠀⠀⠀⠀⠀⠘⣿⠶⣄⡀⠀⠀⠀⣰⠏⠀⢸⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠀⠀⠀⢀⣀⡤⠤⣄⣀⣀⠀⣀⡈⠙⠶⣄⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠈⠳⣄⡉⠓⠦⣄⣇⠀⠀⠸⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠪⣝⡛⠛⢦⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠛⢦⡀⠀⠉⠙⠲⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡇⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢸⠀⠀⠀⠀⠀⠀⠀⠀ ⡀⠀⠀⠀⠀⠀⢳⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠀⠀⠀⠀⠀⠀⠀⠀ ⠳⡀⠀⠀⠀⠀⠈⢧⠀⠙⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣦⣄⣀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠀⠀⠰⡼⠀⠀⠀⠀⠀⠀⠀⠀ ⠦⣝⢦⡀⠀⠀⠀⠈⣷⣄⠈⠳⠄⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠿⠟⠋⠉⠁⠀⠀⠀⠙⢷⣤⣄⡘⢧⠀⠀⠐⣆⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠸⡇⠀⠀⣴⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⢦⡀⠉⠛⠒⠀⠀⠀⢻⡈⠳⣄⠀⠀⠀⠀⠀⠀⠀⣰⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠈⠙⢮⣇⠀⠀⢹⣄⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⢻⡀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠻⣦⣄⡀⠀⠀⠀⠀⠹⣄⠈⠳⢦⠀⠀⠀⠀⠘⠁⠀⣀⣤⣶⣶⣶⣶⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⡸⠙⢦⡀⠀⠀⢷⡀⠀⠀⠀⠀⠀⢳⡄⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠳⢭⣗⣲⠀⠀⠀⠘⢧⣀⠀⣀⣀⣀⠀⠀⣠⣾⣿⡿⠿⠛⠛⠿⢿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⣇⣠⠇⠀⠀⠙⠦⣀⠈⠳⡄⠀⠀⠀⠀⠀⠹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢦⡀⠀⣀⡼⠷⣬⣙⣀⣀⣠⠴⠛⠉⠉⠀⢸⣿⣿⣿⣿⡟⠀⠀⠀⠀⢀⣸⡏⠻⣿⡿⡄⠀⠀⠀⠀⠘⠋⠁⠀⠀⠀⠀⠀⠈⠙⠒⠿⢦⡀⠀⠀⠀⠀⠈⠧⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⣽⠛⢁⣠⣀⡈⢻⡽⠋⠀⣀⡤⠀⠀⠀⢤⡷⣿⡏⢸⠀⠀⠀⠀⠀⡟⠁⠙⠢⣿⡷⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⢠⡍⠲⢤⣀⠀⠀⠀⠈⢑⣶⠆⠀⠀⠀⠀ ⢼⠁⢠⠟⠀⠀⢩⠏⢀⡴⠋⠁⠀⠀⠀⠀⠀⠀⢻⡇⠸⡄⠀⠀⠀⠀⠳⣄⣠⠀⠁⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣿⣷⣴⡿⠁⠀⢦⡈⢻⡍⠉⠉⠉⠀⠀⠀⠀⠀⠀ ⣾⠀⢸⣄⡀⠀⣇⣰⠋⠀⠀⠀⠀⢀⠀⠀⠀⠀⠈⠿⣆⣙⣦⣄⣀⣀⡠⠞⠁⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠿⠛⠉⠙⠿⠯⠼⠀⠀⠀⠙⢦⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢿⠀⠘⣄⠉⠛⢻⠃⠀⠀⢀⡤⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠓⠦⠤⣀⡀⣰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠰⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠸⠦⣀⠀⠹⡆⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⢳⣄⠈⠓⠒⡇⠀⢀⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⣧⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠓⠢⠤⣇⣠⠎⠀⢠⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠲⠦⢤⣤⣤⡤⠞⠙⢧⠀⡄⠀⠀⠀⠀⠀⠀⠀⣹⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢺⡏⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡄⠀⠀⠀⠀⠀⠀⢳⣄⣰⠶⣄⠀⠀⡇⢠⢶⡾⠀⠈⢦⡀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⡇⢀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠾⣇⣀⣏⡿⠋⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢣⣸⡇⠀⢰⠏⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃⠀⠀⢀⣀⡤⡴⠧⢤⣀⣀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⠔⠚⠛⠚⢿⡇⠀⣼⠀⠀⠀⠀⠀⣰⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡼⣧⠔⣲⠒⠛⠓⠛⠳⠤⣀⡀⠉⠓⠢⢤⡏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣰⠊⣡⠤⠤⠤⢤⠀⢳⠀⡇⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠙⢷⡶⢤⣤⣤⡤⠶⠚⢉⣻⣽⡿⠯⠤⣤⣄⡀⠀⠀⠈⠙⠲⠀⠀⠀⠉⠲⣄⠀⠀⠀⠀⠀⠀ ⣰⠷⠋⠀⠀⠀⠀⠀⢀⣈⣷⣇⠀⠀⠀⢀⡏⣠⠶⠚⠉⠓⠲⢤⡀⠀⢀⡼⢳⡀⠀⠀⠙⢷⣠⠟⢷⠀⠸⣍⣨⡟⠀⠀⠀⠀⠀⠈⠙⠶⣄⡀⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠋⠀⠀⠀⠀⢀⡤⠞⠉⠁⠈⠹⣆⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⡭⠷⠊⠁⢈⡇⠀⠀⠀⠀⠉⠳⠦⣇⣀⣸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠀⠀⠀ ⠀⠀⠀⠀⣠⡟⠁⠀⠀⠀⡀⠀⠈⠧⣀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⢧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠿⠳⣿⠛⠓⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀ ⠀⠀⠀⠀⣿⠀⣠⠴⠒⡶⠃⠀⠀⠀⠈⠙⠒⠚⠃⠀⠀⠀⠀⠀⠀⠀⠐⠋⠀⠀⠈⠑⠲⢤⣀⡀⠀⠀⠀⢀⣸⣷⠒⠛⠀⠀⠀⠀⠉⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀ ⠀⠀⠀⠀⣿⡾⠁⢀⡾⠁⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠒⠚⢉⣥⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀ ⠀⠀⡠⠀⠉⠁⠀⣼⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠶⠤⠶⠖⠉⡽⠀⠀⠈⠙⠲⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⠇⠀⠀⠀⠀⢻⡀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠤⣀⣀⣴⠃⠀⠀⠀⠀⠀⠀⠀⠈⠛⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⡆⠀⠀⠀⠀⠀⠙⢦⡀⠈⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
pls note the ai inflicts emotional damage (ᵕ—ᴗ—)
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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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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣼⡿⠇⠘⣇⠀⢹⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⣶⡀⠀⢸⡇⣀⡤⠼⣤⡈⣯⡻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⠶⣶⢶⣶⣤⣤⣀⢻⣷⣄⠀⢿⣿⣀⣼⠋⠁⠀⣀⣤⣯⣿⣿⡝⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣺⣿⣿⠿⠟⣛⣛⣛⣛⣿⣿⣿⣿⣿⣿⣷⣼⣿⣿⠃⠀⣴⣾⣟⣩⣍⠙⡿⣿⣎⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣻⣭⣷⣾⣿⣿⣿⣿⢁⣤⡹⣷⠿⠿⠏⢹⣿⣾⣿⠃⣄⣾⢫⡍⢉⠛⣿⣿⣿⣿⣿⣎⣿⣦⠀⠀⠀⠀⢀⣀⠤⠒⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⠀⠀⠀⠀⠀⠀⠀⣠⠾⠛⠋⢉⣩⡽⣻⣽⣶⣶⣿⡿⣿⣗⣺⣾⣿⣟⣷⣾⣿⠏⢠⣿⣽⡇⠀⠀⠀⠹⢷⣮⡍⣿⢿⣿⣿⣧⡀⠀⠠⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⣀⣴⢟⣿⣾⡿⠘⠿⡋⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⢀⣿⡏⡙⠁⡀⠀⣀⠀⠀⠀⠀⢉⣯⢿⣿⣿⣷⡀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠳⢤⡀⢀⣠⣤⣴⠾⣋⣵⣿⣿⡻⠟⡀⢰⣷⣾⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⣼⣿⡃⢇⡀⡁⠀⠁⣀⡀⣤⠶⢾⣣⣾⡿⠋⢻⣧⢀⡀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣰⠃⠈⢿⣶⣾⣿⣿⡟⠿⢿⣷⣾⣷⣾⣟⣿⠟⠛⠻⣿⡿⣿⠋⠀⠀⠀⠛⠿⢶⣾⣧⣕⣶⣶⣿⣧⣴⠶⠟⠋⠁⠀⠀⠈⣿⢿⡇⠀⠀⠀⠀⡧⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡇⠀⠀⠀⠉⠛⠿⢿⣶⣶⣾⣿⣿⣟⣿⣿⠃⠀⠀⠀⢹⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠓⠦⣄⠀⣀⣤⡄⠀⠀⢠⡟⣿⡇⠀⠀⠀⢠⠇⠀⠀⠀⢀⠀⠀ ⠀⠀⡇⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣯⣾⣿⡏⠀⠀⠀⠀⣾⣿⣿⣿⠿⠛⠛⢲⣦⣤⣤⣤⣤⣤⣴⡶⠒⠚⠉⢉⣠⣤⣤⣄⡾⠀⢹⡇⠀⢀⡴⠋⠀⠀⠀⣰⣿⠀⠀ ⠀⠐⠁⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣀⣀⣤⣾⣿⣯⣷⠶⠞⠛⣻⣿⠟⣿⡛⡿⡿⣿⣿⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣆⠈⢿⣾⡏⠀⠀⢀⣤⣾⣿⣿⠀⠀ ⠀⠀⠀⠀⠀⠈⠓⠦⢤⣀⣀⠀⣀⣀⣠⠤⣶⣿⡿⣿⢿⣿⣿⣟⣻⣁⡄⠀⢠⣿⡏⢰⡏⠀⣷⣖⣿⣿⡀⠀⣰⣿⡿⣿⣿⣿⣿⣿⣿⡇⠈⣿⣷⣤⣶⠿⢛⣱⣿⠇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣉⣉⣭⣭⣶⣿⣿⣿⠇⢿⣎⠻⣿⣿⡗⢨⡇⣠⣿⠏⢀⣿⣷⣶⠟⠛⠛⠛⠓⢛⣉⣡⠾⠿⠿⣿⣿⣿⣿⡇⠀⣿⣿⣥⣴⣶⣿⣿⠋⠀⠀⠀ ⠀⠀⠀⣤⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣘⣸⣿⣷⣬⡛⠓⠚⠚⠋⣀⣴⣿⣿⠟⢳⣄⣀⣄⠀⠀⠀⠀⢀⣤⣤⣄⣀⣈⣭⣿⣧⠀⣸⣿⣿⣿⣿⣟⡁⠀⠀⠀⠀ ⠀⠀⠀⣿⣷⣯⣭⣽⠿⣿⣿⣿⠿⠟⡛⠛⠛⠛⠿⠿⠿⠿⣿⣿⣿⣿⡿⠿⠿⠛⠋⠁⢀⣴⣿⣿⣿⠀⠀⠀⠀⠈⠀⠀⠀⠉⠙⣻⣥⣰⣾⡿⣿⣿⣿⣭⣛⣿⣷⣶⣦⡄ ⠀⠀⣼⡿⣿⣿⣿⡇⠀⣿⡏⢁⣴⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣷⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃⣝⣿⣿⡿⠿⢿⣟⠿⣿⣿⣋⠉⠀ ⠀⢸⣟⢰⣿⣿⠿⢁⡼⠟⠀⠘⠛⠛⢋⣥⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⢋⣽⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢶⣿⣿⣿⣿⣿⢳⣶⣿⢷⣮⡙⢿⣷⡄ ⠀⠈⢿⣶⣬⣵⡶⠋⠀⢰⣿⣿⣿⡆⠘⠿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⣿⣟⣋⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⣠⡾⣿⣿⠿⠈⢻⠉⢶⣿⣻⣷⣝⢿ ⠀⣀⠀⠀⠀⢹⣿⣦⣤⣀⡀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠤⠶⢚⡫⠟⠉⠀⠀⠀⠀⠀⠀⢀⠉⠙⠲⣦⣤⣶⣿⡿⠿⣿⠉⠀⢀⣾⣶⣼⣿⣿⣿⣿⣿ ⠀⠈⠳⡄⠀⠀⠘⣽⡇⡈⠉⠛⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠛⠉⠉⠉⠁⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⢉⣩⠟⢿⣟⣘⣣⠀⢸⣿⣿⠿⣿⣿⣿⣛⠉⠀ ⠀⠀⠀⣷⠀⠀⠀⢸⣇⣵⠀⠀⠀⠀⢀⣠⣤⣖⣶⠭⠷⠖⠒⠚⠛⠻⣗⠒⠲⠤⣤⣀⡀⠀⠀⠐⠦⢤⣤⣤⣤⣴⡶⠚⠉⠀⠀⠀⠻⣾⣷⡐⣿⣿⣿⣷⣦⣌⠙⠻⢿⣦ ⠀⠀⣠⠃⠀⠀⠀⠈⠉⢩⡷⢦⣷⣶⣬⣿⣯⡅⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠈⠉⠓⠲⡶⠶⠶⣶⡞⠛⠁⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣯⣘⣿⣁⡸⣿⣿⣦⣀⠉ ⠀⠈⠁⠀⠀⠀⠀⠀⢠⠏⠀⠀⠉⠉⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢠⠞⠀⢀⡾⡑⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⢿⣿⠰⣾⣿⣿⣷ ⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠛⠀⠀⠀⠀⠀⠀⠁⠀⣠⡞⠁⢁⡴⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣏⠨⠅⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣟⣁⣤⡤⠀⠀⠀⢀⢀⣤⣴⣾⣭⡴⣾⢋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠈⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣀⢀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣴⠏⠁⠹⠿⣧⠀⣰⠋⠁⠉⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⡇⢻⢠⣯⠀⠀⠈⢂⢻⡐⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⠀⠀⢰⡗⠀⠀⣼⣁⣾⢸⡇⠀⠀⢀⣼⢨⡇⢀⣾⡴⠿⣯⠀⠀ ⠀⣴⠿⢛⡿⣦⡘⣧⡀⠀⡼⣳⡟⢸⣇⠀⢠⣈⠍⣹⣿⣾⠙⠀⢢⠹⣧⠀ ⠀⣿⠀⠀⠸⡮⢻⣎⠻⢷⡿⠋⠀⠀⠙⠳⢾⣿⠞⠁⣿⠁⠀⠀⠸⠃⣿⠀ ⢠⣿⡄⠀⠀⢸⠸⣏⠀⢀⣴⣾⡿⣿⣦⣤⣦⣤⣄⠀⢹⡆⠀⠀⠀⡆⣿⠄ ⠀⢿⣏⠁⠀⢸⣣⣿⢀⣿⠋⠀⠀⠀⠉⠉⠉⠉⠻⣷⠀⢿⡄⢀⡞⣠⡟⠀ ⠀⠐⢿⣯⣀⡾⠛⢃⣼⡏⠀⠀⠀⠀⠀⠈⡆⠀⠀⢿⣧⠸⠿⣿⠾⠋⠀⠀ ⠀⠀⠀⠈⠉⢣⣶⡿⠛⠀⠀⠀⠀⠀⠀⠀⠉⢶⣤⡈⢻⣧⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡽⢿⠁⢰⣿⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢻⣿⣶⣦⣄⡀⠀⠀⠀⠰⣿⣏⣤⣞⣀⣼⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⢿⣦⣄⣤⣴⡾⠛⠉⠟⠉⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠁⠀⠀⢀⣠⣴⢛⣉⣁⣀⣀⡤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣰⣶⣶⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣼⢿⣶⣾⡿⣻⣿⢟⣫⠽⠿⠟⠓⠒⠶⢤⣤⣄⣀⣤⣤⣄⣀⣤⣾⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢾⣿⠛⢿⣦⣀⣹⡿⠒⠶⠖⠒⠚⣿⣿⣿⣿⣿⣿⣿⣴⡟⠡⣶⣶⣶⣦⣬⣭⣅⣤⣶⡿⠋⠁⠀⠀⠈⢻⣿⣿⠋⠀⢸⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠘⣿⠀⠈⣿⣿⡏⠀⠀⠀⠀⢀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⣍⣉⠍⠙⢻⣯⣥⣤⣤⠀⠀⢀⣴⣾⣿⣃⠀⢀⣼⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⣷⢶⠽⠋⠁⠀⠀⢀⣴⣿⣿⣿⡟⣻⣿⣿⣿⢿⣿⡏⣁⠉⠉⠙⠿⢿⣏⠛⠻⢷⣄⡀⠤⠀⠁⢀⡴⠛⠫⢄⣼⠛⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠘⣿⣇⠀⠀⠀⠀⢠⣾⡿⢯⣼⢟⣿⣿⣿⣿⠇⣾⡎⣿⣿⣷⣴⣦⡀⠀⠙⢷⣄⠀⣀⣛⢦⣀⠀⡏⠉⣀⣠⡾⢻⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠹⣷⣿⣶⡀⢐⣿⠟⣠⣿⣿⡿⣽⣿⡿⣿⡆⢻⠀⢾⡟⢷⣝⢾⡝⠷⣤⡰⣿⣷⣍⠛⢿⡿⣦⣵⠸⡏⠁⢠⠞⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠨⣷⣾⣿⣾⣻⠎⡿⢠⡏⢰⣻⣿⡇⣿⡇⢸⡆⠘⣷⡀⠙⣷⡙⢧⡈⠻⣮⠳⣟⠃⠀⠙⢮⢻⣾⠷⣶⡒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣤⣼⡿⣁⡞⠀⡾⢰⢏⠏⣿⢰⠋⡃⠘⣇⠀⢹⢷⣄⠀⠙⢧⡝⣦⡀⠳⣌⢧⡀⠀⠸⣧⡻⣆⢸⡏⠓⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠤⠖⠉⢸⣟⣾⢻⡇⠀⢡⣯⠟⣼⢻⠸⡆⢣⡀⠙⠀⢸⣷⠙⢷⡤⡀⠹⣶⣝⢶⣌⣾⡷⡄⠀⢿⣷⡽⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣿⡼⠁⢸⡇⠀⣿⣟⡼⡁⢸⣷⣿⠀⠳⣄⠀⠈⣿⣆⠀⣙⣿⣅⠈⠿⣿⣾⣿⣷⠻⡀⠀⢿⣿⣾⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⠴⠋⣿⡇⠀⠸⡇⠰⢹⣿⣧⣤⣀⣿⡈⣧⠀⠈⠳⣄⢻⢹⡆⢨⣵⡿⢛⣻⣿⣿⣿⣿⠀⢱⠀⠘⢹⣿⣿⢬⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣼⡟⢧⠀⠀⢷⡀⢾⠟⠛⢿⣷⣿⣿⠿⣷⣄⠀⠀⠘⡇⠹⣬⣷⣿⣿⣿⡟⠁⣸⢿⠀⡾⠀⠀⣸⣿⣿⡄⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠇⣧⠘⣧⠀⠈⢧⡘⡿⣦⡀⠻⢿⣿⡿⠿⠌⠻⢦⡀⢻⡄⠙⠿⠟⢛⣛⣡⡴⠋⢸⣴⠃⢠⢠⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⢦⠈⢧⡀⠈⢳⡕⠈⠛⠲⠤⢤⣤⠀⢀⣀⠀⠉⣿⣧⡄⢈⣩⠭⠍⠁⠀⢀⣾⡿⠀⣠⣿⣿⣿⠻⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢸⠛⢦⠀⢹⣶⡀⣀⣠⣄⡈⠁⣍⣻⣷⣦⣾⡉⠰⢁⣠⠴⠋⠀⢒⢿⣷⣷⣾⣿⣿⣿⣿⠀⠀⠉⠓⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⣿⣦⣻⡿⠁⠀⠀⠈⠓⠼⣏⣁⣀⣸⡆⠀⠛⠁⠀⠀⠀⠀⠀⣿⣿⣿⡿⣿⣻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⢹⣿⣿⣿⣆⢀⡀⠀⠀⠀⠙⠛⠛⠉⠀⠀⠀⠀⠀⠈⠓⣦⣼⣿⣿⣿⣤⣾⣷⡹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⣧⣿⣿⣿⣿⣄⠀⠀⠀⢀⣀⣀⣀⣀⣀⠀⠀⠀⠀⣠⡿⣻⣿⣿⣿⣿⣿⣿⣿⣮⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣽⢹⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠈⠀⣀⡤⠞⡯⢀⣿⣹⡾⠻⢿⣿⣿⡁⢿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠋⣹⡏⠀⡙⢿⣿⣿⠉⢻⠹⡗⠦⣤⣀⡤⠶⠞⠉⠀⢸⡇⠘⢻⡏⣧⠀⠈⠻⣿⣇⢸⡟⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣀⣠⣤⣴⣾⠏⢯⠀⢠⣿⣷⠀⠙⠻⣿⣿⡇⢸⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⡾⠁⠀⢸⡇⣿⠀⠀⠀⠉⢻⣿⠃⠀⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣠⣴⣾⠿⣿⣿⡏⠹⣦⠘⣧⡈⠻⣿⣧⠀⠀⠻⢻⣷⣸⡇⠀⠹⡄⠀⠀⠀⠀⠀⠈⠁⣠⠤⡺⠁⡿⠀⠀⠀⣠⣼⠋⠀⣀⣿⡿⣧⡆⠀⠀⠀⠀⠀⠀⠀ ⢴⣿⣿⠟⢉⣿⣿⣿⠦⣌⡷⣾⣷⡀⠙⠻⣷⣄⠀⠙⢿⣿⢿⠀⠀⠀⠀⢠⠀⣀⡴⠞⠉⠀⣠⠇⡸⠃⢀⣴⠞⠉⠀⣀⣴⣿⠟⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⣠⢸⣿⣿⣿⠀⢈⠙⠛⠿⣷⣄⠀⠈⠛⠿⣦⣜⠿⣿⣇⠈⠙⠓⠚⠋⠁⠀⠀⠀⣰⣁⣼⡷⠞⢋⣀⣤⣶⠿⠛⢁⣠⡴⠾⠛⣻⣦⣀⠀⠀⠀⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⡀⠀⡀⠀⠀⠈⠛⢷⣦⣤⡄⣨⡙⢷⣽⣿⣇⠀⠀⠀⠀⢒⣶⣴⢿⠟⠋⢀⣠⣶⣿⣛⣯⣥⣶⣾⠟⠉⠀⠀⠀⣼⠿⣿⣷⣦⣄⠀⠀ ⠀⠈⠙⠻⣿⣿⣿⣿⣷⣀⡃⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣾⣿⣿⣿⣦⣤⢶⣛⣛⣁⣁⣠⣴⣶⣿⣿⠿⠛⠉⠉⣠⡾⠋⠀⠀⠀⠀⣼⣿⣴⣾⣿⣿⣿⣷⡄ ⠀⠀⠀⠀⠀⠉⠛⠿⣿⣽⣛⠿⢶⣤⣄⡀⠀⠀⠀⠀⡍⠐⠪⢹⠿⠿⢿⣿⣿⣿⣿⣿⣿⠿⠟⠋⠁⠀⠀⠀⣠⠟⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⡿⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⢶⣴⣭⡙⠳⠶⠦⡄⠀⠀⠀⠈⠁⠶⠆⠠⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⢷⣦⣤⣄⡀⠀⠀⠀⠉⠁⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢀⣀⣤⡾⠿⠿⠿⠿⠿⠟⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠉⠉⠛⠛⠲⢶⣤⣤⣤⣶⣶⠶⠒⠂⠒⠚⠋⠉⠙⠛⠛⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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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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⠀⠀⠀⠀⠀⠀⠘⣿⣿⡇⢰⣶⣦⡈⠻⣿⣷⣦⡀⠀⠀⣿⣿⣷⢸⡿⣿⣴⡿⠟⣿⣿⣧⣶⣿⠿⠟⠁⠀⢠⣿⣿⣤⣶⣿⣿⣿⣟⣧⣶⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⣾⠁⠙⣷⡀⠀⢙⢿⣿⣦⡀⣿⡟⢿⣾⠇⣿⠋⠀⠾⠛⠛⠛⠁⠀⠀⠀⠀⣰⣿⣿⠿⢋⣽⣾⣿⣿⡿⢟⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⠃⡇⢸⡦⣜⣿⡀⠀⠀⠙⣿⣿⣿⣿⡀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣫⣴⣶⣾⠟⠁⠀⠀⠀⠀⣀⡄ ⠀⠀⠀⠀⠀⠀⢀⣿⣿⣼⠁⠸⣷⡌⠹⣧⠀⠀⠀⠈⠻⣯⠻⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠴⠾⠿⠿⢿⣻⣿⡿⢛⣁⣀⣤⣤⣴⣾⣿⡿⠁ ⠀⠀⠀⠀⠀⠀⢸⣿⡟⡜⢲⣄⣙⣞⠀⢿⡆⠀⠀⠀⠀⠻⡆⠘⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠾⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⢉⣿⡿⠃⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠘⣿⣍⠉⠁⠘⣷⠀⠀⠀⠀⠀⢳⠀⠈⠻⢿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⣿⡿⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠹⣿⠷⠀⠀⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣻⣿⠋⠛⠋⢻⣷⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣞⣯⣿⣿⠟⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⣿⡄⣶⡶⠞⠛⠁⠀⠀⠻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠀⠀⠀⠀⠀⠹⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⣋⣿⣿⡟⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠸⣿⣿⡄⠈⠳⣤⣀⣀⡀⠀⠸⣾⣗⠀⠀⠀⠀⠀⠀⠀⣠⠟⠀⠀⠀⠀⠀⠀⠀⠈⠻⣝⣳⣤⣀⣀⡀⠀⢀⡠⢔⣛⣻⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣹⣿⣵⠀⢀⣈⡿⠷⣆⠈⠻⣯⣅⣀⡀⠀⣀⣤⠴⠚⠁⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠈⠉⠛⠻⢯⡛⠛⠛⠛⠛⠛⠻⣿⣏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⣷⣿⣷⣆⠈⢿⣄⡀⠹⣿⣶⣦⣬⣽⣷⠾⠋⠁⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣦⣰⠀⠀⢻⠀⠀⢀⣴⠾⢶⣹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡛⠆⠀⠻⣿⣿⣿⣿⣷⠦⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣭⣭⣽⣆⠀⠁⠀⠀⠈⠀⢸⣾⣏⡀⢨⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⠀⣿⣿⣿⣷⣄⡀⠈⣻⣿⣿⣶⡶⠴⠒⠀⠀⢀⠀⠀⠀⠀⠀⠛⣿⣿⣿⠹⣇⠀⠉⣿⡆⠀⠀⠀⠀⣠⣾⣿⢾⣷⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣿⣆⣿⣿⠈⢛⣿⣿⣿⠿⠛⣉⡄⠀⠀⠀⢀⣴⠏⠀⠀⠀⠀⠀⠸⠿⣿⣿⡟⣿⠀⠁⢸⠁⠀⠀⣠⠞⠙⢿⣿⡼⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⠀⠉⠻⠿⣷⣶⣿⠟⠁⠀⠀⠀⣼⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣇⡀⠀⣸⠀⣠⠞⠁⠀⠀⠘⢿⣷⣯⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⣿⠙⢿⣿⠀⠀⣠⣾⣿⣯⣥⠶⠒⠤⠀⠀⢹⣥⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠒⠂⠉⠭⠵⠾⣯⡀⠀⠀⠀⠀⠀⠉⠙⠿⣿⣿⣷⣦⣤⣄⣀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢹⣿⡆⠀⠘⠇⣰⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⣴⠋⢀⣠⣤⣤⣤⡀⠀⠀⠀⠙⠳⠦⣄⣀⡀⠀⠀⠀⠀⣼⣿⢿⣿⣿⣿⣿⣿⣶⣦⣄ ⠀⠀⢸⣷⣦⣄⣿⣿⡀⠀⢰⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⢸⠃⠀⢹⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠈⠉⠛⠛⠶⣾⣿⣿⢿⣿⣿⣾⣿⣿⣿⣿⣿ ⠀⠀⠀⢻⣿⠻⠿⠿⣧⣀⣿⣿⣶⣴⣾⣥⣴⣒⣛⣁⠀⠀⠀⠀⠻⣆⠀⠀⠀⣼⠀⠀⠈⢿⣿⣿⡟⢻⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⡿⣿⣿⣿⣿⣿⣿⡿ ⠀⠀⠀⠀⢻⣷⣄⠀⢀⡼⠛⠛⠉⣹⣿⡿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠙⢧⡀⠀⢹⠀⠀⠀⠘⣿⣿⣧⢸⡈⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⡿⠀ ⠀⠒⢶⣶⣶⣿⣿⠿⠶⠂⠀⢀⣴⣿⣷⠶⠶⣿⣷⣶⣮⣥⣤⣤⣤⠴⠆⠈⠂⠘⣆⠀⠀⠀⠈⠙⢿⣿⡟⠹⣽⢿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡿⢟⣽⣿⠁⠀ ⠸⣶⣶⣿⣿⣿⣷⣶⠶⠊⠁⠈⠁⠀⠀⣀⣤⣶⣿⣿⣷⡶⠞⠋⢁⣤⠞⠁⠀⠀⠹⡄⠀⠀⠀⠀⠀⠙⣿⣶⢻⠻⢼⡻⣿⣷⣶⣤⣤⣤⣤⣶⣾⣿⣿⣄⣠⣾⡿⠃⠀⠀ ⠀⠘⢿⣿⡭⢍⡁⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⣿⣿⣯⣥⣴⣶⣾⢟⣡⣤⣶⣶⣦⣤⣿⣀⡀⠀⠀⠀⠀⠈⠻⣿⣷⣄⠉⢹⣁⣽⡻⢿⣿⣯⣥⣤⡼⢙⡿⠿⠛⠁⠀⠀⠀ ⠀⠀⠈⣻⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⣿⣿⡿⠟⠋⠉⣠⡿⠙⠛⠿⣿⣿⣷⣤⣄⡀⠀⠈⠻⣿⣦⣀⡵⢺⣍⠠⠝⢿⡿⣿⠻⠞⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠹⣿⣿⣿⣿⣶⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠋⠀⠀⠐⢻⣿⡀⠀⠀⠀⠀⠉⠛⠿⣿⣷⣤⣀⠀⠈⠛⠿⣷⣾⣽⣝⣓⣚⣷⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠻⣿⣦⣉⣉⣉⣉⠂⠄⠀⠀⠀⢀⣀⣴⡾⠁⠀⠀⠀⠀⢀⡞⠈⠹⣦⡀⠀⠀⠀⠀⢰⣿⡟⢿⣿⣷⣦⣀⠀⠀⠈⢉⣉⣉⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣀⣴⣾⣿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠈⢷⡀⠀⠀⢠⣿⣿⣇⠀⠈⠙⠿⢿⣿⣶⣶⣶⣿⡿⠟⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣠⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠙⠛⠻⢷⣤⡀⠀⠀⠀⠟⢸⠀⠀⠀⠈⢷⡀⠀⠸⣿⢿⣿⣷⣤⣤⣶⣾⡿⣿⣿⡏⢀⣤⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣶⡀⠀⠀⠸⡆⠀⠀⠀⠈⣧⠀⠀⢻⡄⠉⠉⠙⠛⠉⢉⣴⣿⣯⣶⡿⢫⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡄⠀⠀⢿⡄⣆⠀⠀⠸⣆⠀⠀⠓⠀⠀⠀⠀⠒⠛⠉⠉⠉⠁⣠⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡆⠀⠈⢧⢹⡄⠀⠀⠹⡆⠀⠈⠙⢦⣀⡀⠀⠀⠤⣤⣶⣾⣿⣯⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠸⠘⣦⠀⠀⠹⣆⠀⠉⠓⠦⣉⠙⠋⠘⠳⣶⣶⣿⣿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣀⣠⠄⢂⣀⣤⠤⠖⠚⠉⠀⠀⠀⣀⣀⡤⠄⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠄⠀⠈⠳⠄⠀⠀⠀⠦⠤⣤⣀⠀⢙⣻⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀
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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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⢰⣶⠒⢲⣶⣶⣶⣶⣾⣷⣿⣷⣿⣾⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⢾⣿⣿⣷⣾⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡓⠲⢶⣶⣶⣶⣶⣶⣶⣶⡖⣤⡤⠀⠀⠀⠀ ⢸⣧⠀⠀⢈⣿⣿⣟⢿⡿⣿⣿⡋⢙⣿⣷⣌⢿⣿⣿⣿⣿⣿⣟⣚⣿⣿⣿⣁⡀⠙⠃⠀⢸⣿⣷⡬⣟⢿⣿⣿⣿⣿⣿⣼⣿⣿⣿⠇⠀⠀⠀⠉⢛⣿⣿⣿⣿⡇⠖⠁⠀⠀⠀⠀ ⢸⣿⣷⣿⣿⣿⣿⡏⠀⠀⣹⣿⣿⣿⣿⣿⣿⡟⠻⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣄⣀⡀⠰⣪⣿⣿⣿⡍⡻⣿⣿⣿⣿⣽⣿⣿⣿⣿⣀⠀⠀⠀⣴⣿⣿⣿⣿⣻⣿⡤⠅⠀⠀⠀⠀ ⢸⣿⣿⠻⣟⣿⣿⣿⢛⣿⣿⠿⣿⣿⣿⡟⣷⣷⡄⠀⠙⠓⠯⠿⠿⣛⣿⣿⣿⣿⣛⣻⣿⣿⣿⣿⣿⣿⡶⡘⡎⢿⣿⢽⡾⣿⣿⣿⣿⣿⡶⠾⣿⣿⣿⣿⣿⠉⢈⣿⣾⣾⣶⡄⠀ ⢸⣿⣿⠀⢿⣿⣿⣿⣿⣷⠟⢛⣛⡻⣭⣿⣻⡳⠿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣽⣇⠀⠀⣿⣾⢸⣿⣿⣿⣿⣿⣷⣰⣿⣿⣿⣿⣿⡻⠟⢛⣿⢿⣟⢿⣦ ⢸⣿⣭⡀⢠⣽⣿⣿⣯⣏⣎⣠⣬⣝⡚⠻⣌⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣾⡄⠀⡽⠁⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⢀⣿⣷⣌⢿⣷⠻ ⢸⣿⣿⡇⣿⣿⡟⣿⣿⣿⣏⣶⣶⣮⠷⠶⠛⠋⠉⠉⠛⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⠾⠼⠿⢟⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⣼⣟⣽⣍⢻⣿⣃ ⢸⣿⣿⣿⠻⣿⣿⡏⣷⡦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⣰⢏⣾⣻⢿⣇⢻⣿ ⢸⣿⣿⣿⣼⣿⣿⣿⢡⠙⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢫⡿⣳⣿⣧⢿⡌⣿ ⢸⣿⣿⣿⣿⣿⣻⠿⠚⠋⠉⠙⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡄⠀⠀⠀⠀⠀⠀⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢾⣧⡿⣱⠟⡜⣿⣸⣇⢻ ⢸⣿⡿⣿⠟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢫⣧⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡽⡏⢼⣧⣿⣿⣿⢸ ⢰⣿⣯⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢞⣯⠟⠸⡄⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡴⣀⠋⣿⢻⡇⢸ ⢸⣽⢆⠙⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠟⣁⣜⠥⢴⡾⠿⡄⠀⡀⠰⣤⣏⣧⠀⠀⡀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡘⠝⣿⢸⡇⣾ ⢸⣿⣿⣗⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣖⣋⡡⠴⠚⠉⠀⠀⠹⣄⠸⡄⢻⠷⣝⣟⠷⢦⣀⢀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠁⡟⢀⣿ ⢸⣿⣿⣿⣷⣿⣽⣖⣦⣤⣤⣤⡤⠀⣀⣴⣿⣋⣭⣿⣿⠉⢤⣤⣤⡀⢲⡄⠀⣰⠙⢦⣻⣼⠀⠈⠙⣶⠲⢮⣽⣷⣼⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⣜⡏ ⢸⣿⣿⡻⣯⣷⣶⠂⠈⠉⠙⢳⣶⣶⣿⣿⣻⣿⣿⣿⣿⣽⣿⣶⣄⣸⡦⡀⢰⡏⠀⠀⠙⢿⣶⠂⠈⣟⣳⣶⣷⣿⣬⣿⣟⢷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣌⢌⣾ ⢸⣿⣿⣷⣾⣿⣾⠏⠙⠻⠶⢦⣽⣿⣿⣿⡏⠁⠘⢿⢿⡟⠛⠛⢿⡛⠃⠙⡼⠁⠀⠀⠀⢈⣻⣶⣿⣿⣷⣾⣿⣿⣹⣿⣿⣿⣿⣦⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿ ⢸⡿⢻⠛⡻⠋⠀⠀⠀⠀⠀⢀⡾⠁⣿⢹⣿⡀⠀⠈⠻⣄⣀⡤⢾⣟⢛⣛⣷⣤⠀⠀⠀⠀⠀⡟⠉⠀⠈⢁⣹⠋⠀⠈⣿⣿⣽⣿⣿⣁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣇⠃⡼⠁⡀⠀⠀⠀⠠⢠⣾⠁⠀⢸⠸⣿⣿⣷⣶⠿⠛⠉⠀⠈⠛⣿⠟⠛⠻⢦⣄⡀⠀⠀⠛⠷⣤⣤⠟⠁⠀⠀⣴⠿⠟⠋⠁⠉⠻⣄⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⣀ ⢸⣿⣼⣵⡞⠁⠀⠀⠀⠀⣾⠇⠀⠀⣼⠀⠘⠛⠛⠁⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠈⠉⠓⠦⣄⡀⠈⠹⣿⣶⣶⣾⣿⡆⠀⠀⠀⢸⡀⠹⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣽⣿⣿ ⢸⣿⡿⣽⠁⠀⠀⠀⣠⣞⣩⣤⡄⠀⢹⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⣤⠾⠶⢤⡀⠀⠀⠀⠀⠀⠀⠉⢳⠶⣤⣘⠳⠟⠿⠇⠄⠀⠀⠘⠃⠀⣿⣧⣀⡀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿ ⢸⣿⣿⣝⣿⡶⣶⠿⠛⠋⠉⠩⠀⠀⢸⠀⠀⠐⠗⠀⣀⣀⣀⠴⢋⣀⣀⣀⣀⡈⠲⣄⠀⠀⠀⠀⠀⠘⠀⠀⠸⠛⠶⢤⣄⡀⠀⠀⢀⠀⣸⡏⡟⠛⠿⢷⣶⣦⣠⠀⠀⠀⠀⢙⣮ ⢸⣿⣿⣿⡟⡾⠃⠀⠀⣀⣀⣴⣿⠷⠾⣄⡀⠀⠀⠀⠈⠹⣄⣸⣿⣿⣿⣿⣿⣿⣷⠀⢙⡦⣄⣠⠴⠁⠀⠀⠀⠀⠀⠀⡞⠙⠓⠦⡾⢀⣿⡷⣇⠀⠀⠀⠈⠙⡿⢿⣷⣤⡀⣬⣿ ⢸⣿⡿⣿⢱⠁⣠⡾⠉⠉⠉⠉⠁⠀⠀⣇⢷⡄⠀⠀⠀⠀⢻⣯⣿⣿⡿⣿⢿⣿⣿⣠⣾⡤⣤⠏⠀⠀⠀⠀⠀⠀⠀⣾⢧⠀⠀⢰⠃⣸⠟⠀⠹⣷⣄⠀⢰⡾⠃⠀⠈⢙⣇⡟⣿ ⢸⣯⠀⣿⢸⣴⣿⠁⠀⠀⠀⠀⠀⠀⠀⠸⣤⡇⠀⠀⠀⠀⠈⣿⣿⠿⢺⡿⠶⢿⣿⣿⣿⣷⠏⠀⠀⠀⠀⠀⠀⠀⢰⣿⠏⠳⠤⠬⠞⠁⠘⣧⡀⠈⢻⣷⡌⠀⠀⠀⠀⠈⣿⡇⠙ ⣼⠛⢾⢿⢸⣏⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⠀⠀⠀⠀⣿⢻⣄⠈⢁⣴⣦⣹⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣶⡀⠀⠀⠀⠀⠀⠘⢷⡀⠀⠙⢿⣆⠀⠀⢀⣷⡟⠀⠈ ⠹⣤⡌⣶⣬⠞⠙⠧⣀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣧⡀⠀⠀⠀⠘⢧⣙⣒⣛⣛⡼⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡳⢤⣀⣀⠀⠀⠀⠀⠈⢷⡄⠀⢰⠹⠀⣠⣟⣟⣶⡆⡲ ⠀⠘⠻⣿⣿⡀⠀⠀⠈⠙⠲⢄⣰⡀⠀⣀⡴⠋⠁⠙⢦⡀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⠟⠋⢀⣽⣿⡟⠉⠀⢀⣠⡤⠤⠶⠴⠾⠛⠛⢻⣭⣟⠗ ⠀⢀⡔⠙⣷⣿⣒⣦⣄⠀⠀⠀⣻⣿⡞⠋⢴⣄⣀⠀⠈⣿⣄⡀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡿⠟⣻⠃⢀⡴⠋⢸⣿⡴⣠⣴⢟⣥⡄⠀⠀⠀⠀⠀⠀⠀⢻⠈⠐ ⢰⡟⠁⠀⢈⣿⣿⡟⣼⡦⣤⣔⣿⣿⣝⣦⡈⢿⣿⣿⣿⠟⠿⢷⣦⣄⠀⠀⠀⠀⠀⢀⣀⣤⣤⣶⡾⠛⠋⡥⢂⣴⠓⠀⠉⠀⠀⠸⣿⣿⣿⠃⡟⣰⠇⠀⠀⠀⠀⠀⠀⠈⠘⡂⢰ ⢸⣷⣶⣾⣷⣿⢿⡧⣽⣿⣿⠯⠿⠿⠿⠿⠿⠶⣽⣿⣿⣆⠀⣀⣳⣿⣿⣯⣽⣿⣿⣿⠿⠟⠉⠀⢀⡴⠊⣤⡞⠁⠀⠀⠀⠀⠀⠀⠿⣿⣯⣠⠾⡏⠀⠀⠀⠀⠀⠀⠀⠀⢘⠃⠀ ⢸⣿⣿⣿⣿⣿⡿⣿⣿⣥⣤⣤⣤⣀⣀⡀⠀⠀⠀⠈⢹⠻⢌⣿⣿⣿⣬⠷⠿⠛⠉⠀⠀⢀⣠⠞⠉⣠⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣼⡃⠀⠀⠀⠀⠀⠀⠠⠤⢺⠀⠀ ⢸⢿⣞⣋⠟⣡⡟⠁⠀⣆⣀⢠⣀⣈⣙⠛⠶⣶⣖⡒⠚⠛⠛⠛⠿⣿⣆⠀⠀⠀⢀⣀⠒⠋⠀⢀⣾⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢀⣰⣃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠁

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⠀⠀⠱⡀⠈⠙⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡄⠀⡠⠖⠉⠁⠀⠀⠀⠀⠀⠀⠉⠲⣎⣀⣀⣀⣀⡀⠀⠀⠀⠀⠹⡄⠀⠀⠀ ⠀⠀⠀⠹⡀⠀⠀⠈⠱⣤⣀⠀⠀⠀⠀⡰⠋⢰⢡⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠉⠁⠀⠀⠀⠀⠀⠉⠒⢤⡀⠀⡇⠀⠀⠀ ⠀⠀⠀⠀⢣⠀⠀⠀⠀⠈⠮⡑⠢⢄⣘⠁⠀⠼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠉⠉⠓⠒⠷⣒⠺⢦⡇⠀⠀⠀ ⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠈⠲⠄⠀⠉⠒⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢤⠇⠀⠀⠀ ⠀⠀⠀⠀⢸⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀ ⠀⠀⠀⠀⠸⡄⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠀⠀⠀ ⠣⡀⠀⠀⠀⠱⡀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⡿⠶⢄⣀⠀⠑⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⠀⠀⡎⠀⠀⠀ ⡑⠻⢦⣀⠀⠀⢿⢦⡈⠁⠀⠀⠀⠀⠀⣠⡴⠟⠋⠁⠀⠀⠀⠀⠘⢷⠢⣌⣆⠀⠐⡆⠀⠀⠀⡆⠀⠀⠀⠈⡇⠀⢰⠃⠀⠀⠀ ⠙⣦⣀⠀⠀⠀⠈⢆⠙⠢⣀⠀⠀⠀⠔⠁⠀⣠⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠹⡄⠀⡟⢦⠀⠀⢰⠀⠀⠀⠀⠘⣄⡸⠀⠀⠀⠀ ⠀⠈⠙⢿⣶⣄⠀⠀⠳⣄⣀⣀⣤⡀⢀⣴⣿⠿⠛⠛⠻⣿⣿⣦⡀⠀⠀⠀⠀⣧⡰⠁⠀⠑⠦⣀⠳⡀⠀⠀⠀⠈⢷⡀⠀⠀⠀ ⠳⣤⡴⠚⠓⢦⢤⡤⠒⠉⠀⠀⠘⣿⣿⠿⡏⠀⠀⠀⣤⠾⣜⣿⣳⡄⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠉⠛⠢⣀⠀⠀⠀⠑⢤⣀⡀ ⣰⠃⡰⠚⠒⡾⢉⡠⠖⠋⠀⠀⠈⠉⣿⠀⡇⠀⠀⠀⢇⡀⠈⢹⠉⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣄⣠⡖⠈⣙⠲⡆⠀⠐⠛⠁ ⡇⠀⣅⡀⢰⣥⠊⠀⠀⠀⡀⠀⠀⠀⠘⢦⣙⣦⣀⣀⡴⠋⠀⢸⠀⠀⠀⠀⠀⠀⠀⢰⣿⠟⠛⠛⠻⠯⠆⠀⠈⠳⣷⠀⠀⠀⠀ ⢣⡀⠣⣈⣉⠇⠀⣀⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠲⠤⣼⡀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠈⠓⢄⠈⡆⠀⠀⠀ ⠀⠙⠦⣄⣸⠀⡴⠁⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠀⠀⣠⠤⣄⣀⣀⣀⡤⢤⡀⠀⠀⠀⠀⠀⠀⠳⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⡟⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠀⠀⠀⠀⠀⠯⣠⡤⢄⠉⢣⢠⣶⠃⠙⢆⠀⠀⠀⠀⠀⢣⠀⠀⠀ ⠀⠀⠀⠀⠀⢇⢠⠃⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣅⠀⠀⠀⠀⠀⠀⠀⠉⠙⢦⡮⠟⠁⠀⠀⢸⠀⠀⠀⠀⠀⢸⠀⠀⠀ ⠀⠀⠀⡠⠤⠬⣾⠀⢠⠃⠀⠀⠀⢠⠆⠀⠀⠀⠀⠀⠀⠙⢆⠀⠀⠀⠀⠀⠀⠀⢀⣼⣁⣠⠤⠶⠾⢏⡉⠒⠢⢄⣀⡜⠀⠀⠀ ⠀⡔⣋⠤⠤⠤⠈⣇⢸⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⡀⠈⠙⢶⠤⠀⣤⠤⠖⢛⣿⡿⠯⠤⣀⣀⠀⠈⠑⠢⠀⠈⠑⢦⡀⠀ ⡼⠋⠁⠀⠀⢀⣠⠼⢾⡀⠀⠀⣾⠴⠊⠉⠉⠒⠤⣀⣠⠋⡆⠀⠀⠙⢶⡛⣆⠘⢧⠟⠀⠀⠀⠀⠈⠙⠲⢤⠀⠀⠀⠀⠀⠙⢆ ⠀⠀⠀⢀⡴⠉⠀⠀⠀⠱⣄⠀⠸⡄⠀⠀⠀⠀⠈⠉⠀⢀⣏⠀⠀⠀⠀⠈⠙⠒⠚⣲⣤⡤⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡿⢀⡠⢤⡾⠀⠀⠈⠓⠢⠼⠀⠀⠀⠀⠀⠀⠰⠊⠀⠙⠲⠄⣀⠀⠀⠀⢀⣷⡤⠃⠀⠀⠉⠒⠤⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⠏⠀⡞⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠉⢉⣡⡄⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⡀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⠉⠉⢠⠃⠀⠀⠈⠉⠒⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠳⣄⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠧⣀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⠠⠄⡀⠀⠀⠀⠀⠀⣀⣒⡤⠤⠂⣁⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⡀⢤⠀⡠⠙⡹⠁⠀⡞⠀⠀⠀⠀⠀⢀⡆⠈⠓⢌⠑⠢⣀⡈⡁⠒⠀⠄⡀⠀⠈ ⠀⠠⠺⠁⢰⠃⠀⠠⠁⠀⠀⠀⠀⠀⢸⢰⣀⠠⠀⠱⣄⠈⢗⠨⡉⠲⢂⠠⢁⠂ ⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⢿⢸⠈⠣⠱⠀⠐⢂⠀⢡⠀⠀⡀⠑⢄⠈ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢸⠀⠀⢣⢡⡀⠀⡆⠀⠆⠄⠘⣆⠀⠑ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢗⡒⠒⠂⢓⠛⡉⠹⡄⢰⡸⡄⠘⡿⡀ ⠑⠃⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠶⢾⠀⣳⣒⣒⣾⣂⠒⢠⡱⢸⢡⢯⣆⢠⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡄⠌⢉⣠⡤⠶⢺⣾⣻⢿⣿⡉⠋⢠⠃⢸⢾⣼⣢⣉⡄⠀ ⠀⢀⣴⡤⠀⡣⠀⠀⣇⠰⠀⠁⠀⢠⠈⠺⡈⡉⠀⣠⢀⣠⠨⣃⢌⢯⢹⠉⢢⠀ ⠀⠸⡿⢿⢰⠁⡆⢠⠛⡄⢃⠀⠀⠀⡰⢤⠞⠣⣀⠔⠁⣁⣎⢔⠕⢉⢼⠆⠈⠀ ⠀⠀⡀⣸⣁⣼⡇⢸⠀⠘⡄⢆⡀⠀⢹⠈⢓⠪⠀⠉⠻⠋⠔⢑⢕⠕⡉⣧⠀⠀ ⠄⠠⠚⣾⣿⣧⠇⢸⠜⢄⡰⠘⠳⡄⠀⠣⡙⢆⠀⠀⠀⠀⠀⣠⣵⣶⠀⣟⡳⠄ ⢀⠀⡈⡏⠏⠸⡇⡌⣸⣶⣦⣇⢣⡙⢦⠀⠀⠀⠉⠂⢄⠀⣜⡿⠿⠧⠰⣬⣷⣉ ⠸⣤⢡⡧⣀⣺⡇⢣⢿⡟⣏⣿⢎⣿⠦⠝⣦⡀⠀⠀⠀⠑⢿⣎⠐⢲⣤⡈⠘⣧ ⠀⠁⠆⠁⢱⠻⡇⢸⢸⡇⠏⢻⠈⣿⠀⠲⢹⡻⣦⣀⠀⠀⠀⢩⣣⣚⡉⠁⠀⢸

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