⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠓⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠓⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠢⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠒⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣀⠀⠈⠙⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣀⠀⠉⡇⠀⠀⠈⠉⠲⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠳⠃⠀⡏⠉⠳⢄⣀⡀⠈⠙⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⢁⡶⡀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠉⠑⠒⠦⣄⡀⠈⠉⠓⣼⠀⠀⠀⠀⡤⣄⡀⠈⠉⠓⠦⣄⡀⣴⡗⢫⣁⡴⠁⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣄⡀⠀⠀⠀⠀⠀⠈⠙⠲⢄⡀⠀⠀⠛⠦⣄⣀⠀⡏⠀⠀⠀⡇⠹⠞⠁⢀⡤⠎⠀⠈⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠙⠢⣄⡀⠀⠀⠀⠀⠀⠈⠑⠒⠄⣀⠀⠈⠁⠀⠀⠀⡇⣀⡴⠃⠁⠀⠀⣠⠎⠁⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠓⠢⢤⡀⠀⠀⠀⠀⠀⠈⠑⠢⢄⡀⠀⠙⠓⢶⠒⠤⠤⢼⠁⡴⢤⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠂⠤⣄⡀⠀⠀⠀⠈⠓⢦⣸⠀⣀⡀⠀⡇⠉⢁⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣄⣀⠀⢸⠀⠉⠉⠀⡇⣰⠃⠀⢈⠷⠯⣄⡔⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠉⢯⡁⠀⠀⣠⠞⠁⢀⡎⠀⠀⣨⠏⠒⢢⢆⡁⠀⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡽⠓⠦⣄⣐⠁⠀⢀⡞⠀⠀⡴⠃⠀⠀⡞⠉⠙⢲⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠀⠈⡳⢯⣀⡴⠋⠀⠀⠀⡎⠀⠀⡰⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠉⠲⠄⣔⠁⢠⠎⠀⠀⢀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠰⠃⠈⠉⣒⠮

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣋⣤⠤⠶⣏⢀⡀⠀⠀⣀⣤⡴⠶⠛⠙⠛⠛⠛⠿⢶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⠿⠛⠋⠁⠀⢀⣀⣈⣩⣭⣿⡟⠉⠉⢻⣦⠤⠤⢤⣄⣀⡀⠀⠀⠉⠛⠿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⠟⠋⠀⢀⣠⠶⠒⢋⣉⡥⠤⠴⠶⠬⡇⠀⠀⢸⡇⠒⠦⠤⢤⣈⡉⠓⠶⢤⣀⠀⠈⠙⠿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠋⠁⣀⡴⠚⢉⠤⢒⡪⠉⢡⡴⠒⢒⣤⣿⡇⠀⠀⢸⣷⣦⣄⠀⠀⠀⠉⠙⠲⢤⣈⠙⠲⢤⣀⠈⠛⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠋⠀⢠⡞⠁⣠⣾⠵⠋⠁⠀⠀⠀⢻⣾⡿⢿⣠⣧⡤⣤⣼⣧⡿⢿⣧⡀⠀⠀⠀⠀⠀⠈⠙⢦⡀⠉⠳⣦⡀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠒⠂⢀⣀⡤⢤⣄⠀⣴⠚⢿⡏⠀⢀⡴⠋⣠⡾⠟⠁⠀⠀⠀⠀⠀⢠⣿⣫⡴⠛⠁⠀⠀⠀⠀⠉⠛⢦⣽⣿⡄⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⠈⠻⣤⡀⠻⣷⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⡟⢸⡏⠀⢀⣿⠶⠏⢀⣼⡃⣠⠏⠠⣸⠋⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠗⢦⠘⢿⣦⡈⢻⣦⠀⠀⠀⠀⠀⠀ ⠀⢂⠈⣿⡄⠈⠁⠀⠀⠀⢸⡿⠳⣦⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⢰⠟⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⢻⡄⠀⠀⠀⠀⢀⡴⠲⣦⣽⠂⠸⣧⣤⣿⡓⣄⠙⣷⡀⠀⠀⠀⠀ ⠀⢨⠀⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⡶⢦⣄⣀⠀⠀⠀⠀⢀⡟⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⢷⠀⠀⠀⠀⠸⣄⠀⠛⠀⠀⠀⠉⠁⠀⣳⢸⡇⠈⢷⡄⠀⠀⠀ ⡀⢤⢦⣻⣦⣀⡀⠀⠀⠀⢠⣴⣾⢏⡐⠉⠲⣮⣝⣿⠶⣤⣀⣸⠁⠀⢹⡄⠀⠀⠀⣴⣺⣶⡷⠀⠀⠀⢠⡟⠀⢸⡆⠀⠀⠀⠀⢹⣇⠀⠀⠀⠀⠀⠀⣴⠻⡈⢳⣤⡈⢻⣄⠀⠀ ⡇⠅⠸⠡⠈⣿⠁⠀⠀⣠⣰⣿⠋⡦⠄⣾⣿⣿⢯⣹⠷⠆⠈⢻⡄⠀⠀⢻⣦⡀⠀⢻⡍⣭⠃⠀⢀⣴⠏⠀⠀⢠⡇⠀⠀⠀⠀⠀⠻⣄⣀⡀⠀⠀⢀⣸⠆⠙⣆⠹⣷⡄⠹⣄⠀ ⡇⠖⠰⠆⣰⢻⣷⣶⡞⢹⣿⠁⠀⡁⢐⠁⣛⣚⣒⣛⣒⣁⣀⣈⣿⣦⢤⣄⠙⠻⡷⢾⠀⠈⣶⣾⠟⠁⣠⡤⣤⡞⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⣀⣴⠟⠁⠀⠀⠈⢧⠙⡿⡄⠹⡄ ⠀⠀⠀⢠⡇⣸⣿⠛⠛⢻⣧⣿⠛⠛⣿⡟⠛⠛⣿⠛⠛⣿⠟⠛⠛⠛⢻⠹⣿⠛⠛⠛⠛⠛⢻⡟⠛⠛⠛⠓⢦⣿⣶⠛⠛⠋⢳⠀⡞⠛⠛⣶⠛⠛⢷⡞⠛⠻⣦⠞⠋⠉⠙⠲⡟ ⡆⠀⠀⢸⣀⡟⢿⠀⠀⢸⣿⣿⠀⠀⢸⡇⠀⢀⡏⠀⢰⣿⠀⠀⢰⣶⣾⣰⠿⣶⡆⠀⠀⣴⣾⡇⠀⠀⡆⠀⠀⣿⡏⠀⢀⠀⠘⡇⡇⠀⠀⣿⠀⠀⠈⣷⠀⢰⡏⠀⠀⣿⡀⠀⣻ ⣤⠀⠀⢸⣿⣄⣸⠀⠀⢸⣿⣿⠀⠀⢸⡇⠀⠘⠀⠀⣿⢻⠀⠀⠘⠛⣿⣉⣀⣀⡇⠀⠀⣿⣽⡇⠀⠀⠃⢀⣠⣿⠇⠀⢸⠀⠀⣿⡇⠀⠀⣿⠀⠀⠀⠸⠀⢸⣿⣄⠀⠈⠛⢿⣿ ⠀⠀⠀⢸⡿⣿⣿⠀⠀⢸⣿⣿⠀⠀⢸⡇⠀⠠⡀⠀⢻⣸⠀⠀⢰⣶⣿⢹⣯⠈⡇⠀⠀⡟⢹⡇⠀⠀⡇⠀⠈⣿⠀⠀⠺⠀⠀⢹⡇⠀⠀⣿⠀⠀⣆⠀⠀⢸⡿⠿⠷⣤⠀⠀⢻ ⢠⠀⠀⢸⠀⠀⢹⠀⠀⠘⠛⣿⠀⠀⣸⡇⠀⠀⣇⠀⠈⣿⠀⠀⠘⠛⢻⡆⣿⣦⡇⠀⠀⣷⣾⡇⠀⠀⡇⠀⠀⡏⠀⠀⣠⡄⠀⠸⡇⠀⠀⣿⠀⠀⣿⡀⠀⠘⣿⠀⠀⠿⠀⠀⢸ ⠸⣦⣤⣼⠀⠀⢸⣤⣤⣤⣤⣿⣤⣤⣿⣧⣤⣴⣿⣤⣤⣼⣤⣤⣤⣤⣼⢿⣹⣿⣧⣤⣤⡿⢿⣧⣤⣤⣧⣤⣤⣧⣤⣤⣿⣧⣤⣤⣧⣤⣤⣿⣤⣤⡿⣧⣤⣼⠟⣷⣤⣤⣤⣴⠏ ⠀⠉⠁⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⠀⠉⠻⣯⣟⢿⣍⣛⠻⢿⣿⣟⡛⠿⠿⠿⠾⣿⣯⣤⠶⠿⠿⠿⠛⠛⣛⣋⣭⠿⠟⢋⣩⡽⣻⡿⠟⠉⠉⠉⠀⠀⠉⠉⠀⠀⠉⠉⠉⠀⠀

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