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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢻⣬⣶⣤⣤⣤⢦⢦⢦⡤⢦⡤⢤⠤⠤⠤⠤⣠⣾⡿⠿⠿⠿⠻⠟⠛⠛⠚⠚⠛⢻⡟⢛⣳⣀⣤⣤⣤⣤⣤⣤⣤⢤⡤⣄⣀⢀⣀⠀⣾⣿⢿⠇⠀⠀⠀⣿⠛⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠁⠀⠀⠀⡇⢠⣾⣧⣤⣤⣤⣤⣤⣤⣴⣶⣶⣶⣶⣦⣼⣿⣿⣿⣿⣿⣿⣶⣶⣤⣤⣤⣤⣤⣤⣴⣤⣴⣴⣴⣶⣤⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⡆ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣠⣶⢿⠞⠛⠚⠛⠛⠛⠛⠛⠛⠛⠛⢋⣿⣟⣟⣫⣽⡿⠋⠀⠀⠀⢀⣠⡀⠀⣀⣀⣤⢴⣾⠷⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢀⣀⡀⠠⣿⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡇⢸⣶⣾⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣀⡀⠀⠀⠀⣀⣀⣀⣤⣤⠴⠶⠾⠛⠋⠁⢀⠀⢹⡄⢂⢀⡀⠂⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣶⠀⣀⣠⣤⣴⣶⠿⠿⠛⠛⠉⠉⠀⠀⠀⠀⢠⣤⣴⠄⠀⠀⢠⡴⠶⠶⠖⠒⠒⠒⠛⠛⠛⠛⠛⠉⠉⠉⠉⠙⡟⢻⣄⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣀⣀⣀⣴⣿⣿⣛⣋⣉⣉⣉⣉⣉⣉⣉⣉⣍⣍⣭⣍⣹⣿⣯⣾⣽⣿⣿⣿⣿⣬⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣭⣭⣿⣿⣿⣿⠀⠀⠉⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣠⣤⣤⣤⠶⠶⠶⢖⡻⢛⡛⠏⡍⢩⣉⡘⠤⠁⠦⠄⠀⠉⡉⠙⠛⢉⠍⠩⡁⠆⣰⠊⠀⠀⠀⠀⢳⡀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣟⠿⠟⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣀⡀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣸⡟⢸⣾⡇⠀⠀⠀⠀⠀⣀⣠⣴⣶⣿⣾⣿⣿⣿⣿⣿⣿⣷⣾⣶⣷⣶⣧⣷⣾⣷⣿⣿⣯⣵⠿⠿⠟⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀ ⢠⣤⣶⢾⡛⣟⠻⣛⠭⣋⣭⢣⠵⡒⢲⢩⡙⡜⣤⠒⡥⢒⠣⡙⢄⠂⡔⠠⠡⠂⠌⠈⠀⢁⠐⠀⡌⢰⠡⡑⢞⠁⠀⠀⠀⠀⠀⠀⢱⡀⠀⣿⠀⠐⠀⡇⠀⠀⠀⠀⠂⠁⠀⠀⠀⠀⠂⠀⠤⣄⣀⠀⠀⠀⠶⠀⠀⠀⠈⠁⠀⠸⠟⣲⣷⣖⣀⣀⣀⣀⣙⣿⣿⣿⣿⣿⣽⣿⣭⣽⣽⣯⣿⣶⣶⣶⠶⠶⢿⣿⣶⣲⡶⣶⣶⣿⡿⠟⠛⠉⠉⠉⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢾⣿⣧⢣⠽⣸⠱⣍⢻⣱⢦⠳⣬⠳⣉⢦⡙⢴⢢⡙⠴⡉⢎⢁⢊⡔⠠⠐⠂⡀⢂⠠⠄⠐⣀⠡⢌⠂⡱⠐⡌⢧⡀⠀⠀⠀⠀⠀⠀⠁⠀⣿⣰⣄⣂⣤⣠⣤⣦⣤⣤⣦⣤⣴⣤⡶⣦⣶⡶⣶⣿⣶⣶⠶⠾⠾⠿⠷⢶⣴⣶⣶⡶⠛⣿⠯⣯⢭⡯⢯⠯⠧⠞⠈⡏⠓⠶⡾⠃⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⣿⣿⣹⢮⠷⣛⡭⢧⡓⢮⡳⣌⠳⣍⠲⣉⢆⠣⡜⢤⠃⡭⡈⠦⡐⢢⠑⡌⡐⢠⢠⠒⢉⠠⡐⢄⠃⠔⢣⠸⢤⡙⣒⡄⣦⣴⣴⣶⣿⠿⠟⠋⢹⣿⡿⠿⡿⠿⡿⡿⣾⣷⣿⣶⣦⣿⣿⡇⠈⣿⠋⠀⠀⠀⠀⠀⠀⢸⡇⢰⡔⢺⣄⣾⠀⢻⢸⠹⣼⡻⢸⢱⠀⢿⡄⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢻⣿⡷⣛⢯⡱⣙⢦⣛⢦⡓⣬⠳⣌⢣⢇⢎⡳⡘⢦⡙⢤⢓⡘⢤⠃⡜⠤⡑⡂⢆⡘⡄⢢⠑⣌⠱⣊⢦⣙⣦⣽⣾⡿⠿⠛⠉⠉⠀⠀⠀⠀⠈⢻⣿⣆⠀⠀⠀⠀⠀⡄⠀⠀⣤⣼⣿⡇⠀⢻⣄⠀⠀⠀⠀⠀⠀⠘⡇⢸⣿⣴⠇⢸⡆⢸⡌⣧⣏⣇⡏⡏⡆⠸⣷⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⡷⣭⠶⣍⣳⢮⡜⣖⢻⣌⡳⣌⠳⢎⡚⡴⣉⠦⣙⠢⣍⠜⡆⢳⢌⣲⢡⢓⠬⣒⣜⣥⣯⣶⣿⡿⠿⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠅⠀⠀⠀⠀⠀⣰⣿⣿⡿⢿⠁⠀⠀⠙⠲⠄⠀⠀⠀⠀⢀⡗⠛⢾⡏⠈⡏⣷⠘⢣⢹⣹⣹⢹⣹⢻⠀⢿⣧⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⣿⣿⣚⣝⢣⣳⢺⡼⣩⠞⡴⣓⣬⢛⡬⡕⣲⠡⢧⡩⢖⡜⢎⣙⣣⢮⣴⣧⣾⣷⠿⠟⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠀⠀⢰⠀⠀⣸⣿⡿⠋⠀⠈⠑⠒⠒⠒⠒⠒⠒⠒⠒⠒⠉⠁⠠⢸⠁⠀⢹⣸⡆⢸⡞⣷⢿⣧⢏⣏⣇⠘⣿⡄⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢹⣿⡧⣏⠷⣊⢷⡘⢧⡛⡴⣩⢆⡳⠼⣜⠲⣍⡳⣜⣮⣼⣻⣾⡷⠿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠇⠀⢠⡇⠀⢰⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⢿⣷⠀⢹⣸⣞⣼⡿⡜⡽⡄⠹⣿⡀⠈⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⣿⣿⣜⣫⣝⢦⡟⣲⢏⡵⢣⣎⢷⡻⣜⣻⣭⡷⠿⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡏⠀⠀⡾⠀⢠⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣧⠈⢧⣻⣽⣹⡽⣽⡿⡄⠹⣷⡀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⣿⣿⣭⢗⣮⡳⣏⢷⣺⣝⣯⣾⠿⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡟⠀⠀⣸⠃⠀⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣻⣆⠘⢯⣷⣳⣳⣷⣽⡽⡄⠹⣿⡄⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢻⣿⣯⣾⣶⣿⡾⠟⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠁⠀⠘⡼⠀⣼⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣆⠘⢯⣷⣻⣷⡿⣽⡿⡄⠙⣿⣆⠈⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠙⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠃⠐⠀⠀⠇⢰⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣻⣆⡘⢯⣷⡿⡿⣽⣽⣞⢆⠊⢿⣧⡀⠘⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ 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