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⠀⠀⠀⠀⠀⠀⠀⡄⣿⣿⣿⣿⣿⣿⣿⣿⣾⣤⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⢀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⡇⣿⣿⠸⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣷⣿⣿⣿⣿⣿⣴⢀⠀⠀⠀⠀⠀⠀⣀⣤⣿⣿⣿⣽⠀⠀⠀⠀⠀⠃⡃⠹⠋⠛⠟⠿⡿⣿⣿⣿⢿⠉⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡄⣿⣿⣿⣿⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⡿⣿⣿⣿⠛⠿⠿⡿⣿⣿⣿⣋⣶⣶⣴⣤⣀⣀⢀⠀⠀⡀⢧⠘⠀⠀⠀⠀⠀⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣿⣿⣿⠀⠀⠀⠀⣘⢧⠀⠉⠟⣿⣿⣶⢠⡇⣶⣴⣤⣤⣠⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠰⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣯⣿⠈⠀⠀⠉⡋⡟⣿⣿⣾⣤⢀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢹⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣷⣿⠿⣿⣿⣶⣴⣠⢀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢳⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⣘⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠸⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⡿⢿⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠁⠉⠈⣄⠳⠈⠀⠀⠀⠀⠀⠁⠋⡶⣷⣯⣶⣷⠻⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀ ⠀⠀⠀⠉⠒⠤⣤⣀⣀⣀⣀⣀⠀⣀⣀⣤⣶⢿⠚⠙⠛⠯⣿⢛⠛⠛⠛⡚⠙⣍⣿⢬⠓⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢰⠀⠀⠀⠀⠀ ⠀⠁⡟⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⣿⡶⣤⣀⢀⠀⠀⠀⠀⣀⢀⡤⣑⣤⠲⣙⣦⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡼⠀⠀⠀⠀⠀⠂ ⠃⡴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⡴⣜⢀⠀⠒⠖⡲⣔⣤⣠⢀⠀⠀⠀⠀⠀⠀⡀⢦⠛⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⣰⠀⠀⠀⠀⠀⠀⡀ ⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⢠⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣷⢾⠛⠉⠈⠀⠀⠀⠀⠋⡶⢠⠆⠈⠀⠀⠀⠀⠀⠄ ⢱⠀⡀⡀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠇⢠⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⣀⣄⣤⣤⣤⣯⢀⠀⡜⠸⡀⠲⠈⠀⠀⠀⠀ ⡇⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢹⠀⠀⠀⠀⠟⢠⠀⠀⢸⠇⠚⡐⠀⠀⡇⠙⠀ ⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠋⡴⢑⣤⠱⠈⠇⠀⢀⠛⠀⠀⡼⣶⢇ ⠀⡇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠞⣧⣄⠳⡙⠣⡈⡄⡑⠘⠀⣀⠀⠎⠀⠁⢠ ⠀⠀⢧⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢿⠟⣼⢤⡶⠟⣽⠶⠙⣦⠛⠉⢤⢀⠁⡰⠀ ⠀⠀⠀⣆⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢳⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⠀⠀⡀⣧⠀⡀⢷⡎⡸⢧⠀⡄⠠⠀ ⠀⠀⠀⠀⡀⢦⠓⠈⠀⠀⠀⠀⠀⠀⠀⠀⣆⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⣿⣿⣸⠉⠉⠈⡀⢸⠀⡀⢷⢸⡀⢻⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⢼⠲⠙⠈⠀⠀⠀⠀⠀⡀⢦⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠰⠃⣿⣿⢻⡀⢧⣄⠳⢸⠀⠀⡇⢸⠀⣿⠈⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⣀⢤⠢⠛⠙⠉⠀⠁⡊⣔⠳⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⡠⠁⡿⣿⣿⣿⠙⡀⢸⡀⢹⠘⠀⡄⠀⠀⣼⣢⠭⠀ ⠀⠀⠀⠀⠀⠀⠁⡔⠀⠀⠀⠀⠀⠀⠁⣟⠿⠙⠀⠀⠀⠀⣄⠿⠐⠈⠀⠀⠀⠀⠀⠀⠈⠔⡠⠀⠁⡿⣿⣿⣿⣿⣿⠀⢇⠀⡇⣴⠈⠀⠀⡇⢈⠄⠶⢽ ⠀⠀⠀⠀⠂⠜⢀⠀⠀⠀⠀⠀⠀⠟⣿⣿⣿⣿⢿⠙⠀⠀⠀⡀⠳⠀⡀⣀⠀⠀⠀⠀⠀⠀⠁⠟⣿⣿⣿⣿⣿⣴⢹⠀⡇⠀⡄⠀⢁⠀⠀⣸⢄⠑⠀⠀ ⠀⠀⠀⠀⠀⢸⠀⠀⠁⠋⠟⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠭⠬⠲⢗⠙⠉⠀⠀⠀⠉⠋⠿⣿⣿⣿⣿⣿⣿⢠⠀⡇⠀⡇⠀⠀⠀⡄⠈⡇⢀⠀⠀⢄⠀ ⠀⠀⠀⠁⡔⠀⠀⠀⡼⠧⠻⣟⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⠘⠀⡆⠘⡌⠀⠀⠀⠀⢸⣸⠀⠀⠀⠀⠀ ⠀⠀⠀⢢⠀⠀⠀⠀⢳⣈⣀⣧⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢔⣠⠀⠀⢸⢸⠃⡄⠀⠀⢿⢀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢃⠀⠀⠀⠀⣄⠳⡋⠀⣔⣤⣦⣷⣻⣗⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣾⢹⠀⠀⠀⠀⣿⢰⢸⠀⠀⠃⣾⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠁⣞⠿⠒⠿⠿⠿⡿⣿⢶⠿⣻⢙⡉⣪⣷⣿⣿⣿⣿⣿⣨⣃⣖⠸⣤⠼⣧⡤⢸⠀⠀⠃⣷⠀⢀⠀⠀⡃⢸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠰⠀⠀⠀⠀⠃⣺⠤⣀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣀⣀⣀⣄⢤⣶⣾⣷⣾⣼⠀⠘⡇⠀⢸⡆⡞⢀⠁⠋⣴⡹⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀ ⠀⠀⠁⡰⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠉⠛⡶⢟⣛⣽⣠⠀⣸⠀⠀⠀⠀⡇⢰⠀⠀⠀⠀⠀⠀ ⠀⠔⢀⠀⠀⠀⠀⠀⠀⡄⠳⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠚⠚⠒⠒⠒⠓⠚⠑⠉⠊⠒⠴⣠⣄⣦⠸⡀⣦⡄⠹⡇⢸⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⠤⠤⠶⠼⠧⡭⣉⣁⢸⠀⠞⢾⠑⠀⡀⠀⠀⠀⠀⠀⠁⠁⠂⠻⣗⠈⠀⠀⡇⡿⢸⠃⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⣼⠀⢾⣠⢃⣿⡿⢀⡇⠙⠇⣆⣸⠀⠀⠀⠀⠀⠀⠉⠹⢨⡀⢱⣄⠘⠀⠀⢸⣌⡳⠀⠀⠀⡇⢹⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢸⢸⡞⢀⠁⡴⣏⣯⢿⡟⣿⣿⡟⢠⠀⠀⠀⠀⠀⡜⣄⠾⡕⢆⡟⠀⡇⠀⠀⢃⢙⡏⠀⠀⠀⡇⢸⢄⠓⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢸⢱⢸⠀⡸⠀⣻⠵⡸⣴⣯⣿⢨⠀⠀⠀⠀⠀⠀⣿⠻⠙⡏⡿⢳⠹⠀⠀⠀⡇⠕⣞⠀⠀⠀⡀⢸⠀⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠁⠀⠂⢰⡇⠀⠁⠞⣣⢴⠤⣀⣀⢾⡝⢶⡿⣿⣿⣿⣿⣿⣠⢠⠀⠀⡇⣸⠀⠀⠀⠀⠀⢸⠀⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠈⠀⠀⠀⠀⢄⡗⠘⡼⠀⣀⠀⠀⠀⠃⢠⠀⣁⣋⢴⠯⢾⡤⣇⠀⠀⠀⠀⡸⢰⠀⠀⠀⠀⠀⢸⠀⠀⢣⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢳⠈⠀⠘⠀⠀⡆⣿⣤⠠⠀⠀⠀⠀⡎⠀⠎⣠⠀⠞⣠⠀⠃⣮⠀⠀⠀⠁⣿⠀⠃⠀⠀⠀⡇⢰⠀⠀⠀⢄⠐⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢿⠈⢇⠀⠀⠀⣷⠀⠔⠀⠄⠑⡀⢽⡼⢤⠤⠤⠀⠀⠁⢣⢰⠀⠀⠀⡏⣠⠀⡍⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢿⠈⢠⠀⠁⡖⡄⠀⠀⠀⠀⢸⣼⠁⠀⠀⠀⠀⠂⢡⡰⠀⠀⠀⡇⣉⣤⣨⣧⠀⠀⠇⢠⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣷⠹⠀⡄⠘⣿⠂⠤⠂⠉⢻⢀⠀⢃⠈⠀⠎⢁⡔⠀⠀⠁⠞⣩⢗⢆⠎⣅⠸⠋⣰⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⢿⠝⡳⡈⠱⠀⠀⠀⡀⠤⠉⠏⢓⠀⠋⡠⠀⠀⠀⡀⣾⣷⡻⠿⣤⣁⠞⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣤⢷⣌⡷⠚⠀⠀⠀⠀⠀⢡⡺⡤⢀⠀⠀⠀⠋⡴⢀⡀⣀⢉⠞⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢤⣶⠗⠫⣝⣬⣠⣀⠀⠀⠀⠀⠖⡠⢁⠋⠯⣶⡤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠤⠦⠤⠤⠤⠤⡤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠂⠐⠤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀