⠀⠀⠀⡅⠠⡉⠆⡝⢿⣭⣿⠏⣜⠵⢤⢒⣛⣞⡫⡴⢈⠄⢸⠀⠀⠀⠀⠀ ⠀⠀⠀⢹⠀⠸⠆⠈⣈⠛⣘⢛⣧⡾⠖⠈⢽⡟⢁⠰⠇⠀⡟⠀⠀⠀⠀⠀ ⠀⠀⠀⠘⣦⢠⢎⣱⣬⢢⣵⠏⣀⣷⠀⠀⠀⠀⣾⠱⡁⣸⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠘⢳⡽⣎⣿⠜⣹⡷⠘⢸⠯⠇⠀⡆⠰⣖⢣⢉⣯⢀⢀⡀⠀⠀⠀ ⠀⠀⠀⣠⢞⣽⢿⣾⢼⡭⣏⠁⢾⠀⡃⠀⣿⣦⠶⡾⣁⢳⡋⠉⠉⠀⠀⠀ ⠀⠀⠈⠛⡿⣿⣿⢑⣳⠁⢓⡎⠘⠀⢁⣧⠙⢏⣥⡿⡿⣦⣵⡄⠀⠀⠀⠀ ⠀⠀⠀⠘⠛⡿⣯⢙⡷⣶⣿⠿⢀⡰⣸⢷⣶⠾⢁⣟⣼⡾⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠃⢻⣿⡆⠉⠁⠠⠊⠀⠀⠈⠉⣘⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⣿⢿⣆⠀⠀⠀⠀⠀⠀⣠⡿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢣⠀⣹⣷⣤⡄⢠⣴⣾⠟⢀⡍⠀⠀⠀⠀⢠⡀⠀⠀⠀ ⠀⠀⠀⠀⠠⣤⢀⡀⣻⣷⣶⢿⡿⢿⡽⣶⣼⠏⢀⡀⠀⠀⢀⢢⣇⠀⠀⠀ ⠀⠀⣀⣤⡀⣰⣻⣿⡿⢋⣽⣻⣏⡿⣛⣿⣭⣷⣆⣿⣤⣤⣬⣿⡟⣿⣆⠀ ⠀⠀⢺⣿⣯⣿⣷⣿⣿⣾⣿⣯⡏⢹⣽⣷⣿⣿⣼⣿⣿⣿⡅⣈⣷⠉⠈⢆ ⠀⢀⣿⢿⣿⣿⣿⣿⡟⡻⠻⢾⡇⢸⡷⠟⢻⠻⠋⠙⢿⣿⣿⣿⣿⣿⣜⢺ ⢠⣿⣿⡘⣿⣿⣿⡿⢟⣶⡮⠤⠭⠭⢤⣽⡶⣿⣄⣀⣾⣿⣿⣿⣿⣿⣿⣿
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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣾⡿⢿⣦⣄⡀⠀⢁⣀⣀⣤⣜⣿⣿⣤⣾⣷⣶⣶⠦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⠙⠻⡷⢶⣤⡀⠀⠸⠃⡆⠀⠀⠀⠀⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡾⠟⠋⠉⠀⠀⢀⣩⣿⠿⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠀⠈⠳⡌⠙⢷⣄⡔⠁⠀⠀⠀⠀⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣭⣄⣀⠀⢀⣤⡾⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠀⠀⠀⠘⠦⣤⣈⣳⣦⡀⠀⠀⢀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⡾⠿⠛⠛⠛⠋⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢉⣵⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⠀⠀⠀⠀⠀⠈⠉⠉⠉⣇⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣀⣤⣴⣶⠿⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡆⠀⠀⠀⠀⠐⢄⢀⡼⠙⢧⣼⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣴⣿⣟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣠⣾⣥⠤⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠟⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠈⢯⡀⠀⠈⠻⣿⢿⣷⣦⣤⡀⠀⠀⠀⠀⠀ ⠸⣿⣿⣄⠀⠀⠀⠀⠀⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣏⠉⠛⠛⠉⠉⠉⠀⠀⢀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠟⠁⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠠⡀⠀⠀⠀⢳⡄⠀⠀⠹⣆⠀⠈⣼⡇⠀⠀⠀⠀⠀ ⠀⠈⠻⣿⣦⠀⠀⠀⠀⠀⠉⠙⠓⠶⠤⣤⣄⣀⣀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⣰⠻⡇⠀⠀⠀⠀⢠⠾⣆⣠⠴⢋⡝⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠙⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠘⣦⣄⠀⠀⠱⡀⠀⠀⢹⣆⣾⠟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠻⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠈⠻⢦⣤⣠⣞⠛⣟⠛⠧⣄⣀⣠⣴⠿⠶⣧⠀⠀⡞⠀⠀⠀⠀⠀⡟⢿⡀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⡀⠀⠹⡈⠛⠓⡆⠁⠀⠀⠀⢻⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠙⣿⣿⣶⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠶⠶⠒⡲⠀⠀⢠⢾⡟⢰⣾⣿⣿⣶⣞⣯⣵⣶⣿⠓⢸⡇⢸⠁⠀⠀⠀⠀⣰⠃⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⡙⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠹⣿⢦⡀⠳⠀⠀⢻⡄⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⢿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⢲⠏⢸⣷⣦⣭⣷⣿⣿⣿⣿⡿⠿⠛⠀⣸⢡⡏⠀⠀⠀⢀⣴⡏⠀⠀⠸⣆⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠈⠳⣌⠉⠀⠀⠀⢷⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⢀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠞⠁⣼⠃⠀⠀⣠⣾⡟⠀⠀⠀⠀⠘⢷⣄⡀⠀⢰⡀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡀⠈⠻⢦⣀⠀⢸⣇⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠉⠀⠀⢰⡟⠀⣀⣾⣿⡟⠀⠀⢲⡒⠚⠛⠛⠻⣿⣶⣾⡇⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠋⠉⢩⠇⠀⠀⠀⠉⠻⣾⣿⡀⠀⠀⠀⢹⣷⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣦⣄⡀⠀⠀⠀⡄⠒⣹⠁⠈⢿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⣼⣇⣴⣿⣿⠋⠀⠀⠀⠀⠙⠳⣤⡀⠀⠈⠛⣿⡟⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⢀⡴⠃⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠈⣿⣆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⣿⣷⣦⣄⣜⡴⠃⠀⠀⠈⠙⠛⠉⠸⣿⣿⣿⡇⠀⠀⠀⠀⢠⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⠤⢼⠃⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⡀⠀⢸⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⠀⠀⠀⠀⠈⠻⣷⣆⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡿⠟⠀⠀⠀⠀⠀⡔⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⢸⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣋⣀⣤⢾⠁⠀⠀⠀⠀⠀⠀⢠⠃⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡀⠀⠀⠀⢹⠀⠈⠙⣿⠆ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣼⡿⠟⠋⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⢸⣿⣿⡏⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⡎⠀⠀⠀⠀⣸⡆⠀⡾⠳⣄⡀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⠀⢸⡀⢀⣼⠟⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣟⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⣸⠛⢻⡇⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣄⣀⡀⠀⠀⠀⠀⠀⡘⠀⠀⠀⢀⡴⠁⡇⣰⠁⠀⠀⠉⠀⢀⣀⣤⣴⣶⣶⣶⣤⣄⣀⡀⣿⢿⠀⠀⠀⠈⣷⣿⠋⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣦⣄⣀⣠⣤⣤⣤⡶⠖⠀⠀⣿⡇⠀⠀⡟⠀⣸⠀⠀⠀⠀⠀⣸⠀⠀⠲⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⠀⠀⠥⢤⡤⠶⠋⠀⠀⠳⠁⠀⠀⠀⠠⣾⣿⣿⠿⠿⣿⣿⣿⣿⣿⡿⠁⢿⢸⡆⠀⠀⠀⢿⣿⣷⡄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⠟⠋⠀⠀⠀⠀⢿⣇⠀⠀⢻⡟⠋⠀⠀⠀⠀⠀⣿⡄⠀⢀⡈⠻⠿⠿⠟⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⢭⣽⡶⠀⢸⠀⡇⠀⠀⠀⢸⣿⡟⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠃⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⡇⢧⠀⠀⠛⠿⠗⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠀⢿⠀⠀⠀⢸⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⠀⠀⢸⡇⠀⠀⠀⠀⠀⢠⡇⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⠀⢸⠀⠀⠀⢸⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⠁⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⠿⣄⠀⠘⣿⠀⠀⠀⠀⠀⢸⡇⠀⠈⠻⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢖⢒⡖⠒⠒⠂⠒⠲⣶⣂⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⠀⠀⠀⢸⠀⠀⠀⢸⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣥⣤⣤⣤⣶⣶⣿⣿⣿⡿⡟⠋⠀⠀⠈⠧⡀⣿⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠉⠛⠓⢲⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠄⠁⠀⠀⠀⠀⠀⠀⠹⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⠖⣻⠀⠀⠀⢸⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢻⣿⠛⠉⠉⠉⠀⠀⣿⡀⠀⠀⠀⠀⠈⢻⡆⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⢸⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⢀⣴⣾⣿⣷⡄⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⣷⣤⣤⣤⣤⡴⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡇⠀⠀⢸⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣧⣤⣶⣾⣿⣿⣿⣿⣿⣿⣦⣀⠀⠀⠀⢿⠀⠀⠀⠀⠀⣷⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⢿⣇⠀⠀⣾⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠙⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠸⡇⠀⠀⠀⠀⢻⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⡀⠀⠀⠰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠃⠨⣿⠀⠀⣿⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠸⡇⠀⠘⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⠀⠀⠀⣿⡄⢰⡟⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠟⢋⣡⣦⣝⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⣷⠀⠀⠀⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⠇⠀⠀⠀⢸⡇⣼⠇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⣽⠟⠋⠉⠙⣻⡿⢿⣷⣄⠀⠀⢻⣷⣦⣄⡀⠈⠛⢿⣶⣦⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⠿⠛⠻⣿⣿⣿⡟⠀⠀⠀⠀⢸⣷⡟⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠋⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠈⠻⣦⡀⠘⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⡏⠛⢿⣿⣶⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣴⣶⣿⣿⡛⠉⠀⠀⠀⠀⠈⠛⠟⠁⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⠀⠀⠀⠈⠻⣦⣽⣿⣿⣿⣿⣿⡿⢿⣿⣿⣧⡀⠀⠉⠛⢿⣿⣶⣦⣤⣤⣀⣀⣠⣼⢛⡿⣿⡛⠉⠉⢹⢹⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣆⠀⠀⠀⠀⠀⢈⣤⣿⣿⣿⣯⣽⡿⣟⣿⣿⣿⡀⢤⣤⣤⣬⣝⡛⠿⢿⣿⣿⡿⣟⣭⣾⣿⣿⣷⠒⢾⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣦⡀⠀⠀⠀⠸⣿⡿⣿⣿⣿⣿⣷⣿⣿⣿⣿⡻⢦⣙⠿⣿⣿⣿⣿⢿⣿⣿⣷⣻⣿⣿⣿⣿⢸⣶⡌⠺⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⢿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣦⡀⠀⠀⣿⠃⣽⣯⡉⠙⢿⣿⣿⣿⣿⣧⠀⣿⣿⣶⣭⣍⣛⣌⠻⢿⣡⣫⣾⣿⣿⣿⣾⣿⣿⣶⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⠀⠈⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣷⣤⣿⣾⣿⣿⣷⣦⣄⡙⢿⣿⣿⡿⢳⣿⣿⣿⡿⠟⣛⣙⣏⡏⣿⡙⠛⢿⠻⢿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⠟⣩⣯⣭⣉⠛⢿⣾⡿⠛⠁⣾⣿⣿⣿⣷⠀⠛⣡⡞⠛⢯⡛⢃⣾⠀⠀⢹⠻⠿⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡋⠁⠀⠀⠈⠛⢦⡙⢿⠀⢠⣿⡿⠿⢿⣿⣿⣿⣿⡇⠀⠀⠻⡿⠻⣧⣴⣿⣤⡤⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢶⣄⣀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠴⣶⣾⡇⠀⠀⠀⠀⠀⠀⠙⢼⡆⠈⠿⣷⣄⣀⡀⠀⠀⠈⢧⠀⠀⠀⢳⣾⣿⣿⣿⣿⣦⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣯⡁⠀⠀⠀⠀⠀⠀⠀⡀⠈⠁⠀⢻⣖⣲⠦⢤⣤⣤⠤⣼⣿⣿⣿⡿⠿⠿⠛⠿⠛⠛⣻⣦⣶⡾⢾⣿⣿⣿⡿⠛⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠿⠶⣶⣶⣶⣾⣯⣤⣶⡾⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⡷⣾⣷⣶⣶⣶⣾⣿⣿⣯⣥⣶⠶⠾⠻⢿⣶⣶⣶⠶⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
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