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