Thinking Face Butt Emojis & Text

Copy & Paste Thinking Face Butt Emojis & Symbols ⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠚⠋⠉⠉⠉⠉⠉⠉⠉⠉⠑⠒⠲⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠚⠋⠉⠉⠉⠉⠉⠉⠉⠉⠑⠒⠲⣄⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠉⢦⡀⠀⠀⠀ ⠀⠀⠀⢀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⢿⣦⠀⠙⣆⠀⠀ ⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠙⢷⡀⠈⠧⡀ ⠀⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠀⠀⠁⠀⠀⢳ ⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⠟⠀⠀⠛⣷⣤⣸ ⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⢸ ⡇⠀⠀⠀⣄⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣄⡀⠀⢸ ⡇⠀⠀⠀⠈⢧⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡞⠙⢦⡘⠉⠀⢠⠖⡿⢸ ⡇⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⢳⡀⣠⠋⣼⠀⡘ ⡇⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠿⠁⠀⠉⠛⡇ ⣧⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⣽ ⠘⣦⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⢀⡏ ⠀⠈⠓⠦⣤⡈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢧⡀⠀⠀⠀⡤⠏⠀ ⠀⠀⠀⠀⠀⠉⠉⠙⠶⠤⣤⣀⣀⣀⣀⡀⣀⣀⣤⣴⠋⠁⠀⠉⠑⠛⠉⠁⠀⠀

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

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⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣦⣓⡆⢀⠦⣄⠀⡀⢰⡠⡑⣨⠉⡝⢩⠛⣛⠻⡛⠿⠿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢿⣳⣟⣮⢳⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⡛⢿⣿⣿⣿⣿⣿⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢇⠠⢈⠀⢂⠰⣿⣷⣿⣷⣿⣿⣷⣿⣶⣷⣽⣮⣵⣜⣶⡴⣮⣝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⢿⡽⣾⡹⢾⣿⣿⣿⣿⣿⣿⡿⢣⣛⠜⡠⢉⠿⣿⣿⣿⣿⣿⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡽⣌⠆⡐⢀⡈⠄⠂⠭⡙⢋⠟⡛⢟⠻⢟⠿⢿⠿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⢿⡽⣧⢻⡹⣿⣿⣿⡿⣟⠣⣍⠣⢜⢢⡑⢦⣜⡽⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢆⣠⢀⢀⡈⢤⣷⣯⣿⣮⣷⣮⣷⣬⣮⣤⣳⣌⣦⣱⣊⡵⣩⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢾⣻⣽⢣⡳⡹⢿⡿⣵⢊⡱⢠⡍⢦⣣⣟⡿⣾⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣙⠦⣹⣯⣀⡘⡿⢻⠿⡻⢿⠿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⢿⡽⣾⢯⣗⣯⢯⡝⣆⠳⣜⢧⡟⣷⣻⣾⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣯⡗⣯⣜⣿⣴⣧⣮⣵⣎⡶⣤⣃⣆⢦⡱⣨⢱⡩⢍⣋⢟⡹⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢯⣿⣽⣻⢾⣝⡾⣽⢎⡷⣈⠎⡝⣎⢟⣿⣿⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⡙⣿⢸⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣾⣿⣷⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣞⡷⢯⣟⡾⣽⣳⡟⡶⣥⢚⡘⣤⢋⠾⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣧⣙⡯⢜⣳⣌⡖⣌⢦⣡⢋⡜⡩⢍⢫⡙⣋⠟⡛⢟⡻⢟⠿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⢷⣯⣟⣳⢎⡳⢧⣏⠿⣽⢖⡯⣞⡶⣍⢏⣿⣿⣿⣿⣿⣿⣿⣿⣧⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠧⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣼⣷⣽⣶⣳⣮⣷⣾⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣾⣽⣻⢮⡱⢫⡜⣹⢎⡽⢺⡵⢻⡜⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢤⡛⣷⢸⡏⣍⢫⠝⣋⠟⡹⢛⠻⡛⢿⠻⠿⢿⠿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢯⣿⡽⣧⣻⡕⣮⡱⢎⡔⢣⢚⡕⢺⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⡷⢺⣿⣾⣿⣿⣾⣽⣷⣯⣷⣽⣦⣽⣜⣦⣳⣌⡶⣰⣎⡼⣧⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢯⣿⣽⢯⡷⡙⢦⢻⡜⣬⡓⣎⡜⣣⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⡼⣯⢹⡟⢿⠻⡟⠿⡿⢿⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⢫⣟⡯⣟⢾⡹⣏⠳⣉⠢⡙⡟⣶⡹⢆⡿⣱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡼⣧⢻⣽⣶⣷⣮⣷⣼⣎⣦⣵⣢⢦⡱⣌⣣⢍⡹⣩⠛⣝⣫⢟⡿⣻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣫⢞⡵⣋⠶⡱⣍⠳⢄⠢⢱⡙⢦⡙⢮⡜⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣖⠀⠀⠀⠀⠀⠀ ⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⢧⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⡼⣝⢮⡱⢎⡵⣊⡕⣣⢎⡳⣌⢇⠾⣱⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀ ⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢺⣧⢿⣳⣜⣦⣕⢮⣡⢏⣭⢫⡝⣋⠟⡛⡟⡻⠿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣹⢚⡶⣽⣺⢵⣫⢶⡝⣮⢻⡵⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢆⠀⠀⠀⠀ ⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢯⡷⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣿⣴⣫⣼⣍⣟⣿⣻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⢿⣷⡿⣯⢷⣏⢿⣼⣳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀ ⠀⠀⠼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢺⣗⣿⣭⣋⣟⣹⢋⡟⡹⢛⡛⣟⠻⡟⢿⠿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣽⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀ ⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡽⣾⣽⣿⣿⣿⣿⣿⣾⣿⣷⣿⣼⣷⣿⣮⣷⣵⣦⣧⣝⣮⣝⣯⣻⣽⣻⣟⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀ ⠀⠀⡸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣞⡷⣯⢟⡛⣟⠻⣟⠿⡿⢿⢿⡿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⠀ ⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣺⣽⣻⣿⣿⣾⣿⣾⣿⣽⣾⣶⣳⣭⣾⣴⣣⡽⣌⣯⣹⣙⣏⡻⣝⢯⣛⣿⣻⣟⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀ ⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣵⣳⣿⢿⢻⠟⡿⢿⠿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄ ⠀⢀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣞⡷⣿⣧⣿⣾⣵⣯⣾⣼⣳⣮⣷⣭⢯⣹⣍⣻⣙⡟⣛⡟⣛⢻⡛⡟⢿⡻⣟⠿⣿⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷ ⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢺⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏ ⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⢻⣞⣿⣦⣳⣴⣦⣵⣬⣖⣭⣞⣭⣏⡿⣹⣛⣟⣻⠻⣟⢻⠟⡿⣻⠿⣟⡿⣟⡿⣿⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⡶⠾⠿⠿⠿⠿⠿⢶⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠙⠻⣷⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠛⠛⠋⠀⠀⠀⠀⠈⠻⣷⡄⠀⠀⠀⠀ ⠀⠀⠀⣠⣿⠋⠀⠀⠀⠀⠀⢀⣠⣤⣄⡀⠀⠀⠀⠀⠀⠀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣦⠀⠀⠀ ⠀⠀⣰⡿⠁⠀⠀⠀⠀⠀⠰⡿⠛⠉⠙⠿⠃⠀⠀⠀⠀⢰⣿⠀⢀⣴⡿⢿⣦⡀⠀⠀⠀⠀⠀⠈⢻⣧⠀⠀ ⠀⢠⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⡀⠀⠀⠀⠀⠈⠁⠀⢸⡟⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⠀⢻⣇⠀ ⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠉⠙⣿⡆⠀⠀⠀⠀⠀⠀⠸⣿⡀⢀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠈⣿⡀ ⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣇⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇ ⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣦⣴⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇ ⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇ ⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇ ⠀⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⠿⢷⣦⠀⠀⠀⢰⣿⠀ ⠀⠈⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⠀⠀⠀⠀⢀⣴⡿⠋⠀⣠⣾⡟⠀⠀⢠⣿⠇⠀ ⠀⠀⠘⢿⣆⠀⠀⠀⠀⠀⠀⢀⣤⣴⣦⣤⣀⠀⠈⠉⠉⠉⠀⠀⣠⣾⠟⠉⢀⣠⣾⠟⠁⠀⠀⢠⣿⠏⠀⠀ ⠀⠀⠀⠈⢻⣧⡀⠀⠀⠀⠀⠸⣿⣄⠀⠉⠻⣷⡀⠀⠀⢀⣴⡿⠋⠁⣀⣴⣿⣿⣄⠀⠀⠀⣴⡿⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⠀⠀⠈⢿⣦⡀⠀⠘⢿⣦⣴⠟⠋⠀⠀⠀⠘⠉⢀⣸⡏⢀⣠⡾⠏⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⠻⣶⣄⡀⠀⠀⠻⣷⡄⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠿⠛⢿⣿⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢷⣦⣤⣘⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣯⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⣻⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢀⢤⣔⠕⢂⣀⠴⠂⠀⠈⠉⠙⠒⠚⠯⠽⣒⠤⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠁⡨⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⢵⣦⠀⠀⠀⠀⠀ ⠀⠀⠺⠒⡔⠁⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠙⣵⡄⠀⠀⠀ ⠀⣀⣤⡌⠀⠀⡀⠀⡠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠘⣷⡄⠀⠀ ⢀⣾⡟⠀⠀⠰⠀⡨⠎⡅⠀⠀⠀⠀⠀⢠⠾⠁⠀⠀⠀⠀⠀⠀⣆⠀⢸⣷⠀⠀ ⣿⡿⠃⠀⠀⣗⣈⣀⠀⢧⠀⠀⠀⠀⡰⠁⠀⢇⠀⠀⠀⠀⠀⠀⢹⠀⠀⣿⠇⠀ ⡿⣀⠀⠀⢸⠋⣿⣿⣿⡿⢦⡀⠶⢴⣥⣠⣄⡈⢆⠀⠀⠀⠀⠀⠀⠣⡀⢇⠇⠀ ⠉⠺⣽⣦⣀⡆⣆⠛⣱⠃⠀⠈⠁⢠⢟⣿⠿⡟⠿⢲⠀⠀⠀⠀⢀⣠⠔⢋⠀⠀ ⠀⢸⢻⠁⡇⠀⠈⠉⠁⠀⠀⠀⠀⠘⢆⣉⡴⠁⢀⠃⠀⣀⠄⣰⡟⠀⠀⠀⠑⡅ ⠀⣾⡏⠀⠍⢢⡄⠐⠒⢠⠀⠀⠀⠀⠀⠀⠀⠐⢳⠶⠧⠤⡴⠛⣀⣉⠙⢿⢿⠚ ⠀⣿⡇⠀⠄⣸⡀⠀⠀⣹⡀⠀⠀⠀⠀⠀⢀⣠⡼⠁⠀⠀⢰⡀⠈⠻⡿⣴⠊⠀ ⠀⠸⣿⡀⠀⡏⠉⠒⢒⣿⠏⢿⣉⡮⠝⠛⠷⡤⠃⠀⡐⠀⢸⣿⣦⢤⣬⣺⣷⠀ ⠀⠀⠙⣷⡾⠁⠀⠀⢸⣤⠷⠫⢥⣖⠂⠉⠉⢳⡶⠊⠀⢀⣿⠇⠀⠉⠁⠉⠉⠀ ⠀⠀⠀⢹⣧⡀⠀⢂⡏⠀⠂⠀⠀⠈⠳⡄⣠⠮⠤⠄⣲⣿⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠙⠿⢭⡟⣉⣦⣼⣶⡦⠤⢤⣧⣀⣁⣶⠄⣝⡇⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢀⣾⣿⣿⣿⣿⣾⣽⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⣿⣿⠃⠀⠀⠙⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⢹⣿⡆⠀⠀⠀⢹⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣿⡇⠀⠀⠀⢸⣿⡟⢦⣀⡀⠀⠀⢀⣄⣀⣀⣠⣠⣤⣤⣴⣶⣦⣄⠠ ⠀⠀⢠⣿⣿⠇⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠛⠛⠉⠉⠈⠙⣿⣧ ⠀⢠⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⡟ ⠀⣾⣿⣿⠀⠀⠀⢰⣾⣦⠀⠀⠀⣀⣀⠀⠀⠀⢀⣀⣀⣤⣤⣴⣶⣿⣿⣿⡯⠜ ⡀⣿⣿⡟⠀⠀⠀⠈⠛⠁⠀⠀⠀⠻⣿⠃⠀⠀⠀⠀⢻⣿⣻⣿⠿⠟⠛⠉⠀⠀ ⣗⣿⢿⣿⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⣤⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀ ⡛⣧⠀⢹⡆⠀⠀⠀⠛⠋⠉⣙⠛⢷⣄⠀⠀⠀⠀⢀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀ ⣿⡟⠀⠈⠿⠶⠖⠒⠒⠛⠋⠉⣷⠀⠁⠀⠀⠀⠀⣾⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀ ⣿⠁⠀⠀⠀⠀⠀⠀⢶⣶⡶⠛⠁⠀⠀⢀⣀⣠⣴⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⡀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣬⣷⣄⣀⣀⣀⣀⣠⣿⡿⠋⠙⠛⠋⠉⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⢞⣭⡴⠒⠀⠒⣢⣬⠤⠀⠐⠒⠒⠒⠺⠦⠤⠬⣭⣿⣛⣛⠢⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⠖⣫⡿⠿⡞⢁⣠⡶⠖⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠲⣮⣍⠒⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⠞⠁⠚⠁⠀⣠⡖⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢦⣝⢶⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⡴⢀⡀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡝⢦⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠐⠀⠞⠉⣠⡾⠁⠀⠀⠀⠀⠀⠀⠀⢀⣴⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠹⣆⢳⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣰⠃⠀⠀⠀⠀⠀⠀⠀⣀⣾⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠹⣷⢿⡀⠀⠀⠀⠀ ⠀⠀⣷⣿⣿⠇⠀⠀⠀⠀⡼⠁⢀⡼⣫⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⠀⠀⠀⢸⣆⢳⡀⠀⠀⠀ ⠀⢠⣟⣽⡇⠀⠀⠀⠀⣼⠁⠀⣨⡾⠃⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⡀⠀⠀⢻⡟⣧⠀⠀⠀ ⣸⣿⣿⣿⠁⠀⠀⠀⢰⣇⡤⠞⠁⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠁⡀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⠀⠀⠘⣧⢹⡆⠀⠀ ⣿⣿⡾⠃⠀⠀⠀⠀⣿⢉⣀⣀⣤⡀⠀⢿⡄⠀⠀⠀⠀⠀⠀⢠⠟⠀⠀⠈⠹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠄⠀⠀⢿⢸⡇⠀⠀ ⣿⡋⠀⠀⠀⠀⠀⠀⡿⠛⣻⣿⣿⣿⣶⣾⣿⡀⠀⠀⣾⣄⢠⣟⠀⠀⣀⠀⠀⢹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⠀⠀⢸⠀⡇⠀⠀ ⣿⡙⢶⣤⣄⠀⠀⠀⣇⠀⡿⠟⣿⡿⠿⡿⠀⠙⠦⣄⣡⠈⠛⢻⣿⣶⣿⣷⣦⣄⣹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀⢸⡆⠃⠀⠀ ⠀⠉⠳⣦⣽⣷⣄⠀⠹⡆⣷⠐⠟⠓⣼⠃⠀⠀⠀⠀⠉⠀⢠⣿⠛⣿⣿⣾⣿⡟⣿⠟⢷⠁⠀⠀⠀⠀⠀⠀⣤⠀⣀⣴⠞⠉⡀⠀⠀⠀ ⠀⠀⢰⡿⣸⠏⠸⡟⠉⠁⠙⠧⠤⠞⠁⠀⠀⠀⠀⠀⠀⠀⢸⣇⠘⠻⡅⢀⡿⠁⠀⠀⣾⠀⠀⠀⠀⠀⠀⢀⣼⡟⠉⠀⠀⠀⠸⣆⡑⠄ ⠀⠀⢸⢁⡏⠀⡄⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⣀⡤⠞⠀⠀⢀⡾⠁⠀⣀⣤⠴⠃⣠⢾⣟⣀⣀⣀⣀⣀⣀⣈⠻⢀ ⠀⠀⡎⢸⡇⠀⢳⡈⢦⡀⠀⣠⠤⠤⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢯⣤⣤⣼⣅⠀⠀⣨⡵⢏⠀⠈⠉⠛⢿⣿⠭⣥⣶⠿ ⠀⠀⡇⣾⡇⠀⠘⡇⠀⢹⠟⠁⠀⠀⢀⣈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⡙⡛⠛⡛⣯⠀⠀⠳⣤⣤⣤⣤⣌⠿⢸⡇⠁ ⠀⠀⡇⣿⡇⠀⠀⣧⠀⣿⠀⠀⠀⠀⠀⣸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡏⠁⠁⠁⠉⠁⢻⡄⠀⠀⠈⢷⣟⢦⣤⡴⠛⠁⠀ ⠀⠀⢳⢸⡇⠀⠀⠀⢸⡿⠲⣤⣄⣀⣀⣿⣿⠶⠶⣶⠦⣤⣤⠴⣶⣶⠶⣒⡋⢉⡿⠀⠀⠀⢀⠀⠀⣸⣿⣦⡀⠀⠀⠙⢶⣍⠳⢤⠀⠀ ⠀⠀⠸⣧⢻⡄⠀⠀⣼⡧⠀⠀⠈⠉⣹⣿⣿⠋⠉⢻⣤⣶⠶⠚⠋⠉⠉⠙⣿⡟⠁⠀⠀⣠⡟⠀⠀⣿⣿⡿⣯⣛⡲⠶⢶⣬⣿⢸⠀⠀ ⠀⠀⠀⠘⢯⣻⣦⣠⠟⠀⠀⠀⠀⠀⣿⢁⣹⣤⡞⣋⣁⣠⡴⠶⠛⠛⠉⠙⣿⣤⣤⣤⠾⠉⠀⠀⢠⣿⣼⠃⠀⠀⠉⠉⠛⠛⠛⠋⠀⠀ ⠀⠀⠀⠀⠀⣿⣿⡿⠀⠀⠀⠀⠀⢀⡿⠻⣇⠀⠀⠀⠛⠛⠳⣄⠀⠀⠀⠀⠀⢹⡿⠃⠀⠀⠀⣠⡾⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢹⡾⣧⡀⠀⠠⠴⠛⢙⡀⠀⠈⠓⢦⡀⠀⠀⠀⠈⢳⡄⠀⣠⣾⣃⣀⣀⠤⠶⣿⡿⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠻⣎⡻⠶⠤⠴⣾⡿⢧⡀⠀⢤⣄⣻⡄⠀⠀⠀⠈⣷⠉⠛⠦⣌⣀⠀⠐⠺⡏⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⢛⡛⢓⣾⣉⢡⣤⣿⣷⣿⣭⡭⠽⠟⠛⠛⢻⣿⣦⣤⣤⣤⣬⡟⣓⣐⣯⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣶⣶⣶⢾⣿⣿⣿⣿⣿⣻⣶⡦⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣄⣘⣻⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠱⣿⣿⣿⡟⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡿⠿⠘⢽⣿⡿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⣿⠹⠉⡺⣿⣿⣿⣶⣤⣿⣿⣿⣿⣯⣽⣿⣿⢣⡸⣿⡏⠙⠒⠛⠉⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣿⡇⠃⠁⡀⣠⠀⣟⣿⣿⣾⣿⣿⣿⣿⣿⣿⣻⣿⣯⣇⣺⣩⣇⠠⣄⠀⠀⣶⡽⣿⣩⣧⣷⣾⣿⣿⣿⣿⠇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⢗⠯⠀⡄⡔⡿⣿⣏⠳⠈⠻⣻⠟⠻⠛⢋⣁⠋⠻⢽⠿⡿⢿⣿⣿⠿⣟⣭⣽⣶⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣼⣽⣻⠀⡀⡸⢃⣾⠁⠛⠟⠂⣁⣠⣴⣶⣿⣿⣿⣿⣿⣿⣿⣾⣶⣷⣾⣾⣿⣿⣿⣿⣿⣿⣿⡿⠟⣛⣉⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣰⣿⣻⣻⢀⣴⣇⣃⠷⣤⣠⣶⣿⣿⢿⠿⣿⣿⢿⢛⣛⣯⣿⣿⡿⠿⣿⣿⣿⠿⣟⣿⣿⣽⣿⣾⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣴⣿⣿⠟⢿⣋⢝⠏⣶⣤⣼⣿⣿⣆⣀⣸⣶⣷⣿⣿⣟⣿⣽⣿⣿⣿⣷⣶⣶⡤⣌⣶⣔⣯⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢰⣿⣿⡿⣅⠀⠹⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⠟⢽⣟⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⢿⣷⣌⣛⢿⣿⣿⣿⣿⣿⣿⣛⢋⣿⣯⣿⡭⢻⣿⣿⣿⣿⣗⣻⣬⣷⣤⣿⣿⣿⡿⠟⣛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⣿⣿⣿⣍⠓⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⠿⢛⣭⡷⠿⠿⣿⣿⣿⣷⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣿⣿⢯⡻⣝⠿⠦⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠉⠙⢿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣿⣿⠷⡈⠈⢳⡉⠛⠿⢻⣿⣾⣻⣿⣿⣿⣿⣿⠿⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣸⡿⢿⡟⠲⣼⠦⠵⣤⣌⣜⣿⣼⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⡙⢮⠳⡀⠈⣣⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢀⣠⣶⣶⣶⣦⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⣯⣦⣤⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣧⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠛⢛⣿⡿⠋⢹⣟⣿⣿⣿⣿⣿⣿⢭⣽⡆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇⠀⢸⣿⠁⠀⠀⠉⠉⢿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠘⢿⠀⠀⠀⠀⠀⠈⠻⢿⠿⠿⠿⠟⠛⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣤⣶⣟⣽⣿⣿⣿⣿⣭⣴⣶⣶⣿⣿⡟⠛⠛⠛⠿⠿⢿⣝⣲⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣴⡿⠋⠋⣠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠈⠛⠛⠋⠹⢿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⡿⠋⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠹⠿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣴⡿⡃⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⣋⡀⠀⠙⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠦⣀⠀⠀⠀⠀⠀⠀⠀ ⢠⣾⠏⠀⠀⠀⠀⠀⠙⠻⠿⣿⠿⠿⣿⣿⣿⣿⣆⠈⢻⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠇⠀⠈⠉⠁⠀⠀⠀⠀⢀⣀⣀⣀⣠⣤⣤⣤⣴⣶⣤⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀ ⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⠿⠛⠁⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠸⣦⡄⠀ ⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄ ⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣄⣀⠀⠀⠀⠀⠈⠻⠿⠿⠟⠛⠻⣿⣿⣿⣿⣿⡟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿ ⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣄⣀⠀⠀⠀⠀⠙⠿⣿⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿ ⢿⣻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⢸⡿⣧⠀⠀⠀⠀⠀⠀⠀⢀⣴⣦⣄⠉⠙⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗ ⠀⠀⠙⣧⠀⠀⠀⠀⠀⢰⣿⠁⠀⠙⣷⡀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⢿⣄⠰⠆⠀⠸⣿⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⠹⣷⡒⠂⣀⣿⠀⠀⠀⠀⠙⠷⢤⣤⣤⣤⣤⣤⣤⣤⠄⠀⠀⠀⠀⠀⠀⠉⣉⡛⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⢷⣶⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡆⠀⠀⠈⠉⠛⠻⠿⢿⣿⡿⠋⠀⠀⡤ ⠀⠀⠀⠀⠀⠀⠀⢸⡏⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⣀⣀⣀⣀⣀⣀⣠⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⢹⣟⢴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⢲⣄⣠⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣾⣛⣭⡿⠟⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠿⣧⣤⣴⣦⣄⠀⠀⣠⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠒⣾⣿⡿⠛⠉⠉⠉⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠉⠛⠷⣾⣿⣤⣄⣀⣀⠀⠀⠀⠀⢀⣠⣴⢶⣴⣾⡿⠶⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⠾⠟⠛⠒⠚⠟⠛⠹⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢋⠘⠈⠃⠈⠣⠁⡅⠈⠌⠈⠈⠁⠁⠀⠈⠌⡈⠈⠈⠅⠀⠀⠀⠀⠈⠈⠈⢀⠁⡀⠀⠀⠈⠀⠀⡉⢀⠡⠁⢈⠀⠈⠀⠀⠀⠡⢀⠁⠌⠀⠀⠀⠀⠀⠀⠐⢀⠈⠄⠠⠄⠀⠀⠀⠀ ⠆⠀⠀⡀⠀⢣⠐⠄⡑⡈⠄⠀⠀⠀⡀⢐⠀⣀⢂⣡⣤⣶⣼⣶⣷⣬⣅⠢⡄⠐⡀⠀⠀⠀⠀⠀⡐⢂⢂⠡⠐⠀⠀⠀⠀⠀⡁⢂⢈⠐⢁⠂⠀⠀⠀⠀⢈⠄⡈⢂⠁⠂⠀⠀⠐⠀ ⠦⡄⠤⡀⠤⠄⠂⠀⠁⠐⠀⢀⠀⠄⠀⠀⣠⣣⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣌⠒⠀⠤⠀⠄⢀⠀⠁⠂⠈⠀⠉⠀⠠⠀⠠⢀⠐⠀⠂⠈⠐⠀⠤⠀⠄⣀⠐⠀⠐⠠⠀⠡⠀⠤⠤⠄ ⢃⠐⡀⠁⠒⠀⠀⠀⠀⠁⠌⠤⣄⣸⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡂⠁⠊⠀⠁⠀⠀⠠⠀⠀⠡⠡⡈⠁⠢⠀⠀⠀⠀⠀⡈⠠⢁⠂⠤⠀⠀⠀⠀⠀⠀⡁⠂⢡⠂ ⠃⠔⢠⠉⡔⠀⠀⠀⠠⡄⣾⣼⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡻⢟⠿⡻⢖⡶⢦⣤⣄⣀⠁⠄⡁⠒⠀⠀⠀⠀⠀⠠⠁⡌⢐⠠⠁⠀⠀⠀⠀⠐⡀⢉⠀⠄ ⠀⠈⠀⠀⠀⡐⠀⢂⢰⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣎⡖⡱⣎⠼⣥⢚⢬⢋⠟⡷⢦⣄⡐⠢⠀⠆⠐⠁⠀⠀⠀⣀⡀⢦⠐⡀⠔⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⣼⢾⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡻⢋⠦⣙⠤⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣖⡌⡳⢆⡭⢂⢏⡚⣌⠳⣘⠻⢷⣦⣐⣤⣤⣶⣾⣿⣿⣿⣿⣦⡇⠠⠄⠀⠀⠀⠀ ⠀⠀⠀⢠⣾⢻⣉⠶⣩⠛⡽⢿⣿⣿⣿⡿⢟⡭⣶⣿⣿⣷⣷⣮⣑⠣⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢎⠵⣋⣜⣩⣦⣝⣶⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⢀⠀⠀⡀⠀ ⠀⡡⢀⣿⢇⢣⠎⣇⢣⢏⡴⣋⠬⣑⠎⡴⣩⣾⣿⣿⣿⣿⣿⣿⣿⡱⢌⠽⣻⣿⣿⣿⣿⣿⣿⣿⣬⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠇⢀⠈⡐⠀⡀ ⠀⠂⢨⣿⡘⢦⡛⢤⣋⠶⣘⠜⡺⡜⣜⠰⢿⣿⣿⣿⣿⣿⣿⣿⣿⢽⣊⠶⣡⢎⡛⠿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠀⠀⠀⢂⠄⢁⠀ ⠀⠁⠀⣿⡘⢦⣙⠲⣌⢳⣉⠮⣱⡙⡆⣏⠲⡹⣿⣿⣿⣿⣿⣿⠟⣢⡙⢎⡕⠮⡜⣡⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠻⡛⢯⡓⡬⢻⣶⡀⠀⢠⠈⠀⠈⠀⠀ ⠀⠀⠠⣟⡜⡱⢎⠳⣌⠳⡜⠲⢥⢣⡓⢬⢣⡕⣪⠙⡝⢻⢍⠣⡞⡥⣚⠥⣚⠵⣹⠰⡌⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡴⡘⣦⢳⡙⢦⡹⣔⠣⠞⣷⡄⠂⠄⠀⠀⠀⠀ ⠀⡀⢘⡧⣚⠵⣋⠳⣌⡳⢭⠹⡌⢧⢜⠣⠞⡬⣡⣋⡜⢥⢪⠱⣡⢃⡇⡎⢥⢛⠤⡛⣜⢢⡙⣛⠻⣛⠻⣩⢿⣿⣿⣿⣿⣿⣿⣿⡿⡑⢮⢥⡙⣆⠳⣌⢧⡙⠴⣻⡄⠂⠀⠀⠀⠀ ⠀⡂⢨⡗⣥⢛⡬⢳⣌⠳⣌⣷⣼⣦⣉⠯⣱⢣⣃⠦⣙⢆⡣⡹⣐⠫⡜⡩⢎⡝⢲⡱⣌⢳⡜⢆⠳⣡⢳⡐⢏⣿⣿⣿⣿⣿⣿⣿⡙⢧⣋⢦⡙⢆⡛⣔⢪⡱⢣⡙⣷⡀⠒⡈⠄⠂ ⠀⠡⢈⣿⢤⢋⡖⢣⣼⡿⣿⣛⡾⡽⣷⣞⠴⣓⣾⣿⣿⣿⣿⣷⣷⣷⣾⣵⣮⣼⣥⣲⣌⡣⢜⡩⢃⣇⠣⡝⢢⢎⡹⢻⠿⣛⠍⡦⣙⠦⡍⢦⡙⡬⡓⣌⠧⣜⢣⡱⢩⣷⠀⠐⡀⠁ ⠀⠁⠀⣿⡎⡸⡎⣁⣿⣹⢾⡹⡿⣷⣹⣾⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣷⣸⣇⡎⣰⠇⡾⡈⡎⢱⡈⡶⢹⡆⢷⡸⢱⡈⡾⡈⣇⠇⣇⣿⡆⠀⠁⠀ ⠀⠀⠀⢸⣯⡵⡹⣄⢻⣯⣷⣛⡷⣯⢷⣳⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣼⣵⣼⣒⣥⢊⠧⣉⠷⣩⠲⠭⣌⠳⡔⣺⡇⠀⠀⠀ ⠀⠀⠀⠀⢿⣖⣹⠜⡢⢝⣷⣯⡽⣞⡷⣻⣖⣻⢿⣿⡿⣿⢿⣻⡟⣿⣻⣟⢿⣻⣟⡿⣻⣟⣿⢻⣟⢿⣻⢯⣻⡽⣏⡿⣽⠾⣵⣫⣏⠿⣿⣿⣿⣾⣶⣥⣯⣲⣡⢛⣬⢹⡇⠀⠀⠀ ⠀⠠⢀⠀⠘⢿⡧⡺⡝⡦⢜⣻⣷⢫⣟⣧⣟⣳⢯⡾⣵⡻⣞⣧⣟⣳⢯⣞⣯⢷⣫⢷⣛⣮⣽⣛⣾⣫⣽⣳⢯⡷⢯⣟⡾⣽⣳⢯⣞⣟⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⢿⡇⠀⠠⠀ ⠀⡡⠂⠈⠄⠈⢿⣧⡑⣏⠖⣽⣯⣟⣾⢳⡾⣝⡾⣽⡞⣷⣻⢮⡽⣯⣟⣾⣹⢾⣝⣯⣟⣮⣗⡿⣼⣳⡽⣭⢷⣻⡟⣮⢿⣱⢯⣻⣼⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡞⣷⠀⠁⠄ ⠀⠔⠠⠁⠂⠀⠀⢹⣶⡉⢞⣿⣳⣞⣳⢯⡷⣯⣟⡾⣽⣳⢯⣟⣵⣻⣞⣾⣹⡟⣾⣳⣞⡷⣾⣽⣳⢯⡽⣏⣟⣳⣻⣝⡾⡭⢟⡻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣃⣿⡇⠈⠀ ⠀⠀⠀⠀⠀⠈⠄⡀⠙⢿⣾⡿⣵⢯⣛⡷⢯⡷⢾⡽⣞⣵⣻⢞⣧⣟⡾⢾⣵⣻⣳⡽⢾⣵⣳⢧⡿⠾⠽⢞⣋⢳⢩⡜⡴⡱⢣⠞⡥⢫⡔⢮⡜⡹⢛⠻⠿⡿⢟⢫⡑⢧⡿⠀⠀⠀ ⠀⠀⠀⠀⠀⢁⠂⠄⣼⣿⣻⡼⢯⣻⣭⣟⣯⢟⣯⢷⣻⢞⣭⣟⣾⣺⣽⢻⣼⣳⠿⣼⣻⠌⡕⢮⡔⡫⢞⡼⢌⠧⡓⢬⡱⢍⠧⣫⠜⣣⠞⡱⡜⡱⣍⠳⣅⢣⠍⡦⣩⣿⠁⠀⠀⠀ ⠀⠠⢀⠀⡐⠈⢠⣾⣿⢳⡷⣻⣏⡷⣞⣾⢺⡽⣞⣯⢷⣻⠾⣽⢶⣳⢯⣟⡾⣭⣟⢧⡿⢌⡹⢲⡜⡱⢎⡴⡩⢞⡙⢦⡙⣎⠳⣅⠻⢤⢫⡱⡸⢱⣌⠳⣌⡚⢬⣱⡿⠁⠠⠀⠄⠂ ⠀⣁⠂⠐⠰⠀⣿⣟⡾⣏⣷⣻⣼⢻⣞⣞⢯⣷⡻⣼⣛⣾⣻⡽⣳⢯⣟⡾⣽⣞⢾⣫⡟⣌⣓⢣⣚⡱⢫⡔⣱⢫⡜⣣⢚⡔⣫⠔⣋⢦⣓⢲⣑⠣⣎⠳⢬⠱⣦⡟⠁⠈⠠⠁⠌⠀ ⠀⠄⠂⠁⠌⠀⣿⣿⣳⡟⣶⣳⡞⣯⣞⢾⣏⡶⣟⠷⣽⢞⣵⡻⡽⣧⡟⣾⢳⣞⣿⠏⡜⢦⢪⠕⣦⡙⢧⡜⢢⢳⣘⠱⢎⡲⢥⢛⡜⢆⢎⠖⣌⠳⣌⠛⣤⡿⠋⠀⠀⠈⠄⠡⠈⠄ ⠀⠀⠀⠀⠀⢁⠀⠛⠷⣿⣵⢯⣽⢳⣏⣿⣼⣷⣛⢛⡛⢞⣓⡛⢳⡓⢟⡛⢯⡙⢦⢛⡬⢣⡍⡞⢤⡙⢦⡜⢣⠳⣌⠻⢬⠱⣎⡱⢌⡫⢎⡝⡰⣍⣶⠟⠋⡀⢂⠡⠈⠆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢈⠐⢈⢀⠀⠉⠛⠾⠷⠟⠋⠁⠈⠙⠷⣾⣢⡥⣙⢣⠞⣦⡙⢦⡹⣌⢣⡜⣡⢎⡙⢦⡙⢦⣉⢇⡳⢬⡙⡬⢳⠬⣑⢫⣜⣶⡼⠛⠉⢀⠀⠈⡐⢀⠂⢁⠂⠀⠀⠀⠀ ⡂⠄⡀⠠⢀⠈⠀⠂⠀⠘⠀⠠⠀⠀⢀⡀⠈⠈⠀⠀⢀⠉⠙⠳⠾⣼⣤⣙⡦⡑⢎⡱⢜⡱⢊⡵⢊⡝⣢⠙⢦⡙⢦⣱⣡⣷⡾⠟⠛⠉⠁⠀⠄⠠⠀⠠⠐⠀⠂⠁⠂⠠⢀⠀⡀⠀ ⡇⢂⠠⢀⠃⠀⠀⠀⠀⠂⠁⠤⢁⠃⡈⡇⠀⠀⠀⠀⢈⠀⠰⠄⠠⠄⠈⠉⠉⠛⠛⠻⠶⠷⠿⠶⠷⠾⠶⠟⠛⠛⠋⠉⠉⠠⠀⠀⠀⠀⠁⠈⠤⠑⡈⠄⡃⠀⠀⠀⠀⠠⢀⠂⠔⠀ ⠝⠦⠰⠦⡘⠀⠀⠀⠀⠀⠁⠀⠤⠁⠀⠃⠀⠀⠀⠀⠀⠐⠀⠂⠄⡂⠀⠀⠀⠀⢀⢀⣀⣄⣠⣤⣀⣀⣀⣀⠀⣀⠂⡁⡐⢀⠀⠀⠀⠀⠀⠀⠄⠁⠂⡐⠀⠀⠀⠀⠀⠐⠀⠌⠒⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣶⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⢤⣶⣶⣿⣿⣿⣿⣿⣷⣍⠉⠐⠒⠀⠤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⠂⢻⣿⣿⣿⣿⣉⡘⢿⣿⣿⡆⠀⠀⠀⠀⠀⠈⠂⢄⠀⠀⠀⠀⠀⠀ ⠀⢠⠃⠀⠀⠀⠉⠋⢿⣿⣿⠀⠛⠟⠃⠀⣀⣀⣀⣄⣀⣀⡀⠑⠠⡀⠀⠀⠀ ⠀⠆⠀⠀⠀⠀⠀0⠀⠀⠉⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⡗⠀⠀⠐⢄⠀⠀ ⠰⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠹⠿⠿⠿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⢁⠀ ⠀⢂⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣶⣦⣄⠀⠉⠋⠁⠀⠀⠀⠀⠀⠀⠀⠈⡆ ⠀⠀⠣⡀⠀⢀⡴⠢⡌⠉⠛⠿⢿⣿⣿⣿⣿⣷⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⡁ ⠀⠀⠀⠐⢄⠘⡦⡙⢼⠀⠀⠀⠀⠀⠉⠙⠛⠿⣿⣿⣿⣿⣷⣶⣤⣀⠀⠀⠀ ⠀⠀⠀⠀⠀⠁⡗⡘⡜⡒⢖⡒⢒⡂⢎⠭⣉⢏⠱⡌⠉⠛⠿⣿⣿⣿⡷⠀⡆ ⠀⠀⠀⠀⠀⠸⣆⠱⡆⡉⠶⣈⢱⠸⡈⠶⠷⠾⠏⠀⠀⠀⠀⠀⠈⠉⢀⠎⠀ ⠀⠀⠀⠀⠀⠀⠘⠡⢜⣌⣣⢆⡙⡆⠀⠀⠀⠀⠀⠀⣀⡀⠤⠄⠒⠊⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠂⠀⠒⠒⠒⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⡼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⣠⠎⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠈⣇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⢀⡼⡇⠀⠀⠀⠀⠀⠀⢸⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⢠⠞⠀⢹⡄⠀⠀⠀⠀⠀⠘⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⣰⠁⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⢹⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⡴⠃⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⡇ ⠀⠀⠀⠀⠀⠀⠀⢰⠋⠀⠀⠀⠀⠀⠀⢀⡾⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⢸⡁⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⡇ ⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⡾⠀ ⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⣼⣥⣤⣤⣤⣤⣤⣤⣤⣀⣀⣀⣀⠀⠈⢧⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢀⡇⠀ ⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠉⠙⠻⢿⣿⣿⣿⣿⣿⣿⠛⢦⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⡇⠀ ⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⠳⠀⢳⡀⢹⡇⠀⠀⠀⠀⠀⡾⡇⠀ ⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡿⠘⠀⠀⠹⣼⡇⠀⠀⠀⠀⢠⠇⠀⠀ ⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⡏⠣⠀⠀⠀⠀⠀⠀⠀⠈⣿⡿⠁⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⡾⠀⠀⠀ ⠀⠀⢠⡏⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⡼⠁⢁⣳⣀⣀⠤⠠⢄⠀⠀⢿⠁⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⢸⠁⠀⠀⠀ ⠀⠀⡾⠀⠀⠀⠀⠀⡾⠁⠈⠛⠳⡷⣟⡃⠒⠒⠒⢓⡦⠒⢛⡶⠆⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⡟⠀⠀⠀⠀ ⠀⣴⠁⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠈⠏⢍⢂⠀⢀⠎⡍⡊⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢸⡇⢀⠇⠀⠀⠀⠀ ⣾⠃⠀⠀⠀⠀⡞⠁⠀⠀⠀⠀⠀⠀⠅⠀⣬⠟⠪⡅⠀⡷⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠈⡇⢸⠀⠀⠀⠀⠀ ⠹⡀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠷⠏⠀⠀⠀⠀⠑⠻⠇⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣾⠀⠀⠀⠀⠀ ⠀⢳⡄⠀⠀⠀⠀⠘⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⣿⠀⠀⠀⠀⠀ ⠀⠀⣷⡄⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⡏⠀⠀⠀⠀⠀ ⠀⢀⡇⢹⣄⠀⠀⠀⠀⣀⠉⠓⠶⢄⡀⠀⠀⠀⠀⠀⢀⣠⠴⠋⠣⣄⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⣸⣧⠀⠀⠀⠀⠀ ⠀⣴⣿⠋⠘⣆⠀⢰⠶⠤⢍⣛⣶⠤⠿⣷⣦⡀⠒⠚⡟⠀⠀⠀⠀⠈⠛⠢⠤⡄⠀⠀⢀⡴⢯⠴⣳⠇⠀⠀⠀⠀⠀ ⠀⠀⠉⠀⠀⠘⢦⡈⠻⣖⠤⣤⣉⣉⣹⣯⣭⠉⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠛⣫⣼⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠑⣄⠉⢦⡀⠀⠀⠈⠉⠁⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢿⣷⢚⡝⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢶⣷⠇⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠷⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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