Tensa Bankai Emojis & Text

Copy & Paste Tensa Bankai Emojis & Symbols ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣾⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⡈⠻⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢹⡀⠈⠙⡲⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⣿⡆⠀⠀⣿⡇⠀ ⠀⠀⠙⢦⣄⠀⠈⠏⡳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⣿⠀ ⠀⠀⠀⠀⠈⠑⢤⢀⠀⠁⠋⠗⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡏⠉⠉⡏⠉⠉⠉⠉⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠁⠢⡂⢔⠠⢀⠁⠋⠗⣲⣄⠀⣠⣠⣼⠶⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠌⣔⣉⣐⣠⢀⡈⣾⡿⠉⡀⣠⣴⡾⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠿⠶⠶⠶⠶⠆⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠛⣾⠗⣿⣷⣶⣿⣿⣿⣷⣦⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡇⠉⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣆⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣴⡿⠟⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣶⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣾⣟⠛⠋⠛⠻⢿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣷⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⢿⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡿⠋⠉⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣖⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣥⠶⠶⠸⣶⣦⡈⠉⠛⠿⢿⣿⣿⣿⣿⣟⣿⣿⣿⣿⠃⣀⢰⡺⠏⠛⠚⠯⡶⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠈⣿⡇⢀⣀⠀⠀⠈⠉⠻⠿⣿⣿⣿⡟⠁⣴⡿⠁⠀⠀⠀⢀⣠⣼⠝⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣷⢰⣻⠇⠘⠉⢀⢸⢰⢰⡆⠀⣿⡏⠉⠁⡸⠿⠁⠀⠀⣰⢾⡻⠏⠋⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⡾⠟⠓⡩⣿⢷⡦⣔⡢⣖⣬⠯⣑⠉⠑⠘⣦⣠⣼⠟⣡⣲⡾⠓⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣱⣯⣀⢾⠟⠁⠁⠀⠀⠀⠀⠈⠉⠃⠛⠛⠿⢟⠛⡡⣞⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠙⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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