Grim Political Emojis & Text

Copy & Paste Grim Political Emojis & Symbols ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⡶⠶⠛⠋

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