Princess Jasmine Emojis & Text

Copy & Paste Princess Jasmine Emojis & Symbols

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

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