Wiggum Emojis & Text

Copy & Paste Wiggum Emojis & Symbols ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⢉⣒⣄⠠⠤⠤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⢉⣒⣄⠠⠤⠤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠷⠒⠉⠁⠀⠀⠀⠀⠀⠈⠙⠒⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠨⡓⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠱⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⠴⣖⣒⣛⣻⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⣀⣤⢶⢺⣯⣿⠶⠛⢋⣍⠉⠛⢦⡀⠸⣶⠂⠙⠚⣝⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣠⣴⢶⣻⡵⠖⢛⡉⠀⠘⢦⡀⠘⣇⠀⠀⠀⠻⡄⠘⢧⡀⠀⠈⢳⡌⠛⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⣴⣿⣿⢟⠋⠵⣄⠀⢻⡀⠀⠀⠘⣇⠀⠘⠦⠄⢀⣰⣿⣤⡶⢿⣷⣶⣾⣶⡶⢼⡗⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠟⠉⢠⡏⠀⠀⢻⡀⠀⠳⠤⠀⣚⣩⣤⣶⣾⣿⣿⣇⠀⣀⣾⣾⣿⣿⡿⠋⣠⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣼⡟⠘⢻⠀⠀⣇⣴⠶⡞⣁⣠⣶⣾⡿⢙⣿⣯⣷⣶⣶⣶⣾⣷⣴⣿⣭⣿⣁⣴⠾⠋⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⣿⡏⠀⠀⣼⢸⠋⢻⡇⠀⠻⣿⡿⠟⠋⠉⢉⣿⠉⠉⠛⢿⠿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠈⡟⠃⠀⠀ ⠀⠀⢀⡀⠀⠀⣿⢹⣅⠀⢈⣽⣿⣇⠀⠹⡄⠀⠈⠳⣄⠀⠀⣿⠇⣸⠛⢶⡾⠷⣦⣶⣾⣟⣉⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢿⠀⠀⠀ ⢰⡿⠋⠉⠉⢉⣿⢀⣤⣾⣿⣿⣿⣟⢷⡄⠀⠀⠀⠀⢎⣷⣄⣇⠀⠙⠤⣀⣁⠀⣀⣿⠤⢟⡈⣹⠆⠀⢀⣴⣆⣀⢤⣤⣀⣸⡀⠀⠀⠀ ⠘⢷⣦⣤⣤⣼⣷⣍⣈⣉⣩⣭⠭⠿⣯⡞⢷⡀⠀⠀⠸⢻⡈⠁⠀⠀⠀⠀⠀⢹⡋⠤⠀⢠⣈⢿⡙⠛⠺⣿⣿⣿⣟⣿⣿⣿⣿⣷⡦⡀ ⠀⠀⠀⠉⠉⠈⢿⡀⢹⠏⡘⣦⣴⣶⣿⣇⠀⢷⡀⠀⠀⠀⢧⠀⠀⢀⣀⣀⣀⠀⠉⠀⠀⠀⠀⠁⠈⠓⣦⣿⣿⣿⣿⣿⣿⣿⣧⣴⡧⠁ ⠀⠀⠀⠀⠀⠀⢰⠷⡟⠗⣥⡈⠛⡻⢿⣿⠀⠈⣧⠀⠀⠀⠼⡄⠀⠈⠉⠉⠉⠛⠓⠤⢤⣤⣤⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣇⣼⣧⠀ ⠀⣠⣶⣿⣿⣿⠟⢛⢷⣄⠹⢛⣷⣦⡿⢿⣄⠀⢻⡆⠀⠀⠀⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠁⢀⣀⣼⣿⣿⣿⣿⣿⣿⡛⣹⣇⠀ ⢰⣿⣿⣿⣿⣿⠀⠀⢸⡟⣷⠿⠋⠄⠀⠈⠉⠀⢺⡇⠀⠀⢀⡷⠶⠤⠤⠴⠦⠤⠶⠶⠶⠶⠿⠛⠛⠛⠉⢉⣿⣿⣿⣿⣿⣿⡿⢻⢋⡀ ⣿⣿⣿⣿⣿⣿⡀⠀⢸⣿⡃⡀⠒⠁⠀⠀⣠⡴⠟⠀⠀⢀⣼⣃⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⡤⠶⠶⠛⠛⠛⣯⠉⠉⠉⠀⢸⣼⠀ ⣿⣿⣿⣿⣿⣿⠷⠶⢿⣷⠀⡁⢀⣀⣤⠞⠋⠀⢀⣠⣴⣟⣉⣉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⣀⣀⣀⠀⠀⠀⢻⡌⡀⠀⠀⢸⣿⠀ ⢻⣿⣿⣿⣿⣿⠀⠀⣾⠈⢿⣆⣉⣉⣀⣀⣤⡶⣿⡿⠛⠋⠉⠉⠛⠲⣄⠀⠀⠀⠀⠀⠀⠀⢠⡶⠙⠋⠉⠙⢦⡀⢸⣿⡧⠀⠀⢸⡸⡀ ⢸⣿⣿⣿⣿⣿⠀⠀⣿⠀⠀⠋⠙⠛⠛⢙⢡⡾⠃⠀⠀⠀⠀⠀⠀⠀⠈⢣⠀⠀⠀⠀⠀⢰⡅⠀⠀⠀⠀⠀⠀⢻⣼⣼⠁⠀⢀⡵⡣⠀ ⢸⣿⣿⣿⣿⣿⡇⠀⣿⠀⠀⠀⠀⠀⠀⢸⣼⠀⠀⠀⠀⣤⣤⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⣧⠀⠀⠀⠀⢠⣦⣤⠈⣿⢹⠓⠛⠉⠊⠀⠀ ⢸⣿⣿⣿⣿⣿⡿⠀⡿⠀⠀⠀⠀⠀⠀⡼⢻⠀⠀⠀⠀⠻⠿⠃⠀⠀⠀⢀⣿⠀⢀⣤⣤⣿⣄⠀⠀⠀⠈⠙⠛⢠⣿⢸⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⡇⠀⡇⠀⠀⠀⠀⠀⠀⡇⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠎⣼⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⣠⠏⢺⢸⠀⠀⠀⠀⠀⠀ ⠈⣿⣿⣿⣿⣿⣿⣸⡇⠀⠀⠀⠀⠀⠀⡇⠀⠀⠳⢤⣀⠀⠀⠀⣀⠴⠫⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣷⣐⡺⠑⠁⢹⢸⠀⠀⠀⠀⠀⠀ ⠀⢿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠉⠈⠛⠃⠀⠁⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⠿⣄⠀⠀⠀⣽⢸⠀⠀⠀⠀⠀⠀ ⠀⣼⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢰⡇⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠿⠿⠿⠛⠉⠀⠈⠙⢢⡀⣿⢸⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢸⠇⠀⠟⠷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢻⣿⢸⠀⠀⠀⠀⠀⠀ ⢰⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠸⣿⣿⣿⣶⣶⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣶⣾⡭⠂⠀⢻⢸⠀⠀⠀⠀⠀⠀ ⠸⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⢸⢸⠀⠀⠀⠀⠀⠀ ⠀⠀⠉⠉⠛⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⢸⢸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⢸⢸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⣿⣦⡀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣾⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣾⡍⠙⢻⣷⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠴⡋⢿⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠹⣿⣦⡌⢄⠊⣛⠻⡿⠗⢲⣤⡤⠤⢤⣀⣀⣀⣀⣀⣀⣀⣀⢀⣀⡠⠤⠤⠤⣴⣒⠚⠯⠅⠒⠁⠃⣸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣷⣤⣤⡠⠇⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠛⠛⠛⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⣀⡠⠴⡛⠅⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣿⣶⣦⣤⢤⣤⣤⠤⢤⣄⣀⣀⣀⣄⣀⣀⣀⣀⣀⣤⠤⢤⣾⡛⠯⠁⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣍⠁⠐⠒⠒⠺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠁⠿⠿⢿⣿⣿⣿⣿⡿⠄⠀⠀⠀⠀⠀⢈⢁⠉⡉⡉⠉⠉⢉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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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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