Velma Dot Art

Copy & Paste Velma Dot Art 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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⣿⣏⣿⣿⡇⣿⣟⣿⣿⣿⠿⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢿⣿⣿⡿⢻⠭⠉⠉⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣼⣿⣿⣿⣼⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣴⠀⢀⡀⢡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢨⣽⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠈⢠⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣻⣿⣿⣿⣿ ⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⣿⣇⢠⢀⣿⣿⣿⣿⣿⣿⣿⣿⠀⡿⠟⠁⣾⣿⣿⣿⣿ ⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⠀⠀⠀⠀⣶⠀⠀⠀⠀⢀⣿⠀⠀⢀⣾⠿⢿⣷⣾⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⣼⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⣸⡟⠀⢀⣾⠏⠀⠀⠈⠙⠻⣿⣿⣿⣿⣿⣿⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣼⣿⠀⠀⠀⢠⡿⠁⣠⣾⡏⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⡇⠀⢸⣷⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⣴⠏⢹⠀⠀⣰⣿⣧⣾⠋⠹⣧⠀⠀⠀⠰⣦⣀⠀⠀⠈⠻⣿⣆⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠀⢀⣼⠏⠀⡿⢀⣼⣿⠟⠉⠀⠀⠀⢹⣧⠀⠀⠀⠈⠻⣷⡄⠀⠀⠹⣿⣧⡀⣸⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣸⣦⠾⠁⢀⣼⡿⡟⠉⠁⠀⣀⣤⢤⣄⡀⠹⣧⠀⠀⠀⠀⠈⢿⡄⠀⠀⠘⣿⣿⠿⠿⠉⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠛⠁⠀⠀⠙⠉⠀⣿⡀⠀⣴⣿⡿⠶⠟⠋⠀⢻⣦⠀⠀⠀⢀⠈⣿⡀⠀⠀⠹⣿⡆⢀⠀⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⢀⣤⣶⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡰⠟⠁⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠻⣷⣿⡇⠀⣀⠀⢻⣿⡈⠁⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⣿⠃⠀⠉⠀⠀⠀⢀⣠⣄⡀⠀⠀⠀⠀⠘⢷⡄⠀⠀⠀⢀⣠⣴⠆⠀⠹⣆⠀⠀⠘⣿⠁⠀⢻⣷⣌⣿⣷⠀⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣰⠏⣀⣿⡿⠿⠆⠀⠀⠀⠈⠻⣿⡛⠛⠛⠉⠀⠀⠀⠀⠘⣧⡀⠀⢹⡆⠀⠈⣿⣿⣿⣿⠀⢿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠟⠋⠉⠀⠀⣠⡄⠀⠀⠀⠀⠀⠈⠻⢶⣄⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀⣿⠀⠀⣿⣿⣿⣿⡀⠸⣿⣿⣿⠃ ⠀⠀⠀⠀⢰⡿⢷⡀⠀⠀⠀⠀⢀⣀⣴⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⠀⠀⠀⠀⠀⠀⠈⢿⣤⡿⠀⠀⣿⣿⠁⠀⠀⠀⠻⠿⠟⠀ ⢀⠀⠀⠀⠘⣿⠈⢿⣆⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⡀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⡇⠀⠀⠀⠈⠀⠈⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⢸⣦⡀⠀⠀⠀⢀⣴⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⢀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠸⣷⠀⠀⣦⠀⠀⠀⠈⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢻⣇⢠⣿⣧⡀⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⢻⣿⡏⠙⢿⣦⡀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣴⡶⠟⠁⠀⢰⡀⠀⠀⠀⠀⠀⠀⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀ ⡀⠀⠀⠹⣿⠀⠀⠙⢿⣦⡀⢻⡆⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠿⠛⠉⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀ ⣧⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢾⣿⡀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⢸⣿⡀⠀⠀⠀⠀⠀⠀⠀ ⢻⣷⣄⠀⠀⠀⠀⢀⣄⠀⠀⠀⠙⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⢀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢿⣿⣷⣄⠀⠀⠘⣿⣧⣄⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣷⣄⠀⢻⣿⣿⣷⣦⣄⡘⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣶⣴⣿⠟⠀⠀⣠⡾⠟⠛⠛⠳⢦⣄ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇⡀⠀⠀⠀⠀⣠⣦⣿⣿⠙⢿⣧⣀⣾⠟⠀⠀⠀⠀⠀⠀⠉ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⢻⣿⣷⣦⣄⣀⠀⠀⠀⠀⢋⣸⣇⣰⣧⣼⣿⠛⢿⡆⠈⠀⠈⠻⣯⡀⠀⠀⠀⠘⠳⣤⡀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⢿⠇⠈⣿⠆⠀⠀⠀⠀⠀⠀⠙⠻⣦⣀⣀⣀⡀⠈⢳⡄
⠀⠀⠀⠀⠀⠀⢠⡶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⣥⢿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⣸⡇⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⢳⣤⡖⢦⠀ ⠀⠀⠀⠀⠀⠀⣿⠻⣷⠀⠈⠛⠛⠛⠓⠶⠶⣶⣦⡾⢁⣴⡄⠛⠀⢸⡇ ⠀⠀⠀⠀⠀⠀⢿⣆⣸⣷⣶⡀⠀⠀⣠⣾⣿⣦⡿⠁⣼⠃⢹⣿⠾⠟⠀ ⠀⠀⠀⠀⠀⠀⠀⠹⣿⡿⠿⣤⠀⠀⢉⣭⣝⣿⣧⠈⠋⠀⣠⡿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⡿⢠⣄⢸⠀⠀⣾⢁⣬⣿⠉⠀⠀⠻⣯⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣠⡼⠷⠼⠿⠏⠀⠀⠘⢾⣿⡾⠁⠀⠀⠀⠙⣷⡀⠀⠀ ⠀⠀⣴⣾⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀ ⢀⣸⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀ ⣿⠋⠻⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⢀⣤⣿⠁⠀⠀⣀⠀⠀⠀⠀⣿⠀⠀ ⢿⣄⠀⠈⣿⠋⠁⠀⠀⠀⠀⠀⠀⣾⠁⣿⠀⠀⢰⡇⠀⠀⠀⠀⣿⠀⠀ ⠀⠹⣦⠀⣿⣄⠀⠀⠀⠀⠀⠀⢀⡿⠀⡟⠀⠀⠀⣷⠀⠀⠀⠀⣿⠀⠀ ⠀⠀⠘⢷⠟⢹⠛⠷⢶⣤⣤⡶⠟⢁⣼⠇⠀⠀⢠⡇⠀⠀⠀⠀⡟⠀⠀ ⠀⠀⠀⠀⠀⡾⢦⣄⣀⣀⣀⣀⣴⡾⠋⠀⠀⠀⡾⠀⠀⠀⠀⢸⠇⠀⠀ ⠀⠀⠀⠀⠀⠷⣤⣤⡤⠭⠭⠉⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⣼⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢧⣤⣤⣤⣤⠤⠴⠶⠶⠞⠁⠀⠀⠀⠀⠀⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣴⠾⠛⠛⢿⣠⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣴⡿⠋⠀⠀⠀⢸⡟⠉⠙⢷⣤⡴⣦⡀⠀⣀⣀⣀⣤⠶⢶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⠾⠛⠉⢻⡆⠀⠀⢀⣤⣤⡀⠀⣾⡟⠻⣶ ⠀⣸⡟⠀⢠⡿⠿⣦⣿⠇⠀⡀⢸⡟⠀⠈⣿⣰⠟⠉⢻⡏⠀⣠⡈⠻⣧⣤⣄⢠⡶⠶⣄⠀⣿⠉⠀⢀⣀⠀⢸⣷⠶⢶⣿⠁⡈⢻⡄⣿⠁⠀⣿ ⠀⣿⠁⠀⢺⡀⠀⠀⣿⠀⣸⠿⣿⠁⡼⡇⣿⡟⢀⡆⠀⡇⢸⣿⡏⠀⣿⠀⢸⢻⡇⠀⣿⠀⣿⠀⣰⡟⣿⠀⢸⡇⣠⠀⣿⠀⣿⠈⣷⣿⠀⢸⡟ ⠀⠹⣧⡀⠈⠻⢶⣤⣿⠀⣿⠀⣿⠀⣇⡇⣿⠃⡞⡇⢰⡇⠈⢛⣀⣼⣿⠀⣿⣾⠇⢠⡏⢀⡏⠀⣿⢰⡟⠀⣾⢀⢿⡇⣽⡀⡏⡇⣿⣿⠀⣾⠁ ⢀⣠⣭⣻⣶⣤⡀⠈⢿⠀⣿⣠⣿⠀⣿⠁⣿⢠⣷⠃⣼⡇⠀⣠⡉⠻⣿⡀⠈⠁⣠⣿⠷⣾⡇⠀⣿⣸⠇⠀⣿⢸⢸⡇⣿⣇⠛⠁⣿⡇⢰⡏⠀ ⣸⡏⠈⢻⣆⣽⠇⠀⣸⡀⠛⠋⢹⡄⠀⣸⣇⠘⠋⢰⣿⡇⠘⣯⣿⠀⣿⣿⠀⢠⣿⣤⣤⣾⡇⠀⣿⡿⠀⢰⣿⠘⠿⢀⡏⢿⣦⣠⣿⣇⣼⠁⠀ ⢸⣧⠀⠈⠿⠏⠀⢠⡿⣷⣄⣠⡾⠿⠶⠟⣿⣄⣠⡟⢹⡇⠀⠛⠋⣠⣿⡟⠀⣼⡇⠉⠀⢸⡇⠀⠛⠁⠀⣾⢿⡄⠀⣸⠇⠀⠉⢹⡾⠻⣯⠀⠀ ⠀⠹⢷⣦⣄⣠⣴⠟⠀⠈⠉⠉⠀⠀⠀⠀⠈⠛⠋⠀⠘⠿⠦⠴⠿⠻⣿⣤⣼⠏⠀⠀⠀⢸⣧⣀⣀⣤⡾⠋⠈⠻⠿⠋⠀⠀⠀⠘⢿⣶⠿⠀⠀ ⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢀⠎⡇⠀⠀⠀⣤⣆⠀⠀⠀⠀⠀ ⠀⣾⣄⠑⠀⣀⣠⣿⣿⠃⠀⠀⠀⠀ ⠘⡝⡇⠘⠙⢡⠂⣈⣏⡀⠀⠀⠀⠀ ⠀⡜⠀⠀⠀⡉⠁⠉⢉⣼⣿⣿⣷⠄ ⠀⠇⠀⠀⠀⢤⡀⠀⠀⠛⠿⡿⢋⠄ ⠀⡀⠀⡀⢁⠈⣧⣀⠀⣀⢴⡡⠁⠀ ⠀⡆⠀⠡⠃⠀⠹⣿⣏⠨⡀⠀⠀⠀ ⠀⢱⠀⠀⢂⠀⠀⠉⢁⡀⠁⠀⠀⠀ ⠀⡜⡄⠀⠀⠁⠀⠀⠰⣄⠀⠀⠀⠀ ⠀⢡⡈⠐⠠⠀⠀⢀⡤⡏⣇⠀⠀⠀ ⠀⠀⠉⠒⠤⠤⠀⢀⣤⣿⣃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢯⣄⡟⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⡤⠂⠀⠀⠀⠀⢀⣀⣤⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣤⣀⠀⠀⠀⠀⠀⠐⣤⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣴⡿⠁⠀⠀⣀⣴⣾⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣶⣤⣀⠀⠀⠘⣿⣆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⣾⡿⠁⢀⣴⣾⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣷⣄⠀⠘⣿⣷⡀⠀⠀⠀⠀ ⠀⠀⠀⣰⣿⡿⠁⠀⠸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⠀⠀⠸⣿⣿⡄⠀⠀⠀ ⠀⠀⣸⣿⣿⠃⠀⠀⠀⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⢹⣿⣿⡄⠀⠀ ⠀⢰⣿⣿⡏⠀⠀⠀⠀⠘⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠀⠀⠀⠀⠀⣿⣿⣷⠀⠀ ⠀⣿⣿⣿⠃⠀⠀⠀⠀⠀⢹⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⠀⠠⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠇⠀⠀⠀⠀⠀⢸⣿⣿⣇⠀ ⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣤⣄⢠⣾⣿⣿⠃⠀⠀⠹⣿⣿⣷⠀⢀⣴⣿⣿⣿⣶⣶⣶⣦⣴⣿⣿⡏⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⠀ ⣸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇ ⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⣠⣤⣤⣤⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣤⣤⣄⡀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣧ ⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿ ⣿⣿⣿⣿⣤⣤⣤⣄⣀⠀⠀⠀⣀⣴⣿⣿⣿⡿⠿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⡿⢿⣿⣿⣷⣄⡀⠀⠀⠀⣀⣠⣤⣤⣼⣿⣿⣿⡏ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⣁⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠀⠀⠉⠉⠙⠛⠻⠿⢿⣿⣿⡿⠟⢁⣠⣾⣿⣿⣿⠿⣫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⢿⣿⣿⣿⣦⣄⠙⠻⣿⣿⣿⡿⠿⠛⠛⠉⠉⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢀⣴⣿⣿⣿⠿⢋⣵⣾⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣷⣭⡛⢿⣿⣿⣷⣄⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡿⠟⢁⣶⣿⣿⡿⠋⠁⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠈⠻⣿⣿⣿⣦⠉⠻⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⡿⠋⠀⠀⢸⣿⣿⣿⠁⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠸⣿⣿⣿⡄⠀⠈⠛⢿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣠⣾⣿⣿⠟⠁⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠙⢿⣿⣿⣶⣄⣀⠀⠀⠀⠀ ⠀⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⡇⠀ ⠀⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⡇⠀ ⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀ ⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀ ⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣧⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀ ⠀⢸⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀ ⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⠀⠀ ⠀⠘⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠀⠀ ⠀⠀⢿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⡇⠀⠀ ⠀⠀⠸⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠁⠀⠀ ⠀⠀⠀⢻⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⠇⠀⠀⠀ ⠀⠀⠀⠀⢻⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⠏⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠻⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⣰⣿⣿⡿⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⡄⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⣴⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠂⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⡄⠀⠀⠀⠀⠀⠀⣰⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⠀⠀⠀⠀⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⡴⠚⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣼⠁⢰⠃⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣸⣇⠀⠘⠳⣄⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⣿⣿⣧⡀⠀⢸⠆⠀⠀⣠⣤⣠⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⡏⣿⣿⣿⠁⠀⣸⠖⣫⣿⠟⠉⠁⠠⡾⠿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢿⡌⠻⣿⠀⠀⠇⠀⠉⢠⡶⠻⢻⡄⣠⢤⡜⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢻⡦⠈⠀⠀⢀⣀⣀⡀⣿⣷⣠⠟⣷⣤⣿⣸⡶⠶⢶⣲⣶⣤⣀⡀⠀⠀ ⠀⠀⣼⠃⠀⠀⠀⠉⠁⠀⠈⠉⠉⠁⠀⠛⠋⠉⢀⣴⣾⣿⣿⣿⣿⣿⣿⣦⡀ ⠀⢠⡟⠀⠀⠀⠀⠀⠀⢠⡞⠋⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣧ ⠀⢸⡇⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⡿⠋⠀⡏ ⠀⣾⠀⠀⠀⠀⠀⠀⣰⠈⠛⢻⡿⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢻⠏⠁⢠⠞⠀ ⠀⣿⠀⠀⠀⠀⠀⢠⠇⠀⠀⠸⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⡴⠃⠀⠀ ⠀⣿⠀⠀⠀⢠⡆⢸⢰⡆⠀⠀⢿⣿⣦⣤⣀⣀⣀⣠⢴⠞⠷⠤⠴⠃⠀⠀⠀ ⠀⢹⡄⠀⠀⠈⢿⣸⡞⠀⠀⠀⠸⣿⣿⣿⣿⣿⡏⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⡇⠀⠀⠀⠈⢿⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣄⠈⠙⣆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣿⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠈⠛⠿⠟⠁⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢹⡄⠀⠀⠀⠀⠹⣆⠀⠀⠀⠙⢦⣀⡀⠀⢀⡤⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣨⣧⠀⠀⠀⠀⠀⠈⠳⣤⡀⠀⠀⠈⠉⠉⣹⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡏⢸⡄⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠒⠒⠛⢳⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡇⠀⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢯⣽⣆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢿⡀⠀⠈⠛⠦⣄⣀⠀⠀⠀⠀⠀⠀⣀⣤⣄⣸⠃⢹⣆⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⢿⣦⡀⠀⠀⠀⠉⠙⠓⠒⠒⠒⠚⠛⠛⠛⢿⡆⢸⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠛⢶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣿⠟⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠻⠶⠶⠶⠶⠶⣾⣿⠿⢿⣷⣦⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡏⠀⠀⣸⣿⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡙⡿⣷⣶⣿⠃⠀⠀⠀⠀⠀⠀
⠐⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠂ ⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀ ⠀⢸⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡇⠀ ⠀⠸⣿⣿⣷⣦⣀⡴⢶⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⣴⣾⣿⣿⠇⠀ ⠀⠀⢻⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⡟⠀⠀ ⠀⠀⣠⣻⡿⠿⢿⣫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣻⣥⠀⠀ ⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿⣟⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀ ⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⡹⡜⠋⡾⣼⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀ ⠀⠀⣿⣻⣾⣭⣝⣛⣛⣛⣛⣃⣿⣾⣇⣛⣛⣛⣛⣯⣭⣷⣿⣿⡇⠀ ⠀⠰⢿⣿⣎⠙⠛⢻⣿⡿⠿⠟⣿⣿⡟⠿⠿⣿⡛⠛⠋⢹⣿⡿⢳⠀ ⠀⠘⣦⡙⢿⣦⣀⠀⠀⠀⢀⣼⣿⣿⣳⣄⠀⠀⠀⢀⣠⡿⢛⣡⡏⠀ ⠀⠀⠹⣟⢿⣾⣿⣿⣿⣿⣿⣧⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀ ⠀⠀⢰⣿⣣⣿⣭⢿⣿⣱⣶⣿⣿⣿⣿⣷⣶⢹⣿⣭⣻⣶⣿⣿⠀⠀ ⠀⠀⠈⣿⢿⣿⣿⠏⣿⣾⣛⠿⣿⣿⣿⠟⣻⣾⡏⢿⣿⣯⡿⡏⠀⠀ ⠀⠀⠤⠾⣟⣿⡁⠘⢨⣟⢻⡿⠾⠿⠾⢿⡛⣯⠘⠀⣸⣽⡛⠲⠄⠀ ⠀⠀⠀⠀⠘⣿⣧⠀⠸⠃⠈⠙⠛⠛⠉⠈⠁⠹⠀⠀⣿⡟⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢻⣿⣶⣀⣠⠀⠀⠀⠀⠀⠀⢠⡄⡄⣦⣿⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⣿⣷⣻⣿⢷⢶⢶⢶⢆⣗⡿⣇⣷⣿⡿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣛⣭⣭⣭⣭⣭⣻⣿⡿⠛⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠟⠛⠛⠛⠻⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢻⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣠⢶⠏⢠⡏⠀⠀⠀⣀⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣰⠏⠀⣸⠀⣾⠀⣤⠶⠾⢿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢰⣿⠀⣠⠇⠀⣿⣿⣿⣷⣤⣾⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡸⢘⡷⠋⠀⣼⣿⣿⠟⠛⠁⠛⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣰⡇⠈⠁⠀⠀⠉⠉⢁⣾⣿⣦⣼⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⣿⣭⣽⡏⢷⣾⣧⣀⣀⣀⣀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠁⠀⠀⠉⠁⢀⣼⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡞⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠽⣿⣿⣿⣿⣿⣿⡿⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⠃⠀⠀⠀⠀⠀⠀⠀⣿⢡⣦⡀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⠟⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡿⠀⠀⠀⠀⢠⡄⢀⡄⠙⠋⠛⠻⠦⣤⡀⠀⠀⠀⠀⠀⠀⢨⡏⠁⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⢻⣻⣄⢷⠀⠀⠀⠀⠀⠘⢷⣀⠀⣀⠀⢀⣰⠏⢀⣴⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠙⢿⣿⣧⡀⠀⠀⠀⠀⠀⡉⠙⠒⠚⡿⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢻⠀⠀⠀⠀⠀⠀⠀⠙⠛⢿⣦⡀⠀⠀⠀⠻⣦⣤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⠦⠶⠚⠃⠘⢧⣤⣄⠀⠀⠀⢀⣀⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢻⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠈⢳⣀⡴⠋⠀⠀⠩⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁⠀⢀⡟⠀⠀⠀⠀⠀⠀⠈⠻⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠁⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀ ⠀⠀⠀⠘⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡆⠀⠀⠀⠀ ⠀⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠁⠀⠀⢀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀ ⠀⠀⠀⠀⢀⡼⣦⠀⠀⠀⠀⢀⣴⠞⠉⠀⠀⠀⣠⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀ ⠀⠀⠀⠀⡾⠁⣹⡷⣶⡴⠞⠋⠀⠀⠀⠀⣠⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀ ⠀⠀⠀⠀⡇⢠⣿⣿⠁⠀⠀⠀⠀⢀⣤⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⡀⠀ ⠀⠀⠀⢸⣧⠼⡏⢿⢷⣶⣦⡴⠾⠏⠁⠠⠤⠤⠤⠤⠤⠀⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⡯⢷⣄
⠀⠀⢀⡔⢻⠀⠀⠀⠀⠀⠀⢀⣠⣶⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡞⠀⢆⡀⠀⠀⠀⠀⠀⢾⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⣼⣿⣄⠀⢹⠀⠀⢀⣀⣰⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀ ⢸⢻⣿⣿⠀⢸⠒⣿⠟⣉⡁⠼⠿⣿⠁⠀⠀⠀⠀⠀⠀⠀ ⠈⢧⡙⠧⠀⠃⠀⠁⣾⡉⢱⣴⠲⡾⡄⢀⣀⣀⠀⠀⠀⠀ ⠀⢠⡏⠀⠀⠐⠚⠓⠛⠛⠋⠸⠟⠓⢋⣭⣶⣿⣿⣷⣦⡀ ⠀⣾⠀⠀⠀⠀⠀⣰⠒⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⢻ ⢀⡇⠀⠀⠀⠀⠀⢷⣀⣀⠀⠀⠀⠀⠈⠻⢿⣿⣿⠟⠁⡜ ⢸⡇⠀⠀⠀⠀⡇⠀⠸⣏⠀⠀⠀⠀⠀⠀⠀⢠⠃⣠⠞⠀ ⢸⡇⠀⠀⢠⢸⣠⠀⠀⢿⣦⣄⣀⢀⣀⣠⠴⢧⡤⠃⠀⠀ ⠈⡇⠀⠀⠸⣼⠏⠀⠀⠘⣿⣿⣿⡿⠁⣞⠀⠀⠀⠀⠀⠀ ⠀⢿⠀⠀⠀⢹⠀⠀⠀⠀⠙⢿⣿⡿⠀⠀⡇⠀⠀⠀⠀⠀ ⠀⢸⡆⠀⠀⠀⢧⡀⠀⠀⢤⣀⠀⠀⣀⠔⠁⠀⠀⠀⠀⠀ ⠀⢠⣧⠀⠀⠀⠀⠙⠦⣀⡀⠈⠉⣉⠏⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⠸⣆⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⢷⢤⡀⠀⠀⠀⠀⠀ ⠀⢸⡀⠈⠲⢄⡀⠀⠀⠀⠀⠀⢀⣀⡘⡟⢷⡀⠀⠀⠀⠀ ⠀⠈⢳⣄⠀⠀⠉⠓⠒⠒⠀⠐⠛⠛⢻⣇⣸⠇⠀⠀⠀⠀ ⠀⠀⠀⠈⠛⠶⢤⣄⣀⣀⠀⢀⣀⣠⣤⣿⣋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⢉⣿⠋⠙⢻⡟⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⢶⣤⡿⠁⠀⠀⠀⠀
⠀⠀⠀⢸⣦⡀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣏⠻⣶⣤⡶⢾⡿⠁⠀⢠⣄⡀⢀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀ ⠀⠀⣀⣼⠷⠀⠀⠁⢀⣿⠃⠀⠀⢀⣿⣿⣿⣇⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠴⣾⣯⣅⣀⠀⠀⠀⠈⢻⣦⡀⠒⠻⠿⣿⡿⠿⠓⠂⠀⠀⢂⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠉⢻⡇⣤⣾⣿⣷⣿⣿⣤⠀⠀⣿⠁⠀⠀⠀⢀⣴⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠸⣿⡿⠏⠀⢀⠀⠀⠿⣶⣤⣤⣤⣄⣀⣴⣿⡿⢻⣿⡆⠂⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠟⠁⠀⢀⣼⠀⠀⠀⠹⣿⣟⠿⠿⠿⡿⠋⠀⠘⣿⣇⠀⠄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢳⣶⣶⣿⣿⣇⣀⠀⠀⠙⣿⣆⠀⠀⠀⠀⠀⠀⠛⠿⣿⣦⣤⣀⠀⠀ ⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⠿⠋⠁⠀⣹⣿⠳⠀⠀⠀⠀⠀⠀⢀⣠⣽⣿⡿⠟⠃ ⠀⠀⠀⠈⠀⢰⠿⠛⠻⢿⡇⠀⠀⠀⣰⣿⠏⠀⠀⢀⠀⠀⠁⣾⣿⠟⠋⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⣰⣿⣿⣾⣿⠿⢿⣷⣀⢀⣿⡇⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠋⠉⠁⠀⠀⠀⠀⠙⢿⣿⣿⠇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀ 𐙚 -`♡´-˙✧˖°📷 ༘ ⋆。˚˙✧˖°📷 ༘ ⋆。˚˚˖𓍢ִ໋🌷͙֒✧˚.🎀༘⋆˚‧。⋆🌻⋆。‧˚⛷🧚‍♀️🛖
⬜⬜⬜⬜⬜⬜🟫⬜⬜⬜⬜⬜⬜⬜🟫⬜⬜⬜ ⬜⬜⬜⬜⬜⬜🟪🟫⬜⬜⬜⬜⬜🟫🟪⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜🟫🟫🟫🟫🟫🟫🟫⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜🟫🟫🟫🟫🟫🟫🟫⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜🟫⬛🟫🟫🟫⬛🟫⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜🟫⬛🟫🟫🟫⬛🟫⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜🟫🟫🟫🟫🟫🟫🟫🟫🟫⬜⬜⬜ ⬜⬜⬜⬜⬜⬜🟫🟫⬛⬛⬛⬛⬛🟫🟫⬜⬜⬜ ⬜⬜⬜⬜⬜⬜🟫🟫🟫⬛⬛⬛🟫🟫🟫⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜🟫🟫🟫🟫🟫🟫🟫⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬜🟫🟫🟫🟫🟫⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜🟦🟫🟫🟫🟫🟫🟦⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜🟫🟫🟦🟦🟦🟦🟦🟫🟫⬜⬜⬜ ⬜⬜⬜⬜⬜⬜🟫🟫🟫🟫🟨🟫🟫🟫⬛⬜⬜⬜ ⬜🟫⬜⬜⬜⬜⬛🟫🟫🟫🟫🟫🟫⬛⬛⬜⬜⬜ 🟫⬜🟫⬜⬜🟧⬛⬛🟫🟫🟫🟫🟫🟫⬛🟧⬜⬜ 🟫⬜🟫⬜🟧🟧⬛🟫🟫🟫🟫🟫🟫🟫🟫🟧🟧⬜ ⬜⬜🟫⬜🟧🟧🟫🟫🟫🟫🟧⬛⬛🟫🟫🟧🟧⬜ ⬜⬜⬜🟫🟧🟧🟫🟫🟫🟫🟧🟫⬛🟫🟧🟧🟧⬜ ⬜⬜⬜⬜🟧🟧🟧🟫🟫🟫🟧🟫🟫🟫🟧🟧🟧⬜ ⬜⬜⬜⬜⬜🟧🟧🟫⬛🟫🟧🟫🟫🟫🟧🟧⬜⬜ ⬜⬜⬜⬜⬜⬜🟧🟫⬛⬛🟧🟫🟫🟫🟧⬜⬜⬜ ⬜⬜⬜⬜🟧🟧🟫🟫🟫🟫🟧🟫🟫🟫🟫🟧🟧⬜ ⬜⬜⬜🟧🟧🟧🟫🟫🟫🟫🟧🟫🟫🟫🟫🟧🟧🟧
⠀⠀⢠⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⡟⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⡾⠁⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣾⠁⣤⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠉⠙⠳⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⠀⠀⢸⡇⠀⢀⡶⠛⢶⣶⢶⣶⣶⡿⠶⣤⣤⣼⡇⠉⣛⠶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⠀⠀⠘⣧⣀⢸⡇⠀⣼⠁⠀⠀⡟⠀⠀⣤⡀⢉⡹⣟⠉⠀⠈⠻⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣏⠀⠐⠟⠛⠛⢿⡇⠀⣿⠀⠀⢸⡇⠀⠀⢘⣷⡿⠁⢻⡀⠀⠀⠀⠀⠙⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠙⢷⣤⡀⠀⠀⠘⣇⠀⣿⠀⠀⢸⡇⠀⠀⠘⢿⣿⣄⢸⡇⠀⠀⠀⠀⠀⠈⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠛⢦⣄⠀⢿⡀⢹⡄⠀⢸⡇⠀⠀⠀⠀⠙⠿⠿⠷⠶⠶⠦⣤⣀⠀⠀⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣼⡇⠸⣧⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠈⠻⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⣷⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢹⣆⡹⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣤⣀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠷⠶⠶⢤⣤⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣦⣀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠲⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⣤⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢶⣄⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⣄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣴⠚⡄⢫⠉⢩⠃⠀⣰⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠠⡞⠳⡜⠦⠚⠘⠒⠋⠀⢰⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠚⠁⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣤⣄⣀⡀⣠⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⠉⠉⢰⠂ ⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠟⠛⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⡇⠀⡰⠃⠀ ⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠃⠀⠀⢰⡆⢻⣿⣿⣿⣿⣿⡿⠛⠛⠻⣿⣿⣿⣿⠀⠀⠀⠀⢰⠁⡰⠁⠀⠀ ⠀⠀⠀⠀⣶⣦⣤⠘⣿⣿⣆⠀⠀⢿⠇⣼⣿⣿⣿⣿⠛⢸⡇⠀⠀⠙⣿⣿⣿⣇⠀⠀⠀⠈⠒⠁⠀⠀⠀ ⠀⠀⠀⠀⢀⣀⣁⠀⠻⣿⣿⣷⣦⣤⣶⣿⣿⣿⣿⣇⡀⣾⠃⠀⠀⢠⣿⣿⣿⡇⠀⡔⠒⠲⡄⠀⠀⠀⠀ ⠀⠀⠀⠘⠛⠋⠉⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣤⣴⣾⣿⣿⠟⠀⠀⠱⠤⣀⠇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⢀⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠀⠀⣀⡀⠀⠉⠙⠓⠀⠀⠀⠀⠀⠀⠀ ⠀⡗⡤⡲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣴⣫⢸⢷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⢡⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣷⣾⠹⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⠿⡏⠀⠈⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄⣇⣀⣤⣤⣿⣄⣀⠀⠀⠀⠀⢀⣠⠶⡿⢻⠹⣆ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣿⣿⡦⢀⣀⣙⠻⢦⣤⠾⠛⠁⢰⢃⡾⠀⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣻⣿⡉⠁⠸⠿⢿⣷⡄⠀⠀⠀⢠⣏⣼⡇⠀⣿ ⠀⠀⠀⠀⠀⠀⣀⠀⣀⣀⠀⠀⣠⠞⢉⣀⠀⡷⠋⠙⠣⡈⣿⣇⠀⠀⠀⢸⡏⠸⣧⣀⣿ ⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣉⠛⠻⠦⣿⡿⠆⣡⡾⠶⣄⠹⣆⡤⠶⢤⡀⠀⡁⣸⡏⠉⠉ ⠀⢠⡾⢻⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠉⠒⠒⠺⠋⠁⣀⣄⠀⠀⠈⠉⢿⡄⠀⠀ ⢠⡿⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⢀⣤⣄⠈⠁⢹⡏⠀⠀⠀⠸⣷⠀⠀ ⠘⣧⠀⠀⠉⢻⣿⣿⣿⠿⠋⠁⠀⠀⠀⠀⠀⢠⡾⠃⠀⢰⢤⣤⣼⠏⠀⠀⠀⠀⢿⡆⠀ ⠀⠹⣧⠀⢠⡄⢹⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⢸⡀⠹⣼⠀⢸⢦⡆⠀⢸⡇⠀ ⠀⠀⠈⢳⡀⠤⠸⣇⠀⠀⠈⠁⠀⢀⠛⠀⠀⠀⠀⠀⠀⢸⠓⢦⡟⠀⢸⣸⠇⠀⠘⣿⠀ ⠀⠀⠀⠀⣇⠀⠀⠙⣦⣀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⣰⣿⣀⣼⠁⠀⢸⡟⠀⠀⠀⣿⠀ ⠀⠀⠀⠀⠙⠳⠶⠞⠁⠉⠳⢤⣄⣀⠀⠀⠀⢀⣠⣾⡋⠀⣽⠇⠀⠀⣼⠁⠀⠀⠀⣿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠋⠹⠿⢶⣾⣏⣁⣀⣷⠾⠃⠀⠀⣰⡏⠀⠀⠀⠀⣿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠻⢷⣤⠤⠤⣄⡀⠀⠀⠀⠀⠀⠀⣰⡿⠀⠀⠀⠀⠀⣿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣻⣧⡀⠙⢣⠀⠀⠀⠀⠀⣠⣾⠟⠀⠀⠀⠀⠀⢀⡿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠛⠉⢹⡿⠶⠮⢥⣤⠴⠶⠛⠋⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣤⡄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠁⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣼⠙⣿⣿⣿⣽⣆⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⡾⠗⠉⣹⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢻⣾⣟⠁⠉⠙⠛⠻⠿⠽⣷⣾⠯⠽⠿⠛⠛⠉⠁⣀⣤⠾⠋⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⣉⡙⠛⣉⣉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠸⣿⣿⣾⣿⡿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡘⠻⣿⠟⣡⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣶⣤⣼⠟⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢡⣶⣦⡌⠻⡿⢁⣾⣷⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢻⣿⣿⣦⡀⢸⣿⡏⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠙⢿⣿⣿⣆⠙⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡌⠻⣿⣿⣷⣄⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢡⣴⣤⡘⢿⣿⣿⣧⡈⢿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢋⣁⠘⢿⣿⣿⣆⠙⣿⣿⣷⡀⢻⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠀⣿⣿⣷⣄⠻⣿⣿⣿⣿⣿⣿⣷⠈⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⡟⢠⣶⣤⡈⠻⣿⣿⣷⣿⣿⣿⣿⣿⣿⠏⣰⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⡈⢿⣿⣿⣶⣼⣿⣿⣿⣿⣿⣿⣿⠋⣰⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠙⢿⣿⣿⣿⣿⣿⣿⡿⠟⣡⣾⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣉⠛⠛⠛⢛⣉⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣰⡿⠿⠿⣷⣦⣠⣤⣾⠟⠛⠳⣦ ⡏⢀⢀⣠⣶⠟⣹⣿⠷⣦⡀⢀⢘⡇ ⢣⣤⣴⠿⠃⢀⡿⢿⡆⠈⠻⠿⠟⠁ ⠀⠀ ⠀⠀ ⣠⠃⠈⠳⡄ ⠀⠀ ⣰⡟⠁ ⠀⠀ ⣸ ⠀⠀⢰⡏ ⠀⠀⠀ ⢠⡟ ⠀⠀⠘⣇ ⠀⠀⠀ ⢸⡇ ⠀⠀ ⢿ ⠀⠀⠀⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠋⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⠀⢀⣀⣀⣠⣤⣀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠟⠛⠛⠋⠉⠉⠛⣷⡄ ⠀⠀⠀⠀⠀⠀⠀⢠⣿⢀⣀⡤⣤⢤⡤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇ ⠀⠀⠀⠀⣀⣤⣶⠿⠛⠋⠁⠁⠀⠀⠀⠉⠛⣯⣳⡀⠀⠀⠀⠀⠀⠀⢠⡿⠃ ⠀⣠⣶⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡻⣿⠀⠀⠀⠀⠀⣠⡿⠃⠀ ⢸⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠉⢹⡆⠀⠀⢸⣿⠀⠀⠀⠀⢠⡿⠁⠀⠀ ⢸⣧⡀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠈⠀⠀⢀⣮⠏⠀⠀⠀⠀⠘⣷⡀⠀⠀ ⠀⠙⠿⣶⣤⣀⠀⠀⠀⠀⠈⠻⢦⣤⣤⣤⡶⠟⠁⠀⠀⠀⠀⠀⠀⠘⣷⡄⠀ ⠀⠀⠀⠀⠉⠛⠿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄ ⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣦⣤⣤⣄⣀⣀⣤⡿⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⣠⣾⠏⠀⠀⠀⠈⠉⠉⠙⠛⠉⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣄⠀⠀⣠⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣡⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⢿⠈⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⣸⣠⣤⠽⣦⣀⠀⠀⠀⣠⠔⡿⡏⢷ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠿⠀⣶⣬⡙⠶⠋⠁⢸⢰⠃⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠞⠋⢹⡤⠦⢍⢻⣿⠀⠀⠀⣿⢻⡄⢸ ⠀⠀⣠⣾⣿⣿⣿⣟⡛⠻⠼⠿⠆⣥⠶⢄⣳⡥⠤⠤⠀⣉⣸⠏⠋ ⢠⡞⢹⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠒⠚⠁⠠⢤⡄⠀⠈⢻⡀⠀ ⢿⠀⠀⢿⣿⣿⣿⡿⠟⠁⠀⠀⠀⢀⡴⠚⣂⣀⢸⡇⠀⠀⠘⣧⠀ ⠘⢧⡀⢀⢙⡏⠁⠀⠀⠀⠀⠀⠀⠸⠀⠀⢻⠙⣿⠀⣴⣄⠀⢿⠀ ⠀⠈⠳⠀⠂⢧⠀⠀⠁⠀⠌⠀⠀⠀⠀⠀⡞⠓⡞⠀⣿⡇⠀⢸⡇ ⠀⠀⠀⢧⣄⣠⠗⢦⡀⠀⠀⠀⠀⠀⢀⡾⠳⣼⠁⠀⡿⠀⠀⢸⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⣽⠛⠶⢶⣶⣞⢉⣧⠼⠁⠀⣸⠇⠀⠀⢸⡇ ⠀⠀⠀⠀⠀⠀⠀⢀⣙⣶⡶⢤⡄⠈⠉⠀⠀⠀⣰⠏⠀⠀⠀⢸⡇ ⠀⠀⠀⠀⠀⠀⠀⢀⣠⠿⣦⣀⣠⣀⣀⣀⣤⠞⠋⠀⠀⠀⠀⢸⠁ ⠀⠀⠀⠀⠀⠀⠀⠉⠀⢀⡞⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀ ⠀⠀⠀⠀⠀⠀⣴⣾⡇⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⠀ ⠀⠀⠀⠀⠀⠀⣏⣹⡿⢿⣿⣤⣀⣀⣀⣀⣀⣤⣤⡶⠞⠛⢁⡏⠀ ⠀⠀⠀⠀⠀⠀⠹⠿⠤⠀⠀⠉⠉⠉⠉⠉⠉⠉⠀⠠⠴⠞⠉⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠱⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡙⡆⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢄ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⡅⢣⣠⣤⠷⣤⣤⡀⠀⢀⠞⣓⠚⠀⡼ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⡹⠯⣍⡠⢄⢹⡟⢦⠎⠀⡇⠱⡎⠀ ⠀⠀⠀⣀⣤⣤⡤⠤⢴⡎⢠⡤⠏⢀⠀⡟⠁⠀⠀⢰⢀⣠⠇⠀ ⢀⣤⣾⣿⣿⣿⣿⣦⡀⠈⠉⠁⠰⠝⠳⠁⠀⠀⠀⠀⢻⠀⠀⠀ ⡎⠀⢿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠸⡆⠀⠀ ⢧⠀⠈⠻⣿⡿⠟⠋⠀⠀⠀⠀⠀⠀⣀⣀⡵⠀⠀⠀⠀⡇⠀⠀ ⠈⢢⡀⠀⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠸⠀⢰⠀⠀⠀⣿⠀⠀ ⠀⠀⢁⠀⠈⢦⡀⠀⠀⠀⠀⠀⠀⢀⣼⠇⠀⡸⠀⠀⠀⡏⠀⠀ ⠀⠀⠈⠒⠊⡗⢫⡑⠲⠤⠤⠤⠴⠋⡜⠀⢠⠇⠀⠀⠀⡇⠀⠀ ⠀⠀⠀⠀⠀⠳⣄⠉⠒⠤⠤⠤⠔⠊⠀⢀⡞⠀⠀⠀⢸⠇⠀⠀ ⠀⠀⠀⠀⠀⠀⢧⡉⠉⠀⠀⠀⠀⢀⡰⠎⠀⠀⠀⠀⣸⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡽⠓⠒⠒⠒⠛⠉⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀ ⠀⠀⠀⢀⣀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣁⠀⠀⠀⠀ ⠀⠀⠀⡟⠻⣁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡯⠫⡇⠀⠀⠀ ⠀⠀⠀⡇⣰⠟⠉⠑⠒⠒⠤⠤⠤⠤⠒⠒⠈⠁⠀⣸⠁⠀⠀⠀ ⠀⢀⣤⣼⣿⣤⣄⡀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠔⠋⠁⠀⠀⠀⠀ ⢀⡏⠀⠀⢉⡟⠉⠀⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣧⣴⠶⠾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠁⠟⠿⣿⣿⣿⣿⣿⠿⠻⠈⠀⠀⠀⠀⠀⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀ ⠇⣿⣿⣿⣿⣶⣶⣶⣿⣿⣿⣿⠸⠀⠀⠁⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⠈ ⣿⣿⣿⣿⢠⠀⠀⠀⡄⣿⣿⣿⣿⠀⠀⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿ ⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿ ⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣾ ⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⣿⣿⣼⣧⣿⣿⣧⣿⣿⣧⣿⣿⡄⣠⢀ ⣀⣀⣀⣀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⡀⣤⢀⡄⣶⢠⡇⣿⣿⡄⣦⣠⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⣿⣴⠀⠀⠀⠀⠀⠀

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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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