Pompompurin Has a Letter Emojis & Text

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠴⠶⣤⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⢻⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣰⣶⣄⣀⡀⠀⠀⣇⠀⠀⠀⠀⢸⡧ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⣿⣿⣿⣿⣿⣿⣿⣷⡯⠇⠀⠀⠀⠀⣼⠇ ⠀⠀⠀⠀⠀⠀⣀⡼⠛⠘⠛⠿⠿⠿⠿⠿⠻⠛⠀⠀⠀⠀⢀⡼⠟⠀ ⠀⠀⣀⣴⠞⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡋⠁⠀⠀ ⠀⣰⠏⠀⠀⠀⡠⠂⠀⠠⠆⠀⠀⢀⣀⠀⠀⠀⠦⠀⠀⠸⣧⠀⠀⠀ ⠰⡇⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⢖⣠⢇⣰⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀ ⠀⠻⣤⣤⣠⡇⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⢻⡀⠀⠀ ⠀⠀⠀⠀⢈⡿⠀⠀⢀⡀⠀⡁⠀⠀⠀⠀⢸⣦⠏⠀⠀⠀⠀⡇⠀⠀ ⠀⠀⠀⠀⢸⠃⠀⠀⠀⠉⠉⡇Text⠀⠀⠀⠀⢸⠀⣀⡴⣿⠀⠀ ⠀⠀⠀⠀⢸⠀⠀⠀⠙⠓⠒⡇here⠀⢸⠉⠁⠀⣾⠀⠀⣾ ⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣧⣤⡄⠀⠀⢸⠀⠀⠀⠀⠀⠀⡟⠀⠀ ⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⣰⠃⠀⠀ ⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠹⣆⣀⣠⠿⠛⠛⠛⠛⠛⠛⠻⢧⣀⣸⠏⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⣶⣶⣶⣶⣶⣤⣤⣄⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣀⣀⣀⣤⣤⣤⣶⣶⣶⣶⣶⣶⣤⣄⡙⠢⣄⡀⠀⠀ ⢀⣤⡠⠖⣡⣾⣿⠿⠿⠛⠛⠛⠛⠛⠛⠛⠿⠿⠿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠛⠛⠛⠛⠛⠛⠻⢿⣷⣦⡙⢾⣷ ⠸⠿⠃⡾⠟⠉⠀⠀⠀⠀⠀⠀⣀⢀⡀⣀⢀⣀⣀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠀⡀⢀⠀⡀⢀⡀⢀⡀⠀⠀⠀⠀⠀⠀⠙⠻⣾⢹ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠀⠀⣀⣀⣀⣀⣀⣄⣠⣄⣤⣤⣀⣀⠀⠀⠀⠀⠀⠈⠈ ⠀⠀⠀⠀⠀⠀⢀⣤⠞⠋⠁⢹⣿⣿⣿⣿⣿⣏⠹⣿⡉⠀⠀⢻⠄⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⢩⡿⠋⢹⣿⣿⣿⣟⣻⡇⠈⠙⠳⢦⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠿⣳⢦⣤⣤⣼⣿⣿⣿⣿⣿⣋⣄⣈⣻⣆⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣔⣏⣄⣤⣼⣿⣿⣿⣿⣿⣥⣶⣶⡾⠟⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠛⠁⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠋⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⡟⠉⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⡶⠶⠶⠶⠿⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⢰⣿⠛⠷⡞⠛⢳⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠛⣷⠾⣻⢷⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⣷⠑⡆⢳⡆⠀⣿⠀⠀⠀⠀⠀⢭⢓⠿⠇⠀⠀⠀⠀⠀⣿⠀⢰⡟⠐⢃⡞⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⢅⡹⡈⠿⡀⢹⡇⠀⠀⠀⠀⠈⠛⠃⠀⠀⠀⠀⠀⢹⠉⣀⠏⡽⢁⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠐⡜⠣⠬⠙⠦⢄⠀⠀⠀⠀⠀⠀⠀⢀⣠⠼⠛⠶⡟⠐⠃⣞⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⣤⠛⠛⠛⠛⣤⣍⡏⠁⠀⠀⣀⣀⠈⢻⡄⠀⠀⠀⠀⢠⠟⠁⣀⣄⠀⠀⠈⣿⣩⣤⠛⠛⠛⠻⣤⣀⠀⠀⠀ ⠀⣠⡔⠉⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠙⠛⠀⢨⣿⠀⠀⠀⠀⣞⡇⠀⠛⠃⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠹⢧⣀⠀ ⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⡟⠀⠀⠀⠀⢣⣤⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄ ⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⠀⠀⠀⠀⠀⠀⠀⠈⠉⣿⡏⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇ ⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⣤⣤⣤⠀⠀⠀⣀⠀⣼⠇ ⠀⠻⢆⣴⣤⣤⣤⣯⣭⣵⣦⣤⣤⣼⣄⡸⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣾⣧⣤⣴⣾⣿⣿⣿⣤⣤⣼⣤⡼⠛⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⡀

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⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠄⠒⠒⠉⠉⠉⠉⠉⠓⠂⠤⢀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⠄⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢄⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀ ⠀⠀⡰⠁⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠢⠀⠀ ⠀⡐⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣦⠀⠀⣰⣾⣿⣿⣿⣿⣷⣦⣄⠀⠀⠀⠱⠀ ⡰⠀⠀⢀⣴⣿⠟⠉⢈⠟⠁⢹⣿⣿⡇⢀⣿⠟⠁⠀⡬⠛⣿⣿⣿⣷⣄⠀⠀⢡ ⡇⠀⣠⣿⡿⠁⠀⠀⢎⠀⢀⣼⣿⣿⡇⢸⠏⠀⠀⠘⠀⣰⣿⣿⣿⣿⣿⣦⠀⢸ ⡇⢠⠃⡿⠁⠀⠀⠀⠀⣷⣿⣿⣿⣿⡿⢸⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡆⢧⢸ ⡇⡞⠀⡇⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⡇⢸⣆⡀⠀⢀⣼⣿⣿⣿⣿⣿⣿⡇⢸⢸ ⡇⢧⠀⢷⣄⣀⣀⣴⣿⣿⣿⣿⣿⣿⡇⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⢸⢸ ⢰⠸⡄⠘⣿⡟⠻⣿⣿⣿⣿⣿⣿⡿⠁⠀⢻⣿⡉⠙⣿⣿⣿⣿⣿⣿⡏⠀⡞⡸ ⠀⢂⠹⣄⠘⣧⣠⣾⣿⡿⢿⣣⡿⠁⠀⠀⠀⠻⣿⣿⢿⡿⢟⣾⣿⠏⢀⠜⠠⠁ ⠀⠀⠢⡈⠑⠚⠿⠷⠶⠿⠟⠋⠀⠀⠀⠀⠀⠀⠈⠛⠿⠾⠿⠿⠕⠛⠁⡰⠁⠀ ⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀ ⠀⠀⠀⠀⠀⠑⠠⡀⠀⠀⠀⠀⠀⠠⠞⠙⠦⠀⠀⠀⠀⠀⢀⡠⠊⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠤⢀⣀⣀⣀⣀⣀⣀⣀⡠⠔⠂⠁⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⢀⣴⠟⠉⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣀⢀⣾⠿⠻⢶⣄⠀⠀⣠⣶⡿⠶⣄⣠⣾⣿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢻⣿⣿⡿⣿⠿⣿⡿⢼⣿⣿⡿⣿⣎⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠉⠛⢛⣛⡉⠀⠀⠙⠛⠻⠛⠑⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣧⣤⣴⠿⠿⣷⣤⡤⠴⠖⠳⣄⣀⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣀⣟⠻⢦⣀⡀⠀⠀⠀⠀⣀⡈⠻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠉⡇⠀⠀⠛⠛⠛⠋⠉⠉⠀⠀⠀⠹⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⠀⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠈⠑⠪⠷⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣦⣼⠛⢦⣤⣄⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠢⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠲⠖⠛⠻⣿⡿⠛⠉⠉⠻⠷⣦⣽⠿⠿⠒⠚⠋⠉⠁⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣾⠛⠁⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⠀⠀⠀ ⠀⠀⠀⠀⣰⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀ ⠀⠀⠀⣰⣿⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣧⣄⠀⠀⠀⠀⠀⠀⢳⡀⠀ ⠀⠀⠀⣿⡾⢿⣀⢀⣀⣦⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⣫⣿⡿⠟⠻⠶⠀⠀⠀⠀⠀⢳⠀ ⠀⠀⢀⣿⣧⡾⣿⣿⣿⣿⣿⡷⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢿⣿⣧⠀⡀⠀⢀⣀⣀⢒⣤⣶⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⠀⡾⠁⠙⣿⡈⠉⠙⣿⣿⣷⣬⡛⢿⣶⣶⣴⣶⣶⣶⣤⣤⠤⠾⣿⣿⣿⡿⠿⣿⠿⢿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⣸⠃⠀⠀⢸⠃⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⠟⡉⠀⠀⠀⠈⠙⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⣿⠀⠀⢀⡏⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠛⠉⠁⠀⠀⠀⠀⠀⠉⠠⠿⠟⠻⠟⠋⠉⢿⣿⣦⡀⢰⡀⠀⠀⠀⠀⠀⠀⠁ ⢀⣿⡆⢀⡾⠀⠀⠀⠀⣾⠏⢿⣿⣿⣿⣯⣙⢷⡄⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣻⢿⣷⣀⣷⣄⠀⠀⠀⠀⢸⠀ ⢸⠃⠠⣼⠃⠀⠀⣠⣾⡟⠀⠈⢿⣿⡿⠿⣿⣿⡿⠿⠿⠿⠷⣄⠈⠿⠛⠻⠶⢶⣄⣀⣀⡠⠈⢛⡿⠃⠈⢿⣿⣿⡿⠀⠀⠀⠀⠀⡀ ⠟⠀⠀⢻⣶⣶⣾⣿⡟⠁⠀⠀⢸⣿⢅⠀⠈⣿⡇⠀⠀⠀⠀⠀⣷⠂⠀⠀⠀⠀⠐⠋⠉⠉⠀⢸⠁⠀⠀⠀⢻⣿⠛⠀⠀⠀⠀⢀⠇ ⠀⠀⠀⠀⠹⣿⣿⠋⠀⠀⠀⠀⢸⣧⠀⠰⡀⢸⣷⣤⣤⡄⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⢼⡇ ⠀⠀⠀⠀⠀⠙⢻⠄⠀⠀⠀⠀⣿⠉⠀⠀⠈⠓⢯⡉⠉⠉⢱⣶⠏⠙⠛⠚⠁⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⠀⠀⠀⠀⠀⠻⠄⠀⠀⠀⢀⣿⠀⢠⡄⠀⠀⠀⣁⠁⡀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⢀⣐⡟⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢠⡇

⠀⠀⠀⠀⠀⠀⢀⣤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⢤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡼⠋⠀⣀⠄⡂⠍⣀⣒⣒⠂⠀⠬⠤⠤⠬⠍⠉⠝⠲⣄⡀⠀⠀ ⠀⠀⠀⢀⡾⠁⠀⠊⢔⠕⠈⣀⣀⡀⠈⠆⠀⠀⠀⡍⠁⠀⠁⢂⠀⠈⣷⠀⠀ ⠀⠀⣠⣾⠥⠀⠀⣠⢠⣞⣿⣿⣿⣉⠳⣄⠀⠀⣀⣤⣶⣶⣶⡄⠀⠀⣘⢦⡀ ⢀⡞⡍⣠⠞⢋⡛⠶⠤⣤⠴⠚⠀⠈⠙⠁⠀⠀⢹⡏⠁⠀⣀⣠⠤⢤⡕⠱⣷ ⠘⡇⠇⣯⠤⢾⡙⠲⢤⣀⡀⠤⠀⢲⡖⣂⣀⠀⠀⢙⣶⣄⠈⠉⣸⡄⠠⣠⡿ ⠀⠹⣜⡪⠀⠈⢷⣦⣬⣏⠉⠛⠲⣮⣧⣁⣀⣀⠶⠞⢁⣀⣨⢶⢿⣧⠉⡼⠁ ⠀⠀⠈⢷⡀⠀⠀⠳⣌⡟⠻⠷⣶⣧⣀⣀⣹⣉⣉⣿⣉⣉⣇⣼⣾⣿⠀⡇⠀ ⠀⠀⠀⠈⢳⡄⠀⠀⠘⠳⣄⡀⡼⠈⠉⠛⡿⠿⠿⡿⠿⣿⢿⣿⣿⡇⠀⡇⠀ ⠀⠀⠀⠀⠀⠙⢦⣕⠠⣒⠌⡙⠓⠶⠤⣤⣧⣀⣸⣇⣴⣧⠾⠾⠋⠀⠀⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⣭⣒⠩⠖⢠⣤⠄⠀⠀⠀⠀⠀⠠⠔⠁⡰⠀⣧⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⢤⣀⣀⠉⠉⠀⠀⠀⠀⠀⠁⠀⣠⠏⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠒⠲⠶⠤⠴⠒⠚⠁⠀⠀

“s-stop aruguing!” shut the fuck up im trying to find symbols dumbass ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠒⠋⠉⠭⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⡋⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠶⠛⠋⠁⠀⠀⠀⠁⠹⠝⠛⠢⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣴⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢨⠛⢦⣄⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠲⣌⠙⢦⣰⠿⠋⢀⣀⡠⠴⠶⠒⠚⣫⣽⣯⣉⡛⠒⠲⠶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣶⢻⣶⠚⠋⠁⠀⢀⣠⢤⣾⡿⠟⠛⠻⢿⣤⣀⣀⠀⠀⠉⠓⠢⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣾⣧⠀⠚⠉⠉⠁⡿⠋⠀⠀⠀⠀⠈⠀⠀⠉⠛⠲⣤⢀⠀⢀⣽⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⠲⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠽⡇⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⠿⠻⢿⣿⣗⣆⠀⠀⠀⠀⠀⠀ ⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⢀⣠⣤⣂⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠈⠳⡄⠀⠀⠀⠀ ⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢄⡀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢠⣿⠟⠉⠀⠈⠓⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠀⠀⠙⣆⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢦⡀⠙⢦⡀⠀⠀⠀⠀⣼⠁⠀⠀⡾⠁⠀⣠⣀⡀⠀⠈⣧⠀⠀⠀⠀⣠⡴⠖⠦⣤⡀⠀⠀⠀⠀⠀⠘⣧⠀⠀ ⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠙⢦⡀⢀⡴⠃⠀⠀⢰⠃⢠⡞⠙⣿⣿⡆⠀⠸⡆⠀⠀⣼⠃⣅⣀⣀⠀⠉⢳⡄⠀⠀⠀⠀⠸⣆⠀ ⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠶⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠀⢻⡉⠐⠓⠒⠤⢼⣀⢸⣿⣶⣿⣿⣿⠀⢀⡇⠀⠀⡇⣾⠛⢻⣿⣧⠀⠀⢹⡀⠀⠀⠀⠀⠹⡀ ⠘⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠲⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⠘⡇⠀⠀⠀⠀⠀⠈⠛⢿⣿⣬⣿⠃⠀⣼⠁⠀⠀⣷⣿⣷⣿⣿⣿⠀⠀⠀⣷⠀⠀⠀⠀⠀⡇ ⠀⠻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣇⣠⠤⣤⣀⡀⠀⠀⠀⠻⡉⠁⢀⡴⠁⠀⠀⠀⠘⣿⣿⣇⣿⡟⠀⠀⢂⡟⠀⠀⠀⠀⠀⠁ ⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡈⠻⣦⠀⠀⠀⠀⠀⠀⣠⠟⠁⠀⠀⠀⢻⡙⠂⠀⠀⠀⢹⠔⠋⠀⠀⠀⠀⠀⠀⠙⢎⡉⠁⢀⣠⠤⠾⠦⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠘⢦⡶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠈⢧⣀⣀⣠⡤⠞⠁⠀⠀⠀⠀⠀⠀⢻⣄⠄⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⢸⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⣀⣤⣤⣀⠀⠀⠀⠀⠀⡀ ⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣳⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠽⣿⣆⠈⠙⠲⠦⣄⣀⣀⣀⠀⠀⠀⠀⢀⣀⣈⡵⠞⠁⠈⠁⠀⠀⠀⢀⠇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠲⠤⠤⠤⠴⠖⠺⣏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢿⣿⣷⣄⠀⠀⠀⠀⠀⠉⠉⠉⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⡟⠻⢿⣷⣶⣤⣄⣀⣀⣤⣾⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠻⠿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡽⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⣘⣦⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⠿⠿⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠦⠖⠒⠀⠀⠀⠀⠀⠀⠀⣠⡴⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⠤⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠷⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠀⠀⠀⠠⠀⠀⠀⠀⠠⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⢾⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠃⠀⠀⣀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⢀⠀⠋⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⡟⠀⠀⢀⡀⠀⠀⠀⠀⠀⣀⣀⣂⣀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⠷⠛⣫⣭⡉⠉⠲⣾⡿⢋⠉⣩⣭⣍⠛⢶⣄⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⠁⠀⠟⠧⠀⠸⣿⣿⣿⠀⠈⠛⠐⠀⠀⠈⠀⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠉⠋⠁⣠⣆⣀⣀⣠⣄⠉⠉⠅⠀⠀⠀⠀⠀⠂⠀⠀⠀⡁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⢈⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀⠀⡀⠠⠀⠀⠁⠁⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡶⡀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀ ⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠈⠙⠛⠻⠿⢿⣿⡿⠟⠛⠛⠉⠁⠀⠀⠀⠀⠀⠄⠀⡐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⢆⠀⠀⠂⠠⠀⠀⠀⡀⠀⢀⠀⠀⢄⠐⡁⠐⠀⠀⠀⠀⠀⠄⠀⠀⠀⢠⠀⠀⠀⠀ ⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠐⠀⠀⠀⠀⠙⠠⡀⣆⠀⠀⡂⡢⠐⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀ ⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠄⢀⠐⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠠⢸⡇⡇⠀⠀⠀ ⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⢀⣀⣀⣂⣀⣀⣠⣀⣀⣀⣀⣀⣀⡀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⠁⢃⠀⠀⠀ ⠀⠀⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠻⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⡇⢸⠀⠀⠀ ⠀⢸⣿⣿⡇⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣾⣦⣤⣄⣀⡀⠀⠀⠀⠀⠈⠀⣀⣤⡄⠀⠀⠀⠁⠀⣹⣿⣿⣿⣿⢿⣷⢸⡀⠀⠀ ⠀⣼⣿⣿⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⣠⣿⣿⣿⣿⠃⠀⣿⡏⡇⠀⠀ ⠀⣿⣿⡇⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⣀⣤⣶⣿⣿⣿⠟⠁⠀⠀⠉⠁⡇⠀⠀ ⠀⡿⠛⠃⠀⠀⠀⠀⠀⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⡇⠀⠀ ⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⡀⠀⡇⠀⠀ ⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡟⠛⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⡇⠀⠀ ⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠁⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⢹⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣷⠀⠀ ⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣿⠀⠀ ⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢹⡄⠀ ⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡀ ⢸⣿⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣣ ⣾⣿⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢀⣿ ⢿⢿⡄⠀⠀⠳⡀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠁⠀⣾⡟ ⠸⡈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁ ⠀⠑⢌⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠞⠉⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣤⡴⠋⠀⢀⣠⢿⡇⠀⣀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢸⣿⠀⠀⠀⠻⣀⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⠀⠸⠛⠓⠢⠄⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡤⢶⡲⠛⠽⠯⠽⠯⠿⠹⢖⡶⢤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⣴⣟⠟⣋⣁⠄⡐⢀⠂⠄⠂⠄⡐⠠⠀⠄⣈⣙⡫⢿⣦⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⣞⠟⣣⡾⠛⣉⣉⡛⢶⡄⠌⢠⠉⡐⠠⢡⡾⢛⣩⣉⡛⢷⣝⠫⡗⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⡞⡇⡁⢦⣏⢰⡏⠉⣿⣿⡆⣻⡌⠀⢆⠠⣁⡿⢰⠋⠹⣿⣿⡄⣻⡤⢈⢫⠷⡄⠀⠀⠀ ⠀⠀⢠⢿⣸⢃⠸⢸⣇⠿⠧⠼⠿⣻⡧⢸⢃⠛⣀⠤⡘⡧⢼⣧⠼⠿⠻⠧⣸⡇⠜⣀⡿⡸⡄⠀⠀ ⠀⢠⡟⢦⡹⢌⡸⣔⢶⣲⡖⣦⠔⡠⢂⠍⡎⡘⡄⠦⡑⢍⠰⣀⠦⣴⢲⣶⣲⠬⡍⢆⢯⡱⣛⡄⠀ ⢠⡿⣘⢣⡜⢪⠴⡌⢎⡡⠜⡄⣊⠱⣈⠒⠤⡑⢌⠰⡁⢎⠰⡐⢢⠌⡱⠢⣅⠳⣌⠳⣌⠶⣡⠿⡀ ⣸⠵⡩⢊⡜⣡⠞⡘⣤⣵⣮⣶⡶⢃⠉⡍⢩⠉⠍⡩⢉⠍⢩⠐⢷⣾⣴⣵⣨⠱⡌⣧⢩⠘⢕⡚⣇ ⣟⠼⣁⠧⣊⣽⣾⣿⣿⣿⣿⣿⠃⠈⠀⠀⠀⠈⠀⠀⠀⠈⠀⠊⠘⣿⣿⣿⣿⣿⣷⣧⣣⢚⡌⣝⢺ ⣿⠸⣉⢯⡙⢿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡿⡜⢫⡜⡌⣿ ⣷⡡⣏⠦⣙⠼⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⠧⡙⣥⢺⢄⣻ ⢱⣇⢸⢎⡱⣊⢽⣿⣿⣿⣿⣿⣿⣷⣤⣀⡀⠀⠀⠀⢀⣀⣤⣾⣿⣿⣿⣿⣿⣿⡟⡸⣑⠦⡏⣸⡇ ⠈⣟⡄⢫⠖⡥⢎⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⡜⡱⠜⡼⢠⣷⠀ ⠀⠘⣽⡌⢳⡜⡢⢕⡹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢯⡘⠲⣍⡝⢡⢯⠃⠀ ⠀⠀⠘⣾⡄⢳⡍⠚⣴⢩⢻⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⡟⢱⢢⡍⢳⡜⢠⣿⠃⠀⠀ ⠀⠀⠀⠘⢿⡦⣙⢣⡓⢮⡘⢭⢛⡿⣿⡀⠀⠀⠀⠀⠀⠀⣿⢿⡛⣍⡚⢥⢎⡹⢆⣱⡿⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢶⣣⡙⢦⡙⢦⢋⡶⠱⡌⡟⠯⣍⠻⡻⢱⠩⣖⢱⠸⣘⠣⢎⣵⡮⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠻⢵⡼⣂⡅⠊⠝⠛⠼⠳⠬⠳⠗⢋⠋⠱⢈⣅⢧⡻⠚⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠚⠿⠶⣞⣖⣦⣤⣥⡖⣶⠮⠿⠛⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠋⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⡼⠇⠀⠀⠀⠘⡆⠀⠀⠐⠀⠀⠀⢀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠓⠢⢼⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⣠⠎⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠈⣇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⢀⡼⡇⠀⠀⠀⠀⠀⠀⢸⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⢠⠞⠀⢹⡄⠀⠀⠀⠀⠀⠘⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⣰⠁⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⢹⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⡴⠃⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⡇ ⠀⠀⠀⠀⠀⠀⠀⢰⠋⠀⠀⠀⠀⠀⠀⢀⡾⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⢸⡁⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⡇ ⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⡿⣯⡷⡴⢦⣤⡠⣶⡶⠀⢷⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⡾⠀ ⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⣼⣥⣤⣤⣤⣤⣤⣤⣤⣀⣀⣀⣀⠀⠈⢧⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢀⡇⠀ ⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠉⠙⠻⢿⣿⣿⣿⣿⣿⣿⠛⢦⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⡇⠀ ⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⠳⠀⢳⡀⢹⡇⠀⠀⠀⠀⠀⡾⡇⠀ ⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡿⠘⠀⠀⠹⣼⡇⠀⠀⠀⠀⢠⠇⠀⠀ ⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡿⠁⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⡾⠀⠀⠀ ⠀⠀⢠⡏⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠁⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⢸⠁⠀⠀⠀ ⠀⠀⡾⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⡟⠀⠀⠀⠀ ⠀⣴⠓⣾⣳⣀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠃⠀⠀⠀⠀⠀⠀⢸⡇⢀⠇⠀⠀⠀⠀ ⣾⠃⠀⠀⠀⠑⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠈⡇⢸⠀⠀⠀⠀⠀ ⠹⡀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣾⠀⠀⠀⠀⠀ ⠀⢳⡄⠀⠀⠀⠀⠘⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⣿⠀⠀⠀⠀⠀ ⠀⠀⣷⡄⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⡏⠀⠀⠀⠀⠀ ⠀⢀⡇⢹⣄⠀⠀⠀⠀⣀⠉⠓⠶⢄⡀⠀⠀⠀⠀⠀⢀⣠⠴⠋⠣⣄⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⣸⣧⠀⠀⠀⠀⠀ ⠀⣴⣿⠋⠘⣆⠀⢰⠶⠤⢍⣛⣶⠤⠿⣷⣦⡀⠒⠚⡟⠀⠀⠀⠀⠈⠛⠢⠤⡄⠀⠀⢀⡴⢯⠴⣳⠇⠀⠀⠀⠀⠀ ⠀⠀⠉⠀⠀⠘⢦⡈⠻⣖⠤⣤⣉⣉⣹⣯⣭⠉⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠛⣫⣼⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠑⣄⠉⢦⡀⠀⠀⠈⠉⠁⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢿⣷⢚⡝⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢶⣷⠇⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠷⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠙⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⡆⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⣾⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣷⡦⠀⠀⠀⠀⢰⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠃⣠⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣆⠀⠀⠀⣾⣿⣿⣿⣷⠄⠀⠰⠤⣀⠀⠀⣴⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠃⢺⣿⣿⣿⣿⡄⠀⠀⣿⣿⢿⣿⣿⣦⣦⣦⣶⣼⣭⣼⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣷⡆⠂⣿⣿⣞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢙⣿⣿⣿⣿⣷⠸⣿⣿⣿⣿⣿⣿⠟⠻⣿⣿⣿⣿⡿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢿⣿⣿⣿⣿⡄⣿⣿⣿⣿⣿⣿⡀⢀⣿⣿⣿⣿⠀⢸⣿⣿⠅⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡀⣠⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠠⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣻⣿⣿⣿⣿⣿⡟⠋⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠙⢿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⠿⢿⡿⠛⠋⠁⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣅⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⣿⣿⣿⡟⠃⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⣿⣿⣿⣿⣿⣤⡀⠀⠀⠀ ⠀⠜⢠⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣦⠄⣠⠀ ⠠⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠛⣿⣿⣿⡿⠏⠀⠀⠀⠀⠀⠀⢳⣾⣿⣿⣿⣿⣿⣿⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿ ⠀⢨⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⡿⡿⠿⠛⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠏⠉⠻⠿⠟⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣠⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠘⣿⣿⣿⣿⠟⠁⠀⠀⠀⠹⣿⣿⣿⣿⣿⠟⠁⠀⠀⠹⣿⣿⡿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⢼⣿⠀⢿⣿⣿⣿⣿⠀⣾⣷⠀⠀⢿⣿⣷⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⣿⣿⣿⣷⡀⠀⠀⠈⠋⢀⣿⣿⣿⣿⣿⡀⠙⠋⠀⢀⣾⣿⣿⠀⠀⠀⠀⠀ ⢀⣀⣀⣀⣿⣿⣿⣿⣿⣶⣶⣶⣶⣿⣿⣿⣿⣾⣿⣷⣦⣤⣴⣿⣿⣿⣿⣤⠤⢤⣤⡄ ⠈⠉⠉⢉⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⣀⣀⡀⠀ ⠐⠚⠋⠉⢀⣬⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣥⣀⡀⠈⠀⠈⠛ ⠀⠀⠴⠚⠉⠀⠀⠀⠉⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠋⠁⠀⠀⠀⠉⠛⠢⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⣀⡀⠀⡇⠀⠠⠁⠂⡔⣿⣿⣿⣿⣿⣿⣏⡛⠻⣆⠀⢂⠌⣑⠢⠄⠀⠀⠐⠀⠉⠋⠉⠁⠀⠀⠀⠄⢂⠡⠒⠄⡡⢨⣿⠟⠉⢰⣿⣿⣿⣿⣿⣿⠐⠀⡀⠄⠀⠀⠀⠀⠀⠀⣤⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠋⢿⣇⠀⠃⠈⠄⡁⠆⢤⣿⣿⣿⣿⣿⣿⡗⢨⢱⣬⡗⢈⡘⠄⢂⠌⡒⠤⠀⠆⠀⡀⡤⠂⠀⠒⠙⠤⢂⠄⡉⠐⢰⣿⣿⠀⣴⣠⣿⣿⣿⣿⣿⣿⡀⡀⠒⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠜⣿⣆⠀⡌⠠⠡⠌⠤⠿⣿⣿⣿⣿⣿⡇⢀⠂⡹⣷⡠⠌⠰⣉⢄⡐⠀⢊⠀⠁⠐⠀⠂⠸⠦⠀⢀⠂⠄⠃⣼⢂⣿⣯⣼⣉⣼⢻⣿⣿⣿⣿⣿⣄⡝⠀⢀⠀⢀⡜⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⡄⠀⠀⠈⣿⣤⣇⠄⠱⣈⠲⣉⣿⣿⣿⣿⣿⡗⡤⠈⢀⠹⣿⣎⣴⣌⠀⠀⠐⠠⠤⢠⠀⠀⢀⠀⠀⣆⠀⠠⢈⢼⣣⣿⣿⣿⣿⣹⣾⢹⣿⣿⣿⣿⡿⡜⢀⢠⡞⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠀⠁⠀⣹⣷⠻⢷⣆⡀⠣⣿⣿⣿⣿⣿⣿⣟⠰⣧⠈⠌⣿⣿⣧⡝⡃⠌⡀⠀⠀⠀⠠⠔⠂⠀⠈⠙⠀⢤⣮⣿⣿⣿⣿⣿⡟⣹⣰⣯⣿⣿⣿⣿⡗⣠⡷⢈⠡⣠⣿⣅⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣾⣾⣿⣿⣧⠈⡝⢿⣴⣉⡿⣿⣿⣿⣿⣯⠘⡹⢧⠄⠪⠟⢛⠻⠷⢶⣄⠠⠀⠀⠀⠀⠀⢀⡀⢤⣔⣴⡾⠷⠶⠆⠨⠋⢡⠉⢻⢹⣿⣿⣿⣿⡖⢉⣰⣾⣿⣿⣿⡿⢻⡿⢶⣄⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡾⠿⣿⡏⠡⢘⢭⣿⣾⢿⣷⣶⣤⣽⣦⣼⣿⣿⣿⣿⣿⡃⢄⠃⡘⠄⡐⠠⠐⠈⡀⠈⠛⠿⠶⠶⠾⠿⠿⠿⠿⠛⠡⠐⠀⠀⢂⡐⢀⠂⠌⣸⣿⣿⣿⣿⠗⠚⠻⣿⣿⣿⡯⢿⣿⣦⡝⡠⠌⠙⣿⡻⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣾⠋⢀⠠⣿⡆⢰⢋⢞⣿⣧⣻⣿⡇⠀⠈⠛⠾⢉⣿⣿⣿⣿⣗⡂⠡⢘⠀⠂⠥⢢⠀⠄⠐⠀⡀⠀⠀⠀⠀⠀⠀⢠⠀⠡⠄⠠⢈⠶⢀⠃⠄⠂⣼⣿⣿⣿⠏⠀⠀⠘⣿⣿⢿⣳⢍⣿⣿⣷⣵⠨⡐⠘⣷⣤⠬⣙⡻⢶⣤⣀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠛⣿⣿⠚⠉⢰⣿⣏⠥⠂⢎⣿⣿⣾⡿⣧⡀⠀⠀⠀⠹⣶⣿⣿⣿⣧⢸⡀⠡⣌⠰⣀⠣⡀⢒⠠⢰⠀⠀⠀⠀⠀⠂⠀⠈⠄⠐⣈⠦⣉⠂⠆⡈⠄⢩⣿⣿⡿⠃⠀⠀⠀⢸⣿⣯⣿⣿⣷⡾⢟⠻⣿⣇⠡⢃⠾⣿⣶⠈⠙⠾⠏⠹⣷⣄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⡄⢠⣻⡇⠄⠈⢲⢻⣿⡰⣁⠊⣿⣿⣿⣿⠿⣿⣆⠀⠀⡀⠠⠈⢿⣿⣿⣅⣰⣨⠄⢂⠄⡂⠵⠊⠔⢢⠀⠀⠀⠂⢀⠂⠀⠰⣌⡒⠌⠂⠔⡈⢆⠱⣈⠆⢡⣿⣁⠀⠀⠀⠀⢹⣿⣿⣿⠉⢿⣧⣨⣿⣿⣿⠀⠂⣴⡿⢿⣧⠀⠀⠹⠀⠹⣿⣆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣇⣄⣿⣿⣶⠁⠾⣿⣿⣇⠦⡙⠿⣿⣿⣯⣽⣬⣿⠇⢀⡀⡁⡐⣬⠻⣿⣿⣮⣕⠈⡰⢈⠔⡠⠉⠆⢂⠖⠀⠀⠠⠈⠄⡈⢣⠐⣈⠐⣉⠐⡌⠄⣶⣦⣴⣾⡟⠃⠀⠀⠀⠀⠀⠙⠻⣮⡟⢠⣹⢿⣄⠀⢹⡷⣅⣾⠀⠀⢻⣆⠈⣱⡇⡡⣿⣿⡆ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡏⠈⣿⡏⢉⣿⣿⠎⡱⣿⡿⢿⣧⠙⣛⣿⣿⣺⣿⣿⠏⢀⣀⣤⣼⠿⠬⣿⣿⣿⢿⣟⣶⣵⣮⣶⣷⣿⣾⣶⣿⣄⣤⡧⢥⣦⣴⣥⡾⣤⢿⣦⣿⣿⡿⣶⣿⣿⢿⡁⢀⠀⢀⠀⠀⣀⣀⣀⣈⣻⣿⣻⠳⣿⣇⣸⡗⡋⣿⣄⣀⣘⣿⠐⢲⣽⣷⣿⣿⠇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⣿⡿⠓⠂⣿⣿⣿⣿⣃⢠⣱⣿⠓⠻⣿⣃⣼⠟⢛⣿⣿⠇⠀⠀⠀⠥⠤⡤⠠⠀⠀⠀⢸⡏⠨⠀⠀⢀⣀⣀⣸⡁⢀⣀⠀⢃⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣉⣙⣿⣿⣋⣿⣷⠙⣿⣯⠽⡿⣿⣾⢿⡿⢿⣿⡏⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠩⢭⣿⣷⣿⣏⠙⠋⠉⠉⠉⣀⣾⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁⠀⠀⠀⠠⠄⠀⠄⠀⠤⠀⠀⠙⠀⡀⠀⠠⠁⡀⠈⠐⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠿⠷⣶⣿⡇⠐⢶⣿⣼⣸⣄⣸⣧⠀⠀ ⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠃⢀⡀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠒⠀⠠⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠩⣟⣛⢛⡋⠉⠀⠀⠀ ⠈⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢠⣼⠋⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⣀⠀⠀⠀⢀⡀⠁⠈⢁⡀⢀⢀⣀⠀⣀⠀⠀⡀⠀⠀⠀⡀⠀⡀⠀⠀⠀⠀⠀⠀⢀⡀⢀⠀⠀⠀⢀⡀⠀⠀⠀⠘⢩⠤⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⠿⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣾⡇⠀⣿⣆⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⡶⠟⠋⠉⠁⣤⣤⠀⠉⠉⠛⠷⣦⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣾⠋⢀⣴⣶⣾⣿⣿⣿⣿⣿⣶⣦⡀⠈⢻⣆⠀⠀⠀⠀ ⠀⠀⠀⣾⢃⣠⠾⠿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠷⣄⡀⢻⡆⠀⠀⠀ ⠀⠀⣸⡿⢋⡁⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⢈⡙⢾⣇⠀⠀⠀ ⢀⣾⠋⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡄⠙⢷⡄⠀ ⣾⡇⠀⣼⠀⠀⠀⠛⠀⠀⡀⢲⡶⢀⡀⠀⠛⠀⠀⠀⢿⠀⢸⣷⠀ ⠸⣧⡀⢹⡄⢀⣀⠀⠀⠈⠧⠞⠑⠖⠃⠀⠀⢀⣀⢀⡿⢀⣼⠇⠀ ⠀⠈⠙⢻⡿⠉⠉⢳⣄⣀⡀⠀⠀⢀⣀⣀⡞⠉⠉⢻⡟⠛⠁⠀⠀ ⠀⠀⠀⠀⠻⠶⠶⠾⠉⠛⠛⠛⠛⠛⠛⠉⠻⠶⠶⠟⠁⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⢲⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠖⠒⠛⠉⠉⠉⠛⠻⢦⡀⠈⡇⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡤⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣿⠀⡏⡬⣍⣲⡤⠤⠤⠤⠤⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⡤⠖⠚⢉⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⡧⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠦⣀⠀⠀⠀⠀⠀ ⠙⣷⠅⢀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠤⠤⢄⣀ ⠀⠘⣦⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⠋⠀⠠⡇⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡈⡆⡟ ⠀⠀⠈⡏⠀⠀⠀⠀⠀⠀⠠⣿⣷⠀⠰⡏⢻⠉⠀⢸⡀⠀⠀⡇⠀⢹⣿⢆⢀⡀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠟⡼⠁ ⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠸⣸⡆⠀⠀⠁⠀⠀⡇⠀⢰⡇⠈⠉⠛⠂⠸⣿⠆⠈⠁⠀⠀⠀⠀⠀⡟⠀⠀ ⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀ ⠀⠀⠀⠀⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠢⠧⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀ ⠀⠀⠀⠀⠀⠛⠿⣦⣀⣀⣠⣤⣤⠖⠀⠀⠀⠀⠀⠐⢦⣳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣰⡿⠃⠀⠀⠀⠀⠀⠀⢢⠀⠈⠉⢻⡗⠂⠀⠀⠀⠀⠀⠀⠙⠲⣶⠦⠤⠔⠚⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣻⠁⠀⠀⠀⠀⠀⠀⠀⠈⣉⣙⠚⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢱⡟⠲⡴⠒⠲⠆⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⡞⠻⡄⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠢⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⡸⠻⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⠙⠚⠛⢳⡤⣦⣄⣰⣴⠶⠶⠴⠶⠼⠷⠶⠤⠤⠤⠤⠤⠦⢴⡋⠉⠁⣰⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣴⣿⣿⠿⣟⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣏⡏⠀⠀⠀⢣⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣟⠧⠤⠤⠔⠋⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⣿⡀⢀⣶⠤⠒⠀⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢹⣧⠀⠀⠀⠀⠀⠈⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠈⢿⣆⣠⣤⣤⣤⣤⣴⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣾⢿⢿⠀⠀⠀⢀⣀⣀⠘⣿⠋⠁⠀⠙⢇⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣾⢇⡞⠘⣧⠀⢖⡭⠞⢛⡄⠘⣆⠀⠀⠀⠈⢧⠀⠀⠀⠙⢿⣄⠀⠀⠀⠀ ⠀⠀⣠⣿⣛⣥⠤⠤⢿⡄⠀⠀⠈⠉⠀⠀⠹⡄⠀⠀⠀⠈⢧⠀⠀⠀⠈⠻⣦⠀⠀⠀ ⠀⣼⡟⡱⠛⠙⠀⠀⠘⢷⡀⠀⠀⠀⠀⠀⠀⠹⡀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠹⣧⡀⠀ ⢸⡏⢠⠃⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠸⣷⡀ ⠸⣧⠘⡇⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⣿⠇ ⠀⣿⡄⢳⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠈⠆⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀ ⠀⢹⡇⠘⣇⠀⠀⠀⠀⠀⠀⠰⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⣼⡟⠀⠀ ⠀⢸⡇⠀⢹⡆⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢳⣼⠟⠀⠀⠀ ⠀⠸⣧⣀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⢃⠀⢀⣴⡿⠁⠀⠀⠀⠀ ⠀⠀⠈⠙⢷⣄⢳⡀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⣠⡿⠟⠛⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠻⢿⣷⣦⣄⣀⣀⣠⣤⠾⠷⣦⣤⣤⡶⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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

⠀⢀⠀⢀⣀⣠⣤⣤⣤⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣠⣤⣤⣤⣤⣀⠲⢦⣄⡀⠀⠀ ⡶⢟⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠰⣷⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣬⡛⢷⣔ ⣾⡿⠟⠋⠉⠁⠀⡀⠀⠀⠀⠀⠈⠉⠉⠙⠛⢻⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠈⠙⢛⣛⣛⣛⣛⣉⢉⣉⡀⠀⠀⠀⠀⠀⠈⠉⠛⢿⣷⣝ ⠃⠀⠀⠀⠀⠀⠀⣛⣛⣛⣛⣛⣛⢛⡛⠛⠛⠛⣰⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣌⠛⠛⢛⣛⣛⣛⣛⣛⣛⣛⣓⣀⠀⠀⠀⠀⠀⠈⢻ ⠀⠀⠀⢀⣤⡾⠛⢻⣿⣿⣿⡿⣿⡟⢻⣿⠳⠆⠘⣿⣦⠀⠀⠀⠀⠀⠀⠀⣰⣿⠁⠐⠛⣿⡟⢻⣿⣿⣿⣿⢿⣟⠛⠻⣦⣀⠀⠀⠀⠀ ⠀⠀⢴⠿⣧⣄⣀⣘⣿⣿⣿⣿⣿⡿⣀⡙⢷⠀⢀⡿⠁⠀⠀⠀⠀⠀⠀⠀⠈⢻⡖⠀⣾⣋⣀⣺⣿⣿⣿⣿⣿⣏⣀⣤⣴⠿⢷⠀⠀⠀ ⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠙⠉⠉⠉⠉⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠉⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠆⠀⠀⢀⣿⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⠟⠁⠀⠀⠀⣾⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣤⣤⣴⣶⣾⠿⠛⠋⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠞⠛⠛⠉⠉⠉⠉⠉⠙⠛⢦⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⠉⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠐⢹⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⡾⠋⠀⠀⠀⠀⢀⣀⣤⣤⠴⠶⠶⠶⠶⠶⡶⡾⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣴⠋⠀⠀⢀⡴⠾⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡼⠁⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠃You forgot something... ⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⣰⣏🧠⣀⣀ ⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠀⠀⠀⠀⠀⢸⡇⣠⠏⠉⠛⠛⠋⠁ ⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⢸⣿⠋⠀⠀⠀⠀⠀⠀ ⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀ ⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⣼⠃⣧⠀

⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⡀⠀⠀⠀⣀⣀⠀⠀ ⠀⣾⠛⠛⠻⢶⣤⣤⣤⣤⣤⣴⠏⠀⠈⠻⣶⠞⠛⠉⠙⣷⠀ ⠀⣿⠀⠀⠀⠀⠈⠉⠀⠀⢠⡟⠀⢠⡖⣶⠿⢶⣄⣀⣤⣿⡄ ⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠸⣇⣀⣈⣻⡇⠀⠀⢹⣯⠀⠈⣿ ⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠳⢤⣴⡿⠾⠀⢀⢿ ⣺⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⠶⠿⣷ ⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⠻ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

☁️ ☀️ ☁️ ☁️ ☁️ ✈️ ☁️ --🌲🌲-------🌲--🌲- / | \ / |🚔 \ / 🚔 | 🚔 \ / | \ / |🚘 \ 𝐓𝐇𝐄𝐘 𝐒𝐄𝐄 𝐌𝐄 𝐑𝐎𝐋𝐋𝐈𝐍 𝐓𝐇𝐄𝐘 𝐇𝐀𝐓𝐈𝐍

⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢰⣿⡿⠗⠀⠠⠄⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⡜⠁⠀⠀⠀⠀⠀⠈⠑⢶⣶⡄ ⢀⣶⣦⣸⠀⢼⣟⡇⠀⠀⢀⣀⠀⠘⡿⠃ ⠀⢿⣿⣿⣄⠒⠀⠠⢶⡂⢫⣿⢇⢀⠃⠀ ⠀⠈⠻⣿⣿⣿⣶⣤⣀⣀⣀⣂⡠⠊⠀⠀ ⠀⠀⠀⠃⠀⠀⠉⠙⠛⠿⣿⣿⣧⠀⠀⠀ ⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡇⠀⠀ ⠀⠀⠀⣷⣄⡀⠀⠀⠀⢀⣴⡟⠿⠃⠀⠀ ⠀⠀⠀⢻⣿⣿⠉⠉⢹⣿⣿⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠉⠁⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣦⣤⣄⣀⢀⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣤⡶⠒⠚⠋⠉⠉⠀⠀⠀⠀⡉⠛⢾⡄⣀⠀⠀⠀⠀⠀ ⠀⠀⠀⢲⣾⠿⢿⣿⣿⣦⡀⠀⠀⠀⠀⠀⣴⡿⠛⠿⢿⣿⣿⣽⣆⠀⠀⠀ ⠀⠀⣴⣿⠁⠀⣰⣿⣿⣿⣷⠀⠀⠀⣠⣾⡏⠀⠀⢀⣼⣿⣿⣿⣿⣦⠀⠀ ⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⢰⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⡏⢣⠀ ⢸⣿⣿⣿⣿⣿⡿⢿⣿⡿⠃⠀⠀⠸⣿⣿⣿⣿⣿⣿⡿⠻⣿⣿⣿⠇⠘⡇ ⢀⣿⣿⣿⣿⣯⣠⠾⠛⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣧⣴⠿⠟⠁⠀⠀⡇ ⠘⡇⠈⠉⠉⠉⠀⠀⠀⢀⡀⠀⠀⢀⣀⡀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⢀⡇ ⠀⢿⡀⠀⠀⠀⠀⠀⠀⠘⠻⣦⣶⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠀ ⠀⠈⣳⡀⠀⠀⠀⢀⡴⠒⠲⢄⣀⠤⠶⢤⡀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀ ⠀⠀⠐⢝⣦⣀⣠⣼⣧⡀⠀⠀⠀⠀⣰⣾⣧⣤⡀⠀⠀⠀⣠⠔⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⢽⡟⠀⣿⣷⡄⠀⠀⣨⣿⡏⠻⠎⣷⡤⠖⠊⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣼⠃⠀⠈⢿⣷⡀⠀⢿⡅⠀⠀⠀⢹⠇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⠦⢤⣤⠞⠉⠉⠉⠉⠙⠦⢤⠤⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡶⠾⠛⠛⠋⠉⠉⠉⠉⠉⠛⠛⠻⠶⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⣦⣄⣤⣤⣤⣤⣤⣤⣀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠈⠙⢿⣄⠀⠀⠀⠉⠙⠻⣦⡀ ⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠉⠳⣄⠀⠀⠀⠀⢸⠁⠈⢣⠀⠀⠀⠙⢧⡀⠀⠀⠀⠀⠹⣧ ⠀⠀⠀⠀⠀⠀⢠⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠸⡆⠀⠀⠀⠸⣇⠀⠈⣧⠀⠀⠀⠀⠻⣄⠀⠀⠀⠀⣿ ⠀⠀⠀⠀⠀⣰⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⣀⣠⣿⠀⠀⠀⠀⢻⣷⣾⣿⡆⠀⠀⠀⠀⠹⣆⠀⠀⢰⡿ ⠀⠀⠀⠀⢠⡿⢀⣠⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⡇⠀⠀⠀⠘⡿⠿⠟⣇⠀⠀⠀⠀⠀⢹⡆⢀⣿⠃ ⠀⠀⠀⢠⣾⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡌⠉⠀⡇⠀⠀⠀⠀⠹⡀⠀⡏⢀⣴⣿⣿⣿⠀⢿⡿⠁⠀ ⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⣶⣶⡄⠀⠳⣤⡼⠁⠀⠀⠀⠀⠀⠙⠚⠁⡈⣛⠟⠛⠉⠀⢸⣧⠀⠀ ⢀⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠿⠿⠃⠀⠀⢀⢲⡦⡀⠀⠀⠀⣀⣠⣤⣾⡿⠏⠀⠀⠀⠀⠀⣿⠀⠀ ⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡯⠭⣭⣿⠿⠟⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀ ⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⢶⣿⣿⡛⠛⠛⠛⠾⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀ ⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⠋⠁⠐⠛⠛⠋⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀ ⠈⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⠀⠀ ⠀⠀⠉⠛⠷⢶⣶⠶⠶⠶⠖⠛⠋⠁⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⣦⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⢠⣾⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠹⣷⣀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⢀⣴⡿⠁⠀⠀⠀⠀⡤ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣶⣄⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⢀⣤⣿⠏⠀⠀⠀⠀⠀⠲⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⣠⡴⠋⣹⡏⠀⠀⠀⠀⠀⠀⠀⠈ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣋⣠⡴⠶⠛⠁⠀⣰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠟⠉⠉⠀⠀⠀⠀⠀⣴⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷⣤⣄⣀⣀⣀⣤⡴⠞⠋⠀⠀⠀⠀⠀⠀⠀⢀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀⠀⠀⠀⠀⢀⣤⣶⠆⢀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣄⠀⠀⠀⠙⣛⣡⣶⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡿⢿⣿⣦⣄⣀⣀⣀⣤⣤⣤⣤⣴⣶⣾⣿⣿⢿⣿⣶⣶⣿⣿⣿⣄⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⢫⣞⣽⣻⣿⠿⠛⠋⠉⠉⠉⠉⠙⠋⠛⠻⠿⢶⣿⣼⣏⠸⣿⡿⢿⣶⣤⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣯⣿⣟⣿⡿⠶⢶⠶⠶⠶⡶⢶⣶⣦⣤⣄⣀⠀⠀⢻⣯⢳⣭⣿⣷⣍⠿⣿⣦⡀⠀ ⠀⠀⠀⠀⣠⣶⣶⣶⣦⣄⡀⠀⢀⠠⢀⣴⣿⣿⣯⣩⣷⠟⠁⣀⠃⡄⢂⡑⢂⠐⡠⢀⠠⢀⠉⡙⣿⡀⠀⢿⣿⣟⣣⠜⣿⣖⡈⢻⣿⣆ ⢀⣤⣶⢟⣻⠟⡹⢏⣷⣿⣿⠀⠀⣠⣿⡿⠁⠀⢹⣿⠃⠠⢘⡀⠆⡈⢶⣍⠠⢈⠔⡀⢆⠈⢲⣔⠘⣷⣤⣶⠿⠛⠿⢿⣖⣿⣇⠀⠹⣿ ⢫⡷⢏⠿⣉⠎⡥⣛⣾⣲⡟⠀⣰⣿⠟⠀⠀⣀⣿⠇⠀⠀⠀⠀⠀⢈⣿⠇⠀⠁⠂⠐⠈⠂⠍⣿⣦⠈⠙⡀⡐⢈⠠⠈⠹⣿⣿⡆⢁⢹ ⣿⣧⣈⢦⡑⣎⡴⣯⡷⣿⠇⢠⣿⡟⢠⡖⢸⣹⣿⠀⡐⢂⠒⠀⢶⣾⣻⠃⠀⠤⡀⠄⡄⠀⠤⣿⣿⡄⢀⠰⣽⠀⡐⢈⠀⠌⠛⠃⡄⢈ ⣿⣽⣿⣷⣿⣻⣟⣧⠿⠋⠀⣼⣿⣣⣿⠀⢆⣿⣿⣤⣅⡂⠌⢈⢧⡟⢹⡁⠌⡐⠠⠈⠄⡁⢊⣿⠞⣿⡄⠘⣿⡄⠰⢡⢈⡒⠈⡔⢈⠄ ⠀⠀⠉⠉⠙⠉⠉⠁⠀⠀⠀⣻⣿⣿⣿⣈⣶⡝⠋⠟⠛⠿⠿⠞⠿⠃⠸⠶⠶⢶⣶⠧⣔⡠⢂⣿⠁⢺⣿⡀⢿⡃⢄⢃⠢⡱⢈⡐⠌⢂ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⡿⡟⢿⡅⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠻⠧⠀⢸⡟⣷⣻⡇⠀⢎⠰⣁⠢⡐⢌⠂ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⢷⣙⣼⣶⣿⣄⣀⠀⠀⠈⠄⠀⠁⠂⠐⠠⠀⠀⠀⠀⠀⠀⠀⠀⣿⣻⣿⡧⢈⠢⠑⡄⢢⠁⢆⡉ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⢏⣾⣿⠿⣿⣿⣿⣿⣷⡀⠀⠀⠀⡀⠀⠂⠀⠀⠠⠀⣴⡄⢀⠀⠀⣹⡷⣿⡷⠀⢂⠱⢈⡐⠌⢢⠐ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⢣⢾⣿⠃⡒⢄⠠⠈⠛⠿⠁⠀⠈⠀⠀⠐⠀⢀⣼⣿⣿⣿⣿⣶⣬⡄⢘⠧⣿⡏⠐⡀⣚⠠⠐⠌⡂⠌ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣯⣵⣿⣇⡘⠤⡉⠢⢁⠠⠀⠀⠀⠈⠀⠀⠀⠠⠘⠛⢛⠻⠿⠿⣿⣿⣿⣮⣞⣿⠅⠠⢐⡇⠄⢃⠘⡄⢃ ⠀⠀⠀⠀⠀⠀⣠⣾⡿⠟⡛⡍⣩⢙⡛⠿⣿⣦⡁⠀⠀⠘⣿⣄⣠⣴⣶⣿⣷⣿⣶⣦⣖⣠⠃⠤⣉⠉⡽⣾⡟⠀⢂⣿⢎⡁⠢⢈⠔⡡ ⠀⠀⠀⠀⠀⣴⣿⠟⡜⠁⠈⠑⡆⢣⠜⡳⣸⡽⣿⣦⡀⣴⣾⠿⠛⠉⣀⣤⡠⠤⣌⠩⡛⠿⣿⣦⠄⡽⣹⣿⠇⡈⣼⣟⡮⢀⠑⠠⢃⠖ ⠀⠀⠀⠀⣼⣿⠃⣼⠃⠀⠀⢠⡙⢢⢍⡱⢌⣿⣾⣽⣿⠟⢁⣤⡶⢟⠩⢤⡑⢎⡔⢣⢍⠲⣉⠻⣿⣔⢣⣿⠡⢰⣿⢎⡗⠠⠉⠄⢫⠜ ⠀⠀⠀⢀⣿⡿⠀⣿⡇⡔⢢⡁⢄⢣⢎⢲⠡⢎⡛⢭⢡⠛⣏⠱⣘⢢⡙⢦⡘⢦⡘⢥⡊⠵⡨⣇⠹⣿⣾⣏⢲⣿⣏⢾⡇⠐⡉⠄⢣⠚ ⠀⠀⠀⠀⣿⣷⠈⣿⡔⢬⠣⣜⠪⡜⣌⠲⡍⡖⣩⢆⢣⡙⡤⢓⡬⢢⡙⡤⣉⠦⡙⣤⠙⢦⡑⣿⡀⣿⣿⠧⣿⣏⢮⡳⡇⠱⢠⠈⢰⢋ ⠀⠀⠀⠀⢹⣿⡄⢹⣗⢌⠳⣌⠳⣘⢤⠳⣘⡜⣰⢊⡵⢬⣑⢣⡜⢥⡚⠴⣑⠮⣑⠦⡙⢦⣿⣿⠀⣿⣿⢻⣿⣜⢧⣻⡥⢙⡄⠈⠄⣫ ⠀⠀⠀⠀⠈⢿⣷⡀⢿⣎⡱⢌⡣⢍⠶⡙⢦⡜⠦⣍⠲⡥⢚⡆⡞⣥⢎⣣⠓⡼⣡⢞⣽⣿⣿⡏⣰⣿⣯⣿⣿⠿⣿⣼⡇⢺⠄⡁⢂⠱ ⠀⠀⠀⠀⠀⠈⢻⣿⣴⣮⣵⣾⣿⡌⡖⣹⠲⣘⠳⣌⠳⡜⣣⢞⡰⣭⣿⡿⣿⣴⣿⢿⣿⡽⡫⣴⣿⣿⡷⣿⢫⡝⡞⣿⣷⢹⡆⠐⠠⠘ ⠀⠀⠀⠀⠀⠀⠀⢹⣿⠛⠛⢣⣿⡿⢿⣿⠡⣇⠻⣌⠳⣜⢢⢿⣿⡿⠿⠃⠈⠛⠁⢸⣿⣓⣷⣿⣿⣿⣿⣏⢧⠯⣝⡜⣿⡧⣟⠠⢁⠂ ⠀⠀⠀⠀⠀⠀⢀⣿⣿⡇⠀⠀⠀⢸⣿⣧⡳⣌⠳⣌⠳⡜⣬⣷⣾⠟⠂⠀⠀⠀⠀⢀⣿⣿⣿⣿⡿⣽⣿⣎⢯⡝⣾⡜⣿⡿⣱⠂⣂⠡ ⠀⠀⠀⠀⠀⠀⣼⣿⡿⣿⣆⡀⢂⣶⣾⡟⢏⡴⢫⠜⣣⢓⡬⣛⢿⣷⣦⣔⣢⢶⣴⣾⢿⡙⣿⣿⣿⣟⣿⣯⢞⡽⣳⣹⣿⠷⣍⠖⡠⢂ ⠀⠀⠀⠀⠀⢠⣿⣿⡜⡽⣻⣿⣿⣿⣷⣾⣮⠔⣋⢎⡱⣊⠴⣯⣾⣍⣿⣿⣿⣟⣯⣓⢮⡝⣦⢻⣿⣿⣻⣿⣾⡱⣧⣿⣏⠿⣐⠯⣐⠡

⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉⠉⠈⠈⠈⠉⠉⠉⠉⠉⠉⠉⠉⠙⠻⣄⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⣄⠀⠀⢀⠀⢀⣀⣤⠄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣉⣩⣤⠴⠶⠶⠒⠛⠛⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠤⠶⠒⠚⠋⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣾⡍⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣫⣭⣷⠶⢶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠶⠶⠖⠚⠛⠛⣹⠏⠀⠀⠀⠀⠀⠀⠀⠀⠴⠛⠛⠉⡁⠀⠀⠙⠻⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡷⠷⢿⣦⣤⣈⡙⢿⣿⢆⣴⣤⡄⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⣤⡀⣸⡄⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣿⣟⣩⣤⣴⣤⣌⣿⣿⣿⣦⣹⣿⢁⣿⣿⣄⣀⡀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⣿⠋⠻⢿⡁⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠿⠛⢦⣽⣿⣿⢻⣿⣿⣿⣿⠋⠁⠘⣿⣿⣿⣿⣿⣿⣼⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⠁⠀⠀⠙⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠿⣿⣯⣼⣿⡿⠟⠃⠀⠀⠀⣿⣿⣿⣿⣿⡛⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣧⣴⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⠟⠃⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⢁⣀⣀⣀⣀⣀⣠⣀⣀⢀⢀⢀ ⠀⠀⢿⠿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠙⠛⠛⠙⢻⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⡇⠀⠘⠃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡟⢿⣿⣆⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡼⠁⢀⣀⡀⠀⠀⠀⣦⣄⠀⣠⡄⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣷⣬⢻⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⣰⣿⡿⠿⠦⢤⣴⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠒⣿⣿⣿⡿⠟⠹⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⠸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡖⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡿⣾⣿⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣆⣀⣀⣤⣴⣶⣶⣾⣿⣷⣦⣴⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡇⣿⣿⡛⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢾⡟⠛⠛⠻⠛⠛⠛⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠓⢁⣬⣿⠇⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⢰⡿⣻⠇⠀⠀⠀⠀⠀⣠⣶⣶⣶⣶⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢐⣯⠞⠁⠀⠀⠀⠀⠀⠀⣄⠱⣄⠀⠀⠀⠀⠸⡧⠟⠆⠀⠀⠀⠀⠘⠿⢿⠿⠿⣿⡿⣿⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡈⠂⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⡄⠀⠀⠑⠄⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣦⣦⣼⡏⠳⣜⢿⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢠⣷⣦⣤⣀⣀⣀⣴⣿⣿⣿⣿⣿⡿⠻⠆⠸⣎⣧⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⣠⡄⠀⣿⢹⡇⢸⡀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣻⠟⠛⠛⠳⣯⡓⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣞⡿⠋⠀⠀⠀⠀⠀⠻⣮⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣀⢴⣿⣭⣭⣟⠶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⠁⠀⠀⠀⠀⡀⠀⠀⠘⢷⡹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣰⣻⠟⠁⠀⠀⠈⠻⢦⡑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣞⡾⠁⠀⠀⠀⠀⢠⡿⠀⠠⠀⠈⢷⡹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣸⣳⠏⠀⠀⠀⠀⠀⠀⠈⠹⣦⡓⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣞⣾⠁⠀⠀⠀⠀⢀⣿⠃⢀⠁⠠⡀⠈⣷⣹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⣯⡟⠀⠀⠀⣤⠀⠀⠀⠀⠀⠈⠻⣮⡣⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⣼⠃⠀⠀⠀⠀⠀⣼⡟⢀⠠⠐⠀⢡⠀⠘⣷⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣼⣿⠃⠀⣴⠀⠹⣷⡀⠀⠀⠀⠀⠀⠈⢷⣜⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠏⠀⠀⠀⠀⠀⢰⣿⠀⠄⠂⠐⡈⠀⢃⠀⢹⣎⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡟⣿⠀⠀⠏⠀⡀⠻⣷⡀⠀⠀⠀⠀⠀⠈⢻⣌⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣏⡿⠀⠀⠀⠀⠀⠀⣸⡟⠀⠰⠀⠂⠡⢀⠸⡀⠈⣿⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣟⡏⠀⣠⠂⠐⠀⡀⠙⣿⡄⠀⠀⠀⠀⠀⠀⠙⣧⡳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠃⠀⠀⠀⠀⠀⠀⣿⠇⡂⠁⠄⡁⠐⠠⠀⢡⠀⠸⣏⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⡇⠀⣟⠀⠠⠁⠀⠄⡈⢿⣆⠐⠀⠀⠀⠀⠀⠈⢿⡜⢦⣀⣤⢴⣖⣶⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⠀⡇⠈⡐⠀⠌⠐⠠⠘⡆⠀⢿⣼⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⡇⠀⡯⠀⢂⠠⠁⠠⠀⠌⢿⣆⠀⠀⠀⠀⠀⠀⣀⣿⣾⡿⠛⠋⠉⠉⢹⡄⠀⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⣠⣐⡀⠁⠌⠠⢁⠀⢣⠀⠸⣏⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⡇⠀⢃⠐⠀⠄⠠⠁⡐⠈⡈⣿⡆⠀⠀⢀⣴⠿⠛⠉⢸⡇⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⢟⠛⢻⡧⠐⠈⡐⠠⢀⠂⠆⠀⣿⣽⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⡇⠀⠀⠂⢈⠀⢂⠐⠀⢂⠐⢸⣧⠀⠀⠀⠀⠀⠐⠀⢸⡁⠀⠀⠀⠀⠈⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣧⣴⣤⡀⠂⢂⠀⡃⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⣿⡇⠀⠀⠡⠀⠂⠄⠂⢡⣾⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠋⠉⠉⣿⡇⠀⠡⠀⢸⠀⠈⣧⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡿⣿⠀⠠⠁⠐⠠⠐⠠⡘⢿⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⢈⠐⠠⠈⠀⠀⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⠀⠀⡃⢀⠂⠀⣿⡿⠛⠿⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⢀⠈⠄⠐⡀⠀⢼⡾⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢿⣿⡇⠀⡇⠀⡀⠂⢹⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠈⠳⣄⡀⠀⢀⣾⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠈⢿⡄⠢⠐⠠⠀⠀⢸⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⣧⠀⠰⠀⠠⠐⠀⠹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⣾⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠘⢿⣄⠂⠐⠀⠀⣼⢧⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⣿⣿⠀⠘⠄⠐⠀⠌⢠⡿⠀⠀⠀⠀⣀⣤⣦⣶⣤⣴⠏⠀⣀⣤⣴⣶⣶⣶⣦⣤⡀⠀⠀⠙⢿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠜⣿⡀⠈⠀⢠⣿⣿⠁⢀⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠸⣿⣇⠀⠻⡀⠈⠀⣿⠃⠀⠀⢠⣾⣿⣿⡿⢿⣿⠏⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠉⢿⡛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠐⠘⣿⣀⣴⣿⣿⣿⣿⣿⣭⣟⢦⣀⣀⣀⠀⠀ ⠀⠀⠀⢻⣻⣆⠀⠱⣀⢩⣿⠀⠀⠀⠠⠟⠋⠁⠀⣰⠃⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡟⠙⣿⣿⠁⠀⢹⣿⡿⠿⣯⡻⡆ ⠀⠀⠀⠈⢻⣻⣦⠀⠉⢸⡗⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠈⠛⠿⣿⣿⣿⠿⠛⠉⠀⠀⠀⠀⣀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡶⠀⣿⣿⡀⠐⠈⢁⠠⠀⣼⣇⡇ ⠀⠀⠀⠀⠀⠙⢽⡷⣦⣽⡇⠀⠀⠀⠀⠀⠀⠀⢰⡇⢀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣝⣿⡼⣿⣧⡐⠈⣠⣤⢾⣫⠟⠁ ⠀⠀⠀⠀⠀⠀⠀⠙⢻⣿⠇⠀⠀⠀⠀⠀⠀⠀⢸⠇⠘⣧⠀⠀⠀⠀⠀⢀⣾⣧⣄⣀⢀⣀⣠⣾⠋⠀⠀⠀⠀⠙⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣻⡇⠀⠘⢿⣿⣛⡿⠷⠋⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡾⣿⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠈⠳⣶⣤⡴⣾⢿⡹⢮⡝⣯⢻⣽⣿⣿⣄⠀⠀⠀⠀⠀⠀⠉⠓⠦⣤⣄⣀⣀⣠⣤⠿⢻⡞⣷⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣾⣷⣿⠀⠀⠀⠀⠀⣀⡴⠋⠀⠀⠀⠀⠀⠹⣷⡹⣎⢷⡹⢧⣻⣼⠿⣿⣄⠉⠙⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⣽⣧⣤⣀⣀⣠⡴⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣯⣞⣭⣻⣟⣷⡀⢀⠛⢿⡄⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣶⣶⣶⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⢿⣿⡿⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠻⣧⡈⠐⢈⣡⣾⠏⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣯⠿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⢿⣓⣶⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠛⠋⠁⠀⠀⠀⠀⠀⠀⠶⠛⠉⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣺⣿⣿⣻⢦⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣿⣧⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣾⠹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠛⣯⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣷⡿⠀⠘⠻⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠁⠀⢿⣸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠖⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢶⠀⠀⢸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠒⠒⠒⠖⠶⠦⠤⠤⢤⡤⣤⠤⣤⢤⡤⣤⢤⡤⠤⠤⠤⠴⠶⠒⠒⠒⠒⠊⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

Oh 😨 my 🫡 gosh! 😱 You 🫵🏻 had 🤨 a 🤓 crUsh 😻 on 😖 Jake 😮‍💨 and 🧐🤔 didn't 🙂‍↕️ tell 🗣️ me?!? 😤 crazy 🤯 if 😒 you 🙃 told 🎙️ me 🥲 that 😄 I 🤩 wouldn't 🫣 have 🙄 told 🙊 Jake 🫤 I 😯 had a crUsH 😍 on 🥺 Jakeyy 😛JoshUa!! 😎 and 🫥 not 🤒 youuuuu 🤭🤭🤭😵

⠀ ⠀ (\__/) (•ㅅ•) Don’t talk to ＿ノヽ ノ＼＿ me or my son `/　`/ ⌒Ｙ⌒ Ｙ ヽ ever again. ( 　(三ヽ人　 /　 | |　ﾉ⌒＼ ￣￣ヽ ノ ヽ＿＿＿＞､＿_／ ｜( 王 ﾉ〈 (\__/) /ﾐ`ー―彡\ (•ㅅ•) / ╰ ╯ \ / \>

The FitnessGram™ Pacer Test is a multistage aerobic capacity test that progressively gets more difficult as it continues. The 20 meter pacer test will begin in 30 seconds. Line up at the start. The running speed starts slowly, but gets faster each minute after you hear this signal. [beep] A single lap should be completed each time you hear this sound. [ding] Remember to run in a straight line, and run as long as possible. The second time you fail to complete a lap before the sound, your test is over. The test will begin on the word start. On your mark, get ready, start.

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠶⠦⢤⣀⠀⠀⠀⣼⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠁⠀⠀⢀⡴⠾⢷⡤⣾⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣃⣀⣀⣀⣴⣿⡿⣷⣿⣧⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣤⣦⣀⠀⠀⣿⣿⣿⣿⣿⠋⠉⠓⠛⡋⠁⠀⠈⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠻⠿⠛⠛⢿⣿⠿⠾⢝⣧⣀⣀⣠⠶⠛⠓⢒⠶⡎⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣀⣴⡿⡿⠛⠋⠙⠀⣀⢴⡟⠀⠀⠘⠦⢄⣀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡉⣿⣧⣠⣤⡴⢶⣫⣷⡟⠀⠀⠀⠀⠀⠀⠙⣿⣷⣶⣿⣧⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⣼⣟⠙⢻⣟⣛⠿⠛⣛⡩⠔⠁⠀⠀⢀⡖⠀⢀⣾⣿⣿⣿⣿⠀⠈⠑⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣰⣿⣿⣿⡿⢻⣦⡀⠉⣉⠉⠉⠉⠀⠀⠀⠀⢀⠞⠁⣠⣾⣿⣿⣿⣿⣿⡄⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⠋⣿⣿⣿⣿⣿⣤⡙⠻⣦⣄⡀⠠⣤⡀⠀⣠⡴⣯⡴⣻⣿⣿⣿⢿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⣸⠃⣰⣿⣿⣿⣿⣿⣿⣟⣷⣤⣍⣿⣷⣾⡿⠟⠹⣚⣩⣾⣿⣿⣿⣿⣿⣿⣿⣿⢳⡄⠈⢲⡀⠀⠀⠀⠈⢦⠀⠀⠀ ⠀⠀⠀⣼⡧⣴⡟⢿⣿⣿⣿⣿⣿⣿⣿⣥⣀⠀⠀⣀⣠⣴⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠻⣆⠈⢿⡄⠀⠀⠀⠀⠣⡀⠀ ⠀⠀⣾⢟⢘⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡏⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⣿⣦⣿⣿⣴⡦⠂⠀⠀⢱⠀ ⠀⣼⡟⠈⠸⡿⢠⣾⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⠗⠉⠀⠘⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡈⢻⣿⡿⠋⠀⠀⠀⠀⠘⡆ ⢸⡏⣠⠠⠶⠇⣾⣿⣿⣿⣿⣿⣿⣿⠟⠃⠀⠀⠀⠀⠀⠀⠉⠉⠁⠈⠉⠀⠀⠈⠉⠉⠉⠛⠻⠿⠃⣿⣿⡅⠀⠀⠀⠀⠀⢰⠇ ⣿⡿⠡⠀⠀⠀⠙⣿⠉⣏⠉⠬⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⣿⠇⠀⠀⠀⠀⠀⠀⡸⠀ ⢹⣷⢐⠀⠀⠀⠀⠹⣇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⡀⠀⠀⠀⠀⠀⡸⠁⠀ ⠀⢹⣿⣰⡀⠀⠀⠀⣿⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣄⣈⡀⠀⠀⠀⢰⠃⠀⠀ ⠀⠀⠹⣿⣷⢠⡄⠠⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣟⠉⠙⠻⠷⢶⡦⡞⠀⠀⠀ ⠀⠀⠀⠘⢿⣾⣧⣳⡿⣧⠀⠀⠘⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⢿⡟⠀⠀⠀⠀⠀⠁⣧⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⢿⣦⡀⠀⠙⠻⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣀⣤⣶⣿⠿⠋⠁⢀⣯⣤⣄⣀⣀⣀⣴⡿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⡇⠹⢿⣿⣶⣤⣤⣿⣿⣶⣶⣶⣶⣤⣶⣶⣿⣿⠿⠟⠋⠀⠀⠀⠀⢸⠀⠉⠉⠀⠉⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡤⠀⠀⠈⠙⠛⢻⣿⣿⠿⠿⠿⠿⠟⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⣸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡀⣌⣷⣀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⣤⣀⠙⠂⢦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⡤⢶⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⠙⢻⣿⣶⣤⠤⠭⣇⣀⣠⣀⣀⣀⣤⢤⣶⣶⣿⢋⠁⠀⢰⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣠⡟⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⢿⣿⣿⣇⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣎⠹⣟⠺⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⢰⠉⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⢹⠃⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣇⣼⣧⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡆⣉⣴⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⡿⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣠⣿⡧⠻⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⣖⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣩⣿⣿⣦⣶⣤⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣿⣿⣿⣯⣿⣿⠟⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣴⡾⡿⠟⠿⢻⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠉⠛⠓⠒⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣄⣉⣙⣛⣻⣛⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⢔⣶⣒⠒⠒⠒⠠⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⢊⡡⠔⣶⡿⠛⠛⠁⠉⠉⠐⠢⣤⣭⡲⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⢀⠔⢡⠖⠁⠀⠘⠁⠀⡀⠀⠀⠀⠀⠀⠀⠛⠛⢷⡀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠠⠊⢎⠀⠀⠙⢦⡀⠀⠀⡰⠃⡐⠁⠀⠀⠀⢠⣮⠴⠒⠿⣄⠀⠀⠀⡠⠤⢤⡀⠓⡄⠀⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠱⠀⡰⠁⢰⠁⠀⠄⡀⠀⣶⠃⣠⡤⡄⠙⡄⠀⣼⠞⠉⠙⠻⣇⠸⡄⠀⠑⡀⠀⠀⣠⠚⠛⠛⡗⢄⠀⠀⠀ ⠀⠀⠀⠈⠆⠀⠀⠀⠀⠀⢀⢠⠃⠀⠀⠁⠀⠀⠤⣁⣸⢸⣧⣿⢹⠀⣷⠀⣿⣞⣿⣧⠀⠘⡆⠀⠀⠀⢳⠀⡞⡁⠀⠀⠐⠁⠈⡆⠀⠀ ⠀⠀⠀⠀⠘⣀⠀⠄⡤⠤⣾⣼⡀⠀⠀⠀⠀⠐⠂⠒⠌⠹⣿⡷⠋⢠⡟⠀⠈⣿⣯⡽⠁⢀⡇⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀ ⠀⠀⢠⡴⠋⠀⠀⠀⠀⠀⠀⠈⠙⠳⣄⠀⠀⠊⠉⠱⡒⠄⠪⠱⠶⠋⠀⠀⠀⠈⠣⣤⡴⠞⠁⠂⠀⠀⢀⣇⣧⣤⣄⠀⢀⡸⠀⠀⠀⠀ ⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠜⡆⠀⠀⠀⠀⠘⣦⣀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠨⣻⠭⠀⣠⠞⠋⠁⠀⠀⠀⠀⠀⠩⡲⣄⠀⠀ ⢰⠁⠀⠀⠲⣀⡠⠔⠂⠀⠀⠐⠒⠲⢖⣇⠀⠀⠀⠀⠀⢹⣧⡉⠐⠒⠤⠤⠤⢤⣤⠖⠊⠁⠀⢰⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢪⢧⠀ ⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⢿⣿⣶⣤⣄⣀⣤⣾⠇⠀⠀⠀⢀⣼⠞⠛⠉⠉⠉⠑⠒⠠⢄⠔⠀⠀⠀⠇ ⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣬⠀⠀⠀⠀⠀⠀⢢⠙⡟⢿⣿⣿⡿⠀⠀⠀⠀⠸⡅⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀ ⠘⡆⠀⠀⠀⠀⠀⢲⠊⠁⠀⠀⠈⠑⢳⢮⡀⠑⢠⡀⠀⠀⠀⠀⠙⠳⠤⠿⠛⠁⠀⠀⠀⠀⠘⣄⣀⢤⠤⠤⠤⣀⠀⡀⠀⠀⠀⠀⠀⡀ ⠀⠘⢆⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⡜⠻⡦⡀⠉⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠙⠏⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡰⠁ ⠀⠀⠀⠑⠄⣀⠀⠀⠀⠀⠀⠀⣀⠠⠊⠀⠀⠈⠙⠳⢦⣄⠀⠀⠀⠀⠀⠀⠀⣀⡀⠔⠊⠁⠀⠐⢄⠀⠀⠀⠀⠀⠈⠀⠀⠀⢀⠜⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⡤⠀⠀⠀⠠⡴⠊⠁⠀⠀⠀

⠉⠉⠉⠉⢉⣩⣽⢿⣛⣛⣛⣛⣛⡛⢿⣿⣍⡉⠉⠉⠉⠉⣉⣉⣭⣭⣿⢿⡿⠯⣭⣭⣏⣉⠉⣉⢉⡉⡉⠍⠛⢿⣿⠉⠁⠁⠉⠈⠁⠉ ⠀⠀⠀⠰⢛⣭⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣌⠻⢷⣦⣾⣿⣿⣻⣿⣿⣿⣿⣿⣿⣷⣦⣍⡙⠻⣦⡀⢢⠑⡨⠘⣾⣟⠀⠀⠀⠀⠀⠀⠀ ⠀⣀⠰⢡⣿⣿⣿⣿⣿⠛⠉⠉⠙⠛⠿⣿⣿⣧⡀⠹⣿⢓⣼⣿⡿⠛⠉⠉⠉⠛⠿⣿⣿⣿⣦⠈⢻⣆⠘⡠⢑⡸⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⡄⢂⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⡄⠐⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣧⠀⢻⡆⡑⢤⠛⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡐⠠⣿⣿⣿⠃⠀⣠⣶⣶⣶⣤⡀⠀⠀⠀⠙⣿⡧⠘⣿⡏⢠⣤⣶⣶⣶⣦⡀⠀⠀⠀⠉⣻⣿⡆⠘⣿⣦⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠠⠀⠐⡿⣿⣧⡀⣾⣿⣿⣿⣿⣿⣿⣆⠀⠀⢠⣿⡷⠀⣿⡇⣾⣿⣿⣿⣿⣿⣿⡄⠀⠀⣾⣿⣿⠇⢠⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠠⢁⠀⢹⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⣸⣿⡗⠘⢻⣿⡛⠿⢿⣿⣿⣿⡿⠁⠀⢠⣿⣿⡟⠀⣾⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡀⠣⢀⠈⢻⣿⣿⣷⣭⣉⠛⠉⠋⠉⠁⣠⣾⣿⡟⠀⡀⠀⠻⣿⣦⡀⠀⠈⠉⠀⢀⣴⣿⣿⠟⠀⣼⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠠⢍⢀⠣⢀⢹⣛⠿⣿⣿⣷⣶⣶⣶⣾⣿⠟⠋⣠⣾⣿⣤⠀⠉⠻⣿⣷⣤⣴⣺⣻⡽⠞⠁⣠⣾⠟⡤⣉⣿⠃⠀⠀⠀⠀⠀⠀⠀⢀⠴ ⠐⡈⢆⡐⠀⠘⠻⢷⣮⣽⣛⣛⣛⣛⣃⣤⣴⠾⠛⠻⠿⣿⣿⣶⣤⣀⣈⣁⣉⣉⣡⣤⠶⢛⣿⣟⢢⠵⣸⣿⠀⠀⠀⠀⠀⠀⠀⢠⢸⣻ ⢂⡁⢢⠐⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠉⠁⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠛⠋⠉⠉⠀⠀⢠⣿⡉⢆⡣⣿⡏⠀⠀⠀⠀⠀⠀⡀⢦⡹⢧ ⠂⠌⡄⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⡘⢦⢱⣿⠁⠀⠀⠀⠀⠀⠄⡘⢦⡹⣏ ⠈⡔⠨⢄⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡧⡑⢎⣣⢿⠂⠀⠀⠀⠀⠀⢂⡑⢮⡵⢯ ⠡⣌⠱⡨⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡧⣙⠆⣧⣿⠁⠀⠀⠀⠀⠐⡠⡘⢧⣛⣿ ⡑⢆⡣⢱⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣗⡹⢎⢿⡇⠀⠀⠀⠀⡈⢐⠰⣹⢧⣻⣞ ⣉⠖⣡⢃⠎⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡧⣝⣮⣿⠇⠀⠀⠀⡁⢐⢈⠲⣍⠾⣧⢿ ⢤⢋⠴⣉⠖⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣻⡟⣿⡄⠀⢀⣂⣀⣡⢈⡶⣭⣿⣽⣿ ⢆⣫⢞⡱⣎⣿⣎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣝⣞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⣀⠄⠆⡶⡜⠶⠣⠓⠚⠈⠂⠐⠀⠀⠀⠀⠀⢀⣿⣿⣿⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⠇⢻⣷⣦⠀⠀⠀⠀⠀⠀⠤⢈⠴⡰⢎⡱⢒⠆⠒⠠⠂⠀⠀⠀⠀⠀⣼⣿⢹⣷⣿⣷⣯⣷⣟⡾⣽⣫⢷⣯⣟⣾⣳⣟⣿ ⣿⣿⣿⣿⡟⢰⣄⠻⣿⣦⡀⠀⠀⠀⠀⠀⠀⠂⠁⠂⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⣸⣿⠣⡌⣿⣿⣿⣽⣷⢯⣟⣯⢿⡽⣾⡹⣞⡷⣽⣞ ⣿⣿⡿⣿⡇⠘⣿⡆⠹⣿⣷⣂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣿⡏⣾⣇⢹⣿⣿⣿⣾⣿⣿⣿⣿⣿⣷⣿⣿⣽⣳⣞ ⣿⣿⣽⣻⡇⢈⣿⣷⠀⢿⣿⣿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⣿⣻⣿⣧⠚⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣳⣟⣾ ⣿⡷⣯⢿⡇⡘⣿⣿⣄⢸⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⡽⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⣿⣻⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠁⠈⠉⠛⢻⣶⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠋⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠁⠀⠀⢰⣿⠂⠀⢀⣤⣼⣿⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⠁⠀⠀⠀⠀⠀⣠⣶⠿⡛⡜⢿⣷⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠁⠀⠀⠀⠀⢀⣾⡿⠿⠿⣷⣼⣢⢻⣿⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⠘⠻⣿⣤⣿⡃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠈⠻⠟⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠇⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣤⣶⢶⣦⣤⣀⣀⣀⣄⣠⣤⣤⣤⣤⣤⣴⡾⢿⡄⠀⠀⠀⠀⠀⢸⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣾⠏⠀⠀⠈⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠈⢻⣆⡀⢀⣀⣤⠾⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣻⢿⠉⠀⠀⠈⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣽⣻⠀⠀⠀⠀⠀⠈⢻⣧⠀⠀⠀⠀⠀⠀ ⠀⠀⠹⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣻⢷⣿⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠙⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡷⣯⣿⢾⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢿⡽⣟⡿⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⣿⡽⣯⠇⠀⠀⠀⠀⠀⠀⠀⣸⡟⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠋⠁⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠿⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⢀⡀⠀⠀⣀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣶⣶⣶⣿⡟⠉⠛⠛⣶⠛⠛⢻⣿⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⢩⡙⣿⣄⠀⠀⠀⠀⠀⠀⣾⣏⢹⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡟⢢⠱⡩⢿⣆⠀⠀⠀⠀⢸⣿⢄⠫⡹⠟⠿⣻⣷⣦⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣋⠬⢥⢣⡑⢎⣿⣦⠀⠀⠀⠀⠻⣯⣶⣡⢋⠖⡡⣾⣾⠗⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣯⣴⣿⣶⡣⣼⣦⣙⣿⡆⠀⠀⠀⠀⠈⠛⠿⣾⣼⣷⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠘⠿⠟⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀

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

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⠀⠀⠀⠀⠀⢀⡤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⢄⠙⣠⠇⠀⠀⣠⠠⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠳⠁⠀⠀⢰⠁⠀⠀⠈⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠘⣆⢀⣀⠤⠖⠒⢢⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⡮⠁⠉⠁⠒⠤⢀⡼⠖⠀⠐⣗⠢⡀⢸⣏⡁⠀⠀⢀⡠⠥⠒⠲⠤⢄ ⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⣀⣈⣍⣈⡿⡘⠁⣹⡚⠁⠀⠀⠀⠀⠀⣼ ⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⣇⣠⡶⣍⣀⣠⠴⠛⠻⢇⣜⡁⠺⠽⠀⠀⠀⢠⡞⠁ ⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⢷⡀⠀⠀⢀⡏⠀⠀ ⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡉⢳⡄⣸⠁⠀⠀ ⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠿⢻⡖⠒⠂ ⠈⠉⠸⡍⠈⠀⠀⠘⣶⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⣶⡄⠀⠀⠠⢸⠅⣀⠀ ⠀⠀⠔⢷⠈⠀⠀⠀⠘⠛⠁⠀⠀⠀⣤⢤⠀⠀⠀⠀⠸⠿⠁⠀⢀⣠⠟⠀⠀⠀ ⠀⠀⠀⣀⠷⢎⠁⠀⢀⡀⠀⠀⠀⠀⠙⠉⠀⠀⠀⠀⠀⠀⠀⣀⠴⠋⠈⠒⠀⠀ ⠀⠀⠀⠁⠀⠀⠉⡖⠀⠈⠑⡦⠤⠄⠄⠀⠤⠤⠤⡖⠉⠉⠹⡁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⠒⠛⠊⠁⠀⠀⠀⠀⠀⠀⠀⠙⠒⠲⠞⠁⠀⠀⠀⠀⠀⠀

Stares at you with my nuerodivergent little face ⠀⠂⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⢥⣿⣴⡾⣼⣿⣗⣾⣦⣄⡣⣷⣴⣿⠦⣸⣶⣰⣮⡶⣥⣷⣴⡄⡘⣾⣼⣾⣾⣿⣷⣮⣿⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⠛⡿⠾⠿⣿⢿⠘⢿⣿⠻⡟⡇⠙⣿⡟⠻⠧⠠⣼⣿⣛⣷⡟⡻⡿⠇⠀⢹⣿⣿⠚⣟⠻⠞⢿⢻⠆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠄⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣷⣶⣠⡞⠐⣯⣶⣤⣿⣄⣦⢰⣤⣿⣿⣷⣤⣰⣿⣿⣿⢷⢡⣶⣶⣤⣶⣼⣾⣿⣶⣾⣇⣶⣶⣹⣷⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡼⡏⣿⣸⡿⠁⠀⠿⢸⠟⢿⡭⢿⡾⠟⣿⠹⢷⠿⠻⣾⣯⣿⠸⢿⠛⢿⠯⢿⠄⣿⣿⡜⠿⠯⢿⠸⠟⠿⠄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣠⣼⣿⣷⣿⣿⣯⡀⠀⠀⠀⠀⢸⣞⣟⣷⣯⣶⣺⣗⣤⣤⠀⢰⣿⣷⣄⡀⣠⣦⣠⣤⡀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⡻⠉⠁⠀⠈⠉⠙⠿⣶⣄⠀⠀⢸⡧⡿⢿⡄⢿⣼⡏⢿⣿⡁⠘⣷⢰⣿⡟⣯⣤⢿⣿⠅⠀⠀⠀⠀⠀⡀⣀⣶⣶⣶⣶⣶⣶⣤⣀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠊⢻⣷⡧⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠐⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⡿⠟⠉⠉⠀⠀⠀⠐⢙⣿⡆⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⣿⠟⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣷⣆⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣤⣤⣠⣤⣀⣀⣀⣀⣴⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠘⢻⣷⠀ ⠀⠀⠀⠀⠀⠀⣰⣿⣃⣀⣤⣤⣤⣤⣄⣀⣀⡀⠁⠀⠀⠀⠀⠈⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠁⢉⠙⠛⣻⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠄ ⠀⠀⠀⠀⣀⣴⣿⠟⠛⠉⠙⠈⠈⠉⠉⠉⠛⠻⠿⣶⣬⣄⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠂ ⠀⠀⡀⣶⡿⠏⣁⣴⣦⣴⣦⣴⣴⣦⣶⣯⣥⣤⣀⣀⡉⠛⢿⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣾⡷⠿⠾⠷⠿⠾⠷⢿⣶⣦⣄⣀⠀⠀⠀⣿⡁ ⠀⢰⣼⡿⢁⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡙⠿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⠟⠋⠉⢀⣁⣀⣀⣀⣀⣀⣀⣀⣀⡘⠝⠻⣷⣦⣀⣿⠄ ⠀⢸⣿⠁⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠈⣻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣿⠟⠁⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡈⠻⣿⣿⠀ ⠀⢀⣿⣀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⢐⣿⡇⢂⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢹⣿⠀ ⠀⠀⢿⣷⡀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⣀⣼⡿⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⠃ ⠀⢀⠀⠻⣿⣤⠈⠙⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⢿⢿⠿⠛⠉⢀⣤⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣰⡿⠀ ⠀⠀⠀⠀⠈⠻⢿⣾⣖⡀⠄⠀⠀⠀⠀⠀⠀⠀⠠⣀⣀⣴⣾⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡅⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣋⣴⡿⠃⠀ ⠀⠀⠀⠀⠀⠀⠀⠩⣿⡿⠿⢶⣶⣤⣬⣶⡶⠾⠟⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣦⡀⠈⠛⠟⠿⠿⠿⠿⠿⡿⢿⠿⠟⣛⣠⣾⡟⠋⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⣄⡀⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣾⣦⣀⣒⣀⣒⣠⣀⣴⣤⡾⠿⢻⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⡛⠛⠛⠋⠉⠉⠁⢀⣰⡿⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⢷⣶⣤⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣐⣦⣤⣶⣾⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠻⠿⠿⠷⠶⣶⣦⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣴⡶⠾⠿⠟⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣷⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢩⣿⡇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠁⠀⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⠀⣀⣤⣶⢾⠟⠛⠛⠛⠷⣾⣦⣄⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣆⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠐⠠⠠⠠⠐⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠾⠛⠛⠉⠉⠉⠉⠉⠛⠻⠶⣤⣀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⡾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣯⠉⠙⠻⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠟⢀⣼⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠋⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⡀⠀⠀⠈⠙⠷⣦⣤⣄⣠⣤⣤⣤⣤⣄⣀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣄⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠈⠉⠻⣦⡀⠀ ⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⢠⡾⠂⠀⠀⢀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡿⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⠀ ⠀⠀⠀⢀⣴⠟⠁⠀⣀⣤⠶⠞⠛⠻⠶⣤⡀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⢤⣶⢻⡟⣶⢠⡿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃ ⠀⠀⢠⡟⠁⠀⢠⡾⠋⠀⠀⠀⠀⠀⠀⠈⢿⣌⣛⡋⠀⠀⠀⠸⢧⡴⠛⠓⠞⠁⠀⠀⠀⠈⠛⠛⢈⣥⠟⠁⠈⠻⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⠏⠀ ⠀⠀⣾⠁⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡽⠟⠀⠀⠀⠀⠀⢀⣤⣤⣴⣤⣄⣀⣤⣤⠶⠞⠛⠁⠀⠀⠀⠀⠀⠉⠛⠶⢦⣤⣤⣤⣤⣤⡶⠾⠋⠁⠀⠀ ⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣏⣀⣀⣀⣀⣤⣤⣴⡟⠁⠘⣧⠀⠙⠻⠋⠛⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠻⣦⡀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠿⢋⣩⣽⠿⣯⣽⡇⠸⠋⠀⠀⣸⡟⠷⣤⡀⠀⠀⠈⠻⣆⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠙⠛⠶⠶⠶⠚⠛⠋⠉⠀⣰⡟⠉⢀⡀⠀⣿⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⣰⠟⠉⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⣿⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⠘⠷⣤⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣧⣀⣀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⡀⠀⠀⠀⢈⣻⢦⣄⣀⣀⠀⢠⣴⣶⠞⠛⠉⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠛⠁⠀⠈⠛⢷⣤⣤⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⣤⠤⠤⠤⠤⠶⠶⣤⣤⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⣤⠶⠾⠛⠛⠛⠋⠉⠋⢉⣥⣄⣀⣀⣀⣀⣀⣀⣀⣻⣛⣿⢿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣀⣤⡴⠶⠞⠛⠛⠛⢉⣉⣁⣀⣤⣤⣤⣶⣶⣶⠶⢾⡿⠿⠿⠛⠛⣿⣿⢻⡏⠉⠙⠛⠛⠛⠿⠿⣿⣿⣷⣿⣧⣷⡀⠀⠀⠀ ⠀⠀⣴⣿⣯⣿⣷⡶⢶⡿⠿⠛⢻⠛⠋⠉⢹⣿⣿⣯⣧⣿⠀⢼⠁⠀⠀⠀⠘⡗⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠉⠛⡟⠛⠻⣿ ⠀⣸⣿⠋⠀⣽⠀⠀⢰⡇⠀⠀⢸⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⣿⠀⠀⠀⠀⠀⣿⣇⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢳⠀⢸⣿ ⠀⣿⣿⠀⠀⣿⠀⠀⣸⡁⠀⢀⣾⣀⣀⣀⣼⣿⣿⣿⣿⣟⣀⣿⣀⣠⣤⣤⣤⣿⢿⣿⣦⣤⣤⣤⣤⣤⣤⣄⣀⣿⣆⣀⣀⣀⠘⡄⣼⣿ ⠀⡿⠛⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢻⣿⣿⣿⣿⣿⡍⠋⠛⣿⣿⣿⣿⣿⠻⠿⠟⣻⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⢿⣿⣿⣿⠋⠹ ⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⠁⠀⠀⣿⣿⣿⣿⢿⠀⠀⢸⡏⠀⠀⠀⠀⢹⡧⠀⠀⠀⠀⢬⣿⠛⣿⠀⠀ ⠀⣇⣀⣀⣀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⢹⣿⢽⣿⠀⠀⠀⣏⣉⣉⣁⡾⠀⠀⢸⣇⠀⠀⠀⠀⣸⣿⡏⠉⠉⠉⣿⣿⡀⡸⠀⠀ ⡾⡏⠉⠉⠉⣹⠛⣩⣿⣛⠿⢿⣿⡟⠒⠶⢿⡇⢸⣿⢻⣿⡶⠋⠛⠛⠛⣧⠀⠀⢀⣤⣤⣿⣟⣿⣿⣿⣿⣿⡟⠛⠛⠛⣻⣿⣿⣷⣤⣀ ⠀⠻⢦⣀⣠⣿⣾⣯⣿⣿⣦⣸⡏⠁⠀⠀⢸⡇⠈⢻⠀⣿⠃⢀⡴⣿⡛⢿⣧⠀⢸⣉⣿⣿⣿⣿⣾⣿⣿⡟⠳⣤⣤⣶⣿⣿⣿⣿⡟⢻ ⠀⠀⠀⠀⠀⢸⣿⠟⣿⣟⠛⣿⣿⣦⡤⢤⣾⣷⣶⣦⣤⠹⣆⣼⣿⣿⣿⣿⣿⡀⠀⠰⣶⣟⣿⣿⣿⣿⣿⡿⠖⠛⢟⠛⣿⣿⣿⣿⠀⠐ ⠀⠀⠀⠀⠀⠈⢿⢷⡿⢻⢀⣿⣹⠏⠉⠉⠉⢻⣟⣛⣿⣶⣿⡿⣿⣿⣿⣿⡏⡏⢹⣟⣟⣛⡟⠛⢿⣉⣉⣻⣿⢛⡏⣿⠉⠉⠉⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠳⠴⠷⠾⠿⠋⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⢿⠸⣿⣫⡿⢠⠃⣸⠋⠉⠙⠻⠶⢿⠻⣿⣿⠟⣾⣷⠏⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠧⣌⣉⣠⣎⡴⠋⠀⠀⠀⠀⠀⠀⠑⠲⠶⠾⠟⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣶⣦⣤⣄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣄⡈⠙⠛⠻⢿⣿⣿⣿⣷⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣶⣶⣤⣀⣉⠙⠛⠇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⠀⢠⣿⡟⠙⣿⣿⣿⣿⣿⣿⣿⣿⠀ ⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⠿⢿⣿⣿⣦⣤⣿⡟⠀⢸⣿⣿⣿⠃⠀ ⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣇⣀⣸⣿⠋⠉⣿⣿⠿⣷⣿⣿⣿⡟⠀⠀ ⠀⠀⠀⠀⠀⠀⣾⣿⣿⡿⠛⢿⣿⣿⣦⣴⣿⡃⠀⣸⣿⣿⡿⠀⠀⠀ ⠀⠀⠀⠀⠀⣸⣿⣿⣿⣅⣀⣾⡟⠁⢸⣿⡿⠻⣿⣿⣿⣿⠃⠀⠀⠀ ⠀⠀⠀⠀⢠⣿⣿⣿⠟⠛⣿⣿⣿⣶⣾⣿⣀⣀⣿⣿⣿⡏⠀⠀⠀⠀ ⠀⠀⠀⠀⣾⣿⣿⡟⠀⢠⣿⠏⠀⣹⣿⠟⠻⣿⣿⣿⡿⠀⠀⠀⠀⠀ ⠀⣀⣀⣼⣿⣿⣿⣁⣀⣿⣟⣀⣠⣿⣏⣀⣰⣿⣿⣿⣃⣀⣀⣀⣀⠀ ⠘⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠠⠐⠂⠐⠂⠐⠒⠀⠒⠤⠴⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢤⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠬⣍⣒⠢⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⣅⡀⢀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣴⢊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠻⣄⠁⠄⠀⠀⠀ ⠀⠀⠀⠀⡼⢋⣘⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⢂⠻⢦⠀⡀⠀⠀ ⠀⠀⢠⡾⡑⢢⠘⠁⡆⠀⠀⠀⠀⠐⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠐⠢⠌⢷⠀⠀⠀ ⠀⢀⣯⠜⡰⡁⢎⣢⣤⣤⡀⠀⠀⠀⢺⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⢂⡉⠆⣍⠚⡇⡀⠀ ⠂⣼⡹⢌⡱⢸⣾⡿⠛⠛⠁⠀⠀⠀⠀⠄⠙⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠂⡀⠌⡐⠨⡑⢬⡙⣷⡀⠀ ⠀⣿⡱⢎⡔⣫⢫⢅⠣⡘⠠⢁⠀⠀⡀⠀⣀⣈⣯⣀⣀⠀⠀⠀⠀⠀⢀⠉⡀⠐⡠⠐⡰⢠⢃⡝⢢⠵⣹⡷⠀ ⠀⣿⢿⡸⣼⠵⠛⠚⣳⣧⡃⠤⢈⠂⣄⣷⠾⢓⣫⣙⡹⠷⣮⡀⢂⠐⡀⢂⠄⡃⠔⡡⢆⢃⢎⠼⣡⡛⣼⢢⠁ ⠀⢺⣟⣾⡑⠐⣰⣿⣿⠛⢿⡆⢡⢘⣼⠏⣼⣿⠟⣻⣿⣶⡙⣷⢂⠒⡈⢄⠢⡑⢬⡐⢎⡜⡬⢳⢥⡻⣼⠘⠀ ⠀⠘⣯⣿⠤⢘⣿⣿⣿⣶⣿⣿⠰⣨⡇⠸⣿⣿⣿⣿⣿⣿⡏⢹⡧⡘⢤⢃⡱⡘⢦⡙⡲⣜⡱⣏⡞⣽⡿⡀⠆ ⠀⢆⢹⣿⣖⠈⣿⣿⣿⣿⣿⡧⣓⠴⡇⠀⢿⣿⣿⣿⣿⣿⠏⢸⠧⡙⢆⡣⢖⡹⢦⡹⡵⢎⡷⣹⣞⡿⠁⠀⠀ ⠀⠈⠀⢻⣿⣶⡄⠛⠛⠟⡙⢶⡩⢞⣧⠀⠀⠙⠻⠿⠿⠋⢀⣏⡳⣙⢮⠵⣋⡞⣧⢻⣭⢻⡼⣳⡿⢁⡔⠀⠀ ⠀⠀⠀⠈⣽⣿⢷⡦⢦⣐⠷⣎⠷⣎⣽⣄⠀⡀⠀⠀⡀⢠⡼⣏⢷⣛⡼⣲⢏⣷⢫⡾⣝⣮⣳⡟⢃⠜⠁⠀⠀ ⠀⠀⠀⠀⠀⠙⠻⢼⣏⢯⣻⢽⣻⡼⣞⢿⣳⡬⣗⢧⡽⣟⠳⣝⡮⢷⣹⢧⡟⡾⣭⣳⣻⠾⠉⠀⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠬⣗⣳⡝⡾⣹⢎⣷⣏⢾⣳⢞⡻⣭⢻⡭⣗⠯⣞⡵⠗⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⢿⣟⣳⣮⣟⣼⣯⣷⣭⣷⡷⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠠⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡴⠚⠫⠭⠴⢏⢄⣤⣀⡀⠀⣀⡤⣤⣄⡳⠬⣍⡓⠲⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣼⠍⠛⠁⠀⠀⠀⠰⡶⠶⠶⠶⠋⠀⠳⠶⠶⠶⢾⠂⠀⠀⠀⠘⠛⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢹⣠⢀⡐⠤⠤⠤⣼⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡌⠠⢀⠤⢂⡰⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠛⠛⠛⠓⠳⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠷⠾⠞⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⡀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠰⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣿⡇⣶⣶⡦⠀⠰⣿⡿⣾⠶⣦⢰⣶⠷⠄⢰⣶⢿⡶⢶⡆⣴⣶⣦⡜⢫⣿⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠿⠇⠿⠿⠟⠃⠀⠿⠇⠻⠶⠟⠸⠿⠀⠀⠸⠿⠿⠷⠹⠇⠻⠿⠿⠃⠹⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡟⢷⣒⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⠀⢸⠹⣟⠲⣍⠛⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⢧⢸⡆⠙⣆⠈⠙⣻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠘⢯⣀⢠⠟⢷⡾⠁⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡜⠻⡄⠈⠳⣄⡴⠚⠷⠚⠋⠉⠉⢻⡄⠀⠀⣠⠞⠉⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡸⠀⠀⢸⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⢸⢣⠤⢼⠳⢤⣀⣠⡄⠀⠀⠀⠀⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡇⠀⠀⠈⢇⠀⡇⠀⠀⠀⠀⠀⠀⢀⠎⢨⣆⣼⠀⠀⠀⢠⠇⠀⠀⠀⢀⡟⠒⠒⠦⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⠇⠀⠀⠀⣸⠖⢷⡀⠀⠀⢠⠤⠐⠋⠀⠉⣇⡇⠀⠀⠀⠘⣆⠤⢶⠠⣾⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⡞⠀⠀⢀⣼⠁⠀⠘⡷⠤⠤⠾⠄⠀⠀⠀⠀⡇⣇⠀⠀⢀⣀⡤⠶⠋⠀⣼⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀ ⢰⠃⣠⢤⠏⠸⣄⠀⠀⢹⡀⠀⠀⠀⢸⠓⢲⠞⠁⠉⢻⠉⠉⠙⢦⡀⠀⣰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠀⠀⠀⠀⠀ ⣿⠎⠀⢸⠀⠀⠈⠳⣄⢸⡇⠀⠀⢀⡏⠀⢸⣠⠄⢀⡎⠳⡀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⢦⡀⠀⠀⢀⡸⢷⡀⠀⠀⠀ ⢿⠀⠀⢸⡀⠀⠀⡼⣿⠋⠳⠤⠤⠾⠁⠀⡼⠁⠀⡼⠀⠀⠙⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡷⣤⠔⠋⠀⠀⠳⡄⠀⠀ ⢸⡄⠀⠀⣇⠀⠀⢹⠀⠀⠀⢀⡤⢤⣄⡼⠁⠀⢰⡇⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠈⠣⡀⠀⠀⠀⠙⣦⠀ ⠀⠻⢦⣄⣸⡄⠀⠀⣇⣠⠖⢉⡇⠀⠙⡷⡆⢀⡟⢣⠀⣠⠴⠒⢧⣀⣠⠖⠛⢷⣾⣳⡚⠁⠀⢀⡠⠟⠒⠁⠀⠀⢘⡄ ⠀⠀⠀⠀⠀⢷⠋⠉⠀⠀⣀⠾⠥⠠⠾⠵⣧⠞⠀⠘⣟⠁⠀⠀⠀⠹⣍⡀⠀⠀⡏⠙⠛⠋⠉⠁⠀⣀⣠⠤⠖⠚⠉⠀ ⠀⠀⠀⠀⠀⠘⠦⠤⠴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠒⠒⠒⠒⠛⠛⠓⠒⠒⠒⠒⠒⠚⠉⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣤⠶⠛⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⠀⠀ ⠀⣠⣾⠛⠁⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀ ⣰⡿⠁⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧ ⠹⣇⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣆⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠤⠚⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣧⡈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⡟ ⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⢻⠀⠻⣿⣿⣿⣯⣝⢢⣌⣙⣿⣛⠛⠛⣿⣯⠀⠀⠀⠈⢿⠀ ⠀⠀⠙⣿⣿⣿⣿⣿⣿⠋⢀⣀⠼⢧⣤⡙⢿⣿⣻⠿⢿⣟⣁⠀⠈⡇⠀⣾⢻⠂⡄⠀⠀⢸⠀ ⠀⠀⠀⠈⠀⢸⠈⢻⣿⣯⢁⣠⠤⣴⣬⠇⠸⠉⠙⠓⠻⠟⠚⠛⠋⠀⠼⠃⠀⠼⠦⠀⠀⡎⠀ ⠀⠀⠀⠀⠀⠘⣄⠀⡏⠑⠚⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠓⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⠶⣾⡷⠒⠋⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⣠⠴⠒⠊⠉⠉⣙⡳⡄⢀⣤⣶⡭⢤⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⠒⠒⢿⠀⠀⠀⠀⠀⢹⠁⡇⠀⠿⢄⡠⠀⠙⠢⣤⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠻⡀⠀⠀⠿⠇⠘⠃⢧⠀⢠⠊⠀⣠⠶⠖⠙⢆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡥⠴⢧⣄⠀⠀⠀⠀⢀⣸⠤⣇⡀⠚⠀⡼⡅⠀⠘⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠃⠀⠀⠘⠉⢣⠀⠀⡴⠛⠃⠀⠀⠹⡀⢠⡿⠁⠀⠀⠙⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⡇⠀⠀⠀⠀⠀⡼⠀⠀⡇⠀⠀⠀⠀⢠⡷⣾⡑⢤⡀⠀⡾⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⢛⠟⢳⠀⠀⢀⡠⠾⢷⠒⢺⠛⢤⣀⡀⣄⡸⠀⠃⠑⠄⠁⢀⡆⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⠃⢸⠀⠈⡇⢻⡁⠀⠀⣿⠀⢸⡄⠀⠀⢰⣻⠁⠀⠀⠀⢀⠤⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⢧⣀⣓⡠⠼⠞⠃⠀⠀⢽⠄⢸⡇⠀⠀⠀⠀⠉⠲⠤⠞⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⡠⢐⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠑⠄⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⠌⣴⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⢟⢿⡌⣧⠈⢆⠀⠀⠀ ⠀⠀⠀⠠⠁⣼⣿⡟⢽⠻⢻⣿⠿⢿⢿⣟⣿⡿⠿⣿⠃⠀⢨⣿⣾⣦⠄⣄⠀⠀ ⠀⠀⢠⠁⡜⣿⣿⣿⡿⠁⣿⣿⠀⣤⣀⠐⣄⠿⣆⣿⡏⠟⢹⣿⣿⢰⢉⣿⣅⠀ ⠀⠀⢀⠎⢰⣿⣿⣿⠃⠐⢿⡏⣷⣾⣿⡇⢻⣿⠘⡿⠤⠤⣽⣿⣿⢸⣫⠛⣿⠀ ⠀⠀⡎⠀⣼⣿⣿⣿⣆⣤⣼⣧⠹⣿⡝⢝⣬⣿⣦⡀⠁⣶⣷⣴⣿⣌⣿⠁⢻⡇ ⠀⠸⠰⠀⢹⣿⣿⣿⠏⢸⢿⢿⠀⠀⠀⠀⢩⠿⣯⡟⠦⢸⠛⢹⣻⢿⣿⠀⢻⢿ ⢀⠇⠀⢱⣾⣿⣿⣿⡆⠈⠁⠉⠀⠀⠀⠀⠀⠁⠘⠁⠀⠁⣾⠿⣽⣿⡟⡐⢸⠸ ⢸⠀⠀⣾⣿⣿⠏⡟⡗⡆⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⣈⣥⡾⣿⣿⠀⠇⠘⡀ ⠜⢆⣻⣿⣿⣿⡄⢿⠐⣦⣀⠀⠀⠀⠀⠀⢠⠀⣠⣔⣻⣿⣿⣿⣿⣿⢰⠀⠀⠑ ⣴⣿⣿⣿⣿⠏⡈⢈⠀⢍⣿⠇⠦⢊⣤⡔⢃⠾⢃⣼⣿⣿⣿⣿⣿⣿⣼⠀⠀⠀ ⣿⣿⣿⣻⡍⢂⢰⢸⣤⣾⣯⣶⣾⣿⡁⠄⠒⢭⣿⣿⡿⣿⣿⠭⠯⠿⣧⠀⠀⠀ ⣿⣿⡇⠋⠀⢠⡏⠙⣿⣿⣿⣦⡄⠀⠘⣉⡵⣿⣿⣿⣧⠟⠁⢀⡨⠪⡀⠆⢀⠠ ⡿⣃⡇⢀⣷⢾⣿⣾⣿⣿⣿⠟⣡⡄⢠⢋⡇⢹⣿⣿⡿⠙⢋⠉⠀⠀⠀⡉⠀⠀ ⣿⣿⠀⣼⣯⣿⣿⣿⣿⡿⠁⣴⡿⣴⡟⣓⣳⣿⣵⡿⢁⠕⢁⠀⢀⠄⢀⣿⣉⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠶⠶⠒⠒⠒⠒⠲⠶⠤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠛⠉⠀⣋⣀⡀⠀⠀⠀⠶⠄⠀⠀⠀⠈⠙⠲⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣰⠏⠁⢀⣠⡄⠀⠙⠉⠀⠀⠀⠀⠀⠀⢀⣀⠀⠠⠤⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠠⠦⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⡀⠀⢀⣠⠀⢹⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣸⣧⣆⠀⢀⣾⣤⣀⡀⠀⠀⣤⣾⣰⡀⡀⠛⢰⣤⣤⣴⣿⡀⢻⣿⣧⣾⣿⣀⣤⣶⣦⣤⠀ ⢰⣶⢶⡾⣿⣿⢿⣻⣿⣿⣿⣽⣿⣿⣿⣦⣭⣿⣿⣷⣶⡾⠿⠿⠿⣿⣿⣿⣿⣿⠿⢯⣩⣽⡿⠟⠁⠀ ⢰⣿⣿⡦⢬⣉⣸⣦⣍⣀⣬⡍⢸⣯⣀⠀⣉⣉⠙⠋⣡⠤⣴⣖⣾⣿⣯⣽⡟⣻⣷⣶⣧⣽⠃⠀⠀⠀ ⠀⠀⠹⣷⣶⣯⣭⣿⣤⣼⡿⣧⡾⢿⣿⣷⣤⣼⣷⣶⣿⣶⣿⡿⠛⠛⢿⠛⠿⣿⣿⣿⠿⢿⡇⠀⠀⠀ ⠀⠀⢰⡟⣿⠛⣻⢋⢉⣻⠛⠋⢀⣠⣿⡿⠾⢿⣿⣿⠿⠛⠛⠷⣄⠀⠀⠀⢀⡿⢁⣿⣶⣿⣷⠀⠀⠀ ⠀⠀⠈⠳⣼⣿⡿⡿⣿⢿⣷⣶⣿⣿⣿⣦⣴⣶⣇⣼⣶⣿⣿⣤⣘⣿⣷⣶⣿⠿⣾⡶⠟⠉⠀⠀⠀⠀ ⠀⠀⠀⣴⣿⣿⣛⠋⠉⠛⠛⢿⠉⣩⢿⣿⣿⡿⠟⠉⠉⠉⠙⠋⠉⣻⣿⠿⠁⣀⣞⣿⣤⣀⠀⠀⠀⠀ ⠀⠀⠀⣸⣿⣽⠛⣷⣧⣦⣀⣻⠀⠁⠈⣯⠟⠁⣀⣀⣀⣠⣤⣶⣿⣿⣿⣿⠿⠿⠛⢁⣴⣿⣦⡀⣀⠀ ⠀⠀⢀⣼⣿⣿⣿⣽⡟⢻⣿⣿⣄⠀⢀⣿⣾⣿⣿⣿⠛⣛⣉⣠⣤⣄⣀⣴⣦⣶⣶⣿⣿⣿⣯⠹⣟⠁ ⠀⠀⠸⣧⡭⡄⠽⣿⢿⣿⣤⣟⠛⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣛⣿⣿⣿⢿⣭⣥⠥⠤⠿⠇ ⠀⠀⠀⠘⣦⢳⡞⠻⣄⡈⠉⢉⣉⣩⣿⣿⣿⣏⣭⣿⣮⣶⣀⣴⡾⠿⠿⠿⠋⣁⣠⣤⡟⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⢿⣿⣷⣶⣼⣏⣉⡉⠉⠛⠛⠛⢻⣿⣿⣿⠟⠋⠁⢀⣀⣀⣶⣾⣿⣻⠟⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣾⣿⣶⣶⣿⣿⣿⡿⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣷⡄⠀⠀⠀ ⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀ ⣰⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⡄⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀ ⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⢀⣶⣿⣿⣿⣿⣷⣄⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣦⡀ ⣿⣿⣿⣿⣿⡿⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⠋⠉⢻⣿⣧ ⢸⣿⣿⣿⣿⠁⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣾⣿⣿ ⠸⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟ ⠀⢹⣿⣿⣿⡄⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠛⠉⠀ ⠀⠀⠻⣿⣿⣿⣦⣀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⡀⠀⠀⠀⠀ ⠀⠀⠀⠈⠛⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠀⢻⣿⣷⣀⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠈⠻⣿⣿⡇⠀⠀

⠀⢠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⢦⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀ ⢀⠏⠀⢀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢄⠀⠈⣽⡅⠀⠀⠀⠀⠈⢗⠀ ⡜⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⣘⠁⠀⠀⠀⠀⠀⠀⠀ ⠓⢖⢺⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠔⠒⠉⠉⠁⠀⠈⢄⠀⠀⠀⠀⠀⠀ ⠀⠀⠹⣷⠀⠀⠀⠀⠀⣀⣠⠖⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡀⠀⠀⠀⠀ ⠀⠀⠀⢸⠀⠀⣀⡴⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠤⢤⡀⠁⠀⠀⠀⠀ ⢀⡀⣠⢞⣴⠟⠉⠀⠀⠀⠀⠀⠀⢀⡠⣴⢶⠭⠍⢺⠢⢄⣀⡈⢸⠁⣹⡅⠀⠀ ⠁⢻⡵⠋⠀⠀⠀⠀⠀⢀⡠⠔⢨⠷⡉⠀⠈⡄⠀⢸⠀⠀⠀⠷⡀⡄⠘⠁⠀⠀ ⢀⡟⠀⠀⠀⠀⢀⣤⠚⠛⢢⢔⡁⠀⠘⢄⡠⢴⠒⢺⠢⢄⡘⠀⣱⡇⠀⠀⠀⠀ ⠀⢳⠀⠀⢠⠖⣩⣿⣴⡶⠾⠉⠙⣲⣴⡉⢆⠈⣄⣸⠀⡰⠙⡴⠉⡇⠀⠀⠀⠀ ⠈⣿⡀⢰⡗⠉⠛⢻⠛⠋⠙⡖⠚⣻⡶⠿⣿⣯⣷⣤⣿⣶⣾⣏⣻⠒⠂⢶⡀⠀ ⠀⠋⣼⡋⠹⡄⠀⢸⠀⣀⠴⢿⡉⠀⢣⡠⠞⢧⣏⣹⡽⢆⢠⠓⡅⠀⠀⠘⠃⠀ ⣠⡾⢻⣷⠀⢳⢀⡼⣏⠀⠀⠀⢳⣠⠞⠑⢄⡘⠀⠀⡇⡨⢆⢘⠃⠀⠀⠀⠀⠀ ⣎⡽⣏⡿⣦⣸⡏⠀⠈⢦⠀⢀⠜⠳⢄⠀⢨⠋⠉⠉⠋⠀⢸⡟⠀⠀⠀⠀⠀⠀ ⣏⣠⠞⣇⢸⣧⠈⢦⠀⠨⣷⡋⠀⠀⠀⢳⡯⠤⠄⢀⣠⠔⠱⠁⠀⢩⡏⠀⠀⠀ ⡟⣿⡀⣿⣏⠙⣷⣄⣳⡀⠁⠙⢦⡀⢀⡞⠀⠀⠀⠀⠀⡠⠃⠀⠀⠘⠃⠀⠀⠀ ⠧⣽⡿⡿⢸⣦⠹⣿⣿⢿⡖⠢⢄⣙⠾⣤⠤⠤⠤⠤⣖⠀⠀⠀⠀⠀⠀⠀⢀⠀ ⡀⠘⣧⡿⣡⠞⣻⠿⠃⠛⠀⠀⠀⠈⠓⠾⠷⣶⠤⠊⠀⠀⢹⡅⠀⠀⠀⠀⠈⠡

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢇⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡤⡄⠰⣇⠀⣼⠘⣼⡇⣷⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠛⣷⢦⡿⠿⠃⠀⣿⣿⣿⠀⠀⣀⣠⢤⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢹⣇⢷⠀⠀⠀⣿⣿⡷⠖⠋⠁⠀⠀⡇⠀⠀ ⡤⠤⠤⠲⠤⠤⠞⠋⢻⣾⣇⠀⠀⣿⡿⠃⠀⠀⠀⠀⢀⡇⠀⠀ ⣧⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⠊⠉⠀⠀⠀⠀⡜⠑⣞⠀⠀⠀ ⠈⢧⠀⠀⠀⠀⠀⠀⢠⣀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⢹⠒⠒⠒ ⠀⠈⠳⣄⠀⠀⠀⠀⠀⠈⢿⣳⠀⠀⠀⠀⠀⠈⠠⢄⣼⠤⣄⡀ ⠀⠀⠀⠘⣄⠀⣀⠤⠀⠀⠀⠁⠀⠀⠀⢀⣄⡀⢀⣨⠇⠀⠈⠁ ⠀⠀⠀⠀⡼⠻⢥⣀⡔⠀⠀⠣⣄⣤⣴⣫⠤⠛⠻⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⠏⠉⠉⠉⠉⠉⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡠⠤⠒⠒⠲⠤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠁⠀⠀⠀⠀⠀⠀⠁⠙⡮⣂⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣢⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⣦⣂⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⣝⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠱⣥⠄⠀⠀⠀⠀ ⠀⠀⠀⠀⣸⠮⣶⠞⠛⣛⣛⣛⣷⠶⠀⠀⠐⢶⣟⣛⣛⡛⠓⠿⡚⣮⡀⠀⠀⠀ ⠀⠀⢀⢪⠛⠁⠀⣠⣚⣶⣶⡶⡆⡗⠀⠀⠰⡇⣶⣿⣿⣟⡢⠄⠀⠙⣮⢄⠀⠀ ⠀⢀⢦⡋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣳⢆⠀ ⠀⢨⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⠀⠀⠈⢯⠄ ⠀⡬⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⡼⠁⠀⠀⠀⠀⠊⡄ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⡦⠤⠤⠤⠤⠤⠤⠴⠒⠋⠁⢰⠇⠀⠀⠀⠀⠀⠀⡇ ⠰⣳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⠀⠀⢀⣴⠛ ⠀⠁⢷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢵⠙⠀ ⠀⠀⠀⠀⠩⠗⠲⠤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⡤⠴⠶⠚⠋⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠐⠂⠈⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀

∩―――――∩ || ∧ ﾍ || || (* ´ ｰ`) || |ﾉ^⌒⌒づ`￣ \ (　ノ　　⌒ ヽ \ ＼　　||￣￣￣￣￣|| 　 ＼,ﾉ|| ||

⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠁⣾⠏⠸⡄⠀⠀⠀⠀⠀⡆⢰⢦⡀⠀⠀⠈⢷⣄⠀⠀⠀⠈⠲⣄⢆⠀⠀⣄⠰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡼⠋⢸⡼⠃⠀⠀⡇⠀⠀⠀⠀⢰⣿⣼⠿⠾⣶⣄⡀⠀⢻⣷⣄⠑⠦⣀⠈⠺⣷⢤⡀⠳⣽⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡜⠁⢰⠟⠃⢠⡎⠀⣷⠀⠀⠀⣐⡟⢨⣿⣶⣿⣿⣿⡿⣦⡀⠹⣿⣦⠀⠈⢻⡦⢬⣦⡙⠢⡈⠻⣿⣦⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⠁⢠⠃⢀⡶⢹⣿⠀⣿⣗⠀⠀⡼⠁⠹⠋⠻⣽⣧⠟⠀⠘⡟⣦⣿⢸⣧⠀⠘⣧⣼⢪⡻⣄⠈⠳⣜⢿⣿⣦⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⢠⠏⢀⣾⠁⠈⠹⣧⡏⢹⣧⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡟⣻⣯⠀⢧⠀⣿⡇⠀⠑⢌⠳⣄⠈⠑⢿⣜⢿⡶⣄⠀ ⠀⠀⠀⠀⢀⣷⡏⢠⠿⢈⣷⠀⢰⣌⣿⡿⡟⠿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢁⣿⢈⣿⡘⣧⣿⣧⠀⠀⠈⠣⡈⠳⣦⡀⠙⢷⡉⢻⡁ ⠀⢀⡴⢃⣾⡟⢠⣏⣀⡞⢻⡄⠈⢿⣿⢻⠾⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⢿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠈⠢⡈⠻⣤⡀⠙⢦⡉ ⠖⡏⠀⢸⠛⢗⠻⡃⠙⢦⢠⣿⣦⠀⠻⣷⣥⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠈⠢⡈⠻⣦⡈⠻ ⠀⡇⢀⣸⡀⠘⡄⢹⣆⠘⣿⣿⣻⣿⣦⣿⣏⣹⣶⣄⣀⣀⣀⠀⣀⠴⠋⠀⠀⠀⠀⢸⣿⠙⢿⣿⣿⣿⣿⠿⠷⠦⠤⣀⠀⠈⠂⠈⠻⡆ ⢠⠁⠈⠛⢳⣀⣇⣸⣿⣂⠷⠋⣀⣴⠯⠾⠿⠿⠻⣿⣿⢿⣿⠿⠁⠀⠀⠀⠀⠀⠀⣸⣁⣲⣤⠻⠛⠉⠀⠀⠀⠀⠀⠀⢳⢄⠀⠀⠀⠙ ⢾⠀⠀⠀⠈⠿⡿⠟⠉⠀⢀⣾⠋⠁⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠑⠦⠄⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢣⠀⠀⠀ ⣼⡄⠀⠀⠀⠐⠁⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠒⠤⢄⡀⠀⠀⠘⣆⠀⠀ ⠁⣿⡀⠀⠀⠀⠀⠀⣠⣾⣉⣷⠀⠀⠀⠀⠀⢀⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢶⣾⣟⠹⡦ ⣼⣯⠋⠓⠒⠒⢒⠋⣹⣟⡉⣹⣶⣶⣶⣤⡤⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿ ⣈⣿⠀⠀⠃⠀⢸⡴⣁⣀⣽⠛⠛⠻⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣟ ⣩⣏⢀⣀⣤⠴⢯⣀⣸⣿⡏⣀⣠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿ ⣄⣼⠋⠙⣧⣤⣾⣿⠟⢿⣽⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿ ⠉⠉⢻⣿⢛⡋⠁⢸⠀⠸⡏⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠞⠯⡑⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿ ⠀⠀⠈⠀⠀⠀⠀⠘⡀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠁⠀⠀⠀⢹⡈⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠘⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⡼⠀⠀⠈⠙⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠁⠀⣿ ⠀⣄⡄⠀⠀⠀⠀⠀⠸⡀⠀⠸⣷⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⣠⢾⠥⢤⣀⣤⣄⣀⣈⠙⡻⠶⠖⠒⠒⠒⢲⡟⠉⠲⣤⡀⡿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣰⠞⠛⠲⣦⣤⠤⠤⢴⠏⣦⣈⣷⣚⠉⠻⡄⠀⠀ ⠀⠀⠀⣿⣀⠀⠈⠁⠀⠀⠀⢾⡀⢻⡿⠉⠉⣷⡞⠻⣦⠀ ⠀⠀⢀⡿⠁⠀⠀⠀⠀⠀⠀⠈⠛⠛⠷⣤⣴⠿⠿⣠⡟⠀ ⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢦⡶⢻⡄⠀ ⠠⠤⡧⠤⠄⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⠀⠋⢹⡏⠁ ⠀⢀⣿⡤⠄⠘⠿⠁⠀⠠⣞⣻⠄⠀⠀⠻⠏⢀⡈⣽⠛⠃ ⠀⠀⢈⡷⣶⣃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠿⠛⠂⠀ ⠀⠀⠀⠀⠀⠉⠙⠛⠛⠓⠒⠒⠒⠚⠛⠛⠉⠁⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠟⠛⠛⠿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠋⠀⠀⠀⠀⢸⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠀⠀⠀⠀⠀⠰⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠨⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠈⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⢐⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⠠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡇⠀⠀⠀⠀⠀⢰⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⡿⠿⢿⣿⣿⠃⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠋⠀⠀⠀⠹⣿⠀⠀⠀⠀⠀⠀⢸⣿⣷⣶⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣼⣿⠃⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠈⣿⠛⠉⠉⠙⢿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣼⣿⡿⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢹⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣴⣿⠿⣿⠇⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠘⣿⠛⠲⢦⣤⠀⠀⠀⠀⠀ ⠀⠀⣰⣿⠟⠁⠀⣿⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠹⣧⡀⠀⠀⠀ ⢀⣼⠟⠅⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠸⠟⠁⠀⠀⠀⠀⠀⠑⠿⠃⠀⠀⠀⠀⠀⢹⣇⠀⠀⠀⠹⣧⠀⠀⠀ ⣾⠏⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⢽⣧⠀⠀ ⣿⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⠀⠀⠀⣿⣆⠀ ⣿⣆⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀ ⠹⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇ ⠀⠈⢻⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠇ ⠀⠀⠀⠙⢿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡟⠀ ⠀⠀⠀⠀⠀⠙⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠟⠁⠀ ⠀⠀⠀⠀⠀⠀⠈⠹⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠋⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠏⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣶⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣶⣶⣿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⢀⣴⣦⡦⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡿⢯⣿⣿⣿⣧⣿⠿⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣾⣿⣿⣿⠇⢸⣿⡿⠝⠛⠡⣶⢾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠛⠻⠟⠋⠀⠀⠙⡏⣧⠀⠀⣀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠇⠈⡷⠦⠼⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⣠⠶⠒⠚⢹⠻⣄⠀⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⠊⠁⢀⣤⣤⠘⢦⠙⢦⣸⠙⣝⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋⣀⣤⡴⠒⠉⢹⣿⣁⣼⠄⠀⠈⠀⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣇⠈⣿⠉⠀⠀⠀⠀⠀⢻⣿⠒⢶⣤⣄⠀⢀⡼⣆⠀⠀⠀⠀⠀⠀⣠⣾⣶⡆⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆⠸⡄⠀⠀⠀⠀⠀⠈⢯⠣⠀⠀⠡⠶⣿⣧⠘⣇⣀⡠⠤⠶⠚⣻⣿⠿⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⢇⠀⠀⠀⠀⠀⠀⣾⠀⡠⠄⠀⣠⠏⢿⡷⢉⣁⣤⠴⠚⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡘⠒⣦⡀⠀⠀⣸⣿⣿⣾⠟⠓⡇⠀⠀⠙⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣠⢛⣦⠗⢴⣿⣿⣿⣗⣲⢄⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⢰⣿⣿⣿⣿⣿⣿⣷⠯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⡛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⡿⠟⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠟⠻⣿⣿⣿⣿⡙⠢⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡏⠀⠀⠀⣩⡿⠙⢿⣦⡈⠀⠀⠀⠙⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠀⠀⠀⢀⠟⠁⠀⠀⠙⠿⣦⡀⠀⠀⠈⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠀⠀⢀⠜⠁⠀⠀⠀⠀⠀⠀⠈⠛⠦⣄⠀⠀⣹⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⡾⠟⠋⠀⢀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⡴⠛⠁⣠⣴⡶⠤⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣤⠞⠋⣀⡠⠔⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀ ⢰⡞⣶⣺⢿⣁⡴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄⠀⢧⠀⠀⠀⠀⠀⠀⠀ ⢸⣟⡇⢛⣦⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡀⠸⡄⠀⠀⠀⠀⠀⠀ ⢰⣿⢃⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡐⢻⠀⠀⠀⠀⠀⠀ ⠸⣿⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⡿⢧⣀⠀⠀⠀⠀ ⠀⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣿⣻⣤⡤⢌⣛⣓⣶⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠒⠒⠚⠛⠛⠛⠻⠿⠿⠿⠿⠿⠛⠛⠛⠛⠛⠛⠋⠛⠋⠉⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⢀⣾⣿⣿⣟⡿⠛⣩⠟⣉⠽⠛⡂⣀⠀⠀⠀⡀⠬⣍⣓⠦⣈⢢⡻⣯⠳⣄⢺⡦⠙⢷⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡾⢋⣵⠏⢠⠀⣠⣯⠞⠁⢠⣾⠿⡿⡄⣾⣯⡙⣷⡌⠻⣷⡜⢳⣵⡈⢷⡈⢦⠙⣿⣦⠻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣵⣻⠇⡰⣁⡼⢉⠏⠀⢠⢣⡟⠀⠸⢀⡿⣿⡿⣯⠙⣖⡜⢿⣶⡟⢿⡄⢳⡘⣧⠈⢟⢷⡘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣷⡳⢰⢁⣽⠁⡎⠀⢠⠇⣸⠀⠀⡿⠘⠀⢻⠁⢹⡆⢻⡾⡌⢻⣿⣌⢧⠀⢳⢸⣧⠈⢧⠳⣼⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣧⣇⢇⣿⡇⢰⠀⠀⣸⠀⡏⠀⠀⠀⢠⠀⠸⡀⠀⣷⠀⢿⣿⣄⠛⢿⣇⣧⠀⢧⣿⡳⣎⣧⢹⣷⠀⠀⠀⠀⠀⠀⠀⠀ ⣸⣿⡾⡼⣿⠀⣼⠀⢸⡇⢠⡇⠀⠀⠀⢸⠀⡆⡷⡆⠹⡆⢸⣿⣿⡆⠈⢿⣷⠀⠘⣿⣇⢸⣿⣧⢿⡆⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⢷⣷⡇⠀⡿⠀⣿⡇⢸⡇⢰⠀⠀⢺⠀⡀⡗⡁⢸⡗⠀⣿⡈⣿⡄⠈⣿⡇⠀⠉⣿⣮⣿⣷⣈⣷⠀⠀⠀⠀⠀⠀⠀ ⣿⢻⣾⣿⡇⢰⠁⠀⣻⡇⢸⡇⢸⡇⠀⣿⠀⡇⣿⡇⠸⢯⠀⣿⡇⠸⡇⠀⣿⣿⡀⠀⢹⣷⡟⣹⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⢹⣾⣿⣿⡅⡈⠀⢸⣿⠃⢸⡇⣾⡇⢀⣿⡀⢿⣿⡇⠀⡄⠀⣿⡇⠀⢿⡆⣸⣿⣿⣼⠈⣿⡇⣿⣋⠹⡇⠀⠀⠀⠀⠀⠀ ⠸⣿⣿⣿⠃⡇⢠⢸⣿⠇⢸⡇⣿⣿⣸⣿⣷⣶⣿⣿⠀⠇⣽⢿⠃⢀⣰⣿⣿⣿⢻⡿⡄⢿⣷⣍⣉⢋⡇⠀⠀⠀⠀⠀⠀ ⠀⢿⣿⣿⡇⡇⢸⡜⢿⢰⣾⣷⣿⠻⣿⣿⣿⣿⠉⣟⠀⣆⣿⣾⡾⢟⣯⣴⣿⣿⣾⣿⡇⢸⡇⣿⡿⢻⡇⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⣽⡇⡇⢸⡇⢸⣿⣿⠻⣿⣠⣿⣿⣿⣿⠀⢿⣼⣿⣿⠏⢰⣿⣿⣿⣿⡿⣹⣿⢱⡾⣇⡟⢹⣿⠇⠀⠀⠀⠀⠀⠀ ⠀⠀⢻⢛⡇⣷⢈⣿⣾⣿⣿⣆⣿⣿⣿⣿⣬⣿⠀⣸⣻⠿⠋⠀⠘⠉⠽⠿⠿⡾⠟⢹⣸⠀⣿⡷⣻⡿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢻⣷⣿⣸⣿⣿⣿⣿⠿⣿⣿⣿⣿⢧⠄⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⡿⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢻⣿⡏⢹⡟⠋⠙⢶⠌⠉⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⣻⠿⢤⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⡃⢸⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⣿⢀⡇⠀⠉⠒⠤⡀⠀⠀⠀ ⠀⠀⠀⠀⠘⣿⡇⠈⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⢀⣿⣤⠃⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⣿⡇⠀⢹⠋⠉⠳⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠀⠀⢀⣷⢸⣿⢁⣀⠀⠀⠀⠀⠀⠀⢣⠀ ⠀⠀⠀⠀⢀⡿⣷⠘⢸⡇⠀⡀⣏⠳⣄⠀⠀⠀⠀⠀⢀⣀⣀⠠⠤⠒⠋⡀⠀⠀⢀⣿⠏⣼⠁⠈⠈⠉⠙⠲⢤⣠⡄⢸⠄ ⠀⠀⠀⡰⠋⠀⢻⡀⢿⡇⠀⢡⢿⠀⠀⠑⢦⣄⠀⠀⠀⠀⠠⠤⠤⠴⠊⠀⠀⣠⣿⣿⢠⡿⠄⠀⠀⠀⠀⠀⢠⠿⢉⣿⠀ ⠀⢠⠞⠀⠀⠀⢆⢇⢸⣷⠀⢺⣌⡇⠀⠀⠘⢿⣿⢷⡦⠤⣄⡀⠀⠀⠀⣀⢼⡏⣽⣇⣿⠂⠁⠀⠀⠀⠀⠀⠘⠀⣸⣏⠀ ⢀⡇⠀⠀⠀⠀⠈⣞⡄⣿⡶⡈⠙⣿⠀⠀⠀⠈⢿⡳⣄⠀⠀⠈⠉⠉⠉⠁⡸⢹⣿⣿⡏⡖⠀⠀⠀⠀⠀⠀⢀⣼⠏⠘⠄ ⢸⠁⠀⠀⠀⠀⠀⠘⢷⣼⣷⠹⣄⠘⢷⢄⡀⠀⠀⠙⠾⣆⠀⡀⠀⠀⠀⣴⡷⢿⡟⣿⠆⡇⠀⠀⠀⠀⢀⠆⣾⣿⡴⡴⠁ ⢸⡀⠀⠀⠀⠀⣠⡤⠈⢻⣿⣆⠈⢳⠘⢧⠉⠲⣄⡀⠀⠈⠙⠻⢆⣀⡜⠉⠀⠋⡰⠋⠀⣇⠀⠀⠀⠀⠸⠀⣿⣽⣾⡗⠀ ⢸⣇⠀⠀⣠⠈⠉⠀⠀⠀⠹⣟⢆⣀⣧⠀⢷⡀⢀⠉⠓⠦⢤⠀⣠⣿⣿⢿⣄⠀⠀⠀⠀⡇⠀⠀⠀⠀⡆⠀⢸⣷⠎⠀⠀ ⠀⢫⠳⣞⡁⠀⠀⠀⠀⠀⠀⠈⢣⠱⠜⣧⠘⣟⣄⠑⠢⠤⠄⣠⣿⣟⠉⠀⢹⡟⠲⢤⣀⠀⠀⠀⠀⠀⠓⠀⠘⣿⡀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣠⣾⣿⣿⡿⠟⠛⠉⠙⠛⢿⣿⣿⣿⣿⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀ ⢰⣿⣿⣿⣥⣤⠀⠘⠿⠛⠓⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀ ⠘⣿⣿⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠟⠛⢿⣿⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠘⠻⡆⢀⣀⣀⠄⠠⠒⠈⠁⠀⠿⠿⠀⠀⠀⣿⣿⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡰⠁⠀⠺⣷⠄⠀⠀⠀⠀⠀⠀⢀⣀⣴⣿⣿⠂⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⠁⠀⠀⠀⠀⢀⢠⠂⢰⠀⠀⠀⠀⡏⢛⠻⠯⠤⠤⣀⠀⠀⠀⠀ ⠀⠀⠸⡀⠀⠰⣒⡈⢀⣀⠰⠁⠀⠀⠀⡘⠠⢃⠃⡠⠊⠁⠀⠑⣄⠀⠀ ⠀⠀⠀⡱⣄⠀⠀⠈⠁⠀⠀⠀⣀⡔⢰⡐⠡⠂⠌⠀⠀⠀⠀⠀⠈⡄⠀ ⠀⠀⡜⠀⠇⠉⠒⢆⣠⢄⠒⠋⠉⣀⢞⠔⠁⡟⠀⠀⠀⠀⠀⠀⠀⢰⠀ ⠀⢰⠀⠀⡜⡄⠀⠈⢪⠀⠉⠉⠉⠀⡏⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠸⠄ ⠀⢸⠀⠀⠈⢲⠀⠀⠈⡆⠀⡀⢄⠀⢀⠀⡘⡀⠤⠦⠤⠄⠀⠀⠀⠈⠠ ⠀⢸⠀⠀⠀⠀⡇⠀⠀⢤⢠⠁⠀⢙⠼⣠⠋⠈⠉⠁⠒⢤⠀⠀⠀⡀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⣶⣶⣿⣿⣿⣿⣿⣿⣿⣶⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀⠀⠀⠈⠉⠙⠻⠿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⡿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⣾⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⣿⡿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣰⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣆⠀⠀⠀⠀⠀ ⠀⠀⣰⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣦⣤⣹⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⡀⠀⠀⠀ ⠀⣰⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⣠⣾⣿⣿⡿⠋⠀⠀⠀⠀⠀⣸⡄⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡄⠀⠀ ⢠⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⣴⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⣰⣿⡇⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⣿⣿⣿⡄⠀ ⣸⣿⣿⣿⣿⠀⠀⠀⠀⢀⣾⣿⣿⣿⠃⢀⣀⣀⣀⣀⣀⣴⣿⣿⣇⣀⣀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⡇⢻⣿⣿⣷⠀ ⣿⣿⣿⣿⡇⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠁⠸⣿⣿⣿⡆ ⣿⣿⣿⣿⣷⡀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⡏⠀⠀⣿⣿⣿⡇ ⢸⣿⣿⣿⣿⣿⣦⣀⣀⣘⣿⣿⣿⣿⣿⣿⣿⡿⠟⣫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡿⠀⠀⠀⣿⣿⣿⡇ ⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠉⠁⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⠀⠀⢠⣿⣿⣿⣿⠃⠀⠀⢸⣿⣿⣿⡇ ⠀⠀⠙⢿⣿⣿⣿⣷⣤⣀⣀⣀⣀⣀⣤⣶⣿⣿⠿⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⣾⣿⣿⣿⠀ ⠀⠀⠀⠀⠉⠻⠿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠋⠁⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠻⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⣸⣿⣿⣿⡏⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠉⢿⣿⡇⠈⢻⣿⣿⣿⣿⣷⠀⠀⠀⢰⣿⣿⣿⡟⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣤⣼⣿⣿⠀⠸⣿⣿⣿⣿⣿⡆⠀⣰⣿⣿⣿⡿⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠙⢿⣿⣿⠀⠀⠿⢿⣿⣿⣿⣇⣴⣿⣿⣿⡟⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⡇⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣶⣌⠉⢻⣿⣿⣿⣶⣆⠀⠘⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⡆⠀⢻⣿⣿⣿⣿⡆⠀⢈⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣷⡀⠀⠻⠿⠟⠋⠀⠴⠿⠛⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠆⠀⣼⢀⡞⣼⣿⣼⠀⠀⣠⠟⣠⣾⣿⣿⣿⢀⣤⣔⣿⠟⠋⣙⢛⡺⠛⠛⢛⡻⠟⠛⠿⠿⠿⠿⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⣭⣅⢻⣿⣿⣿⣿⣿⣧⡻⣧⠀⠀⣇⣇⠈⠂⠀ ⠀⢠⣇⣞⣼⣿⣿⣿⠀⣰⢃⣾⣿⣿⣿⣿⣿⡗⠿⣍⡠⣒⠽⠊⢉⡨⠖⣯⣥⠄⢠⣄⣀⡀⠀⢀⣀⡀⠀⠀⣀⡀⠀⠀⠀⠀⠀⡙⢃⣸⣿⣿⣿⣿⣯⣿⣿⣾⣷⡀⣿⣿⠀⠀⠀ ⠀⢸⡿⢹⣿⣿⣿⣿⣰⣷⣿⣿⣿⣿⣿⣿⣿⣗⠾⠗⢉⣠⠴⠊⠁⠀⠀⣿⢺⠀⠀⡏⠀⡇⠀⢸⠊⡇⠀⢸⠟⡇⠀⠀⠀⠔⠋⢿⡿⣿⣿⡿⠋⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀ ⠀⣸⠁⢨⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⠖⠋⠀⠀⠐⠒⠦⠤⡏⢸⠶⠶⡇⠀⡵⠶⢮⠀⡵⠶⢦⡇⣷⡶⠖⠚⠛⣠⠟⣠⣿⠿⣿⣿⣿⣿⣿⣿⢟⣥⣼⡿⣿⣷⠀⠀ ⡆⠇⣰⣿⣿⣽⡟⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡙⠁⠀⠀⠀⠀⠀⠀⠀⠷⠾⠁⠀⡿⠾⠅⠀⢸⣤⠁⠠⠼⣧⠇⠀⠀⢠⡾⠃⣻⣿⣿⠀⣾⣿⡿⣟⣿⣿⣿⣿⣻⢁⣽⣿⣶⢠ ⡇⠀⣨⣿⣿⣿⣿⠀⠀⠹⡿⢿⡙⠻⠿⢿⣿⣿⣿⣷⣶⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡠⠂⠀⠀⢀⡴⣋⣠⣾⣿⣿⣯⣾⣿⡽⠾⠋⢠⣧⠸⢟⣽⣿⠛⢿⣿⣾ ⠀⢠⣿⡿⣿⣿⣿⡆⠀⠀⣷⡟⠁⢼⣤⣤⣤⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣾⣿⣿⣿⣶⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣟⣋⣁⣀⡀⠀⠀⣿⠀⢸⣿⣿⣆⣸⣿⣼ ⠁⠈⣹⡇⢿⣯⣿⡇⠀⠀⢻⡇⠀⠈⢷⡀⠀⢠⠉⣽⠉⢩⡛⠛⡿⢿⣿⣿⣿⣟⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢛⡉⠹⡀⠘⡇⠹⣽⡿⠁⠀⠀⢸⡄⣿⣿⡿⡇⢿⣿⢿ ⠀⢰⣿⣇⢸⡍⢿⣿⠀⠀⣾⠂⠀⠀⠈⢻⣆⠸⠀⠸⣄⠈⠯⡤⣤⢤⠛⣿⣿⣿⣿⣿⠖⠋⠁⠈⢾⣿⣿⡿⢛⠁⢸⡀⠉⠥⣶⡦⠖⡇⣰⠟⠀⠀⠀⠀⣾⣿⣿⣿⢗⡇⣬⣿⢸ ⡄⠀⣿⣿⡀⢳⡄⡿⣇⢀⣿⠀⠀⠀⠀⠀⠈⠻⠷⣤⣈⣛⣊⣁⣠⣞⣠⡻⠿⠟⢿⠀⠀⠀⢀⣤⣿⡿⣯⣳⣌⣆⣀⣉⣛⣛⣉⣠⡾⠟⠁⠀⠀⠀⠀⠀⢹⣿⣿⣿⠙⢹⣿⣿⢛ ⠁⢀⡘⢿⡇⡀⣿⣶⣿⣼⣿⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣼⣄⠠⠞⠉⠀⣿⣥⡁⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⣿⣇⢠⣾⡏⠀⠀ ⣶⣿⡇⢠⣿⣞⣿⣿⡿⣿⣧⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠓⠇⠀⠀⠀⠀⢷⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢟⡝⢀⣿⣿⠇⠀⠀ ⣾⣿⡿⠋⠻⣿⣿⡟⠁⢻⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⠀⠀⠀⠀⠀⣼⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⠞⢠⣷⣿⡇⠀⠐⣶ ⣿⡏⠀⠀⢐⣼⡿⣿⣦⣌⣹⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠚⠀⠀⠀⠀⠀⣘⣛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢏⢀⣾⣿⣽⢿⣦⣀⠈ ⠃⠀⠀⢘⡿⣝⢀⣿⠋⠿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⢿⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣾⣾⣿⣿⡟⠈⠛⣿⣷ ⠀⢀⣴⣿⡯⠃⣸⠃⠀⣤⢿⠹⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⢿⠁⣹⠘⠃⢈⣢⡘⢯ ⡾⢛⢥⣬⡂⢠⡏⢀⡞⢏⣎⢞⣻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠶⠤⠀⠀⣤⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠿⢀⣾⡄⢻⡄⠀⠲⡙⢟⡆ ⣿⢕⢿⡫⠀⣾⣶⣯⢯⠈⠎⡜⠃⠻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⢱⣷⠙⢾⡇⠀⠐⢜⢎⠳ ⣟⠕⢋⣴⣾⡿⣿⠋⢸⡌⠰⣿⡄⠀⢻⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣇⢀⣿⣿⣷⣦⣿⠀⠀⠐⠳⡁ ⣷⣄⡉⠸⠋⠘⣡⣦⡜⢧⡼⣡⣿⡀⠀⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⠒⠒⠒⠒⠒⠒⠒⠒⠲⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣏⣿⡇⢻⣿⣿⣿⣟⠛⣷⣀⣤⣴⣿ ⡟⠿⣿⣷⣦⡀⠹⡿⣡⣾⣿⣿⣷⣷⡀⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⢀⣀⡉⠉⠉⠉⢉⣉⢉⣉⢉⣉⣁⡀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⢿⡟⣹⣯⣽⣿⣶⣿⣿⣿⣿⣿⣿⣿ ⣿⣦⡻⣿⣿⣿⣷⣤⣫⠿⢻⣿⣿⣿⣧⡿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⢿⡋⠉⠉⠉⠉⠉⠉⠉⠉⢸⡟⠀⠀⠀⠀⠀⠀⣀⣴⣿⣥⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⡏⠙⣯⣿⣿⣿⣿⣿⣷⣯⣿⣻⣿⣿⣧⣿⣿⣿⣧⣿⣿⣦⣠⡀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣀⣀⣠⣴⣶⣾⣿⡿⠿⢛⣻⣭⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣻⣿⡿⠿⣛⣿⣿⡢⡀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣴⣶⣾⣿⣿⠿⢿⣛⣫⣽⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣷⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢶⣦⣭⣴⣽⣿⣾⡷⢶⣾⣿⣿⣿⣿⣿⣿⣿⣽⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠐

⢠⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⡄ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣦⣀⠙⠛⢿⡿⠛⠋⣀⣼⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣯⣀⣠⣀⠀⠀⣀⣤⣴⣶⢾⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣾⠏⠉⠀⠀⠀⠻⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣶⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⢀⣀⡀⠀⢀⣀⢸⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠘⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀ ⠀⠀⢀⣴⣿⡇⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀ ⠀⣰⣿⣿⣿⣿⡀⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄ ⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃ ⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀ ⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠙⠛⠛⠿⠿⠿⠿⠛⠛⠋⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⠀⠀⡦⣴⣖⣛⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢈⠧⠊⠤⡭⠉⠛⠻⢿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⠅⠂⠀⡱⠀⠀⢐⠀⠈⠟⢿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠐⠒⣷⢇⢡⠀⣷⡆⢀⢸⡄⠀⠸⠀⠟⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠠⣿⣕⣺⣧⣼⣾⣶⡵⠛⣦⣰⣞⣶⠼⢿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠛⣻⡏⠉⠻⠉⠁⠀⠉⠻⠛⢱⡤⣼⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢅⡀⠀⠀⠀⠀⠀⠀⡠⢵⣾⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠳⣖⠂⠀⠀⣠⡞⠀⠀⠙⡟⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⢠⣾⡟⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠇⠧⠀⠀⠀⠀⠈⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡠⡤⠒⢉⣢⣉⠂⢀⡃⠀⢰⡀⠔⢁⠌⠣⡂⠤⢀⡀⠀⠀⠀ ⠀⠀⣠⡒⠈⠐⠊⠀⠀⠀⠀⠀⠉⠐⠂⠀⠀⠂⠈⠉⠀⠀⠀⠈⠁⠈⠉⢒⡄ ⠀⡎⢀⠀⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱ ⢸⠇⠈⠧⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠹⡀⡀⠤⠒⢉⠥⠐⠉⠀⠀ ⠐⠒⠒⠀⠄⠀⠀⠀⡀⠀⠀⡖⠉⠉⢉⣇⣀⣤⠘⠈⡁⠠⠒⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠀⠂⠠⠄⠐⠛⣷⣿⣶⣿⣻⣿⣯⠤⠬⣧⣧⣤⣤⣤⣤⣤⣤⣤⣤⣄ ⢀⣀⣤⣤⠤⣒⣂⡀⠩⠥⠋⠉⢙⡓⢿⡁⣈⣁⡉⢯⣯⠉⠭⠭⠿⡍⠉⠉⠉⠉ ⠒⠊⠉⠉⠀⠀⠀⠀⢠⠴⡒⡹⠙⡿⡿⠖⠉⣤⡀⡀⢸⠈⠉⠀⠀⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠼⡿⠀⢘⣷⡌⣀⠸⡟⠳⢫⠿⠀⣤⣤⣀⡄⠀⠀⠀⠀ ⠀⠀⠀⣀⣤⡤⠤⣖⣂⣸⠃⠐⠘⠃⡍⡐⢀⢸⠒⢲⡞⡿⠹⣋⣟⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⣏⣝⡉⣧⡧⢋⠀⢀⣀⠘⡐⢀⠂⠨⡤⢼⣿⡉⠸⣿⠦⠃⠀⠀⠀⠀ ⠀⠀⠀⠸⡿⠦⠙⢿⠔⡏⣆⡞⡚⠉⠀⠋⣠⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢂⣿⡿⠛⣿⣼⡗⠘⢷⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⡅⠀⠻⡿⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢤⣠⠄⠀⠀⣫⡇⠀⠈⠉⠉⠉⠛⠒⠶⢤⣌⡲⣄⠀⠀⠀⠀⠀⠈⠉⠁⠉⠉⠉⠓⠲⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋⠁⢠⣄⠀⠁⠀⣠⢦⡀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠉⠑⠲⣦⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠶⠋⠀⠀⠀⣴⢿⣽⣆⢀⡼⣷⣿⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣯⠽⠿⠋⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠞⢁⠀⠀⠀⢠⡾⡿⠛⣿⡿⠿⠿⠟⠻⣯⣙⣆⠀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣤⣖⣋⣁⣤⣴⠃⠀⠀⣰⠏⣼⢣⡞⠁⠀⠀⠀⠀⠀⠈⢻⣜⣆⠈⢳⡄⠀⠀⠀⣆⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁⠀⠀⣴⠃⢰⣧⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡄⠀⣿⣆⠀⠀⣿⣄⠀⢻⡄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⠀⠀⡼⠃⢀⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡆⠀⣿⣦⢠⣿⣿⡆⢸⣿⣌⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⢀⠀⣼⠁⠀⢸⠃⠒⢦⣀⠀⠀⠀⠀⠀⢀⣀⡠⠆⠀⠙⣿⡄⠘⣿⣿⡇⠘⣿⡸⣿⡿⣿⣷⡀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠈⠳⣀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣞⣡⢴⢫⡏⣼⠃⠀⠀⣾⠀⠀⠀⠙⢧⠀⠀⠀⠜⠋⠀⠀⠀⠀⠀⠘⣟⡄⠸⣿⡇⠀⢹⣿⣿⡇⠹⣇⠻⡄⠀⠀⠀⠸⣦⡀⠀⠀⠀⠀⠈⠓⢤⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⡼⠋⠁⣾⡞⠐⠃⠀⠀⣠⣿⡌⠙⠒⢦⡞⠀⠀⠀⠀⢔⣲⠴⠒⠒⠒⠢⠼⣵⡀⢿⡇⣠⠀⢿⣿⠀⠀⣿⠀⢹⣄⠀⡀⠀⢹⡙⠢⣄⠀⠀⢶⡒⠒⠉⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠁⠀⠀⢀⡾⠋⣹⢣⠀⢠⣾⡷⠀⠀⠀⣰⠞⠁⠀⠀⠀⢠⣶⣦⢻⡇⠘⢣⡿⠄⠀⢿⠀⢸⣿⡄⠀⡟⢣⠹⣄⠀⢧⡀⠈⠓⢤⣄⠙⠢⣄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣯⡇⠀⣠⠟⠀⠀⡇⠈⠓⣾⠟⠁⠀⠀⠀⠙⠶⠤⣀⣀⣀⣺⣿⡿⠻⡇⠀⣸⠀⠸⡀⠈⠀⢸⣉⢿⡄⣷⠀⠀⠈⠳⡘⠃⣻⡖⠲⠿⠓⠛⠋⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⡴⣿⢫⡇⣰⠟⠲⣄⢀⡇⠀⠀⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⢴⣿⡄⠀⢷⠀⠀⣿⡿⢸⢧⣿⠀⠀⠀⠀⠀⠀⢹⣷⠃⠀⠀⣻⠄⠀ ⠀⠀⠀⠀⠀⠀⢠⠞⠁⠚⣸⡾⢹⡀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣼⣀⣿⡀⠸⡆⢰⣿⣇⡾⠟⢿⠀⠀⠀⠀⠀⢦⡀⠸⡀⢀⣴⣿⠀⠀ ⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠿⠁⠈⣇⣠⠞⠁⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠹⠹⣧⠀⡇⡼⢺⡟⠁⠀⠀⠀⠀⠀⠀⠀⢈⣷⣤⣷⣿⣿⣿⠀⠀ ⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⣱⡀⠀⠀⢠⣤⣤⣀⣒⣒⣒⣒⣲⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⢿⠗⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣾⣿⣿⣿⣿⠀⠀ ⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢉⡽⠁⢣⠀⠀⠈⠻⠿⠭⠍⠉⠩⠝⠋⠁⠀⠀⠀⠀⠀⠀⠀⣰⠟⡿⢻⡟⠀⠀⠀⠀⠀⠀⣀⠀⠀⠰⡶⠶⠤⡬⠿⠛⢿⢻⠀⠀ ⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣋⣀⣀⣀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠁⢀⡟⠛⢻⣾⣦⡀⣀⠀⢀⡏⠙⠶⣤⣻⣅⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣧⣤⣍⡛⠙⠛⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⠶⠋⠁⠀⣠⠏⠀⠀⠸⣿⣛⠛⠿⠿⠾⣵⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⡏⠀⠉⠙⠿⣶⣄⠛⠙⠒⣶⠒⠶⣶⣶⣾⣿⡿⣻⣿⠀⠀⠀⠀⣴⠃⠀⠀⠀⠀⢻⠿⣷⣄⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⡇⠀⠀⠀⠀⢈⣿⣦⠀⠀⢷⠖⠋⠹⡎⠙⡷⠖⠋⠁⠀⠀⣠⡼⠁⠀⠀⠀⠀⠀⠈⡆⢨⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡴⠖⣿⠲⢦⣄⣰⠏⠀⢹⣧⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⣠⠞⣹⠃⠀⠀⠀⠀⠀⠀⠀⠸⡏⠀⢹⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢿⡄⠀⡿⠀⣠⡿⡇⠀⢀⣀⣿⣦⣶⣶⣶⣤⣼⡀⠢⣄⡤⠞⠁⢠⠇⠀⠀⠀⠀⠀⠀⢀⣀⣤⣿⣴⣶⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢰⣯⣤⣽⣦⣧⣴⣯⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⣰⠃⠀⠀⠀⢀⣠⣴⣶⣿⣿⣿⣿⣿⣿⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡴⠃⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⢀⡴⠁⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡴⠏⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠙⠀⠈⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠐⠉⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠤⠒⣲⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣣⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣸⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀ ⠀⢀⠀⠀⠐⠋⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⢏⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⠒⠾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢃⠈⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣴⣿⡷⠟⢛⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⠦⠤⠤⠤⠤⠤⠤⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠞⢁⡀⠤⠤⠤⠤⠤⠤⢀⣀⠀⠀⠀⠙⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⢫⠀⠀⡠⠤⠤⢄⡀⠀⠀⠀⠀⠀⠈⠉⠒⢤⡀⠈⠻⣍⠉⣩⣉⣩⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⡠⠞⢁⣠⠎⠐⠉⠀⡀⠀⠀⠈⠑⠢⢄⡀⠀⠀⠀⠀⠀⠈⠁⠀⠈⡓⠈⠩⣟⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⠖⠉⢀⡶⠋⣸⠀⠀⠀⢠⠈⠓⢄⠈⠉⠒⢄⠈⠑⠢⣄⠀⠀⠀⠀⠀⢄⠈⠛⢗⠢⣿⣀⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡏⠀⣠⣿⢁⡤⠃⢰⠀⠀⠀⢣⠘⢦⠱⣄⠐⢆⠑⣄⠀⠀⠑⢤⡀⠀⠀⠀⠑⢄⠀⠑⠮⣽⣮⣍⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⠀⠰⢁⣿⡁⠀⠀⠀⢣⠀⢂⠀⠳⣴⡳⡈⠳⡌⠣⡡⡑⢄⠀⢠⡉⠢⡀⠑⡄⠀⡙⢿⣦⡈⠛⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⠀⡇⠈⢰⠳⡄⠠⠘⢄⠣⡀⣧⠱⣽⡖⠺⢵⡌⠢⣽⣿⡌⠣⡀⠙⢦⡘⢄⠈⢦⠘⢤⣽⡿⣦⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣸⠀⣿⡇⢸⠆⢸⣆⠱⡌⢢⠱⡙⢷⡈⠻⣦⣄⠉⠳⢮⣿⣷⡶⢿⣀⣤⡙⢮⣯⠣⡳⣈⢻⣿⡛⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣇⠀⣟⠰⡃⠙⣼⠈⢆⠺⣆⠱⡘⠢⣙⠄⢬⣓⣝⣢⣄⡈⠙⢦⡾⠛⣶⣽⣷⣝⣆⡑⢈⠳⡝⡿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣽⣼⣿⡀⠹⣤⡌⢣⡈⠳⢽⣦⠼⠦⡈⠳⣦⣝⣻⣛⣿⣽⢷⡚⢷⡒⠉⠙⡟⠏⣿⣿⣾⣖⣿⣇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⠟⢿⢟⣿⣄⠹⡙⢿⢟⢦⡀⠈⠑⠢⣬⣦⡙⢾⣙⢙⣦⣀⠀⣸⣾⢶⠯⠄⣸⡘⣾⣿⢿⣟⢿⣿⣷⠀⠀⠀⠀⠀⠀ ⠀⠀⣴⡟⠀⠘⣿⣏⢻⡆⢱⣤⣿⣕⢿⣲⣖⡈⡿⠃⣈⠓⠛⠃⠀⡸⣿⡿⣿⣿⣿⣿⠋⠑⣿⢻⣦⣿⣾⣿⠀⠀⠀⠀⠀⠀⠀ ⢰⣯⣿⡧⣴⡀⡟⣿⣦⠹⣦⢣⢈⣿⣑⣬⣿⣿⢤⣀⠀⠣⠀⠀⠀⠀⠟⠀⢻⠿⣿⣿⠃⠀⡿⠃⡼⢧⡼⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠻⢿⣏⡇⡇⠉⡿⣷⣽⣆⢿⣽⣿⡿⢿⣿⣿⣶⡆⠀⠀⠀⠀⠀⠀⠀⠐⠚⢋⡁⠀⠀⣧⠼⢿⠾⣄⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⢉⣧⡆⡇⢿⣿⡛⣿⠚⠋⠀⢚⢻⣿⡇⣠⠶⠀⢀⣀⠀⠀⢀⡤⠚⠉⣹⠂⢀⡇⠀⣀⠀⠀⠹⡍⠑⠒⠤⢄⣀⠀ ⠀⠀⠀⠀⢀⣞⢸⣇⠳⢾⣷⠿⣿⣷⡀⠲⠾⠾⠛⡻⠁⢰⠀⠀⣀⠤⠚⠁⢀⠤⠊⣠⠔⢻⣻⠆⡍⢳⣄⠀⠈⢦⠀⠀⠀⠀⠉ ⠀⠀⠀⠀⠀⠉⠉⠛⠒⠞⢸⢳⣮⣽⣷⡀⠀⠀⡰⠁⢀⡼⠖⠉⠀⢀⡤⣚⡡⠒⠉⢀⣠⣾⣯⠈⠉⠀⠀⠀⢀⠦⣱⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠚⠛⠛⣿⣻⠶⠊⠥⠒⠉⠀⡀⠀⠴⠟⠋⠁⢀⣠⣴⠿⠛⢩⣽⡄⢀⠟⢦⡀⠺⠐⠛⠙⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢺⢈⣹⠀⠀⠀⠀⠤⠚⠀⠀⠀⠀⢠⡶⠟⠋⠀⣠⣶⣿⣿⣷⠐⠒⠊⠉⢀⡀⠀⠀⠘⡄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢼⠁⡉⠁⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⠿⢿⣿⣿⣇⠀⠀⠀⣜⢉⣷⠄⠀⠘⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁⠈⡘⢙⣄⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠋⠉⢀⣠⣾⣿⣿⣿⡆⠀⠀⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⡇⠛⠉⢸⠉⠓⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⡄⠀⠈⠢⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣠⠞⠡⠳⣄⠀⠃⢠⣦⣧⡀⠀⠀⠀⠈⠑⠢⣄⣀⣀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠐⣌⠀⠀⠀⠀

⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀ ⠀⣀⣴⣿⡿⠿⣿⣿⠿⠿⠿⠿⣿⣿⠿⠿⠿⠿⣿⣿⠿⢿⣿⣦⣀⠀ ⣰⣿⠟⠁⠀⠀⣿⣿⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⣿⣿⠀⠀⠈⠻⣿⣆ ⣿⣿⣶⣶⣶⣶⣿⣿⣶⣶⣶⣶⣿⣿⣶⣶⣶⣶⣿⣿⣶⣶⣶⣶⣿⣿ ⣿⣿⠉⠉⠉⠉⣿⣿⠉⠉⠉⠉⣿⣿⠉⠉⠉⠉⣿⣿⠉⠉⠉⠉⣿⣿ ⣿⣿⠀⠀⠀⠀⣿⣿⣀⣀⣀⣀⣿⣿⣀⣀⣀⣀⣿⣿⣀⣀⣀⣀⣿⣿ ⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⠀⠀⣠⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢿⣿⣄⣾⣿⠛⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠛⣿⣿⣿⣿⡿ ⠈⠙⠛⢿⣿⣄⣀⣠⣿⡿⠛⠛⠛⠛⠛⠛⢿⣿⣄⣀⣠⣿⡿⠛⠋⠁ ⠀⠀⠀⠈⠛⠿⠿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠿⠛⠁⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢤⡀⠙⢦⡀⠐⠀⠀⣽⢸⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠈⠲⡀⢳⡀⠀⠀⠿⠾⣀⣙⢦⣀⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠞⠉⢁⠀⠈⠉⠑⠲⠄⠘⣆⠻⣆⢠⠾⠽⠶⠾⠟⢋⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⣠⠔⠋⠀⠀⠀⢀⣀⣀⡀⠈⢧⠘⡯⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⣀⡴⠋⠀⠀⠀⠀⣠⠖⠋⣁⣈⣓⣄⠘⠄⡇⠀⠀⠀⠀⠀⠈⢻⣦⣤⣤⣤⣤⡤⣤⣤⣤⣤⣤⣤⣄⣤⣤⣠⣠⣀⣀⣀⣀⣀⢀⣀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⢀⡴⠃⠀⠀⠀⠀⢀⡼⢃⡴⠋⠁⢀⣀⣉⣷⣄⠃⢀⣀⡀⠀⣄⠀⠈⣿⣗⠒⠛⠓⠒⠶⠾⣧⣤⣤⣀⣿⠋⠀⠀⠀⠀⠀⠀⣠⠁⠀⣠ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⣰⠋⠀⠀⠀⠀⠀⢠⡞⢠⣎⡤⣖⠽⠗⠋⠉⠉⠉⠉⠷⣭⣅⣀⡈⠙⢦⣘⣮⠳⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠳⠶⠶⠶⠶⠾⠧⣤⣴⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠁⡴⠀⠀⢀⡇⢀⠟⢰⣯⠶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⣍⠉⠉⢙⣿⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⢀⠟⠀⣴⠃⢀⠀⢸⢀⡞⣰⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⣄⣼⠟⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣾⠀⠀⠀⡆⠀⠀⠀⠀⢀⡞⠀⡴⢁⡄⢸⠀⠃⣸⣳⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⣤⣤⠟⢹⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣸⡇⠀⠀⠀⡇⠀⠀⠀⠀⡞⢀⡞⢡⠞⠀⢸⠀⣀⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠟⠀⠀⣾⣿⡄⠈⢧⠙⢦⣌⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠇⠁⣸⠀⡇⠁⡀⠀⠀⠰⡳⢋⡶⠃⠀⠀⣸⢸⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⠥⠀⠀⠀⠙⣿⡟⡀⠸⡀⠀⠈⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⡼⠁⠀⡇⠀⡇⢀⣴⡿⠞⠁⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢰⣿⣿⠟⢁⣀⣴⡶⠖⢛⣀⡗⣿⢇⠀⢧⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠿⢴⣤⠤⢣⠀⡟⢉⠀⠀⠀⠀⠀⠀⣇⣰⠟⡼⠀⠀⠀⠀⣀⡀⢀⡀⢳⡄⠀⠀⠀⣸⣟⡟⣰⣿⣻⢶⡀⠀⢸⡿⡇⣿⡸⡆⢸⡆⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠙⢷⣼⡀⣇⡟⠀⠀⢠⠀⠀⡀⢿⡇⠀⡷⣶⣶⣾⣿⣿⣿⣿⣿⡄⠯⢦⠀⠀⢫⠈⣰⠟⢸⠷⠾⠃⣠⠟⠁⢳⣇⠇⢱⠀⢳⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⡏⣿⣽⠃⠀⠀⠸⡇⠀⡡⢸⢷⣸⠁⠀⠀⠈⠉⢩⣝⡋⠛⠇⠀⠀⠀⠀⠸⠀⠛⠀⠘⢻⣯⠟⠁⠀⠀⢸⡙⣶⡌⡆⠘⡄⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⡿⣇⣿⡇⠀⣸⢤⠀⢹⡀⡇⣼⣾⡟⠀⣀⣤⡶⠿⣿⣛⠛⠻⡶⠀⠀⠀⠀⠀⢰⡌⠉⠉⠉⠀⠀⠀⠀⠀⢸⣇⢳⣇⢱⡀⢷⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡾⠁⢻⠹⡟⠓⣧⢠⡳⣾⣿⣷⣿⣿⠁⢸⡅⠀⠀⣴⢿⣿⡇⢠⡆⠀⠀⠀⠀⢀⡀⠓⠀⠀⠀⠀⠀⠀⠀⠀⢸⢻⡘⡿⡈⣇⠸⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣼⡃⣇⠸⡄⡇⠀⣿⡀⢹⣿⣿⣿⣿⣧⠀⠸⠿⠶⢤⣉⣻⡾⠗⠋⠀⠀⠀⠀⠀⠀⠙⠦⣼⠃⠀⠀⠀⠀⠀⠀⡼⠀⡇⢹⢧⠸⡈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣰⡿⡇⢻⠀⣧⢸⡀⢿⢳⣌⢻⣎⠉⠻⣿⣃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⡏⠀⠀⠀⠀⠀⠀⠀⡇⣇⢹⡈⡇⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣯⣇⢱⠈⡇⢹⡈⢇⢸⡆⠘⣷⣬⡉⠳⠈⢧⡀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⡀⠀⠀⠀⠀⣼⡇⢹⡈⢇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤ ⡈⣿⡸⡄⢻⠀⡇⢸⡀⢳⠀⢸⠙⢿⣶⣾⣿⣷⡀⠀⠈⣧⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠞⠁⣠⣿⡆⠀⠀⢠⡟⢸⠀⣷⣌⣀⣀⣀⠀⠀⠀⠀⢀⣴⠶⠶⠶⠶⠶⠶⡖⠉⠀⠀ ⠁⢹⣧⣧⠘⡄⢹⠀⡇⠘⡄⠀⣇⢸⢿⣿⣟⢿⣿⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠧⠤⢾⡫⣾⠀⠀⠀⡼⠀⡌⡇⠸⡆⠸⡇⠉⠉⠉⠀⣠⠟⠁⠀⠀⠀⠀⠀⠀⠀⠈⠐⠢ ⡀⠀⠹⣜⡄⢿⠘⡇⢸⡀⢧⠀⢻⠀⣇⠻⢿⣿⣯⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠘⠓⣺⠽⠛⠁⠀⢀⣼⡃⠀⡇⢹⠀⢧⠀⢳⣰⣶⣤⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠇⣄⠀⠙⣧⠈⡆⢳⠘⣇⢸⡆⢈⡇⢻⡀⠀⠉⠉⢛⣿⠿⣿⣿⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠻⡅⢱⠀⢧⠀⡇⢸⣀⣼⣿⠯⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣆⠘⡆⣀⢈⢷⣳⣨⣤⡴⠾⢗⠚⡏⠉⡏⣗⠶⡶⢣⠀⡀⢸⠙⡏⢻⠿⣿⣿⣿⣿⡿⣷⣞⢻⢹⡄⢧⠀⣷⠈⣆⠘⡄⣸⡶⣿⣍⣉⣉⣹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣹⣄⣸⠹⣼⡶⢲⡞⡇⢹⡀⢸⣄⣹⣄⣳⣽⡆⢸⠘⡇⢳⡈⡆⢧⠈⡇⢸⠉⣇⠀⡄⠘⣿⣾⣿⣷⣸⡧⠼⣶⣹⡶⠟⠁⢰⣃⣀⡠⠤⠤⠝⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠉⠉⠛⠛⠚⠧⢼⣶⠛⠋⠉⠀⠀⠀⠉⠙⠻⠷⣽⣤⣷⣗⣿⣷⣿⠾⠶⠿⠖⠓⠒⠛⠛⠋⠉⠀⢢⡀⠘⠿⣄⠀⠀⠀⠻⣤⡤⠤⠖⠒⠚⠳⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⠀⠀⠤⠄⠒⠒⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⣷⠖⢛⣻⣦⡀⠀⠀⠘⢧⡀⠀⠀⠀⠀⠀⢳⣤⠂⠈⠳⣆⠀⠀⠙⠳⢶⣶⣶⠶⠖⠒⠛⠳⣦⣄⠀⠀⠀⠀⣀⣀ ⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣭⡤⠌⢻⡆⠀⠀⠀⢳⠀⠀⠀⠀⠀⣼⣿⣀⣀⣴⠿⠓⠶⠖⠚⠉⠙⢢⡀⠀⠀⠀⠀⠀⠉⠉⠙⠋⠉⠉⠛ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠶⠖⢋⡇⠀⠀⣠⠎⠀⠀⠀⣀⡤⠶⡟⠋⠁⠉⠑⠶⢤⣀⠀⠀⠀⠀⠉⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠉⢸⠁⠀⠜⠁⣠⠴⠞⡋⠉⠛⠋⢳⡀⠀⠀⠀⠀⠀⠀⠙⠓⠦⠤⣄⣀⠀⠀⠀⠀⠀⠀⠀⢤⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣃⣀⡤⠞⠛⢉⠉⠉⢡⠀⠀⠀⠀⠀⠀⠀⠙⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠐⠂⣉⡿⡷⡖⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠰⠥⠛⣮⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡌⡇⠠⣄⣒⣒⣒⣂⣠⢀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣴⣾⣶⣿⣿⣿⠿⣿⣿⣿⣿⣮⣒⢼⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⠿⢛⣒⠀⠈⠻⠿⢿⣿⣿⣦⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⣿⣿⣿⡇⠀⠈⠉⠀⠀⠀⠛⠂⠈⣿⣿⣿⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠚⢿⣿⡇⠀⠀⠀⠂⠀⠀⠂⠀⠐⣿⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢹⣿⣷⠀⠀⠓⠋⠭⠝⠀⠁⣸⣿⣟⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⠀⠀⠀⡀⠀⢀⠄⢼⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⡎⠀⠀⠀⠐⠀⠀⠀⢸⢏⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡀⠐⡩⠚⡜⢄⠀⠀⠀⠀⠀⢀⠃⣰⠤⠑⠢⡀⠀⠀⠀⠀⠀ ⠀⠀⢀⠠⢎⢋⠁⠐⠀⢧⣀⠑⠂⠠⠤⠐⢁⠴⢸⠀⠀⠁⠈⢳⠠⡀⠀⠀ ⠀⢠⠃⠀⠈⠎⠀⢰⠀⠈⣇⠁⠐⠒⠒⠀⠁⢸⡄⠀⣀⡀⣀⡘⠀⠐⡀⠀ ⠀⡄⠀⠀⠀⠈⡇⠂⠀⠀⠸⠀⠀⠀⠀⠀⠀⣸⢻⣀⢴⣄⣸⠕⠀⠀⢰⠀ ⢠⠁⠀⠀⠐⠄⡇⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⠈⠈⠉⠁⢸⡤⡄⠀⠀⡆

⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣴⣶⣶⣶⣶⣶⣤⣤⣀⠠⣄⡀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⡤⠚⠁⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣷⡄⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠸⡄⠀⡀⠙⢣⣿⡿⠿⣿⣟⢿⡝⠻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⠖⠋⠉⠳⣄⠀⠀⣺⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢁⣄⣸⣶⣿⣶⣶⣿⡏⢀⣿⣿⠂⠙⢤⣹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢨⠀⠀⠀⠀⢸⣶⣾⠁⢮⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣸⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣦⣴⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⠳⠤⠤⣴⣿⣿⣟⢠⡿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣷⣿⣿⠋⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠉⢺⡿⢿⣠⣿⣿⣿⣿⣿⣿⣿⣿⠃⢹⣿⣿⣿⡏⠀⢹⣿⣿⠀⢻⣿⣿⡟⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⣄⣸⣿⣿⣿⣿⣿⡏⢿⣿⠀⠀⢿⣿⣿⠁⠀⠈⣿⠇⠀⠘⢿⣿⠁⢹⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠛⣿⡇⠬⢿⢤⣀⣈⣚⣿⠀⠀⠀⣏⣀⣠⠤⢼⠗⠒⠉⢿⢻⣿⣿⣿⣿⣿⣿⣶⠤⣀⡀⢀⣀ ⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⠿⣦⣈⣧⣤⣤⣤⣤⣌⠉⠛⠀⠀⠀⠉⠁⣀⣠⣤⣤⣤⣄⣸⡶⠻⣿⣻⣿⣿⡟⠛⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⢩⣧⡀⡇⠙⢦⡈⢿⣽⠿⠛⠃⢋⢷⣤⢾⠋⠙⠙⠿⣿⠟⣠⠞⠀⣼⣶⡯⡼⣿⢹⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠠⡇⢹⡏⣿⣿⠻⣆⠀⠈⠉⠉⠁⠀⠀⣼⣿⠉⢿⣆⠀⠀⠉⠉⠉⠀⢀⡴⠛⣿⣷⢣⠏⠂⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢳⡈⠳⣿⣿⡄⠀⠉⠳⠗⠛⠒⠒⢈⠁⡼⠀⠀⠈⠁⠒⠒⠿⠟⠟⠁⠀⠀⡟⢫⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠈⢮⣧⠀⠀⠀⠀⠀⠀⠀⠈⠷⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⡿⠀⠀⣠⠴⠒⠒⠂⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠏⢦⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⣴⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣄⠀⠀⠀⠀⠘⢷⣠⣾⠇⠀⠀⠀⠀⢀⣴⢿⠇⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠁⢹⠀⠀⠀⢘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⠳⢦⡀⠀⠀⠀⣀⡴⠊⠁⠀⠀⣿⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠉⠓⠒⠚⠁⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣦⣀⠀⠀⠀⡋⠓⠂⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⡿⣿⠋⡝⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⢭⡿⠷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠋⠹⣽⣦⡈⠙⢳⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣿⣧⣠⠞⢰⠀⢻⠈⠑⠢⢤⣀⡀⠀⠀⠀ ⠀⠀⣀⡠⠔⠒⠉⠀⠉⠀⠀⠀⠉⠛⠻⢿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⡟⠃⠀⠀⠀⠀⢣⠀⠀⠀⠀⠉⠑⠒⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠒⢦⡈⠀⠀⠹⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⢹⠄⠀⠀⢫⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⡠⠐⠒⡈⢩⡿⣿⡷⣜⠃⠒⠠⢀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢘⣤⠊⠁⠀⠀⠘⣹⣿⡳⠷⠽⣽⣇⠀⠀⠀⠈⠂⢄⠀⠀⠀⠀ ⠀⠀⠀⡠⠋⣿⣆⠀⠀⠀⠀⢽⢿⡧⣔⠻⠸⣣⠀⠀⠀⠀⠀⠀⠑⡀⠀⠀ ⠀⢀⠜⢀⠄⣿⡼⡄⠀⠀⠠⠄⢹⣷⣼⡀⠚⢻⣇⡀⠀⠀⠀⠀⠀⠈⢆⠀ ⠀⡌⠀⠎⠀⠸⣷⡷⠑⠆⠀⢼⣿⣿⣧⠈⡹⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠆ ⠸⠀⠀⠀⣀⠀⠘⣷⢤⠀⠀⠹⣿⣿⣦⣷⣷⣿⣫⣿⣿⠷⡂⠀⠀⠀⠀⠈ ⠀⠀⠀⠀⠈⠛⢗⣦⣴⣧⡀⢾⣿⣿⣿⣯⣵⡿⢽⣿⣷⣦⣱⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⠛⢿⣷⡀⢸⣿⣿⢿⣳⣾⢿⣿⣿⣿⣿⣾⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣯⡿⠿⣿⠄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣾⣽⣹⡇⢻⣿⣿⣿⣿⣿⣷⣽⣾⡅⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⣀⣀⠔⢿⣿⠿⡿⡇⣸⣿⣿⣿⣿⣿⡕⠻⢻⠘⡄⠀⠀ ⠀⠀⠘⢏⣉⣩⠴⡶⢶⡧⡿⡛⠲⠤⢼⣿⣿⣿⣿⣿⣿⠇⢀⣾⢀⠕⠀⠀ ⠀⠀⠀⠀⠙⢾⣥⣴⣢⣦⣴⣴⣶⡖⢾⣿⣿⣿⣿⣿⣿⣦⣴⠟⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⠻⠿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⡿⠿⠋⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⡴⠖⠋⣡⢶⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⣠⠞⠁⠀⠛⠙⠲⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃⠀⢀⡤⠶⠋⠁⠀⠀⠀⠈⠉⠀⠀⠀⠉⠳⣄⡴⠞⠋⠉⠲⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡤⠤⠴⠟⠃⣀⣘⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠂⠀⠀⠀⠀⠈⠙⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢰⠟⠉⠀⠀⢀⣠⡴⠚⠉⠀⠀⠀⠀⠀⣠⠆⢀⣀⣠⠤⠚⠁⠀⢀⡴⠒⠦⣀⠀⠀⡠⢄⡀⠀⣌⠳⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⣀⠈⠀⠀⠀⠀⠀⠀⢀⡤⠞⢁⣴⣿⠏⠀⠀⠀⢀⡴⣋⠀⠀⠀⠘⢦⡀⠂⠀⠁⠒⢨⡑⣌⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⡇⠀⠀⠀⡀⢀⡤⠞⠉⣠⠴⠋⠉⠁⠀⠀⢀⡴⣫⣾⠟⢦⡀⠀⠀⠀⠙⡄⠀⠀⠀⠀⠹⣌⠳⡌⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⢀⡴⢺⠷⠋⠀⢰⠞⠁⠀⠀⣀⡤⢤⡴⣪⣾⣿⡇⠘⢷⡱⣄⠀⠀⠀⠸⣄⠀⠀⠀⠀⠈⠁⠹⣆⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⢰⠋⠀⠀⠀⠀⣠⠏⢀⣠⠶⣛⣁⣤⣤⠀⣽⣿⣿⡄⠀⡄⠻⣮⢆⠀⠀⠀⠹⣇⠀⠀⠀⢧⡀⠀⠘⢦⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡆⠈⢀⡴⠀⢀⡼⠁⣰⣿⠗⠺⠉⣥⡀⢈⣻⣿⣿⢿⣿⣷⣷⡄⠘⣿⢧⠀⠀⠀⢿⣧⠀⠀⠀⠳⡀⠀⠀⢻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⡰⡿⠀⢀⡞⠀⣰⠃⡿⠀⠀⠀⣨⡶⣿⡿⠋⠀⠀⠀⠈⠻⣿⣦⢹⣟⣧⠀⠀⢸⣿⢧⡀⠀⠀⠁⠀⠀⠈⣟⡆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡼⢁⠞⢱⠁⢀⡞⠀⢰⠇⢸⠃⠀⣠⣾⣫⣾⣿⠀⠀⠀⠀⠀⠀⠑⢮⣿⣿⣿⡌⢧⠀⢸⣿⣯⣷⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣷⡏⠀⢸⠀⢸⠁⢠⡏⠀⣸⣦⣾⠟⢟⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣿⣿⡈⣧⢸⣿⣿⣿⣇⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠈⠀⡿⢀⡟⠀⣴⣿⣿⣿⣤⢾⣧⣤⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠙⢿⣷⠸⣼⣿⣏⢿⣿⡄⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣤⠖⢛⡳⣿⣠⡾⣿⡿⣿⠁⣄⢀⣠⣬⣉⡙⠛⠿⣿⡷⠄⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⡞⣿⣷⠀⠀⠀⠀⠀⠹⠄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣴⣿⣿⣿⣿⠇⣿⣧⣿⣶⣾⣿⣿⣶⣶⣝⡻⣯⣍⣂⠀⠀⠀⠀⠀⠀⣠⣾⣿⢛⣟⣿⣷⢸⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠟⢹⡟⠉⠀⣿⡿⠀⠻⣿⠋⠙⢿⣿⣿⣿⣶⡿⠃⠀⠀⠀⠀⢠⡾⠛⠟⢁⣀⣀⣻⣿⡆⢻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⣿⠁⠀⢰⣿⠇⣠⠄⠙⠷⣤⣘⣻⢟⣁⡿⠀⠀⠀⠀⠀⢰⡿⠃⣤⣾⣿⣿⣿⣿⣿⣷⡈⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣯⣿⡇⠀⢸⡇⠘⠁⠀⠀⠀⠀⠈⠉⠛⠋⠁⠀⠀⠀⠀⠀⢿⠦⢾⣁⠸⠿⠿⠛⣳⡿⣿⡇⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡇⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⣶⡖⠚⠉⢨⣾⡇⠀⣼⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⡇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣭⣭⣍⣉⣓⣛⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⢸⡇⠆⡀⠀⠀⠀⠐⡀⠀⠀⠀⠘⢿⣶⣤⣤⣶⣦⠀⠀⠀⠀⠀⢸⣯⣿⡏⠉⠉⣹⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⡆⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⢨⣷⠀⢻⠀⠀⠀⣼⣧⣀⣀⣀⣀⣀⠙⠻⠿⠋⠀⣤⡀⠀⠀⠀⢸⣹⣿⣷⢠⣼⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⢸⣿⡀⠀⡄⠀⠀⠀⠘⢻⣟⠛⠛⠿⠿⠾⣿⣶⡶⠚⠙⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⢸⣽⣧⠀⢷⡀⠀⠀⠀⠀⠻⣷⣶⣤⣄⣴⡿⠋⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⢸⣿⣟⢷⣄⠻⣆⠀⠀⠀⠀⠀⠉⠛⠛⠛⠁⠀⠀⠀⠀⣠⡾⠋⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡎⣿⣿⡀⠻⢦⣈⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠋⠀⠀⣿⣿⣿⣿⡇⠸⢿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⢷⣾⣿⠇⠀⠉⠙⠳⣌⡛⢦⡀⠀⠀⠀⠀⠀⣿⣟⡁⠀⠀⠀⠀⣿⣿⣿⣿⠿⢿⡶⠿⠿⠿⣿⣿⣾⣻⣿⣿⡟⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁⣠⠿⣟⣿⠀⠀⠀⠀⠀⠀⠙⠒⠒⠶⠭⠗⠒⠚⣿⣇⠙⢦⡀⠀⠀⣿⣿⢿⣷⡀⠈⠁⠀⠀⠀⠀⠉⠉⠛⢿⣿⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⢀⣴⠋⠀⢻⣾⠆⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⣿⠊⢦⡀⠙⠦⣤⣿⣧⣮⣿⣿⣿⣿⣶⣶⣦⣤⣄⡀⠀⠀⢹⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠁⠀⡞⣿⠀⠀⠸⣿⡄⢀⠀⠀⠀⠈⠳⢄⠀⠀⠀⠀⠀⠀⢿⠀⠀⠙⣦⡀⠀⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡄⠀⠙⢦⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠀⢀⡾⠀⠙⢦⣀⠀⢹⣇⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠹⣶⣯⡉⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠿⣿⣟⠀⡀⠀⠛⣆ ⢀⠀⠀⢀⣀⠀⣠⡞⠁⠀⢀⡞⠀⠀⠀⠀⠈⠙⠓⠙⠷⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣇⠀⠀⠀⠀⢙⣷⣤⣤⣤⣤⣤⣤⣀⣀⣀⠀⠀⠀⢀⠀⠈⠙⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡶⠶⠛⠋⠉⠙⣷⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⠾⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀ ⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⡴⠶⠞⠛⠋⠙⠳⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀ ⢠⣤⠶⠶⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣄⠀⠀⣀⣀⣤⣤⠶⠶⠛⠀ ⢸⡇⢰⣶⣦⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⡶⠶⠛⠛⠙⠟⠛⢉⡉⣿⠀⠀⠀⠀⠀ ⠸⣇⠈⢛⣁⣠⣤⡴⠶⠞⠛⠋⢹⡷⠶⠶⠶⠶⠶⠶⠶⠶⠾⠶⠿⠀⠀⠀⠀⠀ ⠀⠙⠛⢻⡏⠁⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢠⣤⣤⣤⣤⣤⣄⠀⠀⠀⠀⠀ ⣴⠶⠶⠾⠷⠶⠶⠶⠶⠶⠶⠶⠾⠷⠶⠶⠶⠶⠾⠷⠶⠶⠶⠶⠿⠶⠶⠶⣦⠀ ⣿⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣹⣇ ⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⢠⡆⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⣠⣾⠇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣧⠀⣀⣤⣾⣿⡟⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀ ⠀⠀⣀⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀ ⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠂⣈⢶⡄⠀⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠉⠉⠉⠛⠛⠉⣿⠀⠀⠀⠀⠀⢿⣿⡇⠀⠀ ⠸⣿⡿⠟⠋⡟⢛⣿⣿⣿⣿⣧⡐⠒⠒⢀⣾⣿⠀⠀⣠⣀⠀⢸⣿⡿⠀⠀ ⠀⠀⠀⢀⣀⣲⣾⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣧⡀⠀⠙⢷⣿⣿⡇⠀⠀ ⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠀⣹⣿⣿⠀⠀ ⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧

⠀⢀⣸⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠁⠀⠀⠀⠉⠉⠉⠉⠉⠈⠉⠀⠀⠈⢐⠀⠀ ⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣤⣤⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀ ⠀⢬⣿⣿⣿⣿⡿⠘⠋⠛⠋⠋⠛⠙⠋⠙⠉⠋⠉⠙⠑⠿⠫⠻⣄⠀⠀⠘⢦⠀ ⠰⣼⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⡀⢀⡠⣀⠀⣀⡆⢀⠄⠀⠀⠀⢻⠀⠀⠀⡎⠀ ⠀⠹⣿⣿⣿⡏⠀⠀⠀⢀⡝⠆⢧⢹⣇⣠⡏⣿⢣⣿⣦⠀⠀⠀⠹⣇⠀⢀⡏⠀ ⠐⢾⣿⣿⣿⠀⠀⠀⠀⢾⡇⣼⣸⣾⣿⣿⣿⡹⢸⣻⡭⢄⠀⠀⣌⣿⣦⣾⡇⠀ ⠀⠒⣿⣿⡏⠀⠀⠒⣉⠳⠌⠣⣷⣿⣹⣿⡿⣓⡡⢈⡠⠞⠓⠄⠸⣿⣿⡿⠁⠀ ⢄⢰⣧⡹⡇⠀⣴⣯⣿⣷⣤⡀⠈⠉⣸⢹⡈⠁⠀⣠⣴⣿⣷⣦⠀⣸⠟⡝⡄⠀ ⠀⢹⠈⢵⣿⢢⠘⠻⣢⣭⣯⢭⢿⠟⢇⢠⢻⣾⣭⣭⣿⣵⠾⠋⣠⣏⡮⡢⡀⠀ ⠁⠢⣇⠎⠛⣇⠁⠀⠀⠙⠫⠐⢩⠃⢨⡼⠀⠑⠌⠉⠀⠀⠠⠚⡽⠟⣦⡱⠀⠀ ⠀⠀⠀⠙⠪⢼⡧⡀⠀⠀⠀⠀⢇⠀⢺⡃⠀⠀⠀⠀⠀⠀⣠⢊⠖⠋⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠑⠈⠐⠠⢀⠀⠢⡼⢽⢄⣀⡤⢄⠶⡊⠟⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣶⠶⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢄⠀⠠ ⣿⣿⣶⣶⣄⣀⡀⠀⠀⢀⡀⠀⢀⣀⠀⠀⠀⠀⢀⣀⣤⣤⣴⣤⣤⣤⣤⣀⠙⠛

⠀⠀⠀⢠⠀⠐⢴⣄⠀⠀⢀⣤⣴⣶⣶⣦⣤⣀⡀⠀⢢⠄⠈⠏⠀⠄⠀⠀⠀ ⠀⢠⣠⡨⣆⠀⠈⠀⢢⣿⣿⣿⣿⡟⢻⡙⡿⣿⣿⣦⣘⠃⠀⣶⠆⠆⠀⠀⠀ ⠀⠜⣿⣯⠘⡆⠀⢴⡿⣯⡿⣭⣧⣤⢳⣿⡼⣾⣼⣿⣷⢁⠈⣻⠃⠀⠀⠀⠀ ⣤⠤⢻⣿⡇⠀⢀⣿⢹⣻⣷⣿⣿⣷⡿⢿⣷⣿⣿⣿⣿⣷⢧⡅⠈⠁⠀⠀⠀ ⠀⠀⢸⡏⠙⠄⣞⡟⣾⣿⠏⠉⢏⠿⠅⠘⠛⢘⣛⠸⣿⡿⠈⠧⠶⠂⠁⠀⠀ ⠀⠀⢸⣯⠀⢘⡻⣷⣧⡇⠀⠫⠭⠽⠁⠀⠴⡖⢒⡦⣿⡇⢀⡏⠐⠀⠀⠀⠀ ⠀⡇⠀⡿⠀⣜⢫⢿⡿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⢘⡧⠀⠀⠀⠀⠀ ⠀⡇⢀⡿⣱⡏⣾⣾⣷⣵⡀⠀⠀⠀⢀⣀⠀⠀⠀⢰⣿⣧⠈⢰⠀⠀⠀⠀⠀ ⠀⡇⠀⣼⡿⣼⣿⣳⣿⣿⣷⣄⠀⠀⠐⠂⠁⠀⣠⣿⣿⡟⡀⡄⡄⠀⠀⠀⠀ ⠀⢀⣾⣿⣽⣿⢣⣿⡿⣿⣿⠀⠑⠤⣀⣀⡤⣾⣿⣿⣿⣇⠀⢃⡇⠀⠀⠀⠀ ⣮⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣄⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⡇⢸⠐⠀⠀⠀⠀ ⣿⣟⣿⣿⡿⣝⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠁⠢⡀⠀ ⣟⣾⣯⠟⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠩⠀ ⣿⣿⡏⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢃ ⣿⣿⡇⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠐⣲⠒⢠⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡀⢂⢔⠏⡠⠠⠀⡏⡀⠂⢄⠀⠀⠀⠀⠀⠀⠀ ⠀⡌⢦⣇⣿⣲⣯⣄⡋⢃⣇⣸⡁⠃⠀⠀⠀⠀⠀⠀ ⣶⣿⣿⣿⠏⠉⠉⣇⠈⢻⠉⣀⡇⡄⠀⠀⠀⠀⠀⠀ ⠹⣅⠝⠋⠀⠀⠀⠉⢤⡏⠍⠀⠝⠀⠀⠀⠀⠀⠀⠀ ⠀⠸⡶⠂⠀⠀⠀⢀⠀⠀⢀⠈⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠡⠀⡤⠐⠈⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⢀⠔⠐⠤⣀⡦⣤⣀⠀⠀ ⠀⠀⠀⠀⠤⠐⠃⠀⠀⠂⠀⠀⠀⠀⠀⠈⠂⠑⢧⡀ ⠀⠀⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢜⠃

⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣶⣶⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣝⣎⢻⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⣿⣿⣿⣿⣿⣿⣿⡿⠁⠘⢿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⡿⣿⣿⣿⣷⠀⠀⣸⣿⣿⣍⢿⣹⡇⡏⠀⠀⠀⠀⠀⠀⠀ ⠀⣼⣿⣿⣿⡇⠀⠛⠿⠿⠛⢷⡆⠙⢿⠛⠉⢺⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀ ⠀⠸⣿⣿⣿⣇⠀⠀⠀⠀⠤⣸⡃⢠⡀⠀⠀⢠⣿⡎⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢿⣿⣿⣿⠀⠀⠀⠀⠈⠛⠏⠋⠀⢀⠀⢾⣿⣯⠟⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣻⠻⢿⣿⣧⠀⠀⠲⢿⣿⣩⡍⠒⠀⣠⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠀⠀⠈⠉⠙⡦⢅⣀⣀⣀⣀⠤⠊⢛⠁⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡆⠀⠀⢇⠀⣿⠟⢡⠋⠀⠀⠀⠑⢂⣥⢦⢄⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⡀⠀⣼⠀⢺⠀⠁⠀⠀⣁⣤⣶⣿⣶⣿⣿⣾⣅⠢⡀⠀⠀ ⠀⠀⠀⠀⠀⣀⣤⣾⣿⣷⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡜⡄⠀ ⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠘⢄ ⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢻⣇⠀⠈ ⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣠⣿⣿⡄⢠ ⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢲⣄⠈⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣿⡤⢤⣄⣀⡀⠀⠀⠀⠀⠘⢷⣄⠈⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢤⣉⠉⠛⠲⢤⣀⡀⠀⠙⢦⡀⠈⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄⡀⠀⠈⠙⠦⣄⠀⠹⣦⠈⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠉⠉⠉⠙⠒⠒⠶⠶⠶⠤⢤⣄⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣤⠀⠀⠀⠈⠑⢤⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠠⢤⣾⡀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠓⠒⠦⢤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠈⠳⣄⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⢿⠈⠉⠒⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠒⠶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠘⣆⠙⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⢹⡆⠘⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠦⢤⣀⡉⠳⢦⣀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠈⣧⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣄⠀⠀⠀⠀⢻⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣀⣀⠀⠀⠀⠀⠀⠈⠉⠓⠢⣭⣑⠦⣄⡀⠀⢀⣿⠀⠀⠀⠀⠀⣽⠀⠀⠘⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡀⠙⢤⡀⠀⠘⡇⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣳⣄⡉⠓⠢⠖⠢⠤⠤⣄⠀⠀⠈⠓⠊⣙⣷⣾⠃⠀⠀⠀⠀⢀⡟⠀⠀⠀⠘⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡷⣄⠀⠙⢦⡀⢹⣆⠀⠀⠀⠙⠲⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢹⡾⠿⠀⠀⣀⣠⠤⠴⣾⡷⠦⣤⠴⠞⢋⡵⠋⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠹⡆⠀⠀⠀⠀⠀⠀⠀⠀ ⠙⣟⣄⠀⠀⠉⠃⠹⣦⠀⠀⠀⠀⠀⠈⠛⠒⠦⠤⣤⣤⣤⣤⣤⣤⣤⢴⣿⠟⠛⠋⠁⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣯⣀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠙⣮⢦⡀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣧⠎⠁⠀⣰⠁⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠄⠈⠳⢦⡀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠘⢧⣳⡀⠀⠀⠀⠀⠈⠳⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡏⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠘⣦⠀⠀⠀⠀⠀⢀⣠⠞⠛⠲⢤⡀⠀⠀⠹⣆⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⢳⣝⣆⠀⠀⠀⠀⠀⠀⠉⠓⠶⣄⣀⡀⠀⠀⠀⠀⠀⠀⣇⠀⣒⣒⠚⢉⡩⠭⠴⠶⠀⠀⠀⠈⠙⠲⣶⣶⣞⠉⠀⠀⠀⠀⠀⠈⠳⢦⡀⠘⢦⡀⠀⢹⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⣮⡣⣤⡀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠒⠒⠒⠦⠤⡟⠀⠀⠉⢫⠉⠀⠀⠀⢠⡔⠋⠙⠢⠀⠀⠉⠘⡍⠙⢦⣄⠀⠀⠀⠀⠀⠀⠙⠢⣄⠻⡄⠈⣇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠙⠳⢭⣇⡀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠘⣷⡒⠺⢷⣒⣦⣄⣘⣧⣀⣀⣴⣻⠿⡟⠛⠓⠀⣠⠀⣰⠷⣄⡀⠈⠙⢦⣄⠀⠀⠀⠀⠀⠈⢷⡝⣦⢿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠘⢝⢦⡀⢈⡗⢻⡟⠉⢱⠀⠙⢯⠉⠁⠀⠀⣰⠁⢰⡇⠀⠉⢿⡷⣄⠀⠙⣆⠀⠀⠀⠀⠀⠀⠙⢮⣾⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⣄⡀⠀⠀⠀⠀⠀⠀⠙⢾⡄⠀⣇⠀⠀⣷⡦⣀⠙⠦⠀⢰⠃⠀⠸⢣⠀⠀⠀⠙⢦⡳⢄⠘⢦⡀⠀⠀⠀⠀⠀⠈⢿⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠦⣄⣀⠀⠀⠀⠀⢱⡀⠟⣦⣖⣿⣥⣾⣷⣄⡀⠸⠀⠀⠀⣸⠀⡀⠀⠀⠈⠻⡄⠀⠈⠳⣄⡀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⢦⣤⣤⣿⣟⢛⣻⣽⣯⣽⣿⣿⣿⠀⠀⣤⠞⠁⢸⠇⠀⠀⠀⠀⠻⣷⣄⠀⠈⢳⡀⠀⠀⠀⣼⠀⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠉⢹⣿⣿⣶⡿⠿⠛⠋⠁⣠⠞⠁⠀⠀⣼⠀⢰⡀⠀⠀⠀⠸⣌⠳⣄⠈⢳⡀⠀⢀⡏⠀⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠰⣽⡄⠚⠛⠛⠀⢀⡴⠻⠀⠀⠀⢠⠇⠀⠀⢣⠀⠀⠀⠀⣻⣤⣬⣢⡀⠳⣄⣸⠁⢰⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⣏⣀⣀⣂⣀⣤⠟⠁⠀⠀⠀⠀⡼⠀⠀⠀⠈⠷⣠⢴⡋⠁⠀⠀⠈⠙⠲⢾⣿⠀⢸⠇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠈⣻⡁⡏⠀⠀⠀⠀⡀⠀⠀⣼⠃⠀⠀⠀⣠⠞⠁⠀⠙⢦⡀⠀⠀⠀⠀⢠⡇⠀⠸⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠷⠛⠁⢻⠇⠀⠀⠀⣸⠃⠀⣰⠃⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⢱⡄⠀⠀⣀⣼⠇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⣁⣤⣤⠤⠴⣦⣤⣤⠞⠁⠀⣴⣥⡤⠤⠖⠓⠒⠲⠤⠤⣤⣄⣀⠀⢣⡴⠋⠁⢸⠀⠀⠀⠀⠀⠂⠈ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠖⠒⠛⠚⠉⠁⠀⠀⠀⠀⠀⠀⠉⢳⠖⠩⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠟⠃⠀⠀⠀⣸⠀⠀⠀⠀⠀⠄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⡴⠂⠀⠀⠀⠀⠀⠀⠀⠀⡴⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⢀⢰ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠘⢓⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠁⠈ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡷⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⡇⠀⠀⠀⠀⠀⠀⠈ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⡇⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⢳⡀⠀⠀⠀⠀⠀⠘ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢷⠀⠀⢳⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣀⣤⠾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⡔⣫⠎⢦⡀⠈⣆⠀⠐⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡷⠒⠋⠁⠀⠀⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠽⠽⢛⠑⡋⠀⠀⠀⠙⣦⡈⡆⠀⠀⠀⠁

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⡄⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⠀⠀⠀⠀⠀⠀⠀ ⡒⠒⠒⠒⠒⠒⠒⡏⠀⠀⣀⠀⡀⠀⠀⠀⠀⠀⠀⡀⢰⠀⠈⡗⠒⠒⠒⠒⠒⠒ ⣷⣄⡀⠀⠀⠀⠀⣇⠀⢸⡏⣰⣷⢾⡀⠀⣧⠀⣶⣶⣼⠀⣾⡇⠀⠀⠀⠀⠀⠀ ⣿⣿⠟⠛⠒⠒⠀⡿⠀⢸⣿⢼⣿⣘⣷⣄⢿⣷⣾⣿⣿⠀⣿⠃⠀⠀⠀⠀⠀⠀ ⠉⠁⠀⠀⠀⠀⠀⣷⠀⢸⡧⣼⣷⣦⠈⠙⢻⢿⣿⢯⢻⠀⣿⠀⠀⠀⠀⠀⠀⢀ ⠀⠀⠀⠀⠀⠀⠀⢸⠀⣼⠑⠚⠛⠀⠀⠀⠀⠚⠛⠂⢸⠀⣿⠀⠀⠀⠀⠀⠀⢻ ⣀⡀⠀⠀⠀⠀⠀⢸⢸⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⡟⠀⠀⠀⠀⠀⠀⢩ ⠙⢿⣿⣷⣾⣿⣿⣿⢸⡆⣧⡀⠀⠀⠠⠤⠀⠀⢀⣴⡇⡀⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⡀⡇⣿⣿⠢⢄⠀⠀⢀⠴⢻⡋⡇⡟⡀⠠⠤⠤⣀⢀⠤⠐ ⠀⠸⣿⣿⣿⣿⣿⣿⣇⢷⣟⠛⡄⠀⠉⠉⠁⠀⡌⡻⣇⣿⣾⡏⢠⣴⠈⢟⣦⣤ ⡀⡇⣸⣿⣿⣿⣿⣿⢻⣸⡇⠑⢇⣀⠀⢀⠠⠐⠉⢁⣿⡿⠛⢧⣼⣷⣶⣾⣿⣿ ⡽⠔⠚⣻⣿⣿⠿⠃⠸⢃⣧⠀⠀⣜⣹⣉⣣⠀⠀⢸⣿⠇⠀⠈⠻⣿⡻⠿⣿⣿ ⣰⣴⣿⠿⠋⠁⠀⠀⠀⢿⡼⣄⠼⣿⣿⣿⣿⣷⣀⣿⣿⠀⠀⠀⠀⠈⢻⣦⡀⠈ ⢔⣿⣷⣷⣶⡂⢤⡀⢀⣨⣿⣿⡢⢿⣿⣿⡿⢞⣽⣿⢼⢷⣄⠠⢖⣿⣿⣿⣵⣄ ⠀⠉⢹⣿⠛⣿⣿⡻⠝⠉⡗⠌⠺⣸⣿⣿⡏⠘⠋⠀⢸⢠⣶⣿⣿⣿⣿⠟⠛⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⡿⠋⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣴⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣴⣿⣿⣿⣿⣿⡿⠋⠀⠀⢀⣤⣤⣤⣤⣤⣤⣤⠄ ⠀⠙⢿⣿⣿⡿⠋⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⠟⠁⠀ ⠀⠀⠀⠙⠋⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢴⣿⣿⣿⣿⣿⣿⣟⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣷⣄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠿⠿⠿⠿⠷⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⠟⠋⠉⠀⣠⣦⠖⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠸⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠊⠀⠴⠃ ⠀⠀⠀⠀⠀⠀⢀⣠⣶⣾⣿⠟⠋⠁⠀⠀⣰⢏⡵⠃⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡿⠃⠀⠀ ⠀⠀⠀⢀⣠⣶⣿⡿⠛⠉⠀⠀⠀⠀⠀⡾⢣⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡟⠁⠀⠀⢀⣠ ⣀⣴⣾⡿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⣼⢡⡟⠀⠀⠀⠀⠀⠀⠀⣠⣴⡖⠢⡀⣧⠀⠀⠀⠀⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⠛⠀⠀⠀⠘⠛⣻ ⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⡼⠀⠀⠀⠀⠀⠀⣠⣾⣿⠿⠃⠀⡇⢸⠀⠀⠀⠀⣿⣿⣷⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢸⣿⡁⠀⠀⠀⠀⠀⠀⢷ ⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢀⡇⠀⠀⠀⠀⣠⣾⣿⠟⠁⠀⣼⠀⡇⣿⠀⠀⠀⠀⣿⣟⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣦⡀⠀⠙⣿⣦⣤⡤⠶⠶⠿⠛ ⣿⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠈⡇⠀⠀⠀⣴⣿⣿⡋⠀⠀⠀⣿⠀⣿⠃⠀⠀⠀⢠⣿⣿⡇⠙⢿⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣷⡀⠈⣿⣿⣆⠀⠀⠀⠀⠀ ⠛⢿⣿⣭⣭⣿⠄⠀⠀⠀⠀⠀⠀⣿⠀⡇⠀⢀⡾⣫⣿⣿⡇⠀⠀⠀⣿⢠⡇⠀⠀⠀⠀⣸⡟⣾⠁⠀⠀⠈⠻⣿⣿⣿⣿⣶⣤⣀⣀⠀⠀⠀⠀⢿⣿⡇⠀⠙⢿⣿⣷⣶⣶⣶⣿ ⡿⠿⠿⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⡇⣠⠏⣴⠏⢹⣿⡇⠀⠀⢰⣿⣼⠇⠀⠀⠀⢠⡿⣵⡏⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣸⣿⡇⠀⠀⢠⣌⠉⠉⣹⣿⣿ ⡀⠀⣠⣶⠖⠀⠀⣤⠀⠀⠀⠀⠀⢸⡀⠹⣏⣶⠃⠀⢸⣿⡇⠀⠀⢸⣿⣿⠀⠀⠀⣡⡿⢡⡟⠀⠀⠀⠀⠀⠀⢀⣠⠤⠋⣙⣛⡿⠿⢿⣿⣿⡿⣿⣿⡇⠀⢠⣿⣿⢀⣾⣿⣿⠃ ⢻⣿⣿⠁⠀⠀⣸⣿⠀⠀⠀⠀⠀⠘⢧⣠⠾⠁⠀⠀⣾⣿⡇⠀⠀⢸⣿⣿⠀⢀⣴⡿⣥⡏⠀⠀⠀⠀⠀⢀⡴⠋⢠⡴⠋⠉⠀⠀⠀⠀⠈⠉⣱⣿⣿⠁⢠⣿⣿⣣⣾⣿⡿⠃⠀ ⣾⡿⠁⠀⠀⢠⣿⡇⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⢸⣿⣿⣤⣾⢟⡵⠋⠀⠀⠀⠀⢀⣴⠏⢀⡴⣫⠴⠞⠋⠉⠉⠳⣆⠀⣰⢏⣾⠇⣠⣿⣿⣿⣿⣿⡿⠁⠀⣠ ⡿⠁⠀⠀⠀⣾⣿⡇⠀⣠⠞⡥⣿⢹⠀⠀⠀⠀⠀⣾⣿⣿⠃⠀⠀⢸⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⣼⠏⣰⠏⣴⢃⣀⣀⠀⠀⣀⡴⠛⣰⣿⣿⣏⣼⣿⣏⣼⣿⣿⠟⠁⠀⣰⣿ ⠃⠀⠀⠀⠀⣿⢿⡇⣰⢏⡞⠁⡇⢸⠀⠀⠀⠀⣸⣿⣿⡟⠀⠀⠀⠈⠻⣿⠋⠁⠀⠀⠀⠀⠀⠀⢸⣿⣸⠏⠀⣿⠀⠀⣘⡴⠛⠁⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⣠⣾⣿⠃ ⠀⠀⠀⠀⢠⣿⣸⣧⡏⣸⠃⠀⡇⢸⠀⠀⢀⣼⣿⣿⠟⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⠀⠀⠙⠷⠞⠉⠀⠀⠀⣼⣿⣿⡟⠀⣭⣿⣿⣿⠟⠁⠀⢰⣿⣿⡿⠀ ⠀⠀⠀⠀⢸⡟⣿⡟⢠⡟⠀⠀⡇⢸⠀⣠⣾⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠈⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⡿⣷⣿⣿⣿⠟⠁⠀⢀⣤⣿⣿⣿⢃⣴ ⠀⠀⠀⠀⢸⣿⢹⡇⣼⠃⠀⠀⣿⣾⣴⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣯⣥⣴⣶⣾⣿⣿⣿⠟⢡⣾⣿ ⠀⠀⠀⢩⣿⣿⣘⣿⠇⠀⢺⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⡿⠿⠛⠛⠉⣿⣿⣀⣿⣿⡿ ⠀⠀⠀⣼⣿⡏⠛⠋⠀⠀⣼⣿⠟⣹⣿⣇⣀⣀⣠⣤⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡟⠁ ⠀⣠⣾⣿⡿⠀⠀⠀⠀⢰⣿⡏⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⣶ ⣿⣿⣿⠟⠁⠀⠀⠀⢠⣿⡟⠀⣾⣿⣿⠟⠛⠋⠉⠉⠉⠉⠉⠉⠛⠛⣛⠷⣦⠄⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠻⢿⣿ ⡿⠋⠁⠀⠀⠀⠀⣠⣿⣿⠁⢀⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⣤⠇⠉⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣧⢠⣾⣿ ⣿⣷⣦⣤⣤⣴⣾⣿⡿⠁⠀⣼⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⣤⣶⡅⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⣀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣾⣿⠻ ⠛⠿⠿⠿⢿⣿⣿⡿⠁⠀⣼⣿⣿⠈⢿⣿⣿⣧⠀⠀⣀⣶⣿⢿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠏⠻⣿⣿⣷ ⠀⠀⠀⣠⣿⣿⡟⠀⣠⣾⣿⡟⠁⢀⣨⣿⣿⣿⣆⣴⣿⡿⠃⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⠋⠀⠀⢹⣿⣿ ⠀⢀⣼⣿⣿⠏⠀⣨⣿⡟⠿⣽⣟⣯⠞⠹⣿⣿⣿⣿⠏⠀⠀⣼⣿⠇⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⡏⠀⠀⣠⡟⣿⣿ ⣰⣿⣿⣿⠃⢀⣾⣿⡟⠁⠀⠀⠀⠀⣀⣴⣿⣿⡿⠁⠀⣠⣾⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣹⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡿⣣⡟⠀⣠⡾⢃⡿⠛⣿ ⣿⣿⠟⠁⢀⣾⣿⡿⠀⠀⠀⢀⣴⣾⣿⣿⡿⠋⠀⢀⣴⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣟⣿⣿⣿⣯⣀⣼⠋⣵⠟⠁⠀⣿ ⡿⠉⠀⠀⣾⣿⣿⡇⠀⢀⣴⣿⣿⡿⠟⠉⠀⣠⣶⣿⣿⣿⣯⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⣀⠀⠀⠀⠀⢀⣾⣿⣿⣿⡿⢋⣼⡿⣡⡾⠃⠀⠀⠀⣿ ⠀⠀⠀⠀⠙⠹⣿⣷⣾⣿⣿⠟⠉⢀⣤⣶⣿⣿⡿⠋⠙⢿⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢤⣀⢀⣽⣿⣿⣿⠟⣡⣾⣻⡿⠋⠀⠀⠀⠀⠀⣿ ⠀⠀⠀⣀⣤⣤⣝⠛⠋⠉⠀⢀⣴⣿⡿⠟⣿⣿⠃⠀⠀⠀⠙⢿⣿⣿⣿⣿⣦⣄⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣴⣾⣿⣿⣿⣟⣱⣾⣿⣿⠟⠁⠀⠀⠀⠀⠀⢀⣿ ⠀⢠⣾⣿⡿⢋⣿⣇⠀⠀⣴⣿⠟⠁⠀⣼⣿⡇⠀⠀⠀⠀⢀⣼⡟⠉⠛⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣟⠁⠀⠀⠀⠀⠀⠀⢀⣼⣿ ⣦⣿⣿⣿⣿⣿⣿⣿⣠⣾⡟⠃⠀⠀⢠⣿⡿⠀⢈⡏⠘⢒⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡛⠛⠛⠛⠛⠋⠉⠙⠛⡟⢻⠉⠉⠉⢀⣼⣿⣿⠿⠟⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿

⠀⡰⠁⢀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡄⠀⠀⠀⠀⢣⠠⣄⣌⠑⣄⢷⡈⡁ ⢈⣠⣒⣁⡴⠀⠀⡜⠀⠀⠦⡀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⢳⡈⢻⣿⣮⣿⣿⣶ ⠝⠸⠀⡠⠁⠀⡼⠀⠀⣸⠀⠘⡒⠤⣁⠂⢦⣘⡀⠀⠀⠀⠆⢷⣆⠹⣿⣿⣿⣿ ⢣⠃⡐⠁⣠⣾⠃⡔⣰⠃⠀⠐⠰⠀⠀⠁⠢⣌⢣⠀⠀⠀⣸⢸⣿⣷⣿⣿⣿⣿ ⣾⣼⠴⠚⢩⣂⢼⣶⢋⠀⠀⠀⢃⡆⢀⡴⠊⣁⣹⣤⠀⠀⣿⣾⣿⡿⠛⡻⢿⣿ ⣿⠘⡀⠐⡏⠀⢠⠹⠈⡀⠀⢠⠸⡷⣫⣾⡟⢋⣰⡿⢸⠀⣿⣿⠻⣷⠩⠘⡈⣿ ⣿⢀⠀⠀⣧⠀⡌⠀⠡⠇⠀⠘⣾⠁⠏⠓⠊⠉⠀⡇⢾⣼⣿⣿⠀⢹⡝⡠⣷⣿ ⢿⣿⡆⠀⢇⡦⣗⣶⡶⣿⢀⠇⠸⠀⠀⠀⠀⠀⠀⠏⢸⣿⡏⡏⠀⠀⡋⣰⣿⡇ ⡆⠹⣿⡀⢼⣾⣍⣳⠓⠁⢾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠁⠀⢼⡽⣿⣿⣿ ⠉⠀⠹⣷⡀⢻⣍⠁⠀⠀⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢡⢬⣏⠛ ⠀⠀⢰⡟⢿⢪⣻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠁⠉⠑⢴⠁⠀ ⠀⠠⠋⠀⠘⣏⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⡇⠀⠀⠀⠰⠱⣦ ⠀⠀⠀⠀⠀⠘⠐⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠃⠀⠃⠀⢀⠠⠒⠃⢻ ⡀⠀⠀⢀⠀⠀⠇⠹⣹⣿⣿⠈⠒⠄⡀⠀⠀⣠⠔⠁⠀⠀⠀⡠⠐⠁⠀⠀⠘⠀ ⠇⠞⠳⠛⠛⠂⠈⠂⢩⣿⣿⡆⠀⠀⠈⠁⢁⠨⣷⠄⢀⠄⠊⠀⠀⠀⠀⠀⠀⠂

⣿⣿⣿⣿⣿⣿⡏⢛⣿⣿⡟⠉⠈⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⠟⢛⡳⠤⠴⡺⠿⡛⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⡿⠋⢠⠁⠀⢀⠠⢁⡠⠃⡀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣶⡟⡃⢖⠋⠁⠉⣀⣀⡠⠈⠑⠂⢇⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣷⣶⡎⠀⠁⠀⣀⠠⠐⠒⡢⠀⠘⡄⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⡙⠒⠩⠿⠘⢄⠀⢐⣁⠜⠀⢠⠃⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⢄⠀⠀⠀⠀⠉⠁⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⠀⠑⢄⠀⠀⠀⢶⠒⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⡿ ⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠈⠐⡒⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢢⣽⡟⠄ ⣿⣿⣿⣿⣿⠋⠰⡀⠀⠤⠀⠀⠀⠀⠸⢀⠔⠀⠀⠀⠀⣀⣠⣤⣴⣶⣶⣿⠃⠀ ⣿⣿⣿⣿⣧⠇⡄⠈⣢⣀⣀⠀⣀⣀⢴⡎⣀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀ ⣿⣿⣿⣿⣿⣿⣠⣾⣿⣿⣿⣿⣿⡆⣀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄