Year of the Rabbit ASCII Art

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠉⡆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⢄⡀⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⢸⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡈⠁⠊⢕⠢⡄⠀⠀⠀⠀⡇⠃⠀⠀⣇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠀⠀⠑⡌⢦⠀⠀⠀⡇⡀⠀⠀⢻⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡷⡀⠀⠀⠰⠈⢇⠀⠀⢃⢣⠀⠀⢹⠆⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⠼⢵⡀⠀⠀⠃⠈⡀⠀⢸⠀⢆⢀⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⠉⠁⠀⠀⠀⠳⣄⠀⠸⠀⠱⠠⣘⠀⠈⣆⠏⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠇⠀⠂⠊⠀⠀⢹⡀⠀⠀⠀ ⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀ ⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⡴⠀⢠⣲⠉⠙⠀⠀⠑⠤⣀⠀⠀⠀⠀⠀⠸⠀ ⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⢠⡇⢀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠿⠵⡄⠀⠀⠀⠇ ⡠⡤⠞⢹⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐ ⢧⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠘⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⣆⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠀⠀⣀⣠⠖⠁ ⠀⠈⠢⠤⠬⠦⡀⣀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⢎⠳⢤⣀⣀⡴⢓⡄⠄⠀⠀⠀⠀⠀⡐⠀⠀⠀⢀⠞⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠈⢎⠐⠠⠤⠴⣊⣀⣀⡀⡔⠛⠐⠆⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠒⠊⠀⠈⢦⣀⣀⣤⡸⠀⠀⠀⠀⠒⠒⠁⠀⠀
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pls note the ai inflicts emotional damage (ᵕ—ᴗ—)
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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣧⠀⠀⠀⠀⠀ ⠀⢠⣾⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠉⢿⡟⠀⠀⠀⠀⠀ ⢠⣿⢋⠀⠈⢻⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠏⡀⠀⣾⠇⠀⠀⠀⠀⠀ ⣸⣿⠀⡄⠀⠀⠙⣿⣄⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⣡⠎⠀⣼⡏⠀⠀⠀⠀⠀⠀ ⢻⣿⠀⢷⡀⠀⠀⠘⢿⣧⠀⠀⠀⠀⠀⢠⣾⢋⡾⠁⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀ ⢸⣿⠀⠈⣧⠀⠀⠀⠘⣿⡇⠀⠀⠀⢰⡿⢁⡾⠁⠀⠀⣿⣿⠃⠀⠀⠀⠀⠀⠀ ⢸⣿⡆⠀⢹⡄⠀⠀⠀⢻⣿⠀⠀⣰⡟⠁⣼⠁⠀⠀⣰⣿⡿⠀⠀⠀⠀⠀⠀⠀ ⠈⢿⣷⡀⢸⡇⠀⠀⠀⢸⡇⣠⣴⠏⢀⡼⠃⠀⠀⣴⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠻⣷⡀⢷⠀⠀⠀⢸⡿⠋⣡⠐⠉⠀⡀⢀⣼⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠘⢷⡌⢇⠀⠀⠘⠳⠄⠀⠉⠓⠾⣧⣸⡅⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣧⣀⣔⡡⠂⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣤⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⣶⣿⣦⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀ ⡸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠃⠀⠀⠀⠀⠀⠀⠀⠘⢷⡀⠀⠀⠀⠀⠀⠀ ⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢻⣄⡀⠔⠊⠁⠀ ⠀⠛⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡎⢀⣀⣀⠀⠀⠀⡀⠀⠀⣿⠤⠀⣀⠀⠀ ⠀⠀⠈⣷⡀⠀⠀⠀⠀⠀⠀⡠⠔⣿⡏⢀⡀⠤⠐⡂⠄⠉⢳⣼⡟⠁⠂⢄⠈⠐ ⠀⠀⣠⣿⠇⠀⠀⠀⠀⠀⠈⠀⢀⠍⢻⠧⣀⣀⢎⣀⣠⣴⠿⠋⠀⠀⠀⠀⠁⠀ ⢀⡾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠐⠁⠐⠒⠒⠛⡟⠛⠛⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⣋⣍⢹⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢞⡵⢛⡹⡣⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣴⢣⢏⣾⣁⡩⠞⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡠⠊⠙⡏⣼⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⡇⠷⠟⠀⢠⡇⣱⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣾⣷⣞⣁⣴⠿⠁⢉⣤⣬⡙⣷⣶⢤⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠉⠉⠉⠐⠴⣇⠘⠛⡸⠃⣿⡟⣴⣮⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⠶⠆⢟⡫⠔⢚⡁⠚⠿⢿⣷⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢼⣠⠞⣡⡶⠿⠿⠿⣿⣶⣄⠙⣿⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⢋⣾⣿⠿⠛⠒⠄⢄⠙⢿⣇⠸⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⠁⢰⣿⠋⠑⠈⣧⠈⡟⠀⡇⠀⠀ ⠀⠀⠀⠀⠀⢀⣀⣄⡉⢳⠀⢹⣿⣦⣤⣾⡿⠀⠁⣜⣡⡶⢄ ⠀⠀⠀⠀⢠⣿⣇⠽⠋⣰⣧⣀⠈⠉⠉⠉⢀⣠⡾⢸⣙⣋⡼ ⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠒⠒⠛⠉⠁⠀⠀⠉⠉⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠛⢹⣿⣇⣠⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⣠⣶⢿⡛⠻⣿⣍⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢟⣠⣾⠟⢱⢸⣦⣤⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⢋⣴⡿⡁⠀⠘⣦⡭⢉⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣞⣵⣿⣿⠟⢀⡤⠚⢉⣴⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⢟⣽⢻⣡⡦⢀⣤⠾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠟⠛⠛⣲⣭⠛⠋⢩⣼⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⠾⢻⡇⠀⠉⠉⢻⡿⢃⠀⢰⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡴⠋⢶⣿⣲⣯⢳⣄⠘⢡⣏⠀⢸⡝⣷⣄⠀⠀⠀⠀⠀⢀⣠⣤⣶⠾⠟⠛⠛⢉⣉⣉⣛⠛⠻⢿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣴⣫⠞⠁⠈⠛⠛⠩⠞⠋⢀⠘⢿⣦⠈⢷⡳⣌⡙⠒⠒⢒⣿⣭⡿⢚⣭⣵⣾⠿⢿⣿⣿⣿⣿⣿⣿⣷⣦⣭⣻⢿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡞⢉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣹⠖⡿⢠⠘⣷⡙⣿⣣⠶⣿⠟⣡⡾⠟⣉⣥⣴⣦⡄⢹⣿⡟⢉⣴⣷⡶⣶⣦⣍⡓⢯⡻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⣷⣏⠀⠖⠀⠀⠀⠀⠀⠀⣻⡏⣠⠞⢁⡞⢀⣿⣇⢰⠃⡸⢡⠞⣩⣶⣿⠿⠿⠛⣋⣤⣾⠟⠀⠈⠻⣧⣘⠿⣶⣭⡻⢷⣅⠈⠻⣷⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠙⠦⣤⣤⣄⠀⠒⠒⣊⣩⣼⣓⣶⠟⣡⠞⢹⡿⢰⠃⢱⣣⠞⠉⣀⣀⡬⠉⢉⣉⠉⢁⣀⡤⠤⢖⣒⣋⣩⠥⠌⠙⠲⠝⣦⢠⡘⢿⣆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠻⠿⣿⣯⡁⢈⣴⠏⣿⠇⣾⡄⠀⠀⣴⡿⠋⣡⣴⠞⠉⣠⠶⢋⣥⣶⠟⠋⣩⣤⣴⡶⠖⠒⠂⠀⠘⡆⢳⡈⣿⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⡈⢸⢠⡿⠀⢻⣿⡆⢸⡟⠀⣼⠟⠁⢠⡾⢋⣴⡿⠋⡠⡶⠟⣛⣛⠡⠴⣾⣿⠟⠛⢦⠘⢸⣷⢸⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠙⢸⡇⢰⠶⣭⣉⣀⣷⢠⡟⠀⢠⡿⢡⣿⡿⠁⢰⠾⠛⠻⢿⣿⣿⣿⣷⣶⣤⣀⠀⣠⣾⡟⢸⡟⠒⢶⣶⣤⠄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⡄⣷⡘⠲⢤⣉⠻⠿⢸⣇⠀⢾⡇⢸⣿⣷⠀⠈⢾⣿⣷⠀⣿⣿⣿⠟⠉⢀⣤⠾⢛⡅⠀⠚⠀⠀⣠⡾⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⢮⣍⡒⠀⠙⢿⣶⣾⡿⢠⠘⣿⣄⠻⣿⣷⣦⣬⣭⣥⣾⣿⠟⠁⠀⠈⢁⣠⣴⠟⠀⠀⠀⢚⣩⠟⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⣡⣾⣤⣈⣀⡀⠒⣾⣿⣶⣿⣀⣈⣻⣷⣤⣉⡙⠛⠛⠛⠋⠁⠠⠤⠶⠚⠻⣯⡛⠻⠷⠶⠛⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢒⣫⠿⠿⠒⠋⡵⢶⣦⣠⡴⠚⠉⠀⠀⢀⡴⢋⡴⠋⣡⠀⠉⠉⠉⠉⢉⣅⠀⠀⢀⣀⣀⣀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⣏⡴⡿⠋⢀⣠⠆⠀⢇⣠⡿⠁⠀⠀⠀⠀⠀⠛⢷⣿⣥⡞⠁⠀⣠⠞⠀⠀⣠⡿⠚⠋⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠷⠴⠿⠧⠴⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠛⠓⠖⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⣾⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠏⠁⠹⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⣿⣿⠟⠉⠉⠛⢿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⡟⠁⠀⠀⢀⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⠏⢰⠀⠀⠀⠀⠻⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⠏⢀⡔⠀⠀⣼⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⠀⢸⡆⠀⠀⠀⠀⠘⢿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⠟⣡⣾⠋⠀⠀⣼⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⡀⠘⣷⡀⠀⠀⠀⠀⠈⢻⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡿⢡⣾⠟⠁⠀⠀⣼⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⡇⠀⢻⣷⠀⠀⠀⠀⠀⠀⠹⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠟⢠⣿⠏⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⡇⠀⠀⢿⣧⠀⠀⠀⠀⠀⠀⢹⣿⣿⡆⠀⠀⠀⠀⠀⠀⢠⣾⣿⠃⢠⣿⠃⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠸⣿⣿⡇⠀⠀⠈⣿⡄⠀⠀⠀⠀⠀⠀⣿⣿⣧⠀⠀⠀⠀⠀⢠⣿⡿⠃⢀⣿⠇⠀⠀⠀⠀⢀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⣿⠀⠀⠀⢹⣇⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⢠⣿⡟⠁⢀⣾⠏⠀⠀⠀⠀⠀⣼⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢻⣿⣿⡆⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⢸⣿⡿⠀⠀⢀⣠⣿⠏⠀⢀⣾⡏⠀⠀⠀⠀⠀⣼⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⢿⣿⣿⣄⠀⠈⣿⡄⠀⠀⠀⠀⠀⢸⣿⡇⣠⣶⣿⠟⠁⠀⣰⡿⠋⠀⠀⠀⠀⢀⣾⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠻⣿⣿⣆⠀⢻⣧⠀⠀⠀⠀⠀⢸⣿⣿⡿⠛⠁⣀⠴⠚⠉⠀⠀⠀⠀⠀⣰⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⢿⣿⣦⠈⢿⡄⠀⠀⠀⠀⠸⣿⣇⠀⠀⠛⠤⣤⣀⣀⠀⣼⡀⠀⣸⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⣿⣧⠈⠻⡀⠀⠀⠀⠀⠙⠻⠷⢄⠀⠀⠀⠉⠛⠿⣿⣧⡀⣿⡇⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣇⠀⠀⢀⣠⠏⢀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⣾⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⣦⣾⣡⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣴⣾⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣴⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠜⠋⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⡄⠀⠀⠀⠀⠀⠀⢀⡠⠄⠀ ⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣄⠀⢀⡤⠖⠋⠁⠀⠀⠀ ⠀⢰⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠊⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠘⣿⡞⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠘⠁⠹⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⢁⣀⣀⣀⣀⣀⣀⠀⠀⠀⢸⣦⡀⠀⠀⠀⣿⣟⠒⠲⠦⢤⣀⡀⠀⠀ ⠀⠀⠀⠀⠹⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⣿⣿⠉⠀⠀⠀⣀⣀⠬⠤⠄⣀⠌⠙⠛⣿⣆⣼⣿⠋⠓⠲⢄⡀⠀⠉⠑⠲ ⠀⠀⠀⠀⠀⣹⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠋⠀⣸⠿⣿⣦⠴⠒⠉⠁⠀⠀⡠⠊⠁⠀⠀⢀⣿⣿⡿⠃⠀⠀⠀⠀⠈⠓⢄⠀⠀ ⠀⠀⠀⢀⣴⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣡⠔⠋⡿⠷⣦⣀⡀⢠⠞⢁⣀⣀⣤⣶⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⣀⣀⡤⠤⠴⠶⣿⠿⠿⠿⠿⢿⣿⣯⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣠⠾⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠈⠻⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠹⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⢉⣴⠿⠿⣿⣻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢋⣴⠟⢁⢿⣤⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⣡⣿⡇⠀⡨⠖⣠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⢿⣣⡀⣉⡴⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⡴⠖⣛⣛⣺⠝⠉⣩⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⢞⣹⣃⣤⡀⠹⢋⠄⢸⣿⡀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⠴⠶⢶⣦⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣞⠗⠀⠻⠿⢃⠿⠀⢻⣦⠘⡞⣝⠲⠤⠤⣤⣶⡿⢟⣣⣤⣶⣶⣶⣶⣶⣦⣭⣛⢷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⢰⢋⠁⠀⠀⠀⠀⠀⠀⣀⡵⣺⢠⢸⣎⢿⡲⢾⠟⣡⠾⣋⣭⣤⡄⢹⣿⠟⣽⣷⢶⣮⣍⡻⢟⢷⣄⠀⠀⠀⠀⠀⠀ ⠘⢿⡀⠁⠀⠀⢀⣀⡸⢣⣖⣡⠎⣸⣿⠰⡁⣏⢞⡵⠟⠛⣛⣩⡴⠿⠃⠀⠘⠳⡼⣻⠶⣝⣧⡀⠙⣷⡀⠀⠀⠀⠀ ⠀⠀⠉⠛⠛⠦⠤⠴⣾⣿⡟⠋⢚⢇⡿⢸⡀⠋⢁⡴⠖⣊⡤⠖⣂⠴⣚⣩⠵⠛⣓⣉⡥⠄⠀⠙⡐⡌⣷⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⡄⢹⢸⠇⠸⣷⡀⣿⠁⣾⠋⣠⡞⣡⡾⠋⣴⣾⣿⣟⣥⣶⡿⠛⠦⠃⣿⠸⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣅⢸⡀⡗⠾⣤⣼⢰⡇⢠⡟⢸⣿⠁⠸⣻⣙⠻⣿⣿⣿⠷⠦⢀⣴⠟⢠⠏⠙⢷⡶ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣮⡳⠌⠙⢦⣍⣼⡇⡸⣧⡸⣿⣦⣀⣻⣟⣠⣿⠟⠁⠀⠚⣉⡴⠀⠀⠠⣴⠟⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⣡⣯⣁⣀⠀⣭⣿⣵⣇⣙⣷⣬⣙⡛⠛⠛⠛⠁⠠⠤⠶⢿⡟⠶⠶⠶⠚⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡤⣚⡽⠛⠒⠉⠖⢶⡤⠒⠉⠀⠀⣴⣋⡔⣩⠄⠈⣉⠉⠉⣅⣀⣠⣤⡤⠴⠇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⠿⣿⣀⣴⣁⡤⠴⠛⠀⠀⠀⠀⠀⠈⠛⠿⣧⡤⢼⣅⣠⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠒⠊⠉⠉⠉⠉⠉⠉⠛⠒⠒⠦⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠶⠒⠛⠉⠉⠛⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠞⠋⠉⠀⠀⠀⠀⠀⠀⠀⣠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠋⠁⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠛⠁⠀⠀⠀⠀⠀⣀⣀⡤⠤⠴⠒⠛⠓⠒⠚⠋⣉⣉⣭⠭⠭⣍⡙⣦⠀⠀⠀ ⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠟⠁⠀⠀⢀⣀⡤⠖⠚⠉⠉⠀⠀⠀⠀⠀⠀⣠⠤⠖⠋⠉⠀⠀⠀⠀⠀⣿⡼⠀⠀⠀ ⠀⠀⠀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠋⠀⠀⢀⡤⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠉⠀⠀⠀⠀⠀⠀⣀⣠⠴⠚⠋⢠⡄⠀⠀ ⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢋⡄⠀⠠⠚⠁⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠋⠁⠀⠀⠀⣠⠴⢚⡥⠞⠋⠁⠀⠀⠀⠀⠀⠹⡀⠀ ⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⣀⣴⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠴⠾⠿⠤⠤⠤⠤⠤⠖⢚⣡⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀ ⢀⡏⠀⠀⠀⠀⠀⣠⡴⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠿⠒⠛⠛⠓⠲⣶⡶⠶⠶⠶⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇ ⢸⠁⠀⠀⣠⡴⠛⠁⠀⣠⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠆⠀⠀⠀⠀⠀⠉⠳⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡟⠀⢠⡾⠋⠀⠀⠀⠸⠁⢤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢤⣄⢀⣀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸ ⣇⣰⠏⠀⠀⠀⠀⠀⠀⠘⠿⣿⣃⣀⣀⡀⠀⠀⠐⢤⡀⠀⠀⠀⠀⠀⠈⠻⣿⠳⡄⠰⣄⠀⠀⠙⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⡏⠀⡀⢀⠀⠀⣀⡤⠖⠛⠋⢉⠉⠉⠉⠙⠳⣄⠈⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠄⢹⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢿⣇⣰⡇⠘⠒⠋⠁⠀⠀⠀⠀⠘⠣⢀⣤⠀⠀⠈⠃⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⢸⡟⣿⠁⠀⠀⠀⣠⠀⠀⠀⠰⠷⠀⠻⢦⣘⠒⢦⣴⣏⠀⠈⠳⠶⠤⢤⣤⣤⣤⣤⣤⣄⣀⡀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⡸ ⠀⣧⠘⢧⣤⡤⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⠾⣅⠈⠙⠲⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢶⣄⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⢠⠇ ⠀⠸⣆⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢋⣀⠬⠓⢦⡀⠀⠉⠓⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆⠀⠀⠀⠀⠙⣦⠀⠀⠀⠀⡞⠀ ⠀⠀⠹⣆⠀⠈⠳⣄⣀⡀⠀⠀⠀⠀⠀⠀⠛⠋⠀⠀⠀⠀⠙⢦⡀⠀⠀⠉⠳⣄⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠈⢧⠀⠀⡼⠀⠀ ⠀⠀⠀⠹⣆⠀⠀⠀⠈⠉⠉⠓⠒⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠘⣧⡼⠁⠀⠀ ⠀⠀⠀⠀⠘⢧⡀⠀⠀⠀⠀⠀⠀⠀⠈⢳⠀⠀⠀⠸⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⣠⠟⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⣦⡀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢸⠄⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⣠⡾⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠻⢦⡀⠀⠀⢰⠆⢸⠃⠀⠀⠀⠈⢡⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⣠⡜⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣄⣸⡷⠋⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠈⠉⠉⠓⠒⠒⠶⣦⠤⣶⠶⠒⠒⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡅⢈⣙⣲⢲⣾⣿⣟⣶⣶⣺⣷⡿⠻⠷⣖⢻⣟⠆⢒⣲⡶⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
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⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠐⠂⠈⠉⠉⠉⠉⠉⠐⢒⣀⠠⠤⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⠔⠉⠀⠀⠀⠀⠀⠀⢀⡠⠴⠒⠉⠀⠀⠀⢀⠜⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⢀⠤⠚⠁⠀⠀⣀⣀⠤⠴⠮⠀⠀⣒⣒⣒⣢⡀⠀ ⠀⠀⡴⠁⠀⠀⠀⠀⠀⡠⠚⠁⣀⠤⠒⠈⠁⠀⠀⢀⠠⠒⠈⠁⠀⢀⡀⠗⡁⠀ ⠀⡜⠀⠀⠀⠀⠀⣠⡊⠄⠐⠊⠀⠀⠀⢀⣠⠔⠊⠀⢀⠤⡢⠕⠉⠁⠀⠀⠱⠀ ⢰⠁⠀⠀⣠⠴⠊⠁⠀⠀⠀⠀⢀⡶⠈⠉⠤⡭⠭⠭⠐⠉⠀⠀⠀⠀⠀⠀⠀⢁ ⡄⢀⡴⠋⠀⡔⣁⡀⠀⠀⠀⠀⠀⠉⢀⡀⠀⠀⠙⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠸ ⣧⠎⠀⠀⠀⢀⣺⠧⠤⢀⡀⠢⡀⠀⠀⠈⠛⠗⠄⢄⠈⠑⡄⠀⠀⠀⠀⠀⠀⠀ ⢿⣠⠀⠔⠊⠁⠀⠰⢄⠄⠈⠂⡗⢀⠀⠀⠀⠀⠈⠈⠀⠀⠈⠢⡀⠀⠀⠀⠀⢠ ⢸⢱⣀⣀⠔⠀⠀⠁⠈⠓⢭⡟⠢⢌⡙⠛⠒⠒⠒⠒⠦⣄⠀⠀⠱⡀⠀⠀⠀⡘ ⠀⢇⠈⢆⠀⠀⠀⠀⠀⢠⡯⠈⠑⢄⠈⠒⢄⡀⠀⠀⠀⠈⢆⠀⠀⠘⡄⠀⢠⠁ ⠀⠈⢦⠀⠉⠐⠒⠢⢄⡀⠀⠀⠀⠀⠑⠄⠀⠈⠢⡀⠀⠀⣸⠀⠀⠀⠘⣤⠃⠀ ⠀⠀⠀⠱⣄⠀⠀⠀⠀⢡⠀⠈⣆⡄⠀⠀⠀⠀⠀⠈⠀⠀⡏⠀⠀⢀⠔⠁⠀⠀ ⠀⠀⠀⠀⠈⠓⢄⠀⣆⠎⠀⠀⠈⠞⠀⠀⠀⠀⠀⠀⠀⠀⠑⣀⠔⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠚⠤⢄⣀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠐⠈⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢰⡆⢄⢤⣤⣾⢭⣽⣽⢭⣭⢶⡆⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀

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

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