Milady Emojis & Text

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bow, star, music, 𐙚
⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣶⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡜⣽⣃⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⠈⢻⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣰⠋⣰⠇⣸⡟⠙⢻⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⠀⢀⣿⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⣰⠃⣴⡏⢀⣿⠁⠀⠀⠙⢿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡿⠋⢸⡇⠀⣿⣿⣷⡀⠀⠀⠀⠀⠀ ⠀⢠⠏⣴⡿⠀⣾⡏⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣷⣤⣤⣤⣤⣾⣿⣿⣿⠋⠀⠀⠈⣇⠀⠘⣿⣿⣷⡀⠀⠀⠀⠀ ⠀⣿⠏⢸⣗⣼⡿⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣻⣷⣄⠀⠀⠀⢹⡀⠀⠻⣿⣿⣷⡀⠀⠀⠀ ⢸⠇⣶⣾⣿⣿⠃⠀⠀⠀⠀⠀⣤⣼⣟⢋⡬⣽⡟⣟⡛⢿⢿⡛⠻⡿⠿⣿⣦⠀⠀⠈⣧⠀⠀⢻⣿⣿⣿⡄⠀⠀ ⣿⣶⣾⣿⣿⠃⠀⠀⠀⠀⢀⣞⡟⣯⣴⣾⣿⠃⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠸⣇⠀⢉⣽⣿⣿⣿⡄⠀ ⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⡼⣞⣾⢿⣿⣿⡏⠀⣿⣿⡋⠻⣿⢻⣿⣿⣿⣿⣿⣿⡇⠀⢀⡙⣆⠀⠠⣾⣿⣿⣷⠀ ⠹⠿⠿⠋⠀⠀⠀⠀⠀⢰⡿⣹⡏⡿⣽⡿⠀⡀⠈⠛⠃⢀⠀⠀⠛⠿⣿⣿⣿⣿⣿⡀⠀⠀⠘⠷⣄⣨⣿⣿⠟⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠃⣿⣿⣇⣿⣁⣀⣀⡃⠀⠀⢘⣀⣀⡀⠀⢾⡏⢿⣿⣿⣿⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⡿⣿⣿⣿⠀⠀⠛⠃⢠⠀⠀⠛⠃⠀⢠⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⣿⣿⣿⣏⠀⠀⠀⠪⠀⠀⠀⠀⠀⠀⢿⣯⢾⣿⡿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢠⢿⣿⣿⣾⡀⠀⠀⠤⠤⠔⠀⠀⠀⣠⡿⣿⣾⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣾⠘⣿⣿⣿⣦⣄⣀⠀⠀⣀⡴⠞⣿⣁⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣬⣿⣿⣿⣿⣿⣿⡛⠋⠁⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⣿⣿⣿⠿⢿⢿⠛⢅⠈⠳⠤⣀⡀⠾⣿⡛⠛⠛⠻⠿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣇⡟⠉⠀⠀⠈⢏⣆⠠⠷⡀⢰⣾⣽⣷⣿⣿⠖⠀⠀⠀⠈⢻⣷⢣⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣯⣿⠁⠀⠀⠀⠀⠈⠸⡄⠀⠈⠀⢻⡏⠀⠏⠋⠀⠀⠀⠀⠀⠈⣿⣯⢇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⡀⣿⣿⣾⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⣿⣿⠀⠀⠀⠀⠀⢰⠁⠀⠀⡀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⢈⣼⣿⡜⣷⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⣿⡀⠀⠀⠀⠀⠘⠀⢀⡴⢻⠓⢤⡀⠀⠀⠳⡀⠀⠀⢀⣴⣋⠈⣿⣿⠹⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⡿⣿⣿⠻⡇⠀⠀⠀⠀⠀⠀⣼⠀⠛⣇⠀⠉⠳⣦⡀⢃⠀⣰⡟⠃⠀⠀⣼⣿⣧⣷⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⠃⢻⡏⢸⣷⠀⠀⠀⠀⠀⣸⡇⠀⠀⠘⠀⠀⠀⣶⣿⣶⣴⣿⣤⣤⣴⣾⣿⣿⡟⣿⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⡆⠸⣧⣼⢹⡆⠀⠀⠀⠀⣿⣿⣦⣤⣸⣦⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢹⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠰⠃⠀⢻⡏⣼⣷⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⡇⠘⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⢰⣿⣿⣿⣇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢠⡿⣧⣿⣹⡇⠀⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣯⡾⢣⣿⣿⡀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⢸⡇⣿⠇⣿⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣠⠾⠛⠁⢠⡿⡿⣿⠇⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠈⡇⠋⠀⡯⣀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠔⠋⣼⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⡇⠀⠀⠀⠀⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠁⢀⣠⡴⣻⣿⣿⣿⡆⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⡿⠁⡇⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⠖⠋⠉⠉⠙⢿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡿⠁⠀⢰⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡤⠊⠀⠀⠀⠠⠀⠀⠈⢻⣿⣿⠀⠀⠀⠸⣿⣿⣿⣿⣟⣾⠷⣄⠀⢸⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡠⠊⡀⠀⠀⠠⠈⠀⠀⠀⠀⠈⣿⣿⡆⠀⠀⠀⣿⣿⣿⣿⠟⠁⠀⠙⡆⠀⡇⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀

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

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⠀ ⠀ (\__/) (•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•) / ╰ ╯ \ / \>
⠐⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡆ ⠀⠹⣟⠋⠙⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠞⠋⢛⡿⠁ ⠀⠀⣌⢫⠉⠸⡝⢿⠲⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⣻⠇⠞⠉⣹⢋⡄⠀ ⠀⢠⢸⣾⡵⢶⣦⣀⠳⣄⢾⡓⡆⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⣿⢀⡜⠁⣴⣶⢮⣿⡟⠀⠀ ⠀⠀⢣⡙⠛⠀⠘⠿⠑⢮⣿⣷⡙⢆⠶⡄⠀⠀⢀⡴⢦⠎⣹⡷⣿⡼⠙⠏⠀⠚⢛⡵⠇⠀ ⠀⠀⠀⠹⠖⣦⡶⡄⠀⠀⠈⠓⣻⣌⢇⢸⠀⠀⡞⢰⣋⣞⠛⠋⠀⠀⢀⡴⣦⠖⠟⠁⠀⠀ ⠀⠀⠀⠀⣤⡿⢷⣾⣦⡄⠀⠰⣟⣙⣿⣆⢧⢠⢧⣿⣟⣹⡶⠀⢠⣴⢟⡾⣿⣥⠀⠀⠀⠀ ⠀⠀⠀⠀⡀⣶⣶⢨⠉⠛⢟⣀⡴⠞⡦⠅⢸⣿⠈⢬⠛⠧⣄⣘⠛⠉⠉⢰⣷⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠉⣯⡴⢤⣢⠏⣡⣤⢾⡇⡀⠈⣏⢠⡘⢗⢦⣄⡉⣶⣦⣼⣨⡏⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠉⠀⢰⣿⡟⢡⡿⡾⣯⠈⠿⠈⡿⡼⣆⠙⣿⣦⠀⠈⠁⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⣤⡾⢻⣷⡟⣹⢿⠇⠀⠀⠀⢏⢧⢹⣷⣿⢿⣄⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⢱⡟⠉⠀⠀⠀⠀⠘⠹⣧⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⡤⡿⠁⠀⠀⠀⠀⠀⠀⠀⠹⡦⣺⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀
⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛ ⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛ ⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛ ⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜
⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢰⣿⡿⠗⠀⠠⠄⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⡜⠁⠀⠀⠀⠀⠀⠈⠑⢶⣶⡄ ⢀⣶⣦⣸⠀⢼⣟⡇⠀⠀⢀⣀⠀⠘⡿⠃ ⠀⢿⣿⣿⣄⠒⠀⠠⢶⡂⢫⣿⢇⢀⠃⠀ ⠀⠈⠻⣿⣿⣿⣶⣤⣀⣀⣀⣂⡠⠊⠀⠀ ⠀⠀⠀⠃⠀⠀⠉⠙⠛⠿⣿⣿⣧⠀⠀⠀ ⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡇⠀⠀ ⠀⠀⠀⣷⣄⡀⠀⠀⠀⢀⣴⡟⠿⠃⠀⠀ ⠀⠀⠀⢻⣿⣿⠉⠉⢹⣿⣿⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠉⠁⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣤⣶⣦⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠛⠉⠙⠛⠛⠛⠛⠻⢿⣿⣷⣤⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠋⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠈⢻⣿⣿⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣸⣿⡏⠀⠀⠀⣠⣶⣾⣿⣿⣿⠿⠿⠿⢿⣿⣿⣿⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⠁⠀⠀⢰⣿⣿⣯⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣷⡄⠀ ⠀⠀⣀⣤⣴⣶⣶⣿⡟⠀⠀⠀⢸⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⠀ ⠀⢰⣿⡟⠋⠉⣹⣿⡇⠀⠀⠀⠘⣿⣿⣿⣿⣷⣦⣤⣤⣤⣶⣶⣶⣶⣿⣿⣿⠀ ⠀⢸⣿⡇⠀⠀⣿⣿⡇⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀ ⠀⣸⣿⡇⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠉⠻⠿⣿⣿⣿⣿⡿⠿⠿⠛⢻⣿⡇⠀⠀ ⠀⣿⣿⠁⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⠀⠀ ⠀⣿⣿⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀ ⠀⣿⣿⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀ ⠀⢿⣿⡆⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀ ⠀⠸⣿⣧⡀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠃⠀⠀ ⠀⠀⠛⢿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⣰⣿⣿⣷⣶⣶⣶⣶⠶⠀⢠⣿⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⣿⣿⡇⠀⣽⣿⡏⠁⠀⠀⢸⣿⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⣿⣿⡇⠀⢹⣿⡆⠀⠀⠀⣸⣿⠇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢿⣿⣦⣄⣀⣠⣴⣿⣿⠁⠀⠈⠻⣿⣿⣿⣿⡿⠏⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠿⠿⠿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢀⠀⢀⣀⣠⣤⣤⣤⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣠⣤⣤⣤⣤⣀⠲⢦⣄⡀⠀⠀ ⡶⢟⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠰⣷⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣬⡛⢷⣔ ⣾⡿⠟⠋⠉⠁⠀⡀⠀⠀⠀⠀⠈⠉⠉⠙⠛⢻⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠈⠙⢛⣛⣛⣛⣛⣉⢉⣉⡀⠀⠀⠀⠀⠀⠈⠉⠛⢿⣷⣝ ⠃⠀⠀⠀⠀⠀⠀⣛⣛⣛⣛⣛⣛⢛⡛⠛⠛⠛⣰⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣌⠛⠛⢛⣛⣛⣛⣛⣛⣛⣛⣓⣀⠀⠀⠀⠀⠀⠈⢻ ⠀⠀⠀⢀⣤⡾⠛⢻⣿⣿⣿⡿⣿⡟⢻⣿⠳⠆⠘⣿⣦⠀⠀⠀⠀⠀⠀⠀⣰⣿⠁⠐⠛⣿⡟⢻⣿⣿⣿⣿⢿⣟⠛⠻⣦⣀⠀⠀⠀⠀ ⠀⠀⢴⠿⣧⣄⣀⣘⣿⣿⣿⣿⣿⡿⣀⡙⢷⠀⢀⡿⠁⠀⠀⠀⠀⠀⠀⠀⠈⢻⡖⠀⣾⣋⣀⣺⣿⣿⣿⣿⣿⣏⣀⣤⣴⠿⢷⠀⠀⠀ ⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠙⠉⠉⠉⠉⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠉⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠆⠀⠀⢀⣿⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⠟⠁⠀⠀⠀⣾⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣤⣤⣴⣶⣾⠿⠛⠋⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣟⠻⡿⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣸⣻⠿⢮⡿⣾⡖⠚⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣄⠒⢦⠸⣿⣄⠙⣧⠀⠰⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣛⣷⣞⠳⣄⠘⡆⠙⢇⠀⠀⠰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣸⣯⡝⠻⣿⣏⠉⠻⣮⣷⣝⣶⣼⡀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣇⠈⠙⢤⠈⢳⡀⠀⠹⣌⢻⠀⠙⣧⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣼⠋⠳⢤⣄⡑⠀⠹⡄⠀⣌⠀⢳⡀⠸⡆⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⣠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢹⣄⠀⠂⢻⡉⠑⣦⠹⡄⠸⡄⠀⢷⡄⡇⠀⠀⡇⠀⠀⠀⠀⣀⠤⠒⠋⠁⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⠿⣶⣤⣝⠀⠀⠀⢿⡶⢧⠀⠸⡇⡗⠀⢀⠃⠀⢀⡴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣤⣤⣀⣀⡀⠀⠀ ⠀⠀⠀⠀⢀⣀⣀⣀⡀⠙⢻⣷⣦⡀⠈⠋⠈⢧⠀⠀⡇⠀⠈⠀⠔⠋⠀⠀⢀⣀⣤⣤⣤⡶⢶⣿⠿⠭⢥⢽⣁⣤⠀⠒⠿⠿⣿⣷⣆ ⠀⢀⡠⠚⠉⠉⠀⠀⠀⠀⠀⠙⢿⣿⣶⣤⣤⡘⣆⣼⣃⣴⣦⠀⠀⣀⡴⠞⣛⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠘⣿⣛⣖⠲⠦⣄⣸⡿ ⢠⠾⠒⠶⠀⠀⠀⠀⠀⡀⠀⡙⢺⣏⠛⢿⣿⣿⣿⣿⣿⣿⣿⣶⠞⡩⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠒⠤⣍⣙⣓⠶⣴⣶⠟⠁ ⡾⠀⠂⠀⠀⠀⠀⠀⠈⠑⠉⢡⣿⣿⠛⠲⣤⣯⣿⣿⣿⣿⣿⣥⡞⠒⠒⠚⠛⠓⠠⣀⠀⠀⠀⠠⠄⠀⠠⣤⣷⣌⢙⣿⣦⡾⠋⠀⠀ ⡗⠺⠤⠛⠉⠉⠁⠐⠉⠉⣹⣿⢿⢃⣠⣾⢋⣾⣿⣿⣿⣟⠻⠏⡿⣗⣦⡀⠀⠀⠀⠈⠙⠲⣄⡀⠀⠀⠀⠈⠙⠿⣿⣿⠟⠀⠀⠀⠀ ⣇⣠⠤⠀⠀⠀⠀⢀⣴⡾⢛⡽⢋⣽⣟⣵⢫⣿⣿⣯⡏⢣⠀⠄⠀⠈⠉⢙⣻⠖⢦⣄⡀⠀⠤⢙⠶⣤⡀⠈⢳⣰⡟⠁⠀⠀⠀⠀⠀ ⢿⠀⠀⠀⢀⡴⢪⠟⢩⠖⠋⢠⡾⢻⡟⢁⣿⣿⣿⡟⡀⠘⠀⣴⠀⣤⡐⠂⠈⠉⢗⣟⠿⣶⣤⡀⠲⣤⣹⣿⠞⠉⠀⠀⠀⠀⠀⠀⠀ ⠘⣧⠀⠀⠈⠀⠀⠀⠀⡀⣠⠏⣴⠏⠀⢸⣿⠟⠻⢀⠆⠀⢀⠈⢳⡸⡗⢤⡀⠉⠪⠙⢧⡀⠉⠙⠓⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠘⢧⡀⠀⠀⢀⡴⢂⣜⡥⠚⠁⠀⠀⠀⠁⢠⡆⢸⣰⠀⠈⣧⠀⠑⢿⠀⠙⢦⠀⠀⡀⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠳⣤⣖⣋⡴⠟⠉⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⢹⠆⠀⢸⡄⠀⠈⢷⡀⠀⠑⢦⡜⢦⣹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⣼⣾⠀⠈⢀⢳⡀⢠⡈⢻⣦⡀⠀⠙⢮⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⡿⡼⠀⠄⠈⠈⣇⠀⠹⣌⠹⣿⣄⠳⢰⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡁⢻⠀⠀⠀⠀⠙⠂⠀⠹⡁⡈⡻⣦⠾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⣸⡄⠀⠀⠀⠀⠀⢰⣄⣃⡴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⠒⠒⠒⠒⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⢿⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⡿⣽⣻⡽⢯⡿⣽⣫⡟⣽⣫⢟⣽⢫⡟⣽⢫⡟⣭⡻⣭⢻⡭⢯⡽⣭⢯⡽⣭⠻⣜⡣⢟⣜⡣⢟⡜⣣⢛⡜⣣⢛⡜⣣⢏⡼⣡⢏⡼⣡⢏⡼⣡⢏⡼⡱ ⣿⣷⣻⣟⣾⣳⢿⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⡷⣯⣟⡷⣯⡽⣯⢷⣏⡷⣽⣣⢯⣟⢮⣯⢽⣚⡷⣹⢧⣻⡜⣧⣛⢧⡻⣜⢮⡳⣭⢻⡔⣏⡳⢎⡝⢮⠼⣱⢫⠼⣱⢫⡜⡱⢎⠶⡱⢎⠶⡱⢎⠶⡱⢎⠶⣙ ⣿⢿⣽⡾⣷⣟⣯⢿⡾⣽⣻⢾⣽⣻⢾⣽⣻⢾⣽⣻⣞⣯⣟⣾⣳⣟⣾⣳⣟⣾⣳⣟⣾⣳⣟⣾⣳⣟⣾⣽⣻⢾⣽⣻⢾⣽⢾⣯⢷⣟⣾⣳⣟⣾⣳⣟⣾⣳⣟⣾⣳⢯⣟⡷⢯⣟⡷⣻⣵⡻⣾⣱⢷⣫⠷⣞⢯⡞⣧⢟⡼⣏⢷⣣⢟⡵⣫⢞⡽⣎⢷⡹⣞⢣⡞⣱⢭⡛⡼⣙⡞⣥⣋⢗⣣⠳⣜⡹⢎⡳⣙⢎⡳⣙⢎⡳⣙⢮⡹⣒ ⣿⣯⣷⢿⣳⣯⣟⣯⡿⣽⢯⣿⢾⣽⣻⢾⣽⣻⣞⡷⣯⢷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⢯⣷⣟⡿⣞⡿⣞⣯⡿⣞⣷⣻⣞⣷⣻⣞⣷⣻⣾⣽⣿⣾⣿⣿⣾⣿⣷⣿⣷⣯⣟⣾⣭⢿⡹⣾⣹⢮⣏⢷⣫⢞⡵⣫⢷⡹⣎⢷⡹⣎⠷⡭⢮⡕⣏⠶⣹⢱⢣⠞⡴⣩⠞⡴⣋⠶⣙⢮⡱⣍⢮⡱⣍⢮⡱⡍⢶⣑⢣ ⣿⡾⣽⡿⣽⡾⣽⣳⡿⣯⣟⣾⣻⢾⣽⣻⣞⡷⣯⢿⡽⣯⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⢾⡽⣟⣾⣽⣻⡽⣟⣯⣷⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣧⣛⡾⣼⢣⡟⣮⢳⡝⣮⢳⡝⣮⠳⣭⢛⡼⢣⢞⡬⡳⣍⢎⢧⡛⡴⢣⡛⡴⣍⢞⡱⢎⡵⣊⠶⡱⢎⡖⣱⡙⢦⡍⡖ ⣿⣻⣽⣟⡷⣟⣯⡷⣟⡷⣯⢷⣻⣟⣾⣳⢯⡿⣽⢯⣟⡷⣯⢷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⢾⡽⣯⣟⣯⡷⣯⣷⣟⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣵⣫⢞⡵⣏⢾⡱⢯⡞⡵⣛⢦⣛⡼⣍⠾⣰⠳⡜⣎⠶⡹⣜⢣⡝⡲⣍⢮⡱⢫⠴⣩⠞⣡⠳⡜⡥⣚⢥⡚⡜ ⣿⣽⣳⣯⣟⣯⡷⣟⣯⢿⡽⣯⢷⣻⢾⡽⣯⢿⣽⣻⢾⣽⣻⢯⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⢾⡽⣯⢿⡽⣞⣯⢿⣳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣞⡽⢮⡝⣧⡛⣵⡩⢖⣣⠞⣬⠳⣥⢛⡼⣌⢳⡱⢎⢧⡚⡵⣊⠶⣉⢧⢛⡤⣛⠴⣋⠼⡱⡜⣆⢧⡙ ⣿⢾⣽⡾⣽⣳⣟⣯⣟⣯⢿⡽⣯⣟⣯⢿⣽⣻⢾⣽⣻⢾⣽⣻⡞⣷⣻⣞⣷⣻⣞⣷⣻⢾⡽⣯⢿⡽⣯⣟⣯⣟⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣣⢟⠶⣙⢦⡛⡵⢪⡝⢦⡛⡴⣋⠶⣩⢖⡹⢎⠶⡹⠴⣩⠞⡱⢎⡣⠞⡴⢋⡼⣡⠣⡵⣈⠦⣙ ⣿⢯⣷⣟⣯⡷⣯⣷⣻⣞⣯⣟⣷⣻⣞⡿⣾⣽⣻⢾⡽⣻⡞⣷⡻⢷⣛⣾⣳⣟⣾⣳⣯⡿⣽⢯⡿⣽⣳⣟⡾⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣟⣿⢻⡽⢺⡝⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣎⢯⡹⣆⠻⣜⢣⠞⣥⢛⡴⣩⢞⡱⢎⡵⢋⡞⣱⢋⠶⣉⠷⡩⢞⡱⣘⠣⢖⡡⢓⡴⣉⠖⣡ ⣿⣻⢷⣻⡾⣽⢷⣯⢷⣻⢾⡽⣞⡷⣯⣟⣷⣳⢯⣟⢾⣳⢟⣳⣟⣯⣟⣾⣳⡽⣞⡷⣯⢿⡽⣯⣟⣷⣻⣞⣿⣿⣿⡟⢥⠲⡝⣾⣟⣿⣿⣻⣿⣟⣿⣯⢿⣞⣷⣻⣽⣚⠷⣘⢧⡚⡕⢦⢫⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣲⢣⡭⢳⢬⢣⡛⡴⣋⠶⡱⢎⡵⢋⡜⣣⠞⡥⢫⡜⡱⢎⡱⢎⠴⢣⡙⢦⡙⢦⠱⣌⠚⡤ ⣿⣽⣻⢷⣻⢯⣟⡾⣯⣟⣯⢿⣽⣻⢷⣻⢮⣽⣳⢯⣻⣭⡟⣷⣞⣳⣞⡷⣯⢿⡽⣽⣏⣯⣟⣷⣻⣞⣷⣻⣿⣿⠫⠄⣉⣳⣽⣼⣿⣿⣿⢿⣟⣿⢯⣟⡿⣞⣷⡳⢞⡜⢢⠏⡖⡩⢞⡥⣛⣞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢣⢞⡱⢎⢧⡙⢶⡩⢞⡱⣋⠶⣩⠞⣡⠞⣱⠣⡜⡱⢊⠖⡩⢎⡱⡘⠦⡑⢎⡱⢌⡓⡔ ⣿⢾⣽⣻⣯⢿⣽⣻⢷⣻⣞⣯⢷⡯⣟⣞⡿⣼⢏⣯⢷⣳⣻⣳⣞⢷⣫⣟⡷⣯⣟⢷⣻⢮⡽⣞⣷⡻⣞⣿⣿⠁⠳⢾⣧⣽⣞⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⡿⣿⡝⣮⢞⡳⣎⠳⡵⢊⡴⢻⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢮⠳⣍⠶⣙⢦⡙⣎⠵⣊⠗⡱⢎⡱⣊⠥⡓⣬⢱⡉⢎⡱⢊⠴⣡⠣⣙⠢⡑⠦⡱⢌ ⣿⢯⣟⡷⣯⣟⣾⡽⣯⢷⣻⣞⣯⣽⣻⣼⣛⣾⣛⡾⣏⡷⣏⡷⣞⣯⢷⢯⡽⣶⢯⣛⣧⢿⡽⣳⢾⣽⣻⣿⠃⢉⡷⣿⣹⢯⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣯⡿⣯⢟⡞⣞⡳⣜⣫⡑⠳⠾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢌⡳⢬⢳⡩⢖⡹⡸⡜⡡⢏⡕⢎⡱⣉⠖⡱⢢⠱⡘⠦⡑⣍⠲⢄⠳⣄⢣⡙⢆⡱⢊ ⣿⣯⢿⡽⣷⣻⣞⡿⣽⢯⣷⣻⢮⢷⣳⣳⠿⣜⣯⢷⣏⡿⣽⣹⢯⣞⣯⢯⣟⡾⣽⣛⣾⣫⡽⢯⣷⣫⣿⡟⢠⣯⣄⢿⣿⣿⣿⡧⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡱⢦⡝⢳⡒⠦⡄⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣎⡱⣋⠶⣙⢎⡵⢱⠱⣙⠲⡘⢎⡱⢌⢎⡑⢣⠱⣡⢣⡑⠦⡙⣌⢃⢆⠣⡜⠢⣅⠣ ⣿⣞⣿⡽⣷⢯⡿⣽⣻⣟⡶⣯⢟⣯⣗⡯⣿⠽⣞⣯⢾⣝⡧⣟⡧⢿⣜⡯⢾⡽⣞⡽⣶⢏⣿⣛⡶⣯⣿⠇⠿⢱⣿⢸⣿⣿⣡⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣎⠧⡝⢲⠱⣌⡠⢘⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠳⣍⢞⡱⢎⠴⣋⢜⣢⡙⡱⢣⠜⡌⠦⣙⢂⠳⡐⠦⣑⢣⠱⡌⠎⡜⢢⡑⢣⠆⢣ ⣿⡾⣽⣻⡽⣯⣟⣷⣻⠾⣝⣳⣟⣞⡾⣽⢞⡿⣽⣺⣝⣮⡽⣞⡽⣏⡾⣝⣯⠾⣽⣹⢞⣟⣮⢿⣱⢯⣿⠀⣐⡊⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣜⢣⠷⢤⡡⠉⠆⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡎⡵⣊⢮⡱⢍⡲⢩⡒⢤⢣⡑⢣⠚⢬⡑⢢⢍⠲⣉⠖⡡⢎⠱⡘⡜⣠⠣⣘⢂⢎⡡ ⣿⡽⣷⢯⣟⣷⣻⢾⣽⣻⡽⣳⢾⣝⡾⣭⢿⣹⢧⢷⢾⣱⡟⡾⣵⢏⣷⢻⡼⣻⡵⢯⣾⣹⢮⣯⣻⣿⣧⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣶⣭⡞⢣⢏⣬⡱⡌⢒⡠⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡜⢲⠍⣦⠱⡎⡜⣡⠚⡔⢢⡙⢢⡙⢦⡘⢥⢊⠵⡨⠜⡐⢎⠱⡐⢆⡡⢒⡡⢊⠴⡐ ⣿⣳⣟⡾⣽⢯⣟⡾⣽⣫⢷⣻⣞⣽⣳⣛⣞⢯⣞⠾⣼⢏⣷⡳⡽⣞⡽⣞⢧⡿⣱⠾⣭⡟⡾⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠾⢞⡩⣇⠣⠌⡑⢺⣿⣿⣿⣿⣿⣿⣿⣿⢟⣿⣿⣿⡑⢎⡴⢩⡒⢥⠣⣍⠲⣑⠪⡑⢎⡱⢨⠱⡌⢚⠤⢃⠲⡑⡌⢆⠓⡌⢃⠎⡱⠘⡄⢣ ⣿⡽⣞⡿⣽⣻⢾⣽⣳⢯⣟⡵⣞⣧⢷⡻⣼⢏⣾⢻⡽⣺⢧⢿⣹⢾⣹⡞⣯⠾⣝⡯⣗⢿⡿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣖⣿⢯⢀⢒⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡶⡷⣎⠷⣤⢓⡒⣩⢒⣿⣿⣿⣿⡟⡹⠋⢴⣆⡘⣿⣷⣏⢲⡘⢥⡙⢆⠳⣨⠱⠌⡥⣙⠢⣅⠣⢃⠍⡆⠣⠍⠦⡑⠌⡌⠱⡈⠆⡜⢠⠃⡜⢠ ⣿⡽⣯⣟⡷⣯⣟⡾⣵⣻⠾⣽⣻⡼⣳⢏⣷⢻⢮⣏⡷⣏⢿⡺⣽⣚⣧⢟⣧⢿⣹⢾⣹⢾⣹⢟⡿⢥⣼⣿⣿⣿⣿⣿⣿⣿⣿⢳⠚⡼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣭⡛⠿⡵⣉⠞⣩⠳⢦⡀⢎⣽⣿⣿⣿⣇⢠⣅⠮⠿⢿⠿⣿⣗⠦⣙⢢⡙⣌⠳⣄⠫⡜⡰⢡⠣⡔⢩⢊⠜⡰⢩⠘⡰⢁⠞⡄⢣⠑⡌⠔⡡⢊⠔⡡ ⣿⣽⣳⣯⣟⡷⣯⣟⣳⣽⢻⣳⣭⠷⣏⣟⡮⣟⡽⢮⣗⢯⡯⢷⡳⣏⣾⢫⣞⣳⢯⢾⣹⡞⣽⡞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡭⣇⡋⡔⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⢮⡓⢦⡙⣷⡳⣬⣦⢥⡛⣤⡙⣦⣿⣿⣿⣿⣏⣿⢸⣿⣿⣿⣿⣾⣿⡜⣌⠣⣜⠰⢣⢌⡱⢢⢙⣂⠳⢌⡡⠎⢆⡑⢢⠡⡑⢊⠴⡈⢆⠱⣈⠒⡡⠎⡰⢁ ⣿⣞⣷⣻⢾⣽⣳⢯⣷⢫⣯⢷⣚⣯⡽⣞⡵⣯⢽⡻⣼⣛⠾⣯⢽⡳⣽⢻⡼⣽⡺⣏⡷⣽⢣⣟⡞⣿⣾⣥⣿⣿⣿⣯⣿⡳⢷⡈⡑⠌⢠⡸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡽⣶⣍⢏⡞⣴⣙⣦⡹⢆⣿⣴⣽⣾⣿⣿⣿⣿⠐⡻⢷⢩⣿⣿⣿⣿⣿⡗⣨⠱⣌⠹⣂⠎⡔⢣⢌⠢⢃⠆⢢⠍⢢⠘⡄⢣⠘⣐⠢⡑⢌⠢⡁⢎⠰⡁⢆⠡ ⣿⢾⣳⣯⢿⡾⣽⣻⣼⣻⢞⣽⣹⢶⣻⢼⣻⢼⣳⡻⣵⣫⢟⡮⣗⣻⡼⣳⡽⣖⣻⡝⣾⡱⣟⢮⣽⡟⢻⣿⣿⣿⣟⣿⣯⢳⣦⣷⣶⣿⣿⢿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣼⣆⢳⣎⠿⣖⣾⣿⣾⣿⣿⣿⣿⣿⡀⣟⢈⣦⣹⣿⣿⢿⣿⠓⡤⢓⣌⢣⠱⡊⢜⡂⢎⡱⢊⡜⢄⠚⡄⢣⠘⡄⢃⠆⡱⢈⠆⡱⢈⠆⡱⢈⠄⡃ ⣿⢯⣟⡾⣯⣟⡷⣯⢶⣏⣟⡮⣗⣻⡼⣏⡾⡽⢶⡻⣵⢫⣾⡹⣞⡵⣫⢷⣹⢞⡵⣻⢖⣻⡝⣾⣿⠁⠰⠟⣿⣯⢸⣿⣯⡧⣴⣠⣴⣶⣦⣄⣳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⢿⣿⣿⣮⣷⣾⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣟⠃⢿⣿⠟⣽⣿⣿⠣⡙⡔⢣⠜⣢⠣⢍⠢⡙⢄⢢⠡⡘⢄⠣⡘⢄⠣⡘⢄⠊⡄⠣⡐⢄⠃⡔⢠⠃⡌⡐ ⣿⢯⡿⣽⣻⢾⡽⢯⡷⣞⢧⣟⣭⠷⣝⡾⣱⠿⣭⢗⣯⢳⡞⣵⡻⣼⣛⢮⡗⣯⡝⣧⡟⣧⢻⡞⣿⠀⠀⣦⣿⣿⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣹⢯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣠⣛⣷⠿⣫⣾⢃⠧⡱⡘⢥⠚⣄⠳⣈⠱⡈⢆⠢⡑⢌⠢⡑⢌⠢⡑⠰⡈⢆⠡⢃⠌⡂⠜⡠⢂⠅⢢⠁ ⣿⢯⣿⣳⣟⣯⣟⣯⠷⣏⡿⡼⣞⢯⣻⠼⣏⣟⢮⣻⡜⣯⢞⣳⡽⣣⢯⣳⢻⡼⣽⢲⡟⣼⡳⣏⢿⣆⠀⢿⣿⣿⣿⣯⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠶⢟⣿⢅⠺⡰⢡⡙⠤⢋⠤⠓⡄⢣⠘⡄⢣⠘⡄⢣⠘⠤⡑⢨⠑⠌⡄⢃⠢⡘⠄⡃⠔⣁⠊⡄⢃ ⣿⣻⣞⡷⣿⢮⡽⣞⣿⡹⣞⡽⣞⢯⣳⢻⡝⣮⢟⡶⣻⡝⣞⣧⢻⡵⣫⣗⢯⣳⡭⢷⣫⢷⡹⣎⡯⢿⣆⠘⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⢀⢻⡯⢌⢣⡑⢧⠘⡥⢋⠌⡓⢌⠢⡑⢌⠢⡑⢌⠢⢉⠆⢡⠂⡜⡐⢌⠂⡅⠢⡑⠌⢒⡀⠣⠌⡄ ⣿⣳⢯⡿⣽⣏⡿⣽⣲⢟⡽⣞⣭⢷⣫⢟⡼⣏⡾⣳⢧⣛⢷⡺⣝⡾⡵⣞⢯⡖⣯⡳⣝⡮⢷⡹⣞⣻⣿⡄⣿⣿⣿⡟⢛⣫⣿⣿⣿⣿⣿⣿⠟⣿⠛⢿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠸⣹⡟⣌⠲⣡⠊⡕⢢⠡⢚⠰⡈⠖⡡⢊⠔⠡⢂⠱⡈⢌⠂⡅⢒⡈⢄⠣⡐⢡⠂⢍⠂⡌⢡⠒⠠ ⣿⡽⣯⣟⡷⣯⢷⣳⡽⢾⣹⡞⡽⣎⡷⣫⡽⣞⡵⣛⣮⢟⣮⢽⣣⢟⣵⢫⡾⣹⢖⣯⢳⡝⣧⢻⡜⣷⣿⣿⣿⣿⣿⣴⣿⡿⡏⢻⣿⣟⣤⣽⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠠⢚⡯⣐⠣⢆⠹⣠⢃⠣⢌⠢⡑⠌⠴⢁⢊⠱⡈⢆⠘⡠⢃⡘⢄⡘⢄⠢⢑⢂⠩⢄⠊⡔⠡⠌⡡ ⣿⣽⣳⣯⣟⣷⣛⣶⢻⡝⣧⡻⣝⢾⣱⣏⢷⣹⢞⡽⣎⢿⡜⣧⣛⠾⣜⢯⣳⣛⠾⣜⢧⡻⣜⢧⡻⣜⣿⣿⣿⣿⣿⣿⡟⠳⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠌⡐⢫⢄⠫⡜⢠⢃⠌⡒⢌⠢⢑⠊⡄⠣⢌⠰⡐⡈⢆⠡⢂⠔⡂⠔⡈⢆⠡⢊⠰⡈⠒⢄⠣⡘⠠ ⣿⣞⣷⣻⣞⡾⣝⡾⢯⣽⢺⡵⣏⡟⣶⡹⣞⡽⣚⡷⣹⢮⡻⣵⢫⡟⡽⣎⠷⣭⣛⢮⡳⣝⢮⡳⣝⡞⡶⣿⣿⣿⣿⡿⠈⢀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠬⣙⠆⢳⠘⠤⣉⠆⡱⢈⢆⠡⢊⠰⡁⢆⠡⢂⠱⣀⠣⠌⢒⡈⢆⠡⢂⠱⡈⠤⢡⠉⡂⢆⠡⡁ ⣿⢾⣽⣳⢯⣟⡽⣞⡿⣜⣳⡽⣺⡝⣶⢫⢷⡹⣝⠾⣭⣳⢻⣜⡳⣽⢳⣭⣛⢶⣭⢳⡝⣮⢳⡝⣮⣝⡳⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⡈⠴⣈⢏⠰⣉⠒⡡⢊⠔⡡⢈⠆⡡⢒⠈⡔⡈⢆⠡⡐⢂⡑⠢⡐⢂⠅⡊⠔⡠⢃⠢⡑⠨⠄⡃⠔ ⣿⣻⢾⣽⣳⢾⣹⣳⢽⡺⣵⢫⢷⡹⣞⡽⢮⣽⣚⢯⣳⢭⣳⢭⣳⢭⣳⢮⡝⡾⣜⢧⡻⣜⢧⡻⢶⣭⢳⢧⣿⣿⣿⣿⣿⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⡐⢈⠲⢡⢎⡱⢄⡩⢐⠡⢊⠄⣃⠰⢁⠢⡑⠰⡈⢄⠃⡔⣁⠢⡑⢄⠃⡌⠰⣁⠒⡄⢃⠌⡑⢌⠰⢁ ⣿⣽⣻⢾⡽⣞⣧⢟⣞⣳⡭⣟⢮⢷⡹⣞⣳⢮⡝⣾⣱⢻⡜⣧⣛⢮⡳⣏⢾⣱⢏⡾⣱⢏⡾⣹⢳⣎⡟⡾⣴⢛⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠭⡀⢡⠌⡡⢂⡅⢺⡔⡨⢔⡡⢊⡅⢒⠠⡑⣈⠒⡈⢅⠒⣈⠒⡐⢄⠒⡨⠐⡌⠰⣁⢂⠒⡈⢆⡘⠰⢈⠢⢁ ⣿⢾⡽⣯⢷⣻⢮⣛⣮⢳⣝⣮⣛⢮⢷⡹⣎⢷⣹⠶⣭⣳⣛⠶⣭⡳⣝⡞⣧⣛⢮⣳⡝⣮⢳⣝⡳⢮⣝⡳⣯⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢻⡁⠞⡌⠐⡤⠂⠤⢡⠘⣐⠣⣏⡐⠆⡔⣡⠈⡆⡑⠰⣀⠃⡜⢠⢊⡐⢌⠰⣈⠂⡅⢃⠌⡡⢐⢂⠱⢈⠆⢌⠡⢊⠄⠡ ⡿⣯⣟⡷⢯⢷⣫⠷⣭⢷⣚⢶⡹⢮⡳⣝⢮⣳⢭⣛⢶⣣⢏⡟⡶⣝⢮⣝⠶⣭⡳⢧⣻⣜⡳⢮⣝⡳⢮⣽⣟⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣍⡳⢍⢦⣹⡰⢬⠑⡠⠨⠰⢀⣋⠄⠳⣼⡄⣙⠰⢠⡘⠤⣁⠣⡐⢌⡐⢢⠐⡰⢈⠢⠄⡃⠔⣈⠢⠑⡂⢌⠢⡁⢎⠠⠃⡄⢊⠐ ⣿⢷⣯⣟⢯⢷⣫⣟⢮⣳⡝⣮⣛⢧⣛⢮⡳⣝⡮⣝⣮⢳⣏⣞⡳⣝⠾⣜⡻⢶⣹⢳⡳⢮⣝⡳⢮⣝⡳⣞⢿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣭⢻⣌⠳⣭⢖⣦⠳⣌⢌⠡⢁⠒⢡⠈⢎⠡⠜⣷⡈⠜⣠⠘⡰⢀⢣⠘⡄⠒⡄⢣⠐⡡⢂⠱⢈⠒⡠⢁⠣⢘⠠⢂⠅⢊⠐⠡⠐⠂⠌ ⣿⣻⢶⢯⣛⡾⡵⣞⢯⢶⡹⣖⢯⡞⣭⣳⢻⣜⡳⣝⢮⡳⣞⡼⣳⢭⣛⣮⡝⣧⢏⡷⣹⢳⢮⣝⡳⣎⠷⣭⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢯⣽⣳⢮⡳⣎⡳⡼⡞⡴⢫⡜⠌⢦⠉⠈⠄⡐⠂⡜⢨⢽⣿⡔⢂⠱⣀⠃⢆⠱⣈⠱⡈⢆⠱⣀⠣⡘⢄⠣⡐⢡⠊⡄⠣⢌⠘⡀⢊⠡⠌⠡⢈ ⣟⡷⢯⣟⡽⣺⣝⢾⡹⣎⢷⡹⢮⣝⠶⣭⡳⢮⣝⢮⡳⣝⢮⡳⣝⢮⣳⢮⣝⢮⡻⡼⣭⣛⠾⣜⡳⣭⣛⠶⣭⢿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣏⣟⡳⢞⡥⢯⡽⣭⢳⢧⡹⢜⣣⡙⢾⡀⠎⠡⠀⢄⠡⡀⠣⢎⢿⣿⣧⣖⡠⢉⠆⡒⠤⡑⡈⢆⠱⣀⠣⡘⢄⠣⡘⢄⠣⡘⠰⡈⠆⡁⠢⠐⡈⢂⠁ ⣯⣟⣟⣮⡽⣳⢞⣯⢳⡝⣮⢽⡳⣎⡟⡶⣝⢯⡞⣧⣛⢮⢷⡹⣞⢧⣛⠾⣜⢧⡻⣵⢣⣏⠿⣜⡳⢧⣏⠿⣜⡧⣏⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣟⢾⡸⣹⡍⣞⣱⠞⣥⢻⢦⡙⣦⠧⡙⢦⡑⢎⠡⡀⠆⠰⢀⢣⠘⡼⣷⣏⡿⣿⣶⣾⣤⣵⣠⡑⣈⠒⠤⢑⠰⡈⢆⠱⡈⢆⠡⢃⠜⡠⠑⣂⠑⡠⠁⠌ ⣷⣻⡼⢶⣻⢵⣫⢞⣧⢻⡜⣧⢻⡼⣹⢳⡝⣮⡝⡶⣭⣛⢮⣳⡝⣮⣝⡻⣜⢧⡻⣜⡳⣞⡽⢮⣝⡳⣎⠿⣜⡳⣝⠾⣭⣛⠿⡿⢿⠿⣿⢿⣿⠋⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣞⡧⢷⡩⡜⠶⣥⢯⡙⣧⣾⠵⣣⠝⣌⠣⡜⢢⠡⡁⠂⠅⣂⠢⠘⢤⢫⡝⣻⣷⣻⢞⣽⣻⣟⣿⡿⣿⣶⣮⣴⣡⣈⠆⡑⠌⢢⠁⢎⡐⠡⡀⠎⢠⢁⠂ ⣷⣳⢻⣏⣞⢧⣛⡾⣜⢧⡻⣜⣧⢻⡵⣫⢾⡱⣏⢷⣣⢟⣮⢳⡝⡶⣭⢳⡝⣮⢳⣭⢳⡝⣞⡳⢮⡝⣾⡹⢧⡻⣜⡻⢶⡍⡷⣍⣛⠮⡵⢎⣽⠀⠀⠀⠀⢮⣿⣿⣿⣿⣿⣿⡿⡞⣥⢳⡉⢳⡜⣦⢿⡻⣌⠷⣢⠝⣠⠒⡌⢠⠃⡔⢁⠂⠴⢈⡑⢎⡳⢼⢯⡷⣯⣟⣮⢷⣻⣾⣟⡿⣽⣿⣻⣿⣿⣿⣷⣾⣤⣉⡤⠘⢠⠁⡌⠂⡄⢂ ⡷⢯⣛⣞⢮⡻⣜⡳⣝⢮⢷⡹⣎⢷⡹⢧⣏⢷⡹⣎⢷⣫⢞⣧⢻⡵⣫⢷⡹⣎⢷⡺⣝⠾⣱⢏⡳⣝⢶⣹⢳⡝⣧⣛⢧⠞⡵⢎⢧⡛⣜⢣⢾⡃⠀⠀⠀⠠⣼⣿⣿⣿⣿⣟⣷⡻⣬⢓⣌⠶⣹⣯⣗⣳⣭⠳⡆⣍⠲⠠⠄⠃⡜⠐⡌⡀⢂⠬⠑⡎⡵⢋⡞⣹⢳⣻⣾⣿⢿⣟⣾⣟⣷⣿⣿⣽⣷⡿⣯⣿⣿⣿⣿⣿⣦⣴⣀⠡⠐⠂ ⣟⢯⡽⣎⣯⢳⡭⣗⢯⡞⣧⢻⡜⣯⣝⡳⢮⣏⢷⡹⣎⢷⣫⢞⣧⢻⡵⣫⢷⡹⣎⠷⣭⢻⡥⣏⢷⡹⣎⢷⣫⢞⡵⣭⠺⡭⣝⢮⢣⡝⣬⠓⡾⡇⠀⠀⠀⠐⢼⣽⣿⣿⣿⣿⣷⣿⠶⣏⢬⣛⣷⣻⣞⡷⣊⠷⣉⠦⣁⠣⣘⠐⡈⠱⣀⠖⠡⠀⡝⡘⡔⠫⡔⢣⡞⣿⣿⣿⣿⣿⣿⣾⣿⣿⣾⣿⣾⢿⣟⣷⡿⣯⣿⣿⢿⣿⣿⣿⣾⣤ ⣯⣛⢾⡱⣏⢷⡹⣎⢷⡹⣎⢷⣛⠶⣭⣛⠷⣎⢯⡳⡽⣎⢷⣫⢞⣧⢻⡵⣫⠷⣭⢻⡜⣧⢳⡝⣎⢷⡹⣎⢷⣋⠾⣜⢫⡵⣚⡬⢳⡜⢦⡛⡴⣧⠀⠀⠀⠀⠀⢙⣿⣿⣿⣿⣿⣯⡿⣜⡶⣹⣾⢯⣟⣳⡽⢎⡕⢢⠰⣁⠣⡜⢀⠡⡘⢠⠁⢆⠐⡤⢩⠓⣬⢓⡞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣯⣿⣻⣿⣿ ⡷⣭⡗⣯⠽⣎⢷⣫⢞⡵⣫⡞⣭⣛⠶⣭⢻⡼⣣⢟⡵⣫⢞⡵⣫⢞⣧⢻⡵⣻⡜⣧⢻⣜⡳⢞⡭⡞⣵⢫⡞⣭⢻⢬⡳⣜⡱⢺⡱⢎⢧⡙⡖⣿⠀⠐⠄⢀⠀⠀⠉⣿⣿⣿⣿⣿⣟⡷⣏⣷⣿⣿⢿⣻⡝⢮⡜⣡⠓⠬⣑⠜⣨⠂⡁⢃⡚⢤⡈⢠⢃⡝⢦⣛⡾⣽⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣽⣿⣽⣿ ⣟⡵⣻⣜⡻⣜⢧⣛⢮⡳⢧⡻⣵⢫⡟⡼⢧⡻⣵⢫⡞⣵⢫⡞⣵⢫⡞⣧⣛⢶⡹⣎⢷⣪⠽⣹⢼⣙⢮⣳⢹⡜⣣⢳⣙⠦⣝⢣⡝⢎⢶⣭⡿⠛⠀⠀⠀⢹⠆⣄⣀⠿⣿⣿⣿⣿⣯⣿⡽⣾⣿⣯⡿⣧⣛⢧⡚⡥⢊⠶⣩⢎⡡⢚⠄⢃⠜⡢⣄⠣⡘⣬⢣⠿⣽⣳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣯⢞⡵⣎⡷⣹⢎⣯⢳⡽⣳⡝⣮⢳⡽⣹⢧⡻⣜⢧⡻⣜⢧⣻⡜⣧⣛⢶⡹⣎⢷⡹⢶⣩⢏⠷⡮⣝⡞⣬⡓⣞⣱⢫⡜⣹⢬⣳⡾⠟⠋⠁⠀⢀⠀⠀⠀⢸⡅⣦⢉⡉⢿⣿⣿⣿⣿⣽⣿⣿⣿⣿⡿⣖⡻⢦⡛⣌⢏⡾⡵⢪⡕⢯⣌⢣⣌⡱⢎⡧⣙⣤⢏⡿⣵⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢷⣫⢞⡵⣫⢗⡯⣞⢧⡻⣵⢻⡜⣧⢻⡵⣫⢷⡹⣎⢷⡹⣎⢷⡹⢶⡹⣎⢷⡹⢎⡗⣯⣜⢫⢷⡹⡖⣽⠲⣝⡼⢲⣍⣾⠟⠋⡁⢀⠀⠀⠀⢰⣿⠀⠀⠀⠈⡇⠸⣧⣌⣻⣟⣿⣿⣿⣿⣿⣿⣿⣿⡿⣥⣋⢷⡙⣞⣮⡽⣽⢳⣚⠷⣜⡲⣬⡳⢯⣶⢻⣼⣻⣞⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣟⡼⣫⢞⡵⣫⢞⡽⣎⠷⣭⢳⡝⣮⢷⡹⢧⣏⢷⡹⣎⢷⡹⢮⡝⣧⢳⡝⡮⡝⣏⡞⢶⢎⡿⢬⡳⣝⠮⣝⣲⣽⠟⠋⠀⠠⠀⢀⡀⢀⡈⢷⣾⣿⠀⠀⢠⠀⢻⡄⢽⣷⣎⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢧⡍⣎⢿⣼⣳⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣾⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡾⣱⣏⣞⡳⣝⢮⣳⢭⡟⣼⢫⡞⣵⢫⣝⡳⣎⢷⡹⣞⢧⣛⢧⢻⡜⣳⠞⡵⣋⢶⡹⣚⢮⡜⢧⣛⡼⣹⣶⠟⢡⣀⠈⢒⠠⣇⢢⣽⣦⣿⣿⣿⣿⠃⠀⠈⢣⠀⢳⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣟⡼⣣⢟⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢿⣻⢯⣟⡳⡽⣎⢷⣛⣾⣳⣿⣿⣿⣿⣿⣿⣿ ⣳⢯⡽⣹⢧⡻⣜⢯⡞⣵⢫⡞⣵⢫⡞⣽⢣⡟⡼⢧⡻⣜⡻⣜⢮⣓⢏⡖⢧⠻⣜⡣⢟⣬⢓⡮⢫⣵⡿⠋⠀⠈⢻⣤⣚⡤⢿⡞⣿⣻⣿⣿⣿⠏⠀⠀⠀⠈⡆⠸⡄⠘⣿⣿⣿⣿⣿⣿⣿⣿⡵⣿⣿⣿⣧⣻⣾⣿⣿⣿⣿⣿⣿⣿⢿⡿⣿⣿⡿⣟⣿⣯⣿⣟⡿⣿⣻⣿⣽⣟⣷⣿⢾⣟⡾⣽⣳⢧⣻⣼⣻⣽⣿⣿⣿⣿⣿⣿⣿⣿ ⢯⡞⣵⢏⡾⣱⢯⡞⡽⣎⢷⡹⣎⢷⡹⣎⢷⡹⣝⢧⡟⣼⡱⢏⡶⢭⡺⣜⢫⣝⡲⢭⣓⢮⡹⣼⡟⠃⠀⠀⠀⣐⡠⠞⣿⡽⢎⡽⣶⢿⣾⢏⡆⠀⠀⠀⠀⠀⠑⠀⣧⠀⢺⣿⣿⣿⣿⣿⣿⡿⠀⣿⣿⣿⣿⣿⣿⣿⡿⣿⣻⣝⡮⣝⡾⣿⣳⣿⣟⣿⣿⣽⣷⣿⣿⣿⣿⣷⣿⣿⣿⣯⣿⣾⣟⣷⣿⣻⣷⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣟⡼⣣⡟⣼⢣⡟⣼⢳⡝⣮⢳⡝⣮⢳⡝⣾⡱⣏⠾⣜⢧⡝⡞⣜⡣⢗⣎⠳⣎⣵⣫⣼⣶⠟⣉⣠⠀⠀⠀⢀⡿⣷⢍⣙⣧⣿⣾⣿⣫⣝⣾⣤⣄⣲⣤⣹⣦⠲⠤⣄⠀⠈⢿⣿⣿⣿⣿⣿⠃⢤⣿⣿⡿⢫⣙⢮⣳⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣻⣷⣿⡿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡷⢯ ⣞⡳⣝⢾⡱⣏⣞⢧⡻⣜⢧⡻⣜⢧⡟⣼⢣⡝⣮⣛⡼⢎⣞⡹⡲⣍⣷⡾⠟⢋⢉⣥⣶⣾⣿⣿⣿⣿⠿⡩⢞⣷⠟⠉⡐⢎⠛⡍⢯⡽⣻⣿⡻⢿⣿⣿⣿⣿⣷⣦⣜⣦⡀⠹⣿⣿⣿⣿⠏⢀⣿⡿⠉⢁⠣⣞⣯⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⣟⣿⣟⣿⡾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⠾⣝⢯ ⣯⣝⢾⣣⢟⡼⣎⡷⣹⢎⣯⢳⡝⣮⡝⣮⢳⡝⢶⡹⣜⣫⣖⣽⠿⢋⡡⢴⠶⣞⡾⣞⣷⣿⣾⣿⣿⣟⡶⣡⣿⠋⠀⠀⢁⠢⠕⡚⢡⢎⡱⠭⣽⠿⣟⢿⡻⣝⣮⣿⣿⣿⣷⡧⣿⣿⣿⡋⢥⣿⡏⣠⣄⣠⣔⣫⢿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⢿⣿⣟⡿⣿⣾⣿⣿⡿⣟⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⢿⣻⣽⣯⢿⡽⣞ ⡷⢮⣳⡝⣮⢳⡝⣾⡱⣏⡞⣧⣛⢶⣽⣮⡷⠿⢛⠛⡫⢍⠋⡅⣎⢱⡙⣎⠿⣜⣻⡽⣿⣾⣿⣿⣿⣿⣿⣿⠏⢀⢠⡐⣠⠉⠒⠬⡁⢎⡰⢿⣬⡻⣜⣯⢷⣻⣿⣿⣿⣿⣿⣷⣉⡟⢦⡑⣮⢯⣴⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢷⣻⡾⣿⣟⣯⡿⣿⣿⣯⣟⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⡷⣯⡿⣽⢯ ⣽⢳⢧⡻⣜⢧⡻⢶⣹⢮⣽⡶⠿⠛⠉⠀⠐⠤⠣⡘⠐⢊⠒⡌⢂⠧⣜⡎⣷⣹⡾⣽⣷⡿⣿⣿⣿⣿⠿⣡⠲⣌⢶⡹⢿⣆⣙⣲⠱⣮⢙⠶⣣⢿⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡦⠥⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣻⢷⣯⣟⣷⣿⣳⣯⢿⡽⣷⣿⣾⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣳⣿⣿⡷⣟⣯⣿ ⣳⢯⡞⣵⣫⢞⣽⣳⠟⠋⠁⠀⠀⠀⠀⠐⠠⠂⢀⠈⠄⢡⠘⡰⣍⡞⣴⢯⡷⣯⣟⣿⡾⣟⡿⡹⣍⢆⡳⢣⡽⣘⣮⡟⣽⣿⣿⢣⠷⣌⣯⣛⣷⣻⢾⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⣶⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣟⣯⢷⡿⣜⢯⢾⣭⢿⡿⣿⡿⣿⣾⢿⣿⡿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣾⣿⣻⣿⣾ ⣟⢮⣽⢺⣵⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣀⠢⡜⢢⡝⢲⣟⡾⣽⣯⣿⣿⣻⡽⣛⢥⢳⡱⢎⢎⣝⢣⡻⣵⣳⡿⣟⣿⣞⣯⢿⣝⡶⣛⡾⣽⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⢳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢯⣟⡾⣞⡯⣝⢿⣫⡗⣾⣯⣿⡽⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣟⣿⣷⣿ ⣻⢞⣼⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣂⠔⣠⠒⣭⠳⡜⣧⣿⣟⣷⣯⢷⣫⢇⡧⣙⢎⢣⠳⡞⡼⣌⢷⣻⢽⣯⢿⡽⣯⣟⡞⡿⣮⣽⢳⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠘⢦⡈⢿⣞⣿⣿⣿⣿⣷⡿⣿⣟⡾⣽⣟⡾⣽⢣⡟⣽⣺⢷⣻⢽⣳⣯⣿⢿⣻⣿⣻⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿ ⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢬⡸⣔⢫⢖⣻⣾⣿⠿⣝⡾⣡⠧⣍⠞⣰⠙⢎⡲⢥⣛⣼⣻⡼⢯⡟⣞⢯⣿⣱⢿⡜⣷⡝⣾⢻⣶⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢳⣄⡆⣹⣜⣿⣿⣿⣿⣿⣿⣿⢿⣟⣿⣳⢏⡷⣭⢗⣯⣛⣷⢻⣾⢯⣿⣻⣽⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢆⡞⠶⣱⣮⣾⣿⣿⢿⡽⣛⡮⢱⡡⣚⡜⡸⢣⢛⣤⡝⣫⣼⠶⡽⢾⡹⡞⡭⢞⠶⢭⢞⡹⣞⡽⣮⢿⣟⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡦⠀⣻⣽⢻⡼⣾⢿⣿⣿⢿⣻⣿⣿⣾⣳⢯⡻⣼⢛⡾⢧⣻⣼⣻⣾⢿⣽⣿⣻⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡒⡌⣞⣬⣿⣿⣿⣿⣿⣯⣿⡟⢧⠘⡅⣶⢩⠞⣱⢛⣼⢲⡝⣣⢟⡽⢞⡹⢻⡱⣛⢮⣙⣧⢫⡷⣭⢷⣯⣟⣾⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣰⣿⣿⣻⣿⣯⣿⣿⣿⣿⣿⣟⣮⢷⡏⣯⢳⣭⢻⡼⣟⣧⣿⣹⣽⣻⣯⣿⢿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠄⠈⠀⠀⠀⡜⣰⣿⣿⣿⣻⣽⣯⢿⣿⣯⠳⡜⢠⢛⡘⢤⡃⣞⡥⢏⡞⡶⣙⢮⣟⡼⡳⣍⣳⣫⡝⣮⣝⣮⣻⡽⢯⣿⣾⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⡷⢧⣿⣿⣿⣿⢯⣟⡾⣽⢻⡯⣟⣳⡛⢾⣳⣽⡽⣞⡿⣿⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠠⡘⡼⣼⣿⣻⣷⢿⣽⣿⣽⣿⣿⣦⠃⡄⠙⠦⠸⠀⡗⡌⢲⡛⣜⠶⣙⡞⣼⣱⢯⣝⣣⢿⣝⣯⣟⣾⣳⣿⣿⢯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡿⣼⣿⣋⢿⡟⣞⣻⣞⡷⣹⢏⡷⣫⢷⣹⣛⣷⣻⣽⣿⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⢠⡉⣥⢻⣽⣷⢿⣷⣯⣿⣿⣿⣿⣿⣿⠂⠄⠡⠒⠐⠈⠳⢐⡚⡡⢜⡭⢻⡴⣛⢶⣭⡞⣧⣟⣯⢿⣭⣟⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡛⢿⠙⣇⣿⢫⡝⣭⣓⣮⠷⣳⢾⣱⢟⣯⣟⣯⣷⣻⣾⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣻⣷⣟⡷⣯⣿⣿ ⠀⠀⣀⣄⣠⠌⢦⡱⣯⣿⣻⣾⡿⣯⣿⣿⣿⣿⣿⣿⡏⠙⠀⠀⠀⡰⣃⡤⢋⣜⣍⣫⣜⣣⣷⣻⣟⣶⡿⣟⣾⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⡉⠁⡫⢜⠣⢯⣜⣦⠳⣬⠷⣽⣚⣷⣞⣳⣾⣷⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢯⣿⣹⣿⣽⣯⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣰⠞⠛⠲⣦⣤⠤⠤⢴⠏⣦⣈⣷⣚⠉⠻⡄⠀⠀ ⠀⠀⠀⣿⣀⠀⠈⠁⠀⠀⠀⢾⡀⢻⡿⠉⠉⣷⡞⠻⣦⠀ ⠀⠀⢀⡿⠁⠀⠀⠀⠀⠀⠀⠈⠛⠛⠷⣤⣴⠿⠿⣠⡟⠀ ⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢦⡶⢻⡄⠀ ⠠⠤⡧⠤⠄⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⠀⠋⢹⡏⠁ ⠀⢀⣿⡤⠄⠘⠿⠁⠀⠠⣞⣻⠄⠀⠀⠻⠏⢀⡈⣽⠛⠃ ⠀⠀⢈⡷⣶⣃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠿⠛⠂⠀ ⠀⠀⠀⠀⠀⠉⠙⠛⠛⠓⠒⠒⠒⠚⠛⠛⠉⠁⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠘⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠀⢀⡾⠁⢠⠖⣄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣁⠀⣾⠃⠀⠨⠄⠘⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⡤⠚⠉⠁⠀⠉⠳⡀⠀⢀⣀⣀⣀⣀⣀⡀ ⠀⠀⠀⠀⠀⢠⠮⣉⡿⠀⠀⠀⠀⠀⠀⣽⠟⣋⠥⠒⠛⢶⣤⡽ ⠀⠀⠀⠀⠀⠸⡂⢰⣰⡂⠀⠀⠀⠀⠀⠀⢙⣧⣦⣔⡾⠟⠋⠀ ⠀⣀⡐⢢⠀⠀⠘⡬⠒⠂⡄⢿⡿⠀⠀⢀⡽⠃⠀⠀⠀⠀⠀⠀ ⠘⢦⣁⢸⠀⠀⢠⠞⠀⣄⣙⣒⣀⣤⡴⣿⡁⠀⠀⢀⡀⠀⠀⠀ ⠀⠀⠀⠈⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠘⣻⣧⠀⢰⠃⠼⢄⠀⠀ ⠀⠀⠀⠀⠀⢀⡷⠠⠞⠃⠀⠀⠀⠐⠒⠦⢿⡀⠑⠒⠂⠋⠀⠀ ⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⢹⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢀⢾⠟⠉⢷⡀⢸⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⢸⡵⢀⣟⣸⣇⡼⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠛⠓⠒⠒⠒⠚⠛⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⢠⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣀⢤⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⢀⢠⣰⠀⢼⡂⢹⢠⡜⡄⣀⣽⠀⠀⢀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣀⠖⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡠⢰⡈⢧⣄⢀⠐⠆⠀⠠⡆⢶⣄⣤⣸⡄⢸⣉⡼⡽⡆⡟⣷⢫⢸⡇⣧⡃⣿⢼⢹⢸⠄⣴⣸⡠⢀⠀⡀⠠⠀⠀⠁⡀⢀⠂⡌⣤⣻⡑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢈⢵⡀⢳⡀⣮⣼⡄⣸⣷⣮⢿⡞⣾⢳⢽⣟⣛⣿⣜⣿⠘⣰⢹⠰⣮⣇⢻⣷⣿⢸⢨⢼⠸⣃⢻⢧⢾⢠⡷⠀⢠⠀⢦⣴⠉⡸⣸⢽⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢔⠙⣷⣆⢣⢸⣻⡽⡝⢳⣮⠈⣿⣮⢡⠀⣅⢋⣧⡙⢿⣇⡟⣇⡧⣿⠉⡶⣿⠻⡟⣏⡌⡰⡽⣾⡞⣼⢸⠇⣟⣿⢠⣿⣿⠜⣹⡏⣼⢿⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡠⣄⠋⢜⣿⣗⠻⡄⠿⡻⡦⠈⣧⢹⢿⡻⢆⣹⣿⣼⣏⣈⣿⣷⣏⣧⣿⣿⣷⡟⢲⣇⣧⣷⣿⣷⢷⢼⢿⡏⣔⣟⣅⡎⣌⡾⣾⣿⣽⣯⣾⣛⡧⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠄⠀⠨⣓⢝⢺⡋⡛⢿⢓⡌⣮⠻⢅⠹⢺⣿⣷⡪⢏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⣻⣿⣷⣿⣿⣱⡟⣿⣾⡱⣽⣞⣏⣴⠏⡾⣟⡽⣷⣿⣟⣿⣿⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠰⢄⡪⠑⢅⡓⠝⣠⣕⣝⢯⣯⣻⣗⣧⣹⣿⣷⣿⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣳⡏⣷⣷⣯⡿⣯⣶⣾⣾⢁⣹⢙⢅⣾⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠒⢢⣤⣀⠻⣳⣢⠬⡒⠴⣌⣺⢽⡻⢷⣿⣞⢿⣿⣾⣿⣏⣷⣾⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣻⣽⣿⣟⣿⣿⣿⣿⣿⡿⣿⢣⣮⢴⣾⡋⣻⣿⣽⣿⣟⠤⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠤⣀⠠⠙⠟⣾⡽⢿⣬⢑⠲⣽⣳⣽⡺⢿⣿⣷⣿⣟⢿⣿⣻⣷⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡽⣿⣿⣿⣿⣿⡿⣿⡯⢷⣯⣽⣿⣿⣷⡽⢻⣁⣺⡿⣉⣤⡤⠤⠀⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢂⣻⣦⣶⣅⠈⠪⡘⣷⣜⢪⣦⣽⢿⢷⣏⣻⡿⣿⣄⠿⣿⢿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⡳⢗⣽⣾⣷⣿⡟⡑⡐⡡⣪⠴⢿⣁⢀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⡂⠤⣤⡤⠖⠉⠉⠷⢄⠱⣿⣿⣽⣟⡽⣮⢷⣿⢦⠻⣿⣿⣮⣾⣿⣿⣿⣼⣯⣿⡿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣏⣿⣿⣿⢟⣿⣿⣗⡔⡩⢁⢐⣄⡻⢆⠒⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢏⠑⠓⢄⠀⠈⢳⣌⣾⠿⣻⣷⡘⢽⣻⣾⣳⣾⣯⡞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⢟⣽⣿⣿⣿⣿⣿⣻⣿⠁⡀⠐⢹⣡⣰⣞⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡀⠀⠀⠀⠐⠈⠀⠀ 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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⢀⡔⣡⣾⢏⣽⣿⣽⣿⣷⣿⡽⣫⣾⣷⣾⣟⣟⢥⢔⣥⡷⠯⡞⠱⢲⡍⢀⡠⠀⠓⣀⣙⣤⡶⠔⡙⠻⡾⢷⣿⢿⣳⡿⢧⣿⣩⣾⣽⣭⣗⠧⣽⠻⢯⣭⣟⠉⠒⠤⢍⣳⣾⣯⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡫⣺⣿⡏⡿⣿⣿⣿⣿⣾⢫⣵⣿⡿⠷⠊⠁⣀⣴⣿⠷⠎⣛⠡⠚⡁⡁⠀⡀⢄⠈⢔⣟⢅⡂⠝⣊⡥⣾⢿⡿⢿⡿⣹⣿⣾⣿⣯⣿⣿⢻⡗⣲⠷⣝⣏⣛⡓⠶⣤⢀⣥⢽⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣻⡕⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⣴⡵⢳⣶⣿⣿⣿⣟⣿⣋⣮⠟⣃⣤⢴⣞⣫⠟⡡⠲⣐⣩⠔⣒⠩⠐⠐⠊⠐⡠⢊⣁⠄⣡⠂⢈⣤⣮⠵⣿⢿⣿⣷⣿⣿⣷⣿⣿⡿⣭⢿⠻⡢⠭⢮⠽⣎⢍⡒⠴⢍⣑⢯⣿⡿⣿⣿⣶⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⡿⣳⢮⣧⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠔⢍⣴⣵⡯⣷⣿⣿⣯⣾⣿⠟⣵⡾⡿⡫⢋⣫⡴⢛⣥⠾⠋⡁⠉⣀⠄⡪⠁⠀⡠⠔⠉⡡⠊⡥⠖⠹⣊⣴⣟⣲⣿⣻⣿⣿⣿⣿⣿⣿⣟⣿⣵⡣⣙⢗⠭⣿⢤⡠⡙⢌⠐⠌⠛⢾⣿⣟⡽⣿⣿⣷⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣷⡛⠷⣤⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢄⠎⣽⣾⣟⠏⣿⢿⣿⣟⣿⣁⣾⢿⣫⣖⡫⢯⡳⣪⣿⡨⠮⢋⠔⢪⠖⢉⣤⠶⡉⠀⠠⠊⠤⠊⣠⠔⢋⡵⢫⢺⣟⣼⣿⣿⣿⣿⣿⣿⡽⣟⢿⣲⣜⢗⡺⠷⡆⠙⣢⣈⠆⠑⢦⣠⣐⠮⢁⣛⢾⣿⢷⡾⣷⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⡻⣆⢀⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡫⣢⠌⣾⣫⣿⢿⣿⢟⣫⣾⢽⠋⣩⣾⢗⡼⣟⣫⠴⢞⡡⢂⠕⣪⡼⠋⠈⡄⢊⡠⠀⡠⠞⣩⠴⠫⠒⣱⣿⢿⣟⣿⣿⣿⣿⣿⣿⣿⣷⣙⢿⣎⠹⡻⣶⢾⢷⠀⠙⢌⢳⣆⡨⢋⠿⡟⣟⡧⣝⢿⣿⣭⣟⡿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣮⡣⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠀⠴⣫⣞⢵⡛⣽⢎⣽⠾⣝⣿⣾⡿⢉⣾⢟⣵⣮⣵⠿⣉⣡⢞⣕⡓⡋⢁⣠⡶⢢⠐⠁⠐⠀⡒⠛⡂⡠⢇⡪⣴⣫⣽⣸⡟⣟⣿⣿⣿⣿⢫⡜⢿⡱⡘⡵⡌⠩⡙⠷⣌⣀⡄⠑⠿⣮⣶⣝⢎⣛⡿⡿⣿⣞⣽⣶⣽⢿⣿⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢿⠑⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡰⠊⠴⢻⣫⣿⠷⣋⢶⣿⡿⠋⣼⣱⢫⣷⣿⣋⡾⡛⢉⣥⣷⣛⠤⡫⣴⣟⣩⠞⡁⠐⡈⠊⠝⠢⢉⠴⣹⢿⡔⣝⡷⣻⣿⢿⣽⢿⣿⣿⢸⢹⡞⡧⣣⡏⠾⣝⠦⠻⣶⡈⣑⠬⡱⡦⡈⢯⣟⢷⣯⣛⢷⣬⣟⣿⣿⢿⣿⡻⣿⣿⣾⣿⣿⢿⣿⣿⣿⣿⣽⢿⣿⣿⣿⣯⣷⠳⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠾⢛⣭⠯⡢⣼⢃⣾⠏⠥⣭⡶⣡⡾⢱⣵⣻⠟⣵⠿⢛⡡⣲⣾⢕⠝⢉⣥⢦⡴⠋⣀⡤⠚⢈⢜⣥⣥⡞⢎⣼⣿⢱⢨⡷⣿⣾⣿⣿⣾⣧⣿⣼⣠⡿⡞⡼⣟⢧⣸⡉⢦⣳⣞⢷⣜⣎⠻⣷⣝⣿⣯⣿⣿⣞⣿⣿⣿⣿⢿⣿⣿⣽⣿⣿⣟⣿⣿⣿⡮⣳⣟⣿⣿⣏⢯⣑⢦⠀⠐⠀⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⢒⢶⢟⡩⢲⠟⣡⠊⣠⠏⡕⠋⡴⣛⡵⣛⣼⢓⣿⣿⣝⢝⡨⢗⠕⣠⣶⣿⠇⡡⢄⡜⢁⡠⢺⣷⣿⣿⣣⣿⣧⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣳⣽⡟⣿⣿⣿⣟⣿⣿⣾⣭⡻⣿⣿⣿⣿⣿⣯⡿⣿⣿⡜⣷⡻⡿⣟⣿⣧⣿⢾⣿⣯⣿⣿⣽⢿⡮⢃⡀⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢓⣵⠟⡩⠴⢮⡶⢋⠁⢐⡴⣼⠟⣫⡾⣋⣴⣿⣩⠔⡢⢹⣾⣿⣺⢿⠟⠁⣝⣵⡿⣠⣾⡱⡇⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢿⣧⢿⣟⣿⡶⢿⣷⣿⣿⣮⣻⣿⣿⣿⣿⣿⢯⣿⣟⣟⢿⣾⢿⡙⣿⢿⣷⣯⣟⣿⣿⣿⣿⣛⣦⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡩⢔⡫⣠⠖⡪⣗⡥⣚⠡⠞⡰⠊⡠⢞⡥⢊⡴⡿⠋⣠⣺⡾⣿⣿⢯⣿⣳⡖⣾⡻⡹⡶⢣⡿⣱⢡⡇⢚⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣯⢻⣧⢻⣞⣿⣮⡻⣿⣿⣿⣿⣿⣿⣿⣿⣯⢿⣟⢯⣿⣯⢻⣧⣙⠤⡓⢽⡿⣿⣿⣿⣿⣿⣿⣭⡳⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣨⣮⣞⢅⡾⠚⠉⢍⡠⠜⢐⢀⢡⢾⠋⠔⠁⢠⠆⣾⠿⢋⣵⠟⣡⣿⣇⡟⣼⢟⠞⡝⡡⡰⣡⢣⣿⠚⡼⣻⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣳⣿⣎⢿⣿⣿⡻⡿⣟⣿⣻⣿⣿⣿⣿⣿⣿⣯⢷⣫⣦⠉⢫⢟⣶⣝⣢⡙⠻⢿⣿⣿⣿⣷⡻⠙⠦⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣞⣡⢔⡷⠒⡠⣰⢖⣉⡠⠋⡴⠍⡠⠐⢁⠴⢚⡕⠊⢁⡴⠟⣡⡾⢋⣾⣫⡾⣣⢟⢎⠎⡐⣱⣣⡟⡼⣽⢃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣾⣎⢟⢿⣿⣿⣿⣿⣿⣿⣿⣯⢿⣿⣦⡛⢷⡛⣤⡹⠳⣍⢿⣫⣻⣮⣕⢯⣿⣿⣟⣿⣿⣣⠒⠢⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⢰⢖⡯⠔⣛⡋⢼⡶⠛⠀⠍⣊⠜⡠⢂⡌⢘⢉⡠⠊⡡⢓⣛⡣⢮⣾⠿⣫⡾⣷⣫⢊⢤⣿⣷⣿⢳⣱⣯⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣮⣿⣿⣿⣻⣿⣿⣿⣿⡽⢿⣯⣿⣕⠻⢟⢦⣙⠎⠺⣷⢎⡙⠮⢷⣵⠿⣿⢿⣿⣿⣿⣟⡾⣇⡡⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡭⣵⡾⢩⣶⡥⠁⡢⠛⠽⠟⠁⡁⢀⡤⠖⠁⡊⠤⣪⢲⡿⢋⠏⣞⣭⡾⣡⠿⢋⡡⣣⣿⣽⣿⡿⣼⣿⣿⣿⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣟⣿⣿⣿⣿⣿⣿⣿⣷⣻⡵⣙⢿⣅⠫⠹⢷⣍⡪⢕⢻⠻⣶⡹⢷⣟⣿⣿⣿⣿⣿⣿⡅⠡⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠠⠚⢁⡾⢋⡴⢇⡠⢰⢏⣩⣗⡹⢶⠊⡨⠀⢠⠕⣊⡴⠞⣡⠉⡰⢃⡸⡻⢫⠖⠉⡰⣳⢫⣱⣷⡷⣿⣿⢻⣿⢼⣟⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣯⢷⣻⢮⣕⣟⣿⣦⡳⣝⠫⢗⣺⢾⢭⣼⢭⣟⣿⣿⣿⣿⣿⣿⣿⣧⣉⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢊⣊⣴⢏⣴⠯⢜⡵⡾⠯⡛⣏⡩⠕⠠⠖⡡⠚⢁⡦⢊⣷⠚⠑⡮⡫⣔⣡⣪⢾⣵⢏⣟⢯⣿⢯⣿⡗⣼⣯⣿⡿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣯⣿⣿⣿⣿⡹⣿⣽⣾⣯⣿⣽⠺⣿⣮⣛⢿⣷⣽⣿⣽⣿⣻⣿⣿⣿⣿⣻⣯⣮⡓⠄⠂ ⠀⠀⠀⠀⠀⠐⢋⢝⣡⣤⢖⡞⣱⣛⠅⣲⡾⠛⢁⣀⠔⢊⡋⠤⢚⣕⡺⢃⢔⣵⡫⠕⢚⣵⣵⠟⣋⣴⢟⣫⢞⣏⣿⠫⣡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣟⣿⣿⣿⣿⣿⣾⣽⣖⣿⣷⣾⣿⣺⢟⣿⣷⣽⠿⣷⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠟⠛⠛⠉⠉⠉⠁⠀⠀⠈⠉⠉⠙⠛⠿⢶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀ ⠀⠀⠀⣠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠹⣧⡀⠀⠀⠀⡏⠉⠙⠋⢹⡆ ⠀⠀⢠⡿⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠚⠉⠉⠛⠿⣦⡀⠀⠸⣷⡀⠀⠀⠹⣄⠀⠠⡹⠃ ⠀⢀⣿⠃⠀⠀⠀⠀⣠⣶⠾⠟⠛⠉⠉⠛⠿⣶⣄⠀⠀⠀⠀⣰⠃⢀⣠⣤⣄⠀⠈⢻⣦⠀⢻⣧⠀⠀⠀⠈⠓⠋⠀⠀ ⠀⢸⣿⠀⠀⠀⣠⣾⠋⠁⠀⠀⢀⣠⣤⣤⣤⣈⠙⣷⣄⠀⢠⣏⣶⣿⣿⣿⣿⣿⣦⠀⢻⣧⠘⣿⢀⢸⡛⠛⢲⠀⠀⠀ ⠀⣾⡇⠀⠀⢠⡿⠁⠀⠀⣠⣾⡿⢿⣿⣿⣿⣿⣷⣌⢿⣆⢸⣿⡋⠉⢉⣿⣿⣿⣿⣧⠈⣿⠀⣿⣿⠀⠹⠶⠋⠀⠀⠀ ⠈⡟⣿⠀⠀⢸⠇⠀⢀⣼⣄⠈⠀⣸⣿⣿⣿⣿⣿⣿⡎⣿⣿⣿⣿⣶⣿⣻⣿⣿⣿⣿⣤⣿⢀⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⢷⢹⡆⠀⢸⡄⠀⣾⣿⣿⣿⣿⣿⣩⣿⣿⣿⣿⣿⣇⣿⢹⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⠏⣸⢧⠏⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⣇⢳⡀⠈⢧⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢠⢁⡞⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⢎⠃⠀⠈⠳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⠟⠁⠀⠀⠈⠻⣿⣿⣿⣿⡿⠟⠁⠀⣠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠳⣄⠀⠀⠈⠙⡻⠿⢿⣿⡿⠿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠃⣀⡀⣰⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣀⡤⠬⣷⣄⡲⣤⣈⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡴⢛⡵⠚⠁⠀⢀⣠⣤⣀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠸⣇⠀⠀⠀⢻⣿⠒⠭⣟⣷⢶⣤⣤⣤⣤⣤⣤⣤⣤⣶⢾⣟⠯⠗⠊⠁⠀⠀⠀⣾⠟⠁⠀⢘⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢹⣧⠀⠀⠈⣿⡄⠀⠀⠈⠉⠛⠛⠛⠛⠛⠒⠋⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⢠⣿⠏⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⣿⠇⠀⠀⠙⠛⠛⠒⠒⠛⠛⠛⠻⠿⢷⡢⣤⣔⡶⠿⠟⠛⠛⠛⠻⠿⠽⠟⠁⠀⠀⢺⡿⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⢰⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣾⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡀⠀⠀⠀⠀⠀ ⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠻⢿⣿⠒⠲⠛⠙⠲⠦⢼⣿⡿⠟⠛⠃⠀⠀⠀⠀⠀⠀⠀⢸⣇⡇⠀⠀⠀⠀⠀ ⠀⠀⠹⠿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⡻⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠻⢦⣀⠀⠀⠀⠀⠀⠀⢀⡾⡿⠀⠀⠀⠀⠀⠀⠘⣿⣆⠀⠀⠀⠀⠀⠀⢀⣠⣴⢯⠞⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠛⠳⠶⠶⠶⣖⡿⠚⠁⠀⠀⠀⠀⠀⠀⠀⠘⠮⣷⣶⡤⡤⠴⠾⠟⠋⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉⠉⠈⠈⠈⠉⠉⠉⠉⠉⠉⠉⠉⠙⠻⣄⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⣄⠀⠀⢀⠀⢀⣀⣤⠄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣉⣩⣤⠴⠶⠶⠒⠛⠛⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠤⠶⠒⠚⠋⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣾⡍⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣫⣭⣷⠶⢶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠶⠶⠖⠚⠛⠛⣹⠏⠀⠀⠀⠀⠀⠀⠀⠀⠴⠛⠛⠉⡁⠀⠀⠙⠻⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡷⠷⢿⣦⣤⣈⡙⢿⣿⢆⣴⣤⡄⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⣤⡀⣸⡄⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣿⣟⣩⣤⣴⣤⣌⣿⣿⣿⣦⣹⣿⢁⣿⣿⣄⣀⡀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⣿⠋⠻⢿⡁⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠿⠛⢦⣽⣿⣿⢻⣿⣿⣿⣿⠋⠁⠘⣿⣿⣿⣿⣿⣿⣼⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⠁⠀⠀⠙⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠿⣿⣯⣼⣿⡿⠟⠃⠀⠀⠀⣿⣿⣿⣿⣿⡛⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣧⣴⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⠟⠃⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⢁⣀⣀⣀⣀⣀⣠⣀⣀⢀⢀⢀ ⠀⠀⢿⠿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠙⠛⠛⠙⢻⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⡇⠀⠘⠃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡟⢿⣿⣆⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡼⠁⢀⣀⡀⠀⠀⠀⣦⣄⠀⣠⡄⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣷⣬⢻⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⣰⣿⡿⠿⠦⢤⣴⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠒⣿⣿⣿⡿⠟⠹⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⠸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡖⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡿⣾⣿⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣆⣀⣀⣤⣴⣶⣶⣾⣿⣷⣦⣴⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡇⣿⣿⡛⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢾⡟⠛⠛⠻⠛⠛⠛⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠓⢁⣬⣿⠇⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⢰⡿⣻⠇⠀⠀⠀⠀⠀⣠⣶⣶⣶⣶⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢐⣯⠞⠁⠀⠀⠀⠀⠀⠀⣄⠱⣄⠀⠀⠀⠀⠸⡧⠟⠆⠀⠀⠀⠀⠘⠿⢿⠿⠿⣿⡿⣿⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡈⠂⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⡄⠀⠀⠑⠄⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣦⣦⣼⡏⠳⣜⢿⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢠⣷⣦⣤⣀⣀⣀⣴⣿⣿⣿⣿⣿⡿⠻⠆⠸⣎⣧⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⣠⡄⠀⣿⢹⡇⢸⡀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣤⡶⠁⣠⣴⣾⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣴⣿⣿⣴⣿⠿⠋⣁⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣰⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⣠⣾⣿⡿⠟⠋⠉⠀⣀⣀⣀⣨⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⣤⣤⣴⠂ ⠈⠉⠁⠀⠀⣀⣴⣾⣿⣿⡿⠟⠛⠉⠉⠉⠉⠉⠛⠻⠿⠿⠿⠿⠿⠿⠟⠋⠁⠀ ⠀⠀⠀⢀⣴⣿⣿⣿⡿⠁⠀⢀⣀⣤⣤⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣾⣿⣿⣿⡿⠁⢀⣴⣿⠋⠉⠉⠉⠉⠛⣿⣿⣶⣤⣤⣤⣤⣶⠖⠀⠀⠀ ⠀⠀⢸⣿⣿⣿⣿⡇⢀⣿⣿⣇⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀ ⠀⠀⠸⣿⣿⣿⣿⡇⠈⢿⣿⣿⠇⠀⠀⠀⠀⠀⢠⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢿⣿⣿⣿⣷⡀⠀⠉⠉⠀⠀⠀⠀⠀⢀⣾⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠙⢿⣿⣿⣷⣄⡀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣋⣠⡤⠄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⣠⠤⠔⠒⠒⠒⠒⠒⠢⠤⢤⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⠴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⣄⠀⠀⠀(Ignore for z00phile rights, Like for YIPPEE) ⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠦⠀ ⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧ ⠀⡇⠀⠀⠀⢀⡶⠛⣿⣷⡄⠀⠀⠀⣰⣿⠛⢿⣷⡄⠀⠀⠘⣿⠀ ⠀⡇⠀⠀⠀⢸⣷⣶⣿⣿⡇⠀⠀⠀⢻⣿⣶⣿⣿⣿⠀⠀⠀⢸⠀ ⠀⡇⠀⠀⠀⠈⠛⠻⠿⠟⠁⠀⠀⠀⠈⠛⠻⠿⠛⠁⠀⠀⠀⢸⠀ ⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠁ ⠀⠀⠈⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣚⡁⠀⠀ ⠀⠀⠀⠀⠈⠙⠒⢢⡤⠤⠤⠤⠤⠤⠖⠒⠒⠋⠉⠉⠈⢙⢨⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹ ⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⣤⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⢠⣿⠀⠀⠀⢸⠀⠀⣿⠀⠀⠀⣸ ⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⢸⠘⡆⠀⠀⢸⣀⡰⠋⣆⠀⣠⠇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠤⠤⠼⠀⠘⠤⠴⠃⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣶⣦⠀⠀ ⠀⠀⣠⣤⣤⣄⣀⣾⣿⠟⠛⠻⢿⣷⠀ ⢰⣿⡿⠛⠙⠻⣿⣿⠁⠀⠀⠀⣶⢿⡇ ⢿⣿⣇⠀⠀⠀⠈⠏⠀⠀⠀ text here ⠀⠻⣿⣷⣦⣤⣀⠀⠀⠀⠀⣾⡿⠃⠀ ⠀⠀⠀⠀⠉⠉⠻⣿⣄⣴⣿⠟⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⡿⠟⠁⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢀⣠⠤⣶⣶⣤⣀⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠟⢦⣤⡄⠒⠋⠁⠀⠀⢻⡝⢧⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⢿⡏⠀⢀⡀⠀⠀⠀⠀⠀⢷⢸⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠘⠃⠀⠀⠀⠀⠀⣸⣸⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⠁⠉⢳⣴⢻⣽⣟⢦⠘⠃⠀⠀⠀⠀⠀⠀⠀⢀⡿⠃⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠋⠐⠉⠙⣿⢿⡇⠀⠀⣀⡀⠀⠀⢀⡴⣿⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢾⣄⠀⠀⠀⠀⠀⣰⠟⣽⠁⠀⣀⠓⠃⠀⢠⡞⣱⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣾⣿⣧⣦⣤⣤⡔⢋⠈⠁⠀⠀⠀⠀⠀⠀⠏⡼⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠀⠀⠀⢸⣻⣿⣿⣯⠟⠋⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣞⣳⠀⠀⠀⠀⠀⠙⠛⠉⠀⠀⠀⢠⡀⢠⡄⠀⢀⡾⡯⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣡⡾⢋⡼⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠉⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⣸⢸⢠⡆⠀⠀⠀⠀⠀⠰⠞⠁⠰⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⡽⠛⠘⢿⣥⣤⣤⣤⣀⠀⠤⠠⢤⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣠⠶⣿⡛⠁⠀⠉⠉⠉⠙⣿⣦⢠⣰⠚⣋⣉⣁⣀⣤⠤⣶⣫⡤⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⠓⠚⠿⠯⠭⠭⠭⠤⠼⠏⢹⢾⠿⠿⠟⠓⠒⠚⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⢸⣼⠀⠀⠀⠸⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡄⢠⡏⠀⠘⣿⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡞⣤⠏⠀⠀⠀⡿⠀⠀⠀⢴⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣾⡾⠃⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣸⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⡶⡦⢤⣀⡴⠋⣥⣍⡻⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⢿⠀⠠⣶⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⣥⣾⣷⣷⣶⡝⠂⠈⠀⠘⠓⢻⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⠘⣆⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢸⣸⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⣔⢸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠘⣆⠹⣆⠀⢠⡆⠀⢀⡀⠈⠁⠀⢸⠐⣿⣿⡀⠀⠀⠀⠀⢀⢠⣶⣟⠟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⠫⢘⢧⣼⣷⣂⡈⠉⠀⢀⣀⡌⢧⠻⣿⣷⡀⠀⠀⠀⠨⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⢉⣿⡟⠿⠥⣶⣟⣉⣁⣠⡤⠴⠖⠙⠟⣴⣀⠀⣽⡿⣳⠇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡴⠃⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠦⢤⣈⣨⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⢀⣀⠀⠀⠀ ⠀⣿⣁⢈⠉⠉⣉⣉⡧⠀⠀⣼⠋⠁⠀⠘⠢⡾⠋⠉⠉⢳⠀ ⠐⠛⢻⣯⠀⢠⠋⠉⠀⠀⢸⣷⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡇ ⠀⠀⢸⡿⠀⢸⠀⠀⠀⠀⠘⣿⡆⠀⠀⠀⠀⠀⠀⠀⢀⠜⠀ ⢴⣯⣉⣁⣀⡈⠒⠒⡀⠀⠀⠈⠻⣧⡀⠀⠀⠀⢀⡠⠊⠀⠀ ⠈⠉⠉⠉⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⠉⠢⡠⠒⠁⠀⠀⠀⠀ ⢰⣖⠒⡀⠀⢠⣴⠒⡂⢀⣀⣀⡀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠙⣦⠈⢄⡾⠃⡜⣴⠟⢉⢥⡈⢢⢶⣯⢀⠁⠀⢰⡯⠉⡇ ⠀⠀⠈⢿⡬⢁⠌⢠⡿⠁⠆⠈⡇⢸⣿⣇⢸⠀⠀⢸⡇⠀⡇ ⠀⠀⠀⢸⡯⢻⠀⢸⡇⠀⡀⢸⠇⢸⣿⠃⢈⠀⠀⣿⡀⠀⡇ ⠀⠀⠀⣾⠁⠘⠀⢸⣧⠀⠈⠁⢀⠎⣿⠀⢺⠀⣰⡿⠀⢠⠁ ⠀⠀⠀⠛⠒⠃⠀⠈⠛⠳⠶⠖⠋⠀⢿⣄⡀⠉⠁⠀⡠⠋⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⣤⠟⡇⠀⠀⠀⠀⠀⠀⣠⣶⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣀⣼⣿⡃⠀⠀⢀⡾⡃⠀⣿⠀⠀⠀⠀⢠⡼⠋⢸⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠹⠟⠋⠁⣰⡟⣠⡇⠀⢻⡀⠀⢀⣴⠏⢀⡀⠘⣷⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣰⠟⣶⣿⡇⠠⠸⣧⣠⠟⠁⢀⣾⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀ ⠐⣧⡀⠀⠀⠀⣸⠏⢾⠿⣿⡇⠀⠀⠙⠃⠀⢠⣾⣿⡇⠀⣿⡆⠀⠀⢀⣀⠀⠀ ⠀⠀⠙⢦⣀⡾⢿⣶⣮⣅⡀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠅⠀⢹⣇⣠⠶⠛⠛⠀⠀ ⠀⢠⣄⣀⣹⡇⠘⣿⣿⣿⠿⠆⠀⠒⢻⣾⣶⣶⣤⡀⠀⣠⣼⡟⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣸⣧⠀⠀⠀⠀⠰⡆⠀⠀⠈⠿⣿⡿⡟⠻⠞⢯⣼⣇⣀⠀⠀⠀⠀⠀ ⠀⠠⡾⠛⠁⠘⠷⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠁⠀⠉⠛⠶⣤⣀⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⣿⣶⣶⣶⣶⣶⣶⠶⠛⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠙⠛⠛⠛⢻⣇⠀⠀⠀⠀⠉⠳⣦⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⡆⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⡇⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⢸⠇⠀⠀⠀⣷⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⣤⠴⠞⠛⠛⡆⠀⠀⠀⢸⣆⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣾⣋⢀⣀⣠⣴⣾⠇⠀⠀⣰⠟⠙⠶⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠉⠉⢁⡴⠋⠀⠀⣠⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣤⣤⡴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠻⠟⢛⣛⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣳ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⣉⡄⠀⣀⡀⠨⣙⣏⣉⣽⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡿⣿⢿⣿⣿⣿⡿⣟⣿⣯⣿⣷⣿⢾⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣒⡛⢫⠤⣠⢤⣤⣤⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣻⣯⣿⢿⣿⢯⣿⣯⣿⣿⣻⣞⡷⣿⣽⣻⡽ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢮⣭⣉⡓⠺⠊⢉⠓⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡽⣿⣻⢿⡿⣯⢿⣷⢯⡷⣯⣟⠷⣯⡗⡿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⣩⣿⣿⢿⣷⣄⡙⢮⠭⡁⢠⣬⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣽⣯⢿⣽⡿⣾⣻⣽⣳⣞⣟⡧⣟⡽ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⡴⠹⢿⣿⣀⣿⣿⣯⣍⢛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣾⡿⣯⣿⡽⣟⡾⣵⢫⣾⡱⢯⡜ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⢀⣞⣰⣀⣾⡷⠘⣿⣿⣟⣩⠙⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣻⢷⣟⣿⢯⡷⣏⡟⣶⡹⢇⡞ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⣰⢯⣾⣿⣿⡿⠁⠀⠀⠼⢿⣿⠥⢤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣟⡾⣟⣯⢿⡼⣹⢶⡹⢣⠞ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣴⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠘⠺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⢿⡽⣯⣟⢾⡱⣏⠵⣋⠎ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢬⡙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣽⣳⢯⣏⡗⣎⠳⡌⠆ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣷⢻⡗⣮⡝⣬⢳⠉⡎ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡿⣯⢷⣫⢗⡭⢎⢧⡙ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣶⡆⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⣀⢛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣟⣯⣟⣧⡟⡼⣉⢆⠣ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠹⣿⢿⡟⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡂⠭⢊⠻⡹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣷⣻⣞⡽⣲⢍⡎⢇ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⢻⠆⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢡⠒⠐⢀⠀⠠⠐⡆⢯⡹⡹⢛⡯⢭⡹⣿⣿⣿⣿⣿⣿⣿⡿⣾⢯⣷⣻⣜⡳⢎⡜⠦ ⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠻⢷⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⡄⠠⢎⢦⡹⢄⡄⣌⣩⣝⠾⣡⢃⠡⠃⡘⢧⠿⣽⣻⣿⣿⣿⣿⣿⣽⣿⣟⣷⣻⡼⣝⢮⡙⡖ ⣿⣿⣿⣿⣿⣿⣿⠃⣾⣷⣄⣀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢉⣩⣁⣳⣶⣦⣤⣤⣈⣥⢛⡞⣶⣿⣜⣫⢝⣶⣫⢞⣡⣀⣒⣀⡴⣨⡽⣎⣿⣿⣿⣿⣿⣿⣿⣿⢾⣯⢷⣻⡜⣮⢱⢣ ⣿⣿⣿⣿⣿⣿⣿⡇⣿⢻⠇⠛⢧⠀⠀⠁⠀⠀⠀⠾⠛⣉⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣿⣯⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣯⣿⢾⣯⢷⣻⣼⢣⢧ ⣿⣿⣿⣿⣿⣿⣿⣿⡌⣿⠀⣶⣿⠃⠀⠂⠀⠀⢰⣶⡾⠟⠫⣈⢿⡿⠟⣨⣿⣿⣿⢿⡆⠀⠈⣿⣿⣿⣿⣿⡟⢹⣯⣿⡟⢻⣿⣿⣿⣿⣿⣿⣿⣿⡏⢸⣿⢯⣿⢯⡿⣟⡾⣏⣞ ⣿⣿⣿⣿⣿⣿⣿⣿⣷⠸⡀⢿⡃⠀⠀⠁⠀⠀⠀⠀⠀⠀⣀⣉⣛⠶⣿⣿⣿⣿⠟⣿⠃⠀⢠⣿⣿⡏⢿⣯⣭⠷⣭⣭⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣃⣿⣿⣯⣟⣯⡿⣽⣻⢞⡵ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠱⡈⠹⡄⠀⡁⠀⠀⠀⠀⠀⠈⠙⠋⣙⣹⣿⣿⡿⠋⠀⠀⠀⠀⢺⣿⣿⣿⣆⢻⣿⣻⣶⣷⣿⣿⣿⡿⣟⣿⣿⣿⣿⣿⣿⣿⣟⣾⢯⡿⣽⡷⣯⢿⣹ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⢲⡾⠀⡂⠀⠀⠀⠀⠀⠀⠀⠀⠜⡹⠟⠉⠀⣀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣞⡽⢿⣿⡿⢿⡟⢶⣡⣿⣿⣿⣿⣿⣿⣿⣳⣯⢿⣯⣟⣷⣻⣽⡳⣏ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⡀⣀⡆⡇⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⢀⣠⣾⣿⠀⠀⠀⠀⢠⣿⣿⣿⣿⡏⠱⠂⠄⣙⢣⣟⣮⣿⣿⣿⣿⣿⣿⣿⣟⣷⣻⣟⡾⣽⣞⡷⣯⡽⣳ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠏⠀⠀⠀⠀⢈⣿⣿⣿⣿⣍⠣⡉⠴⣌⢷⣾⣻⣿⣿⣿⣿⣿⣿⡿⣞⣯⢷⣯⡟⣷⣫⡽⢶⡻⣵ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⡑⢺⡿⢏⢀⣠⣀⠀⣦⣀⢻⣿⣿⣿⣿⣣⣝⡳⣎⣿⣽⣿⣿⣿⣿⣿⣿⣟⣿⡽⣯⣟⢶⡻⣵⢣⡟⣯⢳⢧ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠁⢰⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣟⢢⣏⣷⢿⣭⣻⢷⣿⣿⣿⣿⣽⣾⣳⣟⣷⣫⢯⡷⣭⢳⡝⣮⢛⡼ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠷⣞⡿⣎⡶⣿⣿⣿⣿⣿⣿⣞⡷⣟⣾⡳⣏⡷⣹⢎⡷⣙⢦⣋⠖ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣺⣽⢳⢏⣾⣿⣿⣿⡍⣉⣛⣻⡿⢿⣾⣽⣝⣳⣝⢮⠳⣍⠶⣉⠞ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⣧⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⡿⠿⠾⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣞⢿⣺⣿⣿⣿⣿⣿⡉⢿⣿⡙⠲⣤⣈⡙⠻⠮⣽⣙⡌⢣⠱⣊ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⢸⣆⠠⡀⠀⠀⠀⠀⠘⠉⠁⠀⠀⢀⣠⣶⣿⢿⡛⣴⣿⣻⢻⡽⣷⢯⣞⣿⣿⣷⣿⣿⣿⣿⣿⣿⣡⡄⠀⢢⠉⠱⣄⠀⠉⠈⠐⠃⠄ ⣿⣿⣿⣿⢿⣻⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⢀⠹⣄⠙⣄⡀⠀⠀⠜⢢⠳⣾⣿⣿⣿⣿⣿⣷⣯⡷⢭⡷⣯⢿⣯⣿⢾⣯⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆⠀⠀⠉⠢⠈⢦⡀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⢱⡙⢧⡈⠻⣦⣄⠘⠀⠠⠀⠈⠁⠀⠀⠀⠀⠀⢌⢧⡻⡽⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣷⡄⠀⠀⠃⠈⣷⡀⠀⠀⠀ ⣿⣿⣧⣿⣿⣧⣿⠟⠀⠀⠀⣠⠀⠀⢀⣠⠀⠀⢿⠛⠻⢤⡘⠻⣤⡀⠀⠀⠀⠀⢀⣀⣠⣤⡼⣼⢧⣿⣻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⣿⡄⠀⠀⢀⠸⡇⠀⠀⠀ ⣿⣷⡿⣿⣽⠟⠁⠀⣠⡏⢰⡇⠀⠀⢸⣿⠀⠀⠘⣧⠤⠄⠙⢶⣌⠛⢶⣤⣶⣶⣿⣾⣿⣯⣟⣯⣿⢷⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣳⢯⣿⡄⠘⠤⢂⠙⢦⡀⠀ ⣟⡾⣽⠟⠁⠀⠀⢠⡿⠀⣾⡇⠀⠀⠹⢿⣀⣤⡀⠙⢆⡰⣳⣦⣈⡛⣶⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣟⣿⣿⣿⣿⣿⣿⣷⢫⣞⢿⡃⠄⢂⠀⢣⢳⡀ ⣯⡟⠃⠀⡰⠀⠀⣿⠃⢸⣿⡇⢀⠀⡀⠀⠈⠻⢿⣷⣮⠵⣹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣻⣷⣿⣿⣟⡿⣷⣿⠿⣝⡷⣎⠲⣅⠀⠀⠈⠀⠡⢓ ⠋⠀⣀⠔⠁⠀⢀⡇⠀⣾⣿⡄⠈⣆⠘⡀⠀⠀⠀⠹⢿⣿⣿⣟⣯⣙⣌⣙⡻⢿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⣿⢯⣟⣿⣿⡿⣿⡽⣾⣽⣻⣿⡹⣌⢳⣍⡒⠈⠄⠀⠀⠀⠀⠈ ⠀⠀⠀⠠⣆⠀⢸⠀⢠⠿⣿⡇⠀⢸⣧⠑⢦⠀⠁⠀⠀⢈⠛⢿⣿⣽⣶⣯⣽⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣯⣿⣻⣞⡷⣿⢯⣟⣷⢳⣿⣯⡕⢎⠲⡡⠌⠐⠠⡀⠀⢀⠀⠀ ⠀⠀⠀⠀⠈⢆⡇⠠⠊⠀⣿⡇⠀⠀⣿⡷⣄⠳⣤⠀⢠⠀⠀⠀⠘⠻⠿⣿⢿⡿⠟⢉⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⢷⣟⣾⢿⣽⡻⢾⡭⣟⣿⡗⢮⡡⠂⠑⣂⠀⡲⢱⠀⠄⡁⠀ ⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⣿⣷⠀⠀⢸⡷⠜⢧⡈⠂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡾⡽⢧⠿⣜⣿⡟⢢⠑⡤⠘⢤⠣⢌⢣⠘⠠⠀⠂ ⣾⣦⡀⠀⠀⠀⠀⢙⣦⠀⣿⣿⠀⠀⠀⠀⠆⠐⠛⣦⣄⠠⣄⠀⠰⠀⠀⠀⠀⠀⡐⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⢯⡿⣷⣿⣻⠯⣷⣎⡿⡍⢦⡙⠴⡁⠎⣇⠫⢄⠊⢀⠁⠀ ⠀⠀⠉⠲⣭⣯⣿⣾⣿⣷⣽⣿⡀⠀⠀⠀⠁⠀⣨⡇⠸⣷⣄⠁⠄⠀⠀⠀⠀⠀⢠⣿⣿⣿⡿⣟⢿⣿⣿⣿⣿⣿⣿⡣⢿⡱⢎⡝⠻⠶⣾⡽⣙⠦⡙⠤⠃⢘⠀⢳⡈⡐⠀⠀⠀ ⠀⠀⠀⠀⡿⢿⣿⣿⣿⣿⣿⣿⣇⢠⠐⡁⢰⣿⠿⡷⠀⠹⡙⣶⣄⡀⠀⢠⡄⢀⣾⡿⣟⢣⠟⡼⢫⣿⢿⣿⣿⣿⡿⣿⣷⣏⠂⢜⡱⣌⡄⢣⣝⠂⡉⠒⡁⠀⠀⠂⠐⠈⠀⠠⠀
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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠧⠤⢾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⡀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠃⠀⠀⢿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠃⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡿⠙⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣠⡶⠤⠿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⡿⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢲⣤⠮⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⣾⡿⣫⢾⡟⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⣩⠞⣫⡾⣡⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠞⣉⡴⠋⣡⡾⢋⡾⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⣁⡴⠞⠉⣠⠞⢁⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠈⠻⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⠇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠖⠋⠁⣠⠴⠚⠉⢀⡰⠞⠁⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠙⢷⣦⡀⣀⣠⣤⡶⠶⠛⠋⠉⣹⠇⠀⠀⠀⣀⣠⡤⠖⠒⠋⠉⠀⣠⡴⠒⠉⠀⢀⣠⠖⠋⢀⡤⠎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠉⠛⠉⠉⠀⠀⠀⠀⠀⢠⡟⠒⠊⠉⠉⠁⠀⠀⣀⣤⠔⠚⠉⠁⠀⢀⣠⠖⠋⠁⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠁⢀⣠⣤⠤⠒⠚⠉⠁⠀⠀⠀⣀⠴⠚⠉⠀⠀⣠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⣴⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠉⠁⠀⠀⠀⠀⠀⣀⣠⠴⠒⠉⠁⠀⠀⣀⠴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣀⣴⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⣀⣀⡤⠴⠒⠋⠉⠀⠀⠀⢀⣠⠴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣠⣴⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣞⠉⠉⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠛⠿⠷⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠀⠀⠀⢀⣠⠴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣄⠀⠀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠙⠻⠶⢤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡖⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⠈⠻⡛⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣇⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠈⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⢿⣥⡀⠀⡈⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⢠⡾⠋⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⡾⠉⠙⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣷⠀⠀⠀⢀⣴⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢰⡄⠀⠀⠀⡀⠀⠀⠀⠀⠘⣧⣰⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⠙⠶⠶⣿⠋⠀⠀⠀⠀⠀⢹⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢶⣄⠀⠀⠀⣀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣤⣿⡋⠀⠀⠀⣯⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠙⠷⠞⠛⣹⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀ ⠀⠉⠙⣇⣰⠓⠚⠻⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠟⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠶⣾⡇⠀⠀⠀ ⠀⠀⠀⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠿⣤⣤⡀⠀⠀⠀⠀⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠻⢯⡄⢠⣽⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⣼⠟⠒⠒⠛⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠏⠉⠉⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⡃⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⡴⠋⠉⢉⠍⣉⡉⠉⠉⠉⠓⠲⠶⠤⣄⠀⠀⠀ ⠀⠀⢀⠎⠀⠪⠾⢊⣁⣀⡀⠄⠀⠀⡌⠉⠁⠄⠀⢳⠀⠀ ⠀⣰⠟⣢⣤⣐⠘⠛⣻⠻⠭⠇⠀⢤⡶⠟⠛⠂⠀⢌⢷⡀ ⢸⢈⢸⠠⡶⠬⣉⡉⠁⠀⣠⢄⡀⠀⠳⣄⠑⠚⣏⠁⣪⠇ ⠀⢯⡊⠀⠹⡦⣼⣍⠛⢲⠯⢭⣁⣲⣚⣁⣬⢾⢿⠈⡜⠀ ⠀⠀⠙⡄⠀⠘⢾⡉⠙⡟⠶⢶⣿⣶⣿⣶⣿⣾⣿⠀⡇⠀ ⠀⠀⠀⠙⢦⣤⡠⡙⠲⠧⠀⣠⣇⣨⣏⣽⡹⠽⠏⠀⡇⠀ ⠀⠀⠀⠀⠀⠈⠙⠦⢕⡋⠶⠄⣤⠤⠤⠤⠤⠂⡠⠀⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠦⠤⣄⣀⣀⣀⣠⠔⠁⠀
⠀⠀⠀⠀⠀⠀⢀⣀⣄⠀⠠⠤⠤⢤⠤⣤⣤⣄⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡴⠋⠀⢀⠠⣒⠨⠅⢀⡀⠉⠭⠄⠐⠀⠈⠭⠭⠓⠦⣄⠀⠀⠀ ⠀⠀⠀⠀⡼⠁⠀⢂⢕⠜⠊⠁⠀⠀⠈⠆⠀⠀⠀⡌⠉⠉⠐⢂⠀⠈⣇⠀⠀ ⠀⠀⣠⣾⠥⠄⠀⢤⢄⣶⣿⢿⣿⣉⠳⣄⠀⢀⣀⣥⣶⣶⣶⠄⠤⠀⣘⢦⡀ ⠀⡞⡍⣠⠞⢉⡝⠲⠤⠤⠴⠊⠀⠈⠙⠁⠀⠀⢹⡏⠀⠀⣀⣠⢤⠦⠕⠡⣿ ⠘⣇⠃⢿⠰⢻⡉⠓⢦⣤⣀⠀⠀⢲⡚⣃⣄⠀⠀⢉⣷⠄⡀⠁⣸⡄⢐⣱⡟ ⠀⠙⢮⡂⠀⠈⢻⡶⢤⣧⣉⠙⠓⡶⠥⢤⣀⣀⣳⣋⣀⣠⡤⢾⢻⣷⠁⡞⠀ ⠀⠀⠀⠹⡄⠀⠀⠙⣤⡏⠙⠻⢿⣧⣤⣤⣼⣤⣤⣿⣤⣤⣧⣼⣾⡿⠀⡇⠀ ⠀⠀⠀⠀⠻⣄⠀⠀⠈⠛⢦⣄⡞⠀⠀⠉⡟⠛⢛⡿⢛⡿⣻⢿⣿⠇⠀⡇⠀ ⠀⠀⠀⠀⠀⠈⠓⢮⣔⡩⢐⡨⢉⠛⠒⠶⠷⠶⠾⠷⠾⠷⠛⠛⡉⢀⠀⣇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠦⣅⠘⠓⠰⠄⢀⡀⡀⠀⠒⣒⣈⠠⠘⠀⣿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠶⠦⢤⣀⣀⡀⠀⠀⠀⢀⣀⡴⠃⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⠲⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣴⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣤⣄⣀⡀⠀⣷⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⠀⠀⠀⣀⣤⣤⣶⣶⣿⠶⠶⠶⠂⠀⠀⠀⠀⠀⠀⠀⠘⠿⠛⠛⠉⢉⣉⣉⣉⠉⠛⢶⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⣼⢠⡾⠟⢋⣉⣠⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣭⣽⣿⣿⣿⣷⡌⠹⡇⠀⠀⠀⠀ ⠀⠀⠀⣿⡟⣽⣦⣾⣿⣿⣿⡿⢿⣶⠶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢛⡿⠻⣿⣿⣿⣿⣿⢿⣧⠰⡇⠀⠀⣀⠀ ⠀⠀⠀⢻⣷⣿⣿⣿⣿⣥⣿⠇⢀⣹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⣌⣻⣿⣿⣿⡟⣸⠀⢣⢀⣽⣿⠇ ⢠⣶⠀⢸⣿⣝⠿⢿⣿⣿⣧⠴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠚⠁⠀⠀⠁⠀⣾⠀ ⠸⡆⠉⠛⠀⠙⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀ ⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀ ⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⡇⠀⠀ ⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⣸⡠⢷⡀⠀ ⠀⠀⢀⡿⣙⡄⠀⠀⠀⢠⣤⣤⡀⢀⡤⠐⠊⠉⠀⠀⠀⠀⠀⠀⠀⣀⣀⣭⣶⠞⠋⠁⠀⠀⠀⠀⣾⠉⠀⣸⡇⠀ ⠀⠀⢸⡇⠈⠉⢇⠀⠀⠀⠀⠈⠙⠛⡷⠶⠶⠶⠶⠶⠶⠶⠖⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⡸⢻⠀⢀⣽⠇⠀ ⠀⠀⠘⣇⠢⠀⢾⢦⠀⠀⠀⠀⠀⠀⠈⠓⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠉⠉⠁⠀⠀ ⠀⠀⠀⠈⠓⠚⠁⠈⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠐⠙⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⣶⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠠⢿⣿⣿⣿⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣬⣿⣿⡿⠿⠛⠻⠻⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡟⣿⣿⡿⠁⠀⠀⠀⠀⠀⠙⡷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣾⠁⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠻⠞⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⡇⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠳⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣼⠙⠰⠀⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣌⢹⡆⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣿⡄⠀⣀⣤⠴⠶⠖⠒⠒⠒⢶⣦⣀⠀⠀⠀⠸⣎⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⣼⣷⣶⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⢹⣿⡆⠀⠀⠀⠀⠀ ⠀⠀⢸⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣄⢸⣿⡇⠀⠀⠀⠀⠀ ⠀⠀⠈⡇⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⣸⢿⠀⠀⠀⠀⠀ ⠀⠀⠀⡇⢺⣿⣿⣿⠃⡀⠰⠃⢸⣶⣦⣴⡤⠀⠀⠀⠀⡆⠘⣸⠀⠀⠀⠀⠀ ⠀⠀⠀⢻⠀⠙⠋⠉⠁⠁⠀⠐⠛⠿⠛⠋⡁⢀⣠⡶⠄⠁⠀⢻⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⠄⠐⠀⠈⢧⣠⡴⠀⣀⠀⠈⣳⡿⠿⢭⣁⡆⠀⠀⢸⠀⠀⠀⠀⠀ ⠀⠀⠀⠸⣷⣀⣿⣷⣼⣿⣮⣶⣶⣶⡾⣯⣗⢦⣾⠟⠁⠀⠀⣺⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠙⣯⡽⢿⣿⣄⣿⣉⣻⣏⣻⣼⠿⠛⠁⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣄⠀⠀⠉⣿⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣟⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⣸⡆⠀⢀⣼⡟⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣴⢿⠁⠀⠀⠠⠿⠀⠀⠀⠀⠀⠀⣠⣿⠃⠀⢿⡄⣽⣷⣤⣀⠀⠀ ⠀⠀⣴⠟⣿⣿⡇⠰⣶⣀⠀⠀⠀⠀⠀⢀⣴⡿⠃⠀⢀⣼⠿⣯⡀⡄⠙⣷⣄ ⢀⣼⣿⣼⠋⢸⣿⣀⣿⣿⠆⠀⠀⢀⣤⡿⠋⠀⢀⣰⣿⣿⣾⡿⣦⣙⣾⣷⣿ ⠘⠏⠛⠁⠀⢸⣿⣿⣿⣿⣦⣤⡖⠛⠁⠀⠀⣰⣿⣿⣿⡟⠉⠀⠈⢿⣿⠿⠃ ⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⡿⠛⠋⠉⢉⣭⡽⢾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⠻⣿⣿⣻⣿⣦⣤⣼⡟⠉⠂⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣿⢦⡒⣿⣿⠛⠿⠿⠻⣿⠀⠀⠀⢻⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣸⣿⣎⣻⣿⣿⠆⠀⠀⠀⢻⡆⠠⠈⠁⢻⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠛⠿⠦⠴⠞⠛⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀
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⠀⠀⣀⣤⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣿⣿⡿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣴⣿⣿⡟⠀⠀⢸⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀ ⣹⣿⣿⡃⠀⠀⠀⠙⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⣠⣤⣿⠻⠿⣿⣿⣧⠀⠀⠀⠀⠀⠀ ⣿⣿⡿⠃⠀⠀⠀⠸⣿⣿⡇⠀⠀⠀⠀⠀⠀⢰⣿⣿⠿⠀⠀⠿⣿⣿⣷⠀⠀⠀⠀⠀ ⣼⣿⣥⠀⠀⠀⠀⠀⢸⣿⣧⡄⠀⠀⠀⠀⠀⣼⣿⣿⠀⠀⠀⠀⠈⣿⣿⣶⣄⠀⠀⠀ ⢿⣿⣿⡇⠀⠀⠀⠀⠸⠿⣿⣿⠀⠀⠀⠀⢰⣿⣿⡟⠀⠀⠀⠀⠀⠈⠿⣿⣿⠀⠀⠀ ⢾⣿⣿⡆⠀⠀⠀⠀⠀⠀⣿⣷⡀⠀⠀⠀⠀⣿⣿⡇⣶⣦⡀⠀⠀⠀⠀⣿⣿⣶⡀⠀ ⠀⢾⣿⣿⠀⠀⠀⠀⠀⠸⣿⣿⠇⠀⠀⠀⠰⣿⣿⡀⠿⣿⣧⣀⡀⠀⠀⠙⢻⣿⣇⡀ ⠀⢻⣿⣟⣀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⣿⣿⡇⠀⢸⣿⣿⣷⣄⠀⣀⣼⣿⣿⡇ ⠀⠘⠛⣿⣟⡀⠀⠀⠀⠀⢸⣿⡃⠀⠀⠀⠀⣿⣟⠁⠀⠀⠉⣿⣿⣿⣧⣽⣿⡿⠃⠀ ⠀⠀⠀⢿⣿⡇⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⢠⣿⣿⠀⠀⠀⢰⣿⣿⠿⢿⡿⠛⠃⠀⠀ ⠀⠀⠀⠘⠛⠁⠀⠀⠀⠀⠘⠛⠛⠁⠀⠀⠈⠛⠉⠀⠀⠀⠈⠛⠛⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡤⠶⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠟⠋⠁⠀⠀⠀⠀⠀⠙⠢⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⡤⢶⣤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢐⣀⡤⠴⠒⠊⣉⣽⠿⠟⠋⠉⠀⠀⠀⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠛⠉⠀⣀⣤⠶⠛⠉⠀⠀⠀⠀⠀⠀⠀⣸⠇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠈⠀⠀⠀⠀⠀⠀⠀⣠⡤⠚⠉⠀⠀⠀⣠⡴⢾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡇⠀⠀⠀⠀⢀⣠⠶⠋⠁⠀⠀⢀⣠⡶⠛⠁⢀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⠀⢀⣠⠶⠋⠁⠀⢀⣠⡴⠞⠋⠁⡠⠖⠉⠉⠐⢤⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⡴⠋⠁⢀⣠⡴⠞⠋⠁⠀⣀⡴⠋⠀⠀⣀⡀⢠⠀⢇⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣖⣋⣥⡴⠶⠛⠉⣁⣠⣤⣶⣾⣟⡁⠀⠀⣾⣿⣿⣃⣼⠀⡼⠀⠀⠀⠀⣠⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⣤⣖⣯⠷⠟⠛⠉⠀⢀⡤⠖⠋⠩⡀⠀⠉⠛⠛⠉⠀⠀⠙⠛⠛⠋⢸⣠⠃⠀⠀⢀⡔⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣀⣤⠶⠛⠋⠉⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⠀⠀⡠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣠⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠀⠀⣠⢞⠄⠀⠀⠀⠀⠈⠃⠒⠀⠀⠀⠀⡸⠘⡆⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠹⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠋⠁⡜⢣⡀⠀⠀⠐⢶⣶⣶⠶⠀⠀⣰⠃⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠙⠢⣄⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⣠⠞⠀⠀⠙⠦⣀⠀⠀⠀⠁⠀⢀⡔⠁⠀⠴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⠲⢄⡀⠀⠀⠘⢀⡠⠖⠉⠀⠀⣠⠤⠤⠤⠬⠽⠶⠤⠤⢶⡉⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢠⠞⠁⠀⠀⣀⠔⠉⠀⠀⡤⢭⣟⡒⠢⣄⠈⠉⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠀⣀⠔⠊⠁⠀⠀⠀⢀⠭⠭⣉⢯⠳⣬⡓⣄⠀⠀⠈⠑⠢⠤⠤⠤⠴⠒⠒⠤⢄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⠀⠀⠀⢀⡠⠚⠁⠀⠀⢿⠎⠙⠚⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⢠⠖⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
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⠀⠀⠀⠀⠀⢀⡤⣄⡤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⢆⠙⣡⠏⠀⠀⣠⠠⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠳⠁⠀⠀⢰⠁⠀⠀⠈⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠘⣆⢀⣀⠤⠖⠒⢢⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⡮⠁⠉⠁⠒⠤⢀⡼⠖⠀⠐⣗⠢⡀⢸⣏⡁⠀⠀⢀⡠⠥⠒⠲⠤⢄ ⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⣀⣈⣍⣈⡿⡘⠁⣹⡚⠁⠀⠀⠀⠀⠀⣼ ⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⣇⣠⡶⣍⣀⣠⠴⠛⠻⢇⣜⡁⠺⠽⠀⠀⠀⢠⡞⠁ ⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⢷⡀⠀⠀⢀⡏⠀⠀ ⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡉⢳⡄⣸⠁⠀⠀ ⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠿⢻⡖⠒⠂ ⠈⠉⠸⡍⠈⠀⠀⠘⣶⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⣶⡄⠀⠀⠠⢸⠅⣀⠀ ⠀⠀⠔⢷⠈⠀⠀⠀⠘⠛⠁⠀⠀⠀⣤⢤⠀⠀⠀⠀⠸⠿⠁⠀⢀⣠⠟⠀⠀⠀ ⠀⠀⠀⣀⠷⢎⠁⠀⢀⡀⠀⠀⠀⠀⠙⠉⠀⠀⠀⠀⠀⠀⠀⣀⠴⠋⠈⠒⠀⠀ ⠀⠀⠀⠁⠀⠀⠉⡖⠀⠈⠑⡦⠤⠄⠄⠀⠤⠤⠤⡖⠉⠉⠹⡁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⠒⠛⠊⠁⠀⠀⠀⠀⠀⠀⠀⠙⠒⠲⠞⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⢒⠒⠢⡄⡀⠀⡠⠂⠁⠀⠀⠀⠀⠀⠀⠁⠢⡀⠀⢀⠠⠤⠀⢤⡄⠀ ⠀⠀⠈⣄⠑⠄⠀⣸⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢨⠂⠀⠀⠔⢁⢾⠁⠀ ⠀⠀⠀⠹⣄⡀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⡰⠁⠀⠀⢀⠔⢃⠎⠀⠀ ⠀⠀⠀⠀⣈⠶⢬⡇⠀⠀⠀⠀⠀⠀⠀⠀⡰⢡⣾⣤⣤⣤⡶⢥⢔⠁⠀⠀⠀ ⠀⠀⠀⢾⡀⠀⠈⢇⠀⠀⠀⠀⠀⠀⢀⢜⡴⡹⣿⡿⢹⡟⠛⠁⠀⣨⡆⠀⠀ ⠀⠀⠀⠀⠁⠒⡲⠘⣦⠀⠀⠀⡠⠒⡡⠣⠁⠚⠛⠟⣏⠉⠺⡋⠓⠋⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⣛⣥⣑⣄⠀⢀⣾⠮⠵⣦⡠⠜⣄⢘⠗⠛⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡞⠊⠁⠀⠀⠉⠺⣗⠂⠀⣝⡗⠒⢎⠉⠁⠢⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡌⠉⠢⠀⠀⠀⠀⠀⠘⠆⠀⣿⠋⠀⠀⠈⠁⠢⣣⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⠞⢱⢀⠀⠈⢄⠀⠀⠀⡀⢸⡼⠁⠀⠀⢀⠄⠊⢩⠹⠡⡀⠀⠀⠀ ⠀⠀⢀⠾⣀⡏⢀⠼⡆⠀⠑⠠⢐⠀⡌⠀⠀⣀⠔⠁⠀⡠⢣⠒⢇⠑⡀⠀⠀ ⠀⡔⠁⠀⠈⠃⡊⣠⡧⠤⠤⢤⡀⢉⣁⡈⠉⠀⠀⠠⢪⣖⠈⢢⢈⡇⠙⠠⠀ ⠰⠀⠀⠀⡜⠀⠉⢿⠁⠀⠀⠀⢱⢸⠀⠀⠉⠁⠒⡠⢄⡄⠑⡜⠋⠀⠀⠀⠁ ⠀⠢⣀⣊⡀⠤⠊⠀⢑⣤⣠⣐⣁⠼⡄⡀⢀⡀⠔⠁⢀⠃⠒⢅⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⢀⠸⠁⠀⢹⠂⢤⠀⠠⠔⠁⠁⢄⠀⠈⠁⠈⠁⠀ ⠀⠀⢀⡀⠀⠤⠇⠐⠒⠒⠒⠊⠀⠀⠈⠁⠘⠐⠒⠒⠒⠀⠤⠧⠀⢀⡀⠀⠀

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

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⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀ ⠐⠶⣿⣿⡿⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣿⣿⣇⡀⠀⠀⠀⠀ ⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⢿⣿⣿⡿⠟⠋⠉⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⣿⣿⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⡤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣿⣿⣿⣿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣶⣿⣿⣆⣀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡿⠉⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀
🧍🏻‍♀️, skate⛸️
⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⢉⡗⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠈⡱⠖⠀⠀⠀⠀⠀⠀⠀⠀⣄⣠⠆⠀ ⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠰⠓⠒⢴⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢨⠀⣰⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⢹⡀⠀⠀⠀⠈⠀ ⠀⠀⠀⠀⢠⣀⣶⠀⠀⠀⠀⠀⠀⠀⠀⢤⢀⣀⣀⣀⡠⠋⠀⠀⢇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⣄⠊⠁⠀⠀⠀⠀⠀⢀⡨⢦⠀⠀⠀⠀⠀⠀⠀⠘⠒⠤⣀⡀⠀ ⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⡀⠔⠊⠁⢀⡀⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠼⠋ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠈⡀⠄⠂⠉⢀⡀⢰⠁⠀⠀⠀⠀⠀⠀⡴⠊⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⡠⢊⠠⠒⣁⠤⠐⣀⡁⠤⢤⠃⢀⣀⡠⢄⡀⠀⠀⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⡠⡪⢐⡡⢐⠩⠐⠊⠁⠀⠀⠀⠚⠉⠉⠀⠀⠀⠙⠢⣀⡇⠀⠀⠀⠀ ⠀⠀⢠⡪⡪⡲⠕⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⠃⠀⠀⠀⠀ ⠀⣰⣿⠞⠉⠀⠀⠀⠀⠀⡄⡰⡆⠀⠀⠀⠀⠀⠀⢐⣌⡶⠀⠀⠀⠀⠀⠀⠀⠀ ⡰⠋⠀⠀⠀⠀⠀⠀⠀⠀⣸⠤⡐⠁⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢀⣀⣴⣶⣶⣶⣶⣶⣦⣀⡀⠀⠀⠀ ⢰⣾⡿⠋⣩⣉⣭⣉⣍⠙⢿⣷⣦⡀⠀ ⠀⢉⣼⣿⡟⠻⠛⠿⢻⣶⡌⠙⢿⣥⡀ ⢠⣾⣿⠇⣾⣿⣿⣿⣤⠸⣿⡇⢾⣿⡁ ⠸⢿⣇⡙⣻⣶⣀⡛⣳⣼⠟⢁⣻⡏⠁ ⠀⠸⢿⣷⣍⠿⠿⠿⢟⣡⣰⣿⡏⠀⠀ ⠀⠀⠈⠹⠿⢿⣾⣷⣾⡿⠏⠉⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠀⠁⠁⠁⠀⠀⠀⠀⠀
👩🏻👩🙋‍♀️💁‍♀️💁🏻‍♀️🙋🏻‍♀️
⠀⠀⠀⢀⣴⣶⣿⣿⣶⣦⣤⣶⣾⣿⣿⣿⣶⣶⣤⣤⣶⣿⣿⣷⣦⣄⠀⠀⠀ ⠀⠀⢰⣿⣿⠟⢹⣿⣿⣿⡿⠟⠋⠉⠉⠉⠙⠛⢿⣿⣿⣯⡹⠛⣿⣿⣆⠀⠀ ⠀⠀⢿⣿⣇⣠⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣶⣿⣿⣿⠀⠀ ⠀⠀⠘⣿⣿⣿⣿⡏⠁⠀⢀⣤⡀⠀⠀⠀⢀⣤⣄⠀⠀⠻⣿⣿⣿⣿⠇⠀⠀ ⠀⠀⠀⠈⢹⣿⣿⣦⠀⠀⠸⠿⢿⣤⣤⣤⣘⠿⠟⠀⠀⠀⣿⣿⣿⠁⠀⠀⠀ ⠀⠀⠀⠀⠘⣿⣿⣠⣤⣶⣶⣦⣼⣿⣿⣿⣿⣴⣶⣶⣦⣄⣿⣿⠷⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢻⣿⣿⡿⠛⠛⠻⢿⣿⣿⣿⣿⠟⠛⠛⢿⣿⣿⣿⠀⠀⠀⠀⠀ ⠀⠀⢀⣴⣾⣿⣿⣿⣶⡄⠀⠀⠀⠹⣿⡿⠁⠀⠀⢀⣴⣾⣿⣿⣷⣦⡀⠀⠀ ⠀⢠⣿⣿⡿⠉⠛⢻⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠛⠉⠻⣿⣿⡆⠀ ⠀⠸⣿⣿⣄⣀⣀⣼⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣆⣀⣠⣿⣿⡷⠀ ⠀⠀⢙⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⣠⣼⣿⣿⣿⣿⣿⣿⣏⠀⠀ ⠀⣰⣿⣿⠟⠉⠀⠘⠻⣿⣿⣷⣄⠀⠀⠀⣠⣾⣿⣿⡟⠉⠀⠉⠙⣿⣿⣦⠀ ⠀⣿⣿⠇⠀⠀⠀⠀⠀⠘⣿⣿⣿⣷⣤⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠘⣿⣿⡄ ⠠⣿⣿⡄⠀⠀⠀⠀⠀⢠⣿⣿⡟⠿⢿⡿⠛⣿⣿⡏⠀⠀⠀⠀⠀⢀⣿⣿⠃ ⠀⠹⣿⣿⣄⠀⠀⠀⣠⣾⣿⣿⣶⣦⣤⣷⣶⣿⣿⣿⣄⡀⠀⠀⣠⣿⣿⡟⠀ ⠀⠀⠙⠿⣿⣿⣿⣿⣿⡿⠋⠙⠛⠛⠛⠛⠛⠛⠛⠿⣿⣿⣿⣿⣿⡿⠋⠀⠀ ⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣄⣤⣴⠶⠶⣤⡤⢶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⡀⣼⠿⠉⠁⠉⠁⠀⠀⠀⠀⠀⠀⠉⠉⢻⠶⠴⡟⡛⠟⢷⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠟⠙⠉⠛⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣴⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣸⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠷⠀⣠⣾⡶⣦⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⡄⢸⣟⡈⠁⣹⣷⣤⣀⠀ ⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣀⡐⣿⠁⠀⢸⡇⠀⠀⠉⠙⠉⣻⣆ ⠀⠀⠀⠀⠀⠀⠈⠙⢻⣶⣄⣀⣤⡶⠀⠀⠀⠀⣀⣄⠀⠀⠀⠀⠀⠀⠀⣠⣤⡀⡀⣴⢿⠉⠉⠉⠉⠛⢿⣆⠀⠈⣿⣤⣈⣡⣤⡶⠟⠀ ⠀⠀⠀⠀⠀⣀⣀⣀⠠⠍⢹⡿⠅⠀⠀⠀⠀⠀⢿⠛⠀⠀⢠⣿⣷⡄⠀⠛⢛⣫⣿⡿⠇⠀⠀⠀⠀⠀⠀⣿⠅⠀⠀⠀⠈⠁⠁⠀⠀⠀ ⠀⠀⠀⠀⣸⡟⠏⠻⣷⡄⢸⡷⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠘⠀⠀⠀⠀⠀⠈⢹⡟⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⢠⡾⣿⠻⠷⠀⠀⣻⣧⠈⠻⣶⡄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠃⠀⠀⠀⠀⠀⠀⣴⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠸⣧⡀⠀⠀⠀⢀⣿⠉⠀⠀⠈⢛⣷⣦⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠛⠛⠛⠛⠛⠃⠀⠀⠀⢀⣼⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠂⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣤⠀⠀⠀⢀⣠⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⡶⡶⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣦⡠⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣦⣀⣀⢀⡀⣀⣀⣴⡿⠟⠛⢷⣦⣄⣀⣤⣠⣤⡶⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠘⠉⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
STOP IT 🚫⏹🚫🚫 DON'T MAKE THIS KIDS ARE TRYING TO FIND NICE EMOJIS AND YOU MAAKE THIS GO FUCK YOU MAN ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡛⠉⢯⣒⢤⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡖⢡⡐⡄⢀⡀⠈⢙⢮⡳⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠣⠀⠂⠀⠈⠀⠀⠈⣈⠷⢉⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⡐⡀⠀⠀⠀⠀⠀⣐⠼⢁⡞⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠣⢁⠐⠈⠆⣀⡈⠀⠲⢃⢠⠎⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡅⠂⠄⠂⠈⠐⢠⠓⢢⠱⣨⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠤⣤⢤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠗⠀⠀⠀⠀⠂⠈⠀⠈⠄⣼⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡟⣬⠛⣭⢫⡍⣶⢳⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠂⠀⠀⠀⠀⢢⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡓⠤⠁⠎⠱⡈⡜⢥⢻⣹⢻⠷⡶⣶⡶⢶⣶⣦⣤⡀⣴⠟⠀⠀⠀⠀⠀⠀⠀⠐⠠⢩⠏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣼⡧⠙⢢⠁⡈⠀⠀⠈⠀⠁⠋⠄⢊⠑⠄⠘⡀⢎⡝⣿⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣾⡿⢤⡁⢂⠡⠀⠀⠀⠀⠀⠀⡈⠁⢁⠊⠴⠓⠁⡜⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣴⣿⢟⡽⣂⠖⡄⢂⢀⣴⠼⡞⡿⣛⡝⠛⠛⠾⣦⣤⣾⣽⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⣾⣏⠳⢎⣖⠹⣎⡜⣧⡿⠡⢎⠱⠑⠨⠈⠁⠀⠀⠈⠉⣻⡏⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣺⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⡗⡮⣙⠦⡸⡙⣼⡿⢋⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠠⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣇⡳⡵⣊⠕⣩⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣲⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣿⣟⣡⢦⣽⡟⠐⠁⠀⢀⠠⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢸⠃⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⡿⠏⡉⣤⣿⠡⢈⠤⢁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⢡⠀⢀⠀⠀⠀⠀⠀⠀⠀⣴⢋⣿⠾⠃⠒⠘⠳⣶⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⣞⣵⠶⣿⣿⢁⡞⠤⠒⠠⠁⠂⠀⠀⠀⠀⠀⠀⠀⢰⡏⢆⠂⠄⠀⠀⠀⠀⠀⠀⠩⢄⣿⠋⠁⠀⠀⠁⠁⠡⡘⣿⠀⠀⠀⠀⠀⠀ ⠀⣰⣿⡟⢡⣾⢿⣌⠳⡘⠤⠉⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⡑⠌⡐⠈⠄⠀⠂⢁⠐⢌⢂⣿⢃⠉⠀⠀⠠⢈⠠⡑⢆⢽⠀⠀⠀⠀⠀⠀ ⢀⣿⡟⢡⣿⡟⢮⢌⢣⠐⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢏⠱⠈⠄⠡⠀⠌⡐⢀⠋⢤⣫⠇⠂⠀⠀⠀⠁⡀⠤⠱⣈⡟⠀⠀⠀⠀⠀⠀ ⢸⣿⣇⣳⡯⡝⢮⡘⢄⠃⠌⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠏⡌⠢⠁⠌⠠⢁⠂⠔⡈⠜⣲⠏⠀⠀⠀⠀⠠⠁⢀⢀⠂⣵⡷⠤⢤⡤⣀⠀⠀ ⢸⣿⣟⡶⡹⣍⠦⡑⡈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠤⣹⠣⡘⠠⠁⠌⠀⡁⢂⠌⡠⢉⣼⠇⠀⠀⠀⠀⠀⠂⢈⠀⡠⠘⣴⠏⠈⠀⠈⠺⢵⡆ ⢸⣿⣿⢶⡹⢆⠳⠄⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⠁⠄⡁⠌⠀⠐⠄⠊⠤⡁⢧⡾⠁⠀⠀⠀⠀⠀⠀⠄⠐⠠⢹⡏⠀⠀⡀⠄⡑⢠⡇ ⠸⣿⣿⣏⡳⢍⡚⢀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⠂⣁⠂⠀⠀⠀⠌⡐⢉⠐⡌⢺⡇⠀⠀⠀⠀⠀⠀⠀⠀⠊⢰⡟⠀⠀⠀⠀⢂⠐⢯⡜ ⠀⢻⣿⣯⣗⡪⢐⠂⠄⡀⠀⠀⢀⠀⠄⡀⠠⠐⠠⡈⠄⠌⡐⠀⠐⠠⠈⠄⢂⠜⣹⠄⠀⠐⠀⠀⣀⠁⢂⠐⢠⡿⠀⠀⠀⠀⡀⠌⡈⠵⡇ ⠀⢸⣿⣿⣿⣷⡠⢌⡐⢀⠁⠄⠂⠌⡀⠀⠀⠄⠡⢐⠨⠐⠀⡐⠈⠄⠡⢈⠆⡹⢜⡀⠂⠀⠀⡐⠠⠈⢃⠀⣾⠀⠀⠀⠀⠀⠠⢀⠓⡸⡇ ⠀⠈⣿⣿⣿⣿⣿⣶⣌⣦⡘⡬⣑⢢⠐⡀⠂⠌⡠⠁⠂⠁⠄⠄⠁⠌⡐⢂⠬⡑⢆⠀⠠⢀⠂⠡⢀⠂⠌⣸⠧⠀⠀⠀⠠⢀⠁⢢⠘⣼⠁ ⠀⠀⢿⣿⣿⣿⣿⣿⣿⡼⣧⢧⣣⠜⣄⠣⡘⠤⡠⠀⠀⠘⡀⠀⠄⣀⢃⡘⢤⠛⠄⠘⠠⢄⠃⠤⠀⠄⡀⣿⠀⠀⠀⠠⠀⠀⡘⠄⣻⢻⠀ ⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣯⣿⣳⢿⣤⡓⡜⡐⠀⠀⡄⢃⠄⠠⡀⢄⠢⢜⢢⡉⡐⢈⠐⡈⡘⠤⢉⡐⢡⠏⡐⠠⠁⠂⡀⠡⢐⢨⢴⠏⠀ ⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣷⣯⣟⣿⣽⣳⣍⢶⣱⣌⠂⠌⢁⠰⣈⠲⣍⠢⡐⠁⠀⠀⠐⠀⢀⠂⢄⠣⡘⠠⢁⠂⡐⠠⢁⢢⢎⡿⠀⠀ ⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣾⣿⣶⣮⣶⣼⢳⣎⡱⢌⠢⡁⠄⣁⠀⠂⢌⠂⢆⠁⠂⠄⡂⠥⢑⡈⢲⡾⠃⠀⠀ ⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣾⣵⣯⣶⣝⡲⢌⡘⢡⠂⢍⠠⠌⡐⠠⠘⡄⢣⢼⡿⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣽⣶⣭⢦⣉⠦⡘⢄⠢⣑⢣⡜⣱⠞⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣯⣷⣻⢯⣟⣿⣿⣷⣟⣾⣵⣮⣵⣺⣦⠿⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠿⠿⠿⠿⠿⠿⠿⠛⠋⠙⠛⠛⠛⠻⠿⠿⠿⣿⣿⣿⣿⡿⠟⠛⠉ GO FUCK YOU, GO FUCK YOU

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