Tori Emojis & Text

‘ ,🌊★! ‘ . ☻ ┊’.’「 тσяι 」

-« ̶s̶ᷤᵘ̶ⁿ̶ ɪ̶ᷝˢ̶ ̶ᴀ̶ⷶˡ̶ᵒ̶ⁿ̶ᵉ̶ ̶ᴛ̶ⷮᵒ̶ᵒ̶ ̶ʙ̶ᷨᵒ̶ᵗ ̶s̶ᷤᵗ̶ᶦ̶ˡˡ̶̶ ̶s̶ᷤʰᶦ̶ŋᵉ̶ˢ̶»🔥✨

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡋⠉⠀⠀⠀⠈⠉⠓⢦⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠤⠤⢤⣀⣀⠀⠀⠀⠴⢀⣴⡾⠷⠤⣈⡉⠑⠲⢄⡀⠀⠀⠀⠱⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⡤⠤⠒⠒⠒⠦⢤⡀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠦⠒⠒⠒⠒⠒⠛⠉⠀⠀⠀⠀⠀⠀⠈⠉⠓⠤⣄⠀⡼⣀⡀⠀⠀⠉⠓⠦⣄⡈⠳⢤⡀⠀⠈⢇⠀⠀ ⠀⠀⠀⢀⡤⠊⠁⠀⢀⡤⠔⠛⠉⠉⠙⢦⡀⢀⡤⠔⠋⠉⠀⠀⠀⠀⠀⠀⠀⠲⡄⠀⠀⢀⡤⠔⠂⠀⠀⠀⠀⠀⠈⠻⣧⠈⠙⠓⢤⣀⠀⠀⠀⠙⠢⣄⠙⢦⡀⢸⡆⠀ ⠀⠀⢀⠎⠀⢀⡠⠚⠉⠀⢀⡤⠒⠊⠀⣠⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢿⣤⠜⢉⣤⠔⠒⠦⡄⠀⠀⠀⠀⠀⠈⠓⠒⠒⠒⠺⢷⣦⣀⠀⠀⠈⠳⢤⡙⢾⡇⠀ ⠀⢀⡏⢀⡴⠋⠀⢀⡤⠞⠁⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⢾⡿⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠉⠳⣄⡀⠀⠀⠳⡼⠀⠀ ⠀⢸⣤⠞⠀⣠⡴⠋⠀⠀⠀⠀⢠⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⢿⡾⢿⣦⣀⡶⠁⠀⠀ ⠀⢸⠃⣠⡾⠁⠀⠀⠀⢀⣠⢴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⡀⠀⠀⠀⢶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣶⠛⠁⠀⠀⠀⠀ ⠀⠘⣶⡏⠀⠀⠀⣠⠖⠋⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣛⣫⣵⣦⡀⣠⣾⠿⠭⠭⠽⡄⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⢷⠀⠀⠀⠀⠀ ⠀⠀⠘⢧⡀⣰⠟⠁⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠗⠒⠛⠉⠙⠓⠋⠁⠀⠀⠀⠀⠹⡄⠀⢀⡾⢰⡄⠀⠀⠀⠀⡀⠀⠀⠀⠱⣦⡀⠈⡆⠀⠀⠀⠀ ⠀⠀⠀⠀⢹⠳⢤⣀⣀⣠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⣀⡘⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠏⢉⡿⢿⣾⡇⠀⠀⠀⢸⢿⠀⠀⠀⠀⢱⡈⣷⣻⠀⠀⠀⠀ ⠀⠀⠀⠀⡾⠀⠀⠀⢀⡿⠁⠀⠀⠀⠀⠀⠀⢣⡀⢀⣠⢾⡻⣍⣀⣉⣁⠽⠛⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣾⣋⠠⠛⢀⠿⣆⠀⣠⣿⢸⠀⠀⠀⠀⠈⡷⠛⠛⠀⠀⠀⠀ ⠀⠀⠀⢠⡇⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⣽⠿⢤⣀⣙⣿⣛⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣻⡟⠛⠛⢿⣷⣦⣤⠤⠞⢡⢇⡾⠀⠀⠀⠀⢠⣷⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⠁⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⢠⣴⣿⠿⠓⠾⣯⣄⠀⠀⠀⠀⠀⠀⠀⠀⣿⣯⠴⢶⣦⣄⠈⢿⣟⡴⣲⣿⣾⠀⠀⠀⢸⡇⣸⠙⡆⠀⠀⠀⠀⠀ ⠀⠀⠀⡄⠀⠀⠀⢸⡇⢠⠄⠀⠀⠀⠀⠀⠀⠀⣴⣾⣯⡿⠁⣴⡖⢒⣶⡹⠇⠀⠀⠀⠀⠀⠀⠀⢻⣿⣀⣸⣿⣾⣆⠈⢿⣿⣯⡵⠃⠀⠀⣠⣾⡵⠃⠀⠹⡄⠀⠀⠀⠀ ⠀⠀⠀⠃⠀⠀⢀⡞⢧⣾⠀⠀⠀⠰⣀⣀⣀⣴⣯⣁⣿⠁⠜⠻⣿⣾⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⡙⢿⡄⢸⡿⠙⠲⡶⠶⠺⢷⡟⢧⡀⠀⠀⢧⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⠟⠀⠈⣿⡄⠀⠀⠀⠀⠀⢀⡿⢓⣿⡇⠀⣷⣤⣿⠋⠹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡈⣇⠙⣧⣠⠇⠀⠀⠀⠀⣿⡏⠃⢘⣷⡀⢳⡀⠀⠸⡀⠀⠀⠀ ⠀⠀⠀⢀⡴⠃⠀⣠⢾⠁⠙⠦⣀⣠⠖⠛⢿⡀⠀⠙⠇⠀⢿⡀⢹⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢼⣤⡽⠋⠀⠀⠀⠀⣼⢡⡇⠀⢸⢹⣧⠀⢹⡀⠀⢷⠀⠀⠠ ⠀⢰⢠⠎⠀⢀⡴⠁⢸⠀⠀⠀⠈⢿⠀⠈⡿⢷⡀⠀⠀⠀⠈⠳⣼⣤⠖⠃⠀⠀⠀⠀⠀⠀⠶⠄⠀⠀⠰⠦⠤⠖⠲⡗⠀⠀⢀⡯⣾⠀⣰⠋⢸⡏⢧⡀⠹⡄⠘⡄⠀⠀ ⠀⣾⠏⠀⣠⠏⠀⠀⣸⠀⠀⠀⠀⠈⢧⡀⠱⣄⢷⡀⠀⠊⠛⠲⠶⠖⠂⠀⠀⠀⠀⢰⣤⣤⣠⣤⣶⠆⠀⠀⠀⠀⣠⡁⠀⠀⢸⣤⡴⠚⠁⠀⠈⡇⠀⢳⠀⠱⡀⠁⠀⠀ ⢠⠇⠀⡴⠋⠀⠀⠀⡇⠀⢀⡤⠤⠤⣄⣙⣦⣈⣷⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢉⠉⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠏⢹⣀⣀⣀⣀⢻⠀⠈⢷⠀⠳⡀⠀⠀ ⠏⢀⡾⠁⠀⠀⠀⠀⡇⣴⠛⠿⡄⠀⢰⡿⠉⠀⠉⠙⠷⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⣦⣾⡟⠀⠀⠀⠀⠀⠀⣠⣶⣿⡗⠀⠘⡇⢸⠇⠘⢿⡀⠀⠈⢣⠀⢳⡐⠀ ⢀⠞⠀⠀⠀⠀⠀⢀⡿⠁⠀⠀⠹⣯⠙⢧⠀⠀⠀⠀⠀⠀⠈⣹⣶⠀⠀⠀⠀⠀⠀⠀⣀⡈⠛⠋⠀⠀⠀⠀⣠⠴⠛⠻⢿⡀⠙⣦⠀⣿⡿⠀⠀⠈⣳⡀⠀⠈⢷⡈⡇⠀ ⠊⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠘⣦⡈⣧⠀⠀⠀⠀⠀⢀⡏⠈⡗⠦⣄⡀⢀⡴⠚⠉⠳⣄⠀⠀⠀⢀⣴⣿⠀⠀⠀⠀⠙⢦⡈⢷⣿⡇⠀⠀⠀⢿⣧⠀⠀⠈⢧⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠘⢷⡈⢷⡀⠀⠀⠀⣾⠀⠀⢧⠀⢀⡽⠋⠀⠀⠀⠀⠙⣟⣶⢶⡏⡾⠃⠀⠀⠀⠀⠀⠀⢻⡈⣿⠁⠀⠀⠀⢻⣿⠀⠀⠀⢸⠇⠀ ⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⣉⣉⠓⠂⠀⠈⢻⣎⡳⣄⢀⡾⠉⢧⡀⠸⣷⠋⠀⠀⠀⠀⠀⠀⠀⠈⢾⣸⣿⠁⠀⠀⠀⠀⠀⠀⠀⣠⡇⡿⠀⠀⠀⠀⠈⢿⡇⠀⠀⢸⠀⠀ ⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡿⣷⡜⠛⢧⠀⠈⢳⡀⠹⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⢹⡏⠀⠀⠀⠀⠀⠀⣠⡴⠋⢠⡇⠀⠀⠀⠀⠀⠘⡇⠀⠀⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣌⢿⡄⠘⡆⠀⠈⢷⣠⣿⠛⢯⡓⠶⢤⣀⠀⠀⢀⣼⡇⠀⠀⠀⠀⢀⡴⠻⣆⠀⢸⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡧⠀⠇⠀⢠⡾⠋⡟⠀⠀⠉⠓⠦⢬⣤⠴⣿⢻⡿⣤⣀⣴⠾⠋⠀⠀⠙⣦⣸⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣆⣠⡴⠋⠀⠀⣷⠀⠀⠀⠀⠀⠀⢠⣤⣿⣈⡇⡏⠀⠀⠀⠀⠀⠀⠀⣸⠻⣄⡀⠀⠀⠀⠀⠀⠀⢺⣼⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡾⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⠤⠤⠞⠉⠀⠀⠀⠀⠘⢧⣀⠀⠀⠀⠀⠈⠛⣻⣿⣷⣇⢿⣿⠆⠀⠀⠀⣠⠟⠀⠀⠛⢦⡀⠀⠀⠀⠀⠀⡟⠀⠀⠀ ⠀⠀⠀⠀⠀⠎⠀⠇⠀⠀⠀⠀⠀⠀⠀⢀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⠤⣤⡤⢾⣿⠃⡿⢻⣦⣀⣀⣠⡤⠞⢃⡀⠀⠀⠀⠀⠙⢦⣤⣄⡀⠀⡇⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣧⣼⣧⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣭⣭⣤⣄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣷⣤⣤⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⣮⣍⣉⣉⣀⣀⠀⠀⠀ ⠀⠀⣠⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀ ⣴⣿⣿⣿⣿⣿⣯⡛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀ ⠉⣿⣿⣿⣿⣿⣿⣷⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⡟⠸⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀ ⠀⠘⢿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠉⠉⣿⣿⡏⠁⠀⠀⠀⠀⠀ ⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠞⠉⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠓⢄⠀⠀⠀⠙⠑⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⢀⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠈⠹⢦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣀⣠⣤⣴⣶⣶⣾⣟⠟⠀⠀⠠⠃⢠⠎⠀⠀⠀⣰⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠑⣟⢿⣷⣶⣶⣶⣤⣤⣀⠀ ⠀⠸⣿⣿⣿⣿⣿⡿⢻⠋⠀⠀⠀⠁⡰⠃⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢶⡀⠀⠀⠀⠈⢺⠛⣿⣿⣿⣿⣿⣿⠃ ⠀⠀⢿⣿⣿⣿⡿⢳⠃⢀⡀⠀⠀⡼⠁⠠⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠀⠑⠄⠀⠳⡛⢿⣿⣿⣿⡟⠀ ⠀⠀⢸⣿⣿⣿⣤⡇⠃⠀⠀⠀⢰⠃⠀⢡⡎⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢱⡄⠀⠀⠀⠀⢱⢸⣿⣿⣿⠃⠀ ⠀⠀⠀⣿⣿⢫⡟⠸⠀⠀⠀⠀⡏⠀⠀⡎⠀⠀⣸⡀⠀⠀⠀⠀⠀⠀⣄⢯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠈⢦⠀⠀⢫⡹⣿⡟⠀⠀ ⠀⠀⠀⢸⣿⣿⠁⣏⠀⠀⠀⢸⠁⠀⡸⠀⠀⣼⠟⡇⠀⠀⠀⠀⠀⠀⠘⣼⡆⠀⠀⠈⣧⠀⠀⠀⠀⠀⠘⡆⠀⠀⢧⠀⠀⢻⣿⠃⠀⠀ ⠀⠀⠀⠀⣿⠇⠀⠮⠀⠀⠀⡏⠀⠀⡇⠀⡰⠧⠤⠼⡀⢰⠀⠀⠀⠀⠀⠸⣿⣦⠀⠀⠘⣧⡀⠀⠀⠀⠀⠹⡀⠀⠸⡄⠀⠈⢿⣄⠀⠀ ⠀⠀⠀⢠⡟⡄⠀⡳⠀⠀⢰⠇⠀⣼⠁⡰⢁⣀⣀⠀⠹⡄⢣⠀⠀⠀⠀⠀⠙⣌⠛⠦⡀⠱⡙⢦⡀⠀⢣⠀⢣⠀⠀⢇⠀⠈⢏⣏⠛⢖ ⠀⠀⢠⢳⠃⡇⠀⢑⠀⠀⢸⠀⡜⢉⣦⣯⡵⠶⢦⣌⠐⠜⢄⠳⣄⡀⠀⠀⠀⠈⢲⣈⣭⣵⣿⣑⠳⣄⠈⡇⠘⡆⠀⢸⠀⠀⢸⠘⡆⠀ ⠀⣠⠃⡞⠀⢱⠀⢸⠀⠀⢸⡜⢠⣿⠟⢁⠐⢿⣷⣌⢳⡀⠀⠑⠸⠯⠉⠑⠒⢢⡟⠁⠘⣿⣶⡍⠻⣬⡷⣧⠀⢳⠀⠨⡄⠀⢈⠆⢹⡀ ⡜⠁⣼⠇⠀⠈⡆⠈⡆⠀⢸⠐⣾⠃⠀⣿⡖⣶⡽⣿⠀⣧⠀⠀⠀⠀⠀⠀⠀⣾⠀⣷⣶⣷⣹⣿⠀⢹⡾⢾⢀⣾⡀⠀⡇⠀⢸⠀⠀⢣ ⣠⡾⢼⡁⠀⠀⠹⡄⢱⠀⢸⠐⣻⠀⠀⣿⣏⣿⣧⢿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⣿⢿⣿⢿⣻⠀⠀⡷⠞⠉⣯⡇⢀⡇⠀⣸⠀⠀⠘ ⣿⡝⣾⠀⠀⠀⠀⢳⠈⢇⠸⡀⠹⡄⠀⠘⢇⣐⡨⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣔⣂⡸⠃⠀⢸⠓⠂⢰⢿⡇⢰⠀⢀⡇⠀⠀⠀ ⣷⣛⣼⠀⠀⠀⠀⠀⠣⡈⢆⢇⠀⠈⠢⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡄⠋⠁⢀⡷⢫⣗⡸⠀⡼⠀⠀⠀⠀ ⢷⣝⣾⡄⠀⠀⠀⠀⠀⠑⣌⢾⡀⠀⠀⠀⠀⠀⠀⣠⡖⠒⠒⠒⠒⠒⠒⠒⠒⠦⠤⣄⠀⠀⠁⠁⠀⠀⠀⡜⠛⣫⣷⠃⡼⠁⠀⠀⠀⠀ ⠸⣿⣸⣇⠀⠀⠀⠀⠀⠀⠀⢣⣇⠀⠀⠀⠀⠀⢸⣿⡿⠟⠛⠛⠛⠛⠛⠛⠛⠛⠿⣿⡇⠀⠀⠀⠀⠀⢸⣧⢿⢿⡟⡸⠃⠀⠀⠀⠀⢀ ⣧⠘⢿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁⠀⠀⠀⠀⢠⡿⣼⡹⣾⡟⠁⠀⠀⠀⠀⠀⢸ ⠈⠁⠈⠻⡽⡄⠀⠀⠀⠀⠀⠀⠀⠘⢦⠀⠀⠀⠀⠀⠓⢦⡀⠀⠀⠀⠀⠀⢀⡠⠞⠁⠀⠀⠀⢀⣴⣟⡳⢧⣻⡽⠀⠀⠀⠀⠀⠀⢀⡯ ⣿⣶⣤⣄⣹⡽⣆⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡀⠀⠀⠀⠀⠈⠓⠒⠒⠒⠚⠉⠀⠀⠀⢀⣠⣴⢯⡳⣞⣿⣷⣹⡇⠀⠀⠀⠀⠀⢀⣾⢳ ⣿⣿⣿⣿⣿⣿⣯⠷⣄⠀⠀⠀⠀⠀⠀⠀⠹⣿⣷⣒⣦⢤⣤⣠⣀⣄⣠⣤⣤⣴⣶⢻⡽⣻⣮⣗⣻⢼⣻⡟⢾⡇⠀⠀⠀⠀⢀⡾⣭⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣽⣳⢦⣀⠀⠀⠀⠀⠀⠹⡏⠁⠉⠓⠦⣉⡉⠛⣙⣩⠵⢚⠩⠳⣽⣽⣼⣿⣾⣷⣷⣿⣿⠆⠀⠀⠀⣠⣾⣻⣾⣿

⣤⡶⠛⣉⣋⠛⠻⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡟⠀⣾⣿⣿⣿⠀⢻⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣷⡀⣘⡿⣷⠟⢀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠿⠟⠿⣽⡇⢰⣟⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣴⡦⠀ ⠀⠀⠀⣸⣇⣸⣯⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣦⣤⣤⣄⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠋⣡⣤⣧⡈⠹⡗ ⠀⠀⠀⣷⡏⠀⢹⣷⠀⠀⠀⠀⢀⣠⣴⣾⣿⠿⠶⠞⢛⣫⣭⣭⣝⣽⣿⣿⣿⣿⣻⡛⢦⣄⡀⠀⠀⠀⠀⠀⠀⢨⣅⠀⣿⣾⣟⡿⠀⣹ ⠀⠀⠀⠓⠛⠷⠟⠿⠀⠀⣤⣾⣿⠷⠛⠁⠀⣠⣴⣾⠿⠛⠛⠿⠛⠉⠉⠉⠙⠋⠙⠛⠷⣮⣳⣆⡀⠀⠀⠀⠀⠀⠉⢿⡯⠟⠛⢁⣠⡟ ⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⡿⠋⠀⠀⠀⣰⣾⠿⠋⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠙⣦⠀⠀⠀⠙⢮⡿⣄⠀⠀⠀⠀⣤⣾⠁⣴⢾⡿⠟⠀ ⠀⠀⠀⠀⠀⠀⢀⣼⣷⠏⠀⠤⠈⢀⣾⡿⠋⠀⠀⠀⠀⢸⡃⠀⠈⠀⡀⠀⠠⠀⠸⣇⠀⠀⠀⠀⢻⣞⢧⡀⠀⢸⡷⠛⢶⣿⡛⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣾⣳⠏⠀⢀⠂⢀⣿⡟⠀⢀⡄⠀⠀⢀⣿⠀⠀⠀⢰⠇⠀⠐⠀⠀⣿⡀⠀⠀⢳⡀⠹⣏⣷⠀⢚⣷⣀⣤⡿⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣿⡟⠀⢈⠀⠀⣼⡟⠀⠀⣇⠀⠰⠚⢛⡯⠁⠐⠀⢸⠆⠀⠈⠀⠀⢹⡏⠑⠀⠈⣷⠀⢹⣟⡇⠀⠉⠉⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⣿⠃⠀⢂⠀⢠⣿⠁⠀⠐⣿⠀⠀⠀⣾⡇⠀⠐⠀⣹⠆⠃⠈⠀⢠⡞⣷⠀⠀⠀⢿⡀⠈⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣿⣿⠀⡀⠂⠄⣸⡿⠀⠀⢈⣿⠀⠀⠀⣿⣗⠀⢀⠀⣽⡆⠁⠀⠀⢰⣏⣿⡃⠀⠀⢸⡇⠀⣻⣽⣧⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⡏⣟⠀⠠⢁⠢⢸⡏⠀⠁⢈⣷⠀⠀⠐⣿⣿⠀⠀⠀⣿⡇⣶⠀⠀⢸⣧⣟⣇⠀⠀⣿⡇⢠⡜⣧⢿⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣸⣷⣏⠀⣷⠛⠀⣿⡇⠀⠀⢈⣿⣀⣠⣴⣿⣿⣻⣤⡴⣿⣧⡿⣤⢦⣾⣷⣿⣿⣶⣶⣿⡇⠈⣿⡹⣯⣇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣽⣽⠃⢰⡏⠁⣸⣿⡇⠀⡀⠠⣿⣿⣿⣿⣿⣿⣿⣍⠁⠀⠀⠀⠀⠀⣹⣿⣿⣷⣬⡽⢿⡇⠀⣹⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣼⣿⡟⠀⣾⠃⢀⣾⣿⣿⠀⡁⠀⣿⠀⢻⣿⣿⣾⣿⣿⠀⠀⠀⠄⠀⠀⢸⣿⣿⣿⣿⠇⣿⠀⣷⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⣹⠀⢰⣿⠀⢨⣟⡿⣽⡆⠀⡀⢿⡀⠈⠻⠾⣽⠟⠃⠀⠀⠀⠀⡁⠀⠀⠙⠛⠋⠁⡘⣷⠀⢿⣿⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⣿⠀⢸⡿⡀⠈⡿⣷⢸⡇⢻⡄⢺⡅⠐⢄⢠⠀⢀⠀⠈⠀⠈⠀⠀⠈⠀⠄⢂⠂⡑⠀⣿⠆⣻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⣽⡆⠘⣿⣷⡀⢱⠻⣦⣟⠸⣇⠼⣇⠈⠄⠠⠈⠀⡀⠄⠀⠄⠀⠄⢀⠁⠠⠀⠀⣀⣴⡟⠡⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⢳⣹⣆⡹⣶⢋⡔⢣⢜⣻⣎⣿⢀⢿⣄⣀⠀⠁⠀⠀⠀⠀⠀⡄⠀⠀⣀⣠⣤⡶⣿⡏⢄⣷⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢹⣯⢻⣯⣷⣬⣃⢾⡣⢿⣞⣧⢚⣿⠛⠻⠿⢶⣶⣶⣶⣶⣾⢿⣛⠻⣭⣓⣶⣿⡇⢎⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⢻⣿⣬⣿⣿⣿⣿⣾⡿⣯⢿⣏⣿⡌⠱⢌⠆⡆⣌⣩⠳⠙⢷⣾⣿⣻⢿⣿⣾⣙⢾⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡨⢒⣹⣿⣿⣿⣿⡿⢃⣽⣿⡿⣿⣞⣷⠯⠶⡼⣴⣤⣤⣤⣤⠾⣿⣿⣿⡿⣯⣿⣼⣿⣿⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣀⡀⢠⡾⢿⣯⣿⣿⣧⣸⣿⣯⣿⠁⠀⠉⠉⠀⢀⣀⣀⣀⣠⣀⠀⠀⠙⢿⣶⣟⣿⣿⣾⣶⣟⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠂⠀⠀⠀⠀⠀⠀⠀⠁⠀⠠⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡔⠡⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⡀⠈⠢⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⠎⢠⢃⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢡⠀⠑⡑⡀⠀⠀⠀ ⠀⠀⠀⡠⠂⢠⡎⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠐⠌⢆⠀⠀ ⠀⢀⠜⠀⡐⢡⠁⠀⠀⣀⣴⣶⣶⣦⣄⡀⠀⠀⠀⠀⠀⢠⠀⠀⠈⢆⢆⠀ ⢀⠊⢀⢜⡤⡎⢀⣴⣾⢿⣿⡿⢿⣿⢿⣿⣷⣦⣄⡀⠀⠈⡄⠀⠀⠈⠌⡄ ⠠⠀⠞⠋⡐⢠⠂⣿⣿⠈⠙⢧⠀⡼⠀⠙⠿⣿⡋⠱⣿⡦⣴⡀⠀⠀⠀⠰ ⠀⠀⠀⠀⢣⠁⠰⡉⢯⠳⣶⡄⠑⠇⠐⢶⣶⡿⠛⣰⠏⠀⡈⠐⢄⠀⠀⢀ ⠀⠀⠀⠀⠀⠈⠢⠈⢼⡀⠉⠀⠀⠀⠀⠀⠀⠀⣀⡗⠃⠬⠊⡠⠉⠢⠤⠊ ⠀⠀⠀⠀⠀⠀⠀⠡⣀⠉⠓⠒⣲⡶⣶⠖⠚⠉⠁⢀⡠⠰⡁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢓⠁⢸⣷⠈⢳⠤⠤⠊⠁⠀⠃⠰⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢩⡇⠈⡍⠁⠀⡇⠀⠀⠀⢀⠈⠇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢰⣓⠏⡹⠀⢀⠃⠀⢀⡔⠁⠀⢁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠎⠭⠛⠀⠀⢠⣏⣒⡦⠎⠀⠀⢀⡆⢡⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣐⡁⠠⠤⠀⠀⡤⠃⠀⠀⠀⢀⠠⠄⠊⠈⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠒⠂⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⢀⣠⠤⠤⠤⣄⡀⠀⠀⠀⠀⣠⠖⠒⠒⠺⡄⠀⠈⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⠏⠀⢀⡤⣄⣀⡨⠷⠖⠒⠚⠓⠒⠢⠴⣦⣹⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡏⠀⢰⢉⡤⠊⠁⢀⡤⠒⡀⠀⠀⠀⠀⠀⢄⠉⢷⢴⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⣏⠁⡹⠋⠀⠀⡠⠃⡀⠀⠨⠀⠀⠀⠀⠀⢠⠀⠀⠱⡹⣄⠀⠀⠀⠀⠀ ⠀⠀⠘⡿⠁⠀⠀⠀⠁⣀⠈⠢⡇⠀⠀⠀⠀⠀⠈⢣⠀⠀⠃⠘⡄⠀⠀⠀⠀ ⠀⠀⢠⠃⠀⠀⠀⢀⡎⢉⣣⣠⡇⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢱⠀⠀⠀⠀ ⠀⠀⢸⠀⠀⠀⠀⠀⢣⠐⢓⠎⢸⠀⠸⡄⠀⠀⡀⢸⠀⠀⢰⠀⠘⡆⠀⠀⠀ ⠀⢀⡞⠀⡄⠀⠀⠀⡆⢀⠎⠐⠯⢧⡀⢛⠤⠀⣧⡸⠳⣀⢸⠀⠀⡇⠀⠀⠀ ⡤⠊⢀⣠⠇⢀⠆⠀⡗⢋⣠⢶⣶⣦⡈⠁⠀⠀⣠⡴⣦⡀⠻⠀⣰⠀⠀⠀⠀ ⠉⠉⢩⠟⢀⣼⠀⡀⠰⡘⠹⠺⠜⡏⠁⠀⠀⠀⢏⠇⡏⠛⡇⢠⣿⡄⠀⠀⠀ ⠀⠀⠛⠒⢛⢌⣣⣜⣄⠙⢄⡉⠉⠀⢀⠀⠐⠀⠑⠒⠁⢸⣶⣉⣭⣋⣥⢄⠀ ⠀⠀⠀⠀⠀⠠⠿⢿⣿⣟⣷⣦⠤⢄⣘⣄⡜⣀⠤⠄⠲⢻⡛⡆⠀⠀⠸⣨⠂ ⠀⠀⠀⠀⠀⠀⠀⢠⡿⢏⠀⣻⣠⣶⠛⠜⢽⣿⣀⡴⠥⠜⠳⠟⠋⠉⠑⠁⠀ ⠀⠀⠀⠀⠀⣠⣾⢏⠈⢢⣵⣿⣿⣾⣷⢶⣾⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⣴⣿⣿⣇⣦⣮⣽⢟⠛⠛⠿⢖⠋⣂⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣷⣤⣿⣤⣨⣿⡀⠀⠀⠉⠙⠷⣤⠀⠈⢻⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠴⠚⠋⠉⠉⠉⠉⠉⠛⠒⠦⣤⡀⠀⠈⢻⣆⠀⠹ ⠀⠀⠀⣴⢶⣶⡶⠖⢋⡽⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠶⣾⣿⣠⡤ ⠀⠀⠀⣻⠦⢀⣠⣴⡿⠁⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣄⠀ ⠀⠀⠉⠀⢰⣿⣿⣿⣇⠀⢀⣴⡟⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠘⣷ ⢧⣀⠀⠀⢸⣿⡿⠟⢋⣴⠋⣸⠁⠀⠀⠀⠀⠀⠀⣴⢻⡶⡄⠀⠀⠀⠀⠀⠀⠘ ⠀⢨⠃⠀⡿⠋⢀⡴⠋⠀⢀⡟⠀⡀⠀⠀⠀⣹⣾⣅⠈⣇⡇⠀⠀⠀⠀⠀⠀⠀ ⣾⠃⠀⠀⠀⣰⠏⣀⡀⠀⢸⢷⡾⠁⣀⣤⠾⠋⠀⠀⠀⢹⣇⠀⠀⠀⠀⠁⠀⠀ ⡇⠀⠀⠀⣰⠏⣾⣿⣿⠀⠀⠘⠓⠛⠉⠁⢀⣴⣶⣄⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⡟⠀⠙⠛⠋⠀⠀⠀⠀⠀⢀⠀⠺⣿⣿⡿⠂⠀⡟⠁⠀⠀⠀⠀⢠⠀ ⠀⠀⠀⣿⠁⠀⠀⠀⠀⠸⠶⠶⡶⣾⠋⠀⠀⠈⠉⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡄ ⠀⠀⠀⢹⣦⡀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⡇ ⠀⠀⠀⢸⣍⣻⣶⣤⣤⣤⣤⣤⣀⣀⣀⡀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⡇ ⠀⢰⡄⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣷⣶⣿⠏⠀⠀⠀⠀⠀⠀⢠⡇ ⠀⠈⢿⣷⣦⣿⣿⣿⣿⣿⣿⣿⠟⠙⠿⠋⠈⢿⣿⣿⠏⠀⠀⠀⠀⠀⠀⢀⡞⠀

⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⢀⡤⠔⠒⠚⠉⠉⠉⠉⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠰⡏⠉⠀⠀⠀⠀⠈⠉⠒⢤⡀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⣄⠀⠀⠀⠀⠀⠀⣀⡀⠙⡖⡇⠀⠀⠀⠀⠀⠀⠀⢀⠜⠑⠒⠤⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⠀⠀⠣⠈⢢⠟⠞⠁⠀⠀⠀⠀⣀⠴⣋⠀⠀⠀⠀⠀⠉⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣀⡠⠴⠋⠑⠢⠤⠤⠤⠤⠐⠚⠛⢗⠒⠒⠂⠙⠳⠤⡀⠀⠉⠢⡀⠀⠀⠀⠀⠈⢣⡀⠀⠀⠀⠀⠀⠀ ⠘⠿⣍⣁⣀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢿⢆⠀⠀⠀⠀⠈⠑⢄⠀⠈⢢⡀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⢨⠃⠀⠀⠀⠀⠈⢦⡀⠀⠀⠀⠀⡴⡱⠁⠀⠉⠢⢄⣀⠀⠀⠀⠑⢄⠀⠱⡀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀ ⠀⠀⢠⠃⢀⣖⠤⢄⣀⠀⠀⡗⢦⡀⠀⡜⡜⠀⠀⠀⠀⠀⣼⡏⠉⠐⠒⠠⠬⣦⠀⠱⡀⠀⠀⠀⢸⠀⠀⠀⠀⠀ ⠀⢀⡏⠀⣸⣦⢍⣐⡚⠛⣻⠃⠀⠈⠲⠾⣀⡀⠀⠀⠀⢰⢿⢀⡠⢄⡀⠀⠀⠀⢣⠀⢱⠀⠀⠀⢸⠀⠀⠀⠀⠀ ⠀⣸⠀⣰⡏⠸⠉⠒⠛⠛⡟⠒⠉⠁⠀⠀⠀⠉⠁⠒⠒⠾⠦⠬⡤⠤⠤⠄⢠⠐⠘⣇⠈⡆⠀⠀⢸⠀⠀⠀⠀⠀ ⠀⣇⡴⢁⠇⡇⠀⠀⠀⣸⠀⢀⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣷⣦⣄⣸⠆⠀⢸⡀⣿⣄⠀⢸⠀⠀⠀⠀⠀ ⠀⠿⠀⢸⠀⡇⠀⠀⠀⣧⣴⣿⡿⠛⢻⣧⠀⠀⠀⠀⠀⠀⢰⠋⠀⣹⣿⣿⣿⠃⠀⠀⢿⣿⣿⠀⢸⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⠀⡇⠀⠀⢀⢿⠸⣿⠇⠠⠾⢿⠀⠀⠀⠀⠀⠀⡜⠒⠊⠉⠉⢹⠙⠀⠀⠀⡞⣿⣿⠁⠘⡆⠀⠀⠀⠀ ⠀⠀⠀⠸⣷⣧⠀⠀⢸⠀⡇⠸⡄⠀⠀⠀⡇⠀⠀⠀⠀⠀⠹⡀⠀⠀⢀⡞⡇⠀⠀⣰⠷⠟⠁⠀⠀⢻⠀⠀⠀⠀ ⠀⠀⠀⠀⢻⠿⡀⠀⢻⠀⡇⠀⠱⢄⣀⠜⠁⠀⠀⠀⠀⠀⠀⠉⠒⠒⠊⢠⠃⠀⢠⠃⠀⠀⢠⠀⠀⠀⢧⠀⠀⠀ ⠀⠀⠀⠀⡞⠀⠙⢄⢸⠀⣧⡀⠀⠀⠀⠀⠀⠀⡔⠉⠱⡀⠀⠀⠀⠀⠀⡜⠀⡠⠃⠀⠀⠀⣧⣀⠀⠀⠈⢧⠀⠀ ⠀⠀⠀⡸⠀⢰⡄⠈⠙⠇⢻⣏⡒⠤⢀⣀⣀⣀⠙⣦⣔⣁⣀⣀⡠⠤⢾⢃⠜⠁⠀⡇⠀⣸⠁⠈⠉⠒⠢⠤⢷⠄ ⠀⠀⢰⠷⠊⠁⠳⡄⠀⠀⠀⢩⠙⠳⢶⣖⡆⣠⣿⢛⣻⣿⣿⣿⣦⠀⢸⣍⠀⢀⠞⢳⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⢀⣾⠀⡰⢻⣀⡴⣿⣿⠿⣿⠻⣯⠀⢹⣷⣏⢹⡶⠋⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠚⠘⠋⠀⣾⡁⢀⣨⡇⠀⠈⡆⠹⡇⢸⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣄⠀⠀⠀⠀ ⠀⢰⠟⠉⠛⠳⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠋⠉⠀⠀⠈⣧⠀⠀⠀ ⠀⡿⠀⠀⠀⠀⠀⠈⠙⠶⠶⠖⠒⠒⠚⠒⠲⠛⠁⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀ ⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀ ⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⠀⠀ ⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀ ⢸⠇⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⢰⡄⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄ ⣿⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⢀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇ ⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⢤⣀⠀⠀⠀⠀⣀⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇ ⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠀ ⠀⠀⠙⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡤⠞⠋⠀⠀ ⠀⠀⠀⠀⠈⠉⠛⠓⠒⠒⠒⠒⠒⠒⠒⠒⠒⠚⠛⠛⠋⠉⠉⠁⠀⠀⠀⠀⠀

⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠠⠀⠠⠀⠀⠄⠀⢤⡿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠠⠀⠠⠀⠀⠄⠀⠄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠈⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⠀⠀ ⠀⠀⠀⢀⠀⠀⠀⠀⡀⠀⢀⠀⢀⠀⠀⣀⣾⠏⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⣴⠟⠀⠀⡀⠀⠀ ⠄⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡟⠀⡀⠀⢰⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⣠⣾⣿⠁⠀⠰⠀⠀⠀⠀ ⠀⠀⠀⠈⠀⠀⠀⠀⠁⠀⠀⠀⠈⢀⣾⣿⠇⡔⢳⣀⣸⣀⡀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠋⠀⠀⠀⠠⠀⠀⠀⠀ ⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢐⣿⣿⣿⡼⠀⠀⠀⠈⢹⠃⡀⠀⢀⠀⢀⠀⠀⡀⠀⡀⣠⣶⣿⡿⠋⣀⣠⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⢿⡏⠀⠀⠀⠀⠀⠀⠙⠦⠤⠤⠤⢤⣴⣆⠀⢠⣾⣟⣿⣿⠗⠉⠰⠥⠄⣠⠀⠀⠀⠀⠀⠀ ⠁⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⣸⣿⣿⣾⠇⠀⠀⠀⠀⠀⣤⠼⠃⠀⠀⠀⠀⠉⠢⡙⠻⢿⣿⡿⠃⠀⠀⠀⠀⠛⢏⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠿⠋⡿⠿⠀⠀⣠⣤⡤⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠙⠲⣄⠀⠀⠀⠀⠀⣈⣳⠆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⠀⢀⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠈⠳⡄⠀⠀⢿⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⠟⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⢠⡾⠀⠀⡆⠀⠀⠀⠀⠀⣷⡀⠀⠀⠘⢦⢤⣼⡆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⢠⠏⣇⠀⠀⡄⠀⠀⠀⠀⠀⢹⢳⠀⠀⠀⠈⢧⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⢀⢾⠁⠀⠀⠀⠀⠀⣰⣇⣀⣹⡀⢰⠁⠀⠀⠀⠀⣀⣼⣨⣇⠀⠀⠀⣸⣿⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⢀⡴⠋⠎⠀⠀⠀⠀⠀⢠⠃⠀⠀⢸⠀⢸⠀⠀⠀⠀⠀⢠⠇⠀⠸⡄⠀⠸⣿⣿⣿⡆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⡇⠀⠀⢀⡤⠊⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⣇⡆⠀⠀⠀⠀⢀⡎⠀⠀⠀⢳⠀⠀⠈⢿⣿⡁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⣇⣠⣔⣁⠤⠔⠒⠉⣷⠀⠀⠀⢠⠏⣀⣀⣀⣀⡀⢹⠇⠀⠀⠀⢀⡞⢀⣠⣤⣶⣬⣇⠀⠀⡼⢷⣷⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢯⠉⠁⠀⠀⠀⠀⠆⠹⡆⠀⢠⣿⣾⢿⣿⣿⣿⡿⣿⠄⠀⠀⣠⡾⠡⣿⣿⣿⡍⠙⣿⠁⢀⣿⡆⠀⠙⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⢸⠀⠀⠹⡀⣼⡏⠁⣸⣿⣿⢿⡷⡇⠀⣠⠞⢹⠃⠀⡿⡟⢿⠃⠀⡟⡆⢸⠀⠑⠢⠤⠼⠆⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⢸⠀⠀⠀⠳⡇⢳⠀⢻⣄⠀⢰⢣⡧⠞⠀⠀⠀⠀⠀⢿⣀⡼⠀⢰⠇⠹⢻⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢰⠛⠀⠀⠀⠀⢸⡆⠀⠀⠀⠉⠀⢧⠀⢙⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢁⢠⣾⡀⠀⢸⠀⠀⣶⡿⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡎⠀⢠⠀⠀⠀⠀⡇⠀⠀⠀⠀⢲⣄⣿⡌⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⣿⠃⠀⢸⠀⠀⢸⠟⠛⠀⠀⠀ ⠀⠀⠀⠀⢀⠞⢀⣠⠃⠀⠀⠀⡔⢻⢸⡀⠀⠀⠈⡇⠙⠓⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⣠⠟⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⡴⠗⠚⠉⢸⠀⠀⠀⢠⡇⠀⠟⢣⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠉⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⡸⠹⡄⠀⢈⣇⠀⠀⣧⠀⠀⠘⢷⣶⣤⣄⣀⣀⣀⡤⠔⠋⢧⡿⡀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⡇⠀⢙⣶⣿⣿⡆⠀⣿⢦⡀⠀⠀⢹⣿⣦⣀⣩⠟⠀⠀⠀⠈⠁⢣⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠞⢣⡴⠋⠀⢿⣿⣿⡄⣟⣶⡻⣦⣀⢀⣿⣻⣿⣿⣄⡀⠀⠀⠀⠀⠈⢆⢀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⠶⠶⠶⢶⢶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠉⠙⠳⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣽⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⡿⠟⣻⡟⢹⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣙⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡿⠀⠠⠟⠁⣸⡏⠀⠀⠀⠀⠀⠀⣀⣄⣀⣠⣤⡤⢤⡤⣤⣄⣀⣀⣸⣿⣿⣿⣄⠤⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠇⠀⠀⢀⡄⣿⣇⣤⡿⠛⠛⠛⠛⠉⠈⠋⠉⠀⠀⠀⠀⠀⠉⠉⠉⠉⠛⠛⠿⣿⣦⣤⣽⣤⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⠀⠀⠀⢀⣘⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⠀⠀⠉⢦⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣾⣿⠀⣀⣼⣶⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡀⠀⠈⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣾⣿⣿⣾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢠⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣾⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡤⠤⢰⢲⣶⡖⠒⠒⠒⠊⠓⠒⣦⣄⣀⣤⡀⠀⠀⠀⠀⠀⣧⠴⠋⠀⠀⠀⠀⠀ ⠀⠀⢀⣀⣸⣿⣿⡿⠟⠃⠀⠀⠀⠀⠀⠀⢀⣤⠖⠋⡇⡏⢣⠤⡟⢹⡏⣧⠀⠀⠀⠀⣀⣸⠁⡇⢹⠟⣏⠙⢶⣤⡀⢠⠇⠀⠀⠀⠀⠀⠀⠀ ⠀⡔⠋⠀⠸⠟⠑⡄⠸⡆⠀⠀⣀⡤⠖⡎⠉⢸⡀⠀⣿⣇⣸⣤⣇⡈⠀⣸⡞⡇⠀⢠⣧⣇⣀⣧⣟⣀⣸⡀⣸⠀⢿⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠀⠀⠀⣹⠀⠹⡤⠞⠁⠀⠀⡇⠀⠀⢳⣆⣿⡏⣽⣿⣿⣿⣿⠛⠻⢷⢀⡾⠟⣿⣿⣿⣿⣿⢻⣧⡇⠐⡾⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⡀⠀⠀⠀⠀⢀⡟⠀⠀⢷⠀⠀⠀⠀⡃⠀⠀⠀⠹⣿⠀⢛⣻⣿⣿⣿⠀⠀⢸⠟⠀⠀⣿⣿⡿⣿⠀⡟⡿⠁⢸⡟⢿⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠙⢦⣄⣤⠖⠋⠀⠀⠀⣸⢰⠀⠀⠀⢱⠀⠀⠀⠠⣿⠀⠈⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠉⠙⠉⠁⢸⡇⡇⠀⢸⡇⠀⠙⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⢿⡀⠀⠀⠘⡆⠀⠀⡆⢸⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢺⣿⠁⢠⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠏⠀⡇⠀⠀⠀⢿⠀⠀⢸⣸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠟⡿⢀⢢⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⡇⢦⠀⠀⠈⣇⠀⠘⣧⣷⣄⣀⠀⠀⢿⠛⠲⡦⠀⣀⣠⡤⢾⠟⠀⢰⠇⣀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣼⡀⠀⠠⠈⠷⡄⠸⣿⣞⠙⠛⢿⣗⡒⢲⣾⢿⣍⡀⠀⣿⡀⠀⡏⣼⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠉⣿⡀⣠⣶⣷⣿⣶⣿⣿⣦⡀⠀⠈⣿⣼⣷⡀⢹⣿⣶⣿⣧⣾⣸⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣦⣰⡏⢳⠀⢳⣿⣽⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⡋⠳⡀⠀⠀⠀⠀⠀⣠⣿⠿⠿⠃⠈⢿⣿⣿⣿⡟⢪⠻⣧⣼⣆⣾⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣤⠖⠛⠛⠛⠛⡇⠀⠹⢦⣴⣤⡀⢰⣿⣧⣀⣀⣀⣀⣀⢿⣿⢿⣿⣿⣟⣛⣻⣿⣷⢸⣿⣿⣿⡟⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣉⣉⠀⠀⠀⠃⠀⠀⣰⣿⣿⣿⣾⣏⠈⠛⠛⠛⠉⠉⢸⣿⣿⣛⣛⣿⣿⢟⣩⣽⠿⣿⣭⢿⣧⠈⣿⡆⠀⠀⣀⣤⣤⣠⠤⠤⢤⢤⡀⠀⠀ ⠻⣭⢤⡄⠠⠖⠀⠀⣰⣿⣿⣿⣿⡿⠛⢷⣄⠀⠀⠀⠀⢸⣿⡋⣩⣽⣿⣻⡽⠟⠁⠀⠸⣿⡀⣿⡀⡟⣿⡶⠿⣿⣿⣿⣿⣦⠀⢘⢯⡁⠀⠀ ⠀⠹⠭⠴⠶⣦⣴⠾⣿⠛⣾⣿⡿⠁⠀⠈⢻⣷⣄⠀⠀⣿⣿⣶⣿⣿⡏⠉⠀⠀⠀⠀⠀⣿⡇⣸⡇⠁⢹⣿⡀⠹⣿⣿⣿⣿⣷⡀⡰⠿⣦⠀ ⠀⠀⠀⠀⠰⣿⣿⠆⢁⣴⣿⡟⠁⠀⠀⠀⠀⢿⣿⣷⣿⣿⠿⠋⣡⣿⣿⣠⣤⣤⣤⣤⣶⡿⣧⢿⡇⠀⢸⣿⡇⠠⠌⣿⣿⣽⣿⠧⣽⣦⣼⠇ ⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⢻⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⡏⠀⠀⠈⣿⣿⠀⠀⠀⠀⠀⠈⡇⠀⢸⣇⠀⣾⢻⣿⠀⠀⣿⣿⣿⡿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣦⣴⣄⠀⠀⢀⣼⠋⢹⣿⡄⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⣿⡁⠘⣿⣅⠋⠉⣽⣷⣶⠿⠛⠋⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣤⣴⠟⠁⠀⣸⣿⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⢸⡇⠀⠛⣿⣀⣶⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⣯⡁⠀⢀⣀⣿⢿⠀⠀⠀⠀⠀⠀⢸⡇⢀⣀⢿⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠂⠈⠻⢦⣬⠉⣿⡿⠷⢶⣤⣄⣀⣠⣼⣿⡋⠁⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⢿⠶⠶⠶⠶⠶⠷⠿⠿⠷⠶⠦⠴⠾⠿⠿⠿⠿⠶⢶⢿⢿⠷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣷⠀⠀⢰⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⣧⠀⣼⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣿⣿⡆⠘⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣸⣿⣿⣿⡄⠙⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⣿⣿⣿⣷⡀⣿⣿⣿⣿⠿⠿⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀⢻⣿⣿⣿⠟⢿⣿⠛⣦⡀⢻⣿⡇⠀ ⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⣶⡞⠻⣶⠛⢻⡄⠹⠀⠀ ⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣾⣿⣶⣿⣿⠆⠀⠀ ⠀⢠⣿⣿⣿⡄⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣉⣉⣉⣉⣉⣉⣉⣉⣉⡉⠀⠀⠀ ⠀⢸⣿⣿⣿⣷⡀⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠃⠀⠀⠀ ⠀⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣤⠞⠛⣻⣧⣷⣾⣿⣿⣿⣿⣶⣶⣯⣤⣀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⢠⠀⠀⠀⢔⣾⣷⠟⠁⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣭⡢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⢴⣿⣯⡻⣟⣵⣿⣿⣁⠨⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣽⡿⣹⣾⠷⡿⢿⣿⢿⣿⠀⡄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣦⡠⠀⠀⠀⠀⠀⠀⠀ ⢀⣼⠿⣽⣿⠁⢎⡀⢌⣠⠏⢻⡆⢸⣿⣿⢿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣷⣻⢿⣿⣿⣿⣿⣷⡠⠀⠀⠀⠀⠀⠀ ⢸⣯⢿⣿⡿⡀⣘⠎⠙⢶⡀⠌⣿⠑⣿⣯⢿⡿⣿⣿⣯⣟⡿⣿⣿⡿⣿⣽⣟⡿⣭⣟⣾⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀ ⢸⢯⣿⣿⣷⡑⠑⠲⡄⡖⠛⠒⣼⣿⣿⣽⣯⣿⣿⣿⡷⣯⣿⣽⣳⢿⣽⣻⣾⣽⣿⣿⣿⣾⣿⣿⣿⣿⣧⠂⠀⠀⠀⠀ ⢸⣯⣿⣿⣿⠿⣧⣆⠻⣄⣶⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀ ⠘⣷⣿⡙⠁⢀⣻⣿⣿⠛⠻⢿⣿⣿⣿⣿⡿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀ ⠀⢽⣥⣷⠂⡀⢠⣿⣯⣑⣠⣾⣿⣿⣿⣿⠃⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣣⠀⠀⠀ ⠀⠀⠙⣿⣿⢿⣶⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣻⠀⠀⠀ ⠀⠀⢰⣿⡏⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⠀⣀⣀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⠀⠀ ⠀⠀⣿⠇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠀⠀⠀⠈⠻⢿⣯⡻⢿⣿⣟⣿⣿⣿⠿⠿⠿⠟⢻⣿⣿⣿⣿⣿⢇⠀⠀ ⠀⢰⡟⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡛⠿⣆⠀⠀⠀⠀⠀⠀⠉⠁⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣟⣿⣯⠆⠀ ⠀⠺⣧⣄⣠⣿⣿⡿⠛⠻⣿⡿⣿⣿⡇⢀⣠⣤⣤⣤⣅⣒⠀⠀⠀⠀⠀⠀⠀⣮⣶⡾⢿⢷⠖⣿⣿⣿⣿⣿⡹⣿⣧⠀ ⠀⠀⢸⣿⣿⣿⡿⠠⠤⣄⡈⠧⢿⣿⣯⠛⠛⠛⠉⠉⠉⠙⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⡜⣿⡆ ⠀⢠⣿⣿⣿⣿⣿⣄⠀⠘⠮⠖⠈⢿⣿⣧⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⡿⣽⣿⣸⠇ ⠀⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣤⣶⣶⣽⣻⢿⣷⠦⠀⠀⠀⠀⢄⣀⣀⡀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⡿⠀ ⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣤⣀⣀⡀⣠⠞⢉⣶⡤⢤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⣻⣿⣿⣿⣿⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣯⣵⣶⣟⣳⢶⡄⠈⢻⣿⣿⣿⡿⣿⢿⠅⠀⠀⠀⠀⠀ ⠀⠀⠙⢿⣿⣿⣿⣷⣾⠯⣿⣿⣿⣧⣀⠀⠀⠈⠙⠛⠿⢿⡿⣿⣏⣁⣀⣉⣙⣣⠀⣠⣿⣿⣿⣷⣿⣭⣶⣤⡆⠀⠀⠀ ⠀⠀⠀⠀⠈⠉⠉⠉⣱⣻⣿⣿⣿⠋⠚⠻⠭⠷⣲⢤⣀⠀⠊⠛⢤⡈⣻⠋⠈⡽⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠎⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⢰⣿⣿⣿⡿⠁⠀⠀⠀⢀⣠⣶⠞⠘⠯⡲⣄⣀⣽⣅⣀⡞⠀⢹⣿⣿⣿⣿⣿⡿⣿⡿⡅⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⣿⣾⣿⣿⡿⠁⠀⠀⠀⠀⠉⣼⣯⣽⣶⣴⣶⣿⣿⣿⣿⣻⣻⢷⣾⡟⢿⣿⣯⣷⡿⣿⣿⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠛⠿⢿⣿⣛⡶⣤⣀⣀⣀⣀⣀⣿⣿⣷⣿⣲⣌⡻⣛⣿⣿⣿⣿⡿⠟⡻⣿⣷⣿⣿⣧⣸⡇⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠺⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⠀⣿⡟⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠒⠒⠒⠒⠒⠒⠠⢤⣄⣀⠀⠀⠀⠀⡴⠋⠀⠀⠀⢀⡟⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣊⡁⠀⠀⠀⠀⠀⠀⠀⠀⢠⢾⣷⣌⠙⠒⢤⠊⠀⠀⠀⠀⠀⡜⠀⠀⠀ ⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⢀⡤⠊⢹⣽⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀ ⠘⠿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠉⠉⡴⠋⠀⠀⠘⢿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠃⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀ ⠀⠀⠀⠉⠙⠻⢷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠢⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⡚⠉⠉⠁⠒⠒⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⡺⢻⠀⠇⠀⠀⠀⢀⡀⢀⣾⣻⣅⣶⣤⣀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⣠⠞⢓⠞⠂⢾⢘⠀⠀⠀⢀⡜⢩⠏⠀⣀⣈⣦⢱⠀⠉⠲⣄⡀⠀⠀⠀⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⢠⠞⡹⠀⣮⣤⣤⣸⣾⠀⠀⢀⣾⣠⠃⣼⣿⡛⠉⠛⢻⡆⠀⢠⡈⢯⡀⠀⠀⢹⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡰⢃⠀⣇⣼⣿⣷⠀⠉⣿⠀⡠⠊⠾⠁⠀⠡⡞⠁⠀⠀⠀⡗⠀⠀⡏⢒⠿⢦⠀⢸⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⢀⡾⠕⢿⠀⣿⠙⠾⡇⠀⠀⣽⠚⠀⠀⠀⠀⠀⠀⠣⡀⠀⢀⣼⡇⠀⢀⡇⢸⠀⠀⢀⡞⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⠀⠀⡇⠀⣿⡆⠀⠙⠦⠴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⢁⡟⡇⠀⢸⢻⡈⠀⣠⠊⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⠀⢳⠀⡟⢾⣦⡀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⡜⣸⠀⡄⡇⢸⣇⠔⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡈⡆⠰⡈⠢⡀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⣀⣾⠟⣅⣼⡟⠀⡨⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢄⡈⢢⣌⠑⠲⠤⠤⣀⣀⣀⣀⣤⠖⠋⠉⠁⣰⣿⠿⠓⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⣄⡀⠀⠀⠀⠙⣄⢰⣁⠴⠒⠉⢯⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢡⠈⠉⠉⠉⡹⢿⡞⢣⠀⠀⠀⡄⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡼⡀⠀⣠⠊⠀⣸⠁⠀⢣⠀⠀⡿⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣠⠗⣾⠁⠀⠠⠃⠀⠀⠀⢃⠀⡇⠼⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⠃⢰⡇⠀⠀⠀⠀⠀⠀⢷⡿⠀⢣⡴⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡁⠹⣋⣘⠁⠀⠀⠀⢀⠴⣝⡛⠀⢲⠎⣷⣺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⣀⣁⠴⢿⣿⣿⣿⣿⠂⠈⡏⢉⣽⣳⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠤⠴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⡜⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢣⣖⠠⠛⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⠀⠉⢷⡀⠀⠈⢧⠱⡄⠀⠙⣿⣯⠀ ⠀⠀⡜⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣷⠃⠈⢧⡃⢜⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠀⠀⠀⠙⢆⠀⠈⣷⢱⡀⠀⠘⢿⣇ ⠀⢰⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠃⠀⠀⠀⢻⣄⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠶⠶⠶⠒⠋⠳⣄⠚⣧⢧⠀⠀⠀⢻ ⠀⢸⡐⠁⠀⠀⠀⠀⠀⠀⠀⣴⡟⠁⠀⢀⣠⣤⠖⠻⡄⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣏⠀⠀⠀⠀⠀⠀⠙⢮⡸⡞⣆⠀⠀⠀ ⠀⡒⣘⠀⠀⠀⠀⠀⠀⢤⣼⡿⠴⠶⠛⠛⠉⠀⡀⠀⠹⣾⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣡⣫⠗⠀⠀⠀⠀⠀⠈⠳⣿⣸⠀⠀⠀ ⠀⡱⠤⡁⠀⠀⠀⠀⢠⣾⠟⠀⠀⠀⢀⣠⠴⢋⢳⠀⠀⢹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣇⠃⠀⠀ ⠀⣇⠒⡁⠀⠀⢀⣴⣻⠏⠀⠀⠀⠀⠉⠉⠉⠙⠚⠇⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠃⣀⣠⣤⠤⢀⣀⣤⣶⣼⡄⢸⣿⡄⠀⠀ ⠀⡧⡉⡔⠀⢠⠞⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡇⠀⠀⠀⠀⠀⠀⠀⣴⢿⣏⣩⣥⣴⣶⣿⣿⣿⣿⢿⣿⠀⣸⣿⡇⠀⠀ ⠰⣷⠡⡘⢄⣣⠞⠁⠀⠀⠀⣀⣀⣤⣤⠴⠶⠖⣦⡀⠀⠀⠈⣷⠀⠀⠀⠀⠀⢀⡾⢡⡾⣿⣿⣿⣿⣿⣿⠛⣿⡿⢠⡇⠀⣿⣚⣷⠀⠀ ⠸⣧⢃⣼⣞⣡⣤⣤⣤⣤⣴⣴⣾⣶⣶⣿⣶⣶⣶⡟⠀⠀⠀⢹⠀⠀⠀⢀⡴⢋⢔⡿⠹⠓⠀⣿⣿⣿⣿⠀⣿⡟⠈⠀⠄⣿⡜⣿⠀⠀ ⠘⡷⠋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⢻⣿⡟⢻⠛⠂⠀⠀⣸⠀⢀⡴⢋⠔⣡⠞⠀⠀⠀⠀⢿⣿⣿⣿⣤⣿⠃⠀⠠⠀⣿⢺⣽⡂⠀ ⢈⡷⠀⠈⢿⡄⠀⠀⢸⣿⣿⣿⣿⣿⠀⠈⣿⡇⠀⠀⠀⠀⠀⣿⠒⠭⣐⢡⡾⠋⠀⠀⠀⠀⠀⠸⣿⣿⣱⣿⠏⠀⠀⡀⠁⢻⡳⢾⡇⠀ ⠀⣿⠀⠀⠈⠳⠀⠀⠈⣿⣿⣿⣟⣿⣧⣴⣿⡇⠀⠀⠀⠀⢠⡟⢌⣱⠶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠉⠁⠀⠀⠄⠀⠀⢸⣿⣹⡇⠀ ⠠⢹⡄⠀⠀⠀⠠⡀⠀⠘⣿⣿⣟⣧⡯⠿⡿⠁⠀⠀⠀⠀⡼⠗⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⢂⠁⠠⠈⠀⠸⣧⢻⡇⠀ ⠠⡙⡇⠀⡀⠁⠀⠈⠀⠀⠀⠀⠀⠀⠒⠂⠀⠀⡀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠠⠀⠂⠀⠂⠀⠁⠠⢸⣿⣹⡇⠀ ⠠⡑⢿⠀⠀⠀⠁⠠⠈⠀⠂⢀⠂⠄⡀⠄⠈⠀⠄⠀⠀⠀⣀⠀⠀⠀⣀⣠⣴⣶⣤⣤⡴⠋⠀⠀⠀⠀⠄⠀⠁⠀⠁⠠⢠⣿⣷⣹⠇⠀ ⠠⡑⢺⣧⠀⠁⠀⠄⠀⠂⠀⠄⠠⠀⠄⠀⠁⠄⠀⠀⠈⠀⢸⡿⣿⡟⣻⢛⠿⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣱⣿⢫⣷⣹⠃⠀ ⠀⡑⠢⣿⣧⡄⠀⠄⠀⠀⠁⠀⠀⠀⠄⠀⠄⠀⠀⠀⠀⠁⣿⠲⣍⠲⠥⣎⠳⣰⠹⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⡟⣼⢻⡧⣿⠀⠀ ⠀⢡⠃⡼⣿⣿⣶⣄⠠⠀⠀⢀⣤⠤⣤⣄⣀⠀⠠⠀⠀⠁⣿⠱⡎⢭⠓⣌⢣⢣⡝⣼⠃⠀⠀⠀⣀⡤⠶⠒⠛⣿⢧⡻⣜⣿⢳⡟⠀⠀ ⠀⢠⠃⠖⣹⣿⣿⣿⣿⣶⣤⣸⣧⣄⠀⠀⠉⠛⢦⡀⠀⠀⠘⣧⡝⣊⠷⡌⢖⢣⣼⠏⠀⣀⡴⠋⠁⠀⠀⣀⣴⡿⣣⢿⣼⣟⣳⡏⠀⠀ ⠀⠠⣉⠚⠤⣿⣿⣿⣿⣿⣿⣭⣛⣮⡝⢦⡀⠀⠈⢳⡄⠀⠀⠈⠙⠲⠷⠼⠟⠞⢁⣠⠞⠋⠀⠀⠀⣴⣯⣾⣿⣷⡹⣞⣾⢣⣿⠀⠀⠀ ⠀⠀⢢⠙⡰⡈⢿⣿⣿⣿⣿⣿⣿⣾⣿⣆⠃⠀⠀⠀⢻⡶⣤⣤⣄⣀⣀⣤⠶⠚⠉⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣞⢧⣻⢏⠀⠀⠀ ⠀⠀⢠⠩⠔⣡⠊⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠙⠷⢾⠾⠛⠉⠀⠀⠀⠀⠀⣀⣴⠞⢹⣿⣿⣿⣿⣿⡿⣫⠞⣧⣿⠂⠀⠀⠀ ⢄⡀⠀⢃⠎⢤⡉⢆⠻⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠟⠁⠀⣼⣿⣿⣿⣯⣷⣹⣵⣿⣿⢛⠀⠀⠀⠀ ⠢⠜⡐⢌⡸⢄⠚⡄⠣⢌⠻⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠟⠁⠀⠀⢠⣟⣿⣿⣿⣿⣿⣿⣿⡿⢁⠂⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⡐⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠘⠀⠀⢀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⠀⠀⠀⠀⣸⢹⠀⠀⡇⠀⠀⠘⠀⡇⢸⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠈⢄ ⠀⠀⠀⠀⠀⡐⢠⠗⠸⠀⠂⡇⠀⠀⠀⠇⠰⣿⠀⠀⠀⠇⠀⠀⠀⠂⠀⠀⠀⠀ ⠀⠀⠀⢀⢠⠃⡎⠀⠀⡆⠀⣷⠈⠀⠐⢜⡀⠹⡀⠀⠀⡴⡂⢄⢠⠀⠀⠀⠀⠀ ⠀⠀⠀⡌⣼⣶⣥⣥⣤⣬⡓⠼⠣⣠⣀⢸⡌⣄⢘⣤⡀⠇⠈⠈⢸⠀⠀⠀⠀⠀ ⠀⠀⠘⢰⣿⠋⢹⣏⣩⠿⣿⡇⠀⠀⠀⠈⠑⠃⠫⠯⣄⠜⢤⢄⣸⠀⠀⠀⠀⠀ ⣠⠀⠃⠻⣇⠀⠿⠏⠙⠾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⡺⢿⣿⣿⣾⢇⠀⠀⠀⠀ ⡅⣾⠀⢰⣧⠀⠫⡀⠀⢠⡞⠀⠀⠀⠀⠀⠀⠀⠀⣼⡶⣖⣻⣿⣿⣷⡄⠀⠀⠀ ⠙⠼⣆⠸⠙⡄⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠰⣯⠂⠈⠉⠹⣿⠋⡟⠀⠀⠀ ⠀⠀⠈⣆⣋⠉⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠤⢤⠜⠁⡟⢻⣆⡀⠀ ⠀⠀⡘⠀⠀⢀⡤⠞⠛⢉⣉⣉⠒⠠⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⡜⢀⣯⡞⣧⠀ ⢀⠔⠓⠲⢶⢱⠀⡔⠁⠀⠀⠀⠀⠉⠑⠈⠖⡄⠀⠐⣶⣚⠥⡈⣠⠮⠊⠼⡪⠝ ⠁⠀⠉⠉⢺⠐⢧⣤⣀⠀⠀⠀⠀⠀⠀⢀⠸⢳⣀⠔⠁⠀⠉⠻⠁⠀⠀⡜⠀⠀ ⠀⠀⠀⠀⣹⡄⠀⠀⠉⠉⠃⠒⠒⠂⠘⡡⡐⢏⠱⠀⠀⠀⢠⠃⠀⠀⠀⡢⢄⠀

⡶⢫⣭⡝⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣧⣹⡿⢃⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠁⠉⣗⣻⡃⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⢠⡀⢀⠀⠀⠀⠀⠀⠀⠀⡴⣚⣽⡛⢦ ⠀⠀⣿⣨⣗⠀⢀⣤⡶⠟⠛⣉⣽⣶⣯⠿⠿⠿⢯⣷⢤⡀⠀⠀⠀⢦⣼⣿⠇⣸ ⠀⠀⠀⠀⢀⣼⠟⠉⢀⣴⠟⠋⠀⡀⠀⠀⠀⠰⣆⠈⠙⢷⣆⠀⠀⣤⣏⣴⠾⠃ ⠀⠀⠀⢠⣿⠃⠈⢠⡿⠃⠀⠀⣸⡁⠀⢰⠀⠀⢸⡄⠀⣄⠻⣧⠐⣯⣩⠟⠀⠀ ⠀⠀⠀⣿⡇⠀⠂⣼⠃⢸⡄⠉⣽⠀⠀⣯⠀⠀⡘⣧⠀⢸⡄⢿⡇⠀⠀⠀⠀⠀ ⠀⠀⢠⣿⠆⠈⢄⡟⠀⣸⠄⠠⣿⠀⠀⣿⠀⠀⣽⢷⡀⠈⡇⢸⣿⠀⠀⠀⠀⠀ ⠀⠀⢰⣿⢠⡭⢠⡇⠀⢼⣂⣰⣿⣦⣠⣿⢯⣄⣾⣿⣦⣼⡇⢲⣿⡇⠀⠀⠀⠀ ⠀⠀⣼⡏⣰⠃⣾⣇⠀⢺⠟⣿⣿⣿⡅⠀⠀⠀⣿⣿⣿⣹⠇⣼⣿⠃⠀⠀⠀⠀ ⠀⢐⣿⠁⣯⠐⣿⢻⣀⠸⡇⠙⠿⠛⠀⠀⡀⠄⠈⠛⢋⢸⡄⣿⣏⠀⠀⠀⠀⠀ ⠀⠈⣿⡌⣷⡌⠻⣽⡜⣎⡧⠐⠂⠐⠀⡀⠀⢀⠠⠁⠂⣼⢃⣿⡇⠀⠀⠀⠀⠀ ⠀⠀⠉⣷⢾⣇⡳⢸⢷⣧⢻⣤⣤⣄⣡⣠⣔⣤⡴⡞⣿⣃⣾⣿⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⢿⣻⣿⣿⢾⣟⣯⣧⠰⠌⡍⠛⠹⣶⣿⣿⣿⢲⣿⡟⠀⠀⠀⠀⠀⠀ ⠀⠀⡀⣨⣾⣿⣿⣹⣾⡟⠙⠛⠉⡙⡙⣛⠉⠹⣿⣻⣿⣿⣝⡁⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⠶⢖⠦⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣷⡀⠀⠀⠀⠀⠀⠐⠋⠉⠉⠛⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁⠀⠀⢀⠇⠈⢳⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠀⠀⠀⢀⣀⣠⠤⠤⠤⠤⠤⠤⠤⢌⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢻⠀⠀⠀⠀⠈⠀⠀⢸⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⣠⠤⠒⣋⡭⠤⠒⠒⠉⠉⡩⢟⣣⣤⣀⡢⣬⣉⠒⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⢼⠈⠃⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⣉⠴⠒⠉⠀⠀⠀⠀⠀⢀⣞⣴⠟⠋⠉⠛⢿⣾⣎⠑⢤⡀⠙⠢⣄⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢋⡤⢊⣁⡀⠀⠀⠀⠀⠀⠀⠀⣞⣾⠃⠀⠀⠀⠀⠀⠹⣿⡄⠀⠱⡄⠀⠈⠑⣄⠀⠀⢀⣠⣽⠶⠶⠶⠒⠒⠒⠛⢤⣄⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⡴⢋⢔⣭⣴⣿⣷⣤⠀⠀⠀⠀⠰⣽⠃⠀⠀⠀⠀⠀⠀⠀⢹⣇⠀⠀⠘⡄⠀⠀⠈⢳⣶⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠯⠻⣦⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⢡⠎⢠⢯⣿⠋⠁⠀⠈⠻⣷⠀⠀⠀⠀⡏⠀⠀⠀⠐⢷⢶⣄⠀⠀⣿⠀⠀⠐⠁⠀⠀⢰⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠪⠙⣆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⢠⠃⠀⣮⡿⠁⠀⠀⠀⠀⠀⠻⣇⠀⠀⢸⡇⠀⠀⢀⠀⣸⣷⣻⡄⠀⣿⠀⠀⠀⠀⠀⠀⣏⠓⠒⢀⣀⣀⣀⣀⣀⣀⣀⣀⠀⢠⠖⠀⠀⠀⠘⡄ ⠀⠀⣀⣠⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⢀⠇⠀⢰⣿⠇⠀⠀⠀⠀⠶⣶⡄⢹⠀⠀⠀⡇⠀⠀⣾⢹⣿⣿⣏⡇⠀⣿⠀⠀⣀⣤⡤⠤⣼⣶⠿⠛⠉⠀⠀⠀⠀⠀⠀⠉⠙⡇⠀⠀⠀⠀⠀⠀ ⣠⢾⠋⠀⠀⠈⠻⡷⣄⠀⠀⠀⠀⠀⠀⢰⠁⠸⠀⠀⠸⣿⠀⠀⠀⠀⣄⣀⣷⣽⣸⠀⠀⠀⣇⠀⠀⠸⣞⣿⣅⣽⠁⢀⣇⣴⠞⠋⠁⠀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀ ⡇⠘⠂⠀⠀⠀⠀⠁⠘⡆⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⣇⣿⣿⣿⣿⠀⠀⠀⠸⡄⠀⠀⠙⠧⠽⠃⠀⡼⠋⠀⠀⠀⠀⠀⣯⠦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀ ⢳⡀⠀⠀⠀⠀⠀⠀⢀⣹⣤⣤⣤⣤⣄⡇⠀⠰⠀⠀⠀⣿⠀⠀⠀⠀⢻⡽⠿⣾⢹⠀⠀⠀⠀⠻⡄⠀⠀⠀⠀⢠⠞⠁⠀⣀⣀⡀⠀⠀⠘⢧⡀⣠⣤⡶⠖⠛⠛⠛⠒⠒⡞⠀⠀⠀⠀⠀⠀⢀⠀ ⠀⠉⠳⣄⠀⢀⡤⡺⠛⠉⠀⠀⠀⠀⠈⣻⢦⠀⠀⠀⠀⢻⡆⠀⠀⠀⠈⠻⠟⢁⡎⠀⠀⠀⠀⠀⠙⠦⣄⣀⣤⠟⠀⠀⠉⣀⣀⣀⡉⠂⠀⠀⣽⣏⠁⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⢠⡞⠀ ⠀⠀⠀⢈⣷⠋⠀⠁⠀⠀⠀⠀⠀⢈⣩⣤⣼⣧⣤⡀⠀⠀⠻⡄⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⣈⣭⠵⠒⠋⠉⠂⠀⠀⠹⡌⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀ ⠀⠀⠀⣾⠋⠀⠀⠀⠀⠀⢀⡤⠞⠉⠉⠀⠀⠀⠈⣻⡆⠀⣀⣙⡦⠤⣀⣤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠋⣡⡏⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣄⡀⠀⠀⠀⠀⠀⠀⣀⣠⠴⠋⠁⠀⠀⠀ ⠀⠀⢸⠇⠀⠀⠀⠀⢀⡶⠉⠀⠀⠀⠀⠀⠀⠀⠈⠁⡧⠋⠉⠁⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠉⠀⢀⣴⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⠈⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⠀⠀⠀⠉⠑⢏⠀⠀⠀⠀⠀⠀⣀⣤⠶⠶⠾⣧⡀⠀⠀⠀⠀⠀⣤⣤⣤⣤⡤⠒⠒⠉⠁⠀⠀⣀⣤⣶⠿⢿⡿⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⡆⠀⠀⠀⠀⠈⠇⠀⠀⢀⡤⠚⠉⠀⠀⠀⠐⠁⡇⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣶⣶⣶⣶⣾⠿⣿⡟⠁⠀⣼⠃⠀⠀⠀⠀⠀⣠⠞⣠⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠉⠻⡄⠀⠀⠀⠀⠀⠀⣰⠁⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⠃⣠⠏⠀⠀⣰⠏⠀⠀⠀⠀⠠⠞⢁⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠙⣄⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⢀⡴⠋⠳⢄⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⠁⠊⠀⠀⢀⡰⠋⠀⠀⠀⠀⠀⣠⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠑⠦⣀⡀⠀⠀⠀⠀⠀⣀⡠⠖⠋⠀⠀⠀⠀⠙⠢⢄⡀⠀⠀⠀⠀⠈⠛⢿⣇⣀⣀⣠⠴⠋⠀⠀⠀⢀⣀⠤⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠒⠒⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠤⢤⣀⣀⣀⣀⣀⣀⣀⣀⡠⠤⠖⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⠀⠉⠒⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⢳⡀⠀⠀⠀⠁⠒⠀⠀⠤⠄⣀⣀⣀⡀⠀⠠⣄ ⠀⠀⠀⢸⠁⢳⣴⠂⢀⣀⠀⣀⠀⠀⠀⠈⠑⠀⠀⠀⢀⡎ ⠀⠀⠀⢸⣤⡼⠁⢰⠁⠸⡇⢀⠇⠀⢔⠉⣷⠢⣠⣶⣿⠁ ⠀⠀⠀⣸⣿⠁⠀⠈⠁⠀⠉⠁⠐⣻⣫⠒⠯⡠⠛⣿⠃⠀ ⠀⠀⢰⣿⣿⣤⣤⡤⠤⣖⡂⠉⠉⠀⠈⢓⣄⠀⠈⡃⠀⠀ ⠀⠀⠀⢻⣧⣿⡋⣒⠂⠒⠁⡀⠀⢀⠈⠩⣀⣱⣼⠀⠀⠀ ⠀⠀⠀⠀⣯⣵⣙⢦⣀⠀⠀⠈⠉⠉⠀⠀⣐⣼⡿⠀⠀⠀ ⠀⠀⠀⠀⠻⣿⣋⣙⣛⣿⣶⣀⣲⣶⣾⣿⣿⡯⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣹⢿⡞⠛⣿⣿⢿⡟⢻⠛⠋⠁⠀⠀⠀⠀ ⢠⣀⠀⠀⠀⢠⣿⣿⣴⣪⣁⣸⠉⢣⣸⠀⠀⠀⠀⠀⠀⠀ ⠈⠒⠈⠩⠭⠿⢏⡙⠛⠛⠛⠛⠛⠛⢻⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⣇⡸⠀⠒⠒⠲⡀⡎⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⣶⣤⡀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣤⣄⣀⣀⠀⠀⠀⣀⣤⣦⠏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣿⠈⢿⣿⣦⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⠟⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⣤⣄⣼⡇⠀⠀⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠉⠻⣿⡁⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠀⠀⢸⣿⣷⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⣿⡇⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⣼⣿⣿⣿⣆⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⣿⣿⣇⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⢸⣿⣻⣿⣿⣿⣆⠀⠀⠀⠀ ⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀ ⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀ ⠠⣾⣿⢿⣿⣿⣿⣿⡿⠁⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠉⠀⠀ ⠀⠀⠀⢸⣿⣿⣿⡿⠓⠊⣿⣿⡿⠟⠛⠛⠙⠛⣛⣿⣿⣄⡻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀ ⠀⠀⠀⢸⣿⣿⣿⡇⠾⠛⠉⠉⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠋⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀ ⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠟⠛⠻⣿⣿⣿⣿⣿⣿⡄⠀ ⠀⠀⠀⠀⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⢶⡋⠳⢸⣿⣿⣿⣿⣿⣇⠀ ⠀⠀⠀⠀⠘⣿⣿⣿⡀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡗⠚⢁⣠⣾⣿⣿⣿⣿⣿⣿⠀ ⠀⠈⠀⠀⠀⠈⣻⣿⣿⣦⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄ ⠀⠀⠀⢸⣿⠤⠿⢿⣿⣿⣿⣿⣿⣿⣷⣶⡄⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠶⠶⠾⢿⣿⣿⣿⢿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⣀⡤⠜⠋⠁⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁ ⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⠛⣠⣟⣁⠤⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀ ⠀⠀⠀⠀⠀⠀⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⡟⢸⠿⠃⠀ ⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⠤⠂⢉⢀⠄⠀⠀⠀⢀⠈⠐⠢⢄⠀⠀⠀⠀ ⠀⠀⠀⢀⢔⠁⠀⡐⡣⠹⠀⢀⡄⠀⠘⡀⠀⠀⡄⠐⢂⠀⠀ ⠀⠀⡰⢁⡟⠚⣿⠚⠁⢠⠀⡎⠱⠀⠀⠇⠀⠀⢰⠀⠀⠡⠀ ⠀⡰⠁⣾⣁⡰⠁⠀⠀⠈⡀⡇⠀⢣⠀⢸⠀⠀⣼⠀⠀⠀⢃ ⠀⠇⢰⡿⡌⠃⡴⢦⡀⠀⠡⡇⢠⠴⢆⠈⠀⠀⡏⠀⠂⠀⢸ ⠀⠀⠸⢠⣿⠀⠳⠜⠀⠀⠀⠁⠘⢴⠜⢲⡄⢸⠁⢰⡇⢸⠸ ⠀⣇⠇⣿⣿⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣾⣷⡆⠀⡼⡇⢸⠇ ⠀⢸⠠⡿⡇⠀⠀⠀⢀⠻⠀⠀⠀⠀⢰⣾⠁⠀⢀⣿⡇⢸⠀ ⠀⢠⠘⡇⢽⣦⣀⠀⠘⠒⠃⠀⠀⠀⢸⠇⠀⠀⣼⣿⢠⢸⠀ ⠀⠸⠀⣿⣮⣿⡇⢱⣦⣤⠤⠤⠀⣶⡾⠀⠀⢰⣿⠟⠱⣸⠀ ⠀⠀⠱⠉⠻⢿⣄⢀⡽⢉⣤⡔⠊⣿⠇⠠⡶⣿⠋⠀⠀⠈⠀ ⠀⠀⠀⠀⠀⣠⣼⣿⡡⣫⣿⢶⢀⣿⣿⣄⠁⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⣾⣿⣿⣯⡐⢜⣿⢸⡿⢹⣿⠋⠳⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⣿⣿⣿⣧⡟⢸⢣⣾⣿⣿⡏⠀⠄⢹⣷⠀⠀⠀⠀ ⠀⠀⣠⣿⣽⣇⠹⡿⠁⣿⡿⣻⣿⣿⣢⠀⣿⢠⡿⠀⠀⠀⠀ ⠀⢰⡏⣾⠟⢻⣜⡇⣰⣿⣿⡟⠛⣿⠿⠐⡇⢺⡁⠀⠀⠀⠀ ⢀⡿⣸⡿⢡⢸⣿⣿⠿⢏⡾⠉⠀⣿⣱⡤⡏⢸⡇⠀⠀⠀⠀ ⠘⠛⠛⠓⠒⠒⠛⠛⠒⠒⠒⠒⠒⠛⠓⠓⠒⠚⠃⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔⠒⠀⠀⠒⠤⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⢶⡞⡏⠀⠀⠀⠀⠀⠀⠀⠘⣷⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣸⠇⠈⣴⡧⠖⠒⠊⠒⠉⠉⠉⠒⠛⠻⢦⠤⠀⠀⠀ ⠀⠀⠀⣰⣇⠴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠈⠀⠀ ⠀⠀⣰⣿⠇⠀⠀⠀⡀⢤⢖⡰⡶⠀⠀⢰⠆⣤⠤⡀⠰⠊⠀⠀ ⠐⠁⠈⢡⠠⡠⠂⡅⠱⣸⢺⣷⣴⢿⠰⢷⣶⡶⣶⢨⡅⠀⠀⠀ ⠐⠄⠤⠊⠀⣇⠀⠂⠀⢸⠘⠛⠃⠈⠁⠘⠛⢱⡇⠸⠑⠀⠀⠀ ⠀⠀⠀⠀⠰⠙⠀⠘⡀⢛⡁⠀⢀⡀⠀⠀⣠⢜⠁⠇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣤⠀⣑⣜⣿⠐⠲⣺⢪⣅⣇⣬⠏⠀⠀⠀⠀⠀ ⠀⠀⠀⢄⠀⠀⠈⣿⠿⢿⣿⡷⢼⣁⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀ ⣆⡉⠉⠀⢱⣶⣼⠃⠤⠒⣻⣿⣿⣟⡿⣿⣟⢻⠀⣀⣀⠀⣀⠀ ⠘⠧⢤⡤⢿⣿⠋⠱⣤⣀⣿⣾⣟⠉⠀⢹⣸⠈⣏⠻⣿⣧⢨⢄ ⠀⠀⠈⠓⢾⡇⠀⠀⢹⣿⠃⠸⣯⠉⠉⢹⢹⡠⢻⣀⣿⠿⠉⠉ ⠀⠀⠀⠀⠀⠈⠣⠔⠁⣼⠀⠀⣿⠀⠀⢸⠀⢣⠔⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣞⣈⣳⣿⣟⣒⠦⣾⣏⣨⡆⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⢀⡀⠀⠀⠀⠀⠀⣀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣟⢹⡛⠿⣏⡉⠙⠓⠓⣦⡤⠖⠛⠉⠀⠀⠈⠉⠉⠉⠉⠙⠒⠶⣏⡉⠉⠉⠉⣉⡿⠛⢻⣿⡇⠀⠀⠀ ⢻⣖⠃⠀⠀⠉⠳⣶⡿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⡶⠛⠉⠀⠀⢀⣻⡇⠀⠀⠀ ⠘⣿⠇⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀⠀⠀⠀⠈⠻⡅⠀⠀⠀ ⠀⠙⣷⠆⣠⠎⠀⠀⠀⣠⠃⠀⠀⢠⠆⠀⠀⠀⠐⡄⠀⠀⠀⠳⣄⠀⠀⠀⠘⢦⣀⠀⣶⠞⠋⠀⠀⠀ ⠀⠀⠙⣻⠇⠀⠀⠀⢰⠃⠀⠀⠀⡞⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠈⢦⠀⠀⠀⠀⠻⣽⠋⠀⠀⠀⠀⠀ ⢻⣷⣟⡵⠂⠀⠀⠀⡟⠀⠀⣰⢠⡇⠀⠀⠀⠀⠀⠀⢳⠀⢠⠀⠀⠀⢣⠀⠀⠀⠀⢹⣶⠟⠀⠀⠀⠀ ⠀⠀⣼⠁⠀⠀⠀⠀⢻⠀⣾⣿⡟⢻⠦⣤⠀⠀⢠⠀⢸⠷⡚⢿⣝⠒⠺⡇⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀ ⠀⠀⢻⡀⢸⠀⠀⡀⢸⣾⣟⣋⣀⣀⢳⣜⣷⣀⠈⣷⡟⢀⣈⣻⣯⣙⡒⣿⠀⡄⠀⢰⠀⣿⠀⠀⠀⠀ ⠀⠀⠈⢷⡈⢧⠀⣧⡀⣿⣿⠏⢹⡟⣿⠏⠃⠈⠱⠟⠁⠘⣿⣯⣍⠙⣿⣿⣠⣧⠀⣼⢠⡏⠀⠀⠀⠀ ⠀⠀⠀⠀⠙⢿⣷⣿⠗⣾⣿⡁⠈⠉⣹⠀⠀⠀⠀⠀⠀⠀⢏⡈⠉⣠⡯⣿⠋⣯⠜⢿⠏⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢳⠀⠀⢻⡉⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⡼⠀⠁⠀⢸⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣾⠀⠀⠀⠙⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠞⠁⠀⠀⠀⠈⢷⣄⡀⠀⠀⠀ ⠀⠰⣆⣠⠶⣿⠃⠀⠀⠀⠀⠀⠈⠉⠒⠒⠠⣤⣤⣤⡤⠒⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⢧⠉⠁⠀⠀ ⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⣰⠻⣿⣯⡤⣬⣿⣿⠷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠳⣄⠀⠀ ⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⢠⠀⠀⢠⠃⡄⠙⢿⣿⣿⠟⠁⡆⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⢸⣷⡄ ⠀⢸⡏⠀⣠⠀⠀⠀⠀⠀⡎⠀⠀⣿⠤⣷⠀⢀⠟⢧⠀⠀⡿⠶⢿⠄⠀⠀⠀⢀⠀⠀⠀⣼⡇⢸⣿⡇ ⠀⠘⣧⠀⣿⠀⡄⠀⠀⢸⠀⠀⠀⠙⠦⣼⡄⠘⠦⠜⠃⣠⣧⠞⠉⠀⢠⠀⣠⠏⠀⢀⡼⢁⣧⠟⠟⠀ ⠀⠀⢹⡄⡿⣆⠸⣆⠀⠸⡄⢀⠀⠀⠀⢸⣧⣄⣤⡤⣽⢶⣷⡀⠀⠀⣾⣠⡿⢀⡴⠋⠠⠟⠁⠀⠀⠀ ⠀⠀⠀⠹⣿⡌⢦⡙⣷⢤⣹⣼⣷⣀⢀⡞⠀⡇⠘⡇⢹⡄⢿⡹⣤⠞⣻⡟⢷⡞⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⠀⠙⣾⡆⠈⠙⠃⣨⠟⠀⣸⠁⢠⡇⠀⢳⡌⢷⡘⣦⡍⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠙⠓⠚⡟⠒⠺⡷⠦⠴⢿⠒⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⢱⠀⠀⣞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣾⣶⣶⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⣠⣴⠾⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠈⠉⠻⢷⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⡞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦⣄⠀⠀⠀⠙⠻⢦⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠱⣄⠳⡄⠀⠀⠙⢦⡀⠀⠀⠀⠀ ⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⣿⣆⡀⠀⠀⢿⣄⠀⠀⠀ ⠀⢰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⢠⣿⣿⣻⣶⡆⠀⠻⣦⣀⠀ ⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠺⠛⠿⣿⣿⣿⡄⠀⠀⠀⠙⠛ ⣿⠁⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣇⠀⠀⠀⠀⠀⠀⣿⣿⣇⠀⠀⠀⠀⠀ ⡿⠀⢀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡄⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⢹⣦⠀⠀⠀⠀⠀⣿⡌⢿⡄⠀⠘⣔⣦ ⡧⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⠀⠀⠀⢀⡿⣼⡂⠀⠀⠀⠀⠀⠀⠀⠀⡏⠳⣽⣷⡀⠀⠀⠀⣹⣇⠀⠃⠀⠀⢹⣇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣸⣿⠂⠀⠀⢠⣾⡻⣉⣇⠀⠀⠀⠀⠀⠀⠀⠀⣧⠤⠬⡼⣿⣆⠀⠀⡏⣼⠀⠀⠀⠀⠀⠹ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⣿⠇⡆⠀⣠⡟⠋⠉⠉⠹⡄⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠙⢷⣤⡓⢼⡃⠀⠀⢦⡀⠀ ⠤⡄⢤⠠⠤⠤⣄⠲⣾⠃⠀⠀⠀⠀⠀⠀⣿⠸⣁⡴⠋⠀⢠⠤⠤⠤⣿⡄⠀⠀⠀⠀⠀⠀⣿⠴⠦⢀⣀⣀⠀⠙⠻⢮⡇⠀⠀⢸⡅⠄ ⣮⡘⢆⣋⢎⡱⢌⣳⡏⠀⠀⠀⠀⠀⠀⠀⣿⡗⣋⣤⣴⡶⠶⠶⠶⢦⡀⢻⣆⠀⠀⠀⠀⠀⢹⣤⠞⢫⣿⣝⠻⣦⠀⢸⡏⠀⠀⠀⡯⣘ ⠉⠉⠛⠙⠋⣹⠟⢻⠁⠀⠀⠀⠀⠀⠀⢠⡟⠛⡉⡁⢠⣴⣿⣿⣿⣷⡈⠀⠙⢦⡄⠀⠀⠀⠘⣇⣾⣿⣿⣿⡇⠀⠙⣺⠁⠀⠀⠀⢿⠿ ⡆⠀⠀⠀⢠⣯⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⣟⠠⠐⣰⣿⣿⣿⠟⢻⣿⠅⠀⠀⠀⠙⠳⠤⣄⣀⢹⣿⠋⣽⣿⡇⠈⢐⡟⠀⠀⠀⠀⢸⡆ ⡹⣆⠀⠀⣼⢻⡀⣞⠀⠀⠀⠀⠀⠀⠀⠀⣯⠐⡀⣻⣿⠿⡏⣀⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⢧⢴⣿⡟⠀⠀⠼⡇⠀⠀⠀⠀⠈⣷ ⣧⠜⡳⡄⢏⠲⣙⣯⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⡀⠙⠓⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⣤⣄⠀⠉⠛⠚⠋⠀⠀⠀⢆⡿⠀⠀⠀⠀⠀⣿ ⢹⣧⡑⠮⣌⠳⡌⣷⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠠⠀⡀⠂⠀⠀⡀⠀⠀⣀⡤⠶⢶⣦⣄⡀⠀⠀⠀⠀⠈⢀⣼⣿⡇⠀⠀⠀⠀⠀⢻ ⠘⣿⣬⡓⣌⠳⡘⢼⡇⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⣦⣄⣀⡀⠁⠀⠀⠀⢠⡏⠀⠀⠀⠀⠙⢷⣀⣀⣠⣤⡾⢟⣿⡞⠀⠀⠀⠀⠀⠀⣾ ⣄⡹⣟⠿⣶⣧⣝⣢⢿⡄⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⠀⠀⠀⠀⢀⣠⡼⠟⠛⢧⣒⢱⡾⠛⠀⠀⠀⠀⠀⠀⢀⣿ ⠈⠉⠁⠀⠀⠈⠉⣙⣿⠿⣦⡀⠀⠀⠀⠀⠀⠀⢻⡿⢿⣿⣿⣿⣿⡿⣿⣿⣇⣀⣴⠾⠛⠉⡀⠄⠂⠠⠹⣏⡁⠀⠀⢀⣤⠀⠀⢀⡾⠁ ⠀⠀⠀⠀⠀⠀⣰⡿⣅⠀⠈⢷⣦⡀⠀⠀⠀⠀⠀⠹⣶⣎⣹⠿⢯⡱⢺⣿⢻⡽⣆⠀⠂⡁⢀⠂⠁⢂⢀⡏⠻⣶⣶⣫⣇⣠⣶⠟⠁⠀ ⠀⠀⠀⠀⠀⠀⣿⠂⠈⠳⠦⠶⠮⣝⠻⠶⠶⡶⡶⠒⠋⠀⠉⠉⠋⠉⠉⢻⣧⠯⣽⢦⡁⠐⠀⣲⢥⣤⠞⠁⠀⣿⣟⡿⣿⣯⣄⣀⠀⠀ ⠀⠀⠀⠀⠀⣠⢿⣄⠁⠂⠄⠠⢀⠈⣷⢲⢫⣽⠁⠀⠀⠀⠀⠐⢀⠄⠀⠈⣿⡿⢿⣿⣷⣤⡶⠋⠀⠀⠀⠀⢠⣿⢯⣟⡷⣯⢿⡿⣿⣶ ⠀⠀⠀⠀⣰⠋⠀⠙⠷⣤⣈⠐⠀⠺⢻⣇⡿⠃⠀⠀⣀⡀⠀⠀⠀⠉⢂⣀⣀⡀⠀⣻⢶⣧⣝⣛⣳⣶⣤⣴⣿⣿⣯⣿⣽⣻⣯⣿⠷⣿

⠀⠀⠀⣠⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡀⠉⠛⢦⡀⠀⠀⠀⠀ ⠀⢀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⡰⡄⠈⠲⡀⠀⠀ ⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⢀⡀⠀⢘⣿⣦⡤⠹⣄⡀ ⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⡄⠀⠋⠛⣿⣇⠀⠀⠉ ⡇⡠⠂⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⣾⠀⠀⠀⠀⠀⢸⣳⡀⠀⠀⢻⠹⡀⠐⡤ ⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⣼⡝⡆⠀⠀⠀⠀⢠⡙⣻⣄⠀⠞⡆⠁⠀⠻ ⠀⠀⠀⠀⣀⡼⠁⠀⠀⢸⡗⢀⡜⠉⣈⢱⡀⠀⠀⠀⢸⣀⠀⠈⠳⣎⡧⠀⢲⠀ ⣝⣬⣉⣳⣼⠁⠀⠀⠀⢸⣞⡥⠴⢞⣲⡌⢳⡀⠀⠀⢸⡔⣺⣟⡲⡀⡗⠀⢘⣢ ⡀⠀⢀⡏⡸⠀⠀⠀⠀⢸⡁⢰⣾⣿⢿⡷⠀⠙⠢⢄⣀⢿⠟⣿⡇⢰⠇⠀⠀⣏ ⡱⣄⢸⢣⡗⠀⠀⠀⠀⢸⠄⠚⢟⣧⠼⠃⠀⠀⠀⢀⠈⢿⣺⠟⠀⢸⡀⠀⠀⢹ ⢷⣌⠲⡌⢷⠀⠀⠀⠀⠈⣆⠀⠀⠀⠀⠀⠀⡤⠶⢯⣁⠀⠀⢀⣠⣾⠁⠀⠀⢸ ⣘⡷⢷⣘⣺⡆⠀⠀⠀⠀⢻⣿⣷⣶⣦⣤⣼⠀⠀⢀⣘⠶⣞⢫⡽⠃⠀⠀⠀⣸ ⠈⠁⠀⠈⣭⠛⢦⡀⠀⠀⠈⢻⡻⢿⣿⠟⣿⣤⠞⠋⠁⡀⠀⢻⣄⣀⠴⢀⡴⠃ ⠀⠀⠀⢸⠏⠑⠤⠿⡖⢶⡴⠖⠋⠑⠚⠉⢻⣞⣳⡄⠂⡦⠥⠃⢸⣿⣿⢯⣄⡀ ⠀⠀⢠⠎⠳⣌⡀⠤⢼⣓⠞⠀⣀⠀⠐⠢⢀⡋⠹⣟⣻⣤⣤⣠⣾⣟⣾⣻⣟⣿

⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀ ⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀ ⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠛⠛⠛⠻⢿⣿⣆⠀⠀ ⢠⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⣰⢠⠀⠀⢆⡄⠀⡄⠙⢿⡀⠀ ⢸⣿⣿⣿⣿⣿⣿⡟⠁⢀⢇⠏⠪⣗⠤⣘⢿⣦⣸⣄⠀⡟⠂ ⢸⣿⣿⣿⣿⣿⡟⠀⢀⡼⠊⠀⠀⠀⡉⠀⠉⠉⠛⠋⢣⡇⠀ ⢸⣿⣿⣿⣿⣿⠁⠀⡼⢡⣴⠶⠛⠉⠁⠀⠀⠀⠉⠛⠶⡇⠀ ⠸⣿⣿⣿⣿⣿⠀⡸⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⢠⡄⠀⡇⠀ ⠀⠙⣿⣿⡟⡩⣑⣇⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠈⠁⠀⢇⠀ ⠀⠀⠈⠛⢧⠸⡁⠘⠀⠀⣄⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⠀⠀⠀⠁⠒⠠⢄⡀⠉⠀⠀⠀⠀⠀⠈⠀⠀⡠⠚⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡠⠊⣏⠉⠐⢶⣶⡖⠒⡖⢍⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⢾⠀⠀⢹⠴⠚⠛⠉⠉⠓⢧⠀⠳⡀⠀⠀⠀ ⠀⠀⠀⠀⢀⠊⠀⢧⠀⣸⣄⣀⣀⣀⣀⣤⣼⡄⡸⠱⡀⠀⠀ ⠀⠀⠀⠀⠎⠀⠀⠘⣼⣿⣿⣿⣿⠿⢿⣿⣿⣿⡇⠀⢱⠀⠀ ⠀⠀⠀⡜⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⠀⠀⢃⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣤⣔⠚⠓⠒⠢⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⠊⠉⠁⠚⠋⢁⣖⣤⣔⢦⣮⣍⡢⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠊⠥⢼⠆⠀⠀⣤⠾⡚⠛⠈⢙⠓⢏⣷⣁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡁⠀⢞⢻⢸⡗⠀⠀⠸⠇⢸⢹⡇⠀⠀⠀⠀⠀⠀ ⠀⡠⠉⠈⠑⡢⠄⡁⠀⣼⣾⠀⠰⠁⠁⢡⠀⢸⣼⡃⠤⠐⠀⠉⠑⡀ ⠰⠁⢰⠀⡀⠈⢄⠈⠂⢼⢘⠤⣘⣤⣤⣂⣤⡎⡆⠀⠀⢀⡄⠀⠀⠃ ⠃⠀⠈⠀⠃⠀⠀⠠⢀⢸⢘⡏⠙⢲⠜⠊⣰⢢⠅⠀⡠⠁⡇⠀⠀⢸ ⠂⠀⠀⠀⠠⠐⠤⣀⠘⡈⠀⡇⠘⡧⠆⠀⢸⠊⡇⡴⠕⠁⡇⠀⠀⡼ ⠀⢄⠀⠀⠜⠀⠀⠀⠉⢣⡆⡅⢠⢣⠀⠀⠈⠀⡇⠀⠀⠀⠀⠀⠈⠀ ⠀⠀⠈⠈⠀⠀⠀⠀⠠⣁⠁⡇⠆⢠⢂⠀⠀⡇⢃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠰⠈⠀⠃⠀⠀⢸⡄⠀⢰⢸⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡄⢸⣴⠀⠀⢃⣿⣷⡀⣼⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⠃⠀⠀⣾⣿⠛⠳⠈⠋⡆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⣼⣿⣿⡄⠀⣇⠀⢡⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣰⠀⠀⠀⡜⣿⣿⣿⡇⠀⣿⡄⠘⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⢀⡴⠙⠦⢴⡒⠒⠒⠒⠠⠤⣄⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⠔⠳⡄⢀⡀⢨⠀⠀⠀⠀⠀⠀⠀⠈⠲⣄⠀⠀⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀⠀⠀ ⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢠⢀⠀⠀⠈⢷⠀⠀ ⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠈⣠⢞⠃⠀⠠⢀⢸⠱⣅⠀⠀⠘⡆⠀ ⠀⡇⠀⠀⠀⠀⠀⢀⣄⠤⣊⢴⣜⢴⡡⠣⢮⢶⠶⡌⣧⠀⠀⢹⠀ ⠀⡇⠀⠀⠀⠀⠀⢸⢀⠎⣾⣿⡆⠀⠀⠀⠀⣿⣿⠘⡧⠞⠀⠘⡆ ⢰⠀⠀⠀⠀⠀⠀⡌⠀⠀⠩⠿⠃⠀⠀⠀⠀⠙⠋⠀⡇⠀⠀⠀⡇ ⠘⣆⠀⠆⠀⠀⠀⣇⡀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⣠⠇⠀⢀⣶⠃ ⠀⠙⠒⢶⡀⢰⡀⣇⠉⠓⠒⠤⡤⠤⡤⠤⠤⠔⠚⡅⢀⣢⠎⠁⠀ ⠀⠀⠀⠀⠈⠒⠓⢼⣵⠗⠛⠫⠥⠤⠭⠶⢶⡲⠗⠓⠉⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣰⠃⢰⠀⠀⠀⠀⠀⠈⠎⢧⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡴⠃⠀⢸⠀⠀⠀⠄⠂⠀⡸⠈⣇⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⠤⢄⣀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡚⠃⠤⢀⡀⠀⠀⠙⢦⠀⠀ ⠀⠀⠀⠀⠀⢀⡠⠤⠤⠤⣄⡀⠀⠀⠀⠀⠀⣀⡠⠤⠤⠤⠤⠴⠒⠋⠉⠈⠉⠉⠒⠦⣀⠀⡹⠁⠈⠉⠒⠤⣈⠑⢤⡀⠀⠱⡀ ⠀⠀⠀⡠⠊⠀⣀⠤⠒⠉⢉⠙⢦⣀⠴⠒⠉⠀⠀⠀⠀⠀⣀⣦⠀⢀⡤⠒⠀⠀⠀⠀⠀⠙⢧⡈⠑⠢⢄⡀⠀⠁⠢⣈⠢⡀⣧ ⠀⠀⡜⠀⡠⠊⠁⣀⠔⠊⠁⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣙⣷⡡⠔⠊⠉⠓⠀⠀⠀⠀⠀⠈⠉⠉⠉⠛⠦⣄⠀⠈⠑⣌⡏ ⠀⢸⡠⠊⢀⡴⠊⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠲⣾⡷⣤⣀⡼⠁ ⠀⢸⢁⡴⠁⠀⠀⢀⡤⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⣀⣤⣤⡀⠀⠀⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡞⠉⠀⠀ ⠀⠈⢿⠀⢀⡤⠊⠁⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡿⠷⣦⠼⠛⠉⠘⠳⡀⠀⢘⣄⠀⠀⠀⠀⠀⠀⠀⢄⡀⠹⡄⠀⠀ ⠀⠀⠀⠱⢯⣀⡀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⡗⠒⣾⣤⡆⠀⠀⢰⣆⠀⠀⠈⡟⢦⣷⠀⠀ ⠀⠀⠀⢸⠀⠀⠉⡽⠀⠀⠀⠀⠀⠰⣄⣀⠴⣿⣯⡭⠤⠝⠂⠀⠀⠀⠀⠀⠀⣴⣷⣏⡐⠉⠳⠄⢀⣾⣿⠀⠀⠀⢸⠞⠛⠀⠀ ⠀⠀⠀⠈⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⢸⡛⢒⣼⣿⣧⣤⠀⠀⠀⠀⠀⠀⠀⣼⡟⢉⠉⠻⣷⣶⢚⢡⣷⠃⠀⠀⡀⠸⡆⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⠟⣡⡬⣽⣷⠄⠀⠀⠀⠀⠀⢿⣏⢘⣿⣧⠈⢿⣷⣟⠟⠀⠀⣠⣷⠃⠸⡀⠀⠀ ⠀⠀⠰⠀⠀⣠⠻⣼⠀⠀⠠⢄⣀⣰⢯⣡⡏⠐⠻⣷⣿⣧⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⠙⡇⢸⠟⠓⢦⣔⠺⣿⢧⠀⠀⢧⠀⠀ ⠀⠀⠀⠀⡴⠁⢀⡿⢆⠀⠀⣀⣠⡾⠹⢿⠀⣿⠶⡏⠈⢻⠀⠀⠀⠀⠀⠀⠀⢣⣻⠘⣷⠇⠀⠀⠀⡿⡍⠀⣿⡄⠣⡀⠈⡄⠀ ⠀⢠⢀⠎⠀⡴⠋⡇⠀⠙⢺⠁⢰⣧⠀⠀⠀⠘⢆⣇⣠⠞⠀⠀⠀⠀⢠⡀⠀⠀⣉⣛⡥⣤⠀⠀⢸⣴⠁⡰⠉⡷⡄⠳⡀⠡⠀ ⠀⣾⠃⢀⠞⠀⢸⠀⠀⠀⠀⢣⡈⢆⣣⠀⠀⠒⠂⠄⠀⠀⠀⠀⢠⣤⣄⣤⣤⠀⠀⠀⠀⡈⠀⠀⣯⣬⠚⠁⠀⡇⠘⡄⠱⡀⠀ ⠰⠁⡠⠋⠀⠀⢸⠀⣴⡖⠒⢲⣿⠦⠽⣧⡀⠀⠀⠀⠀⠀⠀⠀⠈⣯⠈⢹⡿⠀⠀⠀⠀⠀⢀⣴⠟⢹⡦⣤⠤⣵⠀⠘⡄⠱⢀ ⠀⡰⠁⠀⠀⠀⢸⠞⠀⠹⣤⠼⡅⠀⠀⠈⠉⠲⢤⡄⠀⠀⠀⠀⠀⠘⠿⠿⠃⠀⠀⢀⣠⢶⣿⠛⢆⠀⣷⡇⠀⠹⡄⠀⠘⡄⢻ ⠈⠀⠀⠀⠀⠀⡞⠀⠀⠀⠘⣦⠱⡀⠀⠀⠀⢀⡏⢹⠦⣄⣀⡠⠖⠙⢆⠀⠀⠀⣠⡯⠀⠀⠈⠳⣌⢣⣿⠁⠀⠀⣿⡄⠀⠘⡞ ⠀⠀⠀⠀⠀⢸⠁⠀⢀⣀⡀⠈⢧⡹⣄⠀⠀⣼⡀⠘⣆⡠⠋⠀⠀⠀⠈⢻⣖⣿⡞⠁⠀⠀⠀⠀⠈⡆⡟⠀⠀⠀⢻⡇⠀⠀⡇ ⠀⠀⠀⠀⠀⡞⠀⠀⠐⠀⠀⠀⠠⣿⣮⡶⢾⠀⠹⡄⢹⣄⠀⠀⠀⠀⠀⠀⠙⣿⠀⠀⠀⠀⠀⢀⡴⠋⡇⠀⠀⠀⠈⣏⠀⠀⠁ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠹⣝⣷⠈⡇⠀⠹⣄⣿⠻⣶⠤⢀⡀⠀⢀⣾⠀⠀⠀⢀⡴⢿⡀⢸⠀⠀⠀⠀⠀⠸⡀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡂⠃⢀⡴⠋⡇⠀⠀⠙⠒⠶⠒⡟⢿⣦⠤⠜⠋⠀⠀⠱⣼⠀⠀⠀⠀⠀⠀⢧⠀⠀ ⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠶⠋⠀⠀⢳⡀⠀⠀⠀⠀⠿⣿⣾⣧⣤⣄⠀⠀⠀⣠⠋⠳⣄⡀⠀⠀⠀⠘⡇⠀ ⠀⠀⠀⠀⠈⠙⡀⠀⠀⠀⠀⠀⢀⠜⠁⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⣄⣀⣴⣿⠻⢻⣌⣁⣀⡤⠖⠁⠀⠀⠀⠑⢦⣀⣀⠀⡇⠀

⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⣄ ⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⣀⡀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠿⣿⣿⠿⠿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⢏⡤⠶⢦⡀⠀⠀⣀⠤⣄⡙⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠈⢉⡿⣿⣿⡿⢸⠁⠰⠀⢹⠀⢰⠃⣤⠀⢳⢸⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⡼⢠⠆⠙⠃⠈⠳⠤⠴⠋⠀⠸⣄⢀⣠⠞⢸⣿⡟⢰⠈⢻⣿⣿⣿ ⠀⠀⠀⠀⠀⡇⢿⡀⠀⠀⠀⠀⣠⣤⣤⣄⠀⠀⠀⠀⠀⠈⠛⠃⠀⡗⠚⣿⣿⣿ ⠀⠀⠀⠀⠀⢳⡀⠳⣄⠀⠀⠀⠻⠿⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⡇⠀⠀ ⠀⠀⠀⣀⣀⠀⠣⡀⠈⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠋⠀⡸⠁⠀⠀ ⠒⠒⠒⣣⢤⠇⠀⠙⢦⣄⠀⠈⠉⠛⠛⠉⠉⠉⠉⠉⠉⠉⠀⢀⣠⡞⠁⣏⠣⠤ ⠀⠀⣰⠋⣸⣦⣀⣀⣀⣈⣿⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣾⣿⣿⣿⣷⣮⡳⣄ ⠀⢰⠓⠺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠞

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠾⠛⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡟⠁⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⡟⣇⢀⣠⣶⣷⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⢧⣛⢾⡹⣏⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠻⣿⠂ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⡟⣭⢷⣫⣟⣽⣻⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣯⠟⠀⠀⣿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⡟⡼⣽⣚⣧⣟⣾⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⡀⠀⢀⣽⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡳⣝⡯⣗⡿⣾⣽⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣟⡶⢧⡖⣯⣿⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⢳⡟⣭⢷⣯⣿⣿⣿⢿⣶⣶⣶⣦⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡽⣞⡿⣸⡱⣿⡇ ⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⣭⢷⣫⡿⠿⠛⠷⠾⣮⣓⠜⢢⠣⡙⢎⠻⡝⠿⡿⣷⣦⣤⣀⠀⠀⣠⣿⣿⢷⣻⡽⡞⣥⢻⣽⡇ ⠀⠀⠀⠀⠀⠀⠀⣾⣿⣽⡿⠋⠁⠀⠀⠀⠀⠀⠀⠉⠻⣦⣳⡘⣤⢣⡌⣅⢣⢃⠿⣹⢿⣶⣤⣿⣿⡿⣯⢷⣻⡝⢴⣫⣿⡇ ⠀⠀⠀⠀⠀⣠⣼⣿⠟⠁⠀⠀⢠⡴⠒⠲⣶⣄⠀⠀⠀⠈⢿⣝⢮⣳⣞⣼⠿⠛⠛⠛⠿⢿⣿⣿⣿⡿⣽⣏⡷⣊⢧⣟⣿⠄ ⠀⠀⠀⣠⣾⣿⣿⠋⠀⠀⠀⢰⣿⡄⠀⣰⣿⣿⣷⠀⠀⠀⠀⢻⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣷⣚⡷⡭⣞⣾⡿⠀ ⠀⠀⢀⣿⣿⠿⠁⠀⠀⠀⠀⢸⡽⣿⣿⣿⣿⡿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠛⠛⣷⣦⡀⠀⠀⠹⣷⣏⡾⣵⣻⣿⠀⠀ ⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠐⠛⠛⠛⠛⠻⠯⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣇⣀⣀⣾⣿⣿⡄⠀⠀⢻⣾⣽⣳⣿⡟⠀⠀ ⠀⢰⡇⠀⣀⣠⣤⣴⣾⡟⠀⠀⠀⠀⢰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⡛⣿⣿⣿⣿⣿⣿⠇⠀⠀⢸⣿⣾⣽⣿⠇⠀⠀ ⠀⢸⣷⣿⣿⣿⣿⣿⣛⠉⠀⠀⠀⠀⠈⢻⣦⣤⣤⣤⣤⣤⣶⣄⠀⠀⠈⠉⠉⠛⠻⣿⣋⡥⠞⠀⠀⠀⢸⣿⣿⣿⡏⠀⠀⠀ ⢀⣼⣿⡿⣧⢏⣿⣟⢿⣿⣄⠀⠀⠀⠀⠘⣿⡿⢛⠛⡛⠿⠿⣿⣷⣤⣀⠀⠀⣰⠆⠂⠉⠀⠀⠀⠀⠀⠘⣿⣿⣿⠁⠀⠀⠀ ⢼⣿⣿⣟⣧⢿⣹⣏⡾⣼⣻⣆⠀⠀⠀⠀⢹⡷⢈⠒⢠⢂⡐⠤⣙⣻⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⡆⠀⠀⠀ ⠈⣿⣿⣿⣞⣯⢷⡞⣵⢧⣻⣿⠀⠀⠀⠀⠀⢿⣄⠋⡄⠢⡐⢥⣾⡟⠁⠀⠀⠀⠀⠀⠀⣴⡿⣦⡀⠀⠀⠀⠀⢹⡇⠀⠀⠀ ⠀⢿⣿⣿⣿⣞⣯⢿⡽⣞⡵⣻⣧⡀⠀⠀⠀⠈⠻⣧⣔⣡⣼⠟⠁⠀⠀⠀⠀⠀⠀⢀⡀⣙⣿⣽⣿⣦⣀⡀⠀⢸⠇⠀⠀⠀ ⠀⠘⣿⣿⣿⣟⣾⣯⢿⡽⣯⣽⣿⡿⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⢿⣛⣟⡻⣿⣿⣿⣿⣻⣿⠀⠀⠀⠀ ⠀⣰⣿⢩⡙⢏⠛⠛⠛⠛⠛⠉⣿⣷⢈⡛⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣿⡿⣹⢮⣗⢮⣷⣿⢳⣞⣿⣿⠇⠀⠀⠀⠀ ⣴⣿⡏⢦⡙⢎⠲⢤⣀⡀⠀⢠⡿⠸⣷⣌⡆⠤⣉⠒⠥⠒⡔⠒⢆⠩⡙⣿⣿⣽⣻⣽⣻⣞⣯⢾⣼⣻⣾⣿⡟⠀⠀⠀⠀⠀ ⣿⠟⡌⢧⢸⡉⢗⠢⡜⡸⢡⣿⢧⠓⡬⢙⠻⠷⣶⢯⣶⣭⣴⡭⢆⡑⣶⠏⠻⣷⣟⣾⣳⣟⣾⣻⣞⣷⣿⠿⠃⠀⠀⠀⠀⠀ ⢫⠜⡱⢊⠦⣙⡌⠳⣌⠱⣡⡿⢇⡘⠔⢣⠘⡔⠤⢂⡔⢠⢢⡐⣢⣾⠟⡀⠀⠈⠛⠿⣷⣿⣾⣷⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⣤⣟⡿⣻⣭⣷⡼⣶⣥⣴⣯⣿⢺⣟⣤⣠⡙⣳⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠛⣻⠷⢛⣋⡍⠁⠀⠀⠈⠹⡿⠛⠾⣋⠉⠀⠀⠀⠀⠀⠀ ⣤⣴⡒⠲⠆⣴⢮⣓⡎⢧⠋⠀⠀⠀⠀⠀⠀⠡⡄⠣⡌⠳⡀⠀⠀⠀⠀⠀ ⠀⣀⣀⣠⠾⣯⣟⡾⣭⠇⠀⢰⠁⢸⠀⠀⠀⠀⡇⣠⣿⣦⠽⡄⠀⠀⠀⠀ ⠛⠃⢉⣹⣿⣻⣼⣳⡿⠀⢀⡇⢀⠾⡆⠀⠀⢀⠿⡀⠙⣧⠀⢏⡗⠀⠀⠀ ⠶⠿⣿⣻⢷⣻⢶⣻⡝⡀⢸⡴⠋⢉⠹⣄⠀⢸⠉⡙⢄⣹⠀⠈⠑⣲⠀⠀ ⣠⣤⣜⣯⣟⣾⡯⣟⣟⠀⣾⡽⣿⣿⣯⠉⠳⣮⣿⣿⡻⣽⠀⢰⡚⠁⠀⠀ ⠉⢀⣿⣾⡽⢾⣽⣳⢾⡀⢿⡇⢿⣷⡟⠀⠀⠀⡘⢿⠇⣿⠀⠀⢇⠀⠀⠀ ⠛⠛⣿⣽⢻⣻⣳⣽⣺⣇⢺⡽⣄⠀⠀⠀⢠⡶⠄⠀⢀⡏⠀⢀⢸⠄⠀⠀ ⣤⣬⣷⣿⣯⢿⣽⢶⣻⡜⣦⢿⣿⣷⣦⣅⣀⢀⣠⡴⢫⠃⢀⠌⡼⠀⠀⠀ ⠀⠀⠈⣙⣟⣯⠿⢿⣖⡻⢮⣹⢻⣿⣿⣿⣿⣿⠿⠟⠁⡪⠥⡖⠁⠀⠀⠀ ⠾⠛⠛⠙⢚⣿⣿⣿⣿⠿⣭⣿⣿⣿⣿⣿⣿⣿⣷⠶⠋⢀⣰⡇⠀⠀⠀⠀ ⣠⣤⣤⢶⣾⣯⣿⣶⣿⢿⣿⡿⠟⠈⢩⡙⠛⠉⠉⠑⣌⠁⠀⢹⡆⠀⠀⠀ ⠁⣀⣀⣴⣿⣟⣟⣾⡽⣾⣧⣄⣀⣠⣜⠳⣄⣀⣀⣼⠥⢷⠤⢲⣿⡀⠀⠀ ⠛⢫⣿⢿⣽⣻⣿⠟⡉⣴⢿⠀⠈⠀⠩⣣⣉⣨⠖⠞⠣⣬⣆⡀⠑⢯⡢⡀

⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⡀⠀⣀⣤⣄⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣠⣴⠶⡏⣶⢎⡿⢻⡏⠶⢞⡇⠀⠀⠀⠀ ⠀⠀⣠⡾⠋⠁⠀⠀⠙⠐⠚⠁⠀⠛⠲⠛⠙⢷⡄⠀⠀ ⠀⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡆⠀ ⢸⡇⠀⠀⠀⠀⠀⠀⢠⢆⠀⠀⠀⠀⢠⢲⠀⠀⠀⢿⠀ ⢸⡀⠀⠀⠀⠀⠀⠀⠈⠢⡑⠤⢀⡠⢃⠎⠀⠀⠀⣬⠀ ⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠂⠁⠀⠀⠀⣰⠏⠀ ⠀⠘⠵⣴⣆⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⣀⡤⡾⠋⠀⠀ ⠀⣀⣠⡿⠉⠛⣳⣶⠶⠶⠾⣿⠶⠛⠋⠉⣹⣧⡀⠀⠀ ⠈⠫⣎⣷⠀⠋⡜⢳⠀⠀⠞⢫⣑⠂⠀⠐⠁⢃⣉⢠⠄ ⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠂⠀⠀⠀⠂⠐⠀⡞⢡⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠐ ⠀⠀⠀⠀⠁⠀⠀⠀⠀⢀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠈ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⢤⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠟⠁⢀⠀ ⠠⠀⠀⠀⠀⠀⠀⠀⣼⣿⠌⠀⠉⠹⡀⠀⠀⠄⠠⠀⣠⣾⣟⠡⠄⠀⠀⠀ ⠐⠀⠀⠀⠀⠀⠀⢰⣿⡿⠀⠀⠀⣠⠎⠈⠉⠙⢕⠺⣿⠟⠁⠀⠑⢎⠀⠀ ⠀⠀⠀⠀⠀⠀⡠⠋⠘⠃⢀⡶⠊⠀⠀⠀⠀⠀⠀⠱⡀⠑⢄⠀⢠⡄⠃⠀ ⠀⠀⠀⠀⠀⡜⠁⠀⠀⠀⠌⠀⠀⠀⢠⡆⠀⠀⠀⠀⢱⡀⠀⠣⣤⠇⠀⠀ ⠀⠀⠀⠀⡘⠀⠀⠀⠀⡜⠀⠀⠀⢠⣁⣇⢰⠀⠀⠀⣸⣡⠀⠀⣵⣀⠀⠀ ⠀⠀⠀⠀⡇⠀⠀⡠⠊⠃⠀⠀⢠⠃⠀⢠⠈⠀⠀⠀⠆⠀⠆⠘⢿⣿⠀⠀ ⠀⠀⠀⠀⣇⡄⠪⠄⠐⡆⠀⢠⢃⣀⣀⣘⠇⠀⠀⡜⣠⣤⣼⡀⢠⢫⢆⠀ ⠀⠀⠀⠀⢰⠀⠀⠀⡄⠹⡀⡿⠋⣿⣿⣽⠁⡠⠺⠘⣿⡿⠈⠇⡘⠣⢈⣢ ⠀⠀⠀⠀⢀⡄⠀⠀⡇⠀⠱⠸⡈⢇⡠⠹⠊⠀⠀⠀⠧⠆⣸⠘⠃⠀⣀⡀ ⠀⠀⠀⠀⡌⢀⠀⠀⢁⠀⠀⢠⣱⡔⠀⠀⠀⠀⠀⠀⠀⠀⢾⠀⠁⠀⠿⠃ ⠀⠀⢀⡜⠄⡆⠀⢀⠘⡤⠀⠀⡆⠁⠀⠀⠀⠀⠐⠀⠀⡠⠃⠀⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⢃⠀⠘⢂⢀⣇⠀⣇⠀⠳⣦⠤⠄⡤⠐⠹⢇⠀⠀⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⠤⢇⡔⠻⣿⣆⣯⡢⣀⢸⢿⣶⡁⠀⠀⠀⠆⢸⠁⠀⠀⠀

⢰⢲⠲⢖⠒⢒⡤⠔⠊⠉⠑⠂⠀⠒⠲⢒⠀⢀⡲⠖⣶⡄⠀ ⠈⣯⠀⠀⡩⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡉⠀⠀⢸⠃⠀ ⠀⠙⣖⡔⠁⠀⠔⠀⢀⠂⠀⠐⠄⠀⠐⢄⠀⠈⢢⣠⠖⠁⠀ ⠠⣤⣾⠀⠀⢸⠀⡀⡈⠀⠀⠀⠘⡀⡀⠀⢂⠀⠀⢻⡴⠀⠀ ⠀⠀⡇⠀⠀⢸⣸⡿⠙⡖⣄⠐⣄⠛⢽⡭⢘⡄⠀⢀⢱⠀⠀ ⠀⠀⠳⡰⡈⡄⣿⡟⣟⡞⠋⠑⠏⢸⣯⡍⣷⣧⡇⣼⡜⠀⠀ ⠀⠀⠀⠈⢟⠋⣟⠢⠄⠂⠀⠀⠀⠈⠂⠐⠃⡇⠋⢹⠀⠀⠀ ⠀⢀⠀⣀⡜⠀⠈⠢⢄⣀⠀⠀⠀⢀⡀⠤⠊⠀⠀⠈⠦⠄⠀ ⠀⠈⢉⠝⠀⠀⠀⠀⠀⡰⣾⣯⣻⡶⢄⠀⠀⠀⠀⠀⢈⢦⠀ ⠀⢠⠇⠀⠀⠀⢀⠁⣠⣱⠈⠻⡋⢈⣌⡆⠀⠀⠀⠀⢨⠀⣷ ⠀⠘⡄⡇⢄⠀⡌⠀⠘⠨⡇⠣⢜⢸⠔⠁⢠⢠⠃⣠⢎⡷⠚ ⠀⠀⠱⣟⢌⢦⣘⣰⡄⢠⠃⠒⠒⡙⡧⣀⢾⢾⡔⠁⠉⠀⠀ ⠀⠀⠀⠈⠀⠻⠀⠙⠠⣃⣼⣠⡇⢱⣐⣽⠇⠈⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠇⠠⡃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠿⠻⣿⣦⣀⣀⣴⣾⠿⠿⢿⣦⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣿⣿⠰⣿⣿⢉⣿⠟⢿⣿⠁⢾⣿⠉⣿⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⣴⡾⠟⠛⠉⠀⠘⢿⣦⣍⣀⣾⡟⠀⠈⢿⣦⣄⣠⣾⡿⣷⣦⡀⠀⠀⠀⠀ ⠀⠀⠀⣠⣾⠟⠉⠀⠀⠀⠀⠀⠀⠀⠉⠉⠋⠉⠀⠀⠀⠀⠉⠙⠋⠉⠀⠈⠻⣿⣄⠀⠀⠀ ⠀⢀⣼⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣧⠀⠀ ⠀⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇⠀ ⣸⢿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⢦⠀⠀⠀⠀⠀⠀⠀⠀⡴⠲⡄⠀⠀⠀⠀⠸⣿⠀ ⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡈⢣⡀⠀⠀⠀⠀⠀⣰⠁⡼⠀⠀⠀⠀⠀⠀⣿⡆ ⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠉⠒⠦⠤⢤⠞⢁⡼⠁⠀⠀⠀⠀⠀⢰⣿⢡ ⠸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠢⠤⠤⠖⠋⠀⠀⠀⠀⠀⠀⢀⣾⠇⠀ ⠀⠹⡿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣿⠏⠀⠀ ⠀⠀⠙⢮⣷⣴⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⠟⠁⠀⠀⠀ ⠀⠀⠀⠀⢨⣿⡿⠿⣶⣤⣤⣄⣀⣀⣀⣀⣀⣸⣷⣄⣀⣤⣤⣴⣶⠿⠛⣿⣇⠀⠀⠀⠀⠀ ⠀⣀⣠⣴⣿⡿⠁⠀⠀⢈⣉⣿⡞⠛⠛⠛⠛⠻⣿⣟⠛⠉⠉⠀⠀⠀⢀⣿⡿⣦⡀⠀⠀⠀ ⠀⢻⣉⣼⠛⣷⠄⠠⢟⠋⣽⠻⡖⠀⠀⠀⢠⡾⢻⡛⠳⣶⠒⠒⠒⠴⠟⠁⡇⢈⡛⣀⡀⠀ ⠀⠈⠉⠛⠒⠻⠀⠤⠬⠴⠯⢄⣷⣀⣀⡀⣜⣡⣼⡧⠤⠁⢀⠠⠤⠄⠠⠀⠀⠒⠂⠀⠛⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣀⣤⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⣛⡶⣽⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠋⠹ ⠀⠀⠀⠀⠀⠀⣰⣿⢣⣯⣽⣷⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣇⣀⣴ ⠀⠀⠀⠀⠀⣰⡿⣏⣿⣾⡿⢿⠶⣤⣤⣤⣀⡀⠀⠀⠀⢠⣿⣟⣾⡱⢿ ⠀⠀⠀⠀⣸⣿⡽⠋⠉⠁⠉⠛⢾⡤⣱⢨⡙⠽⣳⣦⣤⣾⣿⣻⢶⣙⣿ ⠀⠀⢀⣴⡿⠁⠀⣴⠈⢹⣦⡀⠀⠹⣧⠷⠛⠋⠉⠙⠻⢿⣯⢷⣫⣜⣿ ⠀⢠⡿⠟⠀⠀⢐⣿⣷⣿⣿⠇⠀⠀⠁⠀⠀⡤⠒⢶⣄⠀⠹⣯⢷⣾⠇ ⠀⡎⢀⣀⣠⣤⠀⠀⢀⡍⠉⠀⠀⠀⠀⠀⣸⣷⣶⣿⣿⠆⠀⣿⣿⣾⠀ ⠀⣿⣿⢿⣿⣥⠀⠀⠀⢳⣶⣦⣶⣶⣄⡀⠉⢈⡛⠿⠋⠀⠀⣼⣿⠇⠀ ⢺⣿⣯⣟⢯⣞⣷⠀⠀⠈⣷⠀⠤⡈⢝⣿⠖⠋⠀⠀⣀⠀⠀⠈⢻⡇⠀ ⠸⣿⣿⣞⣯⣞⠾⣇⠀⠀⠘⣯⣠⣱⠞⠁⠀⠀⠀⠐⣯⣷⣄⠀⠀⡇⠀ ⠀⣿⢿⡿⣾⣽⠿⣿⡳⣄⠀⠀⠀⠀⠀⠀⠀⣰⣾⡟⣯⣿⢿⣿⣿⠁⠀ ⣼⡏⢖⠲⣀⣀⢀⡟⣳⣤⣋⡔⠠⡄⢢⠐⣿⣿⣳⣟⣧⣟⣯⣿⡇⠀⠀ ⠟⡬⣉⠳⣄⢣⣺⠧⡑⠬⣉⠛⣛⢫⢁⣾⠃⠙⠷⣿⣾⣽⣾⡏⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣮⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠘⡷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⠀⠙⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠀⠀⠀⠹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⠀⠀⠣⡙⢯⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⢸⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⣿⡂⠀⠀⠱⡀⠙⢷⡦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⡟⠀⠀⠀⠈⡄⠈⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢻⡈⠁⠀⠀⠀⠑⡄⠀⠙⢗⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠿⠁⠀⠀⠀⠀⡇⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠸⡄⠀⠀⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⡀⢸⠿⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢿⠀⠀⠀⢦⢄⣘⣟⠀⠀⠀⠈⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠺⠧⣀⣀⠀⢠⢧⡘⡆⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠸⣧⣀⣀⣈⣣⡀⠉⠳⣄⠀⠀⠀⠙⢟⢦⡀⠀⢀⣀⢀⣀⢀⢸⡧⠀⠀⠀⠉⠛⠀⠱⡇⠀⠀⠀⢯⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣿⠬⠂⠀⠀⠀⠀⠀⠈⠳⣄⣀⠤⠔⠓⠛⡛⠉⠉⠉⠉⡝⠉⠀⠀⠀⠀⠄⣀⠀⠀⢻⠀⠀⠀⠈⣟⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢐⣞⡉⠀⠀⠀⠀⠀⠀⣀⠤⠖⠊⠁⠀⠀⠤⠒⠒⠉⠁⠀⠑⠢⡈⠉⠒⠤⣀⣀⡀⠀⠉⠁⢸⡀⠀⠀⠀⢱⣧⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠉⠻⣽⢀⡤⠖⠉⠀⠀⡔⠁⣠⠔⠊⠑⠒⠤⢄⡀⠀⠀⠀⠈⠢⡀⠀⢀⣍⡠⠤⠒⠒⠋⢦⠀⠀⠀⠀⢿⢆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⢄⠾⠋⠁⠀⠀⠀⢀⣎⡤⠊⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⢄⡀⠀⠈⠢⡉⠀⢀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠱⡳⡀⠀⠀⠀ ⠀⠀⢀⡤⠊⠁⠀⠀⠀⠀⠀⢠⠟⣹⠡⠤⠤⡄⠀⠀⠀⠀⢠⡤⠐⠀⠀⡈⠑⠢⣀⠈⢢⣸⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠘⣕⡄⠀⠀ ⠀⠀⢸⠀⢠⠃⠀⠀⠀⠀⣰⠃⡜⠉⠒⠤⠔⠁⠀⠀⠀⠀⠈⠳⠤⠒⠉⠀⠀⠀⠀⠑⠦⣹⠀⠀⠀⠀⠀⡠⠀⠘⣄⠀⠀⠀⠈⣞⠀⠀ ⠀⠀⠬⠀⡆⠀⠀⠀⠀⣰⢃⣘⡀⠠⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⣒⣠⣤⣤⡤⠀⠈⠘⡆⠀⠀⡼⠊⠀⠀⠀⠘⡄⠀⠀⠀⢸⢆⠀ ⠀⠀⡧⠘⠀⠀⠀⠀⣼⣧⣾⠟⠛⣛⡿⠶⣿⠀⠀⠀⠀⠀⢀⡿⠟⠛⣛⣉⣉⠛⢿⣶⣄⠰⡇⠀⠀⢰⠀⠀⠀⠀⠀⠹⡀⠀⠀⢸⠘⣆ ⠀⠀⡇⠀⠀⠀⠀⣼⣿⠏⠁⢰⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠐⢀⣛⣿⣿⣿⣷⡄⠙⢿⣷⣅⠀⠀⢸⠀⠀⠀⠀⠀⢀⡇⠀⠀⠠⠀⢸ ⠀⠐⡇⠀⠀⠀⣼⢹⣷⠀⢰⣿⠛⣿⣽⠛⠂⠀⠀⠀⠀⠀⠀⠀⢺⣿⣭⡟⢻⣿⣿⠀⢱⣿⠛⠒⠀⢸⠀⠀⠀⠀⠀⢸⠁⠀⠀⢸⠁⢸ ⠀⢘⡇⠀⠀⢠⣇⡼⠁⠓⠼⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠺⠧⡠⠎⢸⠀⠀⠀⢸⠀⠀⠀⠀⣠⠏⠀⠀⠀⡸⠀⡾ ⠀⢰⠃⠀⢠⢯⡏⣀⣀⢔⡂⠀⠀⠀⢀⣀⣀⣀⣤⡤⢤⣀⡀⠀⣀⡀⠀⠀⠠⣤⣤⣄⣀⣸⠀⠀⠀⢸⠀⠀⠀⡰⡿⠀⠀⠀⢰⢁⣞⡅ ⠀⣾⠀⢀⡞⠐⣯⠟⢡⠀⠀⠀⠀⠀⠀⣾⢯⡛⡱⢪⠕⡪⠵⢾⡙⣆⠀⠀⠀⢀⡉⠺⣭⡿⠀⠀⠀⢸⠀⠃⡰⢱⢳⠀⠀⢀⢧⡞⠎⠀ ⣰⡏⠀⡼⠀⠀⢧⣴⡏⠀⠀⠀⠀⠀⠀⡟⢦⠱⣑⢣⠚⡥⢋⠦⡑⢾⡀⠀⠀⠀⠹⣦⣌⡇⠀⠀⠀⢸⠀⡜⠁⡜⢰⠀⠀⣸⢺⠈⠀⠀ ⡿⠀⢠⠇⠀⠀⠈⣻⡇⠀⠀⠀⠀⠀⠀⣟⢢⠓⣌⠦⡙⠴⣉⠖⣩⢒⡇⠀⠀⠀⠀⢹⣾⠃⠀⠀⠀⢸⡜⠀⢠⡇⢸⠀⠀⡇⢸⡀⠀⠀ ⠁⠀⡞⠀⠀⠀⠀⡏⢳⡄⠀⠀⠀⠀⠀⠘⣎⡱⢌⠲⣉⠳⢌⢎⡑⢎⡇⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⣸⠀⠀⡼⣧⠘⡄⠀⡇⠈⡗⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣴⣶⣾⡿⠿⠿⠛⠛⠛⠛⠛⠛⠻⠿⢿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⡿⠿⠛⠛⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣤⣾⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣴⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡆⠀⠀⠀⠀⠀ ⠀⠀⢠⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡆⠀⠀⠀⠀ ⠀⢠⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡀⠀⠀⠀ ⠀⣾⠏⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣧⠀⠀⠀ ⣸⡏⠀⠀⠀⠀⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣷⣀⠀⠈⣿⡄⠀⠀ ⣿⠀⠀⠀⠰⢤⣬⣟⣽⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣻⣿⣿⠯⠀⠀⢸⣇⠀⠀ ⣿⠀⠀⠀⢠⡟⠉⢻⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠟⠛⠀⠀⠀⢿⡄⠀ ⣿⠀⠀⠀⡟⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢸⣷⡀ ⣿⡄⠀⢰⣽⣤⣤⠾⣣⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀⠀⣀⣼⣿⠀⠀⠀⣿⡇ ⢻⣇⠀⠸⣿⣶⣶⣶⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⢿⣿⠟⠁⠀⠀⠀⣿⡇ ⠈⣿⡆⠀⠀⠙⢿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⣿⡇ ⠀⠘⣷⠀⠀⠀⠈⢿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡏⠀⠀⠀⠀⢀⣿⠀ ⠀⠀⠘⣇⠀⠀⠀⠈⢻⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡟⠁⠀⠀⠀⠀⣸⠇⠀ ⠀⠀⠀⠿⣇⠀⠀⠀⠀⠹⣿⣷⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⠟⠋⠀⠀⠀⠀⠀⣠⡟⠀⠀ ⠀⠀⠀⠀⢿⣧⡀⠀⠀⠀⠀⠈⠙⠻⠿⣿⣶⣦⣤⣀⣀⣀⡀⠀⠀⠀⠀⠀⣀⣀⣠⣴⣾⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⣰⠟⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠿⠿⠿⠿⠿⠿⠿⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠞⠋⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⠶⠶⠶⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⢀⠎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠀⠀⠀⠀⠀⡔⠀⠀⠀⠀⠘⠰⠀⠸⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡗⠐⠀ ⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⡖⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀ ⠂⠠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠁⠀⣄⠀⠀⠀⣸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀ ⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⡇⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀ ⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⢡⡇⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠈⡇⠀⢸⡀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠐⠊ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠇⢸⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⣇⠀⠈⡇⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀⣸⡄⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⢧⠀⣸⡿⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡳ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⢠⡿⠵⠯⢽⡧⠤⠴⠂⠀⣿⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠘⣇⡟⡇⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⣺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⣿⠇⠀⠀⠀⡇⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠹⡿⡇⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⠀⢸⡟⠀⠀⠀⠀⢹⡀⠀⠀⠀⡟⡆⠀⠈⠑⠒⠂⠠⢤⡘⣆⠀⠀⢻⣝⠀⠀⠀⠀⠀⠀⣼⣠⡤⣄⣀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡴⠂⣿⠁⠀⡾⠁⠀⠀⠀⠀⠈⣧⡀⠀⠀⢧⢿⡀⠀⠀⠀⠀⠀⠈⢷⡹⣆⠀⠀⠹⣄⠀⠀⠀⠀⠀⣿⠘⢦⡀⠉⠳⣄⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣸⠁⢸⡇⣀⣠⡇⠐⠊⠉⠉⠉⠉⠙⢿⡻⣆⠸⡌⣧⠀⢀⡀⠀⠀⠀⢸⣿⠘⢧⡀⠀⠈⢷⣄⠀⠀⠀⡿⡄⠀⠉⠳⠤⠼⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢰⠇⢠⣏⣿⣟⣧⣶⣾⣿⣟⣛⣟⣿⣷⣶⣌⠉⠛⠻⠘⠷⣬⣷⣄⣀⠀⠀⡟⡆⠀⡷⣄⠀⢦⣙⠳⣄⠀⡇⣧⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡏⠀⣸⣿⣿⣿⡿⠟⢛⣿⣿⠟⠻⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠉⠙⠛⠻⣷⣀⢻⡈⢷⠒⢿⣻⠀⠀⣇⠸⣆⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣼⠁⢰⣿⣿⡿⠋⠀⠀⣾⣿⠁⠀⣀⣿⣿⣿⣿⣿⣿⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠘⠷⢼⣷⣦⣄⠸⡄⠙⢷⡦⣤⣀⠀⡿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⠀⠀⠀⢰⠇⢠⣾⣿⣿⠁⠀⠀⣸⣿⣿⣿⣿⣿⣇⣤⢼⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣙⣷⣶⣤⣬⣗⣢⣿⡳⣧⣷⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢈⢼⡄⠀⣼⠀⠈⢹⣿⣿⠀⠀⠀⣿⣿⣿⠉⠁⠘⢿⣿⠿⢿⣻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣩⡿⣿⣿⣿⣿⣿⣷⣯⡺⠿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⢸⡇⢀⡇⠀⠀⢸⠈⣟⢦⡀⠀⣁⣉⠈⠀⠀⠀⠀⠀⠀⠒⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠁⠀⠀⢿⣿⣿⣿⣿⣿⣿⣦⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⠈⣿⣸⠁⠀⠀⢸⡆⣻⡄⠑⠀⠸⣧⠀⠀⠀⠀⠀⠀⢀⣴⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⢦⣤⡶⠟⠻⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⡄⠸⣿⡀⠀⠀⢸⣿⣽⣳⠀⠠⠀⠙⢷⣄⠀⠀⠀⣠⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⣿⠟⠛⢿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀ ⠙⢿⡄⢻⣇⡄⠀⠸⡇⠻⣿⡁⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣥⣅⣹⠀⠀⠈⠉⠉⠉⠻⣷⣿⣿⡿⠋⢿⣿⡆⠀⠀⠀⠀⠀⠀ ⠀⠈⠙⠳⠿⣷⡀⠀⣇⠀⠈⢿⠒⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⢹⣿⡿⠃⠀⣼⠉⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⢷⡄⢸⡖⠋⠙⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣦⡀⠀⠀⠀⠀⡁⢀⣾⠛⠁⢸⣼⣟⣼⡵⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢨⣿⣄⢱⣄⠀⠀⠉⠳⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠲⠶⠶⣶⠿⠋⠀⠀⣾⠋⠀⢸⣷⠃⡆⣼⠀⢀⠄ ⠀⠀⠀⠀⠀⢠⠏⠀⠈⠉⠉⠉⠀⠀⠀⢈⣩⡷⣖⣶⣶⣶⣶⣶⣶⡲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠏⠀⢠⣿⢋⡾⣽⣽⠀⡀⠀ ⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⢀⡴⣾⠿⠚⠉⢁⣀⣀⣀⣀⣀⠀⠀⠈⠉⠓⠲⢯⣓⡦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠇⠀⢀⡾⣡⣞⣷⠁⡟⣸⠁⠀ ⠀⠀⠀⠀⣰⠃⡴⠒⢶⠀⢀⡴⣫⡞⠁⠀⠀⣰⡏⠀⠀⠉⠉⠉⠉⠉⠙⠲⠤⠤⠤⣀⠉⢳⣝⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⠴⠖⠋⣡⠋⠀⠀⣾⡿⣫⣞⣀⡼⣡⡷⠾⢤ ⠀⠀⢀⡾⠛⠛⠳⠿⢟⡛⣾⠁⡟⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠹⡳⡝⣦⠤⠴⠖⠒⠚⣿⣫⣍⠉⢳⣄⡠⠞⠁⠀⣠⣞⣥⠞⠋⢀⣴⡷⠋⣠⠶⠛ ⢀⠖⠉⠀⣀⣤⣤⣄⡀⢹⡇⢠⢻⡄⠠⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⢠⢹⡆⠀⠀⠀⠀⢿⡟⠻⠯⣭⣥⣴⣶⣴⣾⠟⠉⠀⠀⠈⠉⠁⣠⠞⠁⠀⠀ ⠁⠀⠔⠚⠉⠀⠀⠀⠉⠲⡇⠈⠳⣝⢦⡈⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣟⠟⡇⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠈⢻⡿⠁⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡀⢠⣀⢀⡇⠀⠀⠈⠓⠯⡓⠿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠔⠋⠀⢰⡟⢷⠶⠛⠁⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣸⡀⠀⠀⠀⠀⠀⠉⠓⠈⠝⢛⣛⣲⠶⠶⠶⠷⠿⠷⠚⡛⠭⠀⣾⠓⠦⣏⠐⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⠀⠀⠀⠀⠀⠀⠀⣼⣤⡀⠀⠀⠀⠀ ⢀⠀⠀⠀⢀⣀⠀⠀⠠⣾⡍⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⠉⠁⢀⣀⢀⠀⠀⢀⡏⣻⣄⠀⠙⢦⡀⢸⡄⠀⠀⠀⠀⠀⠀⣠⡞⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠙⠳⣄⡀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠾⡏⢀⣼⠟⠉⠀⠀⠀⠸⣷⠇⠀⠀⠈⢻⣆⠸⡏⠳⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠃⢰⡇⣾⠃⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢻⡄⢷⠀⠈⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⠀⠀⢸⣿⠃⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⢻⣾⡄⠀⠁⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣾⠋⠀⠀⠀⣾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⢿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠉⢷⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⡇⠀⣀⣀⣻⣶⣤⣄⣀⠉⠻⢷⣦⣄⡉⠓⢦⣄⣀⠐⠦⣤⣀⣀⠀⠀⢀⣀⣀⣀⣀⡀⢸⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣤⠾⠛⠋⠉⠁⠀⠀⠀⠀⠉⠙⠳⣶⠿⠦⠉⠙⠒⠛⠻⠟⠓⠒⢿⣿⠿⠛⠛⠋⠉⠉⠙⠛⠛⠿⣦⣄⠀⠀⠀⢠ ⠀⣰⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣇⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡄⢠⡿ ⢠⣿⠀⠰⠷⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠆⠀⠈⢿⣾⠃ ⠀⢿⢧⡀⠀⢀⣠⡤⠤⠄⠤⣄⠀⠀⠀⢀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠹⣇⠀⠀⠀⠀⠀⢀⣠⣤⣀⡀⠀⠀⠀⠀⣸⡏⢀ ⠀⢈⡿⣽⡶⠋⠁⠀⠀⠀⠀⠈⢷⣤⣴⠟⠁⢤⣀⣀⠀⠀⠀⣀⣀⣀⠀⠙⠷⣦⣄⣠⠞⠉⠁⠀⠈⠙⠳⣦⣀⣴⡿⠟⠋ ⠀⢸⠇⣽⠁⠀⠀⠀⠀⠀⠀⠀⣸⣿⠉⠓⢲⠶⠤⠭⠭⣭⣭⣭⡭⠤⣤⠤⠖⠚⣿⣿⠀⠀⠀⠀⠀⠀⠀⠘⣿⢻⡇⠀⠀ ⠀⢸⠀⠹⣄⠀⠀⠀⠀⠀⠀⡾⠋⠘⢧⣄⣘⡇⠀⠀⠀⢸⠀⠀⠀⠀⡟⠀⠀⣠⣿⣻⣦⠀⠀⠀⠀⠀⠀⠀⣼⠈⡇⠀⠀ ⠀⢸⡇⠀⠉⠓⠦⣤⠤⠄⠀⠀⠀⠀⠀⠠⠿⠷⢤⡀⠀⢸⠀⠀⠀⢀⡇⣰⣞⣉⠀⠀⠀⠀⠀⢀⣀⣀⣤⠾⠃⠀⡇⠀⠀ ⠀⠈⢷⡀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠞⠛⠒⠾⣦⡖⠒⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠉⣹⢻⣇⣀⠀⣸⠇⠀⠀ ⠀⠀⠈⠿⣦⡀⢀⣼⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠘⠉⠁⣴⠟⠀⠀⠀ ⢀⣠⠴⠖⠋⢉⣩⣥⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠳⣶⣾⠋⠀⠀⠀⠀ ⠈⠙⠛⠚⠛⢉⡿⠋⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢦⣄⣉⣛⣶⣄⠀⠀ ⠀⠀⠀⢀⣴⢋⣠⣴⠿⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⡀⠙⠻⣍⡉⠁⠀⠀ ⠀⠀⠀⠘⢋⣿⠋⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠈⠻⣿⠲⠼⠿⠆⠀⠀ ⠀⠀⠀⢠⡿⠁⠀⢀⣾⠛⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⣠⡾⠗⢲⣤⠾⠧⢶⣿⠛⠛⠛⠛⢻⠃⠀⠀⠐⠒⠒⠒⠒⠒⠒⠒⠒⡶⠶⠶⠶⠶⠤⣾⡟⠀⠀⢸⡇⠀⠀⠀⠀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠤⠖⠒⠒⠒⠒⠒⠒⠒⠢⠤⠤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠚⠋⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠚⠁⠀⠀⢀⡴⢂⣴⡇⠀⠀⣸⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠈⠙⠲⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⠀⠀⣰⠟⣠⠎⢹⠁⠀⠀⣿⣲⡀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⡀⠀⠀⠙⢦⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⠞⢥⡴⣄⣀⠀⢠⡾⣣⡞⣡⠀⡿⠀⠀⠀⣿⣟⣷⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠱⡄⠀⠀⠀ ⠀⠀⠀⠀⢀⡴⠋⢀⣾⠓⠲⠭⣝⣻⣿⠷⠚⠀⠀⢷⠀⠀⢰⡿⠀⠹⡄⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠘⣆⠀⠀ ⠀⠀⠀⢠⡾⠁⢀⣾⡟⠀⠀⢀⣾⠏⠀⠀⠀⠀⠀⢸⠀⠀⢸⡇⠀⠀⢻⡀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠹⣆⠀ ⠀⠀⢀⡞⠀⠀⣾⣿⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠘⣇⠀⢸⡇⠀⠀⠈⢧⠀⠀⠀⠈⡇⠀⠀⠀⠀⣤⢸⠀⠀⠀⠀⠀⠀⣼⡆ ⠀⠀⣼⠁⠀⣸⣿⣿⣓⣒⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⢻⣦⢸⡇⠀⠀⠀⠈⣇⠀⠀⠀⣷⠀⠀⠀⠀⣿⡼⠀⠀⠀⠀⠀⠀⠘⢳ ⠀⢰⡇⠀⠀⣿⣿⣿⠀⢉⡟⠀⠀⣸⣤⡀⠀⠀⠀⠀⠀⢳⣾⡇⠀⠀⢀⣠⣼⣇⠀⠀⢻⠀⠀⠀⠀⣿⡇⠀⠀⡦⠀⠀⠀⠀⢸ ⠀⢸⡇⠀⢠⣿⡟⢸⡄⣾⠁⠀⣾⠫⠉⣻⡄⠀⠀⠀⠀⠈⢿⡇⠀⢠⣿⠋⠉⢻⣆⠀⢼⠀⠀⠀⢰⣿⠁⠀⠀⡇⠀⠀⠀⠀⢸ ⠀⢿⡇⠀⢸⡟⠀⣰⣷⢿⠀⠀⢿⣦⣠⣼⠇⠀⠀⠀⠀⠀⠀⠻⠀⠸⣷⡠⠠⣠⡿⣶⣼⡀⠀⠀⣼⡏⠀⠀⣸⣿⠀⠀⢸⠀⢸ ⠀⢸⠀⠀⣿⠃⢠⣿⣿⡏⠀⠀⠀⠙⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠛⠉⠘⣿⣇⠀⢀⡟⠀⠀⠀⣻⣿⠀⠀⢸⠀⡘ ⠀⢸⡆⢰⡏⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣄⣾⠃⠀⠀⢠⣿⣿⠀⠀⢸⣶⠇ ⠀⠀⢧⣼⠁⢸⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⢤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⠿⠟⠀⠀⠀⣼⠋⣿⠀⠀⢸⡏⠀ ⠀⠀⠘⡇⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢸⣿⠟⠀⠀⠀⠀⢰⡿⣸⣿⠀⠀⢸⠁⠀ ⠀⠀⠀⡇⠀⣾⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢨⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣿⡟⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⣾⠀⠀ ⠀⠀⢸⡇⠀⢻⣿⣿⣿⣷⣀⠀⠀⠀⠀⠀⠀⠸⣝⣈⣷⡀⠀⠀⠀⠀⠀⠀⠀⢨⡏⡿⠁⠀⠀⠀⠀⠀⣿⣿⣿⡏⠀⠀⣿⠀⠀ ⠀⠀⢸⡇⠀⢸⣿⣿⣿⣿⣿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃⠀⠀⠀⠀⠀⣼⣿⣿⣿⢃⡼⠀⢹⠀⠀ ⠀⠀⠀⣇⠀⢸⣿⣿⣿⣿⣿⣿⣿⠈⢻⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣾⡏⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⠟⢧⠀⠸⠀⠀ ⠀⠀⠀⢻⠄⠀⣿⣿⣿⣿⣿⣿⡿⠀⠀⢻⣿⣿⣶⣶⠖⠒⠒⠒⠒⠋⢹⣿⣿⣿⠁⠀⠀⠀⠀⣠⣿⣿⣿⡿⠋⠀⠈⢷⣇⠀⠀ ⠀⠀⠀⠘⣷⡞⠉⠻⣿⣿⣿⣿⡃⠀⠀⠀⠻⣿⡿⠹⡀⠀⠀⠀⣀⡠⠟⢿⣿⡟⠀⠀⢀⣠⣴⣿⣿⣿⠏⠀⠀⠀⠀⠀⠙⠀⠀ ⠀⠀⠀⠀⠈⠣⠀⠀⠈⠙⢿⣿⣿⡀⠀⣠⣴⡟⠀⢀⣹⣦⣒⠋⠉⠀⠀⣸⣿⠇⢀⡴⠋⣼⠏⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣻⣾⣿⡟⠀⣠⡿⠿⢿⣌⣳⠀⠀⢀⣿⣿⣼⣏⠀⢠⠟⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⢀⣼⢋⣴⣿⣾⡙⣯⡇⠀⣼⣿⣿⣿⣿⣷⣎⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡷⠋⢨⠟⣻⣿⠛⡁⢹⢱⣼⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠈⡴⢃⣿⡆⡇⢸⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢹⣾⠃⢸⣿⡇⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⢠⢿⡟⠀⡞⡟⢹⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⡾⣼⠀⢸⡇⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠷⠃⠀⢸⢁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠚⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠓⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⢀⣀⣠⣤⣤⠴⠶⠛⠛⠉⣩⣷⣶⣤⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀ ⠶⠶⠛⠛⠛⢉⣋⠀⠀⢰⣷⡀⠀⣸⣿⠏⠙⣿⣿⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⣿⢷⣤⡈⣿⣧⠀⣿⣿⡀⠀⣿⣿⠃⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠸⣿⣏⠻⣿⡾⣽⡆⠘⢿⣿⣾⣿⠋⠀⠀⠀⢀⡀⠀⠸⣇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⣿⡄⠈⠙⠟⠃⠀⠀⠀⠁⠀⠀⢀⣀⣼⠋⢧⠤⠖⠻⣆⠀⠀ ⡀⠀⠀⠀⠀⢀⣠⣍⠁⠀⠀⢀⣀⣤⣤⣶⣶⣿⣿⣿⣿⣿⣦⣀⠠⠀⠂⠙⣦⠀ ⣧⠀⢀⣀⣠⣼⡟⢸⣷⣿⣿⣿⣿⡿⣿⢿⣻⣟⣯⢿⡽⣯⣿⣿⣆⠀⠀⠀⠘⣦ ⠙⣿⣿⣏⣡⠤⠔⠾⣿⣻⣽⣳⢯⡿⣽⢯⡷⣟⡾⣯⣿⣿⡷⣯⣿⡆⠀⠀⠀⠹ ⠀⣿⣽⣏⠀⠀⠀⠀⣿⣯⢿⣽⡿⣿⣯⣿⣽⣻⡽⣿⣻⣷⣿⣿⣷⣿⡄⠀⠀⠀ ⢠⣿⣳⣿⡄⠀⠀⠀⢸⣿⢸⣿⣿⡿⠿⠿⠞⠛⠛⠋⠋⣀⣹⣷⣾⠻⣷⠀⠀⠀ ⢸⣷⢯⣿⣧⠀⠀⠀⠀⢻⣿⣋⣹⣿⣷⡄⠀⠠⠀⠀⢰⣿⣯⡹⢿⠀⢻⣧⠀⠀ ⢸⣯⢿⣿⣿⡆⠀⠀⠀⠸⣇⠹⡿⠩⢿⠇⠀⠠⢀⣴⣇⠈⢆⡐⢃⠆⠁⣿⡆⠀ ⢸⣿⣻⡇⠠⣷⠀⠀⠀⠀⢻⡆⡡⢁⠆⠠⠈⢀⣾⠛⣽⡆⢂⠉⢂⠌⢰⣿⣿⡀ ⢼⣷⣻⣿⣄⢸⡇⠀⠀⠀⠈⣷⡀⠃⠌⠐⠀⢸⣇⢣⣼⠇⠀⠈⢀⣠⣾⣿⡽⣷ ⣿⣳⢿⣿⣿⣿⣿⡀⠀⠀⠀⢹⣇⠤⡄⢠⢀⢀⣉⡋⣁⣠⣤⣶⣿⣿⣿⣿⣻⣽

⠀⠀⠀⠀⠀⠀⡶⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⡇⠀⠀⠈⠑⠲⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣤⡄⠀⠀⠀⠀⠀⠉⠓⢦⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⡀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠙⠒⠢⢤⣤⣤⣤⣤⡤⠤⠤⠤⠤⠶⢶ ⠀⠀⠀⠀⠀⢸⡟⡄⢻⣄⣴⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠙⠦⠀⠀⠀⠀⠀⠀⢀⡾ ⠀⠀⠀⠀⠀⢸⠁⠀⠈⣿⡟⠁⠀⣠⠶⠒⣿⠛⠲⢤⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⣠⣼⡇ ⠀⠀⠀⠀⠀⢸⣧⡆⢰⡏⠀⠀⡞⠁⠀⠀⣿⠀⠀⢀⡇⠀⠀⢰⠋⠀⢹⡏⠳⣄⢠⣶⣿⣿⡟⠀ ⠀⠀⠀⠀⠀⢸⣿⣧⡟⠀⠀⠀⠻⢤⢀⢀⡿⠤⠖⠋⣤⣠⣄⣸⢷⣀⢸⡇⠀⢘⣿⣿⣿⡿⠁⠀ ⠀⠀⠀⠀⠀⣼⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣉⣿⣥⣞⠘⠛⠲⡴⠞⠁⣿⣿⠃⠀⠀ ⠀⠀⠀⠀⣾⣿⣿⣿⢀⠀⠀⠀⢀⣀⣠⣤⠴⠒⠚⠋⠉⠁⠀⠈⠙⢦⡀⠀⠀⠀⠀⣿⠃⠀⠀⠀ ⠀⠀⠀⠀⢻⣿⣿⡿⣿⣿⣿⠿⠛⠉⠙⠻⢶⡄⠀⠀⠀⠀⠀⢀⣀⣤⠿⢶⣄⠀⠀⡗⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢻⣿⣷⣿⣿⠉⠉⠓⠒⠐⠚⠉⠀⢀⠀⠀⠀⠀⠈⠉⢱⡀⠀⠹⣷⣤⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⡿⢿⡛⢶⡈⠉⠀⠀⠀⠀⠀⠘⠲⠒⠦⠟⠀⠀⠀⢉⡉⠛⣿⣿⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣷⣶⣷⣄⣙⢷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣾⣿⡿⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⠟⠛⠿⢿⣿⣿⣶⣄⠀⠀⣤⣤⣤⣶⣾⣿⣿⣿⣽⡁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣶⣦⣴⢶⣾⣿⣿⣿⣷⣴⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⢧⣿⠛⠛⣿⣿⢿⣿⣿⣿⡟⢻⡿⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣷⣾⢇⣀⣤⡿⠟⢺⡗⠲⣿⠃⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣰⣤⣀⡀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣾⣯⣶⣦⣄⣸⡇⠀⢈⣻⣦⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⠣⢤⣈⣉⣉⡉⢙⣛⣿⡟⠛⢿⠿⠿⠾⢿⣿⣿⣯⣽⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⢿⣶⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡀⢸⡏⠉⠉⠛⠛⠛⠻⣏⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠞⠀⠀⠀⠀⠀⠀⠀⠻⠾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⠶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⡀⠚⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠃⠤⢮⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣍⣿⢾⣿⣦⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣌⢺⠌⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣿⣿⠿⢫⣿⣤⣿⣿⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣳⠀⠀⢹⠈⠆⠐⢹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢞⣹⣿⡇⡚⢙⣳⢿⡺⣇⣷⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡧⠀⠀⠈⢿⡦⠀⠀⠙⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⣡⣾⠛⠵⣻⠭⠾⠠⡬⠣⡙⣾⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⡟⣀⣄⠐⠈⠓⠚⠓⠐⠂⠉⠛⠶⣦⣄⣀⣀⣀⣀⣀⢀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⢁⣿⡟⣡⢽⡛⣻⣟⣶⡂⣹⠀⠁⠈⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠈⠋⠉⠉⠹⣏⣩⠍⣉⢉⣩⣟⣷⣿⡿⣽⣽⣿⢣⢴⣽⣷⣺⣿⣿⣿⣷⣄⠀⠠⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠛⢿⡅⣿⣟⣉⣽⣿⣿⡖⢍⣼⣿⣿⣿⣿⣿⣿⢟⢸⣻⣽⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠟⠉⠀⠀⠀⠀⠀⠀⢢⡀⠀⠀⠐⣆⠀⠀⠀⡠⠊⠀⠁⠀⢀⡀⠀⠁⠀⠀⠀⠀⠻⣿⣦⣾⣆⠰⠚⢭⣿⣿⣿⣿⣿⢏⡞⣰⣿⣽⠇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⠁⠀⢠⢄⠀⠀⠀⠀⠀⠀⡞⠀⢖⠁⡴⠋⠀⢀⣴⡇⡴⠾⠔⠢⣏⣁⡤⡄⢠⠆⠀⠀⠀⠚⢹⣿⣟⣄⣴⣾⣿⣿⣿⣿⣿⠯⡵⢫⣾⡿⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⢀⡘⠂⢀⠢⡀⠀⠀⠀⣽⡔⡜⡾⠁⢀⡄⡼⣺⢟⢿⣿⣩⠾⢛⡑⠾⠅⠲⠄⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣫⢄⣀⣿⣿⠁⠀ ⠀⠀⠀⠀⠀⢀⣴⠟⠀⠂⠀⢀⠬⠉⠈⠀⣾⡀⠇⠀⢠⠀⡏⢀⡟⣅⣦⣫⣿⠝⠉⠀⠈⠈⠩⢷⡿⣋⣵⠲⢄⠀⢀⠀⠈⢂⡀⡄⠀⠈⠛⡸⠿⣟⡉⡏⡟⢿⣿⠟⣿⡀⠀ ⠀⠀⠀⠀⢠⠟⠁⡬⣄⠀⠀⣭⣶⣷⣶⣦⣝⣿⠀⠀⠀⠀⠁⢹⣹⣻⡭⠋⠉⠀⠀⢀⡟⣠⠖⠙⠹⠷⢟⡒⠶⣁⡂⠀⢀⡤⠄⠀⠀⠀⠀⠀⠑⢺⣧⣤⡘⢼⣶⣾⣿⡇⠀ ⠀⠀⠀⣠⢏⡤⠚⠉⠈⠓⣺⣿⣿⣽⣿⣿⣿⠇⠀⠀⠀⠀⠠⢆⠨⢹⢳⣄⠀⡀⠀⣾⢏⢀⣀⣠⠀⠀⠈⠹⣷⣤⣍⣀⡀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠙⢧⡙⢿⣿⣿⣿⡇⠀ ⠀⠀⢠⢧⠏⠀⠀⠀⢀⠀⣿⣼⣿⣿⣿⣿⠿⠁⠀⠀⠀⠀⢀⠁⠀⠘⠸⠸⢦⣨⣾⣴⣾⣿⣿⣿⣿⣎⢽⣄⣔⠶⠦⡙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢏⣻⣿⣿⡇⠀ ⠀⠀⡟⡞⠀⠀⠀⠀⠀⢀⠛⣿⣿⡿⠿⠋⠀⠀⠀⠐⠀⠁⠀⠀⢰⢸⣴⣴⣮⣿⣿⡟⢉⣿⣾⣿⣿⣿⣿⣿⣷⠀⠀⠀⠈⠀⠀⠀⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⢳⡽⣿⠀⠀ ⠀⠐⡝⠁⠀⠀⠀⢸⣄⡠⠞⣿⠊⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢯⣿⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⣿⣿⠟⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢹⠀⠀ ⠀⠀⡀⠀⠀⠀⠀⠱⡷⡤⠞⠁⠀⢀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⢄⠰⣍⠧⡟⠛⠿⢿⣿⣿⣿⡿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀ ⠀⠀⠑⢄⠀⠀⠀⢀⣨⣦⣤⣤⣤⣧⣤⠤⠀⠀⠀⢀⠀⠀⠀⠀⠐⠬⠬⡒⢤⡀⡳⠥⢙⣽⠚⡁⢀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀ ⠀⡀⠀⠀⠑⠃⣴⣿⣿⣿⣾⣿⣯⣽⣿⣿⣷⣆⠁⠉⠀⠀⠀⠀⠀⠀⠀⠈⠁⢡⠹⠮⢟⡷⠤⠤⠤⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀ ⠠⠬⣽⣂⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⡀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⢳⡀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀ ⠀⠀⠀⠠⠲⣰⣾⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢯⡀⠠⠀⠂⠀⠐⠀⠀⠀⠄⠀⠀⠙⢦⠀⠀⠀⠀⠑⠦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀ ⠀⠀⠶⢖⡋⢑⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⣴⢾⣦⡿⠰⠂⠍⠛⡖⠒⠒⠀⠲⠿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀ ⠀⠀⠉⡐⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣇⣋⣥⣽⣥⣆⣨⠱⡄⠀⠠⠀⠀⠀⠀⠠⡹⠙⠲⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀ ⠀⠐⠋⡈⢹⣿⣿⣿⣻⣟⣿⣻⢿⢿⣿⣿⣿⣻⡿⣿⢻⣾⣯⡳⡿⡧⡐⣒⣦⣀⡀⠀⠀⠀⠀⠂⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀ ⠀⢀⡞⠁⠀⠙⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⡟⣽⣿⣿⣏⡹⠿⡹⣌⣿⣾⣿⣿⣿⡀⣀⠀⠀⠀⠀⣑⡳⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⠃⠀⠀⠀⠀ ⠀⠘⠀⠁⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣩⣼⣷⣾⣿⣿⣿⣿⣿⡷⢷⠉⠒⢤⠈⠁⠐⠊⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣾⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠰⠋⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣯⣟⠛⢽⡋⢆⠀⠀⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢚⡿⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⠎⡈⠙⠿⣿⣿⡿⣿⣃⠝⠽⡟⣿⡽⣳⣽⢿⠛⠙⢧⠁⠈⠀⠙⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⠀⠀⠀⠀⠟⢸⠃⠀⠀⠈⠉⠐⠈⠉⠀⠁⠹⣭⠙⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⢷⡀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠰⢀⠀⠱⡀⠀⠐⠆⠀⣀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⢈⣵⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⢷⡴⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⡜⢠⠈⠖⠢⣍⠙⢆⢀⠀⠀⠃⠀⠀⠈⠑⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢦⣴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠹⣦⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⢀⡇⢾⠰⣼⡀⠙⣆⠀⠛⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣠⠴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠁⠘⣇⠁⣧⠘⣜⠙⠄⠀⠀⠀⠑⠆⠀⠈⡄⠀⠀⠀⠀⠀⢒⣛⣷⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢀⠘⣆⠾⢀⠀⢀⠀⠀⠀⠀⠀⠠⣹⢦⠰⣄⣭⡷⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢦⣤⡠⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⢀⠱⣀⠠⢴⣄⡀⡐⣳⣽⠴⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⣙⣲⠶⠾⠒⠾⠯⠷⠤⠤⠤⠭⠴⠯⠥⠽⠒⠚⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⢀⠤⠐⠀⠀⠒⠂⠄⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⡠⠁⠀⠀⠀⠀⠀⠀⠀⢸⣦⠀ ⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢃ ⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⢠⣄⠀⠀⠀⢀⣀⠘ ⠀⠀⠀⠀⠌⠀⠀⠀⠀⢀⠘⢍⠀⣄⠤⡨⠯⠀ ⠀⠀⠀⡐⠀⠀⠀⠀⠀⠈⠈⠃⠀⠀⠀⠑⠒⠸ ⠀⠀⢠⣱⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇ ⠀⡠⠻⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀ ⠔⠁⣼⣐⡄⠀⠀⠀⢠⠀⠀⠀⠀⡄⠀⡜⠀⠀ ⠑⠚⠉⠀⡄⠀⢀⠴⡏⠀⠀⢠⢞⣧⠌⠀⠀⠀ ⠀⠀⠀⠀⠑⠚⠓⠉⠗⠧⠒⠉⠉⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠤⢤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠉⠀⠀⠀⠀⠀⠀⠉⠓⠦⣀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣞⢆⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⠘⡆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣤⡀⠀⠀⠀⠀⠀⣤⣤⠀⠸⡄ ⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⢀⡩⣛⡋⠁⢠⠀⢀⡀⠈⠛⡟⠀⠀⡇ ⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⣇⢠⢀⡇⠀⠈⠓⠚⠁⣜⢉⠉⡧⢰⠁ ⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠘⠚⠒⠃⡘⠀ ⠀⠀⠀⠀⢀⠎⣰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀ ⠀⠀⠀⠀⣼⣴⣿⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀ ⠀⠀⠀⣼⡿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀ ⠀⢀⠞⠁⢰⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀ ⡴⠋⠀⢠⣾⡈⢳⡀⠀⠀⠀⠀⠀⠀⣰⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⣰⠃⠀⠀⠀⠀ ⣇⣀⣰⣯⠽⠋⠉⣹⠀⠀⠀⠀⠀⣴⡏⠀⠀⠀⠀⠀⢀⢾⡄⠀⡰⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⢀⣤⠞⣻⡀⠀⠀⠀⠀⣴⠋⣹⣽⠚⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠳⠤⠽⠧⠞⠋⣿⡧⢷⢀⡤⠞⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⣠⣾⣿⣋⣤⣶⣥⣾⣿⣾⣿⣿⣿⣿⣿⠿⠛⠉⠉⢀⣿⣿⣾⣿⣿⣾⣧⣤⣷⣀⢠⣴⣾⣿⣧⡛⢿⣿⣿⣿⣿⣧⡀⠙⢦⡤⠖ ⠀⡀⠀⡽⠋⢉⡴⢛⣿⣿⢻⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣽⣿⣿⣿⣿⣷⡄⠈⢧⠀ ⠀⠀⡞⠁⠀⠀⣴⣿⢡⡇⣼⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣽⣿⣿⣿⣿⣿⣿⣿⣷⡀⠈⣧ ⣀⣼⠁⠀⢀⣾⣿⠇⢸⢹⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⢻⣿⣿⣿⣿⣿⣝⣿⣷⠀⠘ ⢿⣿⠀⢀⣾⣿⡟⠀⣾⣼⣿⣿⠗⠒⠲⠤⠤⢄⣀⠀⠀⠀⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⡄⠈⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀ ⠀⢹⠀⣾⣿⣿⠇⠀⣿⣿⣿⠉⠀⠀⠀⠀⠀⠀⠀⠉⠉⠂⣿⣿⣿⣿⣿⠘⣿⣿⣿⣿⣿⠸⣿⣿⣿⣿⡇⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⠀ ⠄⢸⣴⣿⣿⣿⠀⠀⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⡿⡟⠀⢹⣿⣿⣿⡿⠒⣿⣿⣿⣿⣇⣀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡀ ⣄⢸⣿⣿⣿⣿⠀⠀⢻⣿⣿⣿⣿⣿⣷⣶⣦⣄⡀⠀⠀⠀⠀⠘⣿⠇⢷⠀⠀⢻⣿⣿⡇⠀⢸⣿⣿⢸⠅⠈⠙⣿⣿⣿⣿⣿⣿⣿⣿⢿ ⠈⣿⣿⣿⣿⡿⠳⡄⠸⣿⣿⢿⣇⠀⢈⣿⠻⢿⣿⣷⡄⠀⠀⠀⠘⠀⠀⠀⠀⠀⠻⣿⡇⠀⠀⣿⡏⠘⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀ ⠀⢹⣿⣿⣿⡟⠒⣻⣦⣿⣿⡆⠙⠂⣸⡃⠀⠀⣿⢹⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣥⣶⣶⣶⣾⣆⣤⣄⣀⠀⣿⢿⣿⣿⣿⣿⣿⡇⢠ ⠀⣿⣿⣿⣿⡇⡜⠉⣨⡟⢹⠀⠀⠀⠀⠉⠑⠚⠛⠒⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⣿⠟⢿⣿⠛⢻⣿⠿⣿⣭⣏⣾⣿⣿⣿⣿⣿⠀⠘ ⠀⣿⣿⣿⣿⠟⠀⡰⢡⠁⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠤⣸⣟⠀⠘⣿⠀⣠⠿⢻⣿⣿⣿⣿⣿⠇⠀⠀ ⢦⣿⣿⣿⡟⠀⠀⠀⣾⣧⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⣾⣿⣿⣿⣿⡟⢰⠁⢀ ⣼⣿⣿⣿⡇⠀⠀⣸⣿⡿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⡿⢁⣧⣾⣿ ⣿⣿⣿⣿⡀⠀⢠⣿⠟⠅⢈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⠇⣾⣿⣿⣿ ⣿⣿⣿⠋⠀⣠⣿⠏⠀⣠⠎⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣼⢛⣿⣿⠇ ⣿⣿⣣⡴⣿⣿⠃⣠⠞⠁⠀⣠⠴⣸⢓⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢓⣿⣿⣿⣿⣿⢿⠃⣼⣿⡟⣼ ⣿⣿⣿⣿⣯⣯⣾⣁⣀⣴⣋⣡⡾⠗⣋⡉⣹⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣖⢛⣿⣷⣾⣿⣿⣿⣿⣿⡏⢸⢸⣿⣿⣿⣿ ⡿⣫⠴⣿⣿⣿⡏⣿⣶⣾⣿⣿⣿⣿⣿⣼⡿⠿⢿⣿⣷⣶⣦⣤⣤⣶⣶⠾⠛⣿⡿⠿⣤⠿⠬⣧⣘⣟⣿⣿⣿⣿⣿⡇⢸⣾⣿⣿⠟⠉ ⡟⠁⠸⢿⣿⢻⣧⢹⣿⣿⣿⣿⣿⣿⣿⣿⠤⠶⠦⣤⣄⡉⠛⢟⠉⠁⠀⢀⣼⣯⣤⣶⣬⠓⢦⣤⣄⣉⣉⡛⣿⣿⣿⡇⠸⣿⡿⢁⣠⣾ ⠀⠀⠀⠸⣿⣟⣿⡞⣿⣿⣿⠿⢿⡛⢿⣿⠀⠀⣀⡀⠈⠙⠷⣄⠳⣤⣴⣿⣿⣿⣿⣿⣿⣷⣦⣽⣷⣶⣿⡿⢟⢿⣿⣿⠀⢹⣿⣿⣿⡿ ⠀⠀⢀⡠⠽⢛⣻⠿⠿⠛⠶⣈⠙⢿⣌⣿⡖⠺⢅⠈⠢⣀⣠⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣫⣷⣿⠿⠛⢙⣿⡄⠹⣿⣿⣿⠃ ⠀⡸⢁⡠⠔⡏⠀⢤⡀⢀⠄⠈⣆⣸⡟⠁⠉⠒⢄⡈⠂⠈⠻⡿⢿⣿⡿⢿⣿⠿⣛⡿⢟⣫⣿⡿⠟⠋⠁⠀⠀⡰⠂⠈⢧⠀⠹⣿⣿⡀ ⡴⠋⠁⢀⠔⢻⠀⠀⠻⣟⢒⣠⠟⠁⠉⠒⠢⠄⠀⠈⠢⡀⠁⣧⠀⠈⠛⠷⣶⣯⡷⠾⠛⠉⠁⠀⠀⠀⠀⢀⠞⠀⠀⠀⢸⡄⠀⢻⣿⡇ ⠀⣠⡮⠁⠤⣾⠀⠀⠀⠘⣿⣿⣆⣑⡄⠀⠀⠀⠀⠀⠀⠀⢀⠟⢦⣀⣀⠀⠈⠑⢶⡆⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠈⣧⠀⠀⢻⡗

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠐⠒⠠⢄⠀⠀ ⠀⠀⠀⡠⠄⢀⣄⡀⠀⢀⡀⠤⠀⠀⠐⠂⠀⠀⠒⠤⣠⢋⠀⠂⠅⠢⡀⠡⠀ ⠀⠠⢀⠄⢊⠡⠀⡸⠊⠁⠀⠀⠀⠐⢣⡔⠍⠠⠀⠀⠈⠒⠊⠲⢄⡈⠂⣢⠃ ⠀⡗⡡⠂⠁⢀⠌⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⢞⡦⠊⠀ ⠀⠻⣀⠤⠊⡌⠀⠀⠀⠀⠀⠀⡔⠿⠦⠔⠛⠛⡄⢈⠄⠀⠀⠀⠀⣄⢡⠀⠀ ⠀⠀⡈⠐⢲⠁⠀⠀⢀⢀⣤⣒⣑⠄⠀⠀⠀⢀⣧⡪⠻⠀⣠⡇⠀⠸⠽⠀⠀ ⠀⠀⠁⠀⠇⠀⠀⠀⠀⢁⣴⠷⠶⡀⠀⠀⠀⣿⢭⣍⢷⣬⣮⠁⢠⡸⠆⠀⠀ ⠀⠐⠀⡠⢶⠀⠠⠄⢼⣽⢁⢻⢾⡅⠀⠀⠀⢻⠾⡟⡆⠟⢣⠔⣟⠅⠘⠀⠀ ⠀⣀⠔⡠⠊⠁⢤⢲⡅⠙⠘⣹⣀⠇⠀⠀⡀⠀⢚⣜⡁⠀⣌⢀⢿⢌⢆⠃⠀ ⢀⠃⠔⠀⡇⢀⣈⣂⡪⡄⠈⠐⠀⠀⠀⡶⢴⡆⠀⠀⠀⢠⢷⣁⡈⡈⠎⠎⠀ ⢀⠊⠀⠀⡗⠙⢄⢏⠀⠉⠒⣤⠀⠀⠀⣘⠾⠁⠀⡠⠶⡛⡄⣾⠈⢃⠈⠌⡇ ⠀⠀⠀⢰⠀⣀⠈⢪⢂⠀⢠⠁⡍⠒⠈⠈⢢⣤⡾⠁⠀⠈⢊⡇⠀⢸⡆⠈⠀ ⠀⠀⠀⡄⠀⠀⠀⠀⢷⡗⠇⠱⡸⣤⣀⠀⠀⢙⠁⠀⠀⣠⠊⠁⠀⠀⠇⠀⠀ ⠀⠀⠀⠃⠀⠀⠀⠀⠈⠻⡘⡠⠋⠁⠑⠊⢐⡞⡦⠔⠊⠈⢾⠀⠀⠀⠘⡀⠀ ⠀⠀⠀⠢⠀⠀⠀⠀⠔⠒⠋⠀⠀⠓⠄⣀⣈⡿⢿⣛⣀⠠⠃⠈⠢⣀⡀⡇⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣤⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⠶⠾⠿⠟⠛⠉⠉⠉⠁⠀⠈⠉⠙⠛⠿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣠⡾⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣰⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⠀⠀⠀⠀⠀ ⠀⠀⠀⣼⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠀⠀⠀⠀ ⠀⠀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇⠀⠀⠀ ⠀⣸⠏⠀⠀⢠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠈⢿⡄⠀⠀ ⢠⡏⠀⠀⣀⣘⡿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣧⠀⠘⣧⠀⠀ ⠈⡇⠀⠀⣰⠛⢿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠃⠀⠀⢻⡄⠀ ⠀⡇⠀⠰⡇⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⢀⡀⠀⠈⣷⠀ ⠀⣷⠀⢸⣟⣚⣫⣾⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣦⣴⣾⠟⠀⠀⣿⡆ ⠀⢻⡆⠈⠙⢿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠇⠀⠀⠀⣿⠃ ⠀⠀⢳⠀⠀⠈⢻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⠀⠀⠀⠀⡿⠀ ⠀⠀⠀⣷⠀⠀⠀⠹⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⠟⠁⠀⠀⠀⣼⠃⠀ ⠀⠀⠀⠘⣷⡀⠀⠀⠈⠙⠻⠷⣶⣤⣤⣀⣀⣀⠀⠀⠀⠀⢀⣀⣠⣴⡾⠟⠋⠁⠀⠀⠀⠀⡴⠃⠀⠀ ⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠻⠿⠟⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠟⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠔⠋⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⠶⠶⠶⠶⠶⠶⠶⠶⠶⠾⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⢶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢤⣴⠞⢉⣠⣴⢾⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠛⠋⠉⠁⠀⠀⠁⠈⠉⠉⠀⠀⠈⠉⠓⠲⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⣿⠓⠲⣤⣀⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁⠀⠀⠀⠀⠀⠀⢀⡞⠀⡴⠀⢠⠀⠠⡄⠀⠀⢰⠞⠛⠁⠈⠻⢤⣴⡄⢈⠇⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⣠⡟⠀⢰⠇⠀⠀⡇⠀⣧⠀⠀⠸⡷⠄⠿⠿⠀⣼⣿⣅⣼⣷⢾⣷ ⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⣴⣿⠁⠀⣿⠀⠀⠀⡇⠀⢹⡄⠀⠈⠷⠤⢶⣄⣼⠏⣠⣍⠉⣿⡋⠁ ⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⣠⡾⠁⣿⠀⠀⣿⠀⠀⢰⡇⠀⡾⢻⣄⠀⠀⠀⠀⠈⢷⣄⡙⠛⣀⣿⣇⠀ ⠀⠀⠀⠀⠀⠸⡇⠀⠀⣀⣴⠾⠋⠀⠀⢹⣆⠀⠹⣇⢀⡾⠀⣰⠃⠀⠹⣦⡀⠀⢸⡆⠀⠙⠳⠞⠛⠉⣿⠀ ⠀⠀⠀⠀⠀⠀⡇⠀⠀⢹⡇⠀⠀⠀⠀⠀⠙⢷⣄⣹⣿⣥⠾⠃⠀⠀⠀⠈⠛⠶⣼⡇⠀⠀⠀⠀⠀⠐⡏⠀ ⠀⠀⠀⠀⠀⢀⡇⠀⠀⢸⡇⠀⢀⣀⣀⣲⠀⠘⠛⠋⠉⠁⠀⠠⣤⣀⣀⡀⠀⠀⢸⡇⢸⠦⣤⡀⠀⠀⣇⠀ ⠀⠀⠀⠀⢀⡾⣰⠂⠀⢸⡇⠈⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠓⠂⢸⠃⢸⡄⠀⢳⠀⠀⢻⠀ ⠀⠀⢀⣠⠞⣡⣿⠀⠀⢸⡅⠀⠀⠀⠀⠀⢀⣠⣄⠀⣀⣄⠀⠀⠀⠀⢸⣰⠆⠀⣿⠀⢸⡇⢀⡾⠀⠀⢸⠀ ⠒⠚⠋⠉⠉⠁⣿⠀⢀⣸⣇⠀⠀⠀⢀⣀⣿⠉⠹⣷⠃⢸⣄⡤⠤⡄⠈⠀⠀⣼⠇⠀⣼⡷⠟⠀⣠⣄⣾⠀ ⠀⠀⠀⠀⠀⠀⠹⣦⣈⢿⣽⣷⣤⣄⣿⡉⠻⣦⣀⣿⣆⣾⠏⢀⣴⣁⣀⢀⣴⣯⣤⣾⠋⢀⣀⣴⣿⠿⠃⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⡿⣿⡋⠉⠛⢷⣿⠟⢛⠙⠻⣶⠛⠉⠀⣹⠟⠛⠛⠛⠛⠛⠉⠙⢳⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣨⡽⠿⠿⠟⣿⠸⣿⣦⠄⢸⡶⠚⠛⢧⡀⠀⠀⠀⠀⠀⠀⢠⡞⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣯⣀⣀⣠⣤⢿⣧⣈⣛⣴⡿⠷⣤⡤⠜⠁⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠉⠉⡿⠉⣠⡾⠀⢹⡟⠙⣷⣄⣀⣹⠷⠶⠶⠶⠶⠶⠒⠚⢯⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠛⠛⢻⡁⣀⣾⣇⠀⣼⠛⠉⠉⠙⠳⣄⣠⣤⡶⠶⠦⣼⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣠⣾⣿⣿⢻⡋⠛⠁⣀⣀⣤⠤⠀⠈⢡⡟⠀⠀⠀⢸⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⢀⣠⢴⡟⠋⠸⣿⣾⣷⢦⡈⠉⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠘⣧⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣾⡁⣸⣇⠀⠈⣿⠛⢙⣶⣟⠛⢷⣄⣤⡴⠞⠃⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠘⢋⡿⣦⣀⣽⣡⡿⠦⠉⠀⠈⠙⠃⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⡀⠀⠀⠀⠐⠋⠉⣿⠏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠉⠁⡠⠀⠀⠀⠀⠀⠈⠁⠒⠠⢀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⠖⠁⠀⣠⢎⢼⠇⠀⣧⡀⠀⠀⢣⠀⠀⠀⠀⠉⠢⡀⠀⠀⠀ ⠀⠀⠀⢀⠞⣲⣦⠤⣴⣕⠅⢸⠀⢀⡿⢇⠀⠀⠘⡀⠀⠀⠘⡀⠀⠘⢄⠀⠀ ⠀⠀⣰⠃⣰⠇⠀⣼⠋⠁⠀⠈⡆⢸⡅⠈⡆⠀⠀⡇⠀⠀⠀⡇⠀⠀⠘⢆⠀ ⠀⢰⠃⢰⣿⡤⣴⠁⠀⠀⠀⠀⢣⣸⡇⠀⠘⡄⠀⢰⠀⠀⢰⡇⠀⠀⠀⠸⡄ ⠀⡎⠀⣿⠿⢀⡏⢀⡷⣄⠀⠀⠈⢿⡇⢀⡴⢾⡀⢸⠀⠀⣸⠃⢰⠀⠀⠀⡇ ⠀⡇⢀⡟⢠⣿⠀⠸⣆⡼⠀⠀⠀⠈⠃⠸⣇⣀⡷⣾⡀⠀⡟⠀⢸⡆⠀⠀⡇ ⠀⡇⢸⢁⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⣾⣇⣰⠀⠀⣿⡇⠀⣧⠁ ⠀⢸⡆⢸⣿⡟⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⢸⣿⡟⠃⠀⢠⢹⡇⠀⡇⠀ ⠀⢀⠁⢸⣿⣇⠀⠀⠀⠀⠀⣏⡇⠀⠀⠀⠀⠀⣾⡟⠀⠀⠀⣼⣿⡇⢠⠀⠀ ⠀⠸⠀⢸⣿⣿⣶⣄⡀⠀⠀⠓⠚⠀⠀⠀⠀⠀⣿⠁⠀⠀⢠⣿⣿⣠⠸⠀⠀ ⠀⠀⡆⠸⣿⣿⣿⣿⠈⢶⣤⣀⣀⣀⠀⠠⣤⣶⡏⠀⠀⢀⣿⣿⡿⠹⣠⠀⠀ ⠀⠀⠰⡖⠻⢿⣿⣏⠀⠈⢻⠟⠇⠀⣀⠰⢻⣿⠀⢀⣤⣾⣿⠋⠀⠀⠙⠀⠀ ⠀⠀⠀⠈⠀⠀⠙⠻⣦⣾⠏⣠⡾⣗⡄⠀⢸⣯⣔⠁⠏⡿⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣤⣾⣿⣯⠼⣵⣿⠏⢿⣠⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣴⣿⣿⣿⣿⠧⣈⡜⣿⠀⢰⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⣿⣿⣿⣿⢠⡿⢠⠟⣦⣾⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀ ⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⠃⠸⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀ ⠀⠀⣼⣿⣿⣿⣿⣿⣿⡀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣧⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀ ⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀ ⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀ ⠀⠀⡤⠄⣀⠀⠀⠀⡠⣲⡟⠻⣕⢢⡄⢀⠄⣊⠁⣎⠀⠀⠀⠀⠀ ⠀⢰⠁⢀⠤⡉⠢⣜⣾⣸⡠⠴⠞⢧⣸⠁⠊⠔⡇⢉⠀⠀⠀⠀⠀ ⠀⠘⠀⢽⠤⠈⠀⠈⠲⠼⣀⡠⠤⠚⠁⠀⠀⠀⠈⠘⢄⠀⠀⠀⠀ ⠀⢰⠠⠂⠀⠀⠀⢀⠰⣹⢄⠀⠄⠀⠀⢄⠀⢢⡀⠀⠀⠡⠀⠀⠀ ⠀⠀⠃⠀⠀⠀⠀⣼⣠⡇⠀⢂⢰⠀⠀⢸⡧⠈⠆⠀⠀⠠⠁⠀⠀ ⠀⢸⠀⠀⢠⠀⡠⢁⣎⣟⣄⠀⡞⠦⠰⡾⣷⡺⣼⠀⠀⠀⡞⠀⠀ ⠀⠀⠀⢀⢂⠔⢇⠟⣝⣿⣶⡀⠀⠀⠀⢸⣾⣿⡌⠇⠀⣜⠁⠀⠀ ⠀⡄⠀⠈⠁⠸⠺⠀⢯⣛⣫⠇⠀⠀⠀⠈⠳⢟⣀⡈⢄⠀⢱⠀⠀ ⢀⠁⠀⠀⠀⠀⠀⢡⣖⣴⠆⣄⡀⠤⠤⠤⣴⠎⠛⠋⢠⠀⢸⠀⡆ ⡌⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⡀⠀⠀⠀⠀⡸⠀⠀⡠⠂⠰⠤⠝⠃ ⢀⠀⠀⠀⠀⢃⠨⢴⣿⢄⡀⠑⠤⠤⢤⣚⠥⠐⠈⠀⡠⠔⠁⠀⠀ ⠁⠊⠂⠤⣄⣀⢈⡽⠉⢩⠘⢥⠶⢥⠈⠎⠳⣄⠤⠒⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠁⠒⠒⠀⠘⠀⠐⠃⠘⠈⠈⠂⠀⠀⠀⠀⠀⠀

⠀⠀⠠⠤⠤⢼⢤⣤⣮⣾⣿⣿⣿⣿⣿⣿⣿⣷⣤⣠⡔⢁⣼⡟⠀⠀⠀ ⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀ ⢼⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⡂⠀ ⠀⢙⣿⣿⣿⣿⣿⣿⣿⣿⣿⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠂ ⣰⠿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⣻⣿⣿⣿⣿⣿⢹⣿⣿⣿⡗⢖⠋⠀⠀ ⠁⠀⣿⣿⣿⣿⣿⣿⡿⠓⢁⡀⢻⣿⣿⣿⣿⡏⠈⢿⣿⣿⡟⠀⢃⠀⠀ ⠀⠀⢿⣿⣿⣿⣿⣿⢁⣭⡴⠶⠆⢻⣿⡿⣿⣧⣌⣸⣿⣿⡿⠖⠊⠀⠀ ⠀⠀⠈⠙⣿⠿⢿⡟⠆⠀⠀⠠⠀⠔⠋⠀⠀⠉⠉⠸⣿⡙⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣇⠩⣒⠁⡰⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡇⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠓⠤⠤⠤⣄⡀⠀⠀⠀⠀⠀⠀⣀⡤⠚⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣇⣀⣰⠒⠋⠉⠀⠀⠀⠀⠸⠆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡌⠃⠉⢉⠹⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⡄⠆⠋⠛⢄⠀⠀⣖⢟⠋⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡘⢘⢅⠠⣀⠀⠀⠢⠘⢌⠒⢷⢤⡉⡒⠄⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠖⠚⠉⠁⠀⠀⠈⠉⠉⠓⠲⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⢦⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣽⢦⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⢿⣮⢳⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⣾⡎⣷⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠘⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢽⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡀⠀⢸⡆ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠟⠇⠀⡀⠀⠀⠀⠀⠸⣿⣿⠧⠀⠀⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡔⠋⠙⠲⡆⠀⠀⣿⡀⣰⡧⠀⣤⠤⠦⢤⠀⢠⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡀⡇⣰⠇⠀⠀⠈⠉⠉⠀⠰⡇⢠⠄⢸⠆⢸⠀ ⠀⠀⠀⠀⠀⠀⠀⢰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⠾⠶⠏⠀⡏⠀ ⠀⠀⠀⠀⠀⠀⢠⡏⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀ ⠀⠀⠀⠀⠀⢠⡎⢠⢯⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀ ⠀⠀⠀⠀⢀⡼⣲⣯⣟⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀ ⠀⠀⠀⠀⡾⢷⠇⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀ ⠀⠀⢠⡾⠁⠈⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⠀⠀⠀⠀ ⠀⣰⠏⠀⠀⢠⡇⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀ ⡞⠁⠀⠀⣰⣿⣦⣆⣘⣦⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀ ⣧⣀⣀⣼⣯⠴⠟⠉⠀⢸⠀⠀⠀⠀⠀⠀⠀⣴⣿⠀⠀⠀⠀⠀⠀⠀⢀⡼⣿⡀⠀⣠⠟⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⢀⣠⡾⢿⡇⠀⠀⠀⠀⠀⠀⣰⠏⢙⢧⢻⠴⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⣀⡤⡞⢛⣷⡴⣿⣇⢠⡄⠀⠀⢀⡼⠿⠶⠾⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠉⠉⠀⢿⣏⣈⣇⡴⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⡾⢯⡰⣷⢿⣿⣿⣿⠟⠋⠁⢰⣿⣿⣿⣷⣾⣦⣶⣾⣿⣽⢿⣿⣷⡌⢣⠂ ⠈⡘⠀⢨⡾⡍⣾⣿⠟⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⡯⣿⣿⣿⣿⣿⡄⢡ ⢶⠁⢰⣿⠃⣷⣿⠯⠤⠀⣀⡀⠀⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⠈⣿⣿⣿⣿⣿⠀ ⠀⣯⣿⡟⠀⣿⣯⠀⠀⠀⠀⠀⠉⠻⣿⣿⠈⣿⣿⣇⣻⣿⣿⠀⢻⣿⣿⣿⣿⡇ ⣄⣿⣿⣇⠀⣿⢷⡶⢴⣦⣤⡀⠀⠀⢻⠛⠀⠹⣿⡇⠸⣿⢿⠉⢸⣿⣿⣿⣿⡷ ⠘⣿⣿⠧⢥⣹⣯⠣⣰⠇⢹⡟⡆⠀⠀⠀⠀⠀⢙⣥⣤⣯⣀⡀⢸⣿⣿⣿⣿⢃ ⢸⣿⣿⡴⢁⠊⡅⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⢸⡋⣿⢉⣿⠛⣿⣾⣿⣿⡟⠈ ⢼⣿⡿⠀⢀⣧⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠈⣰⣿⣿⣿⡱⣀ ⣿⣿⣇⠀⣾⠏⠳⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣿⣿⣿⢣⣿⣿ ⣿⡟⣠⡼⠃⡰⠁⢐⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⠎⣿⣇ ⣿⣽⣮⣧⣊⢠⣪⣽⣛⢡⣦⣀⠀⠀⠀⠀⢀⣀⣠⡤⡂⡶⣶⣿⣿⣿⢹⣸⣟⣾ ⡗⠹⣿⣿⣸⣿⣿⣿⣿⡎⠭⣙⡛⠻⡟⠛⢉⣾⣩⣝⢍⣑⣛⠻⣿⣿⠘⣿⢏⣡ ⠀⠀⢻⡽⣯⡿⡛⢯⡹⣇⢠⠠⡈⠑⣜⣶⣿⣿⣿⣿⣷⣿⣶⣻⣿⢿⡇⢷⣿⡟ ⢀⡊⠄⡎⠠⣀⠌⢆⢿⠉⠂⢅⠊⡻⠿⣿⡿⢿⡻⣟⡿⠿⠛⠉⠠⠊⢱⠘⣿⡇ ⢁⡔⠈⡇⠀⠙⣶⣇⡄⠈⠁⠀⠐⢀⢇⣀⠉⠻⣭⠀⠀⠀⠀⠐⠁⠀⠈⡆⠘⣷

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣴⡤⣤⡀ ⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣶⣄⣀⣀⡀⣀⡀⠀⠀⠀⠀⣸⣤⣻⠻⣾⡇ ⠀⠀⠀⠀⠀⠀⢉⣽⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⡿⠳⣄⠀⠘⢿⢻⣿⣟⠇ ⠀⢠⣤⣤⣤⣾⣿⣿⣿⡟⠋⠀⠀⢉⡿⢿⠛⣿⡿⡑⡀⠘⣷⡀⢀⡏⠉⠀⠀ ⠀⠘⠿⢿⡿⠋⣱⡿⠋⠀⠀⠀⡌⠉⡧⠆⠿⠵⢼⡀⠱⡀⠈⠙⠛⢲⣶⠀⠀ ⠀⠀⠀⣿⡓⠊⠁⢀⠀⢀⡆⠀⡇⠀⡇⠀⢀⠀⠀⡇⠀⡇⠀⠈⠻⡏⠁⠀⠀ ⠀⠀⣰⠇⠉⢙⠏⠁⠀⢸⠁⢀⠷⡀⢣⠀⠸⠆⠀⡇⡸⢣⠀⢇⠀⣿⠀⠀⠀ ⡤⠞⢁⣠⠆⢸⠀⠀⢠⠏⠀⡜⠉⠑⠬⠆⠀⠀⠩⠗⠉⠀⢃⠘⡄⡿⠀⠀⠀ ⠙⠛⢹⠏⠀⢸⠀⣠⠋⣠⣾⣶⣶⣦⣄⠀⠀⠀⢨⣶⣶⣶⣬⣆⠹⣇⠀⠀⠀ ⢠⠖⠋⣀⣠⣼⣯⠤⠚⢏⠀⠣⣘⡫⠇⠀⠀⠀⠀⢎⣃⠇⠈⡟⣝⢾⠃⠀⠀ ⠈⠛⠛⢻⣿⣧⡘⡄⠰⢌⣢⠄⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡱⠻⠾⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣹⣿⣦⣀⢳⣎⣑⣦⡀⠀⠀⠁⠀⣀⣴⣿⣞⣳⠆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢉⡽⣿⠏⣾⠿⢷⣷⣿⣿⣿⣽⣿⡿⣽⣟⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣰⠋⢰⢿⠚⢿⡿⡿⠋⠘⢿⣟⣻⢽⣿⣷⣿⡇⠀⠀⠀⠀⠀⠀

⠀⠀⢀⠠⠤⠀⠠⠄⡀⠀⢀⠔⠂⠉⠉⠀⡉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⢃⠀⠀⠀⢠⢀⠱⠂⠀⠀⠀⠀⡠⠓⠠⢄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣀⠅⠄⣀⡀⠀⠹⢧⠤⠤⠐⡈⠂⢄⠀⠀⠈⠢⠀⠀⠀⠀ ⠘⠩⠥⠀⠀⠠⠀⠀⠀⠀⡠⠃⠀⠀⠈⠀⠀⠑⠀⠀⠀⠐⠀⠀⠀ ⠀⠀⢀⡤⢀⣀⣰⠀⠀⢜⠂⠀⠀⢬⠐⠀⠄⠢⡈⠄⠀⠀⠀⠀⠀ ⠀⠄⡌⠶⠊⠁⠇⠄⠈⠀⠀⠀⠠⣦⣀⣢⠀⡀⠱⠘⡀⠀⠀⠀⠀ ⢠⡆⢁⠀⠀⢰⣠⣶⢦⡀⠀⠀⠀⠰⠟⣿⣦⡇⠀⣦⣧⠀⠀⠀⠀ ⠀⠀⢸⠀⠀⡾⠻⡇⠐⢷⠀⠀⠀⠄⠀⠉⢹⠇⠀⣘⣿⠀⠀⠀⠀ ⠀⠀⢻⠇⠀⠅⡆⠣⠀⠘⠀⠀⠀⠀⠀⠀⢡⠀⠠⠉⠀⠀⠠⠀⠀ ⠀⠀⠄⠀⠢⡆⣧⢀⠀⠀⠀⢇⡀⠀⠀⢀⡌⠐⢡⠀⠘⠠⠀⣡⡀ ⠀⠰⠒⠙⠄⠀⠈⠗⢢⠏⢩⣟⣿⡿⢧⢀⡏⢀⠎⡤⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠐⠌⠗⢡⠂⣙⠏⠉⢴⠸⣷⡜⠁⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⠀⠀⠀⣠⡖⢳⡏⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠉⢦⡀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠏⠀⠀⠀⣠⠆⠀⠀⠀⣰⣿⠁⠀⠀⠀⣠⠞⠃⣰⠋⡇⠀⠀⠀⠀⢀⡇⠸⣆⠀⠀⠀⠀⠙⣧⡀⠀⠈⠒⢦⡀⠀⢳⡀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⢀⣴⡟⠀⠀⢀⡴⢋⡇⠀⠀⣠⠞⠁⢀⡾⠁⠀⢡⠀⠀⠀⠀⡾⣏⠀⣿⡙⠲⢤⡀⠀⢸⣿⢦⡀⠀⠘⣿⢦⣀⠱⢄⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡐⠁⠀⢀⣾⣿⠃⠀⢠⠞⠁⢸⠁⣠⠞⠁⠀⣠⢿⠀⢀⠀⠘⣆⠀⠀⢰⠃⣿⡄⠁⠛⢦⡀⠙⠳⣄⠻⡆⠙⢦⡀⠘⣖⣯⠓⢦⣁⠂⠘⢷⡒⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⢇⠀⢠⡞⣽⢹⠀⣰⠋⠀⠀⣧⠞⠁⣀⣤⣶⡿⢿⡷⢾⣧⡀⠹⡀⠀⣾⠀⣿⢧⡄⠐⢦⡿⣶⣶⣪⣤⣹⡄⠀⠙⢦⡘⠯⠳⣖⠚⠛⠋⢹⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡟⢸⢡⠏⠀⡇⠇⡼⠃⠀⠀⢀⣇⡴⠚⢉⣿⡟⠀⠀⣧⠈⣇⠀⠀⠻⡄⢻⠀⢿⠘⣧⠀⠀⠑⢌⠳⣄⠈⠙⢿⣤⠀⠀⠙⠒⠀⠈⠳⣄⠀⢸⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⠀⡾⠈⠀⢸⠁⠈⠀⠀⠀⠀⣸⠁⠀⢀⣾⣿⡇⠀⢀⣸⣆⣸⡄⠀⠀⠙⠎⠀⠸⣧⢹⠀⠀⣀⣀⣀⡈⢷⡀⠘⡏⠻⡆⠀⠀⠀⠀⠀⠈⠓⠶⠦⣤⡤⠤⢀⠄⠀ ⠀⠀⠀⠀⠄⢀⡇⠀⠀⢸⠀⠀⠀⠀⠀⠀⣿⠀⢀⣟⠀⣿⣷⣭⣭⣭⣿⡿⣿⣆⠀⠀⠀⠀⠀⡟⣯⣿⣿⣭⣶⣶⣿⣯⣿⣖⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀ ⠀⠀⠀⢸⠀⢸⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡟⢀⡾⢈⣿⠿⣿⣿⣏⢹⡿⡟⣿⡝⣦⡀⠀⠀⠀⢻⡘⣿⣿⢿⣿⣽⡇⢹⣿⣿⣾⣧⡀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠞⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢿⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⠛⣄⣿⣿⣿⣼⡇⠀⠘⢧⡈⣷⣤⡀⠀⠘⡇⠘⠃⣴⣾⣿⣿⣼⡇⠹⣿⣯⡻⣗⠒⠲⣶⠖⠛⠉⠁⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠸⠀⠀⠀⡇⠀⠀⠀⠀⠀⢠⣿⠿⢿⠀⠀⣿⠛⢿⡿⢛⡇⠀⠀⣰⣇⣈⣙⣛⣶⣾⣹⡄⠀⣿⠛⢿⡟⢻⡇⠀⡿⢿⣿⣮⣷⣦⣸⡆⠀⠀⠠⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⣿⠀⠀⠀⢉⡁⠀⠀⣿⡿⠛⠛⠛⠻⣿⡉⠁⠀⣿⠀⠀⠀⣉⠁⠀⠀⣸⣿⠏⠈⡏⢹⡟⠲⡶⢶⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡇⠀⠀⠸⡄⠀⠀⠀⠀⢀⣿⣇⡀⠀⠀⠚⠓⠒⠒⠛⠁⣀⣼⡿⠀⠀⠀⠀⠀⢻⣧⣀⠀⠘⠓⠒⠶⠿⠂⢀⣼⡿⡟⠀⢠⣇⡿⠇⠀⠇⠀⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣧⠀⠀⢠⠁⠀⠀⠀⠀⠀⢻⡟⠿⠷⠶⠤⠤⠶⠶⠿⠿⠛⠋⠀⠀⢠⡆⠀⠀⠀⠉⠛⠛⠿⠿⠿⠿⠿⠿⠛⠋⢰⠀⣠⢟⡾⡇⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⡄⠀⠘⡆⠀⠀⠀⠀⠀⠀⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠚⣡⡾⠁⣇⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⣷⢤⡀⢳⠀⠀⠀⠀⠀⠀⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡷⡾⡟⠀⢀⡟⠉⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢰⣿⠀⠙⣾⡇⠀⠀⠀⠀⠀⢹⠹⣧⡀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⠷⠶⠶⢶⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀⣇⡇⠀⡾⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣷⡇⠀⢸⣿⠀⠀⢸⣿⡀⠀⠀⠀⠀⠻⡇⠙⣿⣦⡀⠀⠀⠀⠀⠀⣿⣥⠶⠶⠒⠶⠶⢴⣿⡏⠀⠀⠀⠀⠀⢀⣼⠟⠀⠀⣿⡇⠀⡇⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⠄⠀⠸⣿⠀⢸⣿⡀⠀⠸⣿⣧⠀⠀⠀⠀⠀⢳⠀⢸⠙⠻⣦⣄⠀⠀⠀⠘⢧⡀⠀⠀⠀⢀⣠⠟⠀⠀⠀⠀⣠⣴⠛⢹⠀⠀⠀⣿⡇⠀⣧⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⢂⠀⢻⡆⢸⠀⡇⠀⠀⡇⣿⣇⠀⠀⠀⠀⠸⣆⡜⠀⠀⢨⡟⢷⣦⡀⠀⠀⠉⠙⠒⠛⠉⠁⠀⢀⣤⣶⡚⢿⠸⡇⠸⡇⠀⠀⢿⣇⠀⢸⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⢄⠀⢻⡇⠀⡇⠀⠰⣇⠸⡞⣦⠀⠀⠀⠀⢿⡇⠀⠀⣼⠑⣦⡏⠻⣷⣄⡀⠀⠀⠀⢤⣶⣿⡿⢻⣿⠁⠈⡇⢻⡄⢷⠀⠀⢸⣸⠀⢸⡄⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⢆⢠⠻⣦⣇⠀⠀⣿⣄⢻⡾⣧⠀⠀⠀⠘⡷⠤⣴⡇⠀⠘⢧⡀⠈⠻⣿⣿⣶⣿⣿⡿⠋⢀⡼⠁⠀⠀⣧⣀⣳⣼⣆⣀⣼⠿⠞⠛⣧⣱⠀⡟⠲⢦⡀⠀⠀⠀⠀⠀ ⠀⠁⠀⠀⠘⣧⡼⠋⣹⡇⠀⣿⠹⣎⡿⠋⢳⡄⠀⠈⢹⡀⠀⣧⠀⠀⠈⠙⢦⡀⠈⢻⣿⡿⠋⢀⡤⠟⢀⣶⠀⢀⡇⠀⠀⠉⣯⠁⠀⠀⠀⡼⢻⢸⡆⢱⡀⠀⢸⠆⠀⠀⠀⠀ ⠀⠀⠠⠀⠀⠈⢧⣠⠇⠇⠀⢸⣠⠞⠁⠀⣴⠟⣦⠀⠀⢻⡀⠸⠀⠀⠀⠀⠀⢉⣷⡄⠀⢀⡶⠋⠁⣴⣿⣿⡆⡾⠀⠀⠀⠀⠘⣧⠀⠀⢠⠇⠘⡄⢧⠈⠧⠤⠼⠀⠀⣇⡀⠀ ⠀⠀⢀⡤⠶⠦⠤⣄⢀⣠⠖⠋⠉⠳⢶⡚⠁⢠⠞⢳⣄⠀⢳⡀⡇⠀⠀⠀⠀⣸⠀⢧⠀⢸⠁⢸⡀⣿⣿⠟⣱⠃⠀⠀⠀⠀⠀⠘⣦⢀⡴⠒⠒⠣⢬⣵⣂⣀⡤⠖⡋⠉⠙⢦ ⠀⢸⠃⠀⡄⢀⡠⠞⠉⢀⣠⢶⣄⠀⠀⠹⣶⠋⣴⡿⢻⠷⣌⢷⣸⡀⠀⠀⢀⡇⠀⠘⣆⡼⠀⢨⡇⠻⠋⣰⢷⡀⠀⠀⠀⠀⠀⠀⣨⢏⡴⠉⠳⢤⣀⣀⣈⣉⣻⠀⠀⡀⠀⠀ ⠀⡴⠒⠺⡷⣼⣶⣶⣚⣯⠶⢯⣈⡳⣄⠀⢹⠟⠉⠀⣸⠀⠈⠻⣷⣷⡀⠀⣼⠻⣆⣀⣻⣇⣠⠟⣧⠀⣰⠋⠀⢷⡀⠀⠀⠀⠀⢀⡏⣸⠀⠀⠴⠶⠶⢶⡶⠾⣋⡴⠛⠉⠀⠀ ⠀⣇⠀⠀⠀⠀⠈⢻⣴⣏⡴⢫⡇⠀⣻⠀⠈⡇⠀⢰⠇⠀⠀⠀⠈⠛⢧⣴⢻⡶⠋⠀⠀⠈⠃⢤⡾⠶⠃⢀⡠⠄⠳⡀⠀⠀⠀⢸⠁⡇⠀⠀⠀⢸⡆⠸⣦⡞⠁⠀⠀⠀⠀⠀ ⠀⠿⣶⣤⣤⣤⡤⠞⠛⠉⠀⣼⠀⠀⣿⠀⠀⡇⢠⠏⠀⠀⠀⠀⠀⣄⠀⠀⠸⣇⠀⠀⠀⠀⠀⢸⡇⠀⣰⠋⠀⠀⠀⠙⢆⠀⠀⢸⡀⡇⠀⠀⠀⠘⡇⠀⠈⣇⠀⠀⠀⠀⠀⠀ ⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢠⠏⠀⣀⡇⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠸⡄⠀⢠⡀⠀⡞⠀⡴⠃⠀⠀⠀⠀⠀⠈⢳⡀⠈⢳⡁⠀⠀⠀⠀⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢈⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⡿⠀⠀⠀⠘⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⢹⡄⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡃⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠻⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠂⠀⠄⠄⢀⠀⠀⡀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⠀⠀⠀⡐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⣄⡀⢀⡩⠞⠋⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⣠⠇⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠸⡆⠀⢹⡄⠀⠀⢠⡀⠀⠀⠀⠀⠹⣆⠀⠀⠀ ⠀⠀⠉⠛⠀⠲⠶⠶⠤⠶⠶⣶⠖⠀⣸⡏⠀⠀⠀⠀⠀⡼⠃⣴⠿⠶⢦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣦⣧⠀⡄⣿⡄⠀⠈⣇⠀⠀⠀⠀⠀⠸⡄⠀⠀ ⠀⠀⠐⠨⠀⠀⠀⠀⠀⣠⠞⠁⠀⢠⣿⠃⠀⠀⠀⢠⠞⢡⡞⠁⠀⠀⠀⠨⣝⢷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⢻⠀⠀⢹⣷⡀⢰⣿⡀⠀⠀⠀⠀⠀⠃⠀⠀ ⠀⠀⠀⠀⠆⠀⢀⣠⠞⠁⠀⠀⢠⣾⡞⠀⠀⠀⢠⠏⣠⡏⠀⠀⠀⠀⠀⠀⠀⠙⢭⣻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠸⣿⣧⢸⣿⡇⠀⢰⡄⠀⠀⡀⠀⠀ ⠀⠀⠀⢰⣧⠴⠋⠁⠀⣀⡤⢞⣿⢿⠃⠀⠀⣠⠋⣰⠋⢷⠀⠀⠀⠀⠀⠀⠀⣤⡀⠙⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⡇⠀⠀⣿⣿⣿⣿⣿⠀⣸⡇⠀⠀⣧⣤⣤ ⣀⣤⠶⢋⣁⣤⠴⠖⠋⠁⢠⣞⡿⠘⠀⠀⣰⠃⣼⣣⠀⠈⢧⠀⠀⠀⠀⠀⠸⡿⠁⠀⠈⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣰⣿⠀⠀⣿⣿⡇⢻⣿⡇⢿⣿⠀⠀⣿⣿⣿ ⠉⠻⠦⣤⣠⣀⣀⣀⠀⣰⠏⢸⠇⠀⠀⣼⢋⣼⡵⠃⠀⠀⠀⠑⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⡿⠭⠍⠉⠉⠹⢿⠀⠀⢻⣿⠃⢸⣿⣷⠈⣿⠀⢸⠹⣿⣿ ⠀⠀⠀⠀⢹⡍⠉⠉⠉⡏⠀⡟⠀⠀⣼⢡⣾⡽⠁⠀⠀⠀⠀⠀⠀⠈⠙⠒⠒⠒⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠘⠛⠁⢀⣤⡄⠀⠀⠀⢸⡄⠀⣸⡿⠀⠀⣿⡿⠀⣿⠀⠈⠀⢻⣿ ⠀⠀⠀⠀⠘⡇⠀⢀⣴⢧⢠⡇⠀⠰⣻⣯⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀⠼⠿⠁⠀⠀⠀⠀⡇⢀⣿⡇⠀⠀⢿⡇⠀⢿⢀⡇⠀⠀⠛ ⠀⠀⠀⠀⠀⣇⣠⠞⠁⢸⣿⠁⠀⣰⢿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠀⠀⠀⠀⠀⠀⠀⡇⠸⡌⠀⠀⠀⠘⣧⠀⠈⢸⠇⠀⠀⠀ ⠀⠀⠀⣀⣴⣟⣡⡤⠴⠚⡿⠀⣰⡷⠴⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣄⣀⣀⣀⣀⣤⡗⠀⠃⠀⠀⠀⣴⣿⠀⠀⡟⠀⠀⠀⠀ ⠀⠀⠈⠉⠉⢹⣀⡤⠖⢻⡇⣼⠻⣦⣀⣼⡆⠀⠀⠀⠀⠀⠀⢺⣿⣯⡉⠙⠛⠓⠲⠤⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇⠀⠀⢠⡏⠸⠀⢠⡿⢿⣛⣻⡶ ⠀⠀⠀⣠⡴⠋⠁⣠⠴⢻⣿⠃⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀⠉⠓⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⠀⠀⡿⣿⠀⠀⣸⡶⠞⠋⠁⠀ ⢀⠴⠛⠁⢀⡴⠋⠁⢀⣾⠃⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⡀⠀⠀⠉⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣸⠀⣸⣹⢿⠀⢀⡿⠀⠀⠀⢀⡤ ⠀⠀⣠⠶⠋⠀⠀⣴⠟⠃⢀⣠⣤⠄⠀⠀⠀⣸⣆⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣿⡇⠀⠀⠀⠀⠀⠀⠀⣠⣿⠀⡏⢠⣿⣿⣼⡄⢸⡇⠀⠀⠀⠀⠀ ⣴⠞⠁⠀⢀⣴⣿⣵⣶⣚⣩⣾⣡⣤⡶⣾⣿⠃⠘⢦⠀⠀⠀⠀⠈⢿⢻⡉⠉⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⢀⡴⠛⣿⠀⠀⠈⣿⡋⢹⣧⡏⣿⠒⠀⠀⠀⠀ ⠁⠀⢠⡴⠟⠉⠉⠉⠉⠉⠉⣡⡾⠋⠉⢻⠏⠀⠀⠈⣷⡀⠀⠀⠀⠈⢧⠙⠲⢤⣄⣀⡀⢉⣻⣿⣿⣿⡟⠋⠀⠀⠀⠀⠀⠀⣠⡞⣡⡾⡏⠀⠀⣰⠃⠙⢮⡿⠙⣾⡄⠀⠀⠀⠀ ⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠐⢿⣀⣀⣠⡞⠀⠀⠀⠀⢿⡙⢦⠀⠀⠀⠈⠳⣄⣀⠀⠈⣉⣉⡥⠽⠋⠁⠀⠀⠀⠀⠀⢀⣠⣶⠛⠹⡇⢀⡇⠀⣴⠿⣄⠀⠀⠳⣄⠈⠃⠀⠀⠀⠀ ⠀⢿⡀⣀⣀⣀⣀⣀⣀⣀⣤⡤⠽⠿⢿⠁⠀⢆⠀⠀⠀⣧⠈⢷⣄⡀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⣀⣠⠴⠋⠁⢸⠀⠀⠙⣾⠁⢰⡏⠀⠘⢷⡀⠀⠘⢦⠀⠀⠀⠀⠀ ⠀⢸⠋⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⡏⠀⠀⠈⢦⠀⠀⠸⡆⠈⢿⣿⣶⣤⣀⡀⠀⢀⣀⣀⣀⣠⡤⠶⠚⢉⣿⣄⡀⠀⠀⢸⠀⠀⠀⢸⢀⣾⢷⠀⠀⠀⠹⣄⠀⠈⣧⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠳⣄⠀⠹⡄⠀⠙⠿⠿⠛⠋⠉⠉⢉⣡⠞⠁⠀⠀⠀⣼⣣⡬⣷⣦⠀⢸⠀⠀⠀⢸⡜⠉⠻⣧⡀⠀⠀⢸⡄⠀⢻⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠈⠁⠀⢻⡀⠀⠀⠀⠀⠀⣠⠴⠋⠁⠀⠀⠀⠀⢠⡏⣿⠀⠈⢿⠷⣾⣇⠀⠀⠸⠁⠀⠀⠀⠁⠀⠀⠀⡇⠀⢸⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⢀⣀⡤⠤⠖⣶⢦⣀⠙⠦⢤⣤⠴⠚⠁⠀⠀⠀⠀⠀⠀⠀⡞⣧⡘⣦⡀⣸⡇⠀⠉⠛⢦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀ ⠀⠀⡆⠀⠀⢳⠀⠀⠀⠀⠀⠀⠘⠒⠚⠉⠉⠀⠀⠀⠀⡇⠀⠈⠙⠓⠒⠶⣄⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠈⠙⢮⣍⠁⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢱⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢀⡾⠳⡀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠉⠳⢤⣄⡀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠒⠿⣷⣤⣀⣹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⣶⠟⠀⠀⠹⣄⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⣤⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠉⠙⠿⣿⣶⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⢠⡾⠁⠀⠀⠀⠀⠘⣆⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢛⢿⣿⣶⣤⣄⡀⠀⣀⣰⢟⠁⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠈⣆⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡞⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠤⠤⠴⠶⠤⣤⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡴⠚⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣦⡀⠀⠀⠀ ⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡄⠀⠀ ⠀⣰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀ ⢠⠃⢀⣸⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣦⠈⡇⠀ ⢸⠀⢰⠉⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⢸⡀ ⠸⡆⢾⣒⣵⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣦⡴⠃⠀⡇ ⠀⢣⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⢀⡇ ⠀⠀⢦⠀⠘⠧⣄⣀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠋⠀⠀⡼⠀ ⠀⠀⠈⠣⡀⠀⠀⠉⠙⠛⠒⠲⠶⠖⠚⠋⠁⠀⠀⢀⡜⠀⠀ ⠀⠀⠀⠀⠈⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠋⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠑⠒⠒⠶⠶⠖⠒⠒⠊⠁⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠤⠶⠶⠶⠶⠤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠾⠛⠛⠁⠁⣡⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣋⠀⢀⣰⢞⣿⡿⣯⡀⠀⠀⢤⠀⢀⡴⠶⠶⣤⡀⠀⠀⠀⠀⠀⠀⠈⠙⣦⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠉⠒⠄⠀⢀⣾⠏⠀⠀⣻⢯⡞⡿⠁⢸⡇⠀⠀⠀⣷⠟⠀⠀⠀⠈⢻⡄⠀⠀⠄⠒⠶⣤⡀⠀⠙⢦⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠏⠀⢀⣴⠏⡾⢰⣇⡀⠈⠃⠀⠀⣰⢿⡇⠀⠀⠀⠀⠈⠇⠀⢠⠀⠀⠀⠈⢳⡀⠀⠀⠙⣆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⣼⢧⣼⣿⠛⣿⡿⣿⣦⡀⠉⠁⣾⣿⣺⣿⣗⣶⣤⡀⠀⠈⢧⡀⠀⠀⠈⠇⠀⠀⠀⠈⢷⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠈⣿⣶⢻⣿⣠⣾⣿⣾⣿⣷⣶⢾⣿⣿⣿⣿⣶⣭⣿⣟⠖⢶⡄⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⢳⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⢸⣿⡳⣿⠟⠛⠛⠻⣿⣿⣿⣦⣿⣿⣿⠛⠿⣿⣿⣿⣨⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠸⣿⣷⠋⠄⠄⠀⢠⠞⠋⠀⠺⣿⡀⠀⠀⠠⠲⢀⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆ ⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠁⠀⠀⠀⠀⢻⡟⠷⣦⣤⣤⢿⡀⠀⠀⠀⠈⠻⡷⣶⡶⠾⠻⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹ ⠀⠀⠀⠀⠀⠀⡠⠄⠾⣄⡀⠀⠀⣀⣠⣸⣧⠀⠀⠀⢠⣤⣅⣀⡠⠤⠐⢫⠀⢸⠁⠀⠀⡇⠀⠀⠀⠀⠰⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡼⠀⠀⡄⣀⣙⣶⣾⣏⠀⢻⡘⢦⠀⠀⠈⢿⣆⠀⢣⠀⠀⢀⡷⠁⠀⠀⠀⣷⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⡤⢲⠃⠀⣠⢿⣏⡁⠀⢹⣿⡶⠞⠁⠈⠳⣄⡀⠀⠈⠑⠚⠓⠂⠁⠀⠀⠀⢀⣴⢿⡄⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡴⢻⣀⣎⠀⣠⣇⠀⠀⠉⠓⢏⢹⡀⠀⠀⠀⠀⠀⠙⢦⣄⡀⠀⠀⠀⠀⢀⣠⣾⠟⠁⠈⣧⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⣿⣄ ⢀⡷⢯⠁⠀⢉⣡⡜⠓⢦⡤⠀⠀⣿⣿⣀⣠⣤⣄⣀⣀⠀⠈⠉⠳⡶⠶⣾⣿⣏⣀⠤⡴⠚⢻⡄⠀⠀⠀⠀⠀⣿⠴⠶⠶⠶⠦⣄⣸⠘ ⠾⣥⣤⠷⣞⣁⠀⣱⣠⠋⠁⠀⠀⣿⡏⠁⠀⠀⠀⠀⠉⠉⠛⠓⠚⢧⠀⢹⡁⠀⠀⠀⠹⡄⠈⡧⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠈⠻⣄ ⠀⠑⢪⡽⠶⠞⠋⠀⡇⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⢣⡀⠀⠀⣀⡽⢾⡟⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⣀⣀⡘ ⠀⠀⠀⠹⡄⠀⠀⠀⠉⠀⠀⠀⠀⡟⢳⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠺⠗⠚⠉⠁⢀⣼⠁⠀⠀⣀⡾⠁⠀⠀⢀⣤⡞⠋⠁⠀⠀ ⠀⠀⠀⠀⠈⣲⡆⠀⠀⠀⠀⠀⢠⣷⣄⠙⣻⣶⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣠⣴⣞⣉⣠⡤⠞⠋⠀⠀⠀⣠⠟⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⢰⠋⣽⠃⠀⣀⣀⡤⠴⠚⢳⣼⠛⠉⠀⠀⠀⠀⠀⢀⣤⣤⣄⡀⠀⠀⢀⣀⣀⠈⠉⠀⠀⠀⠀⠀⠀⠀⣴⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⠀⡏⠉⠉⠀⢸⡄⠀⠀⠸⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⣄⣴⣿⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣼⣄⣳⠀⠀⠀⠀⢇⢀⣠⠶⠛⣿⠄⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡼⠁⠈⠉⠓⠒⠒⠒⠋⠉⠀⠀⠀⣹⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⢲⠆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⡟⠉⠻⣌⠙⢲⣤⠀⠀⢀⡴⠚⣁⠀⠀⣏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡿⠁⠀⠀⠉⠓⠦⣀⠀⣰⠋⡵⢋⡟⠀⠀⠀⣈⣷⡟⠉⣧⡴⢋⡴⠚⢂⡖⠒⠿⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢰⠃⠀⢀⠜⠓⠢⡀⠈⠛⣯⢹⡿⢾⡷⠶⠚⠛⠉⠉⢿⣠⡿⡀⠀⠈⠑⠲⢟⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⠀⠀⢉⣷⢂⠀⠘⠀⠀⠈⠦⢷⣘⣧⠀⠀⠀⣀⣠⠼⠟⠀⠈⠢⠀⠀⠀⠀⠙⠺⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⠀⠀⢙⠟⠁⠀⠀⠀⠀⠀⠀⠀⢮⡙⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⠀⡰⠃⠀⠀⠀⠀⠀⠀⠀⡄⢸⡈⡝⢆⠀⠀⢄⠀⠀⠀⠈⢢⡀⠀⠈⢦⡀⠀⠀⠀⠀⠘⢄⠀⠀⠀⠀ ⠀⠀⠀⠀⣷⠁⠀⠀⠀⠀⠀⠀⠀⢰⠁⢸⡇⢱⠀⢣⠀⠘⡄⠀⠀⠀⠀⣿⣄⡠⠚⡆⠀⠀⠀⠀⠠⡘⡆⠀⠀⠀ ⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡿⠤⣼⡃⣸⠀⠀⢣⠀⣧⠀⠀⠀⠀⣿⣿⠀⢀⠿⢸⠀⠀⠀⠀⢣⣹⠀⠀⠀ ⠀⠀⠀⢸⠀⠀⠀⠀⠀⡇⠀⠀⡼⠀⣠⠋⣿⢧⡀⠀⠀⣧⠿⣀⡤⢤⣾⣿⣿⠶⣾⣄⣿⠀⠀⠀⠀⢸⣾⠀⠀⠀ ⠀⠀⠀⢸⠀⠀⠀⠀⡜⠀⢀⡞⣁⣴⣷⢾⣿⣓⡪⠀⠀⠋⠀⠁⠀⠀⠿⡽⢻⣷⣦⠙⣿⡀⠀⠀⠀⣼⡟⠀⠀⠀ ⠀⠀⠀⢸⠀⠀⠀⡼⢁⡠⢻⠏⣰⠏⢡⣛⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⠈⡇⠀⠀⣴⠁⠀⠀⠀⠀ ⠀⠀⠀⡇⠀⠀⠸⠗⠉⠀⣸⣴⡟⠀⢸⡟⢿⣿⡟⣿⠀⠀⠀⠀⠀⠀⠀⢻⣮⣿⣷⠃⠀⠘⣄⠀⠀⠙⢦⠀⠀⠀ ⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠁⠈⠳⡀⠈⠻⠶⠤⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣡⢶⣶⣄⡌⢦⠀⠀⢸⡆⠀⠀ ⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣴⠟⣤⣴⡆⢀⣀⠀⣀⣀⠤⣤⣤⣤⣤⣾⠁⠻⠟⠞⠀⢸⠆⠀⢸⠀⠀⠆ ⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠋⠚⠋⠉⠀⠘⠙⠋⠀⠀⠀⠀⠀⠚⢿⡏⠀⠀⠀⠀⢀⠎⠀⠀⠘⢤⣤⡞ ⠀⡎⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⢣⠀⠀⡀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁⠀⠀⢀⡤⠋⠀⠈⠛⠒⡶⠊⠁ ⢰⠁⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠑⠤⣽⣿⠁⠀⠀⠈⢦⡀⠀⠀⠀⢀⣠⠞⠁⢀⡠⠔⠋⠀⠀⠀⢠⡤⠊⠀⠀⠀ ⠘⣄⢤⢀⠀⠀⠀⠀⠀⠀⠳⢄⣉⣛⣻⣟⣃⡲⢦⣄⠀⠈⠉⡉⠯⣽⢶⣎⡉⠀⠀⠀⠀⠀⣠⠋⠉⠀⠀⠀⠀⠀ ⠀⠀⠉⠛⠑⠤⠄⢀⡄⠀⠀⠀⢀⣾⠋⠀⠘⡄⠘⢦⣍⡐⠬⢧⡄⠈⢆⠈⠻⣆⣀⣠⠄⠚⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⢐⠿⢇⣀⡀⠀⣱⠀⠀⣽⠀⠀⠈⣷⠀⠈⣦⠤⠋⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⣿⡇⠀⣴⡿⢋⠋⠀⠀⠀⠀⠻⣇⣼⠀⠀⠀⠂⠙⣷⡄⠘⣿⠙⢷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢦⣾⠟⠀⣿⠀⣼⡿⠁⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠈⣿⡄⢸⡇⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠃⠀⢰⣿⣰⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠙⣷⡈⣷⠀⠀⢈⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠟⠀⠀⠀⢸⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⢹⣧⢻⡆⠀⠈⠲⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠏⠀⠀⠀⠀⢸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢻⣾⡇⠀⠀⠀⠀⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇⠀⠀⠀⠈⠢⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣾⡏⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⠀⠀⠀⠀⠘⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣎⡇⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⣴⣤⣄⡀⠀⠀⠤⣄⡀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢹⡇⠀⣀⣤⣤⡼⠿⠿⠶⢶⣤⣀⣀⠙⠻⣿⡷⣶⣄⣀⠙⠷⣶⣤⣀⠈⠛⠷⣶⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⣴⡿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣷⠾⢿⣦⡈⠉⠛⠓⠶⠿⠿⠟⠛⠳⠶⢾⣿⣿⠿⠛⠛⠋⠉⠉⠉⠙⠛⠛⠻⢿⣶⣄⠀⠀⠀⠀⠀⢠ ⠀⠀⢠⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣦⠀⠀⢠⣿ ⠀⢀⣾⠏⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡄⠀⠀⠹⣷⣀⣾⠇ ⠀⢸⣿⡇⠈⠛⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠃⠀⠀⠀⢻⣿⡿⠀ ⠀⠘⣿⢳⡀⠀⠀⠀⣀⣴⡶⠶⠶⠶⢦⣄⠀⠀⠀⠀⠀⣠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡆⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⢸⣿⠇⢀ ⠀⠀⠘⣧⡙⢧⣴⡿⠋⠁⠀⠀⠀⠀⠀⠘⢷⡀⢀⣠⣾⠟⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣧⣄⡀⠀⢀⣴⠟⠛⠉⠉⠉⠛⠿⣦⣄⠀⠀⣠⣿⣿⡾⠟ ⠀⠀⢰⡏⢹⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⢯⣅⣀⣈⡙⠛⠶⠦⠤⠤⠤⠴⠶⠶⠖⠂⠀⠀⣈⣛⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣾⣿⡏⠁⠀⠀ ⠀⠀⢸⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠿⣇⠀⠀⠉⣟⠙⠛⠒⠒⠒⢶⡶⠶⠶⠒⠒⢺⡟⠛⠉⠉⢨⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⢹⣧⠀⠀⠀ ⠀⠀⢸⡇⠘⢷⣄⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠠⢹⣷⣄⡀⢿⡆⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⣼⣟⠹⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠈⣿⠀⠀⠀ ⠀⠀⢸⡇⠀⠈⠛⢶⣤⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢉⣉⣿⣧⣀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣿⠀⣠⣶⠟⠋⠉⠁⠉⠉⠀⠀⠀⠀⠀⠀⢀⣠⡾⠃⠀⣿⠀⠀⠀ ⠀⠀⢹⣿⠀⠀⠀⠀⠀⢹⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⣀⣙⣷⣤⣀⣿⡀⢀⣀⣠⣴⣧⣴⡿⠟⠛⠀⠀⠀⠀⠀⠀⠀⠶⠶⣿⢿⡟⠉⠀⠀⢰⣿⠀⠀⠀ ⠀⠀⠀⢹⣧⡀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠉⠉⠉⠙⠻⣯⡉⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⣼⣧⣶⠄⢀⣾⠇⠀⠀⠀ ⠀⠀⠀⠀⠹⢷⣄⡀⠀⢀⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠛⠁⠀⢀⣾⠏⠀⠀⠀⠀ ⠀⠀⢀⣠⣴⠶⠛⠙⠛⢋⣡⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠿⣦⣤⣴⡿⠋⠀⠀⠀⠀⠀ ⠠⠾⣿⣥⣄⣤⣤⡶⠾⣿⡟⢹⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⢀⠈⠙⠻⢷⣤⣀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⣰⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠘⢿⣶⣶⣤⣬⣿⣷⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣾⠋⣠⣴⣾⠟⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣄⡀⠈⠻⢶⣤⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠐⠛⢛⣿⡿⠋⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠈⠙⢿⣶⠦⣤⣽⣷⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣾⠏⠀⠀⠀⣠⣶⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠈⢻⣆⠀⠀⠉⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣾⠋⠀⠀⠀⣼⡟⠁⠀⣿⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣀⣼⠟⠛⢻⣷⠶⢿⠷⠾⢿⣛⠋⠉⠉⠉⠉⢙⡟⠁⠀⠀⠈⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣿⠛⠛⠛⠛⠿⠶⢶⣿⡿⠀⠀⠀⢠⣿⠀⠀⠀⡀⠀⢀⡀

⠀⠀⠀⠀⠀⠀⠀⢀⠔⣉⣁⣀⣀⣀⡈⠉⣇⡔⠣⠤⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⠴⢓⠞⣉⠀⢄⡤⠀⠈⠠⠃⠀⠄⡀⢀⠀⡈⠱⢄⠀⠀⠀⠀⠀ ⠀⠀⠀⢎⠉⠉⣰⠗⡩⢄⡝⠉⠀⠀⡝⠀⠄⠁⡐⠀⢆⠐⠀⢁⠀⢳⡀⠀⠀⠀ ⠀⠀⡀⢨⠛⣺⢋⡜⣡⠏⠀⠠⠁⢸⠀⠈⠄⠁⠄⠈⠘⡄⠀⠂⠄⠂⢧⠀⠀⠀ ⠀⢸⣝⡻⡹⢆⠯⣴⠇⡐⠈⠄⡁⢾⠀⠀⠈⠀⠄⠂⠀⡇⠐⠈⠠⠐⠸⡄⠀⠀ ⠀⠀⢾⣵⣻⣞⡵⠚⠠⢀⠁⠂⠄⣿⠀⡀⢂⠐⠠⠈⠄⡇⢀⠁⡆⠁⠄⢉⠒⣤ ⣀⣀⡼⣞⡽⣤⣤⡴⠃⠄⠌⢂⢰⠟⣆⠐⠠⠈⠄⠡⢰⢻⣀⠈⣇⠈⡐⢦⡤⠃ ⠹⣯⣽⡾⣵⠷⢊⠡⢈⡰⠞⡩⠋⠉⠸⡄⠡⠘⡆⢑⡏⠁⢧⠀⠸⡄⠐⡈⠦⡄ ⠀⠯⣳⣻⣦⣤⡦⠶⠯⣵⣿⣶⣶⣮⡕⢈⣧⡐⠹⣾⣴⣶⣶⣿⠤⢽⣆⣐⠴⠃ ⠀⠀⠀⠈⢷⡍⡇⢰⠂⣏⠀⢷⡛⣿⠀⠙⠒⠉⠓⠻⣛⡷⠃⡹⢠⠆⡇⠀⠀⠀ ⠀⠀⠀⣀⠀⢣⡸⡌⠳⢬⠆⠠⢀⠀⠀⡀⣀⣈⠀⢀⠀⠠⢀⢙⡇⣼⠁⠀⠀⠀ ⠀⠀⠀⢣⣉⣉⠻⣟⣤⡉⢦⣅⣀⡀⠀⠀⠻⠃⠀⢀⣈⣠⣴⢋⣴⡃⠀⠀⠀⠀ ⠀⠀⠾⣉⣡⠦⢛⣽⣳⣿⣷⣿⣿⣿⣿⣿⣷⣿⣿⣿⢿⣿⡟⡎⠜⢹⡄⠀⠀⠀ ⠀⠀⠀⠀⡏⢰⠏⠈⡾⠛⠿⣦⠙⡓⢾⣿⣿⣿⣟⡾⢿⡟⣿⣿⣶⡶⠁⠀⠀⠀ ⠀⠀⠀⠀⠹⠃⠀⠸⠦⣝⣰⠈⣿⠿⠿⣻⣿⣿⣿⣿⢿⣭⠿⠛⠋⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⣿⣿⡣⠂ ⠀⠀⠀⠀⠀⢠⣎⣥⣤⣤⣤⣤⡝⣦⠤⠤⢤⣤⣤⣀⣀⠀⠀⠀⢘⣶⣶⣍⣿⣣ ⠀⠀⠀⠀⠀⣀⡴⠛⠉⣠⠔⠋⠉⠉⠙⠂⠁⠀⠀⢀⠈⠛⢦⡀⠀⠻⣉⣷⠽⠅ ⢠⡤⠤⠔⢚⡅⠀⠀⡜⠁⠀⠀⠀⠀⢶⠢⡀⢠⢴⠂⠁⠀⠀⢳⡄⠀⣿⠃⠀⠀ ⠈⠓⢦⡴⠋⢀⡠⠎⠀⠀⠀⠀⡀⠀⡧⠔⠽⠷⠦⣇⠀⢠⠀⠀⢈⠛⠒⣲⠀⠀ ⠀⠀⣸⡓⠚⠉⠀⠀⠀⢀⡀⠀⡇⠀⡇⠀⠀⠀⠀⢸⠀⢸⠀⠀⠀⠻⡏⠁⠀⠀ ⠀⢀⠏⠉⠙⣻⠋⠁⠀⢸⠀⠀⡷⡀⢣⠀⠀⠇⠀⢸⠀⡜⣇⠀⢆⠀⢷⠀⠀⠀ ⠴⠋⢀⡀⠀⡇⠀⠀⢠⠏⠀⡘⠒⠓⢌⣧⠀⠀⠀⣿⠞⠁⠈⡄⠘⡀⡸⠀⠀⠀ ⠲⠒⡿⠁⠀⡇⠀⣠⠏⢀⣼⣤⣤⣄⣂⠀⠀⠀⠀⣨⣤⣤⣤⣼⡄⠱⡇⠀⠀⠀ ⣠⠞⠁⠀⣀⡧⢒⣁⡴⡯⠉⢏⠙⢟⡏⠀⠀⠀⠀⢹⡿⢋⡏⠉⡿⡢⢭⠆⠀⠀ ⠦⣤⣤⡾⢱⡉⢏⠀⢆⠱⣄⠈⠉⠉⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⢦⢿⢸⠀⠀⠀ ⠀⠀⠀⠙⠉⠳⣮⢧⡀⢫⣏⠥⢤⡀⠀⠀⠀⠶⠂⠀⠀⣠⣤⣠⣇⠀⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠰⢧⢴⣟⣦⣹⣶⣶⣿⣦⣤⣤⣤⣤⣴⡾⣿⣿⠒⠚⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⠔⢪⡿⢡⣟⡉⣽⣿⢟⣟⠿⣾⡿⢿⣝⡿⢷⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣇⡀⡟⢇⠠⠿⢛⣿⣀⣠⣍⣿⣥⣺⢿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀

⠐⢢⠐⢢⠐⣹⡷⣆⠐⢆⠒⡄⠒⡌⢶⡐⡐⢢⢉⠓⢆⠒⡌⡉⢍⡙⣿⣯⠁⠆ ⡉⢆⡉⢆⠱⡈⣿⠹⣎⠄⠣⢌⠱⡐⠌⣷⡡⢊⠤⣉⠆⡱⠤⡑⠢⢌⣿⢼⡣⠌ ⣿⣤⠘⡄⢣⡐⣹⡆⠹⣯⡐⡃⢆⠱⡈⠜⣷⢈⠲⡐⡜⢠⢃⠜⡡⣚⣯⠀⢿⡔ ⢿⣿⣷⣌⠡⢒⠌⣷⡥⢾⣿⣴⡉⠆⡍⠬⣹⡎⠔⡱⢈⡅⢎⢒⣡⣿⣇⣨⠘⣷ ⣎⢿⣿⢿⣷⣌⢒⠸⣏⠉⡈⠻⣿⣖⡌⢣⢜⡧⢊⣵⠊⡔⢪⢰⣿⡏⠙⠛⠷⠾ ⠈⠳⢿⣳⣍⠻⠿⣦⣽⣆⠠⠁⠘⠻⣿⡷⣾⠇⣭⡟⢸⡈⣵⣿⠟⠀⠡⠈⠄⠂ ⣄⠡⡈⢿⣾⣾⣿⣽⣛⣻⠷⣤⠁⠀⠈⢻⣿⢸⣿⢡⢃⣾⣿⢟⣺⣟⣿⣷⣮⡴ ⣘⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣓⠀⠈⠀⢰⣯⣿⢇⣾⣿⣟⣿⠿⣿⣿⣿⣿⣿⣿ ⣿⠛⠡⣾⣿⢿⣿⣿⣿⣿⠠⠉⠁⠀⣰⣿⢿⣽⣻⠟⠃⠈⠔⢺⣿⢿⣿⣿⣿⡎ ⠻⣇⠀⢻⣯⠟⢿⣯⠙⠋⠀⠀⢠⣾⠿⠛⠏⠋⠁⠀⠀⠀⠀⠘⣿⡏⢿⡋⠙⠃ ⠀⡉⠷⣌⣻⢦⣦⡼⠟⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠘⠿⣤⣼⡧⠚ ⠀⡐⢀⠀⠈⢀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢀⠀⡀ ⠀⠠⠀⢈⠀⠠⠀⢀⠀⠂⠀⠀⣴⣷⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠐⠀⠀⡀⠀⡀ ⡀⠁⡐⠀⠠⠀⠀⠀⠀⠀⠠⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠠⠀⠀⠀⢀⢸ ⢧⡐⠠⠄⠡⠐⠀⠀⠁⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠐⠠⢈⣾

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡟⣿⠿⣯⣝⣳⠷⣌⠳⣄⡞⣀⣠⣤⠟⣡⣿⡦⣿⣎⢯⡀⠀⡇⣈⢽⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡶⣽⣏⣿⠶⡿⣿⣿⣚⣿⣿⠿⠿⠿⠿⠿⣿⣿⣧⢿⣿⢶⡻⢷⡿⣤⣼⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠻⣾⡿⠷⠛⢉⣉⠄⠀⠀⠀⠀⠀⠀⠀⠻⣿⣼⠛⠿⢿⣋⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐ ⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⣠⢶⡫⢥⠲⣬⣉⡿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀⠤⡀⠉⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣶⣞⣻⡽⠯⠵⠞⠋⣰⡾⣟⢧⣛⢧⡛⡴⡞⠁⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠘⡆⠀⠙⢾⡀⠈⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⠀⠀⠀⠀⠀⢀⣴⡿⣽⣹⣮⣽⡲⣝⡼⠁⠀⠀⢰⠃⠀⢸⠁⠀⠀⠀⠀⠀⠀⣷⠀⠀⢺⣷⣄⡀⢻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣠⣤⡴⣖⣶⣲⣛⣯⣽⣭⢷⡶⣿⡱⢯⠇⠀⠀⢀⡏⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⢹⡤⠿⢿⣿⣶⡟⠉⣿⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠛⠉⠉⠉⠀⢉⣿⡿⣾⢽⣫⢾⣵⣻⡿⠀⠀⠀⣼⠁⠀⣤⢞⣿⠀⠀⠀⠀⠀⠀⡟⢧⡀⠀⠙⣿⡀⠀⢸⡌⣹⠃⠀⠀⠀⠀⠀⠀⠀ ⣀⣀⣷⡶⡿⣿⣛⣛⣛⣻⣝⣭⣽⢿⡗⠀⡁⢠⡯⢀⡾⠧⠴⠻⣧⠀⠀⠀⠀⣸⠧⠬⢷⡀⠀⢻⡇⠀⠀⠹⢧⣀⣠⠀⠀⠀⠀⠀⠀ ⠟⠟⠓⢿⣟⣯⣟⡿⣻⡽⣫⣟⢮⣿⡇⠐⡀⢸⣷⠏⠀⠀⣀⡀⣘⣷⣄⠀⠀⢺⡁⣀⣀⠹⣤⡸⡟⠀⠀⠀⠀⢨⣽⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣀⣹⣿⣾⡿⠷⣟⣻⣛⣯⣿⡇⠂⠄⣾⣯⣼⡿⣿⣷⣿⣍⠉⠻⣷⢤⣸⣿⣿⣿⡿⣮⣻⡇⠀⠀⣧⠤⠞⠁⠀⠀⠀⠀⠀⠀ ⡾⡿⠿⢝⣷⡾⣶⣟⣿⣻⢯⣟⣵⣫⣇⠡⠂⣿⣿⠁⣿⣿⣻⣿⡾⠀⠀⠈⠙⠻⢷⣿⢯⣷⠙⣻⡇⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣸⣯⣟⣧⣟⣶⡿⠿⣞⡶⣏⣿⠀⠅⣿⡽⡇⢿⣿⣳⣿⡟⠀⠀⠀⠀⠀⡀⢿⣿⣿⠀⣿⡧⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀ ⣶⣶⡷⣿⣿⡽⣽⢿⡶⣿⣻⢯⣳⢏⡾⣇⠀⣿⡵⢧⠀⠙⠋⠉⠀⠀⠀⠀⠀⠀⠁⠀⠈⠁⠀⢻⡇⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⡾⣽⣯⢷⡻⣽⣣⣟⣧⣿⣽⣻⡄⠹⣟⠮⣷⡀⠈⡀⠁⡀⠁⢰⡿⠿⠇⠀⠀⠀⢠⣿⠀⠀⠀⢀⠀⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⣀⣀⣿⣽⢷⡿⣷⣻⣻⣭⡽⣷⢶⣞⢧⢿⡀⣿⣿⣶⣟⣶⣤⣀⠀⠀⠀⠀⠀⠀⢀⣠⢞⢫⠏⠀⠀⢠⠏⢰⡟⠀⠀⠀⠀⠀⠀⠀ ⠿⠿⠛⠛⢿⣻⣿⣯⣟⣳⢿⣽⢧⡟⣮⢻⡜⡽⡜⣿⣿⣿⣿⣿⣿⣿⣶⣤⣤⣴⣾⣿⡥⣪⢏⠀⣀⡴⠋⢀⡾⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⣻⣙⣺⣽⣯⣿⠾⣽⣭⢷⡹⣷⡹⣜⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠗⠁⠈⢳⢤⣤⣴⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣠⣤⣤⣶⣶⣟⣾⣽⣭⣷⣶⣾⣿⣿⣮⣳⢻⡜⣿⣾⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣤⣀⣀⣤⡶⠉⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠛⠍⠉⠁⠈⠀⠁⢠⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠉⠀⠀⣠⢼⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣀⣀⣤⡴⣮⣟⣟⣯⣭⣵⣾⣶⣿⣿⣿⣿⣿⣿⠗⠋⠉⡟⠛⠟⠿⠟⠻⠛⠋⠳⣖⠚⠉⠀⠀⠙⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⠿⠿⠛⠛⠋⢻⣿⣿⣿⣿⣟⡿⣽⣷⢙⣿⡿⠛⠋⠁⠀⡀⠀⣹⣆⠀⠀⠀⠀⠀⠀⠀⡯⢧⣀⠀⠀⠀⣸⣿⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣴⣿⣿⡽⢿⣛⣯⣻⣭⣾⣿⣷⣿⣀⣁⠀⠁⠀⣰⡏⡞⣳⣄⡀⠀⠀⢀⣼⣙⣦⣭⡷⠴⠖⣟⡹⣇⠀⠀⠀⠀⠀⠀⠀ ⣾⣾⡿⢿⣿⢿⣟⣿⣻⢿⣿⣟⣯⡷⠿⠚⣻⢿⡙⠛⠛⠛⠛⠻⡛⡚⠓⠚⠛⠻⡉⡹⣹⢧⡀⠀⢷⠀⠀⠈⢻⡻⡓⣆⠀⠀⠀⠀⠀ ⠁⠁⣠⣿⢿⣯⣟⣾⣽⡿⣿⣿⢃⠆⡑⢨⣿⠭⡗⠀⠀⠀⠀⠀⠱⣌⣇⣌⣡⢲⠝⣡⠃⠀⠻⣗⢾⣧⣄⠀⠀⠉⢾⣎⠳⣄⡀⠀⠀

⠀⠀⣰⡫⠛⢿⡿⠛⢻⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣶⠄⠀⠀⠙⢫⣿⠋⠙⢢⠀ ⠀⠀⢻⣴⡄⠀⠀⢠⣴⣿⠃⠀⠀⠀⠀⠀⣀⣴⠶⠟⠛⠻⠿⢿⣿⣿⣟⠛⠻⣷⣶⣤⣀⡀⠀⠀⠀⠀⠻⣇⣄⣼⣷⣆⠀⠈⠀⠀⠀⠑ ⠀⢶⣾⡿⠁⢀⣄⢈⣿⡿⠀⠀⠀⣀⣴⡾⠫⠖⠉⠀⠀⠁⠈⠀⠄⠉⠛⢷⣄⠡⠄⢈⣙⠿⣶⣄⠀⠀⠀⠈⠙⢿⡮⠀⠀⠀⠀⠀⠀⡀ ⠀⠀⠀⠀⠀⠻⢿⣻⠟⠀⠀⣤⣾⡛⣡⠞⡡⠀⠀⠀⠁⠁⠀⠁⠁⠀⠀⢀⢿⣦⠀⢷⠉⠻⣾⣝⢷⣼⡟⢶⡄⠀⠙⠲⠷⢄⠀⢀⠴⠀ ⡀⠀⠀⠀⠀⣀⢈⠟⠀⣠⣿⣿⢟⡴⠁⠀⠙⢃⣴⣻⣇⣾⠱⣤⡄⢤⣄⡬⠈⢿⣇⠚⠀⡀⠈⢻⣷⣿⣧⠀⢻⡄⠀⠀⠀⠈⠉⠉⠀⠀ ⣇⠀⠀⣸⡾⠛⠋⢀⣴⣿⡿⠁⠄⠈⠓⡀⠀⣾⢣⡿⢸⣿⠀⠀⠹⠀⠀⠀⠀⠈⢿⣆⢼⠁⠀⠀⠻⣿⡿⣧⢸⣿⡄⠀⠀⠀⠀⠀⠀⠀ ⠈⠉⠋⠋⠀⠀⢀⣾⣿⠟⠀⠀⠀⠀⢰⢇⣾⣿⡿⠁⣾⣿⠀⡛⢳⣄⢰⠟⠙⢦⣸⣿⠎⠇⠀⠀⠀⠹⣿⣻⣿⡟⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣾⣿⠏⠀⠀⣴⠆⠀⠙⣾⣿⠁⠈⣸⣿⣿⣧⠀⠀⢻⣆⠀⠀⠀⠻⣿⡀⡀⠠⣦⠀⠀⢿⡗⣿⣰⣿⣄⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣿⡿⠀⠀⣼⡏⠀⠄⠄⣿⡇⠈⢲⡿⠛⠻⢿⡄⠀⠘⣿⡄⠀⠀⠀⣿⡇⠂⠀⣿⡄⠀⢸⣿⢹⣿⣥⣈⣿⠄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣾⣿⠇⠀⣰⡿⠀⠄⠀⢵⣿⠀⢦⣿⠡⣄⠀⠀⢻⣎⠂⠘⣷⡀⠀⠀⢻⣿⡄⡂⠘⣿⡀⠀⣿⣼⣿⣿⠿⠛⢶⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⣿⠀⣇⣿⡇⡆⠀⠀⣹⡟⢀⡾⠁⠀⠈⠙⠓⠦⢽⣦⡀⠘⣿⡀⠂⢺⡿⣷⡂⠀⠙⣷⡀⣿⣿⣿⣡⣤⣤⣤⠟⠀⠀⠀ ⠀⢀⣀⠀⠀⢸⣿⡇⣹⣿⣇⠂⠀⠀⣿⣧⡟⠁⠀⠀⠀⠰⠦⣄⠀⠀⠻⢦⣬⣿⡆⢸⣷⠘⢷⣄⠀⠹⣷⣿⡟⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⡞⣉⡛⠶⣼⣿⣧⣿⡿⣿⡀⡀⠀⠹⣿⠑⢷⣶⣿⠿⠿⠿⣶⣄⠀⠀⠀⠈⠉⢷⡄⠹⣧⠀⠙⠷⢦⣿⣿⡇⣿⡇⠀⠀⠀⠀⠀⠀⠀ ⣯⡰⣯⣹⠀⣤⣿⣿⣿⣷⢿⣧⠀⢠⡄⣿⡄⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣾⣷⡀⠀⠀⢀⣿⢁⣿⡇⠀⠀⠀⠀⠀⠀⠀ ⠘⢧⣤⣉⣼⠃⢹⣿⡿⠃⣀⣿⣧⣾⡇⣿⡇⠀⠀⠀⠀⠀⠀⢠⠔⠒⠲⠤⢤⣄⣀⠀⠀⠙⠻⠿⣿⣾⡿⣿⢰⣿⣧⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢿⣽⠂⠘⢿⣤⣼⠏⠀⢹⣿⡇⢿⡇⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⢿⣷⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⢿⣇⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⡾⢸⡇⠀⢸⣿⢿⡆⠘⢹⣿⠁⣿⡇⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣾⣿⡄⠀⠀⠀⠀⠀ ⠀⣼⡋⠀⣼⠃⢀⣼⠋⣸⣿⣦⡾⠁⠆⣸⣿⣤⣀⠀⠀⠀⠀⠙⠦⣄⣀⣀⣠⠔⠁⠀⠀⠀⠀⠀⢀⣤⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⢻⣟⣦⠏⢠⣾⠋⢠⣿⣿⣿⡇⢀⣴⣿⣿⣿⣿⣿⣶⣦⣤⣀⣀⣀⠀⠀⠀⠀⠀⣀⣀⣠⣴⣶⣿⣿⣿⡛⠿⣿⡟⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⢁⣴⠟⠡⢄⣿⡟⢹⣿⣷⣿⣿⣿⠿⣏⠀⠤⠌⠙⢿⣿⣿⣿⣿⣽⣿⣿⣛⣉⣹⠿⣿⢿⣿⣿⣿⣷⡀⠈⢷⡄⠀⠀⠀⠀⠀⠀ ⠀⣠⡾⠟⠁⠀⢯⣿⠏⠀⢿⣿⣿⣿⣿⣿⡗⠂⠁⠀⠴⠒⢂⡽⣿⣿⢿⣿⠿⠿⣿⣿⣯⣒⠃⢸⣿⣿⣧⠈⣷⣤⣾⡟⠀⠀⣀⠀⠀⠀ ⢸⡟⠀⠂⠀⢠⡿⣿⣄⠀⠘⢿⣿⣿⣿⣿⣿⡿⠿⣿⣶⣶⣾⣎⡠⠛⢿⣿⣿⣿⣿⣿⣿⣿⣷⠟⢻⣿⣿⣷⣛⠛⠋⠀⠀⢠⡿⣷⠀⠀ ⢸⣧⠀⠀⢠⣿⢱⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⠀⣙⣻⣿⠋⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣿⣿⣿⣿⣿⣶⣤⣤⣼⠇⢹⡇⠀ ⠈⢿⣷⣦⣜⣿⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠁⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⣠⣿⠃⠀ ⠀⠈⢿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⡿⣿⣟⡻⢿⢟⡛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡾⠛⠁⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢰⢤⣀⠀⠀⠀⠀⢠⠞⠉⢧⢀⡴⠚⠁⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⠀⠈⠙⠦⣄⣰⠏⠀⠀⠈⠋⠀⠀⠀⠸⡇⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣀⣀⣀⣀⣸⡄⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⠁⠀⢀⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⢳⡀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢾⣉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⠉⢉⡿⠂⠀⠀⠀ ⠀⠀⠀⠈⠛⢶⡴⠶⢶⣶⣶⣾⣿⣾⣶⣶⣶⣶⣶⣶⣶⣴⣦⡁⠀⠐⡆⣠⣴⣿⣵⣶⣶⣶⡶ ⠀⠀⠀⠀⠀⣼⣀⠄⠇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⣿⣿⣿⣿⣿⣿⠟⠃⠀ ⠀⠀⠀⠀⠀⣿⡳⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⢋⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠻⣥⣤⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀ ⠀⠀⠀⠀⠀⠀⣹⢲⣩⡔⢯⡀⠀⠀⡇⠀⠀⠀⠀⢀⣠⢤⣀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣷⡀ ⠀⠀⠀⠀⠀⢀⡾⠃⣿⣇⡠⠃⠀⠀⡇⠀⠀⢀⢰⠉⠀⡠⠜⢧⢰⠀⠈⢿⡙⠛⠿⠿⠿⢿⣿ ⠀⠀⠀⠀⠀⣾⠁⠀⠘⠉⠀⡐⠉⠀⢱⣶⠀⡞⠯⠴⠛⡲⢀⡞⠀⢸⡶⢼⠇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢻⡄⠀⠀⡰⠀⡈⠉⠁⠈⠸⡜⠀⣄⠀⠊⣠⠞⢱⣤⣀⣷⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⠶⣜⡁⠀⠈⠁⠀⠀⠀⠀⢀⡈⢻⡉⣽⢤⣀⣷⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢻⣶⡶⢶⠋⠉⠉⠉⠉⠉⠉⢹⡆⠉⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢼⡅⣯⢰⢀⠀⠀⠀⢀⣀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣾⡟⣿⣾⣾⣿⣿⣿⣿⢿⣿⣷⣄⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⢸⣿⣿⣿⣿⠿⣛⢿⣿⣓⣼⣻⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⡶⢿⣥⣿⢇⡿⡉⠭⡑⢄⠣⣙⣦⣍⡛⠧⠹⣏⠻⣦⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⣯⣐⣉⣿⣿⢰⡇⡱⢂⠍⢢⡑⢄⠺⣽⣳⣬⣑⣤⠷⣋⢙⣳⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⠶⠏⠀⣩⣾⣿⣿⣼⣧⣦⣵⣮⣥⣼⣌⣱⣧⣯⣽⣏⡰⢡⣶⠟⠛⠖⠲⣄⠀⠀⠀ ⠀⠀⠸⡇⠀⠀⣸⠋⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢿⠛⠉⢻⠀⠀⢀⡿⠀⠀⠀ ⠀⠀⠀⠙⢲⡖⠋⠀⠀⠀⢸⡏⢹⠋⢩⣼⠉⡌⢩⠉⡍⣽⡅⢰⣾⠀⠀⠘⣧⣴⡞⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⡰⢉⣛⡾⢡⡉⢜⡠⢃⣾⡯⢿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⡱⢐⣣⠞⡡⠒⣌⢢⣴⣿⣿⣿⣿⢿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡾⢡⠌⣻⣶⣋⠔⣡⢓⣼⢿⣵⣿⡿⢿⣱⡾⢋⠽⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⢻⣦⡾⡽⢃⠝⣷⣴⠟⠁⠀⠙⣿⠵⣋⠳⣝⢮⣲⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣴⣻⣿⣿⣦⣾⣿⣧⣝⢷⣌⣒⣤⠟⠀⠀⠀⠀⠈⠳⣦⣱⣾⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀ ⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⠙⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⢙⣿⣿⣿⣿⣾⡿⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠛⢿⣿⣿⡿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⠻⢿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⡶⠦⢤⣼⣄⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⡶⠛⠉⠉⠈⠉⠙⠛⠶⣦⣄⠀⠀⠀⠀⠀⢠⡾⠋⠁⠀⠀⠂⠀⠈⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣼⢋⠀⠀⠀⢀⣀⣀⡀⠀⠀⣀⣽⠷⠶⠟⠛⠛⠛⠛⠒⠲⠶⠦⣴⣶⣖⣈⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣼⠃⠀⠀⢠⡾⠋⠁⣩⡿⠟⠋⠁⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⡛⠿⣷⣀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⠀⠀⢀⡿⠁⣠⡾⠋⠀⠀⠀⢀⡴⠚⠁⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⡀⠘⠪⡛⢷⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣇⠛⠀⠈⣷⡾⠋⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠘⢦⡙⢿⡍⠉⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢻⣤⣀⣼⠏⠀⠀⠀⠀⠀⡼⠁⠀⠤⢤⡀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠀⠀⠀⠀⢷⠈⢻⣤⠤⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢻⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⢴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⠀⠀⠈⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⠏⠀⠀⠀⠀⠀⠀⠀⣀⡴⠛⢦⡀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⢰⣏⠀⠀⣀⡷⣤⡾⣧⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡀⠀⠀⢸⡆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡽⢤⡴⠁⢹⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡇⠀⠀⠀⣧⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢈⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⣸⠁⢀⣨⣧⠀⠀⢸⣧⠀⠀⠀⢰⡆⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣼⠁⠀⢠⠀⠀⠀⠀⠀⠀⣼⠀⠀⣰⠃⠀⠺⢤⣹⣦⠀⠈⢿⢷⣄⣀⣀⣧⢀⡿⠛⢆⡀⠀⣤⠀⠀⠀⣾⠀⠀⠀⠀⠀ ⠀⠀⣠⡾⠃⠀⠀⣼⠀⠀⠀⡀⠀⢀⣿⣀⡴⠃⠀⢀⣀⣀⡀⠈⠓⠒⠛⠀⠀⠀⠈⠉⠙⢁⡀⠀⠙⢶⡟⠀⠀⠀⡟⠀⠀⠀⠀⠀ ⢠⡾⠋⠀⢀⣤⣼⡟⠀⠀⣼⠃⠀⠀⣿⠉⠀⣤⣾⢿⣿⣟⣿⣷⡄⠀⠀⠀⠀⠀⢀⣴⣿⠿⣿⣷⡄⠈⡇⠀⠀⣰⡇⠀⠀⠀⠀⠀ ⠈⠛⠛⠛⠉⢹⡿⠁⠀⣰⡟⠀⠀⠀⠘⡆⢾⠟⣿⡸⣅⣹⢿⡏⠃⠀⠀⠀⠀⠀⢸⡟⢹⠗⢾⠹⣿⣴⠇⠀⣰⣿⡆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⡿⠁⢀⣰⠛⣧⡄⠠⡄⠀⠹⣆⠀⠘⢤⣈⣀⡰⠃⠀⠀⠀⠀⠀⠀⢸⡙⠋⠀⡼⠀⢀⡟⠀⣠⣿⣿⣿⣄⡀⠀⠀⠀ ⠀⠀⠀⠀⠛⠗⠚⠋⢹⣦⡈⠳⣄⡙⣦⡀⠈⠳⣄⠀⠀⠀⠀⠀⠀⣀⣀⣀⣓⡀⠀⠉⠛⠉⠀⠀⢘⣿⣿⣉⣀⣩⣟⠉⣹⣄⣀⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⢹⣿⣿⣿⣿⣿⣶⣶⣛⠃⠀⠀⠀⠀⠀⡇⠀⠀⣸⠁⠀⠀⠀⠀⢀⣴⣿⣿⣿⡍⠉⠙⠉⠉⠙⡇⠴⣇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠟⢿⣿⣿⣋⡽⢿⣿⡓⠒⠲⢤⣤⣵⣤⣴⠥⣤⡤⠒⠒⠋⢩⠏⢹⣯⠏⣷⠀⠀⢀⠀⢰⠃⣐⡏ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠋⠀⠀⢻⣷⠀⣠⣾⡿⢯⣈⡟⠷⣾⡷⠀⠀⢠⣃⣀⣠⣿⣇⣹⠾⠛⠛⠛⠛⠖⠋⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣼⠿⣍⠳⣄⠀⣼⣿⣾⡿⣷⡒⠒⠒⠛⣻⣿⣿⡿⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠻⢿⠁⠀⠈⠳⣌⣿⣿⣿⣿⣿⣷⣯⣭⣿⣙⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⢿⣦⠱⡀⢀⣴⠿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⡏⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣇⣷⣞⣿⣾⣟⢣⡉⠉⠉⠉⠛⠛⢋⡏⠀⢀⣨⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⠔⠂⢈⠅⠀⢤⢀⠈⠑⠢⢄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡰⠁⢀⠔⢁⠔⠈⠀⢀⠡⢀⠀⠀⠱⢄⠀⠀ ⠀⠀⠀⠀⠀⡰⠃⣤⢂⡠⠁⠀⡠⢊⣔⢀⢄⠣⢴⢶⡀⠑⡄ ⠀⠀⠀⠀⡰⡡⠀⠇⠸⠁⠀⢀⢡⠊⠁⠀⠀⠀⠀⠀⢸⢢⢡ ⠀⠀⠀⢠⣱⢁⢸⠀⡆⠀⠀⢸⠃⠀⠉⠀⠀⠀⠉⠀⢘⠀⣼ ⠀⠀⠀⢸⢸⣼⣿⣦⡧⠀⠃⡯⠤⠤⠤⠀⠀⠀⢤⣶⢺⠀⢹ ⠀⠀⠀⠀⢀⡏⠸⡀⣿⠀⢳⢷⠉⢙⡄⠀⠀⢰⠁⣸⠆⢠⣿ ⠀⠀⠀⠀⠚⠲⡲⢁⣺⠀⣎⡌⠒⠒⠀⠀⠀⠈⠉⢙⡄⡌⡸ ⠀⠀⠀⠀⡠⠊⠙⢯⡟⣿⡏⢷⢦⣤⠖⠒⠂⢤⠴⣎⠋⠀⠁ ⠀⠀⠀⡜⠒⣄⠀⠸⡧⣼⣇⣴⠗⠁⠀⠀⡀⠬⡆⠉⠀⠀⠀ ⠀⢀⣼⢳⠀⠈⠢⡀⣿⠁⣱⠻⠢⡀⢀⠎⠀⠀⢰⠀⠀⠀⠀ ⠀⢸⢸⠘⠀⠀⠀⠑⣏⡶⠁⠀⣇⠑⠄⠀⡠⣴⡟⠀⠀⠀⠀ ⠀⠜⣿⡄⡇⠀⠀⣰⠋⠁⠀⠀⢼⠟⢿⣼⡞⠁⡇⣀⣀⣀⠀ ⢀⡴⢒⣙⣇⣀⣰⠁⠀⠀⢀⡸⢋⢴⢋⣾⣵⡾⠉⠉⠑⠢⣱

⢸⡇⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣖⠠⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⠂⠀⠀⠀⢠⠀⠲⡀⠀⠉⠉⠁⠀⢀⠀⠄⠈⠀⠈⠢⠄⡀⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⡤⠜⠒⠍⠀⡠⠐⠀⡀⡔⠡⠀⡁⡢⠀⠀⢂⠀⠀⠑⣢⣄⡀⠀ ⢸⡄⠀⠀⢩⠛⠄⠀⡔⠀⠀⡩⠊⠀⣠⢺⠐⠑⢡⠀⠀⠡⡀⠀⠐⡄⠀⠀ ⢸⠇⢀⡴⡧⡉⢀⣼⢀⠠⣼⡥⠐⠎⠐⠛⠂⠤⡈⡄⠀⠀⢡⠀⠀⠘⡄⠀ ⢸⠀⠛⡔⡄⢀⣜⠩⠂⠁⠀⠀⠀⠀⢀⣀⡀⠀⠀⢁⠐⠀⠁⢠⠀⠰⡼⡄ ⢸⠀⢰⣡⠁⡘⠁⣠⣤⡄⠀⠀⠀⠘⢻⣿⣶⠹⣦⢸⡄⠀⠀⣸⠀⠀⠇⠀ ⢸⠀⠈⠁⢾⢰⡞⢹⢿⠇⠀⠀⠀⠀⢈⠘⡸⠀⠘⠈⡷⠀⢸⢣⢂⣄⢠⠀ ⡄⠀⠀⠀⢸⢸⡅⡈⠦⡆⠀⠀⠀⠀⠂⠩⠤⠤⠂⠀⠧⢐⠋⡁⢾⠃⠉⠀ ⡇⠀⠀⠀⢸⢸⠇⠈⠁⠀⠀⣀⣀⠤⣀⠀⠀⠀⠀⠀⠀⠮⢔⢝⡅⠀⠀⠀ ⡇⠀⠀⠀⢸⢈⠣⡀⠀⠀⢺⠋⠀⠀⣀⠰⠀⠀⣀⣤⠺⣩⠃⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠈⢸⡇⠈⡖⠠⠤⠄⡀⣤⠄⣐⠴⠋⠉⢹⠥⣀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⢿⣐⠔⠃⢀⠔⡈⣀⣞⣎⣦⡀⠀⢠⠗⠁⠀⠑⢄⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⡇⡠⠀⢎⠠⠓⠡⣿⣿⠇⠒⠒⠁⠰⠅⠁⠄⠈⢢⠀⠀⠀ ⡇⠀⠀⠀⠀⢀⡧⠀⡀⣝⡌⠀⢀⣗⣯⠀⠀⠀⠀⠸⡀⠀⡰⣈⠑⢃⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣶⣶⣶⣦⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣶⣿⣿⣶⣶⣶⣄ ⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⣀⣀⡀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠉⠉⠙⠛⢿⣿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⣀⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⣾⠋⠁⠀⠙⢷⡄⠀⠀⠀⣠⡾⠛⠛⠻⣶⡄⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⡇⢸⡇⠀⢰⣶⠀⠀⣿⠀⠀⣸⡏⢀⣤⡄⠀⠈⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⢀⡝⠿⣿⣿⠀⠈⣷⡀⠀⠀⠀⣠⡿⠀⠀⣿⠀⠈⠋⠁⠀⢠⡿⢰⣿⣿⣿⡿⠋⡉⠙⢿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⠀⣾⠁⠀⠈⠀⠀⠀⠈⠛⠷⠶⠞⠋⠀⠀⠀⠘⣷⣀⣀⣀⣴⠟⠁⢸⣿⣿⣿⡇⠸⣧⠀⠈⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⢠⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠈⠻⠿⠿⠀⠀⠹⣷⠤⣼⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠈⢿⣄⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⣿⠿⠿⠿⠿ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠿⠿⠿⠿⠿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⠀⠀⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠈⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠋⠀⠀⢰⡏⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⣤⣤⡄⠀⠘⢷⡀⠀⠀⠉⠻⢦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠶⠋⠀⠀⠀⣠⡟⠀⡀⠀⠀⠀ ⡤⠤⠤⠤⠴⠏⠀⠀⣿⠀⠀⠀⠙⢦⣄⠀⠀⠀⠈⠉⠛⠛⠶⠶⠿⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠀⠀⠀⠀⣠⣾⠏⢰⡟⠻⣧⣀⠀ ⠀⠀⠀⠀⠀⣴⡟⢻⡏⠀⠀⠀⠀⠀⠙⢷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⣾⣿⣧⣀⠀⢻⣆⠈⠉⠛ ⠀⠀⠀⠀⣾⠟⠀⣼⣷⣄⡀⠀⠀⠀⠀⠀⣨⣿⣿⣶⣦⣤⣄⣀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣌⠻⣦⣄ ⠀⠀⢀⣼⣏⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣜⣿ ⠀⠀⣸⡇⠉⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⢀⡀⣀⣀⣀⠀⠀⠀⠀⠀⣀⠴⠚⢩⠟⠉⣠⣇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠖⠋⠁⠀⠀⠉⠉⠉⠉⠀⠈⠉⠒⢤⣴⠚⠁⠀⢰⠃⠀⠀⠉⣩⠿ ⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⣫⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢤⣀⡏⠀⠀⠀⠘⠉⡟ ⠀⠀⢀⣀⠤⠖⠋⢁⣤⡞⠁⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⢄⡀⠀⢀⡼⠁ ⢶⡋⠉⠀⠀⠀⠉⢹⠋⠁⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢶⠛⠟⠛⢹⠇ ⠘⣷⣄⠀⠀⠀⢠⡷⠃⠀⠀⠀⠀⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠶⡏⠀ ⠀⠘⢎⣑⢶⣖⠉⣠⠃⠀⠀⠀⢰⠀⣰⠁⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠐⡄⠀⠀⠀⠀⠀⣿⣤⠞⠁⠀ ⠀⠀⠘⢏⣀⡈⢹⠃⠀⠀⠀⠀⣇⡴⢿⠀⡆⠀⠀⠀⠰⡄⠀⢹⢯⠁⢣⠀⢳⠀⠀⠀⠀⠀⠘⢧⣀⠀⢀ ⠀⠀⠀⠀⠈⠳⡏⢀⠀⠀⠀⣾⡏⠁⠘⣆⣿⣄⠀⠀⠀⣧⢠⣧⣼⣷⣼⣷⣼⠀⠀⠀⠀⠀⠠⣄⣨⠽⠟ ⠀⠀⠀⠀⠀⢸⡁⢸⠀⠀⠀⣏⢧⠀⠀⠈⠙⠊⠓⢦⣠⡿⠻⣿⣏⣀⢙⣿⣿⡄⠀⠀⠀⢰⠀⢷⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⣧⢸⣧⡀⠀⢹⡛⠷⠿⢶⣷⡀⠀⠀⠉⠀⠀⣯⠀⠛⢃⣽⠟⢁⠀⠀⠀⡜⠀⡞⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⣛⠟⠉⠓⠾⡧⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠉⠉⢉⣴⣫⣴⡇⠀⢀⣼⡧⠞⠀⠀⠀⠀ ⠀⠀⠀⣀⣠⠤⠚⠁⠀⠀⢀⠀⠱⣄⠀⠀⠀⠀⢠⣀⣄⣀⠀⠀⠀⠀⢀⡴⢻⡤⠔⠋⢸⡇⠀⠀⠀⠀⠀ ⢀⡴⠋⢁⡴⠀⠀⠀⠀⢀⠌⠀⠀⠀⣹⡶⢤⣄⣀⠀⠀⠀⣀⣠⡴⠚⠁⠀⠀⢀⠀⠀⠈⢷⡀⠀⠀⠀⠀ ⢸⠀⢀⣾⠁⠀⠀⠀⠀⠘⠀⠀⣠⠾⣿⣿⣦⡌⢻⡍⠉⠉⢠⠿⣄⡀⠀⠀⠀⢸⠀⠀⢀⠈⢿⡲⠤⠔⠀ ⠸⡄⢸⡇⠀⢠⠀⠀⠀⠸⡀⢰⠃⠀⠀⢻⣿⣿⣾⣿⣦⣤⡟⢀⣏⡿⣆⠀⠀⠀⡇⠀⠀⢳⡀⠙⣆⠀⠀ ⠀⠘⠾⠷⣀⠈⢧⠀⠀⠀⢣⡎⠀⠀⠀⠀⢿⣿⣿⣷⣽⣦⣧⣾⣿⣥⠿⡄⠀⠀⡀⠀⠀⠀⣿⢆⠈⢷⡀ ⠀⠀⠀⠀⠀⠉⠛⠿⠦⢤⣠⠇⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⠃⠀⠙⣆⣠⠃⠀⠀⠀⢸⠈⢧⠀⠇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⢹⠿⣏⠁⠀⠀⠀⠈⠳⣄⠀⠀⣀⡼⠀⢸⣦⠇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠘⡆⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠘⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠒⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠶⣒⠒⠠⠤⠤⠤⠤⢤⣤⠒⠉⠉⠉⠛⢧⠉⠉⠲⣤⣈⠉⠢⢄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠙⣷⣦⣀⠀⠀⢀⠄⠈⠀⣉⡡⠼⠯⢍⣓⠒⠂⠬⣿⡑⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠈⣿⡿⠟⠛⢗⡒⠶⢿⣅⠀⠀⠀⠀⠈⠑⢤⣀⠀⠉⠉⠁⠉⠉⠑⠒⠲⠤⣤⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡵⠊⠁⡀⠀⠀⠀⠈⢢⠀⠈⠣⠀⠀⠀⠀⠀⠈⢿⢏⠢⣄⣀⣀⣤⡴⠒⠈⢡⠃⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⣼⣤⡄⠀⠀⠀⠀⢳⠀⠀⢱⠀⠀⠀⠀⠀⠘⡄⢀⠈⢢⡻⣿⠀⠀⢠⠎⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⣼⠏⢹⠇⠀⠀⢠⠀⠀⡇⠀⠈⢇⠀⠀⠀⠀⠀⢷⠘⡆⠀⠀⠹⣆⠔⢇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⢰⣿⠄⡇⢸⠀⠀⠀⠀⠀⠁⠀⠀⠐⠀⠀⠀⠀⠀⢸⡄⢱⠀⠀⡆⢻⣷⣼⣆⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢻⠀⠀⡟⠁⠀⡇⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠘⡆⠀⢸⠘⣧⠈⣿⠉⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢁⡇⠀⢸⠀⣀⡜⠁⡇⠀⠀⠀⠀⠀⡆⠀⢠⠂⠀⠀⠀⠀⠀⢀⠀⠀⡇⠀⠀⡇⢹⠀⢹⡄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡼⠇⠀⢸⠸⡿⠒⢲⠃⠀⡠⠁⢀⠜⠀⠀⡜⠀⠀⠀⠀⠀⠀⡘⠀⠀⡇⠀⠀⡇⠸⠀⠘⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⣏⡜⣁⡴⠃⠀⠔⠁⡠⠊⠀⢀⡼⠁⠀⠀⠀⠀⠀⣰⠁⠀⢀⠇⠀⠀⡇⠀⠀⠀⠃⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⢋⠀⡇⣀⣿⡿⢻⣦⣤⣤⡤⠮⠤⣤⣴⡟⠁⠀⠀⠀⠀⠀⡰⠃⠀⠀⡼⠀⠀⢠⠁⢠⠀⠀⠀⠀ ⠀⠀⡖⠒⢄⠀⠀⠀⠀⢀⡤⠖⢁⡇⠀⠀⡇⠀⣽⡀⠸⣿⣿⣿⣿⠀⠀⠈⠁⠈⠙⣷⣶⣤⠤⠀⣀⡠⠆⡰⠁⠀⢀⠇⠀⣸⠀⠀⠀⠀ ⠀⠀⠘⢄⠀⠣⡀⠸⠉⠏⠀⠀⢸⡀⠠⠀⡇⠀⣿⡇⠀⠙⠛⠓⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⣿⣱⡾⠃⠀⣠⡞⠀⢠⠇⠀⠀⠀⠀ ⠀⠤⢄⠀⠳⡀⠑⢆⠀⠱⡀⠀⠀⢧⠀⡄⢁⠀⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠃⠀⢈⣛⣩⡔⠊⠀⠣⢀⡏⠀⠀⠀⠀⢩ ⢱⡤⠀⢙⣦⣸⠀⠀⠃⠀⠈⢲⣤⡀⠳⣼⣾⡀⢸⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⡇⠀⠀⢀⡾⠁⠀⠀⠀⠀⣸ ⠀⠑⢄⠀⠑⢌⠀⠀⠀⠀⠀⠀⢇⠹⡀⠻⢿⡇⢸⣿⠿⣿⡗⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⣀⡤⣶⣾⣇⠀⣇⢀⣠⠊⠀⠀⠀⠀⠀⡠⠛ ⠀⠀⠘⠯⡉⠳⣄⠀⠀⠀⠀⠀⣼⠹⣧⡔⡟⠙⣼⣷⠀⠸⠀⢼⡇⠉⢻⠛⠻⠿⢿⡿⠋⠁⢠⣿⣉⣙⣿⣟⣉⠀⠀⣀⡀⠤⢶⠯⠀⠀ ⠀⠀⠀⠀⢸⣦⡈⠀⠀⠀⠀⢰⠿⣼⣿⠀⡇⠀⠹⣿⣄⠃⠀⠀⡇⠀⢀⡵⢖⠒⠉⠀⠀⢀⠎⠛⢻⠛⣿⣿⡿⠿⣿⣿⠳⡀⠁⠀⠀⠀ ⠀⠀⠀⣰⠋⢻⠙⠢⠤⡠⠴⡋⠸⡇⢸⠀⢻⠘⠀⢿⣿⣦⣼⣀⡇⣠⣿⠒⣌⣆⠀⠀⢀⡞⠀⢀⠃⢠⣿⣿⡇⠀⠀⠈⠲⣷⡄⠀⠀⠀ ⠀⢠⠞⢻⠀⠈⣆⢆⠀⢆⠀⢰⠀⠥⢸⡆⠘⡆⠇⢸⣾⠈⢿⠚⠷⣹⠁⠉⡹⠹⡀⣠⢻⠁⠀⡘⠀⠸⡿⣿⡇⠀⠀⢀⣴⣿⡇⠀⠀⠀ ⠀⡇⠀⠸⠀⠀⠘⢞⡆⠈⠄⢀⡇⠀⢸⣷⡘⣇⠰⣿⡇⠀⡜⠃⠀⣧⠤⣤⡇⠀⠉⠁⡆⠀⠀⡇⠀⠀⠀⡆⠀⢀⠔⢡⡯⡟⣇⠀⠀⠀ ⠀⢱⠀⠀⠀⠀⠀⠀⠉⠏⠉⠁⠀⠀⢸⠙⣷⠋⠀⢻⡇⠀⣿⠀⠘⠻⣯⠽⠀⠀⠀⢰⠁⠀⣸⡇⠀⠠⠀⡇⢠⠊⠀⣌⠴⡇⢸⡆⠀⠀ ⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣠⡿⠀⠀⠘⣿⠀⢾⣧⠀⠀⠀⠉⠒⠦⠄⡞⠀⢀⠟⡇⠀⠀⣆⣇⠇⠀⠀⣇⠴⢇⠈⢃⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⠀⠀⠀⡀⡟⡄⢸⠈⢢⠀⠀⠀⠀⠀⢀⠇⠀⢸⠀⣡⠀⠀⠘⣿⠀⠀⠀⠸⡀⠈⠀⠀⠙⠒

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣾⠿⠿⠿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣰⣾⠿⠛⠛⠿⠿⢿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⡿⠟⠋⠁⠀⠀⠀⠀⠀⢻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⢰⣿⠃⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⠀⠀⠀⠀⠀⠀ ⠀⠀⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣷⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀ ⠀⠈⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣷⡀⠀⠀⠀⠀ ⠀⠀⢸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣄⠀⠀⠀ ⠀⠀⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡆⠀⠀ ⠀⢸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡀⠀ ⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⠀ ⢸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀ ⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡆ ⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇ ⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇ ⠸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀ ⠀⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀ ⠀⠘⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣷⣶⣦⣤⣴⣶⣶⡿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠁⠀ ⠀⠀⠹⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠃⠀⠀ ⠀⠀⠀⠈⠻⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⠟⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠻⢿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣴⣶⡿⠟⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⢿⣶⣶⣶⣶⣶⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣶⣶⣶⣶⣿⣿⡿⠿⠿⠟⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⢿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⠈⣿⣿⡏⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⠀⠘⣿⠃⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⡇⠀⠀⢹⣧⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⠇⠀⠀⠀⢻⣦⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⠀⠀⠀⠀⠈⢿⠀⠀⠀⠀⣀⣀⡀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⡄⠀⠀⠀⣠⡀⠀⣤⠙⢿⡄⠀⢸⣿ ⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠉⢡⣄⠉⣤⡄⢻⣆⣿⣿ ⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠁⠀⠉⠀⠀⣹⣿⣿ ⣿⡟⠀⠀⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠶⠶⠶⠶⠶⠶⠶⠶⢶⣿⣿⣿ ⣿⡇⠀⠀⠀⠈⢿⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣼⣿⣿⣿ ⣿⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠚ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠰⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠁⠀⠀⠀⠀ ⠀⠀⢀⡦⢤⡀⠀⢠⣧⠈⠓⢦⣀⠀⠀⠀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⣄⣿⠀⠉⠁⠈⣿⣲⣶⣦⣐⠛⠋⠉⠁⠀⠀⠀⠈⠉⠙⠒⠶⠒⠒⠚⠉⠉⠉⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠖⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠ ⠀⠘⠓⠋⠀⠀⠀⠀⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣶⣶⣶⣶⣶⣶⣶⣶⣿⣠⠇⠀⢀⣤⣤⠀⠀⠀⠰⣶⣮⠽⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔⠊⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣶⣶⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⡟⠀⠀⣾⣿⣼⠀⠀⠀⠀⠱⢄⣀⠀⠀⠀⠀⢀⣀⣀⡤⠤⠖⠊⠉⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⡿⢹⣿⣿⣿⣟⠸⣿⣿⣿⣧⣴⣾⣿⡟⠀⠀⠀⢸⣿⣷⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⡟⣼⡟⠀⣿⡿⣽⠟⠀⠀⢻⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠙⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣥⣿⣤⢠⡟⠀⠋⢀⣄⣀⣀⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠈⢻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡼⠋⢹⣿⣿⣿⠃⠘⣿⣿⡏⠁⠀⠀⠈⠱⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠈⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⠀⠙⠿⠛⠀⠀⠀⠀⠀⠘⠿⠿⠛⣿⣿⣿⣿⣿⠙⠆⠀⠀⠀⠀⠀⢰⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣇⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⢰⣿⣿⣿⡿⠉⠹⣄⠀⠀⠀⠀⢠⣾⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⠀⠀⠀⠀⠀⠀⢁⡨⠟⠋⠉⠉⠉⠉⠙⠳⢤⣀⣠⣶⣿⠿⠿⠋⠁⠀⣴⣯⡍⠹⢤⣴⡿⠋⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⡟⠀⠀⠀⠀⠀⢠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣄⣍⣠⣄⣤⣼⣿⣿⣿⣿⣧⡀⢿⡀⠀⠀⠀⠀⠸⡀⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣤⢸⡄⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠧⢼⡁⠀⠀⠀⠀⠀⡇⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠻⠼⠅⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣀⣶⠚⠿⢿⡿⠋⠁⠀⣹⣿⣿⣾⣿⠛⠀⣸⠉⢱⡀⠀⠀⠀⠀⢸⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢹⣉⣳⡶⠚⠀⠀⠀⠸⣍⢁⠈⠉⠀⢀⡾⠁⠀⢠⡇⠀⠀⠀⠀⣼⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⢀⡞⠉⣷⠶⠶⠋⠀⠀⠀⡼⠁⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡋⣀⠜⠁⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠦⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠑⠒⠒⠒⠒⠒⠚⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡤⣶⡤⣤⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠛⢉⡼⠛⠁⣠⡟⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠖⠛⠉⠉⠽⠓⠒⠓⠒⠿⠉⠛⠒⠦⣤⡀⠀⣠⡶⠋⠁⠀⢠⡟⠀⠀⠴⠟⠛⢳⡆ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⣶⡶⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢯⡀⠀⠀⢀⡏⡆⠀⠀⠀⢀⣼⣋⡅ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠉⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⣄⣸⠁⠀⠀⠀⠀⠉⠀⣸⡇ ⠀⠀⠀⠀⣀⣠⠴⠞⠋⠀⣀⡴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣄⠀⠀⠀⢀⣴⠏⠀ ⣤⡴⠒⠛⠉⠀⠀⠐⠒⠛⣷⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣌⣛⣒⣤⠿⠟⣶⠆ ⢹⣧⡀⠀⠀⠀⠀⠀⠀⣼⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠉⠀⠀⣰⠏⠀ ⠀⢿⡷⣄⠀⠀⠀⠀⢰⡷⠋⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠉⠛⣯⠀⠀ ⠀⠈⢷⣈⠙⢶⣒⠛⠋⢠⠞⠀⠀⠀⠀⠀⡴⠀⢠⡏⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⣿⡦⣴⠟⠁⠀⠀ ⠀⠀⠀⢹⡟⠂⠩⠛⢲⡏⠀⠀⠀⠀⠀⢰⡇⣀⣿⠀⢸⠀⠀⠀⠀⠀⠀⡄⠀⠐⢺⢷⠂⠰⡄⠀⢸⡀⠀⠀⠀⠀⠀⠀⠹⣟⡁⠀⠀⠀⠀ ⠀⠀⠀⠈⠛⠲⢶⠀⡾⠀⠀⠀⠀⠀⢠⢸⡷⠫⢸⡆⢸⣆⠀⠀⠀⠀⠀⢳⠀⢀⡿⠘⢧⡀⢹⣄⠀⣧⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢤⣤⡆ ⠀⠀⠀⠀⠀⠀⠈⢹⠁⢰⠀⠀⠀⠀⢸⢸⡅⠀⠀⠻⣎⣿⢦⣀⠀⠀⠀⣸⡀⣼⣷⣾⣿⣿⣾⣿⢦⣿⠀⠀⠀⠀⠀⠀⠀⢷⠦⠴⠖⠋⠁ ⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⡄⠀⠀⠀⣿⠸⣇⠀⠀⠀⠈⠙⠂⠙⠷⣄⣀⣿⠟⢿⣿⡏⣀⡀⢙⣿⣿⣏⡀⠀⠀⠀⠀⢸⡀⠸⡆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⣿⡀⠀⠀⢸⡷⢿⣶⣶⣦⣍⡢⠀⠀⠀⠀⠙⠀⠀⢸⣟⠉⠽⠿⠍⣻⣿⠟⠀⠀⠀⠀⠀⣸⠁⢰⠇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⣧⡿⢦⣄⡀⣷⠀⠀⠈⠉⠛⠻⢦⠀⠀⠀⠀⠀⠀⠠⠿⠤⠤⠤⢒⡿⠃⣠⡞⠀⠀⠀⣠⡏⢀⡞⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣬⠟⠁⠀⠉⢉⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⡯⠴⣺⣿⠀⠀⢀⡴⣿⡖⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣠⡤⠶⠋⠁⠀⠀⠀⢀⡄⠈⢳⣄⠀⠀⠀⠀⠀⠠⣄⣠⣤⣀⡄⠀⠀⠀⠀⠀⢀⡴⠋⣯⣤⠖⠋⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⣠⡶⠚⠉⢁⡆⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠈⠓⣶⣄⣀⠀⠀⠈⠉⠉⠁⠀⠀⠀⣀⡤⠞⠋⠀⠀⠀⡀⠀⠀⠀⠸⣷⠀⠀⠀⠀⠀⠀⠀ ⢸⠟⠀⠀⣴⡟⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⣴⣿⣿⣤⡉⠛⢿⡖⠦⠤⠤⠖⢛⣿⠋⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠹⣷⣄⡀⠀⢀⡀⠀ ⢸⠀⠀⢸⡿⠁⢠⡄⠀⠀⠀⠀⡇⠀⠀⢀⡼⠛⠻⣿⣮⣙⣦⡈⣿⣆⠀⠀⢀⡾⠛⢷⣤⡀⠀⠀⠀⠀⢸⠀⠀⠀⢰⡄⠙⣮⡉⠉⠉⠁⠀ ⠘⣧⠀⡏⡇⠀⠸⡇⠀⠀⠀⠀⢻⠀⢀⡏⠀⠀⠀⠘⣿⣿⣿⣷⣽⣿⣦⣤⣼⡇⢀⡿⢸⠿⣆⠀⠀⠀⠈⣧⠀⠀⠀⢳⡄⠈⠻⣆⠀⠀⠀ ⠀⠈⢷⣇⣧⡀⠀⢹⣄⠀⠀⠀⠈⣇⢸⠁⠀⠀⠀⠀⠨⣿⣿⣿⣿⣆⢹⣆⣸⢡⣿⣷⡟⣠⣿⡀⠀⠀⠀⣿⠀⠀⠀⠀⣿⢆⠀⠘⢷⡀⠀ ⠀⠀⠀⠀⠈⠙⠲⢤⣹⣦⣀⠀⠀⠘⡟⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣾⠋⠈⢷⡄⠀⢀⡟⠀⠀⠀⠀⢹⡌⢷⡀⠈⢷⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠉⠛⠓⢶⡇⠀⠀⠀⠀⠀⠀⠀⠀⠹⣮⣿⣿⣿⣿⣿⣿⣽⠃⠀⠀⠀⠹⣦⠞⠁⠀⠀⠀⠀⢸⡇⠀⢳⠀⢸⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⣿⠻⣏⠀⠀⠀⠀⠀⠀⠈⢳⣄⡀⠀⠀⣀⡾⠃⠀⢸⣇⡞⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢺⠇⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠋⠉⠀⠀⠀⠼⠋⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣀⣀⣀⣽⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣤⣶⣤⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣶⣿⣿⣷⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⣸⣿⣿⣮⣻⣿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⣤⣤⣄⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣾⣧⣼⡙⢻⣿⣿⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀⠀⠀⠘⢷⣿⣿⣿⣟⣿⣿⣿⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⠿⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋⠀⠙⢿⣦⠀⠀⠀⠻⢦⣴⣿⣷⠿⠟⠀ ⠀⠀⠀⣠⣤⣀⣠⣤⣴⣾⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀⢉⣿⣿⣿⡏⠛⢿⣿⡿⣄⠁⡀⠀⠘⣿⣧⡀⠀⠀⣾⠉⠀⠀⠀⠀⠀ ⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⡿⠛⣹⣿⣿⠟⠁⠀⠀⠀⠀⠠⠴⠟⡿⠀⠈⢷⣤⠟⠉⢳⡈⠀⠣⡀⠀⠈⠛⠿⣶⣬⣉⣀⣀⡀⠀⠀⠀ ⠀⠀⠀⠈⠙⠛⣿⣿⠿⠁⢀⣸⡿⠋⠉⠀⠀⠀⠀⠀⢠⡆⠀⠀⡿⠚⠋⠒⠛⠛⠓⠬⣧⠀⠀⢿⡀⠀⠀⠀⡈⠉⠉⣹⣿⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⣿⣿⡶⠾⠛⠉⠀⠀⠀⠀⠀⢠⠀⠀⢸⡇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⢸⡇⠀⠀⠀⠙⢿⡿⠟⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⡿⣶⣤⣀⣠⣤⣤⠴⠂⠀⠀⣾⠀⠀⢸⣇⠀⠀⣇⠀⠀⠀⢰⡀⠀⠀⢸⠀⠀⣸⡇⠀⢀⡀⠀⠈⢿⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⣿⠃⠀⠉⠉⣹⠏⠀⠀⠀⠀⢰⡇⠀⠀⢸⢿⡄⠀⢹⡀⠀⠀⠻⡇⠀⠀⣸⠀⢠⡏⢳⠀⠀⢻⡀⠀⢸⣷⠀⠀⠀⠀⠀ ⠀⠀⣠⣴⠟⠁⠀⢀⡄⢀⡿⠀⠀⠀⠀⢀⣾⠁⠀⢀⡿⠤⠿⣄⠀⢷⡀⠀⠀⠀⠠⠤⣿⢠⠾⠂⠈⢧⠀⠈⣧⠀⢸⡿⠀⠀⠀⠀⠀ ⢰⣾⠛⠁⢀⣠⣶⡿⠁⢸⡇⠀⠀⠀⢀⣾⠃⠀⢀⡞⠁⠀⠀⠈⠙⠶⠷⠀⠀⠀⠀⠀⠛⠋⠀⠀⠀⠈⣇⠀⠹⣆⢸⡇⠀⠀⠀⠀⠀ ⠈⠛⠿⠿⠛⣿⡟⠀⠀⠸⡇⠀⠀⢀⡾⠁⠀⣠⣯⣤⣤⣤⣤⣁⡀⠀⠀⠀⠀⠀⠀⠈⣩⣥⣤⣤⣤⣄⣸⣆⠀⢻⣾⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣰⡟⠀⠀⠀⠀⣷⢀⡴⠋⠀⣠⣾⠟⠛⣿⠛⢻⣿⣛⡿⠆⠀⠀⠀⠀⠀⠘⡟⢻⣿⠛⡿⠻⡿⣿⣧⣄⠙⣷⣤⠀⠀⠀⠀ ⠀⢀⣴⠾⠋⠀⠀⢀⣠⣴⣿⣏⣠⡤⠞⠛⣏⠀⠀⠻⣀⠈⠛⣡⠇⠀⠀⠀⠀⠀⠀⠀⢹⣄⠋⣠⡇⠀⠈⡏⢻⡍⠻⣿⠛⠀⠀⠀⠀ ⠀⠹⣷⣶⣶⣾⣿⣿⣿⣿⠉⢻⡀⠀⢠⡀⠘⣦⡀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⢧⣸⣿⡆⣼⠇⠀⠀⠀⠀ ⠀⠀⠀⠉⠉⠉⠹⣿⣿⠿⣧⡀⢳⡄⠈⠛⠦⣬⣹⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠟⠘⠿⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣿⣦⡀⠀⢾⣷⠖⠒⠲⢦⡀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⣠⣶⣿⣶⠾⣧⣤⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣶⡄⢿⣷⣶⣶⢾⠷⣤⣄⣀⣀⣀⣀⣀⣤⣤⣾⣿⣿⣿⣿⠶⠶⠟⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣉⣽⢿⣿⠏⠹⣾⡿⣿⣿⣼⣶⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⢠⣏⡟⣠⣾⣿⣦⣴⣶⣿⠟⢁⣿⣿⣿⣿⣿⣿⢿⣿⣶⣝⣻⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⣿⢻⡏⠁⠹⠿⠿⢿⡿⠁⠀⢸⠹⢿⣿⣯⣭⠶⣿⣽⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠢⠐⠁⠀⡤⢠⠃⠀⢀⢎⠮⢀⡀⠀⠀⠀⠀⠀⠀⠀⠠⡇⢱⠀⢂⠀⠀⠂⠀ ⠀⠀⠀⡠⠊⢀⡾⠀⢠⢣⠃⠀⠀⠻⢦⡀⠀⠀⠀⠀⠀⠀⣧⠈⣧⣾⠀⡄⠀⠀ ⣠⠘⠭⠄⢊⢿⠃⡠⣱⠍⢂⠀⠀⠾⠈⠃⠀⠀⠀⢀⣀⡠⣼⠀⣿⢻⣇⡇⢸⣿ ⠀⠉⡇⠐⡇⡆⢰⣽⠋⠀⠀⠁⠒⠒⠂⠀⠀⠀⠐⠋⣭⠀⠀⠀⡿⠈⡏⠁⡀⢻ ⠀⠀⡡⢊⣱⢀⣞⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⡀⠀⠀⡆⠁⠀⣃⠀⠃⠀ ⠀⢈⡩⢒⢼⠞⠂⠇⠀⠀⠀⣾⣍⡀⠒⠀⠄⡀⠀⠀⠈⠉⠁⡇⡆⢰⡝⢸⡲⠖ ⠐⡡⠂⡡⠎⣀⠀⠈⡄⠀⠀⢿⣿⣿⣷⣶⣤⣬⣴⠀⠀⠀⢀⡇⡇⣿⡇⡆⠀⠀ ⠊⡠⠞⠛⠛⡳⠞⡟⠈⢆⠀⠘⡕⢌⣉⣻⣿⡿⠋⠀⠀⢠⡪⡇⢠⠫⡷⢭⠀⠀ ⢰⣀⣀⣀⡠⠵⢶⠁⡀⠸⠱⣄⠈⠒⠒⠂⠉⠀⣀⠤⠊⠃⠣⢀⡎⠢⡈⢆⠀⠀ ⠈⠀⠀⠀⠀⠀⡄⠀⠐⢄⢣⠙⠛⠒⢀⠤⠋⠁⣮⢶⡄⡆⢀⠎⠣⠀⢱⠈⡄⠀ ⠀⠀⠀⠀⠀⢠⣀⠠⠄⢰⠢⢑⣀⠒⠁⠀⠀⡸⢜⡤⠏⠑⢢⠀⠀⠀⠀⠀⠁⠀ ⠀⣆⡘⡀⠀⠀⠀⠀⠀⢸⠀⠀⡤⠓⡀⠀⢠⠁⠀⠈⠒⠄⣈⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠉⠓⠶⣤⣀⡀⠀⡼⠀⡜⠁⠀⠘⢄⠂⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⡿⠿⠿⢿⣿⣯⣥⣶⣷⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠾⠛⠋⠁⠀⠀⠀⠀⠀⠘⣿⣿⠉⠀⠀⠀⠉⠛⢷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠛⢷⡀⠀⠀⠀⠀⠀⠈⠻⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀⠻⣄⠀⠀⠀⠀⢦⡀⠀⠹⣷⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⢀⣤⣤⣤⣤⡀⠀⠀⠀⣠⠟⠁⠀⠀⠀⢠⣿⣦⣤⣀⠀⠈⠳⣄⠀⠈⢿⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠋⠀⠀⠀⠀⠰⠛⠛⠛⠛⠛⠁⠀⢀⡼⠋⠀⠀⠀⠀⠀⠘⠛⣿⠛⠛⠷⠀⠀⠈⠳⢄⠈⣿⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣾⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⠱⢼⣷⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣰⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣆⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⣼⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣻⣦⠄⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀ ⠀⠀⠀⣸⡿⢳⡏⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⠿⢿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣦⣀⣀⡀⠀⠀⠀⠀⢿⡇⠀⠀⠀ ⠀⠀⢰⣿⠃⣼⠃⠀⣀⣤⣴⣾⣿⣿⣿⣿⠟⢷⡄⠉⢻⡇⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡿⢷⡌⠙⢿⣿⣿⠏⠀⠀⠀⠀⢸⣿⡄⠀⠀ ⠀⠀⣿⡇⢠⡟⠀⢀⣿⠻⣿⣿⣿⡟⠁⠀⢀⣤⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⢛⡃⠀⣿⠀⠀⢿⣿⡄⠀⠀⠀⠀⢸⡿⣷⡀⠀ ⠀⢸⣿⢀⡿⠁⣠⣾⠃⠀⠈⢻⣿⡀⠀⠀⠈⠉⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠃⠉⠁⠙⣿⠀⠀⣾⠉⠻⣦⡀⠀⠀⢸⡇⢹⣷⠀ ⠀⣿⣧⡾⠁⣼⡿⠀⠀⠀⠀⢰⠋⠻⠶⣤⣤⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⣄⣠⡾⠃⠀⠐⢿⡄⠀⠈⠳⣄⠀⢸⡇⠀⣿⣆ ⠰⣿⡟⠁⢰⣿⠁⠀⠀⠀⠀⣾⣠⣤⣤⡀⠀⠀⢀⣠⣶⠾⠛⠛⠛⠿⢶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠹⣆⢸⡇⠀⢻⡇ ⣼⡿⠀⠀⢸⡿⢶⣦⣄⣴⡾⠛⠁⠀⠈⠻⣦⣤⡞⠋⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣦⡀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⢻⡄⣿⠀⢸⡇ ⣿⠁⠀⠀⠸⣷⡀⠙⣿⠃⠀⠀⠀⠀⠀⠀⣹⣷⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠙⣷⡄⠀⠀⠀⠀⠀⠀⣾⠿⣆⠀⠀⢸⡇⢻⡆⢸⡇ ⠏⠀⠀⠀⠀⠹⣧⡀⠀⠀⠀⠒⢦⣤⣤⣼⢻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡆⠘⣷⠀⠀⠀⠀⣠⡾⠋⠀⠙⣦⡀⣼⠁⠘⣷⣿⠇ ⠀⠀⠀⠀⠀⠀⠹⣷⡀⠀⠀⠀⠀⢿⣄⠻⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢠⣿⡶⠶⠞⠛⠉⠀⠀⠀⠀⢸⣷⠏⠀⠀⠹⣿⡆ ⠀⠀⠀⠀⠀⠀⢀⣾⠿⣦⣀⡀⠀⠀⣻⣷⣦⠀⠀⠀⠀⠒⠶⣤⣄⡀⠀⠀⠀⠀⣠⣾⡿⠿⢦⣤⡀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⢿⡇ ⠀⠀⠀⠀⠀⣰⡿⠏⠀⠀⠉⠙⠛⠛⠋⠈⣿⣇⠀⠀⠀⠀⠀⠀⠈⠻⣦⠀⢀⣴⡿⠋⠄⠀⠀⠈⢻⣆⣠⡶⠟⠉⠀⠀⠀⠀⠀⠀⡼⣿ ⠀⠀⠀⠀⣰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠻⣷⣤⣀⡀⠀⠀⠀⠀⠈⣠⣾⠏⠀⠀⠀⠀⠀⢠⣾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿ ⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠉⠛⠻⠿⣶⣶⡶⠟⠋⠁⠀⠀⢀⣠⣶⣶⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿ ⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢸⣷⠚⠛⠛⠓⠒⠲⠖⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢛⣧⠀⠙⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿ ⠀⠀⠀⢸⣷⠀⢀⠀⣀⡀⠀⠀⠀⡛⢶⠦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⠶⠶⠛⠉⠀⠀⠀⠹⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠋⠉⠀⠀⠀⠀⠀⠄⡈⠉⢿⡀⢀⣴⣏⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⣠⣤⡴⠶⠒⠒⠓⠲⠶⠦⡄⠀⢀⣷⠯⠤⠤⠤⠈⠉⠉⠛⠲⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠷⡫⠗⠉⢀⡀⠤⢀⢂⡤⠀⡀⢀⠀⠞⠁⠀⡀⢀⠀⠄⡈⠠⠀⠄⡀⠈⠳⣦⡀⠀⠀⠀⠀⠀⠀⠠⠀ ⠀⠀⠀⠀⠀⣠⣤⢤⠴⠟⠒⣠⠞⣡⠖⢋⠡⣐⡦⠞⠉⠀⡐⠀⣠⠀⠄⢈⠐⠀⠄⡈⠠⠀⠁⠌⡀⠐⠠⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢹⡀⠀⠠⠀⣰⡷⢋⠴⡘⠌⡶⠋⠀⠠⢈⠀⠀⣰⠋⠀⠂⠄⠂⠁⠄⠠⠀⠻⡄⠀⠀⠌⠀⠌⠠⠀⠹⣆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⠶⠶⢺⢟⡡⢋⠴⣑⡾⠁⠠⠁⠂⠄⡀⢀⡏⠀⠌⠐⠠⠁⡈⠄⠁⠂⠄⠹⡄⠀⠠⠈⡀⠂⢁⠀⢹⡆⠀⠀⠀⠀⠀ ⠀⠀⢠⣤⣄⣠⣟⣀⡴⡏⢦⡹⣘⢲⡞⠀⠂⡁⠂⠡⠐⠀⢸⠀⠠⠀⠀⢁⠂⠠⢈⠐⠀⠀⠀⣧⠀⢀⠁⠄⠁⠂⡐⠈⣷⠀⠀⠀⠀⠀ ⠀⠀⢸⡧⣏⡭⢭⡙⢶⡙⢦⢣⢓⣾⠁⡈⠐⡀⢁⠂⢁⠂⣿⠀⠐⠀⠀⠀⠈⠀⠄⠐⠀⢀⠀⢳⠀⠂⠈⠄⠈⠄⠐⠀⠸⣆⠀⠀⠀⠀ ⠀⠀⠀⣿⢎⡵⣫⠝⣦⣙⡎⢧⣻⠇⠠⢀⠡⠐⠠⠈⠄⡀⣿⠀⠐⠀⠀⠄⡀⠠⠀⠌⠀⠄⠂⢸⠀⠡⠈⢀⠁⠌⠠⠁⠄⠹⣆⡀⠀⠀ ⠀⠀⠀⠘⢿⢶⣿⣾⣟⣭⠾⠛⠁⡐⠄⠂⠄⡁⢂⠁⠂⢄⣿⡆⠡⢀⠁⠂⠄⠡⠐⠠⠁⠌⠀⣿⠀⡁⠌⠈⡇⠀⠡⢈⠠⢀⠈⠉⢙⣶ ⠀⠀⠀⠀⣸⡷⣾⡹⣇⣀⠠⠀⣁⡴⢀⠁⡂⠐⠠⢈⠐⣸⡏⣧⠐⠠⢈⠐⡈⠄⢁⠂⠡⠈⢤⡿⡇⠀⠆⠁⣿⠀⠡⢀⠢⡄⠈⢐⡸⠃ ⢶⣶⡶⣞⣯⡳⢧⣟⡼⣫⢟⣿⠟⠁⢂⠰⢀⢉⣄⣢⣤⣏⣀⡸⡇⢠⠃⠄⡐⠈⠄⠌⠠⣁⣾⡤⢷⠬⠄⠂⠸⡆⠁⠂⠄⠹⣟⠋⠁⠀ ⠘⣧⣟⣳⢮⣽⣳⢮⣷⡽⠛⠁⡄⠊⠄⢂⡴⢋⠉⣴⠋⠀⠁⠉⠹⡆⠐⠂⠄⠹⡆⠈⠄⣹⠇⠀⠈⣧⠀⡁⠂⢷⡈⠌⡐⢀⠙⠦⣄⡀ ⠀⢠⡿⣿⡻⣭⢿⡉⠠⠄⢊⠡⢀⣡⠼⢋⣐⡴⣏⣁⣀⣀⠰⠦⢄⠙⣎⠈⠤⠁⢻⡄⣼⠓⣀⣀⣀⣈⡳⣄⠡⠈⠳⣄⠐⢂⠐⡀⣸⠃ ⠀⠀⠻⢧⣿⣵⣿⠿⣷⢶⡶⠛⠛⠓⠛⣿⣿⡿⣿⠿⣿⣿⢿⣶⡄⠀⡼⠷⣄⠃⠄⢻⣿⣿⣿⡿⣿⠿⣿⣿⡛⠲⠳⣿⣤⣤⡴⠞⠁⠀ ⠀⠀⠀⠀⠀⠀⢻⡝⣮⠟⣧⠠⢡⠊⠄⣟⠃⠀⢻⣝⣿⢿⣞⡇⠀⠹⠧⠴⠞⠛⠲⠶⢿⣺⡿⣷⣻⠁⠈⡼⢁⢐⠠⢻⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⣿⠀⢹⡠⠙⣧⠈⠜⣆⠀⠈⠻⠤⡬⠟⠁⠀⠀⠀⠀⠀⢀⠀⠀⠈⠳⠤⠼⠋⠀⣼⣁⣦⠋⢤⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⠀⠀⠙⣆⠈⣧⠐⡈⠷⢬⡼⠧⠀⠂⠄⡀⠄⠐⠀⠄⠀⠀⠀⠀⠀⠂⠄⠄⡀⢂⠐⠄⡀⢉⡟⢈⣼⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣾⠓⠶⠶⠾⣿⢾⣧⡈⠒⡌⢳⡀⠠⠁⠂⠀⠄⠀⠄⠀⢸⣿⣻⠗⠀⠁⠀⠄⠀⠂⠄⠂⣰⠞⡁⣲⠏⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢶⣤⣦⠔⡈⢷⣫⢷⣧⡐⢁⠻⣷⣤⣄⣀⡀⠀⠀⠀⠈⠙⠁⠀⠀⠀⢀⣤⣠⣤⣶⣾⠏⢐⣴⣿⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢰⡶⠚⣉⠡⢄⣢⡵⢟⣧⡿⡳⣿⣿⣶⣾⣿⠿⣿⣿⣿⣿⣷⣶⣶⣶⣾⣿⣿⣿⣯⡿⣯⢷⡯⣶⠟⣩⠋⡽⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠙⠒⠒⣾⠋⣡⢂⣿⢻⡷⣽⣿⣿⣻⡹⢿⣿⣷⣛⢯⡻⣿⣿⣿⣿⣿⣿⣳⣷⢻⣿⣿⣿⣥⣿⣀⡁⠀⠰⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⡏⡐⢢⡞⠁⠀⢛⡿⠙⠻⢿⣿⣆⠌⡙⢛⠻⣿⣾⣿⣿⣿⣿⣟⣻⣶⠾⣿⣿⢻⣿⣿⣿⣿⣷⡶⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣷⡴⠋⠀⠀⢠⡟⢡⠙⣢⠒⡌⢻⣮⣤⣷⣶⣺⣿⣿⣿⣿⣿⣿⣿⣷⣤⣟⢻⠾⣻⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀ ⠄⠀⠀⠀⠀⠀⠀⢘⠉⠀⠀⠀⠘⠋⠳⢮⣤⣃⠜⡠⣟⡛⠛⠟⠚⣽⣟⣾⣿⣿⣿⡿⣿⣯⣿⣯⢿⠟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠶⠒⠚⠛⠋⠉⠉⠉⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⠴⠒⠚⠉⠉⠉⠉⠉⠓⠒⠦⣄⡀⠀⠀⠀⣠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⡀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⣤⢤⣀⠈⢫⢹⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠈⠉⠑⠲⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠹⣄⠈⢣⠼⢻⠞⠁⠀⠀⠀⠀⠀⠀⣀⣴⣋⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⣤⠟⠢⣄⣀⠀⠀⢀⣀⣀⣀⠬⠷⢿⡤⠤⠤⠤⠤⠲⢾⣉⠁⠀⠈⠙⠢⣀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣴⣄⣤⠤⠶⠖⠋⠁⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠙⣄⡀⠀⠀⠀⠀⠀⠙⠢⣄⠀⠀⠈⠣⡀⠀⠀⠀⠀⠀⠀⠘⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⠛⠦⠤⢤⡴⠃⠀⠀⠀⠀⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⡱⠳⣄⡀⠀⠀⠀⠀⠀⠈⠑⢄⠀⠀⠈⢦⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⣠⢋⡞⠁⠀⠀⠙⠲⢤⣄⡀⠀⠀⠀⠀⠳⣄⠀⠈⢣⡀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡼⠁⠀⡤⣄⡀⠀⠀⠀⠀⠈⡷⣄⠀⠀⠀⣰⢃⠎⠀⠀⠀⠀⠀⠀⢠⢧⠏⠓⠢⠤⢄⣀⣈⢦⠀⠀⢣⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⣸⠃⠀⢸⡙⠒⠬⣍⣑⡒⠒⣺⡅⠈⠙⢦⣠⢃⠎⠀⠀⠀⠀⠀⠀⠀⡞⡎⠀⠀⠀⠀⠀⠀⠈⠉⢳⡀⠀⢳⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀ ⠀⢠⡏⠀⢀⡿⢭⣗⣲⠤⠤⣍⣩⡏⢀⣀⣀⡀⠈⠛⠲⠤⣄⣀⠀⠀⠀⢸⢻⠁⡤⠒⠒⢤⠀⠀⠀⠀⠀⢳⠀⠘⡇⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀ ⠀⣸⠀⢀⢞⡇⢸⠀⠉⠉⠉⠉⢹⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠓⠺⠞⠒⠒⡒⠒⠒⠒⠒⢲⡖⠊⠙⣇⠀⢸⡀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀ ⠐⡏⣠⠏⢸⠁⡏⠀⠀⠀⠀⠀⡏⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣷⣶⣤⡀⠀⡷⠀⠀⣹⠀⢸⡷⣄⠀⠠⡇⠀⠀⠀⠀⠀⠀ ⢠⣿⠏⠀⢸⠀⡇⠀⠀⠀⠀⣸⠁⢠⣾⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠋⡾⠛⠉⢻⣿⣿⣿⣾⡷⠀⠀⠈⣧⣴⣿⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀ ⠀⠉⠀⠀⣸⠀⡇⠀⠀⠀⠀⣿⡛⣿⢫⡟⠁⠀⢹⣿⡆⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⢀⣼⣿⣿⣿⢿⠀⠀⠀⠀⢹⣿⣿⣿⠀⠸⣇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⢀⡇⠀⠀⠀⢠⡇⢧⠹⣼⠗⠠⠖⠛⠛⡇⠀⠀⠀⠀⠀⠀⠀⣾⠉⠉⠀⠀⠀⠀⣸⢸⠀⠀⠀⠀⡟⢸⣿⡿⠀⠀⢹⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣸⣧⠀⠀⠀⢸⠁⢸⠀⠸⡄⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⢀⡏⡏⠀⠀⠀⣸⣗⡾⠟⠁⠀⠀⠘⣧⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⣿⡿⡀⠀⠀⣿⠀⢸⠇⠀⢳⡀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⠤⣠⠤⠋⢀⠇⠀⠀⢠⠏⠀⠀⠀⢀⠀⠀⠀⠸⣆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣼⠀⠳⡄⠀⢸⠀⢸⡀⠀⠀⠈⠉⠉⠁⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⢠⠏⠀⠀⠀⠀⡏⠀⠀⠀⠀⠹⣄⠀⠀⠀ ⠀⠀⠀⠀⢰⠇⢀⠀⠙⢦⡘⡆⢰⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⢀⡇⠀⣰⠋⢠⠀⠀⠀⢰⠷⢤⣀⠀⠀⠀⠘⣆⠀⠀ ⠀⠀⠀⢠⡏⠀⢈⣆⠀⠀⠙⢷⠘⣾⣮⡑⠲⢤⣄⣀⣀⠀⠀⠙⢲⣶⠚⠀⢀⣀⣀⣤⠤⠖⣿⢀⠞⠁⠀⢘⡆⠀⢀⡟⠀⠀⠀⠉⠓⠒⠶⠼⣷⡄ ⠀⠀⢠⣟⡤⠖⠋⠹⣄⠀⠀⠀⠀⠈⢑⠫⢷⣦⣤⠤⢭⠉⣩⣿⠿⠯⣭⣽⣿⣿⣷⡄⠀⠠⢿⡋⠀⠀⢠⠞⣧⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠁⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⣼⠀⠀⢠⣿⠉⠉⣰⣿⣿⣤⣾⣿⣿⣿⠛⠙⣿⣆⣠⠟⣇⢀⣴⠋⠀⢸⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣄⣸⢻⣄⡴⠋⢸⡦⠔⠻⣝⡿⠉⠛⢇⠈⢟⡄⡀⣿⣿⣷⣄⡸⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠘⡋⠀⢰⣏⡀⠀⣀⣴⡇⠀⠀⢠⡇⠘⣿⠀⢻⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁⠀⠀⠸⢿⣿⣷⣿⣿⣇⠢⡑⢢⠐⡌⢡⠂⡔⢡⠘⡄⢃⠌⡩⢏⡍⡙⢩⠑⡌⢞⡋⠿⢿⣿⣯⣽⣿⣿⣿⠭⣿⣿⠱⣎⠳⢭⡙⢦⢣⣿⣿⡟⠿⣿⣿⣿⣿⣿⣿⣿⣾⣵⣣⣧⢫⠽⣿⣆⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⢂⠻⣿⣿⣿⣿⡰⢁⠢⡁⢆⠡⡘⢠⠂⡅⢒⠨⢄⡑⢊⠤⠑⡂⠥⡘⠤⡑⢂⠍⡟⠻⣿⣿⣿⡿⡱⢻⣿⡳⣌⡛⢦⡙⣎⢿⣿⣿⢸⣹⣿⣇⠶⣌⣻⣿⣏⡟⢿⡿⣿⣧⣟⡼⣿⣄⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⢠⠈⡔⡁⢢⠡⡘⠿⠿⢿⠣⢆⠡⢒⡈⠔⢡⢂⠱⢈⠢⡁⢆⡘⢄⢊⡑⢌⠰⣀⠣⡐⢡⠊⡔⢡⠂⣽⣿⢣⡝⡻⢿⡷⢬⡙⢦⡹⠜⡦⣿⣿⢦⡙⣿⣿⡞⡴⢻⣿⠞⣜⢣⠞⣿⣿⡿⠿⠿⠏⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⡎⡀⠎⠰⡈⣀⠱⢀⠇⡉⠆⢱⠈⡆⢁⠆⡉⠆⢆⠱⡈⢰⠁⢆⠰⡈⡀⠶⢈⠰⣀⠱⠈⡆⠸⠰⢆⢹⣿⡇⢷⡸⢹⣿⣿⣇⠹⣆⢹⠹⡶⣿⣿⣆⢹⡈⣿⣿⡎⡹⣿⣿⡈⣇⠿⣸⣿⣷⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⢂⠅⡒⠨⠌⡑⠰⢠⠑⡌⠰⡁⠎⡄⢃⠌⢢⠘⡐⢌⠂⢆⡑⠢⡘⠄⡃⠔⡡⢊⠄⢣⠐⡌⠡⢌⠡⢃⠌⢢⣿⡟⢦⡹⣹⣿⣿⣌⠳⣌⢧⢛⡴⢻⣿⣎⢧⡹⢾⣿⣿⡕⣿⣿⣞⡴⢋⡼⢿⣿⡄⠀⠀⠀⠀ ⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⡰⢁⠊⠔⢡⠊⠔⡡⢂⠥⡈⢅⠢⡑⡈⢆⡘⠄⡃⢌⠂⡍⢄⠢⡑⠄⣃⠘⠤⠑⡄⢊⠄⡃⢌⡑⠢⢑⠨⡘⢰⣿⡙⢦⡓⡭⢿⣯⠜⡳⣜⣊⢧⢚⡽⣿⣏⠶⣩⠖⣻⣿⣿⣿⣿⣿⣷⣭⢚⣽⣿⠀⠀⠀⠀⠀ ⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⡔⠀⠀⠀⠀⠀⠀⠀⠀⠐⡈⠔⡈⠜⡈⠔⡈⢆⠑⡂⢆⠡⠊⡔⢠⠑⡂⢌⠢⢑⡈⠒⡄⢊⠔⢠⠃⡰⠈⢆⠱⢈⠆⡘⡐⢢⠐⡡⠊⡔⠡⣾⣿⡙⢦⡹⡜⣽⣿⣍⠳⠦⣍⠶⣩⠞⣻⣿⡇⢧⢛⡴⣿⣿⣟⡻⢜⣿⣿⣮⣽⣿⡧⠀⠀⠀⠀ ⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣈⠐⠌⡰⠁⢎⠰⡈⠆⠱⣀⠣⢑⠨⠄⡃⠜⡠⠑⡂⢌⠡⢂⠅⡊⢄⠊⡄⢩⠐⡌⢢⠘⢄⡑⢂⠱⣀⠣⡐⠡⣿⣿⡘⢧⡱⣚⡜⣿⣮⣙⠳⣌⢳⡱⢎⡽⣿⣿⢎⡣⢎⡽⣿⣿⣷⢩⡜⣿⣿⣿⣿⣿⡀⠀⠀⠀ ⠠⣿⣿⠛⠛⠛⠛⠛⠉⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⡘⢠⠑⡌⠢⡁⢆⡉⠒⠤⡘⠄⢣⠘⢄⠣⡐⢡⠘⡄⠣⠌⣂⠱⢈⠔⡈⠆⡡⢂⠅⡊⠤⡘⢠⠃⡐⢢⢁⠃⣿⣿⡙⢦⢳⡑⣎⢿⣿⣌⡳⣌⠳⣜⢣⠞⣹⣿⣧⡙⣎⠶⡹⣿⣿⣷⣎⡭⢻⣿⡟⠛⠀⠀⠀⠀ ⠀⢹⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠡⡐⠡⢒⠈⡅⠒⠤⣈⣱⣦⡕⡈⢆⠡⢊⠤⠑⡂⢅⠢⡑⢌⠰⢈⠆⡘⠤⠑⡄⢃⡘⠤⠑⡄⢃⠜⡠⢁⠆⡡⣿⣷⡙⢮⡱⣚⡜⣺⣿⣧⡳⣍⠳⣌⠧⣛⠼⣿⣿⡗⣬⠳⣱⣹⣿⣿⣿⣷⣿⣿⣷⡄⠀⠀⠀⠀ ⠀⠀⠹⣿⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢌⡑⠌⢒⡈⢑⢢⣰⣿⠟⡠⢑⡈⢆⠡⢂⠱⣈⠢⢁⠒⠌⢢⠡⡘⡐⢌⠡⡘⠄⡒⠌⡡⠘⡄⢢⠑⡨⢐⠡⣿⣷⣝⢦⡓⡵⢊⢷⣿⣿⡷⣌⠳⣌⠳⣍⢞⣿⣿⣿⣶⡙⢦⣿⣿⣿⣿⡿⣿⣿⣿⣿⣆⠀⠀⠀ ⠀⠀⠀⠈⠻⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄⠰⣈⣤⣼⣶⣿⠿⢋⠆⡑⢂⠌⡄⠣⠌⢒⠠⡑⢌⡘⠌⡂⢅⠢⡁⠎⡐⢡⢊⠰⢁⠆⡱⢈⠔⡨⢐⠡⢂⣿⣿⣿⣷⣿⣮⣽⣾⣿⣿⣷⣬⣷⣎⣷⣼⣾⣿⣿⣿⣷⣿⣷⣿⣿⣿⣿⣧⡈⠹⢿⣿⣿⣦⠀⠀ ⠀⠀⠀⠀⠀⠈⠛⠿⢿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣶⣿⡿⠿⢛⠩⡁⢎⠰⡈⠔⡡⢊⡐⢡⠊⡄⠣⢌⠰⣀⠣⢘⠠⡑⢄⠣⠘⡄⠢⡑⠌⡰⢀⠣⢌⠰⠁⠎⡄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠉⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠈⢿⣿⡉⠉⠈⠁⠉⠉⠉⠉⠉⠉⠉⠉⠁⢈⠡⣁⠒⢌⢂⠱⡈⠔⣂⠱⡈⠔⡂⢜⣤⡑⢌⠒⡨⠐⡄⢊⠄⠣⢌⠢⢌⡑⠄⢣⠘⠤⢑⡈⠆⡌⢢⢉⠒⡄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣷⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⢠⠉⡄⢊⣴⣈⣶⣤⣦⣱⣼⣶⣾⣿⣿⣿⣶⣷⣷⣾⣶⣿⠿⡿⠟⡠⢂⠍⡰⢈⠆⡡⠒⡨⢐⠢⠌⢒⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⢿⢿⣿⣿⣷⣿⡾⣿⠾⡷⠷⠿⠿⢿⣛⣻⣿⠿⣿⠿⠿⠛⠛⣻⡟⠛⣿⡍⣉⢉⡉⠩⢄⠃⡔⢡⠂⡅⢊⠄⠣⡐⢡⠘⠤⡁⢆⡉⢆⡸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣟⣩⣍⣤⣴⣦⣴⣤⣸⡟⠁⠀⣻⣿⣶⠠⢌⡑⠂⠥⡘⢠⢊⠰⢁⠊⡅⡘⠄⡃⢆⠱⢠⠘⢤⢳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣭⣿⢛⣛⣛⣿⣿⣿⣿⡏⠀⢀⣤⣿⣿⢿⣷⡆⠰⡉⠔⡈⢆⠢⠑⡌⠒⠤⠑⡌⠰⣈⠢⢁⠎⣜⣳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡈⠛⡟⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣯⣷⣾⣿⣿⠏⢠⣼⣋⣴⣾⣾⡟⠉⢿⣦⡙⣿⡴⢈⠆⡑⠢⠌⡑⠤⢉⠢⡑⢨⠡⡐⢌⠢⡘⢤⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠗⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢩⣾⡟⣽⣯⢀⣾⣿⣿⢿⣿⠇⢠⣄⠈⣿⣷⣿⣿⣦⡘⠄⢣⠘⢄⠣⠌⣂⠑⡂⠥⢘⠠⡑⠌⢢⠽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠋⢀⣿⣿⣿⣿⣷⢿⣿⠏⠀⣠⣿⣷⠿⢿⡿⣿⣿⣶⢉⠰⡈⠆⢢⠑⡠⠃⠜⡠⢃⠢⠑⡌⢢⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⢇⣰⣾⡿⠟⣿⠀⢀⣿⢧⣶⣿⠟⠉⠈⠀⢸⣷⡈⣿⣿⠠⡁⢆⠩⡐⢌⠰⢉⠂⡅⢢⢁⠣⡐⢡⠊⡽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡿⢛⣿⡃⢸⣿⠠⠿⠿⢟⣿⡏⠀⠀⠀⣠⡿⣿⡗⠈⣿⡆⠡⢌⠂⡅⢊⠄⢣⠘⡠⢁⠆⡑⠌⣂⠱⡘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢹⣿⠆⢸⡿⠀⢀⣴⣿⣿⠀⠀⣠⣾⠟⢡⣿⣿⣇⣿⣿⠇⡌⢒⡈⢆⡘⠄⢣⠐⡡⢊⠄⢣⠐⣂⠑⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡁⣾⣧⣼⣿⣿⣿⡟⣠⣾⡿⠋⠀⣋⣿⣿⣿⣿⣿⣿⡐⠢⡐⢂⠌⡘⠄⢣⠐⡡⢊⠄⢣⠠⡉⢆⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠉⢹⣿⡿⠏⠹⣿⢿⣿⡀⢀⣼⣏⣹⣿⡟⢿⣿⣿⡇⠱⢈⠆⡘⠤⢉⢂⠱⣀⠣⢘⠠⡑⠰⡈⢆⡙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣁⣠⣿⣿⡇⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣧⠈⢿⣆⠰⢁⠎⡠⠑⡌⠢⠌⢒⠠⡘⠄⡃⢌⠡⠒⠤⡘⢄⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣧ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⠁⠀⣴⣿⣿⣿⠏⠁⣿⣿⣿⣿⣿⣦⣿⣿⠀⠣⠐⢡⠑⡄⢣⠘⡄⠃⠜⠠⠑⡌⢢⠉⡔⠰⠈⠆⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠈⠛⠿⣿⠟ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡟⠉⢿⣿⣠⣾⡿⣿⣿⠏⠀⢀⣿⣿⡿⢻⣿⣿⣿⣍⣌⣂⣱⣈⣔⣡⣌⣂⣱⣈⣄⣃⣆⣡⣊⣴⣵⣦⣵⣬⣶⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠻⠛⠛⠉⠻⣿⠿⠙⢿⣿⣿⣿⣿⣷⠀⠀⠀⠉⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇⣠⣿⣿⣿⣿⣱⣿⠁⠀⣰⣿⡉⠉⢠⣿⠏⠙⢿⠟⠻⠻⠟⠿⠛⠟⠻⠛⠟⠛⠛⠛⠋⠉⠉⠉⠉⠉⠉⠁⠀⠀⠈⠁⠈⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠋⠙⢿⣿⣿⣿⢠⣶⠟⣿⡄⠀⣼⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠟⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠿⠻⠿⠟⠁⠀⠸⣿⣀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠄⠐⠀⠀⠀⠀⠈⠇⠀⡇⡇⠀⠀⣠⡐⠀⠈⢸⠁⠉⢉⠉⠉⠉⠉⠙⢸⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⠗⠉⠁⠀⠉⠁⠉⠑⠺⣤⠤⠤⠤⣤⣤⣤⡆⢸⣤⣤⣤ ⠀⠀⠀⠀⠀⢀⢀⠜⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠈⢢⠀⠀⠀⠀⠀⢀⢸⠀⠀⠀ ⠀⠀⠀⣀⣀⣸⠃⠀⢀⢐⢆⠀⢠⠈⢆⣀⣀⠀⠐⡄⢃⡀⣀⣀⠀⢸⢸⠀⠀⠀ ⣀⣠⣤⣤⣤⢂⢡⠀⣸⡞⠚⡄⠈⡄⠈⠺⡦⡈⡂⢰⠈⡏⠉⠉⠉⢹⢸⠉⠉⠉ ⠑⢄⠀⠀⢸⠎⠀⠰⠀⣧⣴⡌⡄⠰⠘⢿⣯⢳⣇⠀⡄⠰⡀⠀⠀⢸⢸⠀⠀⠀ ⠑⢄⠳⡄⢻⠘⢰⠀⡿⡟⣿⡇⠏⠢⢣⠘⠛⠀⡟⠀⡇⠠⣹⠛⠛⢻⢸⠻⠟⠓ ⠀⠀⠑⢌⠻⡀⣿⣷⣽⣄⠀⠀⠀⣀⣀⡀⠀⠰⡇⠀⡇⡘⣗⢵⡄⢸⢸⠀⠀⠀ ⠀⠀⢀⠜⣡⢀⣳⢻⠏⡧⡀⠀⠫⣁⡠⠃⠀⡰⠇⢀⢇⢠⢹⠛⠛⢻⢸⠛⠛⠛ ⡠⢔⣡⠞⢹⠊⡼⢸⢀⡇⢸⠒⠀⡤⠤⠐⡏⢸⡀⢸⢸⡀⠆⢇⠀⢸⢸⠀⠀⠀ ⡠⠋⠀⠀⢸⠀⠇⢌⢈⢿⡚⣦⡔⠣⠤⠂⣉⣎⠁⣆⢎⠫⠜⡈⢶⣼⢸⣤⣤⣄ ⢆⡀⠀⠀⢸⡘⢸⡄⠀⢊⢷⡏⠀⠁⠀⠁⠀⡏⢰⡇⠁⠁⠶⠐⡈⢾⢸⠀⠀⠀ ⢄⠉⠢⡀⡘⠀⡜⢌⢄⠀⡏⡧⣀⠀⠀⢀⣠⠁⢸⡁⠀⣨⡔⠱⡈⢄⠻⣤⣤⣤ ⠀⠉⠂⡸⠁⡾⡤⠏⢧⣼⠀⢡⣠⣩⣽⣿⡟⠀⢸⣿⣿⢁⠗⢞⣃⠀⠡⡙⢄⠀ ⠀⠀⠐⠀⡾⡏⠀⠘⡿⠃⠀⢸⣿⣿⣿⣿⡇⠀⢸⣿⣿⠋⠀⢸⡏⢦⠈⢎⢮⡢

⠀⠀⠀⠠⠁⢀⠀⠀⡴⠁⢀⠔⡹⡁⠀⢠⢀⠀⠀⢆⠀⠤⡀⢄⠈⠄⠀⠀⠀ ⠀⠀⢀⠂⢠⡟⢀⠊⣆⠔⢁⣎⠀⢃⠀⡎⡜⠪⡐⢌⠗⢄⠩⣆⢄⣘⡄⠀⠀ ⠀⠀⡌⠰⠱⠣⠁⢠⠅⢺⡏⠹⢩⠈⢄⠀⣸⠈⠩⠫⠙⣄⠑⠃⠃⢀⡃⠀⠀ ⠀⢀⢸⠀⡄⠀⠀⠸⢠⣽⣷⡿⣿⣦⠀⠀⠷⣶⣿⡿⣷⣧⠀⠀⠀⠀⢀⠠⠂ ⠀⠀⠀⠀⡇⠀⠀⣸⢿⢱⠿⡿⠀⢑⠳⣄⡸⠉⡾⡿⡏⢻⣝⣔⠆⠉⡇⠀⠀ ⠀⠀⢰⠀⢀⠀⠀⢻⡀⠨⠤⠤⢀⡼⠉⠉⢧⡁⠣⠤⠇⣰⠏⢨⡏⠑⠇⠀⠀ ⠀⠀⠀⡄⢠⠀⠀⠘⡍⠉⠉⠉⠉⠀⠈⠀⠀⠈⠉⠉⠉⢡⢔⠝⣇⡀⠀⠀⠀ ⠀⢀⠀⡏⠲⡄⠀⠀⡿⣄⠀⠀⠀⡴⣶⣶⢶⡄⠀⠀⢀⠎⡟⢰⠁⡇⠀⠀⠀ ⠀⠘⡆⢿⠀⣷⡀⠀⢠⠈⠳⣄⡀⠫⠄⠠⠝⠁⣠⣴⢹⠀⣧⢸⠀⡇⠀⠀⠀ ⠀⠠⠹⣸⠀⣏⣷⡀⠀⣇⣰⠰⡏⢶⣤⣠⡾⢫⠃⢁⣊⡄⣸⠠⣤⠡⢀⠀⠀ ⠀⠀⠱⡡⠇⣏⠎⣹⢄⠱⡘⠀⠈⢂⡝⢋⠔⣱⡇⠆⠀⠡⠀⠰⠋⡐⠀⠃⣄ ⠀⢊⢉⠕⣊⣄⠙⢤⣣⠷⢵⣇⠀⣈⠰⡈⢠⠛⡽⠀⠀⠀⡱⡟⠍⠘⢒⠅⡀ ⢨⡀⠉⣣⠯⡋⢱⠈⠀⠆⠀⠙⠦⡟⠉⠑⢹⠌⠠⠡⡀⠀⠳⠀⠱⠙⡕⠁⠀ ⠈⠏⠉⠀⠀⡇⠈⢠⠈⠀⠀⠈⠢⠘⠀⠀⢆⠌⠀⠀⠈⠄⠣⠀⢀⠂⠀⠀⠀ ⠀⠈⠀⠀⠀⠀⡀⠁⠀⠀⠀⠀⠀⠑⠀⠀⠌⠀⠀⠀⠀⠈⢀⠡⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⠿⠿⠛⠿⢿⣿⣷⣄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠋⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⢿⣿⣶⣶⠶⠶⠶⣶⣶⣦⣤⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠿⣷⣶⣤⣤⣄⣠⣴⣶⣾⣿⣿⣿⣶⣤⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⠀⠀⠀⠀⠀⠀⣠⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⣄⢀⡀⠀⠀⠀⠀⠀⠛⣿⣿⣿⣿⣿⠿⠛⠛⠛⠿⣿⣿⣿⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣾⡏⠀⠀⠀⠀⠀⣠⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣇⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣧⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⣰⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣧⡀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣧⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⡀⣾⡿⠀⠀⠀⠀⠀⠀⠀⣀⣤⡴⠶⠟⠛⠛⠛⠛⠛⠛⠻⠶⢦⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣧⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣦ ⠀⠀⠀⠀⠀⠀⢰⣿⠁⠀⠀⠀⣼⣿⠁⠀⠀⠀⠀⢀⣴⡾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣷⣄⠀⠀⠀⠀⠀⠀⠈⢻⣷⡀⠀⠀⠀⠀⠀⢸⣿⣿⣷ ⠀⠀⠀⠀⠀⠂⣿⡟⠀⠀⠀⢰⣿⠏⠀⠀⠀⠀⣰⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣄⠀⠀⠀⠀⠀⠀⢻⣧⡄⠀⠀⠀⠀⢸⣿⣿⣧ ⠀⠀⠀⠀⢀⣼⣿⠁⠀⠀⢠⣿⣿⡇⠀⠀⢀⣾⡟⠁⣀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣧⠀⠀⠀⠀⢺⠀⣿⣳⠀⠀⠀⠀⢘⣿⣿⡇ ⠀⠀⠀⢀⣾⡿⠁⠀⠀⢀⣾⣿⣿⢀⠀⠀⢸⣿⣳⢃⢃⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⠀⠀⠀⠈⠀⣿⣧⠀⠀⠀⠀⠈⣿⣿⡇ ⠀⠀⣠⣿⠏⠀⠀⠀⠀⢸⣿⣿⣿⠈⠂⢰⢼⣏⣹⡜⠻⣿⣿⠟⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡷⢤⠀⠐⡆⣿⠀⠀⠀⠀⢀⣿⣷⠀⠀⠀⠀⠀⣿⣿⠁ ⠀⣴⡿⠁⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠈⢺⣿⡘⢿⣿⣿⠇⠀⠀⠀⠰⣿⣶⣦⣤⣠⣄⠀⠀⠀⣸⣿⣿⣇⡀⠀⠀⢰⣿⠀⠀⠀⠀⢀⣿⠇⠀⠀⠀⠀⠀⣻⣿⠁ ⢰⡿⠁⠀⠀⠀⠀⠀⠀⠸⣧⠛⢿⣶⣀⣠⣬⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠉⠛⠋⠀⣠⡶⠟⠉⠉⠉⠙⠛⢀⣾⠏⠀⠀⠀⠠⣦⣿⠀⠀⠀⠀⠀⠀⢹⣿⡄ ⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣤⣿⣿⠿⠉⠈⠙⢿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠋⠀⢀⣠⣶⠾⠻⠷⣿⣿⣄⠀⠀⢀⣾⡿⠃⠀⠀⠀⠀⠀⠀⠰⣿⡇ ⣿⡇⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡟⢻⡟⠀⠀⠀⠀⠀⠮⣝⢻⣷⣶⣤⣤⣤⣤⣴⣤⣤⠀⣀⣠⡶⠟⠉⠀⠀⠀⠀⠀⠈⣿⣷⡀⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿ ⢻⣷⡄⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⡜⠁⠀⠀⠀⠀⠀⠀⢹⣿⢿⣦⣿⠉⠀⠀⠀⠈⠹⣿⣿⢿⠆⢀⡀⠀⠀⠀⢀⣠⣾⠏⢹⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿ ⠀⠹⢿⣆⠀⠀⠀⠀⠀⢾⡏⢿⣿⣧⠀⠀⠀⠀⠀⠀⠀⢰⣷⣼⢻⣾⠀⠀⠀⠀⠀⢀⣿⠷⡈⠀⠀⠈⠓⢀⣸⠋⠁⠀⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿ ⠀⠀⠈⠻⢶⣄⡀⠀⠀⠀⠁⠀⢹⣿⣷⣤⣤⣤⣤⣤⣾⣏⡁⠚⠀⢻⣦⣀⣀⣀⣠⣾⠏⠀⠳⡄⠀⠀⣰⣾⣿⣛⣛⢶⣶⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐ ⠀⠀⠀⠀⠀⠉⠛⢻⣿⣶⣤⣶⣿⣿⡿⠋⠉⠉⠀⠉⠙⢿⣆⡀⠀⠀⠈⠋⠙⠛⠉⠁⠀⠀⠀⣩⣶⡿⠟⠛⠉⠉⠛⣿⣿⣛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿ ⠀⠀⠀⠀⠀⣀⣀⣀⣼⣿⣿⣿⠿⠋⠀⠀⠀⠴⠶⢤⡄⠈⠛⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠉⠀⠀⠀⠀⢀⠀⠘⠟⢻⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿ ⠀⠀⠀⠢⠰⠿⠿⠿⣿⠿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⢹⡖⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⠀⠀⠀⠀⠀⠀⠙⣶⡄⠀⢻⣿⣷⣤⣄⣀⣀⣀⣀⣀⣴⣿⣿⡿ ⠀⠀⢀⣷⣶⣶⣿⣿⣿⣿⣿⣏⠀⠀⠀⢀⡀⠀⠀⢀⣼⠟⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⢀⣾⠇⠀⠀⢀⠀⠀⠀⠀⠀⠈⣷⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁ ⠀⠀⠈⠛⠛⠛⠋⣉⣉⣿⣿⣿⣦⠀⠀⠠⠼⠳⠿⠛⠁⠀⠀⣠⣿⣷⣦⣶⣶⣮⣵⣦⣾⣟⡀⠀⠀⢻⣦⣀⣠⣀⣤⡾⠏⠀⠀⣼⣿⣿⣿⣿⣿⠿⠿⠟⠉⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠸⢿⣿⠿⠿⠿⠿⢷⣶⣤⣤⣤⣠⣤⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣄⣀⣠⣉⣉⡉⣁⣀⣀⣠⣾⣿⣿⣿⣿⣿⣿⣿⠿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⢿⣿⠿⠿⠿⢿⡿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠻⠟⢻⡿⢻⡿⢉⣤⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⣠⠂⠀⠀⠀⡠⢚⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠑⢄⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠁⠀⢀⣼⠁⠀⢀⡾⡇⠀⢀⡴⠊⢠⠎⠈⠀⠀⠀⢠⡧⢰⡦⣄⡀⠀⢹⣦⡀⠈⢹⣦⡀⢂⠀⠀⢣⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠀⢠⣾⡇⠀⣰⠋⢸⢀⡴⠋⠀⣰⡇⠀⠀⢇⠀⠀⡞⢹⠘⠓⢤⡉⠢⣄⠿⡝⢆⠀⢻⣽⠢⢕⡠⠈⣧⠄⠀⠀⠀⠀ ⠀⠀⠀⡼⠀⢠⢋⣿⠀⡜⠁⠀⡾⠋⣠⣴⣾⠿⡷⢾⡤⠘⡄⠀⠃⢸⢷⠀⠺⠿⢶⠾⢦⣷⡀⠙⢦⡙⠓⣞⠛⠉⢻⠀⠀⠀⠀⠀ ⠀⠀⢰⢁⡇⠃⢸⠈⠞⠀⠀⢠⡗⠋⢡⣾⠃⠀⢻⡈⡆⠀⠘⢄⠄⢸⣌⡆⠀⠈⠊⠳⣄⠈⡷⢄⠀⠈⠁⠀⠑⢤⣈⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⠀⠀⡏⠀⠀⠀⠀⢸⠀⢠⡋⢿⣶⣶⣞⣷⣿⣆⠀⠀⠀⠈⣿⣷⣶⣶⣶⣶⣿⣦⣾⠀⠁⠀⠀⠀⠀⠀⠈⠉⠁⣡⠂⠀ ⠀⠐⠀⡎⠀⠀⠇⠀⠀⠀⠀⢸⣠⣏⣽⠿⣿⣿⣹⡿⠿⡟⢦⡀⠀⠀⢯⢻⡿⠿⣿⣏⢹⣿⣿⣧⣀⠀⠀⠀⠀⣀⣠⡴⠋⠁⠀⠀ ⠀⠀⠀⠇⠀⠀⠁⠀⠀⠀⠀⣸⣿⡿⠉⣶⣿⣿⣿⡇⠀⢙⡞⠻⣦⣀⣸⡄⠁⣾⣿⣿⣾⠇⢻⣷⣝⣯⡉⢿⠉⠀⢸⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⢰⣿⠁⠁⠀⢯⠀⠉⠘⠃⠀⢸⡷⠶⠿⢿⣟⠓⠀⣇⠈⠁⠘⠀⠈⢹⣿⠟⡟⢿⠦⣤⣬⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⠀⠀⢳⠀⠀⠀⠀⢽⣧⡀⠀⠚⠒⠒⠚⣀⣤⡿⠁⠀⠀⠀⢻⣦⣀⡙⠒⠒⠟⣀⣰⣿⠇⢀⣧⡟⠀⠻⠸⠀⠀⠀⠀⠀ ⠀⠀⠀⠘⡆⠀⢠⠀⠀⠀⠀⠘⣏⠙⠛⠛⠚⠛⠛⠋⠁⠀⠀⠘⠀⠀⠀⠈⠉⠙⠛⠛⠛⠉⠉⣸⣠⢞⡿⡇⠀⠀⠐⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢳⣀⠘⡄⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣯⣴⡏⠀⡷⠲⡄⠀⠀⠀⠀⠀⠀ ⠀⢀⠀⠀⣾⠈⠳⣧⠀⠀⠀⠀⢹⢻⣄⠀⠀⠀⠀⠀⢠⣶⣿⠷⠶⢾⣷⣦⠀⠀⠀⠀⠀⢠⡞⠉⡿⠀⠸⠀⠀⡇⠀⠀⠀⠀⠀⠀ ⠀⢹⡇⠀⣿⡄⠀⢿⡆⠀⠀⠀⠘⡄⢹⢷⣄⠀⠀⠀⠘⣷⠛⠋⠙⠛⢻⡟⠀⠀⠀⠀⣠⡟⠁⠀⡇⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⢿⡀⡟⡇⠀⢸⢿⡄⠀⠀⠀⢣⣸⠀⠉⢳⣦⣀⠀⠘⠒⠤⠤⠖⠋⠀⢀⣠⢶⡻⡄⢳⠀⠀⣷⠀⢸⠀⠀⡇⠀⠀⠀⠀⠀⠀ ⠀⢀⠈⢷⠁⡇⠀⢸⠘⣿⡄⠀⠀⠘⡏⠀⢀⡇⢼⡟⠳⣤⣀⠀⠀⣠⣶⡿⢻⡿⠀⣇⢳⡘⡄⠀⢸⡇⢸⡄⠀⣇⠀⠀⠀⠀⠀⠀ ⠀⠀⢢⡘⣳⢧⡀⢸⣧⢹⣿⣄⠀⠀⢿⠒⠺⠀⠈⠣⡀⠙⢿⣿⣿⣿⠟⢁⡞⠁⠀⡼⠤⠿⣷⠤⠞⠛⢉⡇⡇⢸⠙⠢⡀⠀⠀⠀ ⠀⠀⠀⢻⣁⣼⠇⢸⣄⡿⠁⢈⣧⡀⠈⢧⠀⠂⠀⠀⠈⠲⣄⠙⠋⣠⠔⢉⣴⣿⢀⠇⠀⠀⠘⡄⠀⠀⡜⢹⢰⠀⢆⣀⠇⠀⡀⠀ ⢀⡠⠤⠤⢭⣀⡤⠚⠙⠲⣴⠋⢠⠟⣦⠈⢆⢰⠀⠀⠀⢰⠙⡆⢀⡇⢀⢸⣿⠟⡞⠀⠀⠀⠀⠘⣄⣠⠖⠺⠤⢑⣂⣠⠴⠚⠉⠠ ⠈⢀⡀⢠⠚⣁⣤⣶⠦⡀⠈⢳⣡⡾⢻⠟⢮⣿⡆⠀⠀⣼⠀⢹⣼⠀⣸⠈⠃⡜⢣⠀⠀⠀⠀⠀⡜⡱⠉⠑⡠⠀⠀⣭⠇⣀⠀⠀ ⠃⠈⠉⠛⢿⣛⢟⡹⡗⠙⡆⠘⡇⠀⡸⠀⠀⠙⢿⡄⣰⣍⠗⠚⠓⠞⣉⣇⡜⠀⣈⢦⠀⠀⠀⢸⢣⠃⠀⠉⡍⠹⣏⡽⠋⠁⠀⠀ ⣷⣤⣀⡠⠴⠛⠋⢰⠃⠀⡇⠀⡇⠰⠁⠀⠀⠀⢀⠈⠁⢯⠀⠀⠀⠀⣿⠀⢠⠎⠀⠀⠱⡄⠀⢸⠘⠀⠀⠀⢰⠀⠙⡄⠀⠀⠀⠀ ⠈⡄⠀⠀⠀⠀⠀⢸⠀⠘⠀⣠⠇⠀⠀⠀⠀⠀⠀⠑⡄⠘⣆⠀⠄⠠⠇⡰⠃⠀⠀⠀⠀⠈⢆⠀⠳⡀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀ ⠀⠑⠀⠀⠀⠀⠀⠈⠀⠀⢀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠈⢂⠇⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠈⢂⠀⠳⡀⠐⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⢱⡀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠢⣀⠒⠒⠒⡢⠭⠍⠙⠎⣉⠲⡌⠐⢄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⢹⠷⠒⠗⡲⢮⠀⠀⠉⠢⣄⡁⠀⠀⠑⠒⡠⠄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⢀⣂⠀⠀⠐⡄⠑⡀⠀⠀⠹⢊⠲⣲⡎⠁⠜⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⡞⠘⡄⠀⠀⠠⠀⢁⠀⠀⠀⡆⡆⠀⢳⣚⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⡸⠁⡄⠃⠀⠀⠀⠀⠀⠀⠀⠀⠃⢰⠀⠆⡏⣯⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠰⡼⠀⡗⡮⢤⠀⠀⢀⠆⢀⠃⠀⠀⠀⠆⢸⠀⢰⠀⢸⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡰⢁⠀⣵⣔⠁⠀⠄⠂⣠⠆⠀⠀⠀⡔⠀⡘⠀⡘⠀⠈⠀ ⠀⢐⠠⠀⢀⣀⠄⢪⠁⢸⠈⡇⢸⣿⠷⠀⠈⠁⢲⣦⣤⣈⡤⡠⠁⠠⠁⡄⠀⠀ ⠀⢈⠢⠑⢌⠰⠀⠘⡀⡘⠀⣧⠀⠈⠀⠀⠀⠀⠈⠿⠯⠙⣟⡡⠔⠇⣰⠁⠀⢀ ⠱⡀⠕⠅⠀⠀⠈⡦⡐⣿⡄⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⣀⡇⠄⠀⡰⠃⠀⠀⢸ ⠀⠘⢄⠣⡀⠀⠀⡸⣦⢴⠡⣿⢈⠁⠏⠐⡒⠲⡶⠊⢡⣯⣹⣾⣈⣀⣠⢄⠦⠀ ⠀⠀⡜⡗⠄⣀⣰⠹⢻⠸⢀⢹⣮⣸⡀⣠⠯⣃⠀⢀⠆⠠⢠⣿⡏⠙⠫⣆⠀⠀ ⢠⠊⡇⠘⣠⠠⠀⡄⠊⠆⡏⣸⡆⠱⠘⣅⡀⠋⠤⠚⠀⡆⠘⢻⠃⠀⢴⣿⠀⠀ ⠈⠀⠀⠀⠈⠒⠂⠁⢀⢻⠃⠸⡇⢁⠐⠳⣿⠀⠀⠇⢰⡀⢠⠈⡐⢡⠥⠋⡆⠀ ⠀⠁⠀⠀⠀⠀⠀⠀⡘⠚⠀⠀⣇⢸⢂⠀⠀⠈⠹⠀⡎⡇⠀⢶⠁⠀⠎⠃⠐⠤

⠀⠃⠀⣰⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠘⣿⡁⠈⠁⢸⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⢀⢂⠟⠀⠀⠀⢿⠀⣿⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⡿⠀⢿⡏⠀⠀⠀⠀⠀⠀ ⠃⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠘⠟⠀⠀⠂⢸⠀⢸⡟⠀⠀⠀⠀⠀⣀⢀⣦⡎⠀⠀⠀⠀⢸⠀⣿⠀⠀⠀⡄⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⢸⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⣼⡿⠛⠛⠉⠉⠉⠛⠛⠛⠉⠙⠓⠲⢦⣼⡀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⢸⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣠⡾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣶⣶⣶⣶⣶⣦ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⢸⡏⠉⠉⠉⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠐⢂⡼⠋⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⠀⣀⡀⠀⣀⣀⠀⠀⠀⠀⠀⠀⢇⠀⢸⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣠⡟⠀⠀⠀⠀⠀⢀⡀⣿⠀⠀⠀⠀⠀⠀⡿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠘⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠋⣀⠀⠀⠀⠀⡀⣸⢠⣿⡀⠀⠀⠀⡆⠀⡇⠙⡄⠀⣀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠒⢻⠇⡸⠁⠀⠀⠀⠀⡇⣿⡞⠀⡇⠀⠀⠀⢹⠀⡇⠠⠿⣟⢻⣍⠓⠲⠤⣀⠀⠀⠸⡄⠀⠹⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⠀⢸⣧⣤⣤⣤⣤⣤⣤ ⠀⠀⢀⣀⣀⣀⡀⣀⣠⣤⣤⡏⢠⠇⢀⠀⠀⠀⣰⣷⣿⠓⠒⢳⡀⠀⠀⠈⣧⡇⠀⠀⠈⢣⣻⢳⡀⠀⠈⡗⠄⠀⢻⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠈⢹⠀⢸⡏⠉⠉⠉⠉⠉⠉ ⣿⠛⠛⠛⠛⠛⠛⠛⠿⢿⣿⢠⣿⠀⡞⠀⠀⣴⣿⢯⡏⠀⠀⠀⢳⡀⠀⠀⠸⡇⠀⠀⣠⢄⣹⣷⣝⣦⠀⣇⠀⠀⠈⡇⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⡇⠀⠀⠀⠀⠀⠀ ⠈⠻⣆⠀⠀⠀⠀⠀⠀⢸⡏⡞⠙⢀⡇⠀⢰⡇⣿⠸⣧⣀⣤⡤⣄⢹⣄⠀⠀⢱⠀⠘⣷⣿⣻⣷⣝⢿⣧⣿⠀⠀⠀⢧⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⢸⠀⣸⠁⠀⠀⠀⠀⠀⠀ ⣄⠀⠘⢷⣄⠀⠀⠀⠀⣸⣧⠃⢠⠈⡇⠀⠀⡇⣏⣼⣿⣿⣿⣿⡷⠌⣿⣆⠀⠀⢧⠀⠁⣿⣿⣿⣿⡀⢿⢻⢸⠀⠀⢸⠀⠀⠀⢻⣆⣀⣀⣀⣀⣀⣀⣸⡆⣿⠀⠀⠀⠀⠀⠀⠀ ⠙⢷⣄⠀⠙⢷⡄⠀⠀⢿⣾⠀⢸⠀⢧⠀⠀⢷⣿⣿⠋⣿⣿⣿⣿⠀⣿⠈⠳⣄⠸⣇⠀⠹⣿⣧⡿⠀⠀⡾⣿⠀⠀⢸⠀⠀⢧⡀⢿⡿⠿⠿⠿⠿⠿⣿⠇⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠙⢷⡄⠀⠙⢦⡀⢸⣿⠀⢸⡄⢸⣤⡀⣿⣿⠻⠀⠹⣯⣦⡿⠀⠁⠀⠀⠈⠓⢮⣃⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⢸⠀⡀⠀⢳⡈⢳⡄⠀⠀⠀⠀⢸⠀⣿⠇⠀⠀⠁⠀⠀⠀ ⠀⠀⠀⠀⠙⢦⡀⠀⠙⢿⣿⠀⠘⣷⢸⣧⣷⡘⢿⣄⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⣸⢿⡆⠀⠀⢸⠀⢧⠀⡎⡿⣦⡻⣄⠀⠀⠀⢸⠀⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠙⡄⠀⣿⣧⣏⣿⡿⣌⢿⢦⡀⠀⠀⠀⠀⠀⣀⣀⠤⢤⣤⣤⣀⠀⠀⠀⠐⠋⢸⠁⠀⠀⢸⠀⢸⡀⢹⣿⣈⠻⢿⣷⡄⠀⢸⠀⣿⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢈⣿⠖⠀⠃⠀⡟⢈⣿⣿⢳⠉⢾⣧⠁⠀⠀⠀⠀⣿⠿⠛⠉⠀⠉⠙⣿⠀⠀⠀⠀⢀⣾⠀⠀⠀⣼⡄⠈⣧⠀⣿⣿⣾⣿⣿⣿⣿⣿⠀⢸⣷⣶⣶⣶⣶⣶⣶ ⠀⠀⠀⠀⠀⢀⣴⠛⠁⣠⣶⠀⣸⣣⣾⠋⢿⠸⡄⢸⠉⢧⡀⠀⠀⠀⠈⠳⣄⡀⣀⣤⠞⠁⠀⠀⢀⣴⠏⡇⠀⠀⠀⡇⣷⠀⠸⡆⠘⣿⠉⠉⠉⠉⠉⢻⠀⢸⡏⠉⠉⠉⠉⠉⠉ ⠀⠀⠀⣠⡶⠋⠀⣠⣾⠿⣿⣰⠷⠋⢹⠀⢸⠀⠀⢧⡆⠀⠳⣦⣀⡀⠀⠀⠀⠉⠁⠀⠀⢀⣠⡶⠋⠀⣦⠇⡀⠀⢠⠇⢹⡄⠀⢳⠀⠸⣆⠀⠀⠀⠀⣼⠀⢸⡇⠀⠀⠀⠀⠀⠀ ⢀⡤⠞⠁⢀⣤⣾⠟⠁⠀⣿⠁⠀⣦⡟⠀⣾⡄⠀⠛⣧⠀⠀⣧⠈⡏⠉⠓⣶⠶⠶⠶⠖⠉⠀⣟⠀⠀⣿⢠⠇⠀⣾⡄⠈⣧⠀⠈⣇⠀⢻⡆⠀⠀⠀⣿⠀⢸⡇⠈⠀⠀⠀⠃⠀ ⠋⠀⢠⣾⡿⠋⠀⠀⠀⢠⣿⠀⠀⣿⠃⠀⣿⠗⢺⣽⡹⡄⠰⡟⢰⠃⠀⠀⣹⠇⠀⠀⠀⢀⣰⠿⣦⣠⡏⡼⠀⢀⡟⠓⣶⣿⠦⣄⠘⡆⠀⢻⡄⠀⠀⢻⡄⢸⡇⠀⠀⠀⠀⠀⠀ ⢀⣴⠟⠁⠀⠀⠀⠀⠀⢸⣿⠀⠐⡏⠀⡼⢁⡴⠋⣠⠿⣿⠛⠓⣾⣶⠶⠛⠉⠦⠤⠤⠖⠋⠀⠀⣈⣿⣢⠇⠀⣸⢀⡼⣅⠙⢧⡘⣆⠹⡄⠀⢿⣿⣶⣿⠁⢸⣧⣤⣤⣤⣤⣤⣀ ⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣸⠁⢰⠣⠋⠀⠚⠁⣠⢿⡄⢠⣿⡏⠒⠦⠤⣄⡀⠀⢀⡤⠖⠋⠁⣸⡟⠀⠀⣿⠛⢦⠈⠳⠄⠉⢸⡀⠹⡄⠈⢻⡉⢹⡇⢸⡏⠛⠛⠛⠛⠛⠛ ⢧⣀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢰⠇⠀⢸⣇⠀⠀⠠⠞⠁⣸⣿⣾⣿⠁⠀⠀⠀⠀⠉⠀⠈⠀⠀⠀⠀⣿⠁⠀⢰⡿⣄⠀⠓⠀⠀⢀⠿⣇⠀⠹⡄⠈⢳⣼⡇⢸⡇⠀⠀⠀⠀⠀⠀ ⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⣻⠏⠀⢀⣿⠟⣦⠀⠀⠀⠀⢳⠈⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⣾⣿⠛⠀⠀⠀⢀⡎⠀⠸⣄⡀⠙⣆⠀⠙⣧⢸⡇⠀⠀⠀⠀⠀⠀ ⣄⠀⠀⠈⠻⣦⡀⠀⠀⢠⡟⠀⠀⣸⠟⣦⡈⣧⡀⠀⠀⢸⡄⢹⡿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⢀⠀⣿⡏⠀⠀⠀⠀⣾⡀⣠⡞⠙⣷⡀⠈⢦⡀⠘⢿⣧⡀⠀⠀⠀⠀⠀ ⠈⠳⢦⡀⠀⠈⠙⢧⣠⡟⠁⠀⣰⠏⠀⢈⣿⣯⠻⣄⣀⢸⠁⠈⣷⠈⠛⢶⣤⣀⣀⣀⣠⣤⣶⢾⡿⠀⠀⠀⣿⣧⣀⣀⣀⣴⣿⢿⣧⠠⠀⢘⣧⠀⠀⠳⡄⠈⠻⣿⡿⠿⠿⡿⠿ ⠀⠀⠀⠙⠦⡀⠀⢀⡽⠀⠀⣴⣿⡀⢀⣼⡏⠹⣦⡀⢈⡽⠀⠀⢻⡆⠀⠀⠤⢀⣀⣤⣶⣶⣿⣿⠇⠀⠀⠀⣿⣿⣿⣶⣶⡿⠃⢸⡟⢷⣴⡷⢿⡃⠀⠀⠘⢦⠀⠙⣦⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⢢⠞⠁⠀⣘⣿⣹⡷⠟⠹⣇⠈⣿⣿⣿⠃⠀⠀⠘⣿⣿⣾⣶⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⡧⣠⡿⠀⠈⠻⣦⣬⣧⠀⠀⠀⢣⠱⣄⠈⠻⣄⠀⠀ ⠀⠀⠀⠀⠀⢠⠟⠀⢀⢬⣿⣿⡏⠀⠀⠀⠻⣿⣿⣿⡏⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⣿⣿⣿⣿⣿⣷⠟⠀⠀⠀⠀⢹⡏⠛⣷⡄⠀⠀⢣⡈⢷⣄⠙⢦⡀ ⠀⠀⢀⢀⡠⠀⠀⠀⣸⣟⠃⣿⠀⠀⠀⠀⠀⢙⡿⠋⠿⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⣼⡇⠀⠉⢿⡆⠀⠀⢳⡈⠻⡷⣌⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣤⣤⡀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⠿⢻⠛⢿⣿⣦⣠⣀⣠⣾⡿⠿⣿⠛⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣶⣿⣿⠁⣾⣿⣿⡌⣿⣿⠿⢿⣿⡏⠁⣾⣿⣷⠘⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⢾⣿⠿⠛⠋⠁⠸⣿⣧⡘⠛⠉⢠⣿⡟⠀⠀⢿⣷⣄⠈⠉⢁⣼⣿⢧⣤⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣶⣿⡿⠛⠉⠀⠀⠀⠀⠀⠀⠉⠿⢭⣽⣾⣽⠟⠁⠀⠀⠀⠹⣯⣽⣲⣯⡷⠋⠻⣿⣿⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣴⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠈⠻⣿⢷⡄⠀⠀⠀⠀ ⠀⠀⢠⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣻⣆⠀⠀⠀ ⠀⢰⣟⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⢻⡄⠀⠀ ⠀⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⠀⠀⠀⠀⠀⠀⠘⣿⣷⠀⠀ ⢸⣧⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⡝⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠕⢸⠃⠀⠀⠀⠀⠀⠀⢽⣿⠀⠀ ⢸⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠻⣄⠀⠀⠀⠀⠀⠀⠀⣼⠇⣠⡎⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀ ⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣄⠈⠛⠲⢤⣤⣤⣤⠞⠃⢠⡞⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠃⡄ ⠸⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⢤⣀⣀⣀⣀⣠⠶⠋⠀⠀⠀⠀⠀⠀⠀⠀⢰⢿⡇⠀⠀ ⠀⢹⡿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣯⡟⠀⠀⠀ ⠀⠀⠻⣎⠷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣞⣿⠟⠀⠀⠀⠀ ⠀⠀⠀⠈⠣⣿⣧⣼⣻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⡷⠟⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⣹⣿⣿⣿⣶⣤⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⢠⣿⣷⡀⢀⣀⣀⣠⣤⢴⣞⡿⠿⣷⣽⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣴⣯⣿⠃⠀⠉⠛⠒⠒⣾⣽⣭⣿⠷⠶⠶⠶⣾⣿⣿⡿⠽⠯⠗⠒⠛⠉⠁⠀⠀⣻⡿⣧⡀⠀⠀⠀⠀⠀⠀ ⠀⣴⣶⡶⠻⣿⣿⠃⠀⠀⢀⣤⣴⠶⣿⣿⠓⠀⠀⠀⠀⠀⠀⣹⣿⣧⣄⠀⠀⠀⠀⠀⠀⠀⣴⡟⢻⠙⠿⣦⡄⠀⠀⠀⠀ ⠀⠬⢳⡤⣾⠋⢹⣿⠒⠂⠚⢥⠀⣼⠏⢹⡏⠉⠉⠉⠁⢠⣾⠋⢿⡀⠙⢿⠯⠉⠉⠉⠉⠚⠋⠀⠸⠇⠠⠬⠥⢤⣀⡀⠀ ⠀⠀⠉⠉⠛⠒⠾⠿⠤⠄⣀⣈⣐⣿⣀⣈⣿⣀⣈⣀⣀⣞⣁⣤⣹⣗⣶⣄⣁⣀⣀⣀⣀⣀⣀⠠⠀⠴⠶⠶⠒⠒⠛⠉⠀

⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠈⡁⡇⢸⡇⠀⠀⠀⠀⠀⠐⠸⠀⠀⠀⡇⣿⠋⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢻⠀⣿⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⡇⢸⣧⣤⠤⠤⢤⣤⣿⠦⣄⣀⡀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠷⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢾⣶⣤⣤⣤⣤⣤⣴⣤⣤⣤⣤⣤⣾⠀⣿⣤⣤⣤⣤⣤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⡀⠀⠀⠀⠀⠉⠉⠉⠉⠉⢫⠀⣿⠉⠉⠉⠉⠉ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢈⡴⠃⠀⠀⠀⠀⡄⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡀⠤⠀⠠⠄⠀⠀⠀⠀⢸⠀⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡞⠁⠀⠀⠀⠀⢆⣧⠀⠀⢀⠀⠘⢣⠀⠀⠀⠀⠀⠀⠀⢦⠀⢱⡀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠐⠒⠒⠲⡏⡰⠁⠀⠀⢰⢸⡾⢹⠀⠀⠈⡇⢠⠠⢷⡻⣖⠒⠤⣀⠀⠈⡆⠀⢷⣤⣤⣴⣶⣦⣤⣤⣼⠀⢿⣤⣤⣤⣤⣤ ⣀⣀⣠⣤⣄⣠⣤⣤⡼⢠⠃⡀⠀⠀⣼⣾⠛⠚⢇⠀⠀⠸⡼⠀⠀⠑⣿⢦⡀⠈⡗⠄⠸⡀⠘⡇⠀⠀⠀⠀⠀⠀⢹⠀⣿⠉⠉⠉⠉⠉ ⠿⣉⠉⠉⠉⠉⠛⢻⣇⡿⢰⠁⢀⡞⡟⣿⠀⠀⠈⢦⠀⠀⢣⠀⢠⣶⣾⣷⣿⣄⡇⠀⠀⡇⠀⢹⡄⠀⠀⠀⠀⠀⢠⠀⣿⠀⠀⠀⠀⠀ ⡀⠙⢦⡀⠀⠀⠀⣼⡺⠁⢸⠀⠈⣇⡇⣿⣶⣿⣿⡜⣷⡀⠈⣆⠘⢹⣿⣿⡎⢻⡇⡄⠀⢸⠀⠀⢳⡀⠀⠀⠀⠀⢀⡆⡇⠀⠀⠀⠀⠀ ⠙⣦⠀⠹⣦⠀⠀⣿⡄⢸⠘⡄⠀⢿⣿⡟⣿⣿⣿⡀⡟⠑⢄⢸⡄⠘⢿⣯⠇⠀⣷⡇⠀⢸⠀⠰⡈⢿⠿⠿⠿⠿⢿⡇⣿⣷⣶⣶⣶⣶ ⠀⠀⠱⣄⠈⠳⣄⣼⡇⢸⡄⣷⣄⢾⡟⠃⠘⠿⠿⠃⠀⠀⠀⠙⠻⠄⠀⠀⠀⢀⣿⠀⠀⢸⢀⠀⣹⣌⢧⠀⠀⠀⢸⠇⡿⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠳⣄⠈⠻⡇⠀⣷⣻⣿⣎⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡼⢻⠀⠀⢸⠘⡆⢳⡟⢪⣷⣄⠀⢸⡀⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⣷⠄⠘⠀⡟⢻⣿⣿⠻⣿⠁⠀⠀⠀⣴⡾⠋⠉⠛⢿⠂⠀⠀⢀⡎⠀⠀⣸⠀⢳⠈⣿⣶⣿⣿⣶⣾⠁⣿⣤⣤⣤⣤⣤ ⠀⠀⠀⠀⣠⠞⢁⣴⡆⣸⣡⡟⢹⠸⡄⡏⢣⡀⠀⠀⠘⠦⣀⡠⠴⠋⠀⢀⣠⠞⡇⠀⠀⡿⡇⠈⡆⠸⡏⠉⠉⠉⢹⠀⣿⠉⠉⠉⠉⠉ ⠀⢀⡴⠛⢁⣴⡿⢻⡷⠛⠁⡇⢸⠀⢸⣷⠀⢹⡦⣤⣀⣀⡀⠀⢀⣠⠴⡏⠀⢶⢁⠀⢠⠃⢷⠀⠸⡀⢻⡀⠀⠀⢸⠀⣿⠀⠀⠀⠀⠀ ⠔⠉⣠⡶⠟⠉⠀⢸⡇⠀⣿⠀⢸⡧⣴⣼⡀⢸⡇⡇⠀⠘⣯⠉⠉⠀⢠⣧⡀⡞⡘⠀⣸⠧⣼⣇⡀⢣⠀⢳⡀⠀⢸⡀⣿⠀⠀⠀⠀⠀ ⢀⡴⠋⠀⠀⠀⠀⢸⡇⠐⡏⢀⢎⡴⢋⡹⣷⠚⢶⣷⠴⠚⠡⠤⠤⠚⠁⠀⣹⣧⠇⢀⣇⡴⡉⠣⡘⡌⢆⠈⢷⣶⣾⡇⣿⣤⣤⣤⣤⣀ ⡋⠀⠀⠀⠀⠀⠀⢸⡇⡸⠀⣎⠈⠀⠉⡠⢿⡄⣼⡏⠐⠲⠤⡄⠀⠤⠒⠉⢸⡟⠀⢸⡟⠢⡘⠂⠈⣡⠈⢆⠈⢯⢹⡇⣿⠉⠉⠉⠙⠛ ⠓⢤⡀⠀⠀⠀⠀⠸⣧⠃⠀⣿⡄⠀⠈⠀⣜⢻⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⣿⡷⠀⠁⠀⡠⠙⡄⠈⢢⠈⢻⡇⢹⠀⠀⠀⠀⠀ ⡀⠀⠙⢦⡀⠀⠀⢰⠇⠀⣸⢯⡘⣆⠀⠀⢸⠈⣿⣆⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⣿⠁⠀⠀⢰⡃⣠⠟⣷⠀⢣⡀⠹⣾⡀⠀⠀⠀⠀ ⠉⠲⣄⠀⠈⠳⣤⠏⠀⣰⠏⠀⣿⣏⠣⢄⣸⠀⢹⡈⠓⠦⣤⣤⣤⣤⣴⣾⠃⠀⢸⣿⣄⣀⣤⣾⢿⣇⠀⢈⣧⠀⠑⣄⠘⢿⡿⠿⠿⠿ ⠀⠀⠈⠑⢄⢀⠎⠀⣰⣿⣀⣴⡏⢹⣦⣤⡞⠀⠈⣧⣀⡔⣢⣴⣾⣿⣿⣿⠀⠀⢸⣿⣿⣿⣿⠁⣸⠛⢾⡟⢻⠀⠀⠈⣢⡈⠳⡄⠀⠀ ⠀⠀⠀⠀⢠⠏⠀⢰⣾⡾⠋⠀⢻⣴⣿⣿⠁⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢸⣿⣿⣿⣿⣼⠋⠀⠀⢻⡿⢧⡀⠀⠱⡑⣄⠙⢦⠀ ⠀⠀⢀⡠⠁⠀⣸⡟⢻⠃⠀⠀⠀⢹⡟⠱⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢸⣿⣿⣿⣿⡁⠀⠀⠀⢸⡇⠈⢻⡄⠀⠱⡈⢷⣌⠳