Shark ASCII Art

Copy & Paste Shark ASCII Art Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⣾⣿⣏⠉⠉⠉⠉⠉⠉⢡⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⢿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡄⠀ ⠈⣿⣿⣿⣿⣦⣽⣦⡀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⠀⠀ ⠀⠘⢿⣿⣿⣿⣿⣿⣿⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠇⠀⠀ ⠀⠀⠈⠻⣿⣿⣿⣿⡟⢿⠻⠛⠙⠉⠋⠛⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⡟⠀⠀⠀ ⠀⠀⠀⠀⠈⠙⢿⡇⣠⣤⣶⣶⣾⡉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠾⢇⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠱⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤⢤⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣬⣭⣿⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣶⣤⣄⣀⣀⣠⣴⣾⣿⣿⣿⣷⣤⣀⡀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣾⣿⣿⣿⣿⡿⠿⠛⠛⠻⣿⣿⣿⣿⣇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣤⣘⡛⠿⢿⡿⠟⠛⠉⠁⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣶⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⡄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⠿⠛⠉⠁⠀⠈⠉⠙⠛⠛⠻⠿⠿⠿⠿⠟⠛⠃⠀⠀⠀⠉⠉⠉⠛⠛⠛⠿⠿⠿⣶⣦⣄⡀⠀⠀⠀⠀⠀⠈⠙⠛⠂ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠀ ⢯⠙⠲⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠸⡆⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡇⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀ ⠀⠀⢰⠇⠀⠀⠀⠀⠀⠈⢷⠀⠀⠀⠀⠀ ⣀⡴⠒⢾⡀⣀⡴⠒⢦⣀⢀⡼⠓⢦⣀ ⣩⠴⠒⢶⣉⣉⡴⠒⢦⣉⣉⡴⠒⠶⣌ ⠁⠀⠀⠀⠈⠁⠀⠀⠀⠈⠁⠀⠀⠀⠈
⢰⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⢧⠨⠢⡀⠀⠀⠀⠀⠀⠀⠲⢒⠒⠦⠤⣀⡀⠀⠀⠀⠀⢀⣠⣤⠴⠒⠋⠙⡄ ⠀⠸⠀⠐⢱⠀⠀⠀⠀⠀⠀⢀⣈⠦⠤⠀⠒⠊⠉⠉⠀⠈⠁⣀⠭⠀⢁⣀⣀⣹ ⠀⠀⠖⠀⠃⠓⢤⠖⠒⠚⠉⠀⠀⡀⠀⠀⠀⢀⣰⢴⠶⠐⢈⣴⣿⠟⠿⢻⣿⡞ ⠀⢰⠀⠀⠀⡤⢤⣄⠀⠀⠤⠤⠀⠀⣐⠄⠀⠼⡏⡧⠄⢢⡾⠋⠀⠀⢠⣎⡟⠀ ⢠⠃⣀⠴⠋⠀⠀⠈⠑⠢⢄⣀⣠⠊⠀⢀⠎⠀⠡⠅⠀⠻⢿⣤⣤⡴⣾⣴⣿⠀ ⡬⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⡼⠃⣠⠶⣇⣀⣀⠀⠀⠀⠀⠀⣀⣌⡠⠤⠘⠋⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣔⡡⠚⠁⠀⠀⠀⠈⠉⠉⠉⠻⡍⠙⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠃⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣷⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣳⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠄⠂⣉⠍⠛⢠ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣶⠒⠓⠒⠒⠤⠐⠈⢀⣤⣤⠊⠁⠁⠀⠸ ⠀⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡄⠀⠀⠀⠀⡀⠀⠘⡿⠋⣀⢤⣲⠶⡆ ⠀⢹⡿⢷⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠈⢇⠱⠀⡈⠀⠸⢿⣹⣷⡿⠀ ⠀⠀⢷⠀⠑⢄⠀⢀⠾⠷⠄⠔⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⠂⠀ ⠀⠀⣨⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⢀⠔⠁⡁⠀ ⠐⠯⠤⠤⠔⠒⠤⣀⣀⡀⠀⣀⡄⡄⠀⠀⠀⢹⠁⢀⡠⠔⠓⢄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠰⠇⠚⠁⠀⡄⠀⠀⢠⠞⠉⠁⠀⠀⠀⠀⠋⠀⠀ ⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⢡⡀⣤⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣴⣦⠈⢁⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠰⢿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
pls note the ai inflicts emotional damage (ᵕ—ᴗ—)
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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠋⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠃⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠶⣿⠟ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⢏⡀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⢠⡾⠃⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠶⠶⠛⠛⠋⠉⠉⠀⠀⠀⠀⠈⠛⠿⠶⠶⠤⣤⣤⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠋⠀⣰⠟⠀⠀⠀ ⠀⠀⠀⣀⣠⡴⠶⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠛⠓⠶⢦⣤⣴⡞⠋⠀⢀⣼⠋⠀⠀⠀⠀ ⣠⡴⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⣾⠁⠀⠀⠀⠀⠀ ⠛⠷⠦⢤⣤⡴⠖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⡀⠀⠀⠀⣀⣀⣤⣤⡴⠶⢿⣄⠀⠀⢿⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠙⠛⠳⠶⠶⢤⣤⣤⣤⣀⣀⣀⣀⣤⣤⣞⡀⠀⠀⠸⣟⠛⠛⠛⠛⠛⠷⣤⣄⣟⠁⠀⠀⠀⠀⠀⠙⢷⣄⠘⣧⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠳⣶⣦⣽⣷⣄⠀⠀⠀⠀⠀⠈⠙⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣿⡆⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⡔⠒⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡜⠉⢧⡀⠀⠀⣇⠀⠀⣈⡷⠋⠁⠀⠉⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠸⡀⠀⣨⠟⠁⠀⠀⠀⠀⣴⢀⣤⡖⣖⡶⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡟⠀⣀⣀⣠⠖⠂⠀⠀⡀⢏⠁⠀⣠⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠓⠋⠀⡏⣀⡤⠴⠒⠙⠦⡈⠉⣛⣉⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⣿⣿⣶⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠟⠋⠉⠉⠙⠻⢿⣿⣷⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠏⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⠻⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⣿⣷⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠈⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣀⣠⣤⣶⣶⣾⣿⣿⣿⢿⣿⣷⣦⣄⠀⠀⠙⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡿⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⠿⠛⠛⣏⠉⠉⢻⡄⠀⢹⠉⠛⣿⣧⡀⠀⠈⢿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠁⠀⠀⠀⢀⣤⣾⣿⣿⠿⠋⠉⣿⡀⠀⠀⢸⣦⠀⢸⣷⠀⢸⣧⠀⣿⠙⣿⡄⠀⠈⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⠃⠀⠀⢀⣴⣿⣿⡿⠋⠹⣦⡀⠀⢿⣿⣆⠀⣿⣿⣇⣿⣿⣦⣿⣿⣄⣿⡇⣿⢻⡀⠀⠘⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⠀⢠⣿⣿⠟⠁⢢⡀⠀⣿⣿⣦⣸⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⢀⣧⠀⠀⢹⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⣾⣿⠛⣆⠀⠘⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠈⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⣿⡇⠀⠹⣿⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠈⢿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⠀⠀⢿⡗⣦⣄⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠙⢿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡆⠀⢸⣇⡘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠻⢿⣿⡷⠈⢿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠙⢿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣧⠀⠀⢿⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⢻⣿⣿⡇⠀⠀⢻⠇⠀⠀⢿⠙⡟⢻⣉⡿⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡀⠀⠈⢷⣽⣿⣿⣿⣿⣿⣿⡏⠻⣿⣿⠀⠀⠙⢿⣇⣀⣤⣬⣤⣤⣤⡤⠶⠖⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣧⠀⠈⠙⠂⣠⣴⠿⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠘⣿⣿⣿⣿⡌⠛⠆⣠⣴⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠹⣿⡻⢄⣙⡴⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣧⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠚⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⡆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣧⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠸⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡆⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣷⣮⣛⠿⣷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣷⡀⠀ ⠀⠀⠀⢀⣀⣠⣶⣾⣿⡿⠿⠛⠿⢿⣿⣿⣷⣾⣥⣄⣀⣀⣀⣀⣀⣀⠀⢀⣠⣶⣄⡀⢤⣀⣀⣀⣀⣤⣴⣶⣿⣿⣿⣿⠿⢿⣿⣿⣿⣶⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣇⠀ ⠈⠉⠉⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠛⠛⠛⠛⣉⣤⣾⣿⣿⣿⣿⣿⣦⣀⠉⠛⠛⠛⠛⠛⠛⠛⠉⠀⠀⠀⠀⠉⠛⠻⠿⠿⢿⣿⣿⣿⣶⣶⣶⣶⠶⠶⠶⠚⠋ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣾⣿⣿⣿⠿⠛⠉⠉⠛⠻⢿⣿⣿⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠴⠶⠿⠿⠿⠛⠛⠋⠉⠀⡀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⠿⠶⢶⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣶⣍⣉⠉⠉⡇⠀⠀⠀⠀⠀⠐⠛⠿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄ ⠹⣿⣿⣷⣦⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠁ ⠀⠈⠻⢯⣤⣶⡂⠀⠀⠀⠀⠀⣤⡄⠀⠀⠀⠀⠀⠀⠰⠄⠀⠀⠼⣿⡏⠀ ⠀⠀⠀⠈⠻⢿⣿⣶⣤⣤⣤⣾⣿⣦⣄⣀⠀⠀⣀⣽⣿⡿⠿⠛⠻⣿⣧⠀ ⠀⠀⠀⠀⠀⣠⣾⣿⣿⢿⣿⣿⣿⣿⣿⡿⠿⢷⣾⣭⣄⣀⠀⠀⠀⠈⠻⣇ ⠀⠀⠀⠀⠰⠛⠋⠁⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠈⠉⠉⠒⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⠀⠀⠉⣳⠤⠒⢊⠉⠉⠉⠉⡍⡉⠉⡐⠒⡲⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠔⠋⠀⠀⠀⡸⡄⠀⠀⠀⠠⣦⣇⡲⣪⣠⠋⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁⠀⠀⠀⠀⠰⣃⣷⢆⠠⠒⢈⣵⣯⣿⠷⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⠊⠀⠀⠀⠀⡀⡠⠀⠀⣹⠁⠀⠀⢀⣀⠴⠊⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡰⠁⢀⠠⢄⣂⠥⢼⠀⠀⣠⠧⠒⠲⡊⢿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⠴⠒⡲⣡⡴⠗⠋⠁⠀⠀⢸⠀⡴⠁⠀⠀⠀⠙⡼⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠉⠉⠒⡟⠉⡆⠀⠀⠀⠀⠀⠘⠼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠸⣴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠖⢲⢶⠶⣶⡶⠶⡶⠶⣖⠒⠒⠒⢒⠒⠒⠒⠒⢒⠒⠒⠒⠒⢒⣒⢶⠶⢶⣶⢶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⣶⣿⣷⣶⣶⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣦⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⠿⠟⠛⠛⠉⠉⣉⣉⣉⣉⣉⣛⣛⡻⠿⣿⣿⣿⣿⣷⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣿⣿⠟⠋⢁⣀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠋⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠋⣀⣴⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠏⢀⣴⣿⣿⣿⣿⠏⣼⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣤⣈⣙⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠛⣻⣿⣿⠆ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠃⢠⣿⣿⣿⣿⣿⡏⠀⢻⣿⣿⠘⣿⣿⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣥⣤⣤⣴⣾⣿⠟⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠃⢀⣿⣿⣿⣿⣿⣿⣧⡀⠈⠻⣿⣦⠈⠻⠄⢹⣿⣿⣿⡿⠟⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣽⣿⠟⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣨⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⠀⠀⠀⢀⣴⠾⠛⠉⠁⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠉⠀⠀⠀⠀⠀⢸⣿⣦⣶⣰⣧⣠⣦⠀⣴⣆⢀⣦⣀⣴⣄⣴⣿⣿⣿⣿⣶⣶⣤⣄⡀⠀ ⠀⠀⠀⠀⣀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠟⠛⠛⠛⠛⠛⠛⠛⠓ ⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠟⠛⠋⠉⠀⠀⣀⣠⣤⣶⡶⠶⠶⠶⠶⠶⢶⣶⣦⣤⣄⣙⠀⠘⠟⠙⢿⡿⢻⣿⡿⣿⡿⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠻⢿⣷⣶⣤⣀⡀⠀⠉⠀⠈⣁⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⠿⠿⠿⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣤⡘⣿⡿⠛⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠛⢧⠈⠁⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠁⠀⠈⠀⡀⠈⠻⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠀⣈⡙⠻⠿⢷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠘⠻⢷⣶⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⢨⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⢸⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡆⠀⢸⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇⣸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
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⠀⠀⠀⠀⠀⢀⡠⠴⠒⠒⠀⠒⠒⠤⢀⡀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠂⠀⠀⠒⠢⢄⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⡠⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⣄⠀⠀⣠⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢄⠀⠀⠀ ⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣳⣞⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄⠀ ⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠈⠁⠀⠀⠀⠉⠑⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄ ⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠋⠀⠀⢀⡠⣤⣤⣤⣀⠀⠀⠈⠓⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁⠀⠀⣠⣴⣅⠀⣿⣿⡇⢀⣵⣦⡀⠀⠀⠑⣄⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⠀⡠⠊⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠢⡀⠀⠈⠣⡀⠀⠀⠀⠀⠀⠀⢸ ⣧⠀⠀⠀⣠⣤⣄⡴⠁⠀⢀⣼⣿⣶⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣴⣿⣦⠀⠀⠙⣄⣀⣀⠀⠀⠀⣸ ⠘⡀⠀⢸⣿⣿⣿⡆⠀⣰⠁⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⣱⡄⠀⣾⣿⣿⣷⡀⢀⠃ ⠀⢳⡀⠈⢻⡿⠛⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⡄⠹⢿⣿⠟⢁⡎⠀ ⠀⠀⢳⡀⡎⠀⠀⠀⣿⣿⣿⣿⡟⢿⣿⣿⠯⠬⠛⠛⠻⠧⠬⣿⣿⠟⣿⣿⣿⣿⣷⠀⠀⢹⢠⠎⠀⠀ ⠀⠀⠀⠙⣄⠀⠀⠀⠈⠉⠛⠛⠓⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠋⠁⠀⠀⣴⠏⠀⠀⠀ ⠀⠀⠀⠀⠈⠣⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠏⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠦⣀⠀⠀⠀⠀⣀⡴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦⠤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡠⢤⣤⣀⣀⣤⣄⣠⣼⣧⣶⠆⠀⠀⠀⡀⠀⠀⣀⠀⠀ ⠀⠀⠀⠀⠀⠉⠉⠉⠛⠛⠛⠉⠭⠙⠛⠋⠛⠒⠒⠒⠋⠀⠂⠒⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠛⠻⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠋⠀⠀⠀⠀⠹⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣰⣿⡇⠀⠀⠀⠀⠀⠰⠿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣼⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⣼⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⠋⠀⢀⣠⣤⣴⣶⣾⣶⢶⣶⣦⣤⣤⡀⠈⠻⡀⠀⠀⠀⠀ ⠀⠀⠀⣸⠃⢠⣾⡟⠋⡁⢸⡀⢠⡆⠀⣦⠀⡍⢙⠻⣦⠀⢱⡀⠀⠀⠀ ⠀⠀⢰⡏⠀⣾⠁⢷⣄⣷⣾⣷⣿⣿⣾⣿⣼⣧⣾⢀⠿⡆⠀⣧⠀⠀⠀ ⠀⢀⣿⡇⢰⣇⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡔⡃⠀⣿⣧⠀⠀ ⠀⣾⣿⠁⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⣿⣿⡆⠀ ⣸⣿⡏⠀⠀⢹⣿⣿⣿⠛⣿⠏⢹⣿⠃⢻⡟⢹⣿⣿⣿⠀⠀⢿⣿⣷⠀ ⣿⡿⠀⠀⠀⠸⡿⠻⠙⣀⣨⠤⠤⠧⠤⠬⣀⡘⠹⠻⡻⠀⠀⠈⢿⣿⡇ ⣿⠇⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇ ⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡗ ⠈⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀
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⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⠉⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⢉⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⣿⣿⣿ ⣿⣿⣷⠘⠿⠤⡄⠄⠀⢈⠙⠻⠿⠿⠋⠀⣠⡆⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⣸⣿⣿⣿ ⣿⣿⣿⣧⠄⣀⠀⠀⠈⠙⠏⠓⠦⣤⣀⡘⠿⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠆⢿⣿⣿⣿ ⣿⣿⣿⣿⣷⡄⠙⣶⣠⠀⢷⡀⠀⠈⠻⡮⣅⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢰⢸⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⠸⠊⠀⢀⣿⣧⠀⠀⠀⠸⣦⡀⠠⡙⠻⣿⣿⣿⣿⣿⣿⡇⠸⠸⢸⣿⣿⣿ ⣿⣿⣿⣿⣿⡀⠀⠠⠴⠿⣿⡿⣶⣄⣀⢄⣀⠀⠀⠀⠐⠈⠻⢿⣿⣿⣿⣷⡀⠀⢸⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣶⣦⡀⠙⢃⢘⠛⠛⡀⠃⣷⠀⢠⠱⣤⡀⡀⢈⣙⣉⣩⡔⠁⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⠄⠒⠊⠙⠓⠄⠨⢸⠰⣦⠠⢬⣀⣒⣛⡛⠩⠀⠀⢻⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⣾⣶⣤⣤⣌⡺⢆⠈⡋⠁⠈⣉⣤⣴⣷⡀⢂⡈⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣼⣿⣿⣿⣿⣿⣦⣄⡈⠻⣿⣿⣿⣿⣿⣷⣦⠁⢹⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣾⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⢒⡒⠂⠀⠀⠀⠀⠀⠀⠐⠶⠶⠖⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠖⠂⠀⢸⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡤⠴⠶⠖⠒⠉⠉⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢼⡿⣶⣤⣼⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⡶⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠈⢻⣦⡙⢿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠁⠀⠀⠀⠀⣀⣠⡴⣿⡄⠀⠀⠀⡀⠀⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠆⠈⠙⠻⣾⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡇⠀⠀⠀⢠⣾⣿⠟⠁⣿⠇⠀⠄⠀⠀⠀⠀⠘⢷⡚⠓⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠶⠛⠀⠀⠀⣰⣿⣾⠃⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⢀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠾⠶⠶⠶⠾⠛⢿⣿⣧⣀⣀⣿⣿⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠼⠿⠿⠶⠶⠚⠛⠉⠉⣀⣠⣤⣤⣤⣶⣶⣶⣶⣿⣿⣿⢿⡿⠷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⢹⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣢⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣽⣿⠻⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡏⠀⢸⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣿⡟⠻⣿⣭⣿⣿⣧⣀⣤⣉⠙⠿⢿⣿⣿⡟⠛⢿⣿⢻⣿⣿⣿⣧⠀⣈⠓⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⡟⠀⠀⢸⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠘⢿⣿⢻⣿⡿⣯⠙⣿⠿⠿⠛⠛⠛⠛⠛⠛⠛⢶⡿⢻⣿⣷⣦⣾⣿⡌⣿⡏⣿⡟⠻⣿⣆⠀⢙⣦⡄⠀⠀⠀⠀⡀⠀⠀⠀⢀⣾⣯⡿⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠈⠈⠓⠾⠥⠤⠤⠶⠖⠒⠋⠉⠉⠉⠂⠀⠀⠁⠀⠉⡞⢃⣿⣿⣿⡜⣿⣿⣇⣄⣾⣿⣧⠀⠉⡻⣷⣦⣴⣾⡇⠀⠀⣠⣿⡟⡿⠃⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠤⠤⣄⣀⡀⠀⣀⠀⠀⠀⠀⠀⠀⠘⢿⠻⣿⣿⣼⣿⡟⠉⠛⠻⢿⣷⣄⣻⣿⣿⣿⣿⣿⣿⣿⠿⠟⣿⠧⠤⠔⠒⠒⢺⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⡇⠀⡀⠀⠀⠀⠀⠈⠀⠳⢮⣿⣿⣟⢷⡄⠀⠀⠀⠈⠻⣿⣿⣄⠉⣍⣩⡿⠛⠳⣄⣿⡀⠀⠀⠀⠀⠨⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⣀⣀⣀⡤⠤⠖⠒⢸⠁⠀⣩⠟⠉⠒⠒⠶⣤⠤⣤⣿⣿⣿⡞⣿⡄⢹⣶⣾⣶⡿⣿⣿⣷⣌⠻⡄⠀⠀⠙⠿⣧⡄⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⣼⣄⢰⠋⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⣿⣿⡞⣧⡀⠀⠙⡿⠀⠀⢹⣯⣽⡿⢷⠀⠀⠀⠀⠀⠁⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠿⣿⡏⣴⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣇⠀⠀⠀⢀⡠⠾⡟⢻⡔⢻⡇⠀⠀⠀⠀⠀⢶⣤⣀⣸⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⢟⠃⣀⣈⡽⣟⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⡟⠀⠀⠀⣽⣷⠚⠡⠴⣟⣿⠷⠦⣤⣤⣴⣴⣾⡿⠟⢻⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣐⣰⡵⠟⠁⣻⣈⣿⠽⠞⠛⠛⣫⠀⠀⠀⠀⠀⠀⢰⣴⠛⠛⢿⣿⣦⣤⡄⠀⢈⣛⣛⣿⠛⠋⠉⠀⠀⠈⠉⠻⣿⡏⠙⠒⢻⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⠭⠥⠤⠶⠞⣋⣽⣶⣤⣶⠶⣶⣿⣶⣦⠀⠀⢀⣴⠟⠁⠀⠀⠈⠻⢿⡿⢻⣾⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⠛⠁⢸⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣿⣿⠿⠿⠿⠟⠛⠛⠛⠛⠷⢦⣤⣌⡻⢶⣤⣴⠟⠁⠀⠀⠀⠀⠀⢀⣠⣾⣼⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⣸⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢉⣻⡟⠀⠀⠀⠀⢠⡏⢿⠶⢟⣡⣿⠿⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢖⡿⠟⠋⠁⠀⠀⠀⠀⠀⠘⣧⣠⠶⠛⠉⠀⢀⣼⣇⣠⣄⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣟⣉⠀⠀⢀⣀⣀⣤⣤⡴⠖⠛⢁⣠⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿ ⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣽⣿⣯⣭⣭⣭⣭⣭⣥⣤⣤⣶⣾⣿⣿⣯⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣤⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣴⠟⠛⠶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠸⡿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⣿⡄⠀⠀⠀⠀⠀⠈⠛⠿⢷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣼⡟⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠉⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣿⠇⠀⢀⣠⣴⢿⠛⢻⠉⡍⢩⢻⣆⠘⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢺⡏⠀⣴⠟⠋⣦⣸⣧⣸⣧⣿⣾⣼⣼⠂⠘⣿⣦⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⡇⢸⠛⣄⣳⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠹⣿⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⡇⠸⡱⣾⣿⣿⣿⣿⣿⣿⢿⣿⢻⣿⣿⡆⠀⠙⢿⣷⡄⠀⠀⠀⠀ ⠀⠀⠀⢸⣿⠀⢫⣿⣿⣿⡿⣿⠘⢿⣀⣉⠀⠩⠝⠂⠀⠀⠀⠙⣿⡀⠀⠀⠀ ⠀⠀⠀⢸⣿⡆⠀⠹⣿⣿⢣⡠⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⠀⠀⠀ ⠀⠀⠀⠸⣿⡇⠀⠀⠉⠒⠉⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣇⠀⠀ ⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡄⠀ ⠀⠀⠀⢀⣜⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⢹⣧⠀ ⠤⠴⠾⠛⠛⠻⠷⠷⠤⠤⢤⣠⣶⣄⡠⠤⠶⠶⠿⠛⠻⠷⣦⣤⣀⣀⣀⣻⠆ ⠀⠀⠀⠀⠀⠀⣀⣤⠴⠾⠛⠋⠉⠙⠛⠶⢤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣤⣤⠶⠶⠶⠶⠾⠛⠛⠛⠛⠛⠛⠛⢿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣿⣛⠛⠛⠛⠓⠢⢄⡀⠀⠤⠟⠂⠀⠀⠀⠀⠀⠀⢀⡿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠾⠛⠉⠑⠤⣙⢮⡉⠓⣦⣄⡀⠀⣹⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⡶⠞⠋⠉⠀⠀⠀⠀⠀⠀⠒⠛⠛⠛⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢰⡟⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠾⠛⠉⣡⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⢺⢿⢉⡽⡟⢓⣶⠦⢤⣀⡀⠈⠳⣿⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠟⠁⠀⠀⣀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠁⠀⢛⠛⠛⠻⢷⡧⣾⡴⣛⣏⣹⡇⣀⣿⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⠞⠋⠀⣀⠤⠒⢉⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠋⠀⣀⠴⠚⠛⠛⠯⡑⠂⠀⠀⡏⢹⣿⡾⠟⠋⠁⠀⠀ ⠀⠀⠀⠀⣠⠞⠁⠀⠐⠊⠀⠀⢠⡿⠁⠀⢰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⣤⡿⠋⠀⠀⠀⠀⠀⠀⡹⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⡞⠁⠀⠀⠀⠀⠀⠀⢠⡿⠁⢀⢸⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡞⠋⠉⠉⠓⠒⠢⢤⣴⣥⣆⣠⡾⠋⠀⠀⠀⣦⠀⠀⠀⠀ ⠀⣼⠋⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⢸⠀⡆⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⢽⣦⠀⠀⠀⠀⠀⠀⣟⡿⣽⡏⠀⠀⠀⠀⠀⡿⣧⠀⠀⠀ ⢸⣇⣤⣤⣤⣤⣄⡀⠀⢀⡾⠁⠀⠀⢘⡆⠱⡈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⢻⡚⡆⣀⠀⠀⠀⢸⡽⣿⠃⠀⠀⠀⠀⠀⡇⢹⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠙⢷⣾⠃⠀⠀⠀⠈⠾⣦⣙⠪⢷⠄⠀⠀⠀⠀⠀⠀⠀⠈⠻⣭⣟⣹⢦⣀⣀⣟⣹⡟⠀⠀⠀⠀⠀⠀⡇⠈⣷⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⣤⠶⠖⠊⠉⠀⠉⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣼⣞⣹⣯⠟⠁⠀⠀⠀⠀⠀⠀⡇⠀⢹⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⡾⠁⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣲⡾⠟⠛⠳⣤⡀⠀⠀⠀⠀⠀⠀⡇⠀⣸⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡟⠁⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠙⣻⡿⣿⣯⣁⠀⢰⡀⠀⠀⠙⠳⣄⡀⠀⢠⡟⠋⡔⣿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⢀⠔⠋⢰⠛⢄⠉⠛⠾⣧⡀⠀⠀⠀⠈⠻⣤⣸⡡⠎⢀⡏⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠙⠲⢤⣈⣉⠳⢦⣄⡀⠀⠈⠻⣄⠀⣼⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⠀⠀⠀⢠⡾⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠛⠶⣤⡙⣾⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⣠⠟⠀⠙⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠟⠻⠇⠀⠀⠀ ⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⣀⣤⠾⠻⣦⡀⠀⠀⠀⠈⠑⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠟⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣏⣠⡴⠞⠋⠉⠀⠀⠀⠈⠛⢶⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⣉⣽⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢋⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠒⠶⠶⢤⣤⣤⣤⣤⣤⣤⣤⡤⠴⠶⠖⠚⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠊⠉⠀⠀⠀⠀⠀⠈⠉⠒⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⢀⡀⠤⠤⠤⠤⡄⢀⣀⠀⠀⢀⣈⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡠⠓⠉⠁⠢⡀⠀⠀⠀⠈⢆⠀⠈⠐⠣⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡰⠫⣀⠀⠀⠀⠀⢱⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠱⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⠎⠀⠀⠈⢆⠀⠀⠀⢎⡀⠀⠀⠀⠣⣄⠀⠀⠀⠀⠀⡇⠑⣄⠀⠀⠀⡠⠒⠉⠑⡆⠀ ⠀⠀⢠⠃⠀⠀⠀⠀⠈⠆⠀⠀⠀⢱⠀⠀⠀⠀⠈⡆⠀⠀⠀⡠⠃⠀⠘⢆⢀⠞⠀⠀⠀⢀⠏⠀ ⠀⢀⠇⠀⡤⣒⡐⢦⠀⢸⠀⠀⠀⡸⠀⠀⠀⠀⠀⡆⠀⠀⠀⠈⢣⠀⠀⠈⠇⠀⠀⠀⠀⡎⠀⠀ ⢀⡜⠀⠸⡸⣿⠟⢠⠂⠀⠀⠀⠺⡁⠀⠀⠀⠀⢎⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀ ⠸⠤⢤⠄⠉⠒⠒⠁⠀⢀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠃⠀⠀⠀⠤⣎⠀⠀⠀⡀⠀⠀⠀⠀⠀⢹⠀ ⠀⢶⡁⠀⠀⠀⠀⠀⠀⢸⠁⠀⢀⡰⠀⠀⠀⠀⣤⠃⠀⠀⠀⠀⠘⠀⢀⠜⠉⠢⣀⠀⠀⠀⡸⠂ ⠀⠀⠈⠓⢄⠀⠀⠀⠀⠆⠀⠀⠉⢢⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⣸⠖⠁⠀⠀⠀⠀⠉⠉⠉⠀⠀ ⠀⠀⠀⠀⠀⠑⠢⣀⡜⠀⠀⠀⠀⡸⠀⠀⠀⠀⢀⠗⠀⣀⠤⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⡖⠢⠶⢊⣀⣀⣀⣠⠴⡯⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠄⣀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠒⠂⠀⠐⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠞⢉⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⡄⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠶⠟⢹⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠈⡇⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣸⣿⠈⠛⢷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠟⠋⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⡇⠀⠀⣸⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⢸⡀⠀⠀⠈⠙⠻⢶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠇⠀⠀⠉⠉⠙⠳⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⡟⠈⢧⠀⠀⠀⠀⠀⠀⠈⠙⠛⠳⣦⣤⣀⠀⠀⠀⢀⣾⡟⠁⠀⠲⣄⡀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠞⢻⣇⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⣶⣶⣶⣶⣾⠇ ⡇⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⡟⠙⣶⣬⠭⣛⡳⠶⠾⣯⣤⣀⣀⣀⣀⠉⠲⠤⠨⣧⢀⣀⣀⣠⣤⠴⠶⠛⠉⠁⠀⠀⢸⡟⣷⢤⣀⡀⠀⣀⡀⣀⣀⠠⢀⣴⠶⠋⠁⠀ ⣷⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⡇⢸⣿⣿⡀⠀⠈⡏⠙⣳⠀⠀⠉⠉⠉⠛⠛⠛⠛⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣽⡟⠀⠈⠉⠓⠒⠒⠒⠚⠋⠉⠀⠀⠀⠀⠀ ⢿⡇⠁⠀⠈⢣⡀⠀⠀⠀⠀⢳⡘⢿⣿⣿⣷⣶⠇⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣀⡀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⣷⡀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠙⠦⢭⣻⡭⠵⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣧⣬⣭⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢹⡇⠀⠀⠀⠀⠀⠉⠒⠤⠤⠤⠤⠤⠞⠒⠒⡒⠲⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⡿⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⡇⠀⠀⠀⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣯⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡞⡟⢻⠃⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⠿⢋⣽⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠻⣆⠀⠀⢀⣠⣤⣾⠛⠋⡏⠙⣺⠏⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⣶⠒⠉⠉⠉⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠛⠻⣍⠀⠀⡇⠙⠲⣾⡾⠃⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⢰⡇⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦⢿⣠⠾⢋⡠⠀⠀⠀⠀⠀⡀⠀⠀⠀⢷⡀⠀⠀⠀⢸⣇⣀⡴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⠷⠿⣏⡀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠻⣿⣦⠀⠀⠈⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠲⠤⢤⣤⣠⣤⣤⣴⣿⠿⣿⡙⢦⡀⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣹⡄⠈⠻⣯⡸⠿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠈⠙⠓⠾⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠷⣍⢳⣭⡹⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⢸⠘⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢠⠃⣿⢠⠀⠀⠀⠀⠀⠀⠀⠀⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡳⣎⡳⢎⡹⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣯⣿⣿⣿⣿⣀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠁⡿⣰⠀⠀⠀⠀⠀⠀⠀⠀⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣛⢧⣿⣧⣧⣧⣿⣿⣾⣽⣿⣿⣼⣿⣿⣯⣿⣿⣯⣿⣾⣽⣿⣿⣾⣿⣿⣼⣿⣿⣷⣽⣿⣿⣷⣿⣿⣿⣯⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⢫⣴⡾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⠠⠁⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠁⢠⡏⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⣿⣼⣿⣿⣿⣿⣿⣯⣿⣿⣹⣿⣿⣿ ⡝⢫⣵⣾⣿⣻⣿⣿⢻⣿⣿⢻⣿⣿⣿⣿⣿⣿⣟⣿⣻⣿⣿⣿⣿⣿⣿⣻⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⡟⣿⣿⣿⣾⣿⣶⣭⢲⣬⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣽⣿⣟⣿⣿⣿⣿⣿⠀⠃⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⡌⠃⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢞⡳⣎⡵⢎⡹⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢦⣘⡳⢂⡵⢊⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠀⠰⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⢠⣾⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⣿⣾⣽⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡼⣚⢵⣫⣜⠳⣿⣿⣯⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡛⢍⣣⠭⢟⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣸⠀⠀⠀⠀⠀⡆⠈⠀⠀⠀⠀⡄⡟⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣾⣟⣾⣿⣯⡿⣷⣿⣿⣿⣿⣿⣿ ⣛⣥⣚⠷⣏⢣⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⢸⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⢣⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⣿⣿⣿⣯⣿⣟⣾⣟⣿⣯⣿⣷⣿⣿⣿⣿ ⡞⣏⡖⢭⡻⢧⣿⣯⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡿⣿⣿⣿⣿⠶⣟⢸⠀⠀⠀⠀⠀⠀⡄⠘⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⣷⣽⢾⣿⣟⢯⣿⣯⣿⢯⣿⣳⣿⣷⣿⣿⣿ ⡧⢛⣧⢎⡹⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⡿⣾⣿⣟⣿⣿⣻⡬⣟⢸⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠇⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⣸⡇⣿⣯⣽⡿⣽⡿⣷⢯⣿⣳⣿⣽⣿⣯⣿⣿ ⢧⡜⢻⣥⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⢿⣾⣿⣽⣿⣿⣾⢳⣎⣏⢻⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⡇⢯⣽⡿⢯⣳⣿⣳⣿⣟⣿⣿⡿⣷⣯⣟⣿ ⣲⡝⢻⣿⣿⣿⣻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣾⣽⢿⣾⣿⣽⣿⣿⣿⣎⠱⢮⣇⣿⠀⠢⠈⠀⠀⠀⠀⠀⠆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣸⡇⢾⣿⡷⣟⣯⡽⣿⢯⣿⣹⡶⣿⣾⣽⣻⣿ ⣿⣿⣿⣿⣿⣾⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣻⣿⣽⣻⣿⣾⡿⣿⣿⣢⠝⣢⡝⢢⣷⠸⠀⡀⠢⠈⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢠⡿⣞⣫⣽⠾⣽⡿⢯⣿⣳⡜⢫⣵⣿⣾⣟⣿ ⣿⣿⣽⣻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣽⢿⣿⣯⢾⣿⣟⢿⣯⣿⣾⣘⢯⡛⢾⡴⣦⡷⢹⡀⠀⠀⡀⠢⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠎⣆⢬⣾⣧⢷⣶⡿⢷⣼⢣⡬⢞⡣⣜⣿⣽⣿ ⣿⣿⣿⣿⣿⣿⣷⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣻⣿⣷⣟⣯⡾⣽⣿⣯⣟⡿⣿⣿⢶⣬⣐⠈⠠⠐⢀⠌⡀⣬⠷⠛⠉⠀⣀⠡⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣴⢀⠀⣾⢀⡇⢺⡤⠓⢢⡝⢢⣞⡍⢳⣎⡱⣿⣿ ⣿⣿⡿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣽⣻⣿⣯⣟⣿⣿⣿⣶⣦⣄⣈⠁⠠⠄⠀⠐⠠⡁⠄⠁⠄⠀⠐⡠⣅⢶⠙⠈⡄⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡲⠄⡤⠀⣐⠀⡟⠆⣈⠱⢦⡙⢬⡞⢎⡱⢞⣩⡼⣿ ⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣟⣎⣜⣳⣤⣾⣭⣶⣷⣾⣶⢒⠷⠂⢁⠄⠂⠁⡀⠐⢈⠄⡀⠈⠐⠠⡁⠀⠠⢁⠂⠀⡠⣌⠲⠻⢄⠑⠀⠀⠀⠀⠀⠀⠊⣨⠐⠠⢁⡀⠀⠏⢨⢢⡔⡙⠦⢊⡱⢞⣍⡴⡞⢋⣴⡟ ⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⢷⢦⠳⡙⢌⠡⠌⠢⠄⠀⠠⠈⠐⠠⠂⠄⠈⠄⠂⢁⠂⠄⡀⠐⠄⡀⠈⠐⢀⠠⠐⠄⡀⢬⠒⢓⠛⠛⠋⠗⡴⢈⠄⠀⡐⠀⠋⡿⢂⡉⢆⡡⠖⣉⠶⣉⠷⣊⡵⢚⣱⡼⡟ ⣷⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣙⠲⠙⠉⢀⠂⣄⠢⠙⢀⠡⢀⠠⠂⠄⡈⠄⠈⠐⢀⠠⠈⠐⠠⢁⠄⡈⠄⠀⡐⠈⢁⠄⡀⠈⠐⡀⠂⠀⠠⡁⠀⠐⠄⠀⢈⠄⠃⣼⠂⠔⠊⢡⡜⠣⣑⠮⣘⠷⣋⢧⡎⣙⡴⡟ ⢳⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣷⣞⣿⣷⣿⣿⣿⣟⣭⢛⣭⡝⠫⣌⠱⡢⣍⠢⠙⢀⡀⢮⠁⠄⡀⠈⠡⠄⠁⠂⠄⡀⠐⠂⠄⡀⠈⠠⠁⠠⢂⠁⠄⠁⠂⢀⠂⠄⡁⠀⢈⡀⠐⠈⠠⡀⠀⠉⠉⣽⠂⢂⡡⠔⢪⡕⢊⡴⠞⣍⠳⢣⢦⡝⡣⣜⡟ ⡹⢧⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣯⡗⢮⣝⡧⣞⣣⣜⣣⠔⣊⠱⢆⠈⢢⡐⢮⠈⠐⠠⡈⠐⠄⠀⠌⠀⠐⠠⢁⡀⠈⠠⢂⠀⢈⠐⡀⠈⠐⠈⠠⠁⠠⢀⠐⠠⠂⠀⢁⠊⠐⠤⣄⢀⡽⣩⠩⢛⡶⢒⡶⠝⢪⡜⣙⠶⣋⡱⢮⣣⡜⢫⡴⡟ ⣜⡳⣎⣗⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣾⣟⣧⣷⡾⢿⣏⡱⢞⡩⢴⡫⠔⢪⡔⠘⢣⠀⠡⢂⢄⠈⠐⢁⠄⠈⠠⢈⠐⠂⠄⡀⠐⢀⠌⠂⠀⢁⠄⠈⢂⠀⢁⠄⡁⠀⠡⠀⠐⠠⠊⡔⢁⠂⠄⠀⠃⣽⣾⣤⣀⠀⠀⠀⣄⢛⢣⣔⠫⣱⡜⢫⡱⢞⣩⠶⣏ ⡴⢛⣩⢶⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣯⣾⣷⣮⣝⣫⣵⣽⣶⣻⣽⡞⢭⣳⣮⠽⣚⡥⢓⡤⠜⢢⡑⢡⡔⠊⠁⢀⠐⡀⠈⠐⠌⠁⠂⡀⠈⠠⢁⡀⠐⠄⠂⡀⠈⠐⠄⠂⡀⠈⠐⠠⠄⠀⡈⠂⡴⠐⠠⠁⠋⠓⠖⣴⢀⠀⠀⠀⠺⠀⠀⠍⡿⢻⣯⢎⡿⣿⢧⡭⠧⢓⣬⡟ ⣥⠞⣋⡵⢎⡭⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⢿⣿⠷⣞⡝⡲⣝⡦⣜⡷⣛⠶⣋⢦⡙⣱⠳⣌⡓⢌⡸⡑⠢⢌⢃⡠⠚⢄⠉⠠⠐⠈⠐⢁⠂⡀⠋⠖⡨⢦⠙⠄⠀⠡⢀⠐⠠⠂⠄⡀⠈⢂⠀⢀⠉⠛⠴⣫⠕⢉⠀⠀⠀⠀⠀⠀⢄⡦⡿⣴⣠⣇⡻⢌⣷⣧⡾⣹⢲⡹⢦⡟ ⣩⠶⢎⡱⢞⣍⡲⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣻⣿⣟⣻⣿⡟⣎⡝⢦⡙⣦⢛⢦⡙⡬⠳⣌⠳⢆⡍⡑⠦⢈⢱⡌⠊⢅⠂⢠⠌⡁⠉⠛⠼⣠⠐⢀⡐⠤⡈⠢⢉⠀⠡⠄⡀⠈⠡⢀⠌⠂⠤⣏⡼⢀⠄⢸⠀⠀⣀⢄⠠⠒⠑⠉⠀⠋⠛⠋⠰⡀⢷⣌⡹⢳⣏⡛⢧⡙⢦⡟ ⢓⣣⢝⣣⡜⢛⣥⠞⣍⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣷⣯⢿⣳⣽⡿⢫⣽⡹⢾⡙⢦⡙⢦⠛⣅⠳⣌⠳⣬⠜⡱⢎⣉⠴⠎⠡⢢⡕⢋⠾⣴⣰⢈⠈⢂⡀⠁⠤⠠⡈⠢⡈⢅⠒⠈⢀⠉⠉⠉⠉⠋⡯⣴⠀⠀⡁⢰⠀⠀⠀⠀⠀⠀⠃⣸⣏⣿⢶⣻⠙⠀⡄⣽⡞⡧⣿⣼⠾⡙⢦⡝ ⡱⢲⡹⢦⡜⠳⣩⠶⣋⡱⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⢿⣻⣽⡿⢯⣳⣞⡷⡞⣛⢮⡙⢦⡙⢣⡱⣎⠳⣎⡓⢦⠝⢪⡱⢓⣩⠿⣦⣈⠰⢃⠀⠖⠄⠂⡀⠈⠐⢁⠂⠄⡀⠢⠈⡄⣀⣌⣳⢾⣗⢫⣼⠀⠀⠀⡀⠠⠀⠀⠀⠀⠀⠀⣰⠏⣒⢠⡀⢽⣄⣻⠼⣿⡜⢻⣧⣳⢬⡚⢦⡝ ⡹⢦⡙⢮⣍⠳⣌⡳⢎⡣⢖⣋⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⡿⣻⣿⣯⢷⣻⣷⣞⣻⢯⣱⢿⣎⢷⡚⢭⡱⢞⢣⣜⡳⣜⠮⣙⢧⡿⣨⡄⢳⡈⠢⠈⠱⠠⢄⠓⠒⠈⠌⠀⠐⠠⢁⠄⡀⠢⢈⠐⠁⣌⣳⢯⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⣄⡶⣰⡇⡗⢞⣙⡼⠳⣌⠳⢆⡝ ⡓⢦⡙⢎⣑⠽⣆⠳⣌⢱⡼⢓⣣⢎⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣻⣿⣻⢿⣷⣟⣾⡽⣻⣽⢾⣻⣷⡟⣭⣳⢾⣝⡾⡝⢫⣕⡺⡗⣎⡟⣿⣿⢷⡘⠀⣐⠢⡈⠣⢈⠤⠒⠁⢄⠁⠬⠢⡁⠉⡀⠐⢀⡈⠳⠀⠡⠀⣇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠷⠿⠀⠁⠀⠀⡏⠃⢽⣺⡵⠣⣒⢎⢣⡜ ⡱⢮⡓⣍⠧⡘⣭⠲⣍⡲⡜⣋⠧⢆⣙⠵⣎⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣯⣟⣿⣯⢿⣾⣽⡿⣟⣯⣟⣯⡷⣟⣯⡷⣞⡿⣏⡽⡾⡟⢯⣏⢿⣿⣻⣽⣿⠻⠒⠌⡠⠢⠌⡑⠄⠁⢄⠕⠑⠂⢀⡁⠄⠀⢈⠂⡀⢄⠙⠂⡄⢸⠀⠀⠀⠀⠀⠀⠗⠾⢧⠏⡿⢶⡉⡟⣩⠀⢠⠀⠁⢰⡇⣹⣬⡛⢆⡣⢆⢢⡜ ⡵⠎⢣⡜⠬⡞⢃⡴⢋⡴⡚⢍⡱⢧⡌⡸⠜⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣻⣿⢿⣿⣷⣟⡿⣟⢯⣽⣻⢿⣳⣾⣟⢯⣽⡾⣟⢯⣳⣿⣿⣽⢾⣻⣷⠿⠙⠈⢀⠡⢄⠐⢂⠈⠡⠀⢄⢕⢕⠑⠈⢂⠀⢁⡀⠐⡀⢔⠑⡆⠀⠀⠀⠀⠀⠀⡄⢸⡇⣸⣶⠿⣧⣰⣿⢸⠀⠃⡰⠀⡞⢃⢦⠙⣣⢄⢋⢡⡔ ⡱⡜⢊⡱⢎⢑⣬⡚⢌⡹⢆⡱⡚⢣⡜⢍⡱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣟⡿⣿⣻⢿⣾⣽⣻⣿⡾⣿⣟⣻⢿⣷⣯⣞⣻⣿⣿⣽⣿⣟⣯⣳⣽⡾⣿⠹⠀⠌⡀⠡⢂⠈⡁⠄⠀⢢⢋⣧⠘⡁⠀⠐⠠⡐⠀⠐⢢⢫⠀⠀⠀⠀⠀⠀⣀⠀⠀⠄⠀⡀⠀⠀⠀⠞⢠⠁⡾⢋⣡⠴⡙⠦⣊⠀⣓⠥ ⠦⡜⢋⣡⠞⣡⠜⢣⢆⡙⢦⡙⠦⢎⡌⠱⡱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣽⢿⣾⣻⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣽⣿⣿⣯⢿⣿⣾⢿⣿⡿⣷⣻⣿⣿⣿⣿⣿⣞⡿⣟⣯⡷⣟⣿⣰⢳⠀⢈⠀⢪⢆⠈⠄⡀⠁⢸⡘⢠⠠⠂⡀⠁⠠⡈⠄⠀⡌⢷⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠔⣠⠉⠞⣼⠣⠰⣙⠦⡑⢣⢌⣀⠧⡂ ⢤⠳⢌⡰⠜⢪⡕⢊⢥⡘⢦⡙⢣⢆⣉⡰⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣻⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⢿⣿⣿⣿⣿⣿⣟⣿⡾⣽⢿⣽⣻⣿⣾⣌⡓⡒⢲⠀⢁⠄⠀⠈⡠⣀⡜⠆⡘⢀⠠⢁⡀⠈⠐⠄⠈⢁⠂⡀⣳⠄⠂⠐⠉⠈⠀⠀⠀⠥⡉⠊⠞⡤⢰⡰⠖⢂⡰⠒⣌⡑⠦⠃⢀⠀⢢ ⣡⠲⣍⡆⠎⢍⡢⠜⢣⡔⢎⡑⠱⢬⡜⡓⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢯⣿⣯⣟⡿⣿⣲⢃⢀⡰⢌⠳⡈⠀⠐⢈⠄⡈⠗⢸⣶⠈⢀⡀⠀⠠⠂⡀⠐⠄⠀⠐⠡⣄⢻⠀⢈⡄⠳⣈⣂⣄⣂⣀⠌⠇⣸⣟⣰⣀⣃⣄⣈⣁⣀⣀⢂⡉⠁⢢ ⢡⡰⣿⢻⢆⡑⢎⡡⢔⡩⢔⡩⠦⡍⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢿⣿⣿⡿⣿⡿⣿⣟⣿⣟⡿⣿⣿⣿⣿⣿⣿⣿⣾⢿⣿⣯⢿⣿⣿⣧⣔⡈⠰⢃⡄⠌⠂⢁⣆⡘⠁⠄⠀⡈⡐⠵⡢⣀⣄⣀⢂⠤⠢⠑⡀⠐⢀⠌⠁⠂⡄⢹⠀⢉⡀⢧⠈⡐⠈⠔⢂⡄⢻⢢⠀⠀⡼⠧⠀⠀⠀⠈⠂⣀⠑⠢ ⡌⡙⡇⣿⣿⠻⢛⣋⡍⠛⣛⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⢿⣻⣿⣿⢿⣿⣿⣺⢉⢢⡑⠌⡐⢘⠣⢀⠱⢀⠢⣇⠈⡈⠄⠀⡐⠡⣂⣈⠐⣁⠄⠤⡘⠁⢣⠀⢁⠂⠀⠐⠠⣇⡈⠁⣂⠠⢷⠈⠐⠡⡄⠆⢸⠀⠀⠀⢇⡿⣏⢧⠉⠀⠁⠀⠂⢡ ⠜⠣⡐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡽⣿⣻⢿⣿⣿⢾⠃⢄⠨⡑⠤⠘⢨⡔⠈⡐⠌⠀⢻⠀⢀⡀⠁⠉⢃⢀⠚⠐⡁⠈⡄⠸⡽⡘⠀⠐⢈⠄⡁⠀⢹⠀⢂⠄⠀⢧⠈⠠⡄⠀⢿⠯⣤⢉⡞⡿⣭⣆⢻⢉⠀⡀⠁⠠ ⠣⢄⠨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣟⣿⣿⡿⣿⢹⠰⢌⡑⠡⢢⠍⢂⠔⢈⠡⠄⣱⣄⣑⣌⣀⢈⠠⠈⠐⠄⠂⠁⠄⣀⢹⢁⢸⢈⠠⠂⡀⠈⠐⡧⡀⠐⢡⢂⠀⢧⡀⠄⠀⣿⣌⣲⣟⣿⡿⣋⣿⡿⣾⣖⢆⡤⠐ ⠑⣠⠜⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢯⣷⣿⣿⣿⢺⡠⠜⠃⡠⠜⠃⢡⡌⠃⢀⠠⡐⢬⠛⡈⠄⠂⠄⠀⡐⠄⠂⠁⠄⠀⣧⡘⠟⠀⠠⢁⠄⠂⠄⡀⠹⡈⠀⢡⠄⡀⢹⢀⠐⣣⢃⠀⡆⣿⣶⡦⣷⡿⢼⠂⠄⠀⠰ ⡁⠢⢈⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⢿⣻⣯⣿⣿⢱⢂⠌⠢⡌⠑⠠⠱⠂⢃⡀⠐⠌⠂⡀⢻⢀⠐⠡⢀⠠⡐⠁⠐⢡⡁⠀⢧⡆⢹⡀⠈⠡⠄⡁⠀⢻⠤⡃⡄⠘⢀⡎⠊⠄⠀⠡⠄⠀⡌⣦⣤⣤⡬⢠⠌⠂⢀⠱ ⠡⢆⠁⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⣈⣤⣷⢿⣯⣟⣿⠈⢠⠒⢁⠤⡘⡀⠱⢀⠰⢉⠠⠐⢈⠄⡆⠹⠄⠂⡀⠂⠄⠂⡀⠐⠣⠀⡐⢠⡆⠁⠄⠀⠐⠠⠐⡇⠠⠀⠸⢃⠄⠈⢇⡀⠄⠈⡁⠄⠀⢈⡐⢁⢀⠠⠌⡐⢈⠣ ⠂⢁⡿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣳⣵⣾⣿⢳⣯⣿⢰⣈⠑⠠⢐⠢⣁⠐⣈⠤⠂⡄⠉⠄⡀⠈⣇⠘⢁⠂⢀⡐⠀⢈⡀⠘⠣⠀⢠⢈⠂⡀⠂⡁⠀⡐⠈⢸⠤⢃⡀⠘⢂⡄⢸⠐⠄⠀⡈⠐⠌⠁⠠⡐⠄⠀⠰⢈⢢ ⠏⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⣤⣤⡤⢤⣲⠱⣈⣿⠃⠈⠠⡐⠂⢅⡈⠤⠂⣁⠠⢌⠂⡁⠄⠈⣆⡙⠢⠑⠠⠐⢀⠎⡀⠇⡀⠘⢁⠂⢀⠂⢀⠐⡁⠂⠀⢸⢈⡁⠲⡖⠄⠀⢣⡀⠈⢀⠌⠁⠂⠁⠠⡐⢁⡀⠠⠐⢢ ⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡷⠉⠚⠗⠽⠿⠿⡿⣼⢁⢰⡁⠄⠈⠡⠂⣁⠄⠢⠌⠄⢈⠠⠐⠄⠂⡀⢆⠑⢄⡈⠄⠀⢌⠀⠸⢇⠀⠐⠠⢈⡁⠂⠁⠠⠀⣷⠀⠠⠁⣛⢎⠄⡀⢹⠀⢈⠂⠁⠠⠂⠀⠇⠂⡀⠌⠀⢢ ⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣶⣠⢋⠟⡯⠻⠙⠈⠄⠈⠐⠠⡐⠅⠂⢀⠒⢁⡀⠄⠈⢀⡐⠀⢦⢜⠂⢀⠆⠀⡄⠈⠸⠐⢁⠄⠀⠌⠁⠂⢀⡇⡉⢈⠴⠤⠥⠍⠩⡅⠸⠀⢈⠂⠁⠠⠀⡍⠀⠜⠀⠌⢂ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣻⣨⢃⠟⣿⣾⣴⡦⣗⣯⣿⠙⠄⠂⢀⡈⠐⠠⢈⠠⠐⡀⠐⠂⢀⠂⢀⠋⡟⠰⢀⠄⡀⠀⣠⢁⠉⠠⡀⠄⠂⠀⠐⠠⡇⡀⣁⣀⣂⣀⠈⣐⣀⠈⢂⠁⢀⠠⠁⡀⠉⠂⠀⠠⠘⢡ ⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡿⣿⣿⣿⣿⣿⣿⣿⢿⡿⣿⣿⣻⣧⣿⢻⠄⠀⠈⠠⢈⠂⢁⠄⡁⠂⠄⠀⢈⡆⢙⠂⡀⣄⣀⣈⣡⠀⢢⠭⠩⣀⢺⠑⡉⠀⢀⡧⡀⠂⡀⠂⠄⠀⠐⢁⠂⠄⠈⠄⡀⠈⠠⠐⢂⠀⢨⠐⠰ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣻⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣹⡽⣿⠸⢁⠂⠄⠀⢈⠐⠈⠠⠈⠠⢁⠄⠁⡀⢏⠤⠠⢁⠄⠈⠖⠬⠒⠃⡒⠑⠉⠋⣖⡀⠈⢧⠈⢂⠀⠠⢈⠠⠈⠐⠡⠀⠠⢁⠂⠄⡀⠈⠐⢀⠠⡜ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣟⣧⣿⣿⣿⣿⣽⣿⣟⢿⣿⣿⣿⣾⣿⣿⡟⣏⢿⠀⠐⠠⢁⠄⠂⠁⠄⠁⡀⠈⠐⠠⠁⡂⣀⣂⠤⠒⠉⠌⡀⢀⠤⡤⢤⠤⠤⠬⠢⠑⠈⢸⠐⢀⠠⠂⠄⠁⠄⠈⠄⡀⠈⠐⠠⢁⠄⠂⣀⠐⠆ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣳⣞⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⢻⣳⣿⠂⠄⡀⠈⠐⠡⠀⠐⠠⠈⠐⠄⡀⠈⠐⠠⢁⠄⠂⡁⠀⣠⣂⣄⣤⣌⣀⢈⡠⢌⠴⠤⢢⠄⡀⠐⢀⠌⠀⠐⠈⠠⢁⠂⠄⡀⠈⠐⠠⡐⠈⢃ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢏⣧⣿⣿⣿⣿⣿⣟⡿⣿⣾⣽⣿⣿⣺⡽⣾⠈⠠⢁⠂⠄⠀⡈⠁⠠⠂⠄⡀⠈⠐⠄⡀⠈⠐⠠⠁⠄⡀⠈⠠⢁⠂⠄⠀⠌⠁⠄⡁⠀⠠⢂⠀⢁⠂⡀⠈⠐⡁⠀⠐⠠⢁⠂⡀⠁⠠⠈⢂ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣚⡷⣿⣿⣿⣟⣿⣾⣿⣿⣿⣿⣿⣳⣟⢸⠀⡐⠀⠐⠠⢁⠄⠀⠌⠀⠠⢁⠂⠄⡈⠄⠀⠌⡀⠈⠐⢁⠂⡀⠀⠐⠠⢁⠂⠀⠐⠠⠂⡁⠀⢂⠀⠐⠠⠁⠠⠂⡀⠂⡀⠂⠀⢈⠠⠂⠀⢈ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢯⣝⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⢧⣼⠀⢈⠂⢀⠌⡀⠈⠐⠡⠀⠠⢁⠂⠀⠠⠄⠀⢈⠂⠄⠀⠌⠀⠐⠠⢁⠄⡀⠈⠐⠠⠄⡀⠈⠐⡀⠁⠠⡁⠄⠀⠐⢁⠂⢀⠂⢀⠌⠀⠂⢀⠌⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢯⡻⣯⣿⣿⣿⣿⣷⡿⣿⣿⡝⣾⢐⢈⠂⠄⠁⠂⠄⠀⠌⠀⠄⡈⠀⠐⠠⢁⡀⠐⠄⠀⢈⠠⠁⠠⠄⡀⠈⠐⠠⠂⠄⡀⠈⢁⠂⠄⡀⠈⠐⠠⠂⡀⠁⠠⠈⠠⢁⠄⠀⡈⠄⠁⠄⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢯⣳⣿⣿⣿⣿⣿⣿⣿⣿⣭⡿⢠⠂⠀⢀⠐⠠⠂⡀⠄⠀⡐⠂⠀⢁⠂⡀⠈⠐⠡⡀⠐⠂⠄⠈⠄⡀⠈⠐⠌⡀⠈⠐⢁⠂⠀⠐⠠⢁⠂⠄⡀⠈⢁⠂⠀⠐⡁⠀⠘⠏⢲⠄⠀⡈⠀ ⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣳⣽⣿⣿⣿⣿⣿⣿⣿⣿⢣⣿⢹⠂⢀⠂⢀⠌⡁⠀⠠⢁⡀⠈⠐⢁⠂⠀⠠⠁⠄⠀⠈⠠⠄⠀⠈⠐⢈⠄⠀⠂⠄⠁⠄⠀⠐⠡⠄⡀⠈⠐⠠⢁⠂⠀⠐⢀⠐⠠⠀⢿⡆⠄⠈⢀⠄⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣳⣽⡿⣿⣿⣿⣿⣿⣿⣷⡟⣿⣿⣿⠘⡁⠄⠁⠂⠀⠠⡁⠀⠠⠁⠄⠀⠁⠠⢀⠐⠀⠠⠁⠄⡀⠀⠐⠂⠀⠄⡀⠁⠠⠀⡀⠀⠌⠀⠐⠠⠂⠄⡀⠈⠐⠠⡁⠀⠠⡐⠀⢸⣇⣀⠐⣌⠣⠈ ⣿⣯⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣻⣽⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⠐⠈⠠⠁⠠⢀⠐⡀⠈⠠⠂⡀⠁⠂⡀⠀⡀⠁⠀⠂⡀⠀⠐⠀⠌⡀⠀⠠⠁⠀⡀⢈⠂⠄⠂⡀⠈⠐⢁⠂⠄⡀⠈⠐⢂⠀⠠⡆⠈⢀⠀⠀⠣⢆ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣟⢯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⠁⠉⡀⠀⠄⡀⠀⠠⠀⠐⢀⠈⠠⠀⠐⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⢀⠈⠐⢀⠈⠠⠁⠠⠂⠀⠠⢁⠂⠄⠀⠠⢁⠂⡄⠱⠀⠀⠀⢻ ⣿⣷⣯⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠟⠿⠿⠿⠛⠙⠈⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠐⠠⠀⠐⠠⠈⢁⠄⡀⠈⠐⠠⢁⡀⠈⠐⢀⠂⢅⠢⠑⣌ ⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣽⣻⣽⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠄⠀⠁⠂⢀⡁⠀⠠⢁⠂⠄⡀⠈⢁⠂⠄⠀⡈⠁⡂⢄ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣳⣽⣻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣳⣿⣾⣤⣐⢀⡐⣀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡀⠀⠐⡀⠁⠂⡀⠈⠐⠠⢁⠂⠀⠐⠠⢁⠂⠀⠡⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⢷⣻⣿⣰⠂⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡐⠀⠌⠀⠂⠄⡀⠈⠐⠡⠄⡀⠈⠐⢁⠂⠀ ⣦⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣽⣾⡿⣸⠁⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠁⣍⢼⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡀⠀⠂⠄⠀⡁⠀⠠⢁⠂⠄⠀⠐⠠⠂⠄⠀⠌⠀ 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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⢿⣦⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⠇⠸⣏⠉⠉⠉⠙⠛⠳⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⡟⠋⠐⣿⡀⣰⡿⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⣏⣀⣤⣤⣬⣽⣏⣁⡄⠀⢠⣤⣤⣤⣤⠤⠤⠤⢤⡙⢦⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣰⣿⡟⠀⣏⠀⠻⠟⠀⠀⠀⣼⠇⠀⠸⡇⠘⠟⠀⠀⠀⠀⣸⠇⠀⠙⢷⣝⢤⠀⠀⠀ ⠀⠀⠀⠀⢀⣴⣾⣷⡿⠀⠀⠙⢷⣄⣀⣀⣠⣾⠋⠀⠀⠀⠙⢶⣤⣀⣠⣤⠾⠋⠀⠀⠀⠀⠙⢷⡕⣀⠀ ⠀⠀⣠⣾⡷⠟⠉⣿⠃⠀⠀⠀⠀⠀⠉⠉⢉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡦⠾⠷⠀⠀⠀⠙⣞⡆ ⢠⣾⡿⠏⠀⠀⢰⣿⠀⠀⣦⢤⣴⠄⢠⡿⠆⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⡴⢶⣾⣿⠇ ⣿⡟⠁⠀⠀⠀⢸⣿⠀⠘⢿⡸⣏⡀⢸⣅⠀⠀⠀⠀⠻⢷⣶⣶⠶⣶⣶⢶⣶⣚⣿⣏⣩⣿⣦⣾⡟⠁⠀ ⠻⠿⠟⠻⠫⠭⠿⡿⣦⡀⠀⠁⠈⠁⠈⠙⠃⠀⠀⠀⠀⠀⠀⠉⠙⠳⠾⣿⠯⣽⣿⣿⣿⡿⢿⣿⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠻⠙⠶⣶⣤⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠛⠻⠷⣯⣭⢿⣳⠋⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣴⠶⠛⠉⠉⠉⠉⠉⠙⠛⠛⠳⠶⠶⠶⠶⠶⠶⠞⣿⡄⠀⠀⠀⠙⣶⢷⠀⠀⠀⠀ ⠀⠀⠀⢀⣴⣿⠿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣄⣀⡀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⢸⣾⠀⠀⠀⠀ ⠀⠀⢰⣿⡿⠉⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢠⡾⠛⣉⣍⣙⠻⣦⡀⠀⠀⠉⠀⢀⢀⣀⣠⣾⣿⠀⠀⠀⠀ ⠀⠀⠸⣿⣗⡒⠒⠚⠛⠉⠹⢿⡇⠀⠀⠀⢸⣇⠰⣿⣄⡉⠛⠛⠃⠀⠀⠀⠀⣿⢻⠝⠛⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣹⡇⠀⠀⠀⠈⠛⠳⣮⣭⣛⠻⣶⡄⠀⠀⠀⢀⡟⡼⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⢸⡟⢶⣄⡈⣿⠇⢸⡇⠀⠀⠀⢸⣷⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⣿⡀⠀⠀⠘⠿⣦⣭⣿⣯⣶⠟⠃⠀⠀⢠⡟⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣟⡝⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢤⣼⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢧⡕⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⠃⠀⠀⠀⠀⠀⣠⣤⣤⣀⡀⠀⠀⠀⠀⠈⢻⡞⡆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣻⡇⠀⠀⣠⡶⣿⡿⠭⠀⠀⠉⠹⣟⢷⣤⡀⠀⠀⢻⣸⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⣤⣾⢫⠟⠁⠀⠀⠀⠀⠀⠀⠀⠈⢻⣻⣆⠀⣾⣻⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢋⣿⣾⡻⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
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⠀⠀⠀⠀⠸⠉⠐⠂⠤⠤⠤⢤⡄⠤⠄⢚⣭⡲⠒⠒⠒⠀⠤⢀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢣⠠⣂⠤⠒⢉⢲⠀⠀⠀⠘⠼⠕⠀⠀⠀⠀⠀⠀⠈⠉⠒⠢⠤⢀ ⠀⠀⠀⠀⠀⡰⠊⠀⡈⡆⡆⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠ ⠀⠀⢀⠠⠜⠐⠀⠀⠁⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁ ⢀⢞⣁⣀⣀⠀⠀⠀⠀⠀⠀⠀⠶⣲⣶⣭⣿⣽⣯⣽⣲⢢⠀⠀⠀⢀⡠⠊⠀⠀ ⠋⠁⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢫⣿⣫⠀⣀⠔⠉⠀⠀⠀⠀ ⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠞⡋⠔⠊⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⣀⡤⠤⡤⠀⠒⠒⠒⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢣⠀⠀⠀⠀⡔⠁⠀⠇⡐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠣⡀⠀⠐⠘⡀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⣀⢤⡶⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠑⠠⣀⠈⠂⠤⠤⣤⢔⣞⣀⡠⠔⢈⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⢂⠄⠀⠨⠤⢄⡀⠀⢎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠈⠢⣀⠑⠠⠤⣤⠴⠂⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠘⣿⣿⣷⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣷⣦⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡿⠟⣛⣩⣭⣭⣭⣭⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⠞⣡⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀ ⠀⠀⠀⠀⠀⠀⡴⢡⣾⣿⡟⣿⡿⣿⢻⣿⣷⣭⣿⣿⣿⣿⣿⣿⣿⡿⠛⣋⣿⠆ ⠀⠀⠀⠀⠀⠘⠁⣿⣿⣿⣇⡙⠷⠙⢘⡿⠟⠋⠉⠉⠉⠉⠉⠉⠉⠉⣹⠟⠁⠀ ⠀⠀⠀⣀⣠⣴⣿⣿⣿⣿⠿⠋⠀⠈⠁⠀⠀⣧⣦⣦⣄⣦⣠⣤⣤⣾⣷⣶⣤⣄ ⠤⠶⠿⠿⠿⠛⠛⠛⠉⣡⡤⠶⠒⠒⠲⠦⣤⣏⡙⠻⠟⠟⠿⣯⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣸⠋⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠲⠶⠞⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢿⣄⠀⠀⠀⠀⢀⣠⡤⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢰⠟⠞⠁⣀⣀⣤⣶⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠀⠀⠆⢉⡛⠿⠍⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⢉⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⢸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢤⣄⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⠿⠹⣷⡄⠀⠀⢸⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⣷⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠃⠀⠀⣴⡇⠀⠀⢸⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠀⣿⣿⣀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠵⠒⠿⠏⠁⠀⠀⢸⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⢀⣾⡦⢁⡝⠛⠛⠛⠛⠲⠦⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣴⣶⣤⣸⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⢶⣄⠀⠀⣰⡿⠃⠉⠀⠀⠀⠀⠀⠀⠀⠒⢮⢻⣿⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣄⠀⠐⣿⣿⣛⣯⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⡠⠞⢁⠀⠀⠀⢀⡠⠤⣄⡀⣠⠴⠔⠲⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⠔⢻⡦⢸⣯⣿⣿⠀⠀⠸⠓⠲⢭⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢟⣤⣖⣤⣀⣤⣴⣿⣿⣽⣿⣏⠋⠽⠓⢄⠀⠀⠜⣿⣿⣿⣿⣿⣶⣿⣿⣶⣦⣄⠉⠈⠉⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢣⢿⣇⠰⣿⣿⣿⣼⡟⢷⣿⢿⣥⠅⠂⢰⠸⣿⣿⣇⣻⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⢤⣀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢉⠋⡌⠛⠳⡾⣿⡁⠹⣷⠍⣀⣀⣄⣼⣶⣮⣯⣧⣿⣿⣿⣿⣗⣿⢿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣷⣯⣵⣦⠀⠀⢸⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡜⣿⢀⠈⠌⠭⠨⢯⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡶⠖⢺⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣇⣿⢾⠀⣶⣶⡲⣾⣿⣿⠜⠿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⢻⣿⠟⠋⢻⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣀⠠⣀⣹⡛⡆⡇⢻⣳⣖⢜⣅⣬⣷⣻⠿⠉⠻⠉⠉⣋⠹⠿⣿⡿⠿⠋⠀⠀⠀⠃⠀⠈⠓⠚⠀⠀⠀⠀⠈⡿⠒⠻⠷⣾⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡽⣟⣒⣤⣾⣾⡿⠳⣷⡸⣿⣿⣿⣿⠿⣟⣹⠄⠈⢱⡔⠞⢋⠉⠉⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⢤⢒⠚⠓⠉⠀⢠⡰⢻⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⣀⣤⣴⡾⠿⠿⠟⢿⡟⠽⠍⠋⢓⡳⠶⠜⢷⡹⣿⣿⣟⠭⢤⡒⠒⠚⠓⠚⠳⠦⠿⠭⢥⢿⡧⣤⠽⠶⠾⠿⣿⣿⡛⠋⣿⡟⠧⠀⠀⢀⣸⠀⡀⣿⣿⣿⣿⣿⣿⣿ ⠀⢀⣤⡶⠿⠟⠉⠀⠀⠀⠈⠀⠤⠂⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⣝⡣⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠠⡄⠀⠀⠀⠀⠈⢇⣡⣾⡁⠐⠀⡀⠀⠘⠇⣾⣵⣽⣿⣿⣿⣿⣿⣿ ⠀⠉⠀⠀⠀⠐⠒⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠔⣢⠂⠀⡐⠒⠒⠛⠓⠄⠀⣀⣀⡀⣀⣀⣀⣀⣀⣀⣀⡀⢠⢤⡤⠴⣶⣌⣯⣿⡷⣷⣤⣶⣧⣠⣯⣶⣿⡟⣿⣿⣿⣿⣿⣿⣿ ⡀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⢀⣀⣤⡴⡠⠄⠀⠀⠀⠀⢀⠀⠀⠊⠕⠻⠷⢟⡥⠤⣩⣷⡴⢲⣾⣎⢗⡿⢽⠩⠿⠛⢩⢮⠟⣍⢹⡏⣭⡻⢻⡶⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠘⠋⠁⠀⠀⠀⠀⠈⠀⠀⠀⠀⡄⠈⢄⣴⣋⣁⣀⢀⡠⡀⢀⣴⠂⠀⠀⣂⣀⠄⠈⣟⣵⣿⠿⣹⣗⣿⣿⣿⣿⣷⣢⣇⣷⣾⣿⢿⣅⣻⣿⡹⣯⣀⣞⣟⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠘⡀⡂⢴⡣⠐⠂⠀⠈⠒⣠⣾⢵⡿⢾⣽⣯⡥⠀⠜⠂⢐⠂⢀⡴⠆⠠⡅⠁⠀⣴⣿⠿⢿⡷⡿⠟⣿⠻⡿⠿⠻⣿⢻⣷⠟⣿⣿⣷⣿⣽⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠸⢋⣭⣵⠀⠀⡠⡧⣴⢶⠯⠓⣴⡂⠈⠱⣀⠴⠄⠐⠒⠁⠐⠀⠠⠐⢀⡆⣲⣿⠟⡩⠀⢀⡗⠲⠀⠀⣨⡓⠶⠞⠉⠼⣿⣰⣷⣿⣿⢿⣭⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢀⠀⢴⢿⠟⠃⢠⢼⣷⣿⣭⣷⣴⣾⠾⢿⣅⣄⣀⡠⢄⡀⠠⣀⣰⡂⢉⣱⣾⣷⣿⣷⠋⢀⡤⢾⠇⡀⣅⡾⠯⠁⠀⢀⣶⢼⡟⣿⣿⣿⣽⣿⣇⠓⣡⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⢀⣠⣤⠿⠋⣟⣿⣛⣻⣿⣇⣀⣸⣯⣼⣿⢛⣣⠀⣸⣇⣻⡴⣾⣿⣿⣿⣾⣋⠤⣴⣫⣌⣰⣏⡜⣳⠀⠀⣤⢟⣽⣈⣷⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⣤⣼⣿⣿⣗⡴⠴⠋⢚⡋⠙⣟⡿⣻⢿⣿⣿⣿⠟⢳⣽⣿⣿⢿⣿⡿⣿⣿⡿⡿⣿⣯⣾⣟⡿⣿⣷⢿⣿⣷⣀⢸⡍⣿⣿⣩⣿⡿⣧⣸⣬⣿⢃⠸⣫⣯⡿⣿⣿⣿⣿⣿⣿⣿ ⣄⣀⣿⣿⣿⣟⣀⣀⣔⣋⣁⣘⣩⣽⣉⣿⣿⣿⣟⣠⣿⣿⣯⣿⣿⣁⣼⣿⣋⣸⣿⣿⣿⣿⣟⣯⣿⣿⣾⣿⣶⣿⣿⣿⣿⣿⣿⣛⣣⣟⣛⣷⣾⣾⣷⣛⣏⣹⣾⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ (ง'̀-'́)ง
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⣴⢲⡞⣽⢻⣝⣻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⢶⡻⣭⢳⣭⢳⡝⣮⢳⣎⡷⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣞⢧⣛⢮⡳⣭⢳⣎⢷⡹⣎⢷⡚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡤⣤⢤⣠⢖⡶⣲⢖⡶⣖⢶⣲⢖⡶⣒⢦⡤⣴⢏⡷⣹⢮⡝⣮⢳⣭⢳⣎⢷⡹⣎⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢤⡖⡾⣏⠿⣜⢧⡝⣮⢳⡝⣮⢳⡝⣮⢳⡝⣮⢳⣏⢾⡹⣎⢷⡹⣎⢷⡹⢮⡝⣮⢳⣎⠷⣎⢷⡹⣎⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢴⡺⣝⢮⡳⣝⡳⣭⢻⡜⣧⢻⡜⣧⢻⡜⣧⢻⣜⣧⣿⣜⡳⣎⣷⣹⢎⡷⣹⢎⡷⣹⢧⡻⣜⡳⣎⠿⣜⢧⡻⡼⣭⢳⡤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢶⡻⣜⢧⡻⣜⢧⡻⣜⡳⣭⢳⡝⣮⢳⡝⣮⢳⡝⣮⢳⣎⣿⣿⣷⡝⣾⣿⣿⣮⢳⣽⣾⣵⢫⡞⣵⢫⠷⣭⢻⡜⣧⢻⡵⣋⢷⡹⢶⡹⣴⢢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⣯⡝⣮⢳⡝⣮⢳⡝⣮⣷⣯⣷⣭⡷⣹⢎⡷⣹⣎⠷⡹⠮⠷⠾⠼⣿⣿⡿⠶⢿⣿⣷⣫⣞⣿⣿⣧⢻⡜⣯⢻⡜⣧⢻⡜⣧⢻⡹⢮⡝⣧⢻⡜⣯⢞⡵⣄⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣴⢻⣭⣛⢶⡹⣎⢷⡹⣎⢷⡹⣾⣿⣿⣿⣿⣿⠓⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⢾⣿⡇⠀⢸⣿⣿⠀⠀⣿⣿⣧⢻⡜⣧⢻⡜⣧⢻⡜⣧⢯⡝⣧⢻⡜⣧⢻⡜⣏⠾⣭⢧⣢⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣴⢻⣜⡳⢮⡝⣮⢳⡝⣮⢳⡝⣮⡳⠟⢿⣿⣿⡿⠏⠀⠀⠀⠀⠀⠀⢀⡀⣀⣤⠀⣿⣿⠃⠀⣸⣿⡇⠀⠀⣿⣿⠹⣧⢻⡜⣧⢻⡜⣧⢻⡼⡍⠛⠚⠧⣟⡼⣣⢟⡼⣻⡜⣧⢳⢷⡀⠀⠀⠀ ⠀⠀⣰⠷⣭⢳⢮⡝⣧⢻⡜⣧⢻⡜⣧⠟⠉⠀⠀⠀⠈⠁⠀⠀⣀⣠⣄⣀⣤⣤⣾⣿⠿⠟⢺⣿⠏⠀⠀⠻⡿⠁⠀⠀⠉⠁⠀⠙⣧⢻⡜⣧⢻⡜⣧⢻⡽⡀⠀⠀⠀⠉⠳⢏⣾⣱⢻⡜⣯⢞⡽⡄⠀⠀ ⠀⠀⢻⡻⣜⢯⡞⡽⣎⢷⡹⣎⠗⠋⠀⠀⠀⠀⠀⠀⣀⣤⡀⣿⣿⣿⣿⠿⠛⠻⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢯⡞⣵⢫⡞⣵⢫⡞⣧⠀⠀⠀⠀⠀⠀⠑⢯⢧⡻⣜⣏⠾⣽⡀⠀ ⠀⠀⠈⢳⣏⠾⣜⡳⣝⡮⠋⠁⠀⠀⠀⠀⠀⠀⣰⡀⢹⣿⠛⢻⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣎⡷⣹⢎⡷⣹⢞⡆⠀⠀⠀⠀⠀⠀⠈⢷⢻⡜⣮⢻⣜⣣⠀ ⠀⠀⠀⠀⠉⠻⢎⡷⠉⠀⠀⠀⠀⠀⠀⢀⠀⢻⣟⡿⠿⣽⡷⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣏⡾⣱⢏⡞⣧⠀⠀⠀⠀⠀⠀⠀⠈⢷⡻⣜⡳⣎⢿⡀ ⠀⠀⠀⠀⠀⠀⠀⠉⠂⠤⣀⣀⣀⣠⣴⣿⣿⠾⣿⣻⡄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢯⡞⣽⢺⠀⠀⠀⠀⠀⠀⠀⠀⠘⡷⣭⢳⡝⣾⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣯⣿⣿⣿⣿⣿⣿⡦⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡜⣧⣛⢾⠀ ⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣾⡿⣟⣯⣿⠀⠁⠒⠤⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡼⣣⢟⣾⠁ ⠀⣠⣤⣴⣿⣟⣿⣾⣟⣷⣻⣿⣭⢿⠝⠓⠀⠀⠀⠀⠀⠉⠉⠐⠒⠒⠂⠐⠠⠤⠤⠤⠤⠤⠤⣤⣤⡤⣤⡤⣤⢤⣤⣤⠤⠤⠤⠤⠤⠤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡱⣏⣞⡺⠀ ⢠⣿⣿⣿⣿⣽⣿⣿⣿⣽⣳⣯⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⡝⣧⢻⣜⡳⣞⣼⡀⠀⠀⠀⠀⠀⠀⠉⠻⣳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣯⢳⡝⣮⠇⠀ ⠘⣿⣷⣿⣾⣿⣿⣿⣾⢷⣻⣽⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢜⡷⣎⢷⡹⣎⣧⠀⠀⠀⠀⠀⠀⠀⠀⢹⣞⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⣎⢷⣹⡞⠀⠀ ⠀⠀⠻⣽⡿⣿⣿⣿⣿⣻⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠺⢧⣻⡜⡾⣆⠀⠀⠀⠀⠀⠀⠀⣸⣏⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⣝⢮⣳⠝⠀⠀⠀ ⠀⠀⠀⠈⠿⣿⣿⣿⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠁⠀⠀⠀⠀⠀⠀⣰⡳⢾⠃⠀⠀⠀⠀⠀⠀⠀⢀⡴⣺⡝⣮⡷⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⢤⡴⣖⢶⣫⢟⡽⣛⢿⡹⣞⡻⣏⢿⡹⢦⡖⡶⢦⣠⢤⢤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣠⡴⣞⢧⡻⠁⠀⠀⠀⠀⠀⣀⣤⢾⣹⢳⢧⡻⠊⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⣞⢧⣏⢷⡹⣎⢷⡹⣎⢷⡹⣎⠷⣭⢳⡝⣮⡝⣧⢻⡝⣧⣛⢮⣛⢶⡹⡞⢶⣓⢶⡲⢧⣛⢶⡹⣎⣟⣁⣀⣠⢤⡴⣺⡝⣯⢞⣣⣏⠗⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⣻⡵⣛⡼⡳⣎⢷⡹⣎⢷⡹⣎⢷⡹⣎⠿⣜⢧⣛⢶⡹⣎⢷⡹⢶⡹⢮⡝⣮⢳⡝⣧⣛⢮⡝⣧⣛⢮⡳⣝⠾⣜⢧⣛⢮⣳⣧⠿⠜⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠓⠛⠺⠧⠿⠜⠧⣻⣜⣧⣻⣜⡻⣜⢧⣛⢮⡳⣝⢮⡝⣧⣛⢧⡻⣜⢧⣛⣶⣹⣮⠝⠶⠽⠮⠷⠛⠙⠚⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠓⠫⣞⡵⣫⢞⡽⣲⡝⣮⢳⣽⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡞⣵⢫⡞⣵⢻⣜⣳⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡜⣧⢻⣜⡳⣎⢧⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡜⣧⢻⣜⡳⣭⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡜⣧⢻⣜⣳⢳⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣜⢧⡻⣜⣮⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣳⡝⣮⢳⡭⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢧⡻⡼⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠾⠏⠉⠀⠀⠀⠀⠀⠀⠈⠉⠳⢶⣄⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠸⠷⠀⠀⠀⠀⠀⠘⠛⠃⠙⢿⣄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⡿⢱⡟⠓⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⡄⢻⡆⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⣧⡈⠙⠛⠁⠀⢀⣀⡀⠀⠀⠀⣀⣀⠀⠀⠁⠀⠈⣿⡀ ⠀⠀⠀⠀⠀⠀⠀⠸⢍⣻⣦⣄⡀⠀⠹⠭⠟⠀⠀⠸⣿⣿⠇⠀⣠⠶⣦⣿⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣧⣈⣻⡷⢶⣦⣀⣀⠀⠀⠀⠀⠀⠀⠈⢛⢡⡟⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣳⠃⡹⠳⡤⡴⡏⠙⠛⣻⠶⠶⢤⡤⠤⠶⣿⠁⠀ ⠀⠀⠀⢀⣠⣤⣶⠶⠋⣵⠋⢰⠇⣼⣱⠁⢹⠗⢲⡟⠦⣤⠼⠛⠦⠞⠃⠀⠀ ⠀⢀⣴⡿⠋⠁⢠⣰⠞⠁⣰⣯⣼⠁⡏⠀⢸⠀⠸⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀ ⠀⣼⠋⢀⣠⡴⣟⢁⣠⡞⢻⡿⠁⢰⡇⠀⢸⣄⠀⢷⠀⠸⣆⠀⠀⠀⠀⠀⠀ ⢸⢇⣴⡿⠋⠄⣼⡿⠁⠀⣾⠁⠀⠸⡇⠀⠀⢿⡄⠘⣆⠀⠹⣦⠀⠀⠀⠀⠀ ⢠⣾⠏⠀⠀⢠⣿⠀⠀⠀⣿⡄⠀⠀⢿⠀⠀⠈⣷⡄⠹⣧⠀⠙⢷⣄⠀⠀⠀ ⢸⡟⠀⠀⠀⢸⣿⠀⠀⠀⢹⣧⠀⠀⠸⣷⠀⠀⠸⣷⡀⠹⣦⠀⠀⠻⣧⠀⠀ ⢸⡇⠀⠀⠀⠀⣿⡆⠀⠀⠀⢻⣧⠀⠀⢻⡆⠀⠀⠹⣧⠀⠹⣇⠀⠀⢻⣧⠀ ⢸⣇⠀⠀⠀⠀⠘⣿⣄⠀⠀⠀⠹⣧⠀⠘⣿⠀⠀⠀⣿⡇⠀⢿⣄⠀⠀⣿⡇ ⢈⣿⡄⠀⠀⠀⠀⠘⣿⣄⠀⠀⠀⠈⠣⡀⢿⡆⠀⠀⣿⠃⠀⠘⣿⡀⠀⢸⡇ ⠀⠘⠃⠀⠀⠀⠀⠀⠈⢿⣧⠀⠀⠀⠀⠀⢸⣷⢀⡼⠃⠀⠀⠀⣿⡇⠀⢸⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⡀⠀⠀⠀⢸⣿⠈⠀⠀⠀⠀⠀⣿⡇⠀⡾⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⣸⡏⠀⠀⠀⠀⠀⣸⡟⠀⠀⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⢀⣴⠟⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
૮꒰ ˶• ༝ •˶꒱ა ♡୧ ‧₊˚ 🍮 ⋅ ☆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣖⣀⣀⣠⣴⣿⣿⣷⣤⣀⣐⣶⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⡞⣛⣉⣽⡿⠟⣉⢛⡛⡡⢄⠤⢤⢠⣀⣉⡉⡙⠛⠷⣬⡙⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠿⣟⣿⣿⣿⠿⠿⢿⢿⡿⣿⣿⣿⣧⣟⡜⢇⡇⡤⣄⠧⣃⠟⡤⣀⠛⢻⣿⠿⣤⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡾⣏⣴⠞⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠿⣷⣜⠲⣌⠳⣍⡞⣱⣌⠳⣌⡛⢷⣬⣿⣆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣞⣩⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⣌⠳⡬⣝⠲⣬⢳⡘⣬⢣⠌⠛⣿⣷⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⣋⠶⣩⢓⡎⢧⡹⢤⢣⢋⡆⠹⣏⣷⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇⡞⡱⢎⡜⣧⡙⢦⢋⡼⣘⢣⠻⣿⣧⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⣭⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⢬⡱⢎⡜⢶⡹⢌⡳⡜⣌⠧⣃⣿⢿⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠋⣉⣁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣟⢢⡓⠮⣜⢣⡝⣪⠔⡯⡜⢲⣩⣿⡿⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣛⣛⠁⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⠳⣍⠳⣌⢳⡙⢦⠛⡴⡩⢇⠲⣿⡇⣿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⠛⠋⠉⢀⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢌⡻⢜⠳⣌⢳⡛⣬⠛⡴⣙⢬⠓⣿⣷⠂⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⠿⣾⠃⠀⠀⢰⣿⣿⣇⣠⣤⣴⣶⣶⣦⣄⡀⠀⠀⠀⠀⠀⣠⣾⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡏⣎⡜⣣⢫⢔⣣⠹⢤⠛⡴⣩⠲⣍⠤⣏⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣾⣿⡿⠃⠀⠀⠀⠈⠿⣿⣿⣿⡿⠿⠿⠿⢿⣿⣿⣶⣄⡀⢀⣴⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠳⣌⠶⣡⢓⣮⣴⣭⣮⣝⡲⣱⢋⢦⣙⡇⠀⠀⠀ ⡀⠀⠀⠀⣠⣿⣟⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⡱⢊⣶⣿⣿⣿⣿⣿⣿⣿⣿⣶⡭⠲⡭⠇⣿⠀⠀ ⠁⠀⠀⢰⣻⣟⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡗⣍⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢱⡙⠆⢻⡇⠀ ⠀⠀⠀⣽⣿⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣏⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢦⠹⣩⣼⡟⡗ ⠀⠀⢰⣿⡿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⡬⢓⡥⢿⡇⣿ ⠀⠀⢸⣿⢻⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡗⣬⠻⣿⣿⣿⣿⣿⣿⣿⣿⡿⢏⡼⢱⡩⢖⡩⣿⡿ ⠀⠀⠈⣿⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡄⠛⣬⠙⢻⡟⣿⠛⡟⢹⡌⢳⡌⣧⠙⡎⣴⣿⡇ ⠀⠀⢸⡏⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡘⢧⡩⢛⡴⢓⡬⢓⡭⢳⢜⡣⡝⣬⠳⡍⣆⣾⡇ ⠀⠀⢸⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣟⠦⡹⢥⢚⡵⡘⠧⣜⢣⢎⡵⢚⡤⢳⠱⣎⣿⣷ ⠀⠀⢸⡇⣿⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣧⠓⣭⢲⢮⡹⣱⠪⣜⢊⠶⣉⠶⣩⣳⣾⣧⣿ ⠀⠀⠸⣧⣿⣧⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣯⠴⣩⠲⡅⣇⠳⠬⣍⣲⣭⣰⣿⢻⣿⡿⣷ ⠀⠀⠀⠀⠉⠉⢿⣯⣉⣛⡛⠶⢶⣤⣤⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣴⣣⣵⣼⣦⡿⢟⣛⣿⠿⠛⠋⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⢿⠷⠶⣶⣭⣭⣭⣿⣷⣶⣟⣛⣛⣛⣛⣿⡶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⢚⣛⣛⣛⣿⣿⣭⣽⠶⠶⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠀⠀⠀⠀⠀⠀⠀⠀⡼⡅⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣾⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠞⠋⢹⠃⠀⠀⠀⠀⠀⠀⠀⢰⠇⡇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣸⢻⠀⠈⠛⠷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⠋⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⡁⠀⠘⠓⠢⣄⡀⠀⠀⠀⠀⠀⠀ ⣿⠈⡇⠀⠀⠀⠀⠉⠛⡳⢦⣄⣀⠀⠀⢠⡾⠋⠀⠠⡀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢀⣠⠴⢻⣆⠀⠀⠀⠀⠀⠉⠓⠦⠤⢤⣴⡶ ⣿⠀⠘⡄⠀⠀⠀⠀⢰⠉⣹⡖⠛⠯⣟⣻⡷⠦⢤⣤⣌⣑⣆⣷⣤⣤⠤⠶⠒⠋⠉⠀⠀⢠⣏⡗⠢⣄⣠⡤⠤⣄⣦⠴⠚⠁⠀ ⢸⡄⠀⠘⢄⠀⠀⠀⠘⡄⣿⣿⣦⣀⡅⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠃⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀ ⠈⣇⠀⠀⠈⠣⣄⠀⠀⠙⠮⣿⣿⡯⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣯⣽⡶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠹⣇⠀⠀⠀⠈⠑⠂⠀⠀⠒⠒⠒⡒⠒⠠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⢀⣤⢾⡇⠀⠀⠀⢣⡀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⢷⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠹⣄⠀⠀⣀⣠⡤⠞⡟⢺⡾⠁⠀⠀⠀⠀⡇⠀⠀⠀⠀⣤⠴⠚⠛⢉⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠙⢯⡉⠸⡉⠒⣷⠞⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⡇⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⢑⣷⣾⡥⠀⠀⠀⠀⠠⠀⠀⢸⣦⡀⠀⠀⣧⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠙⠲⢤⣀⣀⡀⣀⣀⣴⣿⣿⢄⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣟⣇⠙⢷⣍⠿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠈⠉⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠉⠻⣿⢶⣤⡀⠀⠀⠀⠀⠀⢿⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠛⢦⣿⣷⣤⡀⠀⠀⠸⣿⠛⢲⠶⠶⠶⠶⠶⢤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣄⣿⣷⣿⣶⣶⣾⣶⡿⢿⣶⣡⣔⣏⢷⣽⣟⣛⢶⣶⣒⣤⡤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣾⣿⣿⣿⣿⡿⣡⡜⣿⣾⣿⣿⠿⢯⡃⡟⣿⣾⣯⡉⠏⠻⠅⢪⠉⣏⡉⠖⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⡯⢻⠏⢻⣿⣿⣿⣿⣿⣟⣿⣿⣟⡿⣰⠊⢟⣦⡿⣽⢷⠦⢶⡄⠀⢀⣈⣀⣀⣒⣼⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢢⠳⠉⠀⣀⣿⣿⢻⣿⣿⣿⣿⣿⡟⢳⣾⣿⣿⢾⣽⣶⣏⣩⣶⣶⣿⣿⣿⣿⠟⠉⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣀⡤⠤⣖⣚⣫⣽⣯⣿⣿⣷⣿⣿⣿⣿⣿⣬⣨⣷⠀⣴⣿⣿⣿⠿⠿⠟⢛⣩⣁⣠⡾⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠸⠟⠛⠛⠉⠉⠉⠁⠀⠀⠀⠉⠻⢦⣀⠀⠀⠈⠉⠉⠉⠉⠀⠗⠂⠴⠶⠶⠶⠿⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡞⠛⠓⠶⢦⣤⣀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄⠀⠀⠀⠀⠉⢻⣦⡤⠶⠛⠋⠉⠁⠀⠀⠀⠀⢀⣀⠀⠉⠉⠉⠙⠛⠛⠛⣶⢶⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⣠⠶⠋⠁⠀⠀⠀⠈⣆⠀⠀⠀⠀⠀⠀⠉⠉⠑⣦⣀⠓⠀⡠⠊⠁⣸⠇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⣴⠟⠁⠀⠀⠀⠀⠀⢀⠀⣷⢂⠀⠀⠀⠀⠀⠐⣾⣷⣿⣇⡭⠟⣑⣫⣼⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⢠⡜⡇⣿⡮⡇⠀⠀⢀⡠⠔⠚⣉⣽⣿⣷⣺⣏⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡾⢿⣷⣡⠴⠊⠁⠀⢠⠾⠟⠻⠹⢿⣿⠛⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠀⠀⠈⡏⠀⠀⠀⠀⠀⠈⠀⠀⣀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⠀⣀⡤⠔⢊⡟⠁⠀⠀⠀⢰⠇⠀⠀⠀⣀⣠⣤⣶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⣀⠤⠒⢉⣀⣤⡤⣾⠁⠀⠀⠀⣠⠿⠖⠛⠛⢻⣍⠀⢱⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣀⣀⣀⣴⠏⠀⣠⣴⣯⡴⠖⠛⠉⠁⠀⠀⣿⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⠘⢧⣸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣴⣞⡋⠉⠁⢨⣟⣰⣾⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⢹⡆⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠘⠿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠉⠙⠛⠲⣾⠛⠁⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣤⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⢀⠀⢀⣀⡀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀ ⣛⠉⢙⣛⣛⡛⣛⡛⣟⣛⣛⣛⡟⠛⠛⢻⣉⣉⡉⣉⣉⣉⣉⣉⢉⣉⣉⣉⣉⣉⣉⡉⣉⣉⣉⣉⣉⢉⢉⣉⣉⣙⣛⣛⣛⣛⣛⣛⣛⣛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⠖⠚⠋⠉⠉⠉⢙⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠛⠁⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣠⠤⠤⠤⠤⠤⠤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢻⡏⠀⠀ ⠀⠀⠀⣀⣠⠤⠔⠒⠚⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⢮⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⡼⠀⠀⠀ ⣠⠴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠫⠿⠀⠀⠀⠀⠀⡀⠀⠀⡀⠈⠑⠢⢄⡀⢀⣀⣠⠀⠀⣸⠃⠀⡇⠀⠀⠀ ⡏⠀⢴⡀⠀⠀⠀⠀⢀⣴⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠳⡈⢦⠙⡆⠀⠀⠀⠈⠁⠀⠬⣄⣀⡇⠀⠀⡇⠀⠀⠀ ⠸⡄⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⢻⡀⠀⠀⢳⠀⢇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀ ⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⡽⠃⠀⢧⠀⠀⠸⡆⢸⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡀⠈⢧⠀⠀ ⠀⠀⠀⠙⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⢻⣽⠍⠁⠀⠀⢸⠀⠀⠀⠇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠙⢤⡈⢧⠀ ⠀⠀⠀⠀⠀⠀⠉⠒⠤⣀⣀⠀⠀⠀⢀⣀⣤⢶⣻⡷⠟⠉⠀⠀⠀⢀⡤⢾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠈⠙⠓ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠳⠏⠛⡄⠀⠀⠀⠀⢠⢾⠋⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡴⠁⣇⣠⣻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠏⠀⠀⡼⠀⣠⡟⢧⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠶⡾⣤⢤⣾⡷⣏⣻⡽⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠓⠣⠼⠤⠧⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣦⡀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠂⢤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠃⠀⠳⡀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⣠⠶⠤⣀⣀⠀⠀⠀⠀⠀⠀⣀⣠⠴⠚⠁⠀⠀⠀⠀⢱⡀⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠎⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠦⢴⡦⢴⢶⠄⣤⠆⢠⣤⣦⠀⠀⠰⠐⠦⠀⠄⠀⠐⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠹⠁⠀⠀⠀⠀⠀ ⢀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠀⠀⠀⠀⠀⠳⠀⢰⠀⠀⠀⠀⠀⠀ ⢸⠃⠈⠓⠦⣄⡀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⠂⠂⢄⡀⠀⢀⡀ ⢠⠈⠀⠀⠀⠀⣻⡙⢒⢾⠤⠄⠀⠀⠤⠠⠤⠐⠂⠁⢸⡆⠄⣠⠤⡄⠝⠋⠀ ⠘⡄⠀⠀⠀⠀⠻⠷⢞⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣧⡤⠀⠀⠀⠀⠀⠀ ⠀⢱⠀⠀⠀⠀⠀⢉⣴⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠁⣀⠀⡤⡲⢛⠌⠀⠀⢸⠀⠀⠀⠐⠚⡩⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠑⢠⣔⠁⠀⠀⠀⠀⣆⠀⢰⡤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠁⠒⠀⠠⣤⠟⣧⣸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠉⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⠀⠠⠀⠠⠤⠤⠤⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⣀⡀⠀⠈⠉⢳⡀⠀⠀⠀⠀⠀⠀⢀⡤⢖⣩⠔⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⡀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠒⠒⢄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡎⠀⢹⠠⠜⠤⣤⢾⠀⢳⡀⠀⠀⠀⣠⣾⣿⡏⠉⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢲⣄⠀⠀⠀⠀⡜⠁⣖⡄⠀⠀⢣⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢷⠐⢏⡀⠀⡠⠋⠙⢠⠋⠀⠀⣰⠿⣿⣛⠝⠁⠀⠀⢀⡠⠤⠀⠀⠀⠀⠀⠠⠤⣀⠀⠀⠀⠀⠀⡿⢿⣷⡄⠀⠀⡄⠺⣅⡨⠛⠀⢸⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⢄⠀⠉⠉⠁⢀⣀⠏⠀⢠⡾⡇⠀⠈⠁⢀⡠⠖⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⢤⡀⠀⠙⠦⠿⢻⣦⡀⠈⢢⢀⣀⣀⡠⠎⠀⠀⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠐⠢⣼⡁⠀⠀⡰⣇⠓⠀⢀⡠⠒⠉⠀⠀⠀⢀⣠⣤⠶⠖⠉⢭⣽⣒⠤⡀⠀⠀⠀⠈⠒⢄⠀⠀⠀⢧⠹⣆⠚⠉⠀⠀⠀⢰⡢⠞⣇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠳⠌⢀⠴⠋⠀⠀⠀⣠⠴⠏⡽⡟⠉⠣⣠⡔⠋⠉⣇⠉⢻⣷⣤⡀⠀⠀⠀⠱⢄⠀⣼⠞⢹⣆⠀⠀⠀⠀⣰⣃⡀⡬⠓⠀ ⠀⠀⠀⢠⠊⡉⡱⢆⠀⠀⠀⣀⣴⠟⠋⠃⢀⡴⠋⠀⠀⢀⣴⠿⢄⣀⡞⡸⠀⡼⠀⠀⠀⠀⠀⢸⠚⠋⠉⡇⠹⡶⣤⣀⡴⠁⠙⢇⠐⢉⡿⣆⡀⠀⠀⠉⠀⠳⠃⠀⠀ ⠀⠀⠀⣜⣂⣀⣳⠼⠃⡠⠚⠉⠀⠀⡔⣠⠊⠀⠀⢀⡴⢫⡟⠀⠀⠀⢠⠇⠀⡇⠀⠀⠀⠀⠀⡎⠀⢠⠀⢸⣀⣘⣸⡿⡄⠀⢀⣀⣳⡁⠀⡁⠉⠳⢤⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠀⠀⠀⣠⠊⠀⠀⠀⠀⠀⣷⠃⠀⢀⡴⠛⠒⢻⠁⠀⠀⢀⣾⠀⢰⢀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠉⠉⡏⣧⠈⢧⡞⣼⣽⢳⠀⢱⠀⠀⠀⠉⠳⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⢰⠇⢀⡴⠋⠀⡄⠀⡎⠀⡰⣣⠟⢹⠀⢸⠸⡄⠀⠀⠀⢸⠀⠀⢼⣧⠰⡀⠀⢸⡇⠀⠈⠲⡛⠋⠀⢧⠸⠀⠀⠀⠀⠀⠈⠳⡄⠀ ⠀⠀⠀⠀⠀⠀⠓⠤⠄⣀⣀⣀⣠⣾⢶⣟⠀⠀⢠⠀⢀⢇⣼⠕⠁⠀⠈⡇⢸⡇⠻⡄⠀⠀⡟⠀⢠⠟⠈⢇⢳⠀⢸⠇⡆⡔⠀⢳⡀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⢹⡆ ⠀⠀⠀⠀⢀⡴⠀⠀⠀⠀⣼⣽⡉⣽⡜⡜⠀⠀⢸⠀⢸⡟⠁⠀⠀⠀⢀⡘⠚⠱⠤⠵⣄⣼⡇⢠⠎⠀⠀⠈⢧⣣⣸⢠⢁⠇⠀⠈⣇⠀⠀⣧⣀⣀⡠⠤⠴⠒⠊⠉⠀ ⠀⠀⠀⢠⢻⢀⣴⡪⢝⡿⠛⢿⣙⣿⢰⡇⠀⠀⡄⠇⠈⡧⠿⠿⠿⠷⢶⣭⠃⠀⠀⠀⠀⠀⢉⠥⠄⠀⠀⠀⠈⠙⣽⠎⡜⠀⠀⢠⢹⠀⢠⣿⣄⣸⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠘⣼⠾⠋⢀⡎⢀⣴⠛⣿⡧⣿⠇⠀⠀⠳⡘⡄⢳⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠐⠛⠛⠻⠿⢶⣦⣴⠋⡼⠀⠀⠀⣼⢸⣀⣾⡿⣿⣏⠉⢻⠀⠀⠈⠀⠀ ⠀⠀⠀⢰⣹⡀⠀⢸⣀⡿⢋⡩⠿⣿⠋⡟⡆⠀⠀⠈⠻⣦⣓⣄⡀⠀⠀⠀⢀⡤⣤⣤⣀⠀⠀⠀⡀⠀⠀⢀⡜⢁⡜⠀⡄⠀⣠⣿⢸⣿⣿⢻⣧⠀⠉⠙⢦⡀⠀⠀⠀ ⠀⠀⠀⢸⡇⠉⢛⣿⢳⣾⣻⣤⠞⢻⣠⢸⢧⠰⡄⢠⢡⣿⣆⠈⠁⠀⠀⠀⢸⢀⠤⣄⣹⠀⠀⠈⠮⣤⣒⣭⢖⠏⣠⣾⢁⢾⣿⣿⢨⢸⠿⢾⣼⣇⠀⠀⠻⣿⡄⠀⠀ ⠀⣀⠖⢄⠹⡤⢾⡦⠽⠿⠪⠗⡺⣛⣟⡾⣮⣦⢻⡞⢾⣿⢮⢿⣦⣄⡀⠀⠘⠞⠀⠀⠉⢳⣤⠤⠤⠀⠶⢿⢯⣞⣥⢛⣯⣿⡏⢸⣼⠀⢣⣄⣿⢻⡆⠀⠀⣧⡇⠀⠀ ⠸⣍⣀⠎⠀⢱⠀⠀⠀⠲⣄⣼⢣⣿⡿⢀⡿⣏⣻⣧⠈⠻⣌⣿⠛⢾⡿⣷⣶⢷⠀⠀⠀⠈⠀⠀⠀⠀⣶⠼⢒⣿⣡⣿⠛⠻⣇⡟⡇⠀⠀⠻⣿⡿⠁⢀⣰⠛⠁⣀⠀ ⠀⠀⠉⠀⠀⠀⠓⠤⣤⣴⢯⣶⠊⢻⣷⡟⠀⠈⠀⠀⠉⠒⠻⢿⣿⠚⠣⢼⣁⢨⠟⠀⠀⠀⣴⣄⡴⣫⢿⣤⣼⣿⠟⠙⢦⣠⢾⣸⡇⣦⠤⠴⠮⣴⠾⠿⠥⢤⣺⠟⠀ ⠀⠀⢰⣳⡆⢠⡀⠀⠀⢀⣼⠅⢣⡈⢷⡟⣶⡶⠾⢍⣽⣫⠉⠈⠉⠑⢄⡑⢮⡏⠀⠀⠀⠀⢩⢋⢾⠓⢺⢬⠟⠁⠀⠀⠈⣧⢤⣏⢷⠸⣦⡲⣄⠘⡟⡖⠊⠉⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⠶⠶⠟⡎⠀⢀⣷⣌⠻⡿⣠⠖⡽⠋⠀⠀⠀⠀⠀⠀⠹⣿⠀⠀⠀⠙⢲⢇⡿⠞⣉⣽⠋⠀⠀⠀⠀⠀⢹⠒⠿⣟⠀⢸⠳⡌⠣⣹⢹⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡇⡀⠸⡀⢿⣻⣿⡡⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⣟⡟⢸⢀⡠⣧⠃⠀⠀⠀⠀⠀⠀⠈⡀⠀⠈⣤⠏⠀⡸⣀⠹⡾⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡤⠧⣼⡿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⣦⠀⠙⡇⢸⡼⢄⠏⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⣏⠁⠚⠋⡹⢠⣇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠈⠓⢲⢻⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⡟⠀⠀⢷⣈⢛⡞⠤⣀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⢻⣄⣀⣴⡷⠋⣙⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡴⠋⣿⠀⠀⠀⠀⠀⠀⢘⡆⡏⣷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢯⣿⠀⠀⠀⣸⡤⡞⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⣸⣷⠉⠁⠀⠀⠇⠀⠀⠀⠀⠀ ⠀⠀⢠⡞⠁⠀⡟⠀⠀⠀⠀⣠⠖⡉⢹⣿⠘⡇⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣟⠋⠦⠤⠞⣽⡇⠣⡤⢤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⡟⠀⠐⢛⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⠞⠀⠀⣰⡇⠀⠀⣠⢾⣧⢔⡡⡼⣿⡲⢿⡕⢤⡀⢀⣠⠔⠋⣸⣿⠉⠁⠀⠀⣠⣊⠉⢿⠀⣧⣼⣥⣈⣓⣤⣀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠐⡏⣧⠀⠀⠀⠀⠀⠀ ⠀⠸⢄⡀⠞⠁⠓⠤⡾⢯⢘⡷⢋⢡⠇⠈⢙⣻⣿⣆⠈⠋⠀⠀⡴⠛⠙⣇⣤⣴⠊⢁⣸⢿⢺⠀⣿⣹⢡⢿⢿⡻⠿⣿⣿⡝⠛⠥⠴⠞⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⢰⡇⠀⠀⠀⢠⣀⣨⠿⠤⠞⠋⠀⡄⠘⢻⣿⣿⣷⣄⣀⠞⣁⠴⠊⢱⢟⡥⢾⣉⣠⣼⣾⠀⢸⠈⣾⡈⡇⠙⣆⠈⢹⣷⠤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢣⡀⠀⠀⠉⣿⠃⠀⠀⠀⠀⢸⠁⠀⠈⠙⢻⣿⡿⠖⠋⠁⠀⢀⠟⠁⠀⠈⠿⠉⠁⡏⣦⢸⠀⡇⢧⣑⠤⣈⣳⠎⢹⡀⠀⠉⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠙⠦⢄⣀⠸⡄⠀⠀⠀⠀⠌⠀⠠⠔⠒⠉⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⢸⠀⣇⣿⣿⠀⡇⠀⣿⠑⣦⣿⠤⡎⢿⠑⠒⠤⣈⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀
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⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⠋⢿⡏⡻⡇⠙⣿⠻⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⡟⢿⠈⠛⠀⢙⡀⢢⣅⠸⡆⢱⡄⢰⡀⢄⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⢭⡁⠢⣄⠐⢌⡑⢦⡙⢷⡀⢻⡄⢻⡄⢻⡀⢿⠀⡇⢸⡄⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⢤⣉⡛⠦⣍⠓⢄⡑⢆⠙⣄⠻⡎⠻⠀⠛⣈⠡⠤⠥⠬⠤⠤⠤⠅⠈⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠐⠒⠦⠍⠓⢌⡳⢦⡙⠄⣁⠬⠔⠒⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⣉⣉⡒⠲⢬⡐⠉⣠⠔⠉⠀⠀⠀⠀⠀⢀⣤⠀⠀⢠⣶⠀⠀⢀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠒⠲⠤⣌⠂⡨⠊⠀⠀⠀⠀⢠⠿⣀⢠⣭⡥⠀⠀⣴⡞⠉⠀⣴⣦⠅⠀⠀⣤⣦⡀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿ ⡿⠉⠉⣙⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⡉⠀⣠⠞⠁⠀⠠⢖⠀⠐⣶⡏⠀⢸⣿⡇⠀⢠⣿⡇⠀⢠⣿⢩⠂⠁⠀⠹⣿⣷⣠⣤⣶⣶⡄⠀⠙⣿⣿⣿⣿⣿ ⠁⠠⠤⢔⣀⠁⠀⠀⠉⠉⠙⠛⠛⠻⠟⠛⠋⠉⠀⠈⠀⢀⡠⠐⣾⡟⠀⢠⣿⠃⠀⣾⣿⠁⠀⣼⣿⠀⠀⣸⣿⠈⠀⠀⠀⢠⣼⣿⣿⢿⣿⣛⣅⠀⠀⠈⢻⣿⣿⣿ ⣆⠩⠥⠀⣀⣀⠠⠅⠀⠀⠀⠊⠀⠀⠀⠀⢀⡀⠀⠀⢸⣿⠀⠀⣿⡇⠀⢸⣿⠀⠀⣿⣿⠀⠀⣿⡏⠀⠀⣿⡟⢀⠶⠀⣤⣴⣿⣿⡏⢸⣿⡟⠁⠀⠀⢀⡀⠹⣿⣿ ⣿⣷⡆⢀⣀⡀⠤⠀⠀⠀⠀⣰⠀⢀⣴⡆⠀⣼⣿⠀⣸⣿⠀⢠⣿⡇⣤⢄⣒⣒⣀⣀⣀⠀⠈⠉⣁⣀⠸⠿⠁⠈⠀⣆⢸⣿⣿⣿⠁⣾⣿⣿⣤⣀⣠⣾⣦⠄⢈⢻ ⣿⠋⠴⣒⡒⠾⠉⠁⠀⠰⡀⣿⡄⡼⠿⠿⠸⣿⣿⡄⣿⣿⡄⢸⣿⡇⢹⣷⣤⣤⣴⣖⣒⣙⡉⠤⠄⠒⠀⠭⠀⠀⠀⣿⡀⢿⣿⣿⢸⢹⣿⣿⣿⣿⣟⢛⣥⣞⠉⢸ ⡇⡈⠭⠗⠂⠉⣀⣤⣤⣶⣦⣶⣶⣶⠶⠂⠀⢀⡙⢧⣿⣿⣇⢸⣿⣿⠀⡻⣶⣒⣒⣒⠂⠂⠀⠉⠁⠀⠀⠈⠀⣿⣿⣿⣷⣌⠻⣿⣾⣷⣻⠿⣿⣿⠿⣭⣭⡬⠉⣼ ⡇⠒⡩⢐⣡⣾⣿⣿⣿⣿⣿⣿⣿⡏⠀⢀⣒⡶⢹⡌⢿⣿⣿⡜⣿⣿⡄⣷⣌⣛⠳⠖⠛⠉⣒⣒⢂⣤⣶⣶⣶⣿⣿⣿⣿⣿⣷⣌⠛⠿⣿⣿⣿⣿⠿⠟⣋⣴⣿⣿ ⣷⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠉⠁⢀⡠⠔⣻⣦⡙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣼⣿⣿⣾⣿⡿⠿⠿⠿⠿⠿⠿⠿⢿⣿⠿⠷⠒⠂⣀⣠⣴⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠒⢊⡡⠖⡉⠔⡩⢋⡦⣝⡻⠿⣿⣿⣿⣿⡿⠿⠿⠛⢋⠉⠉⠀⠐⠂⠀⢀⣀⣀⣀⣀⣀⣤⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡈⣁⠄⠊⠔⢉⡠⠊⡰⢡⠟⡗⡄⣤⣤⣤⣤⣤⣶⣶⣶⡾⠛⡁⠂⠘⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠊⠁⠀⢈⠔⠁⣨⣄⢰⣿⣿⣿⣿⣿⣿⡿⠋⡀⠊⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣇⣴⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⢀⠌⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⢊⣾⣶⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠶⠒⣷⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⡴⣿⣁⣤⠶⠒⠒⠾⣇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣠⠞⠑⠀⠈⠉⠀⠐⠀⠀⠀⠀⠱⢤⡀⠀⠀⠀⡀ ⠀⣤⡶⢚⡿⢥⣀⣀⣀⣤⠴⠒⠒⠒⢢⡄⠀⠀⠀⠻⡄⣠⠛⣿ ⢸⡇⠠⣿⡀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⣹⠀⠀⠀⠀⠙⠃⢄⡿ ⠈⠒⠲⣾⣤⠤⠤⠤⠤⠤⠤⢼⣏⣤⠴⠛⠱⣤⡀⣀⣰⣼⠓⢷ ⠀⠀⠐⠃⢹⣆⠀⠳⢤⠇⠀⠀⠉⠛⣷⠂⠉⠉⣟⣩⠟⠹⣦⣿ ⠀⠀⠀⠀⢸⣯⡷⢤⣀⠀⠀⠀⠀⠀⠈⢢⣀⣀⡿⠁⠀⠀⠈⠁ ⠀⠀⠀⠀⠀⠉⠁⠀⠈⠉⠒⠒⠒⠒⠊⠉⠀⠉⠁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⠞⠉⠉⠒⡄⠙⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⢸⡀⠈⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡐⠁⠀⠀⠒⠢⣍⠉⡅⠀⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⡮⢒⠒⠐⠒⠤⡀⠑⡄⠘⡄⠠⣷⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣾⣶⣾⡲⢖⣤⣀⠈⠢⡈⢂⢣⠀⡉⠙⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡟⠉⠆⠀⠘⡿⢋⣦⡄⠱⠀⢎⠆⠈⠁⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣧⠀⢠⡇⢠⠁⠀⢰⣻⡄⢣⠘⡰⠀⠀⡗⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠘⣿⠀⢸⠇⢢⠀⠀⠀⠰⢷⣈⠀⠸⠀⠀⠃⠰⡀⠀⠀⠀⠀ ⠀⠀⠀⢀⠙⣆⢸⡆⡈⠐⠀⠀⠀⢸⣿⠀⠀⡇⠀⠸⠀⡗⡄⠀⠀⠀ ⠀⠀⠀⠸⠀⠘⠁⠀⡇⡖⠅⢈⠇⠀⠙⡇⠀⠁⠀⠀⠃⡇⠸⢄⠀⠀ ⠀⠀⠀⡗⠀⠀⠀⢀⣷⠋⠀⡸⢠⡄⠀⡇⠀⡀⠀⠀⠸⠘⠀⢂⠑⠄ ⠀⠀⣰⣷⢖⡠⠤⢤⡇⠀⠰⠁⡼⢁⡶⠁⠀⠦⡀⠀⠀⠱⡀⠀⢂⠀ ⣤⣾⣏⡟⡍⡀⠀⠀⢃⠀⣤⣤⡵⠋⠀⠀⠀⠀⠈⠆⠀⠀⢰⠀⠀⠆ ⢿⣛⡓⠟⠻⠙⢛⣻⡉⠯⠟⠋⠀⠀⠀⠀⠀⠀⠀⠹⠤⡀⠎⠀⠀⠀ ⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠤⡄⠀⢠⠋⠀⠀⠀⠀ ⠀⠀⠀⠁⠂⢄⣀⠀⠀⠀⠀⠀⡄⠴⠚⠁⢀⠀⠉⠀⠂⠗⠊⠛⠣⠤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠓⠒⠤⡄⡀⠈⠤⠠⡀⠈⠑⢆⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠈⠁⠈⠀⠈⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣷⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠋⠀⠀⠀⠙⠻⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠃⠀⠀⠀⠀⠀⠀⢸⡿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠙⢿⣿⣿⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⢿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣤⣶⣶⣶⣶⣶⣦⣄⠀⠙⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣼⣿⡟⠀⠀⠀⠀⢀⣤⣾⣿⣿⠟⠛⢻⡉⠉⣇⠀⢫⠙⢿⣧⡀⠈⢻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣼⣿⡟⠀⠀⢀⣴⣾⡿⢿⡋⠀⢸⣆⠀⢸⣷⠀⣿⣄⣾⡆⢸⡙⣷⡀⠈⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢹⣿⠁⠀⢠⣿⡿⠋⡀⠈⣿⣆⣸⣿⣦⣾⣿⣿⣿⣿⣿⣷⣿⣷⡇⣧⠀⠸⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⠀⢀⣿⠿⣄⠀⢻⣦⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⠀⠀⢻⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⣿⠀⢸⣿⡀⠹⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠻⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢰⣿⡀⠀⣿⠹⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⡛⢿⣿⣿⣿⣷⡀⠀⠀⠈⠻⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⣇⠀⠸⡷⣿⣿⣿⣿⣿⣿⣿⣿⡿⢻⣿⣿⠀⠙⢿⠀⠈⠟⢿⢻⣛⠇⠀⠀⠀⠀⠈⠻⣿⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⣿⡀⠀⠱⣿⣿⣿⣿⣿⣿⠻⣿⡇⠀⠙⣿⣀⣤⣤⠤⠤⠴⠞⠊⠁⠀⠀⠀⠀⠀⠀⠀⠹⣿⣧⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠙⣿⣿⣿⣿⢿⡄⠀⢉⣴⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠘⣿⡿⠛⣆⡤⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠈⠉⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣷⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣷⠀⠀ ⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡆⠀ ⢀⣤⣤⡶⠿⠿⠛⠋⠙⠻⠿⢿⣿⣶⣦⣤⣤⡤⠤⣀⣤⣾⣦⡀⠢⢤⣤⣴⣶⣿⣿⡿⠿⠛⠻⢿⣿⣷⣦⣤⣀⣀⣀⣀⣀⣈⣿⣿⣀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣾⣿⠿⠻⠿⣿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠛⠛⠛⠋⠉⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣤⣶⡾⠿⠿⠛⠋⠉⠀⠀⠀⠀⠀⠉⠙⠛⠿⠷⣶⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢰⡒⠒⠂⠤⢀⡀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⠶⠃⠀⠀⢈⡰⠤⠔⠒⠒⣿⣟⡑⠖⠤⠤⢀⣀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠰⢀⠤⠂⠁⠀⡠⠒⠀⠢⠿⣿⣁⣀⣀⡀⠀⠤⠭⠅⣢⡀ ⠀⠀⠀⠀⠀⠀⣠⠖⠁⠀⠀⠀⠘⠀⡌⠉⠂⠀⠀⠀⠀⠀⠰⠖⠀⠀⠀⡽⠁ ⠀⠀⠀⢀⠴⠊⠉⠉⠀⠀⠀⠀⡇⢸⠀⠀⠀⠑⠢⣀⠀⠀⠀⠀⠀⣰⠟⠀⠀ ⢀⡠⠖⠁⠀⠀⠀⠀⠀⡠⣀⡴⠀⠘⡄⠀⠀⠀⠀⠀⢉⠒⠢⠖⠉⠀⠀⠀⠀ ⠻⠤⠤⠀⠠⡤⠔⠂⡩⠒⠁⡄⠀⠠⡈⠢⢀⡀⠀⠀⡲⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢃⠀⠘⠀⠀⢀⡜⠢⠤⢈⡒⠦⠌⣉⡭⠣⡘⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⢢⠸⡄⠀⢸⡀⠀⢀⡀⠤⠤⠦⠬⢍⡑⠪⡧⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠑⠌⡢⢄⡌⠉⠁⠀⢀⡠⠔⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡗⠀⠀⢠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⢀⡤⣤⣤⢄⢤⢤⣤⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡀⣀⢀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⠤⠤⠤⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣼⣿⣿⣿⣿⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢰⣿⣿⣿⣿⡉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣾⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠻⠻⡿⢿⣿⣿⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣶⣶⠀⠀ ⠈⢹⣿⣿⣿⣿⣿⣦⣼⣷⣦⣀⠀⠀⠀⠈⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠘⠛⢧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣿⣿⠀⠀⠀ ⠀⠀⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣿⣿⣿⡿⠇⠀⠀⠀ ⠀⠀⠀⠈⠘⠿⣿⣿⣿⣿⣿⣿⠛⢿⠛⠟⠛⠋⠋⠉⠋⠙⠛⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠉⠻⡿⡇⢀⣤⣤⣶⣶⣶⣶⣏⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣤⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⠿⣄⠀⠀⠀⠀⠀⠀⠀⢤⣾⣿⣿⣿⣿⣿⠙⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⢾⡿⣿⣿⣿⣿⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠢⠤⢤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣭⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠛⠻⡿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣤⣄⣀⣀⣀⣠⣤⣶⣾⣿⣿⣿⣿⣿⣶⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣶⣿⣿⣿⣿⣿⣿⢿⠟⠿⠛⠛⠛⠙⠿⣿⣿⣿⣿⣿⣾⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠙⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣆⣀⣀⣀⣿⠿⢿⣿⣿⣿⡿⠿⠟⠟⠛⠋⠈⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣷⣆⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣷⣶⣦⣬⣭⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⢿⣿⣿⣀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⡏⠿⠙⠃⠋⠀⠀⠙⠛⠘⠟⠿⠻⠟⢿⠿⡿⠿⡿⢽⠿⡿⠻⠷⠆⠀⠁⠉⠀⠘⠋⠛⠘⠛⠿⠻⠿⠿⠿⣿⢶⣶⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠻⠻⠦⠤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠿⠟⠛⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠓⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣾⡆⠀⠀⠀⠀⢿⣿⡌⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⣻⣟⢄⠀⠀⠀⣾⣿⣿⣄⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢹⣿⣧⠵⠂⠈⢅⠴⠀⠐⠍⠁⢔⠢⢄⣀⠀⠀⠀⠀ ⠀⠀⠀⠀⠻⠁⠀⢀⠄⠡⣼⠿⣦⣀⣄⡀⠇⠀⠑⢑⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⠰⠋⠀⣺⣅⠒⣀⣪⠁⠙⠂⠀⠀⠈⠀⢄⠀ ⠀⠀⠀⠀⠐⣀⠘⠷⣸⣿⣿⣤⡏⣹⢓⣔⡤⢀⣀⣀⣠⡦⠃ ⠀⡀⠐⠁⢀⣠⣷⣦⠌⠹⠲⣋⡷⢻⣾⣧⣾⣩⢏⠊⠀⠀⠀ ⠴⠤⠖⠚⠋⠉⠀⢰⢹⡖⠱⠙⢧⠞⣸⠋⣏⡜⣧⡢⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠈⠁⠀⠈⠉⠀⠉⠉⠁⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣾⣧⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⢀⣀⡀⣤⣤⣤⣤⣤⣤⣤⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⡀⣠⣤⣶⣴⣿⣿⣿⣾⢷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⣹⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣄⣀⣠⣾⣿⡇⠀⠀⢹⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⣀⣘⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀ ⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⣀⠀⠀ ⠀⢻⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄ ⠀⠀⠳⣄⡀⠈⠉⠉⠉⠛⠛⠛⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠛⠁⠀⠉⠉⠉⠉⠉⠀⠀⠀ ⠀⠀⠀⠀⠙⠲⣖⣤⣤⣆⣤⣀⣄⣄⣀⣀⣀⠀⠈⠉⠉⠛⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⠿⠿⠿⠿⣿⣿⣿⠿⠿⠛⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠛⠯⣍⣉⠉⠋⠝⠉⠋⠅⠐⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣶⣅⣰⠦⠗⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠒⣓⣒⣒⡒⠢⠤⠤⠦⠤⠦⠶⣬⡟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⠿⢿⣿⣿⣿⣿⣿⣿⡿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠶⠶⠒⠛⠛⠛⠛⠛⢛⣷⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡆⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣤⡤⠤⠤⠤⠤⠤⠤⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⢫⡾⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣀⣠⡤⠴⠖⠒⠛⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⣸⠃⠀⠀⠀ ⠀⠀⣠⣴⠖⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⡛⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⡏⠀⠀⠀⠀ ⣴⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠀⠀⠀⠀⠀⠀⢰⡆⢠⡀⠢⣄⠀⠀⠈⠙⠲⢤⣤⡤⠔⢲⠖⠀⠀⣼⠁⠀⠀⡇⠀⠀⠀⠀ ⣯⠀⠀⣷⣄⠀⠀⠀⠀⠀⠀⣠⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡄⠀⠀⠀⠻⡄⠹⡄⠙⣦⠀⠀⠀⠀⠀⠀⠀⠐⠾⠤⣄⣰⡇⠀⠀⠀⡇⠀⠀⠀⠀ ⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⢻⡀⠀⠀⠀⢻⡀⢸⡄⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢳⠀⠀⠀⠀ ⠀⠙⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣋⣿⡅⠈⣧⠀⠀⠀⠈⡇⠀⣇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠸⣇⠀⠀⠀ ⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⢿⣬⡿⠉⠀⠀⢹⡄⠀⠀⠀⢿⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠳⡄⠀⠘⣆⠀⠀ ⠀⠀⠀⠀⠈⠙⠶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢴⣿⣉⡷⠼⠂⠀⠀⠀⠀⠘⡇⠀⠀⠀⠾⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠈⠢⣄⠘⢦⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⢄⣀⠀⠀⠀⠀⠀⠀⢀⣠⡤⢾⣟⣹⠷⠿⠉⠁⠀⠀⠀⠀⢀⡤⢾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠉⠙⠓ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠉⠻⣤⡟⠺⣇⠉⠀⠀⠀⠀⠀⠀⣠⣾⠋⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⢀⠞⢱⠃⢠⠤⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⣰⠏⠀⣯⣤⠾⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⢰⠏⠀⣠⣟⠙⣶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢶⣼⣇⣀⣠⣶⣿⢶⡟⢿⣹⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠿⢤⣇⡘⣇⠘⣇⣹⣦⡷⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠉⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠛⢧⡀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⣶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠋⠀⠀⠀⢳⡀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⣠⠶⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠴⠛⠁⠀⠀⠀⠀⠀⠀⢳⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⣠⠎⠁⠀⠀⠀⠈⠉⠛⠒⠶⠶⠶⠶⠖⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⡗⠖⢾⡳⠖⡖⡾⠒⠲⣾⠆⢰⢶⡶⡖⠀⠀⠃⠿⡘⠚⠔⡔⡆⠑⠁⣻⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠊⠉⠉⢩⠇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⣀⠀ ⠀⠀⢀⣀⠠⠤⠐⠒⠒⠂⠀⠀⠈⢀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⢠⢊⠃⠀ ⡴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀⠀⢀⢀⢄⠁⠢⠄⠠⡤⠀⠆⢸⠀⠀ ⢃⠈⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⡀⠈⠎⠆⡆⠀⠀⠀⠉⠘⠀⠘⡀⠀ ⠀⠳⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠗⠁⢣⠀⢸⠸⠁⠀⠀⠀⠀⢠⠔⢄⠡⡀ ⠀⠀⠀⠁⠂⠤⣀⣀⣀⢠⣴⠟⠓⠁⠀⡠⢸⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠑⠓ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⡄⠀⠠⠺⣠⡆⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⠁⣠⣁⣼⡞⠀⠀⠀⠀⠀⠀⠀⠠⡃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⠒⠯⠏⠽⠕⠋⠀⠀⠀⠀⠀⠀⢀⣄⠀⢃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠰⠀⣀⠀⠀⠀⠀⠀⠀⣀⠔⠋⠀⢣⢸⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⠈⠀⠈⠁⠐⠒⠊⠉⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⣠⣄⣤⢀⡄⣀⡄⠠⠤⡄⠀⠀⡄⠀⠀⠁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠊⡝⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣲⠇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⠁⠀⠀⢀⣀⣀⣧⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠊⡞⠁⠀⠀⠀ ⢰⠒⠒⠒⠒⠉⠉⠉⠉⣉⡉⠉⠁⠀⠀⠀⠀⠀⠀⠓⠀⠀⠉⠉⠒⠒⠲⠤⠤⠤⠒⠋⠁⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀ ⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀ ⠀⠓⡦⡤⡤⡤⡤⠤⢤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠒⠚⠛⠓⠒⠪⢧⠀⠀⠀⠀ ⠀⠀⡀⠀⡀⣄⡤⠖⠊⠁⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀ ⠀⠀⠛⠯⠥⠤⠖⠒⠒⠢⠤⠤⢼⡀⠀⠀⢸⣀⡤⠴⠶⠮⠭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣄⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠤⢴⡒⠒⠛⣟⠉⠉⠉⠉⢹ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠛⠉⠝⣍⣒⣤⣀⠱⠀⠀⠀⠀⠀⢀⡏ ⠀⠀⠀⠀⠀⠀⢀⡠⠴⢒⡿⠋⠁⠀⠀⠀⠀⠀⠀⢀⣤⠖⡲⠢⡤⢄⡀⠢⣼⠀ ⠀⠀⠀⠀⡠⠖⢉⡠⢴⠞⠀⠀⠀⠀⠀⠀⢀⡠⠊⣁⡌⢩⠝⠓⢳⢽⣴⡧⠟⠀ ⠀⠀⡠⠊⠀⠂⠁⣰⠃⠀⡇⠀⠀⠀⠀⠀⡯⣊⣈⣀⠀⠀⡑⠀⣨⠞⠁⠀⠀⠀ ⢠⠞⠀⠀⠀⠀⢰⠃⢰⢠⢃⠀⠀⠀⠀⠀⢻⣦⠀⠀⠀⢹⡟⡾⠁⠀⠀⣷⠀⠀ ⠛⠒⠒⠒⠦⣠⠇⠀⠐⡂⡪⣂⡀⠀⠀⠀⠈⢿⣽⢤⣀⢰⢮⠇⠀⠀⠀⡇⣇⠀ ⠀⠀⠀⠀⠀⢹⡀⡴⠚⠈⠉⠀⠀⠀⠀⠀⠀⠀⠈⣓⣷⣭⠋⠀⠀⠀⠀⡇⢹⠀ ⠀⠀⠀⠀⠀⢈⠏⠀⠀⠀⢀⡇⠀⠀⠀⠀⢒⡲⣶⣋⢱⡀⠉⠲⣄⠀⡴⢃⣾⠀ ⠀⠀⠀⠀⢠⠏⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠈⠐⠈⠢⢉⡳⠤⣀⠈⠳⣗⢁⠇⠀ ⠀⠀⠀⢀⠏⠀⠀⠀⣠⠫⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠒⢬⣎⠀⠀ ⠀⠀⠀⡜⠀⣀⡠⠔⢧⡀⠀⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠞⠁⠀⠀⠀ ⠀⠀⠀⢗⠉⠁⠀⠀⠀⠈⠓⠢⠤⢤⣀⣀⣀⣀⣀⣠⠤⠤⠒⠉⠀⠀⠀⠀⠀⠀
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⢸⡷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢷⡀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠤⢤⡀⠀ ⠀⠈⣷⡀⠐⡝⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⡉⠙⠙⠓⠶⢦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⣶⡒⠛⠋⠉⠀⠀⠀⣷⡀ ⠀⠀⢹⡇⠀⠘⡌⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⠀⠀⠳⣄⣀⣩⠽⠷⠒⠒⠚⠛⠛⠟⠋⠁⠘⠿⠃⠀⠜⠁⠀⠀⠀⠈⣿ ⠀⠀⠘⡇⠀⠀⢱⠸⣆⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡤⠴⠖⠛⠃⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⢊⣉⣀⣠⣤⣤⣄⣠⢤⣿ ⠀⠀⠀⣽⠶⠀⠀⠀⠙⢶⡤⠶⠶⠶⠒⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⢀⣤⣆⣔⡰⠤⠒⠉⢠⣴⣿⣿⣿⣿⣿⣯⣯⣿⣿⣿ ⠀⠀⠀⡷⠀⠀⠀⠀⠀⠀⠀⠉⠉⠒⠒⠒⠒⠒⠒⠒⠈⠉⠉⠁⠀⠀⠀⠀⠀⢨⣿⡏⣏⡜⠀⠀⠀⣠⣿⡿⠛⠉⠉⠉⠀⢈⡼⣹⡿⠁ ⠀⠀⣰⠇⠀⠀⠀⠀⣰⡶⠦⣤⣤⠀⠀⠀⠠⠤⠤⠤⠤⠒⠒⠒⣒⡶⠒⢲⠤⢼⣿⣤⢽⠤⠔⠚⣩⡿⠃⠀⠀⠀⠀⠀⣠⡏⣴⡿⠁⠀ ⠀⢰⠏⠀⠀⢀⣠⡾⠋⠀⠀⠈⠙⠳⢦⣄⠀⠀⠀⠀⠀⢀⣴⠋⠁⠀⠀⡼⠂⠀⢻⣸⢸⡆⠀⢸⢿⣷⣀⣀⢀⢀⣀⣀⣇⣉⣙⣿⡄⠀ ⢠⡟⠀⣀⡴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⣤⣠⣴⠋⠁⠀⠀⢠⡞⠀⠀⠀⠀⠛⠀⠃⠀⠈⠛⠿⣿⣿⣿⣿⠯⠿⠿⢿⣿⣾⡇⠀ ⣸⣠⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠇⠀⠀⣜⣵⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⣛⣫⣩⠿⠋⠀⠀ ⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⣠⠾⠋⠉⠛⠓⠶⠶⠤⢤⣤⣤⣤⣤⣤⣤⣤⠼⡽⠿⠛⠛⠉⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⣁⡴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠷⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⣄⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠖⠒⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠁⠀⠀⠈⠻⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡷⠒⠢⢤⣀⠀⠈⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⠀⠀⠀⠀⠈⢣⡀⠀⠘⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⢱⡄⠀⠈⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢀⣀⣀⡀⠀⠀⠀⣄⣘⣧⢤⡀⠀⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁⠁⠀⠀⠈⠉⠙⠢⢧⡀⠀⠁⡆⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢃⣀⣀⡤⠤⣀⣀⠀⠀⠀⠸⣄⠀⠀⠹⣄⠀⠀⠘⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⣾⠞⠉⢠⠀⠀⠀⠀⠈⠙⠦⣄⠀⠈⢳⡀⠀⢻⡄⠀⢸⣻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣾⣣⣤⣶⣿⠚⣷⣶⠤⣄⡀⠀⠈⠳⣄⠀⠹⡄⠘⡇⠀⠈⠋⠃⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⣿⣿⠿⢿⠸⠞⠀⢹⣴⢻⠟⣦⠀⠀⠈⢦⠀⠈⢆⢹⡀⠈⡦⠤⢈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡏⠁⠀⠸⡄⠀⠀⠉⢸⠻⢃⣸⠳⢤⡀⠐⢧⠀⠘⡆⢣⠀⡇⠀⠈⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⡇⢰⠀⠀⡜⠀⠀⠉⢉⣹⣦⠀⢸⡄⠀⢹⠈⡆⠁⠀⠠⡷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⡆⠀⠀⢳⣼⠀⣰⠃⠀⠀⠀⢼⠯⠿⣿⠁⠹⡀⠸⣦⡇⠀⠀⠀⣇⠘⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣷⡇⠀⠀⢸⢹⠀⣿⠀⠀⠀⠀⠀⠀⣼⣋⣆⠀⡇⠀⠈⡇⠀⠀⠀⢿⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⢿⣿⠀⠀⢸⡈⠀⢹⠀⠀⠀⠀⠀⠀⠀⢠⠟⣶⡇⠀⠀⢹⠀⠀⠀⢸⡀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⠀⢻⣧⡀⣾⣧⠀⡞⠀⡞⠀⠀⠀⠀⠀⠈⣿⣿⡇⠀⠀⠘⡆⠀⠀⠀⣇⠀⢰⠙⣆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡼⠀⠀⠻⡷⠋⠁⠀⡇⢰⡠⠋⣠⠖⢶⠀⠀⠀⢻⣽⠀⠀⠀⡇⠀⠀⠀⠸⡄⢸⠀⢘⣦⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⡇⡸⣡⠞⠁⢠⠏⠀⠀⠀⠀⢹⠀⠀⠀⢇⠀⠀⠀⠀⣷⠘⡆⠀⢫⠳⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⢠⠷⡷⠁⠀⠀⣼⠀⢀⡤⠀⠀⢸⠀⠀⠀⢸⠀⠀⠀⠀⠸⡆⠹⡀⠈⢆⠈⠳⠄⠀ ⠀⠀⠀⠀⠀⣸⡁⠀⡀⠀⠀⠀⠀⢛⡼⠁⠀⠀⢠⠇⠀⣞⡇⠀⡀⣼⠀⠀⠀⣼⠀⠀⠀⠀⠀⠱⡀⠀⠀⠈⢆⠀⠀⠀ ⠀⠀⠀⢀⣼⣹⣿⢿⣩⣴⠶⠲⢤⣶⡇⠀⠀⢠⠋⠀⣰⠟⠀⣴⡿⠁⠀⠀⢠⡿⣄⠀⠀⠀⠀⠀⠑⡄⠀⠀⠈⢆⠀⠀ ⠀⢠⣴⣾⡿⣻⡶⠟⠉⠀⠀⠀⢸⠈⡇⠀⠀⢸⠀⠀⣏⣢⣾⠏⠀⠀⠀⠀⠀⠀⠈⠱⡄⠀⠀⠀⠀⠘⡄⠀⠀⠈⢆⠀ ⣾⣿⡿⢿⠧⣿⣤⣿⣰⣦⠀⢀⣸⡀⣹⡄⢀⡯⣧⣟⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⣇⡀⠀⠀⠀⢀⡇⠀⠀⠀⠘⠀ ⢸⣯⠯⠋⠿⠿⡏⢯⠏⠛⠻⠽⠻⡯⡽⣹⡯⠧⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣷⠤⡄⠀⡼⠀⠀⠀⠀⠀⠀ ⠀⠻⣍⠉⠒⠒⠒⠒⠒⠒⠒⠓⠒⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣰⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠑⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣄⡴⠒⣦⡀⠤⠤⠤⡞⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠉⠲⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⠴⠋⠃⠉⠀⠀⠙⠉⠀⠠⣄⣳⠤⠤⠹⣒⡮⡅⠀⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠤⠤⠤⠄⣀⣀⣀⣀⣀⣻⡄⠉⠁⠀⠀⠀⠘⠦⢤⡄⠀⠀⠀⠀⠀⣇⡀⠀⠀⠀⠈⠉⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠗⠚⠳⢆⣀⠀⢀⡀⠀⠧⠤⠤⣄⠀⠀⠀⠈⠻⣆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠦⠊⠀⠀⠀⠀⠀⠀⠑⠦⣀⣠⠄⠈⠓⠒⠂⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣏⠉⠉⠉⠛⠲⠶⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⢤⣴⠄⠀⠀⠈⠙⠲⢤⡀⠀⣀⣀⣤⠦⠴⣾⣿⣟⠳⢦⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡍⠁⠀⠀⠀⠀⣀⡤⠴⠛⠋⠉⠁⠀⠀⠀⣿⣺⣤⢷⠀⠃⠉⠉⠙⠒⠲⠦⠤⣄⣀⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣠⠶⠋⠁⠀⠀⢀⡠⠖⠋⠉⠓⢤⣿⣿⢟⠞⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣈⣉⠛⢶⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣇⡴⠋⠁⠀⠀⠀⠀⢀⠎⠀⢀⡤⠤⡀⠀⠈⠉⠉⠒⠒⠒⠒⠒⠋⠉⠉⡀⠀⠀⠀⠀⠉⣦⡗ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⠀⠀⠀⠀⠀⣸⠀⢀⡞⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠟⠉⠀⠀⠀⠀⢀⡾⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠞⠋⠉⠙⠒⠀⠀⠀⠀⠀⠀⡇⠀⢸⠃⠀⠀⠀⠀⠙⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣷⠟⠀⠀ ⠀⠀⠀⠀⠀⢀⡴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⢸⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣄⡀⠀⠀⠀⠀⢀⣀⡴⠟⠁⠀⠀⠀ ⠀⠀⢀⣀⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⣀⣰⠟⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡙⠓⠲⠤⠴⠋⠉⠀⠀⠀⠀⠀⠀ ⢰⣾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠴⠊⢁⡨⠟⠁⠀⠀⢠⡀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⠉⠛⠒⠒⠶⠤⠤⠶⡖⠒⠋⠉⢀⡤⠞⠁⠀⠈⣆⠀⠀⠀⠱⣄⠈⠑⠦⣄⣀⡀⠀⠀⢀⣸⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⡞⠁⠀⠀⠀⠀⣸⡷⣄⣀⠀⠈⠓⠦⣄⣀⠉⠉⠉⠙⣉⡿⡀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⡇⠀⠀⠀⠀⣰⠏⠄⠀⠉⠉⠉⠛⠛⠉⠉⠉⠙⠻⣿⣍⡀⠘⢦⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠹⡄⠀⠀⠀⣏⠀⠀⠀⠀⠀⣀⣠⠤⠤⠴⠲⠲⠦⢤⣄⡉⠛⠦⣵⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠘⢦⣀⠀⢹⡙⠲⠖⠒⠋⠉⠀⠀⠀⠀⠀⣀⡤⠶⠛⠃⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢦⣈⠱⠦⠇⠀⠀⠀⠀⠀⠀⣀⡴⠞⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢩⡗⠀⠀⠀⠀⢀⡔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⠶⡆⡆⡶⣾⣱⢶⡟⣠⠎⣻⠾⠶⣴⡰⡰⡠⠠⡐⠀
⠀⠀⠀⠀⠀⠀⣴⡆⠀⠀⠀⠀⠀⠀⠀⠀⣲⣶⣎⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣆⠙⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢾⣿⣿⢷⡀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⣧⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣽⣿⣆⢳⡀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣧⠈⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⣿⣿⣿⣦⡙⢆⣀⡤⠴⠒⠛⣛⡉⠬⠭⣘⡓⠼⠓⠢⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⡿⠋⠁⠀⠀⢐⣩⣖⣥⣄⡀⠀⠉⠲⡄⠀⠢⡀⠙⠲⢤⡤⣀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠹⣿⠋⠀⠀⠀⠀⣠⠈⠤⣀⣾⣹⡿⢦⠀⠀⢁⠆⠀⣸⠀⡀⠀⠙⣄⠳⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⡠⡾⠁⠀⣀⣴⠖⠛⠛⠛⠓⢶⠛⠫⣍⡂⠀⠈⠉⠒⠦⣉⠳⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⢸⡇⡇⠀⢈⣩⣥⣖⡚⣛⣛⡓⢦⠃⠀⠈⠛⠀⠀⠀⠀⠀⠈⠁⠘⢦⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠸⣧⣧⠐⣻⣿⣿⣿⡀⢨⡟⠻⣗⢷⣄⠠⣀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣳ ⠀⠀⠀⠀⠀⠀⢀⣀⢈⡧⢦⡀⠉⠙⢇⣹⣿⡿⠿⣷⣿⡇⢠⡏⠑⢪⣕⣮⣍⣒⣒⡒⢲⣖⣢⠯⠞⠋ ⠀⠀⠀⠀⡠⠞⠁⠀⠀⠀⣸⣿⣦⣄⡈⠉⢻⢦⣰⠟⢻⣿⣿⣷⣴⣿⣀⣤⣿⠉⢉⣽⡡⠞⠀⠀⠀⠀ ⠀⠀⡠⠊⠀⠀⣀⣤⣴⣾⡿⠿⠛⡟⢯⣀⠈⢆⠈⣦⣴⠏⠀⣿⠟⣿⡿⣿⣿⢎⣽⡑⣄⠀⠀⠀⠀⠀ ⠠⠾⠵⠶⠞⠛⠋⠉⠉⠀⠀⠀⠀⣿⠌⣿⡿⠚⠳⣄⠙⢗⠶⣇⢀⣿⠁⢸⡈⣦⡟⣷⣌⢦⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠸⠿⠃⠀⠀⠈⠑⠤⠑⠦⠉⠚⠳⠯⠿⠉⠁⠿⠿⠦⣧⠀⠀⠀
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⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⣿⠻⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢹⣇⠀⠙⠿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣄⠀⠀ ⠀⠀⢻⣆⠀⠀⣍⢻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣍⠙⠛⠿⠷⠶⢦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡤⠶⠶⠞⠛⠉⠁⠀⠀⢹⡆⠀ ⠀⠀⠀⣿⡄⠀⠘⣆⠹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡄⠀⠀⠀⢠⡀⠉⠙⠻⠶⣦⣄⣀⣀⣀⣠⣤⣤⣤⣴⣶⠾⠋⢹⣿⣷⠀⠀⢠⡴⠀⠀⠀⠀⠘⢿⣦ ⠀⠀⠀⢹⡇⠀⠀⠈⡄⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣦⠀⢀⡀⠙⠶⠤⠤⠖⠛⠉⠉⠉⠉⠀⠀⠀⠈⠉⠀⠀⠀⠈⠛⣁⡀⠀⠋⠀⠀⠀⠀⠀⠀⠘⣿ ⠀⠀⠀⠸⣇⠀⠀⠀⢹⠘⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡴⠶⠞⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠚⠉⣁⣀⣀⣤⣤⣤⣤⣄⣰⡶⣾⣿ ⠀⠀⠀⠀⣹⣦⡄⠀⠀⠂⠘⢿⣦⣤⣤⣤⣤⣤⡶⠶⠟⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣠⢇⡴⢀⣄⡤⠖⠋⠁⢀⣴⣟⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿ ⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠈⠛⠲⠤⠤⣤⣀⣀⣀⣀⣀⣀⣀⣤⠤⠤⠤⠖⠒⠒⠒⠒⠒⠒⠒⠒⢲⣾⣿⠛⡟⣻⠏⠁⠀⠀⠀⢴⣿⣿⣿⠻⠟⠟⠻⠙⠋⠋⣹⠿⣿⡿⠉ ⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡏⢸⢱⠏⠀⠀⢀⣠⣴⣿⠿⠏⠈⠀⠀⠀⠀⠀⢀⡼⢋⣾⡿⠁⠀ ⠀⠀⠀⣾⠇⠀⠀⠀⠀⠀⢀⣿⠟⠷⢶⣶⡤⠤⠤⠤⠤⠤⠶⠖⠒⠒⠒⠚⠉⠉⠉⣉⣭⠏⠉⠙⡗⠲⢿⣿⡧⡾⢼⠖⠒⠋⢉⣴⡿⠏⠀⠀⠀⠀⠀⠀⠀⢰⢾⢀⣾⣿⠁⠀⠀ ⠀⠀⣼⠏⠀⠀⠀⠀⣠⣴⠟⠁⠀⠀⠀⠉⠛⠷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠟⠁⠀⠀⠀⣠⠗⠀⠈⢻⡇⡇⢸⠀⠀⠀⣾⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⣧⡈⠉⣙⣿⣧⠀⠀ ⠀⣼⠏⠀⠀⢀⣴⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢶⣤⣀⠀⠀⣠⣶⠟⠁⠀⠀⠀⢀⣴⠋⠀⠀⠀⠀⢳⢧⠈⡇⠀⠀⠻⣾⣿⣿⣿⣿⣾⣷⣿⡟⣿⣻⣿⣿⣿⣿⣿⡇⠀ ⢠⡟⠀⣠⣶⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⡿⠃⠀⠀⢀⡄⣠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠿⠿⢿⣯⣉⣉⣉⣩⠽⣿⣿⠟⠀⠀ ⣸⣧⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃⠀⠀⢠⣿⣾⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣈⣉⣽⣶⠾⠛⠁⠀⠀⠀ ⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣏⠀⠀⢀⣴⠟⠋⠀⠉⠙⠛⠳⠶⠶⢶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣶⡾⠿⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠛⢁⣤⡾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣧⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣟⣥⡾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣤⡀⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠦⢿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⢖⡏⠉⠭⡵⠎⠛⠿⢶⣆⠤⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⢿⢟⣏⢍⠄⠐⠀⠄⡆⠄⠰⡌⠃⣭⣷⡽⣖⣄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⢿⣧⢗⢾⣸⣦⡠⣀⠉⠊⢸⠠⡀⢀⣽⣿⣿⣿⣦⣿⣷⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⡿⣿⣿⢇⣿⣯⣿⢿⣿⣟⠀⠤⠀⣶⢠⢾⣷⣿⣿⡿⡟⠻⣿⣟⣿⣷⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡟⣠⡗⡏⣿⣿⣿⣟⣼⣿⡎⣠⡇⣿⣿⣎⣽⣟⣿⣿⣗⣿⣷⣋⣿⣿⡏⠀⠀ ⠀⣠⣧⣀⣀⠀⠀⠀⠀⠀⠀⠀⠹⣿⢣⡚⣹⣴⣿⣩⣿⣿⣿⣿⡄⠻⢹⢻⣿⢿⣿⣾⣿⣿⣿⣿⢿⣿⣿⣿⠀⠀⠀ ⣼⣿⣿⣿⣾⣿⣷⣦⣤⣄⡀⢀⣀⣿⣶⣢⣜⣹⣿⣿⣿⣿⣿⣿⡴⢄⡿⡷⢷⣾⣾⣿⣦⣤⣿⣭⣿⣿⣿⡎⠀⠀⠀ ⠘⢿⣿⣻⣿⣶⣿⣿⡟⢛⡿⣿⣿⣿⣷⣿⣿⡿⣿⣽⣟⣿⣿⠟⣿⣾⣿⣿⣾⣿⣿⢿⠿⠿⠿⠛⠉⠉⣻⣄⠀⠀⠀ ⠀⠈⢯⣿⣿⣿⣿⡋⢼⡁⣛⡯⣿⣿⣻⣥⣿⣿⣿⣿⣧⣿⣿⣾⣿⡾⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⡀⣴⣿⣿⣆⠀⠀ ⠀⠀⠈⢆⢿⣿⣡⣿⣿⣸⡏⣟⣽⣾⣿⣿⣿⣿⣿⣿⣷⡿⠛⠋⠀⠀⠀⠀⠀⠀⠂⠀⠀⣤⡴⡋⠁⣿⣿⣿⣽⠀⠀ ⠀⠀⠀⠈⢿⠳⡿⣿⣿⣿⢿⣿⣷⣿⣿⣿⣿⠟⠹⢿⣟⠢⣄⣄⣀⠀⠀⠀⠀⠀⠀⢀⣀⡴⡺⠃⠀⠉⠙⠻⠋⠀⠀ ⠀⠀⠀⠀⢘⣾⣾⣏⣝⣿⣿⣟⣿⣿⣿⡿⠃⠀⠀⠀⠛⢷⡄⠈⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⣷⣷⣹⢪⢟⣟⠉⢿⡟⠁⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⣿⡿⣿⣿⣯⣷⣷⢰⢷⣷⠀⠀⠀⠀⠀⠀⠀⠀⢻⡤⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⣤⣤⣀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣾⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣷⣆⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⡿⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⣇⠐⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⠇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢯⡐⠻⣿⣷⣦⣬⣤⣄⣀⣀⣤⣼⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⡠⠟⠛⠛⠛⠛⠛⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣷⣾⣿⣿⣿⣿⣦⡌⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⣀⡼⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣤⡤⠴⠒⠊⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣟⣿⣿⣿⣿⣿⣿⣻⣿⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢸⡟⠙⠲⢤⣄⣀⣀⣀⣀⣀⣀⣀⡀⠀⢀⣀⡠⢤⢞⡛⠲⣤⠶⠶⠦⠤⠤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⡀⠀⠀⢀⣠⠤⠟⠛⠉⠉⠀⠀⠘⡟⢻⣧⡈⠂⠀⠀⠀⠀⠀⠀⠈⠉⠒⠤⣄⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⡖⣠⠔⢉⡤⠖⠋⠉⢀⠔⣱⠆⠀⠀⠀⠀⠀⠳⣬⡷⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠒⠶⢤⣀⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⡴⠞⠉⠀⡴⢰⠀⡎⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⢠⠁⡆⠸⡅⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜ ⠀⠀⠀⠀⠀⢀⣠⡼⠥⠖⠃⠀⠀⠈⠃⠘⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀ ⠀⠀⢀⡴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣦⡴⣤⣤⠤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀ ⠀⡴⢋⣀⣀⣀⣀⣠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣯⣿⣿⣷⣿⣿⣿⣻⣧⣴⣿⣧⣿⠓⡄⠀⠀⠀⠀⠀⢀⣠⠞⠁⠀⠀⠀⠀ ⠾⠛⠉⠉⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠾⣟⣿⣿⡾⢿⠀⠀⠀⢀⡴⠋⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣽⣿⡶⠋⢀⡠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠞⠋⣁⡤⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣈⡤⠴⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⣶⠒⠛⢛⡿⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⢸⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⡞⡇⠀⠀⠀⠈⣧⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠹⣦⠀⠀⠀⠀⠁⠘⣄⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⢲⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢄⡀⠀⠀⠈⠳⢄⡀⠀⠀⠀⠀⠀⣀⣤⡆⠀⠀⠀⢀⡤⠖⠉⣠⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣄⣀⠀⠉⠛⠛⠻⠿⠋⣱⠧⠤⠤⠖⠛⠁⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠲⡦⢤⠤⠤⠤⠤⢤⣀⡀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢬⡆⠀⠀⠀⠀⠀⠈⠑⠦⡀⠀⠙⠦⣀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣄⡀⠈⠙⠒⠒⣒⡶⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀
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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡠⠖⡫⠥⠐⠒⡒⢒⠞⠁⡷⢄⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⡴⢋⡴⣯⣠⣤⣴⠾⣿⠏⠀⠀⡶⢄⣙⢦⠀⠀⠀⠀ ⠀⢠⠎⡰⣯⢴⣿⣷⣦⣿⣶⡟⠀⠀⠀⣀⣙⡟⣄⣱⣀⣀⡀ ⢀⡇⣼⡟⢻⡄⠉⠻⡿⠟⠉⠀⠀⠀⠘⣿⣟⣉⣠⣤⣶⡏⠁ ⢸⠀⢸⣿⣿⣿⡤⠊⠀⣀⣴⣶⣆⠀⠀⣠⣾⣿⣿⡿⠟⡇⠀ ⠸⣴⣿⣻⣿⠏⠀⠀⠈⢻⣿⣿⣿⣶⣿⣿⣿⡿⣻⠃⢀⠇⠀ ⠀⢻⣠⡿⠁⠀⢐⣷⣴⣶⣭⣀⠀⠙⠻⣿⣟⠔⠃⢀⠎⠀⠀ ⢀⠞⠹⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⡙⠢⡠⠋⠀⠀⠀ ⠁⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⠛⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀
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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⢂⣉⣬⣥⣭⣭⣁⣉⡀⠲⠤⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⣡⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠶⣀⡵⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⢠⣼⣿⠿⣻⣼⠟⠃⠀⢀⣿⡿⢃⡄⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃⣴⣿⠟⣡⡾⠋⠀⠀⠀⠀⠺⠿⣤⣄⣉⠒⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⢠⣾⡿⢁⣾⣯⣤⠶⠶⠿⠛⠟⠻⠳⠶⢿⣿⣿⣷⣤⣁⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠒⣉⣤⣿⠏⠀⣘⣋⣥⣤⣶⣾⣿⣿⣿⣿⣿⣿⣷⣶⣭⣻⣿⣿⣷⡄⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⢊⣥⣶⣿⠟⠋⣁⣴⣾⣿⣿⣿⣿⣿⣟⠻⢿⡛⢿⡛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣮⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⠄⢊⣤⣾⡿⠟⠉⢀⣴⣿⣟⠋⠉⠀⠀⠀⠀⠉⠛⢷⡀⠙⠄⠁⠀⠀⠉⢻⣿⣿⣿⣿⣿⣿⣧⣵⡠⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⣡⣶⣿⠟⠉⣀⣤⣿⣿⣯⡽⠿⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠟⠛⣉⣉⣤⣤⣤⣬⣉⣉⠛⠲⢬⣑⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⡠⢈⣤⣾⡿⠋⠁⣠⣶⠿⠛⠋⠉⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣡⣴⠾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣬⣙⣶⣅⠢⡀⠀⠀⠀⠀⠀⠀ ⢀⡔⢁⣴⣿⠟⣋⡤⠖⠋⠁⠀⠀⣀⣴⣶⠿⢿⣟⣻⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⢠⣴⡿⠋⢁⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⠛⠿⢿⣿⣿⣿⣎⠢⠀⠀⠀⠀⠀ ⠸⡐⣿⣿⣧⡰⢄⡀⠀⠀⣠⣴⠟⠋⣥⣸⣷⣾⣿⣿⣿⣿⣿⣿⣧⣤⣤⣤⣤⣼⣿⣿⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣽⣶⣿⣷⡄ ⠀⠉⠢⣙⡻⢿⣷⣮⣷⣾⣟⣁⣸⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣿⣿⡟⢻⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀ ⠀⠀⠀⠀⠈⠁⠒⠛⠫⠟⠟⠟⠻⠿⠩⢯⣽⣿⣿⣿⣿⣿⣃⣿⣿⠀⠖⠛⠀⡛⠃⠀⠙⠛⢸⠀⡿⠀⣿⠋⡈⡟⢑⠚⡀⡅⠛⣴⡇⠸⠐⢚⣿⣿⣿⣿⣿⣯⠃⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢿⣿⣿⣿⠿⢉⣼⣿⣿⣯⣭⣴⣤⣿⣇⢠⣾⣿⢨⣴⣿⡀⡇⣼⣷⣄⣸⣧⣼⡄⣷⣬⡇⣸⣬⣭⣽⣿⣿⣿⣟⡏⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⢿⣿⣯⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠉⠋⠙⠋⠉⣉⡭⠍⡩⢍⣉⣉⣹⣻⣽⣿⣏⣽⣿⣿⣿⠛⠛⠉⠙⠙⠉⠉⠉⠉⠉⠙⠙⠛⠛⠛⠛⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⣒⣬⣽⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣯⠉⠉⠉⠉⠉⢻⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢔⣽⡿⢿⡛⠏⠛⠙⠛⠋⠋⠙⠯⠿⣿⡷⣦⠀⣸⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢽⡻⠕⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣤⣿⢯⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡫⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⡿⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡟⣽⢫⡽⣘⡴⢣⣤⣕⢡⣷⣇⡠⠀⠀⠀⠀⠀⠀⢠⡠⠀⠠⣰⠤⣀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⢀⢲⡐⠦⠲⡴⠸⣴⣹⡮⠱⡭⣘ ⡟⣮⠷⣹⢋⣋⣟⣉⠧⢸⠁⠮⠁⢤⠀⢀⣀⠀⠀⠀⢥⢀⠘⡁⢀⡄⠀⠀⠀⠀⠀⠀⡀⠀⠈⠊⠁⢸⠐⢂⡭⠑⡌⢑⠰⢃⢒⠹⠰⢡ ⢩⡐⢣⢷⡚⢢⡗⠉⠊⠏⢀⡲⠀⠓⡜⢖⣢⡄⠀⢀⠆⠥⠀⡄⢠⡀⣀⣎⡠⣄⡠⠀⠀⠀⠀⠀⠀⠀⠓⠪⢅⢨⣱⢔⡂⠌⠠⢁⠊⡄ ⡣⠘⣾⣙⡱⡀⠀⠀⠀⠀⡀⢩⣶⣮⣿⣿⣾⣻⣷⣚⣮⣆⡤⢱⣿⣽⣿⣿⣷⣷⣿⣿⣯⣦⡀⣀⠀⠀⠸⠀⠠⠀⠡⢀⠂⢌⠱⣈⠒⡄ ⡝⣬⣬⢷⡧⣥⡆⢀⢢⢆⣦⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢋⡴⢏⣝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠁⠀⠀⠀⠀⠀⠠⠑⡂⢍⢂⡒⠤⢃⡜ ⣝⢲⡻⣎⣷⣣⡅⢬⠀⣾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡫⠽⣬⡘⢻⣯⣿⠿⣿⣿⣿⣿⣿⣿⡐⠁⢠⠏⠀⠤⣀⠣⠜⠒⠂⠀⠀⠁⢆ ⣈⣁⡛⠫⣝⣫⢿⣻⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣺⣯⢁⢀⠈⠙⡜⠷⣯⣿⣿⣿⣿⣿⣿⣟⣗⠰⢯⠀⠂⠀⠀⠀⠀⠀⢀⠀⡀⡜⢢ ⣥⣃⠚⣀⠳⣬⣻⣸⡇⠘⣯⢻⣿⣿⣿⣿⣿⣿⣵⣿⠃⠄⠈⠀⠀⠎⠸⣉⣿⣿⣿⣿⣿⣻⣾⣏⡁⢊⠀⠀⠀⠀⠀⠀⠠⡔⢮⡑⡎⢧ ⣷⡹⣟⠶⣭⡖⣽⡼⢵⣼⢸⣧⢻⡽⣏⣿⢏⣿⠟⢉⠈⣠⠀⠀⠀⢤⡤⣮⠻⣿⣿⣚⣿⣷⣿⣿⣸⣇⠠⠀⠀⠀⠀⠄⢫⡜⢦⡹⠜⡥ ⡷⡽⣭⡟⣵⣫⢿⣹⣯⣿⣌⣮⢳⣾⡏⢶⣻⠏⣰⠏⢙⠋⣬⣤⢠⠌⡿⠾⣧⢿⣿⣾⣽⣿⣿⣿⣿⣯⠒⠀⡀⠤⡘⡘⢦⣙⢦⡹⡹⡜ ⡿⣽⠶⣏⣷⣫⢟⣿⣯⣾⡿⢽⣷⣾⢌⣟⢫⣿⣯⣰⣶⣾⣿⣾⣿⣷⣾⣦⣹⣿⢞⠻⢻⣿⣿⣿⣻⠷⡨⢅⡠⡀⢥⠙⡮⣜⢲⣓⡳⡝ ⣿⣽⣻⡽⣲⠝⢎⣿⢽⣿⢿⣾⢿⣳⣿⣇⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡏⣿⣿⡮⣹⣾⡶⣿⣭⢳⠑⠎⢤⠑⣪⢑⡳⣜⢳⢮⡵⣫ ⣷⣻⣞⡷⢯⢚⡴⣻⣻⣿⢯⡿⣽⣿⣻⣾⣟⡧⢸⡯⣿⣿⣿⣿⣿⡿⣯⣖⣌⠔⡝⢷⣬⢭⣿⣷⣯⢇⡹⢈⠦⣑⠢⡍⢶⣩⢟⣮⢳⣳ ⣟⡷⣯⣟⣎⠧⡐⠧⣟⣿⣯⣿⣿⣳⢿⢡⣾⠂⢈⣧⣽⣽⣿⣟⣿⣽⣶⣽⣜⡱⢈⢲⡝⣾⣿⣽⣾⠃⡔⡡⢆⠥⢋⣘⢧⣏⢾⣎⡿⣼ ⣿⣽⣳⢿⣼⠢⠜⡰⢹⢾⣿⣿⣿⡟⣷⣾⣧⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣽⣷⣞⣿⡿⢯⡜⣦⣉⣚⡼⣣⢟⡾⡼⣏⣾⢳⢯ ⣿⣳⡿⢯⠲⡁⠒⡀⢩⢞⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡿⣽⢯⡽⣖⣯⢽⣞⡽⣫⢾⡽⣝⣾⣫⣟ ⣿⡧⣜⡷⣯⣽⡒⠊⢰⣫⣽⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣽⢯⡿⣽⢾⣵⣻⢮⡽⣏⡷⣯⣟⣾⣳⣟ ⣿⣿⣿⣯⣭⣭⣒⣀⣼⣿⣯⣿⣾⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣽⣯⣿⣽⣻⣾⣽⣯⣿⣽⣻⣵⣾⣳⣟⣾
⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣤⣤⣀⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢰⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣆⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣆⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣧⠀⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣇⠹⣄⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣧⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣦⠙⢦⡀⠀⠀⠀⠀⣀⣹⣿⣿⣿⠟⠿⠿⣏⣷⡀⢳⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣷⣌⢳⣤⠴⠚⠋⠉⠀⣀⠤⡴⠒⠒⠒⠲⢤⣉⠉⠁⠈⠙⠳⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠐⣋⣴⣎⣥⣤⣀⠀⠀⠀⠈⠳⡄⠀⠀⢳⡄⠀⠉⠳⢶⡦⢤⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡿⠋⠀⠀⠀⠀⠀⢀⡀⢉⣀⠀⣸⡟⣯⣿⣦⠀⠀⠀⠉⡄⠀⠀⢹⠀⠀⠀⠀⠙⢦⠘⢧⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠁⠀⠀⠀⠀⠀⣴⠎⠀⠀⠈⢙⣛⣿⣾⣷⣾⣷⣄⣠⣼⣗⡲⠦⣍⠀⠙⠒⠦⢤⣈⠑⠦⣷⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⢀⣴⢻⡏⠀⠀⣠⣶⠿⠋⢀⣀⣀⣀⣀⡈⠻⡅⠈⠩⣷⣤⠀⠀⠀⠀⠀⠉⠛⢦⣈⢳⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⢸⣿⢸⡀⠀⠀⣠⣤⣶⣯⣭⠭⣭⣭⣉⡙⢧⡉⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠸⣿⡜⣧⠀⢾⣿⣿⣿⣿⣇⠀⢈⡯⠛⢿⡳⢷⣄⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⢷ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣀⣀⠀⠙⠛⢿⣆⠸⣿⣿⣿⣿⣿⣤⣿⡇⠀⢨⡟⠲⣍⡳⢤⣉⠒⠤⠤⣄⣀⣀⣀⣀⡤⣶⣋⣵⠟ ⠀⠀⠀⠀⠀⠀⠀⣠⠴⠲⠶⠞⠋⢹⣦⣀⠀⠀⠙⢾⣿⣿⠋⠉⣹⣿⣿⣷⣠⣿⡇⠀⣰⣿⠛⠻⣿⣷⣶⣶⢦⡤⠞⣿⠞⠋⠉⠀⠀ ⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⢀⣾⣿⣿⣷⣦⣀⠀⠀⢿⠳⢶⡟⠁⠸⣿⣿⢿⣿⣾⣿⣿⣠⣾⣿⡇⢀⣠⣾⠧⠞⠁⠀⠀⠀⠀⠀ ⠀⠀⢀⡴⠋⠀⠀⠀⣀⣤⣶⣿⣿⣿⠿⠟⢻⡟⢿⣄⡀⠈⢧⠀⢹⣦⣶⡟⠁⠸⣿⠟⢻⣿⣿⣿⣿⡿⣍⣿⡈⢦⡀⠀⠀⠀⠀⠀⠀ ⢀⣴⣋⣤⣤⡶⠾⠿⠟⠛⠋⠉⠁⠀⠀⠀⢸⣷⡀⣿⣿⡷⠾⢷⣄⠉⠻⣷⢤⣾⠃⠀⣸⡿⠀⠹⡈⢣⣸⡿⣿⣄⠳⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣿⣿⠃⠀⠀⠈⠳⣄⠈⠳⣌⠓⠶⣏⣳⣤⣴⣳⣾⢿⠁⢹⣿⣧⡙⣆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠐⠛⠋⠀⠀⠀⠀⠀⠀⠉⠒⠊⠛⠒⠀⠈⠉⠙⠛⠁⠀⠀⠛⠛⠛⠛⠚⠂⠀⠀⠀
⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⣀⣄⣰⣾⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⣀⡠ ⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⣠⣴⣦⣷⣿⣿⣿⣿⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢠⣾⣿⡇ ⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢠⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢰⣶⣿⣿⣿⠁ ⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⣀⣀⣀⣀⡀⢀⢀⢀⢀⢀⣀⣀⣀⢀⢀⢀⢀⢀⢀⢀⢀⢀⣀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⣀⣾⣿⣿⣿⣿⡇ ⢀⣀⢀⣶⣤⣴⣾⣿⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⣿⣷⣤⣶⣦⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⢀⣀⣀⡀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⡀⢀⢱⡆⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⣠⣾⣿⣿⣿⣿⣿⣷ ⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣤⣴⣾⣿⣿⣿⣷⣾⣧⣤⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣄⣀⣤⣤⣰⣿⣿⣿⣿⣿⣿⣿⣿⡍ ⢀⠹⣿⣿⣿⣿⣿⣿⣿⣥⣤⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⢀⢀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢀⢀⢀⢀⢀⠈⠉⠉⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠈⡽⠓⠊⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀ ⢀⢀⢀⢀⠈⠻⣟⠟⡻⡩⠝⢏⣉⣉⣿⣏⣻⣿⠭⠽⠟⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠛⠁⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢛⠭⠤⢀⠉⠉⠁⢀⢀⢀⢀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄ ⢀⢀⢀⢀⢀⢀⢴⠾⠾⠾⠋⠉⠁⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⠈⠁⢉⡉⠉⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠋⠁⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢸⣿⣿⡿⢿⣿⡿⠿⠋⠉⠉⢡⣤⣴⠏⠉⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣷⡀ ⢀⢀⢀⢀⢀⢀⠈⠳⢀⡀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⠈⢀⢀⢀⢀⠈⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⠾⠋⠉⢀⡀⢀⠤⠄⠒⠒⡍⢀⢀⢳⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⠉⠛⠿⠿⠿⠿⠿⠿⠿⠆ ⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⠁⠐⠒⢀⠤⠤⠤⠤⠤⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⣀⣀⡈⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡤⠤⠤⢀⣀⡀⢀⡠⢀⢀⢀⢀⢀⡜⠓⠒⠒⠛⠛⠓⠒⠉⠉⢀⢀⢀⢀⢀⢀⢀⠙⠆ ⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⠑⢄⢀⢀⢀⢀⢀⠉⠁⠙⠻⠛⠿⠿⠋⢻⡷⢀⢀⢀⡄⢀⢀⡇⢀⢀⢀⢀⢀⡇ ⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⠑⠂⠤⢀⣀⢀⣀⠜⠁⢀⢀⢀⢀⢀⢀⢀⢀⢀⡇⢀⢀⢡⢀⢀⢀⢀⢀⡇ ⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⠈⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢣⢀⢀⠈⢢⢀⢀⢀⢀⢠ ⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⠈⡆⢀⢀⢀⢇⢀⢀⢀⢸ ⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⣀⠤⠄⠤⠈⠉⠉⠙⠦⠔⠒⠂⢀⢀⢀⠸⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⢶⡒⣙⣍⣹⣍⣉⣟⠶⢶⣀⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣊⡹⢶⡊⠙⣅⠹⡄⢻⠀⡏⠉⡿⠦⣞⢦⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠾⣤⠋⠲⣄⠙⣄⠘⡄⢳⠸⠀⡇⢠⠇⣸⢋⡟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⣳⠿⣄⠙⠦⣈⠳⣌⡧⢽⣼⣴⣵⣧⣎⣴⣱⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣎⣟⠓⠢⢄⣙⡶⠞⣉⠔⠋⠁⠀⠀⠀⠀⠈⠉⠙⢦⡀⠀⠀⠀⠀⠀⠀ ⠀⣏⣹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣖⡷⠯⢈⣉⣲⠖⠉⢀⠖⠁⠀⠀⠀⠀⣠⡴⠦⣄⠀⠀⢠⡿⣶⡆⠀⠀⠀⠀ ⢸⣍⣧⡹⡱⣄⠀⠀⠀⠀⠀⠀⠀⠀⠤⣖⣿⠯⠭⣒⣶⣾⠋⠀⢠⠋⠀⠀⠀⠀⠀⠰⠁⠀⠀⠈⠀⠀⠈⢀⣘⣆⠀⠀⠀⠀ ⢸⣸⠷⣕⢎⡪⡑⠤⣀⠀⠀⠀⠀⠀⠀⠀⣈⡽⠛⢩⣿⠁⠀⢀⠏⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⣄⠀⠀⢰⠋⠀⠹⣧⠀⠀⠀ ⢘⣸⠓⢬⣓⢿⣿⣦⡈⠙⠒⠠⣤⡤⠒⡿⡟⠁⠀⢏⠃⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⣼⣠⣄⠈⡇⠀⠰⣿⣳⢠⠇⠳⡄⠀ ⡄⢸⠙⠒⠢⠽⣷⣿⣿⡆⢠⢾⠋⠀⡸⡼⠀⠀⢸⢸⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⢇⡏⠀⠀⣙⡿⠾⠤⢤⡘⢆ ⠋⢹⠉⠉⣛⣺⡭⣭⣿⠇⢸⡆⠀⠀⡇⡇⠀⠀⢸⢸⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢉⡠⠒⠉⠀⠀⠀⠀⠀⠘⠎ ⢩⠹⡍⢉⡥⢖⣿⡿⠃⠀⠘⣿⡀⠀⣇⣇⠀⠀⠘⣄⠶⡀⠀⠀⠙⢄⡀⠀⠀⠀⠀⠀⣀⠤⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⣧⢟⣩⢞⢝⡡⠔⠒⠒⠒⠺⢷⡄⠘⡽⡀⠀⠀⣟⣳⣻⣦⡀⠀⠀⠉⠀⠒⠒⠈⠉⠀⠀⡄⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⡎ ⠀⢱⡼⣷⡿⠋⠀⠀⠀⠀⠀⠀⠀⠉⣶⣙⣷⡀⢠⣇⡿⢮⣻⢿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠴⡿⣀⠀⢀⣠⠔⠁⠀⠀⣠⠎⠀ ⠀⠈⢣⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⣿⣾⣿⣿⣦⣏⣿⠒⠬⣽⣛⣷⣮⣍⠒⠒⢤⠀⠀⠀⣧⡴⠋⠁⠀⠀⣀⠴⠊⠁⠀⠀ ⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠒⠒⣿⣙⣉⣓⣒⣒⣲⣿⣿⢃⡠⠊⠀⠀⠓⠐⣀⣠⣤⣶⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠽⣔⣶⣾⣿⠯⠒⠛⠒⠒⠒⠛⠛⠛⠻⠯⢽⡏⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣷⣦⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

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