Kirby Dot Art. Emojis & Text

Copy & Paste Kirby Dot Art. Emojis & Symbols ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢔⣪⡵⠞⠛⠒⠉⠉⠉⠙⠭⣙⡛⢗⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢢⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⠧⣕⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣀⣤⠤⠤⣤⣾⡟⠀⠀⠀⣴⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠈⠳⣵⡧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢾⠋⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠛⠛⠃⠀⠀⠀⠀⠀⠈⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠛⠒⠤⡀⠀⠀⠀⠀⠀⠀⣤⡶⠶⡄⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠙⣿⣁⢠⠀⠀⠀⠀⠀⠀⢸⣧⣀⣤⣾⠀⠀⠀⠀⠀⠀⢸⣧⢀⣰⡇⠀⠀⠀⠀⠀⣽⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠙⠓⢲⡧⠀⠀⠀⠘⢏⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⢹⡋⠉⣿⠀⠀⠀⠀⠀⠀⠻⠶⣤⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣸⡀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⣾⠳⣦⡀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣗⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⢺⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡟⣀ ⠀⠀⠀⠀⠀⠀⠈⣟⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣤⡀⠀⠀⠀⠀⣀⣤⣳⠃ ⠀⠀⠀⠀⠀⠀⠀⠉⠙⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⢋⠞⠚⠻⠥⣤⡮⠷⠞⠁⠀ ⠀⠀⠀⠀⠀⣠⣶⢿⣻⣿⢿⡻⢖⠄⠴⢤⢀⢀⣀⣀⣀⣀⣀⣤⣴⡾⠿⣏⣿⣿⣗⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡼⠋⠑⠛⠿⠳⠋⠁⠀⠀⠁⢹⠏⠁⠁⠉⠉⠉⠉⢙⡇⠀⠀⠀⠀⠀⠙⠿⠟⢻⣇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢻⣄⡀⠀⠀⠀⠀⠀⠀⣀⠼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⢄⣀⠀⠀⠀⠀⠀⠀⠀⣸⠏⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠉⠛⠓⠒⠊⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠋⠫⠭⠟⠽⠛⠃⠀⠀⠀⠀⠀⠀

Related Text & Emojis

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

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