Dick Dot Art

Copy & Paste Dick Dot Art Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣤⣀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀ ⠀⠀⠀⠀⢀⣀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⢋⣭⡍⣿⣿⣿⣿⣿⣿⠀ ⠀⢀⣴⣶⣶⣝⢷⡝⢿⣿⣿⣿⠿⠛⠉⠀⠀⣰⣿⣿⢣⣿⣿⣿⣿⣿⣿⡇ ⢀⣾⣿⣿⣿⣿⣧⠻⡌⠿⠋⠁⠀⠀⠀⠀⢰⣿⣿⡏⣸⣿⣿⣿⣿⣿⣿⣿ ⣼⣿⣿⣿⣿⣿⣿⡇⠁⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⠇⢻⣿⣿⣿⣿⣿⣿⡟ ⠙⢹⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⡿⠟⠁ ⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣴⡾⠿⣿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣼⣿⣦⣤⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣣⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣩⣾⡿⢃⣼⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠻⣿⣿⣿⣿⠿⢟⣩⣴⣿⡿⢋⣴⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢴⣶⣾⣿⠿⢛⣡⣶⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠩⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣍⡛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⠂⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⠇⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⡿⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠻⠛⠛⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀
AI Anime Generator
⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⡿⠋⠁⠀⠀⠈⠉⠙⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣿⠇⠀⢀⣴⣶⡾⠿⠿⠿⢿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣀⣀⣸⡿⠀⠀⢸⣿⣇⠀⠀⠀⠀⠀⠀⠙⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣾⡟⠛⣿⡇⠀⠀⢸⣿⣿⣷⣤⣤⣤⣤⣶⣶⣿⠇⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀ ⢀⣿⠀⢀⣿⡇⠀⠀⠀⠻⢿⣿⣿⣿⣿⣿⠿⣿⡏⠀⠀⠀⠀⢴⣶⣶⣿⣿⣿⣆ ⢸⣿⠀⢸⣿⡇⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⣿⡇⣀⣠⣴⣾⣮⣝⠿⠿⠿⣻⡟ ⢸⣿⠀⠘⣿⡇⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠉⠀ ⠸⣿⠀⠀⣿⡇⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠀⠀⠀⠀ ⠀⠻⣷⣶⣿⣇⠀⠀⠀⢠⣼⣿⣿⣿⣿⣿⣿⣿⣛⣛⣻⠉⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⣀⣀⣀⣼⡿⢿⣿⣿⣿⣿⣿⡿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⠛⠛⠛⠋⠁⠀⠙⠻⠿⠟⠋⠑⠛⠋⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⢉⢉⠉⠉⠻⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⠟⠠⡰⣕⣗⣷⣧⣀⣅⠘⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⠃⣠⣳⣟⣿⣿⣷⣿⡿⣜⠄⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⡿⠁⠄⣳⢷⣿⣿⣿⣿⡿⣝⠖⠄⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⠃⠄⢢⡹⣿⢷⣯⢿⢷⡫⣗⠍⢰⣿⣿⣿⣿⣿ ⣿⣿⣿⡏⢀⢄⠤⣁⠋⠿⣗⣟⡯⡏⢎⠁⢸⣿⣿⣿⣿⣿ ⣿⣿⣿⠄⢔⢕⣯⣿⣿⡲⡤⡄⡤⠄⡀⢠⣿⣿⣿⣿⣿⣿ ⣿⣿⠇⠠⡳⣯⣿⣿⣾⢵⣫⢎⢎⠆⢀⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⠄⢨⣫⣿⣿⡿⣿⣻⢎⡗⡕⡅⢸⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⠄⢜⢾⣾⣿⣿⣟⣗⢯⡪⡳⡀⢸⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⠄⢸⢽⣿⣷⣿⣻⡮⡧⡳⡱⡁⢸⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⡄⢨⣻⣽⣿⣟⣿⣞⣗⡽⡸⡐⢸⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⡇⢀⢗⣿⣿⣿⣿⡿⣞⡵⡣⣊⢸⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⡀⡣⣗⣿⣿⣿⣿⣯⡯⡺⣼⠎⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣧⠐⡵⣻⣟⣯⣿⣷⣟⣝⢞⡿⢹⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⡆⢘⡺⣽⢿⣻⣿⣗⡷⣹⢩⢃⢿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣷⠄⠪⣯⣟⣿⢯⣿⣻⣜⢎⢆⠜⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⡆⠄⢣⣻⣽⣿⣿⣟⣾⡮⡺⡸⠸⣿⣿⣿⣿ ⣿⣿⡿⠛⠉⠁⠄⢕⡳⣽⡾⣿⢽⣯⡿⣮⢚⣅⠹⣿⣿⣿ ⡿⠋⠄⠄⠄⠄⢀⠒⠝⣞⢿⡿⣿⣽⢿⡽⣧⣳⡅⠌⠻⣿ ⠁⠄⠄⠄⠄⠄⠐⡐⠱⡱⣻⡻⣝⣮⣟⣿⣻⣟⣻⡺⣊
pls note the ai inflicts emotional damage (ᵕ—ᴗ—)
AI Story Generator
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YALL STFU LET ME LOOK AT PORN ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣶⣦⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⡿⠟⠛⠉⠉⠉⠉⠙⠛⠿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⡟⠁⠀⢀⣄⣤⣶⠲⠟⠛⢻⣿⣿⣖⣦⣄⡀⠙⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡟⠀⣠⣾⣿⣿⢫⢹⣷⡏⢻⠚⡟⣯⢻⡋⠻⡽⢦⡈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠁⢠⣿⣿⣿⣿⣧⣾⣽⣷⠌⠃⣿⣿⣴⣧⢰⣷⢉⣷⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡏⢠⣿⣿⣿⣿⣿⣿⢿⣿⣿⣶⢐⠊⣹⢻⣿⣿⣿⢠⡿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⣿⣿⣧⣼⣿⣿⣿⣿⣿⠏⣼⢇⣿⣿⠈⢭⣿⣯⡿⣿⣿⣿⣧⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣿⣿⣿⣿⣟⣱⣶⣿⣽⠁⣿⣷⣿⣧⣿⣽⡟⣺⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⢿⡿⠻⣯⣻⣿⣿⠲⣽⠟⢁⡿⠫⢾⣿⣿⣻⡿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢸⣿⣿⣇⢿⣯⠁⠀⠈⠉⠀⠠⠚⣁⠴⠛⢆⠀⠀⠉⠉⠁⢸⣿⣿⡇⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡄⢸⣿⣿⣿⣯⡳⡀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢈⡆⠀⠀⠀⠀⣸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⠀⢠⡿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣧⣿⣿⣄⠀⠀⠀⠢⢄⣀⣀⡤⠆⠀⠀⣠⣿⣷⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣌⢳⣄⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⠈⠛⠻⠷⠦⣄⣀⣠⠴⠟⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⡿⢦⣀⠀⠀⠀⠀⠈⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠈⠉⠑⠒⠒⢒⡶⢊⠉⢻⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠼⠛⠉⠉⠉⠉⠉⠙⠛⠯⣍⣁⣀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠈⠀⠀⠉⠛⢻⣿⠿⠿⠿⠿⠷⠤⢄⣀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⢖⠲⣬⠭⣍⠉⠍⢐⣒⠦⣏⣀⡠⠔⣂⡒⠒⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢄⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣷⣶⣶⣶⣶⣤⣤⣤⡖⢉⡤⠚⢉⣠⠽⣗⠺⢧⡀⠀⠈⠁⠀⠁⢀⣨⠤⠤⠤⠤⢤⣠⣔⣪⣭⡿⠉⠹⣒⠦⣄⣀⣀⣻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⢉⣠⠞⠉⢀⠀⢻⣭⣓⢽⣲⣶⣶⣒⢋⣉⣀⣠⣤⠤⣤⣤⣭⣽⣶⢿⣧⣀⠀⠀⠀⠂⠉⠳⣆⠿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣉⣀⣠⣤⣶⣖⣛⣓⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⡛⢻⠷⠶⢿⣿⣿⣶⣭⣛⠻⠶⢦⣄⣀⣤⡟⢦⡈⣇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠯⠿⠟⠛⠛⠒⠲⠾⠷⠯⠭⢭⣿⣿⣿⣽⣿⣓⣲⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⢳⣽⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣏⡍⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠉⠉⠛⠻⢿⣷⣄⠹⣇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣷⣿⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀⢀⠴⠚⠉⠉⠁⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡗⠀⠀⠀⠀⣰⠋⣀⢤⡶⣄⠈⠁⠀⠲⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠲⡒⠒⠽⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⢰⠃⢰⠣⠾⠁⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⠀⣴⢺⢣⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣇⠀⠀⠀⠀⢸⠀⠈⠣⠼⠟⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢛⠚⠦⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡟⠀⠀⠀⠀⠈⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⢿⡿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠃⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⠟⠁⣸⠁⠈⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣦⣦⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡶⠿⠋⠁⠀⠀⣏⠀⠀⠀⠈⠻⢷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢿⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣤⣤⣤⣤⣶⠾⠟⠋⠁⠀⣠⠔⠀⠀⠠⠏⠀⠀⠀⠀⠀⠀⠉⠻⠿⣦⣄⣀⣀⠀⠀⠀⠀⢀⣀⣤⡶⠋⠀⣾⠀⠀⢠ ⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢹⣿⣿⣿⢁⣿⢿⠁⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠟⢉⣿⣿⠋⠩⡉⢩⡽⠋⠀⠀⣰⠃⠀⠀⣼ ⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⡿⢃⣿⣿⣿⡿⠋⠀⠘⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⢸⣿⣿⣾⣿⡷⡜⣧⡀⠀⣰⠃⠀⠀⢠⣿ ⣆⣐⣒⣒⣒⣒⣶⣒⣾⣿⣿⣿⣿⣿⣿⢟⣵⣿⣿⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⡿⠿⣾⡵⠞⠓⠒⠒⠒⣺⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⡤⣼⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⡀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⠀⠀⠀⠀⠀⠀⠀⡀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠞⠁⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⠄⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⡿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⣟⠻⢦⡀⠀⠀⠀⢀⣠⡔⠊⠉⠉⠉⢿⢷⣦⣄⠀⠀⠀⠀⢠⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡏⢩⣿⣿ ⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀⢻⣦⣀⣴⣏⠁⠇⠀⠀⠀⠀⠈⢿⣣⠻⣧⣄⠀⣠⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣽⣿⣿ ⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⢹⣿⡟⣿⢄⠀⠀⠀⠀⠀⠘⡀⢧⢇⠀⠻⣿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿ ⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⣸⣿⠰⡻⡜⡄⠀⢰⠀⠀⠀⠀⢸⢸⠀⢰⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡱⣰⢧⣿⠘⡇⢹⡅⠀⠀⠀⠀⠀⠀⢸⢸⣦⡺⣎⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣳⡟⠉⣿⡇⠈⠀⣇⠀⠀⠀⠀⠀⠀⠘⡞⠈⢷⠸⣏⠳⣄⠀⠀⠀⠀⠀⠀⣀⣠⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣤⣤⣤⡬⠕⠒⠊⠉⠀⠀⠘⣿⢸⠇⡇⡆⠀⢀⠀⠀⠀⠀⠱⡄⠀⢣⠹⡆⠚⠋⠒⠒⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢻⡟⡄⡇⡇⠀⠈⢆⠀⠀⠀⠀⠘⢦⢦⠱⣜⣆⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⣇⢣⠉⠀⠘⢆⠀⠀⠀⠀⠀⠳⡷⡈⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⡄⣿⡜⣄⠀⠀⠈⠳⠀⠀⠀⠀⠀⠱⡳⡀⠘⣷⡀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⢧⣿⡿⡜⢆⠀⠀⠀⠣⡀⠀⠀⠀⠁⠙⢮⣦⡈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⢧⠙⢎⢦⠀⢀⠀⠱⡄⠀⠀⠀⠀⠀⠙⢟⣆⠈⡝⢦⡀⠀⠀⠀⠀⠀⣿⣿⠿⠿⡿⡿ ⣿⣿⣿⣿⣿⣿⣿⣉⡉⡏⠉⠉⠩⠍⠉⣽⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢿⡄⢸⡿⣃⠈⢣⡳⡈⣂⠀⠘⢆⠀⠀⠀⠀⢀⠘⣞⡆⢙⡂⠱⣄⠀⠀⢀⣼⣿⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⣀⡀⠐⢂⣀⣀⠉⢛⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⣼⠁⠈⠙⡄⢳⢱⠈⠑⢦⠈⢆⠀⠀⠀⠀⠣⢹⣿⡲⢄⠈⣹⣄⣀⣼⡿⡀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣷⣶⣶⣿⣿⣿⣿⣿⣷⣶⣄⣀⣀⣀⣠⣄⣀⣹⡼⣷⡀⠀⠀⠈⡏⡆⠀⠈⢣⠀⠀⠀⠄⠂⣀⣄⣿⣽⣷⣾⣍⣛⣿⡭⠀⠠⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣇⠀⠀⠀⢻⡽⠀⠀⠀⢳⡴⢋⣴⣾⠿⠛⢉⠉⠉⠉⠉⠙⠛⣿⡒⠁⠀⠀⠀⢀⣸ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠄⠀⠀⠀⠳⣷⣤⢀⢞⣥⣿⡟⠁⠀⠀⠀⣀⠤⠤⠀⠀⠲⠤⣽⣶⣳⣖⣶⠿⠋ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⠀⠀⠀⠀⠙⢿⣮⣾⣿⠃⠀⠀⣤⡾⠛⠁⠀⠀⠀⠀⠀⠀⠈⠉⠿⣿⠋⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⣅⢢⢹⣻⡇⠀⢠⣞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠐⣟⢻⣸⢻⠁⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠤⡀⠄⠀⣈⡇⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⣜⡆⡉⣿⡆⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠄⠀⠁⠀⠀⠙⡿⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⢷⡈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡆⠀⠀⠀⠀⣰⣷⣀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⡀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠁⠀⠀⢀⣴⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣄⣀⣀⣴⣿⣿⣶⣶⣾⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠿⠿⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣾⣿⣶⣶⣤⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠘⢿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀ ⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠈⠻⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⣀⣤⣶⣶⣌⠻⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀ ⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⠁⣰⣿⣿⣿⣿⣿⣦⡙⢿⣿⣿⣿⠄⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣦⣙⣛⣋⣼⣿⣿⣶⣿⣿⣿⣿⣿⣿⣯⡉⠉⠉⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⡆⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⢻⣿⣿⣿⣿⣿⡇⠀⠀⠈⠉⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⣠⣴⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⡇⠀⠸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠹⢿⣿⣿⢿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢰⣶⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣧⣄⣀⣀⣀⣀⣀⣀⡀ ⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠁⠛⠛⠛⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁
⠀⠀⠀⣴⣾⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⢿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⣉⣩⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣼⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣼⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣾⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⣾⣿⣿⠉⣿⣿⣿⣿⣿⡄⠀⢀⣠⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠙⣿⣿⣧⣿⣿⣿⣿⣿⡇⢠⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣷⠸⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⠿⢿⣿⣿⣿⣿⡄⠙⠻⠿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡟⣩⣝⢿⠀⠀⣠⣶⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣷⡝⣿⣦⣠⣾⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⣮⢻⣿⠟⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠻⠿⠻⣿⣿⣿⣿⣦⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⠇⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⡆⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⠇⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠀⠀⠀⢀⣴⣿⣿⣿⣿⣟⣋⣁⣀⣀⠀ ⠀⠀⠀⠀⠀⠀⠹⣿⣿⠇⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⢠⣞⣻⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢻⣿⣿⣿⣿⣿⣟⣵⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠳⢿⣻⣵⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣤⣤⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣶⢹⣿⣿⣿⣿⣿⣷⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⡏⣿⣿⣿⣿⣿⣿⣿⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⢰⣿⣿⣿⣿⣿⣿⣿⣷ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⠿⠸⣿⣿⣿⣿⣿⣿⣿⡏ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⡿⠟⠀
YALL STFU LET ME LOOK AT PORN ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣶⣦⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⡿⠟⠛⠉⠉⠉⠉⠙⠛⠿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⡟⠁⠀⢀⣄⣤⣶⠲⠟⠛⢻⣿⣿⣖⣦⣄⡀⠙⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡟⠀⣠⣾⣿⣿⢫⢹⣷⡏⢻⠚⡟⣯⢻⡋⠻⡽⢦⡈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠁⢠⣿⣿⣿⣿⣧⣾⣽⣷⠌⠃⣿⣿⣴⣧⢰⣷⢉⣷⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡏⢠⣿⣿⣿⣿⣿⣿⢿⣿⣿⣶⢐⠊⣹⢻⣿⣿⣿⢠⡿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⣿⣿⣧⣼⣿⣿⣿⣿⣿⠏⣼⢇⣿⣿⠈⢭⣿⣯⡿⣿⣿⣿⣧⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣿⣿⣿⣿⣟⣱⣶⣿⣽⠁⣿⣷⣿⣧⣿⣽⡟⣺⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⢿⡿⠻⣯⣻⣿⣿⠲⣽⠟⢁⡿⠫⢾⣿⣿⣻⡿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢸⣿⣿⣇⢿⣯⠁⠀⠈⠉⠀⠠⠚⣁⠴⠛⢆⠀⠀⠉⠉⠁⢸⣿⣿⡇⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡄⢸⣿⣿⣿⣯⡳⡀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢈⡆⠀⠀⠀⠀⣸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⠀⢠⡿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣧⣿⣿⣄⠀⠀⠀⠢⢄⣀⣀⡤⠆⠀⠀⣠⣿⣷⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣌⢳⣄⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⠈⠛⠻⠷⠦⣄⣀⣠⠴⠟⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⡿⢦⣀⠀⠀⠀⠀⠈⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠈⠉⠑⠒⠒⢒⡶⢊⠉⢻⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠼⠛⠉⠉⠉⠉⠉⠙⠛⠯⣍⣁⣀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠈⠀⠀⠉⠛⢻⣿⠿⠿⠿⠿⠷⠤⢄⣀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⢖⠲⣬⠭⣍⠉⠍⢐⣒⠦⣏⣀⡠⠔⣂⡒⠒⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢄⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣷⣶⣶⣶⣶⣤⣤⣤⡖⢉⡤⠚⢉⣠⠽⣗⠺⢧⡀⠀⠈⠁⠀⠁⢀⣨⠤⠤⠤⠤⢤⣠⣔⣪⣭⡿⠉⠹⣒⠦⣄⣀⣀⣻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⢉⣠⠞⠉⢀⠀⢻⣭⣓⢽⣲⣶⣶⣒⢋⣉⣀⣠⣤⠤⣤⣤⣭⣽⣶⢿⣧⣀⠀⠀⠀⠂⠉⠳⣆⠿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣉⣀⣠⣤⣶⣖⣛⣓⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⡛⢻⠷⠶⢿⣿⣿⣶⣭⣛⠻⠶⢦⣄⣀⣤⡟⢦⡈⣇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠯⠿⠟⠛⠛⠒⠲⠾⠷⠯⠭⢭⣿⣿⣿⣽⣿⣓⣲⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⢳⣽⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣏⡍⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠉⠉⠛⠻⢿⣷⣄⠹⣇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣷⣿⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀⢀⠴⠚⠉⠉⠁⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡗⠀⠀⠀⠀⣰⠋⣀⢤⡶⣄⠈⠁⠀⠲⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠲⡒⠒⠽⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⢰⠃⢰⠣⠾⠁⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⠀⣴⢺⢣⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣇⠀⠀⠀⠀⢸⠀⠈⠣⠼⠟⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢛⠚⠦⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡟⠀⠀⠀⠀⠈⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⢿⡿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠃⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⠟⠁⣸⠁⠈⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣦⣦⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡶⠿⠋⠁⠀⠀⣏⠀⠀⠀⠈⠻⢷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢿⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣤⣤⣤⣤⣶⠾⠟⠋⠁⠀⣠⠔⠀⠀⠠⠏⠀⠀⠀⠀⠀⠀⠉⠻⠿⣦⣄⣀⣀⠀⠀⠀⠀⢀⣀⣤⡶⠋⠀⣾⠀⠀⢠ ⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢹⣿⣿⣿⢁⣿⢿⠁⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠟⢉⣿⣿⠋⠩⡉⢩⡽⠋⠀⠀⣰⠃⠀⠀⣼ ⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⡿⢃⣿⣿⣿⡿⠋⠀⠘⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⢸⣿⣿⣾⣿⡷⡜⣧⡀⠀⣰⠃⠀⠀⢠⣿ ⣆⣐⣒⣒⣒⣒⣶⣒⣾⣿⣿⣿⣿⣿⣿⢟⣵⣿⣿⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⡿⠿⣾⡵⠞⠓⠒⠒⠒⣺⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⡤⣼⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⡀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⠀⠀⠀⠀⠀⠀⠀⡀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠞⠁⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⠄⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⡿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⣟⠻⢦⡀⠀⠀⠀⢀⣠⡔⠊⠉⠉⠉⢿⢷⣦⣄⠀⠀⠀⠀⢠⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡏⢩⣿⣿ ⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀⢻⣦⣀⣴⣏⠁⠇⠀⠀⠀⠀⠈⢿⣣⠻⣧⣄⠀⣠⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣽⣿⣿ ⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⢹⣿⡟⣿⢄⠀⠀⠀⠀⠀⠘⡀⢧⢇⠀⠻⣿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿ ⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⣸⣿⠰⡻⡜⡄⠀⢰⠀⠀⠀⠀⢸⢸⠀⢰⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡱⣰⢧⣿⠘⡇⢹⡅⠀⠀⠀⠀⠀⠀⢸⢸⣦⡺⣎⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣳⡟⠉⣿⡇⠈⠀⣇⠀⠀⠀⠀⠀⠀⠘⡞⠈⢷⠸⣏⠳⣄⠀⠀⠀⠀⠀⠀⣀⣠⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣤⣤⣤⡬⠕⠒⠊⠉⠀⠀⠘⣿⢸⠇⡇⡆⠀⢀⠀⠀⠀⠀⠱⡄⠀⢣⠹⡆⠚⠋⠒⠒⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢻⡟⡄⡇⡇⠀⠈⢆⠀⠀⠀⠀⠘⢦⢦⠱⣜⣆⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⣇⢣⠉⠀⠘⢆⠀⠀⠀⠀⠀⠳⡷⡈⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⡄⣿⡜⣄⠀⠀⠈⠳⠀⠀⠀⠀⠀⠱⡳⡀⠘⣷⡀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⢧⣿⡿⡜⢆⠀⠀⠀⠣⡀⠀⠀⠀⠁⠙⢮⣦⡈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⢧⠙⢎⢦⠀⢀⠀⠱⡄⠀⠀⠀⠀⠀⠙⢟⣆⠈⡝⢦⡀⠀⠀⠀⠀⠀⣿⣿⠿⠿⡿⡿ ⣿⣿⣿⣿⣿⣿⣿⣉⡉⡏⠉⠉⠩⠍⠉⣽⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢿⡄⢸⡿⣃⠈⢣⡳⡈⣂⠀⠘⢆⠀⠀⠀⠀⢀⠘⣞⡆⢙⡂⠱⣄⠀⠀⢀⣼⣿⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⣀⡀⠐⢂⣀⣀⠉⢛⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⣼⠁⠈⠙⡄⢳⢱⠈⠑⢦⠈⢆⠀⠀⠀⠀⠣⢹⣿⡲⢄⠈⣹⣄⣀⣼⡿⡀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣷⣶⣶⣿⣿⣿⣿⣿⣷⣶⣄⣀⣀⣀⣠⣄⣀⣹⡼⣷⡀⠀⠀⠈⡏⡆⠀⠈⢣⠀⠀⠀⠄⠂⣀⣄⣿⣽⣷⣾⣍⣛⣿⡭⠀⠠⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣇⠀⠀⠀⢻⡽⠀⠀⠀⢳⡴⢋⣴⣾⠿⠛⢉⠉⠉⠉⠉⠙⠛⣿⡒⠁⠀⠀⠀⢀⣸ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠄⠀⠀⠀⠳⣷⣤⢀⢞⣥⣿⡟⠁⠀⠀⠀⣀⠤⠤⠀⠀⠲⠤⣽⣶⣳⣖⣶⠿⠋ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⠀⠀⠀⠀⠙⢿⣮⣾⣿⠃⠀⠀⣤⡾⠛⠁⠀⠀⠀⠀⠀⠀⠈⠉⠿⣿⠋⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⣅⢢⢹⣻⡇⠀⢠⣞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠐⣟⢻⣸⢻⠁⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠤⡀⠄⠀⣈⡇⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⣜⡆⡉⣿⡆⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠄⠀⠁⠀⠀⠙⡿⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⢷⡈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡆⠀⠀⠀⠀⣰⣷⣀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⡀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠁⠀⠀⢀⣴⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣄⣀⣀⣴⣿⣿⣶⣶⣾⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿🗣⊂=====3
⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⡿⠋⠁⠀⠀⠈⠉⠙⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣿⠇⠀⢀⣴⣶⡾⠿⠿⠿⢿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣀⣀⣸⡿⠀⠀⢸⣿⣇⠀⠀⠀⠀⠀⠀⠙⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣾⡟⠛⣿⡇⠀⠀⢸⣿⣿⣷⣤⣤⣤⣤⣶⣶⣿⠇⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀ ⢀⣿⠀⢀⣿⡇⠀⠀⠀⠻⢿⣿⣿⣿⣿⣿⠿⣿⡏⠀⠀⠀⠀⢴⣶⣶⣿⣿⣿⣆ ⢸⣿⠀⢸⣿⡇⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⣿⡇⣀⣠⣴⣾⣮⣝⠿⠿⠿⣻⡟ ⢸⣿⠀⠘⣿⡇⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠉⠀ ⠸⣿⠀⠀⣿⡇⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠀⠀⠀⠀ ⠀⠻⣷⣶⣿⣇⠀⠀⠀⢠⣼⣿⣿⣿⣿⣿⣿⣿⣛⣛⣻⠉⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⣀⣀⣀⣼⡿⢿⣿⣿⣿⣿⣿⡿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⠛⠛⠛⠋⠁⠀⠙⠻⠿⠟⠋⠑⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣟⡿⣝⣻⠉⠉⠛⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣇⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⢻⣮⢷⣻⣯⡟⣷⢦⡀⠀⠙⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⣤⣾⣿⣿⣶⣄⡀⠀⠀⠀⣰⣿⣛⣾⢻⣼⣳⣿⣳⣻⣭⡟⣿⡄⠀⣹⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡿⠋⢢⠁⠀⠀⣼⣟⡾⣝⡾⣻⡼⣿⣳⡽⣳⢾⡽⣳⡟⣿⣻⡿⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡤⠤⣄⠀⠀⠸⣇⣠⣿⣦⣀⡀⣿⣞⣽⣫⢷⢯⡽⣿⣳⡟⣽⣳⣻⢳⣟⣳⢷⣻⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣏⠀⠀⢹⠀⠀⠀⠉⠙⣿⠋⠁⠀⠙⢾⣧⣟⢯⣯⣟⣽⣷⣻⣳⡽⣳⣟⢾⡽⡾⣽⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⡄⠀⢸⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⢠⣿⣿⣿⡿⣿⢿⣿⣧⡟⣧⢿⡼⣟⣼⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣴⠿⡿⠟⠛⢦⣌⣧⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣟⡾⣷⣟⣯⣿⣞⡿⣿⣯⣷⣿⣽⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣿⠦⣄⣀⡠⣼⠃⣸⡇⠀⠀⠀⠀⠀⠀⠀⣾⣿⣾⣿⣷⣯⣿⣾⣽⣿⣳⡿⣽⣾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⢧⣄⣀⣀⣀⡼⠁⢿⡆⠀⠀⠀⠀⠀⠀⣸⣿⡿⠛⣻⣿⣽⡻⠿⣿⣿⢯⣟⣷⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠸⣧⣈⣉⣀⡝⢂⡼⣧⡀⠀⠀⠀⠀⢠⣿⡟⡠⢲⣿⣿⡟⠀⣴⣿⣿⣿⣟⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠛⠓⠶⣯⣴⣿⣿⣶⣤⣄⡀⢸⣿⡇⠈⣬⣿⣿⡁⠀⣹⣿⣿⣿⣯⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣷⡀⠹⣿⣿⣇⠀⢿⣿⣿⣿⢷⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⣿⣷⣻⢿⣶⣿⡿⣿⣷⣾⣿⣿⢯⣿⣿⡿⠿⠿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣯⢿⣿⣷⣯⣟⣷⣯⣿⣿⣿⣯⣿⡇⠀⠀⠀⣾⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣯⡿⣽⣿⣿⣿⣿⣿⣿⣿⣳⣯⣿⡇⠀⢀⣼⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣽⣻⣿⠿⢿⠟⠛⣿⣟⣷⢯⣿⣧⣴⣿⣿⣿⠿⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣞⡿⣿⡀⠛⢀⣼⣿⣟⣾⣿⢻⣿⣿⣿⣿⣹⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣯⣟⡿⣿⣿⡿⣿⣻⣾⡏⣼⣦⠍⠛⠛⢺⣀⣸⣆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣞⣿⣳⣯⢿⣷⣻⣽⣷⡀⠻⠀⠀⣀⡼⠁⠀⢈⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⠀⠀⢀⣼⣿⣻⣾⡽⣯⣿⢾⣽⣳⡿⣿⣦⣄⡀⠉⠀⣀⡤⠞⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣷⣾⡿⣟⣿⣿⡾⣽⡷⣯⣿⡽⣷⢿⣷⣻⣟⣿⡿⣿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣿⣽⢻⣯⣿⣽⡟⣯⣿⣷⣯⣿⣽⣿⣿⢳⣿⣾⣽⣿⡅⠉⠛⣿⣶⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡀⠀⢠⣾⣿⣻⢷⣻⣾⡽⣿⣞⣯⡿⣽⣿⣞⣷⣯⢿⣽⣻⢯⣿⣳⣯⣟⣷⣷⣦⣄⡈⠙⢿⣦⠀⠀⠀ ⠀⠀⠀⠀⠀⠉⢩⣿⣿⣳⣿⣻⣽⢾⣻⢷⣯⣷⢿⣻⣟⣿⣿⣾⣿⣳⣿⣻⢷⣯⡷⣿⣾⢷⣯⣟⣿⣦⣼⣿⣇⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⣳⡿⣾⣿⣽⣟⣯⣿⢾⣽⣻⢿⣻⣿⣷⣿⣷⣿⣞⣯⣿⣞⡿⣿⣟⡿⣾⣽⢾⣯⣟⣿⣿⠚⠃ ⠀⠀⠀⠀⠀⠀⠸⣿⣷⣻⡷⣿⣟⣾⣽⢾⣻⣽⢯⣿⣻⢾⣿⣟⣾⢷⣻⣽⡾⣽⣻⢷⣯⢿⡷⣯⣿⣾⣽⣾⣿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⣷⣿⣽⣷⡿⣽⡾⣿⣿⡿⣟⣷⢿⣯⣟⡿⣯⣿⢯⣷⣿⣿⣿⡿⣽⣯⢿⣽⣿⣿⣞⣿⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢾⣿⣽⣯⢿⣽⡷⣟⣿⣽⠿⠟⠉⠀⠈⠛⠿⣷⣻⣞⣷⢿⣻⣾⣟⣷⣯⡷⠟⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢿⣻⣟⣿⣻⣟⡿⣟⡿⣿⢿⣿⣿⣆⠳⢌⡚⣧⡙⡜⢢⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣟⣯⣷⣻⣞⡷⣯⢿⣽⣻⡽⣯⣿⣿⣿⡘⢦⡑⣻⡜⡌⢧⡘⠠⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠂⠀⠀⠀⠠⠀⠄⠂⠀⠐⠀⠀⠆ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣻⣞⣷⣻⣞⡿⣽⣻⢾⣽⣻⢷⣿⣿⣿⣿⢄⣳⠰⣿⡘⢦⢁⡇⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣳⣟⣾⣳⣟⣾⣻⡽⣯⣟⣾⣽⣻⢾⣿⣿⣿⣧⣫⠱⡜⣯⡌⢇⣾⠐⠀⠠⠀⠀⠄⠀⠀⠀⠀⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⢷⣻⣞⡷⣟⣾⣳⣯⣟⡷⣯⢷⣯⣟⣿⣿⣿⣿⣿⣷⡧⡘⢭⢷⣊⢼⢧⡈⠀⠀⠀⠀⠀⠈⠀⠀⢳⡀⠀⠀⠠⠀⠀⠁⠀⠈⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡿⣯⢷⣻⣽⢯⡷⣟⣾⣽⣻⣽⣻⢾⣽⣿⣿⣟⡾⣿⣿⣿⣯⣢⢍⡳⢮⣴⢻⡆⠐⠂⠈⠀⠂⠀⠈⢸⣷⢠⠀⠀⠀⠠⠀⠀⠠⠀⠀⠂ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣽⣻⣽⢾⣻⣽⢯⣷⢯⣷⢯⣟⣯⣿⣿⣟⣾⣻⣿⣿⡿⠟⠙⢶⢡⢻⡧⢹⡇⠀⠀⠀⠠⠀⠐⠀⠀⢿⣷⣣⡀⠀⠀⠀⠐⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡿⣾⡽⣾⣻⣽⢾⣻⣽⣻⣞⡿⣾⣿⣿⡿⣽⣞⣿⣿⡟⠀⠀⠀⠘⣇⢻⣇⢛⠠⠀⠀⠁⠀⢀⠈⠀⠀⠀⢹⣧⡕⢦⢲⡁⠀⠀⠌⠀⠀ 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⠉⠀⠀⠀⡜⠁⠀⠀⢀⣵⡟⠛⠛⠫⡑⢊⡁⠒⠀⠀⠈⠈⠀⠀⢀⣚⠷⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⢺⣲⣿⠿⣿⣽⣻⣿⣿⣿⠿⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣏⠦⡹⢷⣾⣿⣿⣿⣿⣇⡇⡀⠀⠀⢹⣻⢈⢷⡀⠀⠐⢄⠡⠆⡑⠠⠀⠀ ⠀⠀⢺⡅⠀⠀⠀⢀⣿⣋⠤⠀⠀⠳⠞⠀⠀⠀⠁⠀⠀⣀⣠⣶⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠅⠛⠉⠙⣿⣿⣿⠄⠈⢿⣾⢂⣽⡿⢟⢋⣁⣀⣀⠰⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡏⣜⣳⣷⣿⣿⣿⣿⣿⣿⣼⣿⣏⠀⠢⠘⣷⡌⡚⠿⣆⡈⠆⣊⠀⠈⠀⠀⠀ ⠒⠠⡏⠀⢄⠀⢠⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⡉⢭⠖⠁⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⢀⡠⠴⢊⣽⣧⣿⡀⠀⠀⠈⠉⠉⠉⠁⠀⠀⢀⠔⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣬⠠⣁⢻⣥⡙⢦⢩⡇⠸⣀⠀⠄⠀⠀⠀ ⠞⠲⠛⢲⣤⣠⡟⠁⠀⠀⠀⠀⠀⠀⣠⠶⠴⢚⡩⢐⠡⣊⡿⠝⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⣏⣠⡴⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⢀⣤⢸⠃⠀⠀⠀⠀⠀⠀⣀⢀⣀⣤⠤⠤⣄⣠⠤⢤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⢏⠴⣩⣹⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⢹⡆⣼⣿⡉⢖⠣⡍⠱⢀⠠⠀⠀⠀⠀ ⣀⠀⠂⠉⠀⠁⠀⠀⠀⠀⠀⡀⣠⠖⡨⣣⢭⡦⠤⢧⣕⡩⣀⣀⡄⠀⠀⠔⠆⠀⠀⠀⣠⠞⡵⠋⢁⣾⣿⡿⡏⠿⠀⢠⠄⠀⠀⠀⠀⠀⠀⠀⢀⡎⠁⠘⠦⣀⡤⣀⠀⢠⠊⠀⠈⡧⡐⣬⢵⣀⢚⡶⢹⡟⢠⢈⡙⣒⡲⠤⠤⠤⠤⠴⠒⡒⠒⣈⢋⠛⡛⠶⣽⣹⣾⣿⢟⣋⣿⣿⣿⣿⣿⢻⣿⣷⣹⣾⡿⡘⢬⠓⡌⢁⠂⠀⠀⠀⠀⠀ ⣀⠤⡄⠀⠀⠀⠀⢀⡤⣲⠟⡩⢁⡴⣋⣁⠀⠀⠀⠐⢋⣥⣻⠋⣠⣠⠆⢲⠇⠀⠀⣴⣳⠞⠁⠀⣾⡿⠃⢈⡡⣾⣾⢋⣀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢀⣶⡟⣆⠸⡀⠀⡴⢹⠐⣛⣺⣤⣟⣴⡿⡼⡐⠢⢔⡙⠻⠭⢿⣚⡳⢸⠦⢵⡌⡀⠆⡡⠘⠖⡛⡋⢭⡙⢮⣼⣿⠞⣿⢏⣽⣿⣿⢟⢷⢋⡱⡘⢆⡳⠨⡄⠂⠀⠀⠀⠀⠀ ⣄⡂⡔⠀⠀⠀⡴⣫⠚⡄⡮⡴⠿⢭⣒⡉⠝⢈⣴⢞⡩⡐⠿⢻⡧⣆⠀⠀⠀⠀⣼⠗⠁⠀⢀⣼⣟⠠⠒⠉⠚⠡⠑⠊⣁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣡⡹⡏⠀⢡⢸⣿⣿⣻⣟⣽⡾⣿⣷⣾⣷⣟⡿⣶⣭⢣⡝⢢⢒⡐⠩⢉⠋⣄⡐⠡⣂⢉⠒⡰⠁⠆⣉⠦⢼⡏⢻⠏⢢⢍⢣⠻⣾⢻⡆⡱⣉⠦⡱⢱⠐⠀⠀⠀⠀⠀⠀ ⡻⣷⠀⠀⢀⣮⠏⡤⢃⡼⠋⡵⠋⠁⠀⠀⠀⣸⠡⢆⡱⢨⢐⣿⢱⡽⡄⠀⠀⢸⡏⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⣀⠔⠉⣀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡗⣇⠀⠎⢈⣻⣿⣿⣻⣽⣿⣿⣿⣿⣟⣾⡝⣧⣎⠱⡈⢇⢊⣄⣓⣈⡒⣌⣹⠷⣈⣍⣛⣖⣶⠶⠤⣎⣘⣉⠆⡘⢄⢊⠤⢣⣿⡯⢇⠳⣌⠲⣡⠃⠌⠀⠀⠀⠀⠀⠀ ⡁⠇⠀⠀⠸⡁⢎⣰⠟⡤⣸⠁⠀⠀⠀⣠⠞⣡⠚⡄⣃⣶⡿⠀⢨⠴⡇⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠤⠄⠰⠥⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⠿⣣⣤⣴⣃⣪⢍⢫⣍⠙⡛⠻⣿⣿⣿⣿⣷⣾⣷⡾⣶⢶⣚⢯⡭⢷⢟⣚⣟⣫⣭⣭⢭⡍⣛⠷⣾⣥⡅⢦⠱⢌⠢⢎⢟⣿⡇⢎⡱⢌⠣⠆⡍⡀⠀⠀⠀⠀⠀⠀ ⡥⠠⣀⠅⣢⠵⠞⠁⡼⢱⡇⠀⢀⡴⠏⡱⠨⣐⠣⢰⡟⠉⣀⡰⢋⠰⡇⢰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠻⠿⣿⠯⠷⢛⣛⡛⣛⢿⠶⠚⠀⠀⠀⠈⠉⡛⠻⢿⣯⣿⣟⣿⣟⣿⢾⣽⣻⢾⣽⣾⣻⢷⣻⢯⣿⢿⣾⣍⢿⢻⢆⠣⢎⠘⢢⠚⣿⠿⣳⠶⣊⠥⢋⠐⠀⠀⠀⠀⠀⠀⠀ ⡯⠑⡄⠊⠉⠀⠀⢀⠟⡼⠀⣰⡿⠛⣷⠠⢃⢠⠱⢸⢣⠏⡡⠒⠭⡐⣿⠋⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢼⣿⡿⠯⠤⣀⡀⠀⠀⠀⠀⠈⠒⠤⢀⡈⠙⠻⢟⠛⠛⠚⢣⠿⢾⣿⣿⣿⣿⣿⣿⣿⣷⣿⠾⣛⠬⡓⡌⠌⡁⢾⣿⠟⣡⡷⣈⢎⢡⠎⠀⠀⠀⠀⠀⠀⠀ ⡜⡱⢈⠁⠀⠀⠀⡼⡰⠃⠚⠃⠀⠀⣼⠣⣉⠦⢨⡟⡼⠖⢳⡉⠖⣡⢻⣸⢒⣳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣁⣀⡤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠉⠁⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠂⠒⠁⠀⣿⣿⣿⣿⣿⣿⣿⡿⣟⡬⠓⣌⠒⡡⠘⢠⠰⣾⣵⣞⡿⢰⢡⢊⡞⠀⠀⠀⠀⠀⠀⠀⠀ ⠗⠀⠀⠀⠀⠀⣠⡟⠁⡇⠀⠀⡠⠉⢸⢰⠡⢊⡟⣏⠡⡎⣹⠰⠩⠄⡟⡗⣾⣠⢗⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡕⠀⠀⠀⠀⠀⠀⠀⣸⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢠⣿⣿⣿⡽⣿⣿⢿⣻⠵⣨⠓⡬⠑⡄⠃⠆⣰⢿⡷⣫⠘⡥⢂⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠆⠀⠀⠀⠀⣰⠟⠀⠀⠁⠀⡴⠁⠀⣸⠌⡜⣉⠻⠯⣰⡇⡏⡜⢡⠭⡇⢃⡽⢯⠞⣳⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⡗⠀⠀⠀⠀⠀⣠⡺⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⣽⣻⣿⣿⣏⢷⣡⢋⡴⢩⡐⡩⣸⣿⣯⢞⣵⡿⢁⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⠏⠀⠀⠀⠀⡼⠁⠀⣰⠋⡜⡰⢄⢃⠣⢼⠁⡇⣎⠡⢊⣥⣦⡜⡍⢢⡼⣠⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢱⠤⢀⣠⣦⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠹⣿⣿⣟⣷⣟⣿⣿⣿⡞⡴⣋⠴⣃⠶⣵⢿⣿⣽⡿⢋⢆⣽⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⢠⠀⠀⠈⠀⠀⡎⠀⣼⠁⠀⠰⣅⠪⡔⢡⠊⡔⢃⢾⡀⣗⢠⣙⣴⢿⠛⠛⠓⠻⢲⠛⠒⠛⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣸⣪⣽⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⣸⣿⣟⡾⣽⡾⣯⣟⣿⣿⣷⣭⣳⣝⣾⣿⣿⡿⣫⡌⢃⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣋⠐⠀⠀⠀⠀⡼⠀⠘⡇⠀⣀⣀⣏⠰⣡⠊⣰⢣⠌⢼⣷⢸⢢⡞⣼⢼⢲⠲⠷⢶⣿⣶⣒⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢾⣠⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣹⣿⣻⢙⣿⣽⢷⣻⢾⡽⣟⣿⣿⣿⣿⣿⣟⡼⢣⠇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠁⠀⠀⠀⠀⢰⠁⠀⢈⡔⠋⠀⡼⠹⢷⢀⡞⡿⢠⠋⡄⣿⣸⠺⡇⣿⡎⠀⠀⠀⠀⠻⡿⢿⣯⢿⠀⠀⠐⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠭⣦⣾⣼⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣿⡿⡑⡎⡔⣿⣯⣟⣯⢿⣽⣞⣿⣿⣿⣿⣯⢜⡡⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡆⠀⠀⠀⠀⣠⢤⣀⠉⠀⠀⠀⣇⢸⣯⠏⣸⠁⢦⡑⣸⢽⡞⡉⢧⡽⣧⣄⡁⠀⠀⠀⠙⣹⣁⣼⡷⠀⢈⣿⣿⣿⣶⢤⣀⣀⣀⣀⣤⣰⡶⢉⣴⡿⣫⠆⠀⡄⠉⢻⢸⠀⢿⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⡱⢜⡰⢻⣟⣾⣽⣻⢾⣽⢾⣿⣿⣿⢏⠆⣑⡾⠀⢀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠁⠀⠀⠀⢊⡐⠆⡌⢣⢀⠐⠀⠈⡟⠁⠀⢯⠘⣼⠋⡇⡾⢁⠜⡈⢷⣆⡉⠛⠶⠶⠶⠛⠋⣉⣁⣀⡴⠞⠋⡉⢁⠀⠌⡐⠲⡤⠶⠖⢧⣾⠋⠵⠛⠁⠤⢁⠐⠈⡜⢸⡀⢸⣿⣿⣿⣿⣿⣷⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣣⢑⠮⡔⢣⢿⣷⣿⣿⣿⣯⣿⣿⣿⣻⡞⡜⢹⡡⠖⠉⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠨⠀⢀⠰⡃⣌⠲⡘⡼⣠⠐⢠⡟⠀⡠⠀⡖⣷⠇⡼⢸⠁⡎⢒⠡⣬⠼⠛⠷⢒⢒⡋⠍⠭⠙⣿⣿⣤⣤⠴⢀⣂⡬⠤⠴⠒⠛⠒⠒⠋⠀⠸⢦⣈⡐⠠⢂⠈⢼⡃⢸⢁⠀⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢃⢎⢲⣉⠦⢻⣿⣿⣿⣿⣿⣿⣿⡿⡓⣥⣼⠋⣠⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠐⡈⢆⠣⡑⠤⢓⣸⢣⠃⠀⡞⣴⡞⢣⠞⣽⠏⡔⡇⣇⠣⡜⢡⣞⣡⠮⢚⢺⠏⡒⢌⣺⡴⣣⣬⡙⠲⣮⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠒⠦⠬⠧⣾⡙⡆⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢣⠚⣤⢃⢎⣿⣿⣿⣿⣿⣿⣿⣿⢣⣟⣿⠵⠋⣀⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣤⣍⢢⠱⣁⠚⢄⡞⡎⠀⣸⣱⡟⡄⢣⠸⢇⠸⡄⡙⡟⡇⢘⡨⢡⠒⣌⡵⢋⠦⢛⣼⢋⡼⣩⢼⡟⠶⣽⣳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⢢⡙⢤⢋⢲⣿⣿⣿⣿⣿⣿⣿⢷⡿⢟⡥⡠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢨⠉⢿⣆⠡⢉⡞⡞⠀⣰⢳⣟⠰⣈⠥⡃⢌⡒⡌⢡⢧⡳⢈⡔⢡⣪⠏⡰⣁⣮⣯⡕⢮⠰⣱⣎⣷⡶⢱⢬⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⡱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠄⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⡜⢢⣋⢼⣿⣿⣿⣿⣿⣿⣯⢏⣿⣷⢏⠀⢀⡤⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠘⣾⠇⠊⡕⢀⠀⣠⢣⠿⢆⠱⡈⠖⣉⣾⡞⣐⠣⡐⠤⣣⡼⠛⣹⢇⣱⣯⣾⣟⣿⠟⣷⣿⣿⣿⣿⡨⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢞⢆⠀⠀⠀⠀⠀⠀⠀⠀⢸⢠⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡧⣍⠣⡜⣾⣿⣿⣿⣿⣿⡟⣴⣻⡿⠃⡏⣠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠜⠃⠈⢨⠔⠒⠚⢁⡾⠘⢤⠣⢍⣲⢋⡏⠴⣁⢒⡡⣾⠏⠀⣴⠿⠋⣽⠟⠋⠉⣀⣾⣿⡟⣿⠻⣇⠠⢤⠉⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠵⠀⠀⠀⠀⠀⠀⠀⠨⣾⣿⡇⠀⠌⢻⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠤⡓⢬⣿⣿⣿⣿⣿⣿⡟⣡⠏⣤⢟⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠁⠀⠀⠀⣅⠪⡑⣤⠞⡡⢍⠢⡑⢂⣵⣾⢟⣰⠾⢛⡷⠋⠀⠘⠃⣠⡞⢀⠂⣁⣲⡿⠭⠛⢿⣯⡶⠿⣆⡘⢤⠹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⢰⣿⣽⡟⠀⢂⠀⢻⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢒⡍⣺⣯⣿⣿⣿⣿⣿⡾⢑⣞⣧⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣀⠀⠦⢙⣠⠷⣛⢡⠚⡰⠌⢒⣵⠟⣱⡿⠋⠀⠀⠀⠀⠀⣠⠶⢋⡁⠐⢰⡏⠉⠀⠀⠀⠀⠀⠉⠙⠢⡈⠑⠦⡁⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⢾⣿⣿⠇⠐⠠⢈⠘⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡣⠜⣿⣿⣿⣿⣿⣿⡟⣴⣻⡼⢫⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢤⠊⡍⠥⣃⠜⡀⠎⢆⠱⢈⢬⡧⠈⠁⠀⠀⠀⠀⢀⡴⠾⠛⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠤⡸⣌⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣧⠀⠀⠀⠀⢀⡇⢻⣿⠠⢈⠡⠂⠄⣹⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢻⣿⣿⣿⣿⣿⣿⡿⣱⢟⠰⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⠃⡜⠰⡁⢎⣰⣉⣆⠃⣬⡾⠁⠀⠀⠀⠀⢀⡴⠋⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡟⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⢸⠁⣾⡿⢀⠂⠔⢀⣢⡟⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⣿⣿⣿⣿⣿⣿⣿⣳⠏⠏⡀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⢃⡼⠛⠋⠉⣉⣴⡯⠾⠋⠀⠀⠀⠀⢀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠸⡀⠀⠀⠀⢾⢸⣿⡇⠠⠈⡀⢶⡟⠐⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⣿⣿⣿⣿⣿⣿⣿⢳⠁⣪⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢿⠟⠁⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⣴⣿⡿⡟⣟⢻⡛⠶⢦⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣡⢳⠀⠀⠀⡏⢸⣿⣯⡁⢂⣵⡟⠄⡃⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡿⡾⣴⢋⡞⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⢏⠶⡹⣌⠳⣜⡹⢎⠶⣬⢹⠻⡶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣏⢰⣦⡀⢰⠃⣸⣿⡿⠱⡟⠉⡄⢢⠀⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡽⣡⢾⡄⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣋⢎⡳⡱⢎⡳⣌⠳⢎⡳⣌⢧⣛⡴⣡⢏⡛⡶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣘⣌⢷⣌⡌⢺⡿⠁⠀⢸⠃⡀⡍⠀⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⢳⢏⡟⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣷⢌⢧⢳⠹⣌⠳⣌⢿⡬⣵⣮⣾⣵⣫⣷⣯⣟⡷⣯⣟⣿⣗⡦⣠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣞⣀⡤⠦⢽⣋⣼⣧⠀⢠⠏⡴⢤⡁⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣏⠞⡾⡈⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⣻⠹⣍⠞⣢⠏⡵⣊⢗⡻⢿⣷⣶⣖⡲⣌⠧⢭⡹⣙⠿⢷⣿⣾⣽⣿⣶⣆⡉⠭⠭⠖⣒⡲⠤⠤⣀⡀⠀⠀⠀⠀⠀⡺⠟⠉⠀⠒⠦⠤⣀⣿⠿⢃⡼⠚⠁⢸⠁⣾⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⡏⣾⣷⠁⠆⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣴⣿⢿⢫⡜⡥⡛⣬⣞⡱⢎⡵⣩⢎⡵⢣⢎⡻⢿⣿⣶⣙⢦⡓⣭⢚⡥⢫⡝⡻⣿⣻⣿⣿⣷⠄⠀⠀⠀⠀⠉⠒⠪⢝⣣⡔⠥⠊⠀⠀⠀⠀⠀⠀⠀⢹⣿⠠⠞⠀⠀⠀⡼⢰⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡟⣥⣿⢈⠰⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀ ⠀⠀⠀⠀⢀⣾⣿⡟⣬⢳⡸⢱⣹⢏⡖⣭⢚⡔⣣⠞⣘⠧⢎⡵⢻⣿⣿⣿⡦⡹⢤⢫⢜⡣⢞⡱⢎⡵⣘⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⣿⡇⠀⠀⠀⢠⢃⣾⣿⣿⣿⣿⣯⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡟⣼⢼⠂⡜⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀ ⠀⠀⠀⢠⣿⣿⣿⣙⢦⢣⣵⣿⡷⣎⡜⢦⢋⡜⢦⢛⢬⡛⡼⣰⢻⣿⣿⣿⣷⡙⢮⡱⢎⡵⢋⡜⣣⠜⣥⢺⣿⣿⣯⡳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢶⣤⢀⡟⢡⠃⠀⠀⢀⡟⣾⢿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⡇⣾⢁⠎⡁⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⣿⣿⡟⣜⢢⣿⣿⣿⠿⣢⠝⡬⢳⣘⢣⠏⡦⢳⡱⢣⢎⢿⣿⣿⣿⢜⡣⡝⣎⠶⡹⡜⣥⢛⡴⣃⢿⣿⣿⣿⣾⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠚⢿⡀⣿⠀⠀⠀⢜⣽⡛⢦⣹⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⣿⡆⡘⢄⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣸⣿⣿⣿⣿⣾⣿⣿⡿⢏⡳⢥⡛⢬⡓⣬⢣⡛⡴⢣⡝⣣⠞⡼⢿⣿⣿⢌⡳⢍⠶⣩⢓⣭⣶⣏⠶⣩⣿⣿⣿⣿⣿⣿⢹⢳⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢹⠀⢀⣼⢏⢧⡙⣶⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⡇⡧⡗⣺⠠⠚⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀ ⠀⢀⣿⣿⣿⣿⣿⣿⣿⡿⣙⠮⣱⠣⢞⡡⢞⡔⣣⠝⣒⠧⣚⠵⣪⠵⣩⢿⡿⢢⢝⣪⠳⣥⢫⠼⣿⣿⣗⣿⣿⣿⣿⡟⣿⣏⢮⡱⣋⠿⢦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⡤⣨⣷⢻⣋⠞⣦⣿⣿⣿⣿⣿⣿⣿⡿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣏⡗⢯⢼⠐⡡⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣸⣿⣿⣿⣿⣿⣿⡟⡲⣍⢞⡡⢏⡎⠵⣋⠼⣡⢛⡬⢓⡍⡞⠴⣋⠖⡮⢜⣣⢚⡴⢋⠶⣩⠞⣿⣿⣿⣿⣿⣿⣿⡿⣉⡖⢮⡱⣍⠞⣥⢲⡡⢏⣛⢳⠲⣦⢤⣤⣶⡞⠿⣌⣣⣜⢾⣿⣿⢿⣋⣾⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⡧⢿⣞⠸⣽⡀⢸⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⢏⡼⣑⢎⡎⡵⢪⡜⣣⠝⣎⠵⢣⡚⡵⢚⡜⣣⠝⢮⡱⣋⠴⣃⠞⣭⢳⡡⢏⣿⣿⣿⣿⣿⣿⣿⡱⡱⢎⡣⢖⡬⢛⡴⢣⡙⢮⡜⣡⢛⣤⡿⡟⣭⠚⣵⣾⣿⣋⠮⡝⣭⢲⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣇⣧⠘⡖⣈⡇⠈⡇⠀⠀⠄⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⣿⣿⣿⡿⣘⠖⡭⠲⡜⣥⠳⡜⣥⢚⡜⣎⠧⣓⠭⣳⠸⣥⢚⡥⢳⣌⠳⣍⠞⡴⢣⡝⢮⡜⣼⣿⣿⣿⣿⡯⣱⡙⢮⡱⣋⡜⣣⠞⣥⢛⡲⣜⣥⣿⢏⡳⣹⢰⣿⣿⠻⡴⣩⠞⣱⣾⣿⣿⡿⣋⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣸⢌⠣⠄⣷⠈⠱⠀⠀⠀⠀⠄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣼⣿⣿⣿⣿⡷⢩⠞⣱⠹⡜⡴⣋⡜⢦⣋⠶⣌⠳⣌⠳⣆⢻⡰⣍⠺⣅⢎⡳⣌⢻⡘⢧⡚⡵⣚⢼⣿⣿⣿⡟⣱⣾⡿⢢⣓⣱⠎⡵⣚⣤⣏⣶⣿⢟⡱⢎⣵⣷⡿⡻⣌⠷⣱⣣⣾⣿⡿⠟⢫⢴⣱⢾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⡜⢎⡱⢨⠸⢀⡈⠀⠄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢹⣿⣿⣿⣿⡏⢧⡛⡴⢋⡼⢱⡜⠼⣡⠞⡜⣬⠳⣬⠳⣬⠳⡜⣬⠳⣜⠪⡕⣎⢥⡛⢦⡙⢶⡩⢾⣿⣻⣿⣼⣿⣿⢍⣇⣾⡿⣹⣾⣿⣿⣿⢻⣱⣮⣷⣿⠿⡹⢼⡱⣮⣿⣿⣿⠟⠉⢀⠀⣞⢫⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡎⡎⠴⡁⠎⡄⢀⠠⠀⠀⠀⠀⠀⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣽⣿⣿⣿⣿⡏⢶⡙⡼⡑⣎⢳⡘⢧⢣⡛⡜⢦⡛⡴⣋⠶⡹⡜⢦⢛⡔⣫⠜⡜⢦⣙⢮⡙⢦⣙⣾⣶⠟⣽⣿⣿⣳⣾⣿⣿⣿⣿⣿⢿⣫⣼⣷⡿⣟⡹⢬⢳⣹⣶⣿⣿⣿⠋⠀⠀⠀⠎⠀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⡧⡙⢦⠉⡆⢃⠠⠀⢀⠀⠀⠀⠀⠂⠀⠀⠁⠀⠀⠀⠈⠀⠀ ⣼⣿⣿⣿⣿⣿⡏⠶⣙⠴⡹⣌⢧⡙⣎⢧⡹⢜⡣⡜⣵⣮⣿⢳⡙⣎⢣⠞⣡⢛⡜⣣⠞⢦⡙⢧⣾⣿⣯⣽⣿⣿⣳⣿⣿⣿⣿⣿⣻⣽⣿⡿⢻⡙⢶⣡⣿⣾⣿⣿⠿⢛⡟⡎⠀⠀⠀⠀⢠⡽⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣧⠝⡢⢕⡘⡌⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀ ⣿⣿⣿⣻⣿⣿⣏⠳⣍⢞⡱⢎⠶⣙⠲⣌⣣⣧⣷⣿⣿⡟⡥⢧⡙⢦⣋⠞⣥⢫⡜⡱⢎⢧⣹⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡟⣏⠳⣜⣣⣽⣾⣿⡿⠛⠉⠀⢄⣿⢱⠁⠀⠀⠠⣙⠝⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⢸⡑⣎⠲⣍⠆⢁⠀⠁⠀⠄⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀ ⣿⡿⠳⣜⢻⢻⡷⡹⣜⢪⡕⣫⢚⣥⣿⣿⣿⣿⣿⡿⢗⡹⡜⣣⠝⣦⡙⡞⡴⢣⡚⣍⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⡛⢯⡑⢮⣱⣾⣿⣿⠿⠛⠋⠁⠀⠀⠠⢨⣾⠇⠃⠀⠠⢀⡷⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⡣⢜⡤⢳⢸⠠⠸⠀⠘⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀ ⣿⡱⢫⡜⣥⠳⣜⡱⢎⡱⢮⣥⣿⣿⣿⢏⣿⣟⢣⡝⡎⡵⢪⢥⣋⢦⡹⢜⡱⣣⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣥⣯⣶⣽⣶⣿⡿⠟⠛⠉⠀⠀⠀⠀⠀⠀⡄⣡⡿⡍⢀⠐⣬⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣗⠪⣔⠣⡎⡗⠀⠃⠀⢃⠀⠀⠄⠀⠀⠀⠁⠀⠀⠀⠀⠀ ⣛⠿⡧⣜⠢⢏⠲⣍⢮⣱⢳⡿⣛⢳⣋⡜⢲⡌⣳⢸⣱⣭⣳⣶⣭⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⡛⢛⣛⠯⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣢⣴⡿⣱⣣⠴⢋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⠸⣄⠳⡙⠽⣤⣁⠀⠈⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⠟⠛⠛⠛⠛⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⡏⢀⣴⣾⣿⣿⣷⣶⣦⣄⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⡿⠀⣸⣿⡿⠋⠉⢁⣀⣀⣀⡀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⠿⠿⠇⢀⣿⣿⡇⠀⠸⣿⣿⣿⣿⣿⣿⣦⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⠁⢠⣤⠀⢸⣿⣿⡇⠀⠀⠈⠛⠛⠛⠛⠉⠉⠀⣸⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿ ⡿⠀⣿⡿⠀⢸⣿⣿⣿⣄⡀⠀⠀⠀⠀⠀⣀⠀⢰⣿⣿⣿⣿⡋⠉⠉⠀⠀⠀⠹ ⡇⠀⣿⡇⠀⢸⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⠀⢸⠿⠟⠋⠁⠑⠢⣀⣀⣀⠄⢠ ⡇⠀⣿⣧⠀⢸⣿⣿⣿⣿⣿⣿⣿⠟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣶⣿ ⣇⠀⣿⣿⠀⢸⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿ ⣿⣄⠈⠉⠀⠸⣿⣿⣿⡟⠃⠀⠀⠀⠀⠀⠀⠀⠤⠤⠄⣶⣾⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⡇⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⡇⠀⠿⠿⠿⠃⢀⡀⠀⠀⠀⠀⠀⢀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣦⣤⣤⣤⣴⣾⣿⣦⣄⣀⣠⣴⣮⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
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⠀⠀⢸⣧⢂⠱⢨⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⢻⣄⠂⢍⣸⣡⣾⠟⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡟⡦⢑⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⠈⢿⡞⣎⡷⠋⠀⠀⠀⠀⠀⠀⣼ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢱⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⠀⠀⠀⠀⠈⢻⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡿⡱⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⢠⣟ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⢥⠃⡌⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⠀⢰⣞ ⠀⠀⠀⠀⠀⠀⠀⠀⣰⢏⡼⠁⠐⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀⢀⡿⣜ ⠀⠀⠀⠀⠀⠀⠀⣼⣫⠞⡀⢡⠂⠀⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⢰⡟⣼ ⠀⠀⠀⠀⠀⠀⣼⡷⢋⡐⢈⠄⢂⠁⠄⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⣸⣽⡳ ⠀⠀⠀⠀⠀⣼⠟⡡⢂⠔⢂⠈⠄⠂⠌⠠⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡀⣿⡞⣽ ⠀⠀⠀⠀⣰⢏⠦⡑⢌⡐⠢⡈⠤⠁⠌⡐⢀⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣯⢿⡼ ⠀⠀⠀⢀⡿⣈⠖⡈⠆⡌⠱⡐⢢⢁⠂⡐⠀⠆⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⢧⣟ ⠀⠀⠀⣸⡓⠴⡈⠴⠡⢌⠱⡈⠆⡌⡐⠠⠁⠂⠌⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣟⡾ ⠀⠀⢀⡟⡬⢱⠘⡄⢃⠎⡰⢁⠎⡐⠀⠑⣆⠁⢂⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⣳ ⠀⠀⢸⢏⡔⡃⢎⠰⡁⠎⡐⠂⠄⠠⠀⠀⠈⢶⡀⠂⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠁⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⡵ ⠀⠀⣾⢡⠚⣌⠢⡑⠄⡃⠄⠁⡘⠀⠀⠀⠀⠀⠹⣄⠂⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠐⢠⢈⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣻ ⠀⠀⣟⡌⢳⠠⣃⠌⠒⡀⠂⠈⠀⠀⠀⠀⠀⠀⠀⠙⣦⠉⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⣀⡾⢀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡷ ⠀⠀⡯⡜⣡⠒⡡⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢆⡴⠏⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡿ ⠀⠈⡷⣑⠢⡱⠡⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⡁⠂⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿ ⠀⠀⡷⢡⢓⡰⢁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⢀⠀⠀⠀⠀⢀⣾⠣⡘⠠⢡⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣷ ⠀⠀⢽⡡⢆⡱⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⣄⣹⣯⣀⣀⣤⣿⠡⠆⡁⢂⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡷ ⠀⠀⣾⢰⢃⠦⡉⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡟⠋⠹⠟⢻⡿⣡⠃⠜⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⡽ ⠀⠀⢽⡎⡜⢢⠑⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡦⠀⠀⣾⡱⡂⠥⠈⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡽ ⠀⠀⢸⡧⡙⢆⠣⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠔⢸⢧⡓⣁⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⢻ ⠀⠀⠸⣗⠭⣊⠕⡨⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠀⣿⢎⡱⠠⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣯⣟ ⠀⠀⠀⣿⡜⢢⢍⠰⡁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⡁⣯⢛⠴⡁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣳⢾ ⠀⠀⠀⢹⣎⠇⣎⠒⡄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡇⣏⢎⡒⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣽⣻ ⠀⠀⠀⠈⣯⢚⠤⡃⠔⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡃⣏⠖⡨⠄⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⣿⢾⣽ ⠀⠀⠀⠀⢻⣍⠖⣩⠘⡄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣼⣟⡯⠜⡰⠠⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⢻⣟⣾ ⠀⠀⠀⠀⠘⣯⢚⠤⡃⠤⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢹⣿⡧⢋⠤⠁⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠐⠸⣿⣽ ⠀⠀⠀⠀⢀⢻⡍⡖⢱⡈⠂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⢻⣿⡧⢩⢀⠃⠄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⢀⠀⢿⣿ ⠀⠀⢈⣄⣠⠸⣏⡼⠡⡌⡑⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⢺⣿⣇⠃⠆⡘⠠⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣰⣲⠤⠘⣿ ⠀⠐⠀⠀⠀⡀⢿⡜⡱⢂⡑⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⢺⣿⡧⢉⠰⢀⠃⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠀⠀⢀⡀⠄⢹
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heres a smut/spicy story for my fellow horny freaks out there ^_^ (for the ppl saying that i shoulndt post this bc of minors, IM A MINOR MYSELF SO SHUT THE ACTUAL LIVING FUCK UP.) cis female submissive y/n ^_^ OK LES START 💖✨🪩🧁 youre driving to your boyfriends house. its 35 minutes away from your home. its raining and storming. you finally made it to your boyfriend (bf)’s house. he greets you with a hug and a kiss. his friends are there, too. hes having a big party. theres bright lights, strong alchohol, loud music, a big couch, and a flight of stairs leading up to his room.. “HEY EVERYONE!! MY GIRLFRIENDS HERE!!” he tells everyone. you love parties, so everyone is exited that youre there. especially the boys. everyone greets you kindly. (bf) turns up the music. everyone is drinking, partying, dancing, vibing and having a great time. 15 minutes later, everyone is playing truth or dare. “hey (bf), truth or dare?” (bf)s friend (mf) says. “DARE!” (bf) says. “I DARE YOU.. TO GO INTO YOUR ROOM WITH ME, AND Y/N.” “bet.” (bf) says. theyre all upstairs in (bf)’s room, with vodka on the side table next to his bed. “so.. what are we going to do? ;)” you say. “i think i know what we can do.. if yall are game tho.” (bf) says. “i aint no pussy! what is it?” (mf) says. “we can get a bit nasty.. if you know what i mean ;)” (bf) says, winking. “BET.” you and (mf) both say. you all get undressed. you get undressed first. first you take off your oversized, fluffy little twin stars sweater, revealing two huge, juicy, sexy titties being only covered by a very small bra. they bounce as you take off your oversized, light pink sweatpants, revealing one juicy, voluptuous ass and a pink, deep pussy being only covered by small panties. you take the panties and bra off. the boys both think you look so sexy and fuckable. they get a boner just THINKING about fucking you. the boys get undressed next. they both have a six pack and one big, veiny, stiff-as-a-rock dick. you lay down on (bf)’s king sized bed with white, silky bedsheets. “this is my first time with (bf) and (mf).. i wonder what their dicks taste like.” you think as your tits bounce up, and down, and up, and down. you and the boys start making out, them touching your tits and bouncing their cocks in and out and in and out of your pussy. “MPH~ HARDER~ DADDIES~” you say, muffled.you grab the vodka from the side table and take a big swig of it, the boys dicks still bouncing in and out and in and out of your pussy. (mf) takes the vodka bottle out of your hand and takes an even bigger swig. (bf) does the same thing. all 3 of you are drunk now and having a threesome. (bf) puts his dick up to your mouth, asking you to suck the tip. you suck the tip like its the nip of a baby bottle. “mph~ yes~ good girl~” he says, now cumming in your mouth. you suck his dick very hard, it getting even more deeper and cum-covered every suck. you eventually deepthroat him. he cums in your mouth. “good girl~ i lovee how you suck me~” (mf) puts his dick super far up your pussy. “AGH~” you make noises of pleasure. “DEEPER~ (mf) DADDY~” he puts his entire 10 inches into your pussy. you squeal with joy as you deepthroat (bf)’s dick and get (mf)’s dick so far up your uterus that you wont be able to piss for 2 months. “its been 12 hours.. are they okay up there? im gonna go check on them.” (ff) says from downstairs. she walks upstairs and opens the door to find all 3 of you smashing. (ff) doesnt say a word except 3.. “c-can i join?” “the more the merrier 😏” (mf) says. your threesome quickly turns into a foursome. (ff) gets undressed. shes very sexy, just like you, but nothing could EVER compare to you. (mf) and (bf) rub their dicks around (ff)’s vagina, and then (mf) sticks it in slowly, giving her time to adjust to his 10 inches. unlike you, (ff) is very new. (mf) eventually sticks his entire dick in (ff)’s pussy. “AH~ TOO DEEP~ IT HURTS~” (mf) takes his dick out slowley. “you guys are so good at sex~” you say. “do you all wanna date?” everyone agrees. “should we get cleaned up and watch a movie now?” (ff) says. everyone says yes. they all take a shower and the rest of the night was filled with popcorn, daiquiris, cuddles and scary movies. smut made by louie (all pronouns) :]
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣤⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⡆⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⠟⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣬⣉⠉⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣍⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⢿⣿⣿⣷⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⡟⢀⣿⣿⣿⣷ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣧⣾⣿⣿⠟⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣶⣄⠀⠀⣸⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣄⠀⠀⠀⠀⠀⣀⡀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣷⠀⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⡟⠀⠹⣿⣿⣿⣦⠀⢀⣶⣿⣿⣿⣷⡀⣿⣿⣿⣿⣿⣿⣿⣿⠇⢿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⠁⠀⣀⣈⠻⣿⣿⣷⣿⣿⣿⣿⣿⡿⠁⠹⣿⣿⣿⣿⣿⣿⠟⠀⢸⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⡏⢠⣾⣿⣿⣷⣜⢿⣿⣿⣦⠀⠀⠀⠀⢀⣀⣈⡙⠛⠛⠋⠁⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣧⣝⣛⣡⣶⣶⣾⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⠛⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣤⣤⣤⣤⣤⣼⣿⣿⣿⣿⡇⠀⢹⣿⣿⣿⣿⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢠⣼⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠉⢀⣿⣿⣿⣤⣤⣄⣀⣀⣀⡀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣾⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠻⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⡿⠛⠛⠛⢻⣿⠿⠛⠛⠛⢿⣿⣿⡿⠛⠛⠛⢻⡟⠛⣿⡿⠛⣻⣿⣿⣿ ⡟⠄⣼⣿⣿⣿⡇⠄⣾⣿⣧⠄⢻⡏⠄⣼⣿⣿⣿⡇⠄⡟⢀⣴⣿⣿⣿⣿ ⡇⠄⣿⣿⣿⣿⡄⠄⣿⣿⣿⠄⢸⡇⠄⣿⣿⣿⣿⡇⠄⣀⠈⢻⣿⣿⣿⣿ ⣿⣄⠈⠙⠛⢻⣧⡄⠙⠛⠉⣠⣿⣷⣄⠈⠙⠛⢹⡇⠄⣿⣧⠄⠻⣿⣿⣿⠀ ⣿⡿⠛⠛⠛⢻⣿⠿⠛⠛⠛⢿⣿⣿⡿⠛⠛⠛⢻⡟⠛⣿⡿⠛⣻⣿⣿⣿ ⡟⠄⣼⣿⣿⣿⡇⠄⣾⣿⣧⠄⢻⡏⠄⣼⣿⣿⣿⡇⠄⡟⢀⣴⣿⣿⣿⣿ ⡇⠄⣿⣿⣿⣿⡄⠄⣿⣿⣿⠄⢸⡇⠄⣿⣿⣿⣿⡇⠄⣀⠈⢻⣿⣿⣿⣿ ⣿⣄⠈⠙⠛⢻⣧⡄⠙⠛⠉⣠⣿⣷⣄⠈⠙⠛⢹⡇⠄⣿⣧⠄⠻⣿⣿⣿⠀ ⡟⠄⣼⣿⣿⣿⡇⠄⣾⣿⣧⠄⢻⡏⠄⣼⣿⣿⣿⡇⠄⡟⢀⣴⣿⣿⣿⣿ ⡇⠄⣿⣿⣿⣿⡄⠄⣿⣿⣿⠄⢸⡇⠄⣿⣿⣿⣿⡇⠄⣀⠈⢻⣿⣿⣿⣿ ⣿⣄⠈⠙⠛⢻⣧⡄⠙⠛⠉⣠⣿⣷⣄⠈⠙⠛⢹⡇⠄⣿⣧⠄⠻⣿⣿⣿⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⢿⣿⣿⠿⠛⠿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠉⠄⣀⡤⢤⣤⣈⠁⣠⡔⠶⣾⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⡿⠛⠋⠁⠄⠄⠄⣼⣿⠁⡀⢹⣿⣷⢹⡇⠄⠎⣿⣿⣿ ⣿⣿⣿⠿⠛⠉⠁⠄⠄⠄⠄⠄⠄⠄⠹⣇⣀⣡⣾⣿⡿⠉⠛⠒⠒⠋⠉⢸ ⡿⠋⠁⠄⠄⢀⣤⣤⡀⠄⠄⠄⠄⠄⠄⠈⠙⠛⠛⠉⠄⠄⠄⠄⠄⠄⠄⠈ ⠄⠄⠄⠄⠄⢹⣧⡈⠿⣷⣄⣀⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⢀⣠⢄⣾ ⠄⠄⠄⠄⠄⠈⠻⢿⣶⣌⣙⡛⠛⠿⠶⠶⠶⠶⠶⠖⣒⣒⣚⣋⡩⢱⣾⣿ ⠄⠄⠄⠄⠄⠄⠄⠄⠈⠉⠛⠛⠛⠻⠿⠿⠟⠛⠛⠛⠉⢉⣥⣶⣾⣿⣿⣿ ⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠒⠶⣿⣿⣿⣿⣿⣿⣿⣿ ⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠈⠻⣿⣿⣿⣿⣿⣿ ⣿⡿⠛⠛⠛⢻⣿⠿⠛⠛⠛⢿⣿⣿⡿⠛⠛⠛⢻⡟⠛⣿⡿⠛⣻⣿⣿⣿ ⡟⠄⣼⣿⣿⣿⡇⠄⣾⣿⣧⠄⢻⡏⠄⣼⣿⣿⣿⡇⠄⡟⢀⣴⣿⣿⣿⣿ ⡇⠄⣿⣿⣿⣿⡄⠄⣿⣿⣿⠄⢸⡇⠄⣿⣿⣿⣿⡇⠄⣀⠈⢻⣿⣿⣿⣿ ⣿⣄⠈⠙⠛⢻⣧⡄⠙⠛⠉⣠⣿⣷⣄⠈⠙⠛⢹⡇⠄⣿⣧⠄⠻⣿⣿⣿ ⣿⡿⠛⠛⠛⢻⣿⠿⠛⠛⠛⢿⣿⣿⡿⠛⠛⠛⢻⡟⠛⣿⡿⠛⣻⣿⣿⣿ ⡟⠄⣼⣿⣿⣿⡇⠄⣾⣿⣧⠄⢻⡏⠄⣼⣿⣿⣿⡇⠄⡟⢀⣴⣿⣿⣿⣿ ⡇⠄⣿⣿⣿⣿⡄⠄⣿⣿⣿⠄⢸⡇⠄⣿⣿⣿⣿⡇⠄⣀⠈⢻⣿⣿⣿⣿ ⣿⣄⠈⠙⠛⢻⣧⡄⠙⠛⠉⣠⣿⣷⣄⠈⠙⠛⢹⡇⠄⣿⣧⠄⠻⣿⣿⣿⠀ ⣿⡿⠛⠛⠛⢻⣿⠿⠛⠛⠛⢿⣿⣿⡿⠛⠛⠛⢻⡟⠛⣿⡿⠛⣻⣿⣿⣿ ⡟⠄⣼⣿⣿⣿⡇⠄⣾⣿⣧⠄⢻⡏⠄⣼⣿⣿⣿⡇⠄⡟⢀⣴⣿⣿⣿⣿ ⡇⠄⣿⣿⣿⣿⡄⠄⣿⣿⣿⠄⢸⡇⠄⣿⣿⣿⣿⡇⠄⣀⠈⢻⣿⣿⣿⣿ ⣿⣄⠈⠙⠛⢻⣧⡄⠙⠛⠉⣠⣿⣷⣄⠈⠙⠛⢹⡇⠄⣿⣧⠄⠻⣿⣿⣿⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣴⣶⣶⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠋⢉⣭⣥⣌⡉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀ ⠀⠀⠀⠀⠀⢀⣀⣀⡀⠻⢿⣷⣤⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠀⠀⠀⢀⣴⣿⣿⣿⡿⢁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀ ⠀⠀⠀⢀⣴⣿⣿⣿⣿⣷⣄⠙⢿⣷⣄⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⠇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀ ⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠙⣿⣧⠈⢿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⡟⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡈⢿⣧⠈⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠈⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⠿⠇⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃ ⢸⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀ ⠀⠁⠀⣼⣿⣿⣿⣿⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⠿⠛⠁⠀⠀ ⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⣾⡳⣼⣆⠀⠀⢹⡄⠹⣷⣄⢠⠇⠻⣷⣶⢀⣸⣿⡾⡏⠀⠰⣿⣰⠏⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⣀⣀⣀⡹⣟⡪⢟⣷⠦⠬⣿⣦⣌⡙⠿⡆⠻⡌⠿⣦⣿⣿⣿⣿⣦⣿⡿⠟⠚⠉⠀⠉⠳⣄⡀⠀⠀⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⡀⢀⣼⣟⠛⠛⠙⠛⠉⠻⢶⣮⢿⣯⡙⢶⡌⠲⢤⡑⠀⠈⠛⠟⢿⣿⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀ ⠀⠀⠀⠀⠀⡸⠯⣙⠛⢉⣉⣙⣿⣿⡳⢶⣦⣝⢿⣆⠉⠻⣄⠈⢆⢵⡈⠀⠀⢰⡆⠀⣼⠓⠀⠀⠀ Nah ⠀⠀⠈⣷⠀⠀ ⠀⠀⠀⠖⠉⠻⣟⡿⣿⣭⢽⣽⣶⣈⢛⣾⣿⣧⠀⠙⠓⠀⠑⢦⡀⠹⣧⢂⠀⣿⡇⢀⣿⠺⠇⠀ ⠀I'd⠀ ⠀⣿⠀⠀ ⠀⠀⠀⠀⠐⠈⠉⢛⣿⣿⣶⣤⣈⠉⣰⣗⡈⢛⣇⠀⣵⡀⠀⠘⣿⡄⢻⣤⠀⢻⡇⣼⣧⣿⠀ Beef on this site⠀⡿⠀⠀ ⠀⠀⠀⠀⠀⣠⣾⣿⢍⡉⠛⠻⣷⡆⠨⣿⣭⣤⣍⠀⢹⣷⡀⠀⠹⣿⡄⠈⠀⢿⠁⣿⣿⠏⠀⠀⠀ ⠀⠀⠀⣇⠀⠀ ⠀⣿⣇⣠⣾⣿⣛⣲⣿⠛⠀⠀⢀⣸⣿⣿⣟⣮⡻⣷⣤⡙⢟⡀⠀⠙⢧⠀⠀⠎⠀⠉⠁⠰⣿⠀⠀ ⠀⢀⡿⠀⠀ ⠀⠈⢻⣿⣿⣽⣿⣿⣿⣴⡏⠚⢛⣈⣍⠛⠛⠿⢦⣌⢙⠻⡆⠁⠀⠀⠀⣴⣦⠀⠀⠀⠐⢳⢻⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠮⠀⠀⠀ ⠀⠀⠈⠙⣿⣧⣶⣿⠿⣧⣴⣿⢻⡉⠀⢀⣠⣴⣾⡟⠿⠃⠁⣠⣤⡶⣾⡟⠅⠀⣀⡄⠀⣾⢸⣿⣏⢻⢶⣦⣤⣤⣄⢶⣾⣿⣡⣤⡄⠀ ⠀⠀⣠⣞⣋⣿⣿⣾⣿⡿⡛⣹⡟⣤⢰⡿⠟⠉⣀⣀⣤⣤⡠⠙⢁⣾⡿⠂⠀⣿⠟⣁⠀⣹⠀⣹⣿⡟⣼⣿⣿⣌⣿⣞⣿⣿⠁⠀⠀⠀ ⠀⢠⡿⢛⢟⣿⣿⣿⣿⣿⣿⡟⣼⣿⣟⢓⠛⣿⣏⣿⣵⣗⣵⣴⣿⢟⡵⣣⣼⣿⢟⣵⣶⢻⣶⣿⠀⠀⣈⢻⣿⣿⣿⢿⣾⢿⣧⠀⠀⠀ ⠀⠘⠃⢸⣿⡾⣿⣿⣿⣿⣯⣿⣿⣿⣶⣿⣿⣟⣾⡿⣫⣿⣿⣿⣽⣿⣿⣿⣿⢫⣾⣿⣿⣿⣿⣿⣴⡆⣻⣿⡏⣿⢻⣧⣿⡿⣿⡆⠀⠀ ⠀⠀⠀⠜⣿⣾⢿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣭⣿⣖⣿⢿⣿⡿⣿⣿⣿⡿⢡⢯⣿⣿⣿⣿⣿⣿⣿⣧⡿⣾⣷⣿⣿⢿⣿⡇⠉⠁⠀⠀ ⠀⠀⠀⠀⣿⣥⣾⣿⣿⣿⣿⣿⣿⣿⡇⣭⣿⣿⣿⣿⠃⠞⠟⣸⣿⠏⣸⣧⣀⠿⢿⣿⣿⣟⣿⣿⣿⣿⣽⣿⢿⣿⣿⣿⣿⠁⠀⠀⠀⠀ ⠀⠀⠀⠈⠛⣹⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣟⣿⣿⡿⢶⣦⣄⣿⠏⠀⣿⣟⣿⣶⠾⣿⣟⣋⣛⣿⣿⣿⣿⡇⣻⣿⣿⣿⡏⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠟⠛⠫⣿⣿⣿⣿⣿⡿⣧⠛⣿⠛⣿⣿⣿⣷⡌⠹⡟⠀⠀⠉⡟⠋⢠⣾⣿⣿⣿⡟⣿⣿⣿⣿⢀⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⠋⣾⣷⣿⣿⣧⠙⠀⠙⢣⠝⠛⠋⣽⣷⢦⠇⠀⠀⠘⠁⣤⣾⣿⠝⠛⠉⠘⢻⣿⣿⢿⣼⣷⡟⢻⣷⠉⠀⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠐⠟⢻⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⣾⠟⠀⢸⣷⣿⡇⠀⠛⠀⠀⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⢻⡿⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠲⣄⠀⡄⠆⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⣀⠀⠀⣠⣾⣿⠁⠀⠀⠀⠀⠀⣀⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢻⣆⠀⠛⠁⠶⣶⣶⣶⣶⣶⣶⡶⠆⠘⠋⣠⡾⢫⣾⡟⠀⠀⠀⠀⠀⠐⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠛⠀⠙⣷⡀⠀⠀⠙⠛⠛⠛⠛⠋⠁⠀⢀⣴⠋⠀⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣰⣦⡀⠸⣿⣦⡀⠀⠀⠀⠀⠀⠀⢀⣴⡟⠁⠀⠐⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⡄⢺⣿⡄⠹⣿⠻⢦⣤⣤⣤⣤⣶⣿⡟⢀⣀⠀⠀⢸⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣮⣿⣿⡀⠹⡷⣦⣀⡀⡀⢸⣿⠏⢠⣾⣿⠀⠀⣾⣿⣿⣿⣿⣶⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⣀⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠘⣷⣻⡟⠀⡼⠁⣴⣿⣿⣯⣥⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣯⣿⣤⣤⣤⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣄ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ 🤞🤞🏻
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢸⢿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢀⠚⣷⣭⠻⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⢆⡸⣹⢏⠘⣿⣷⣫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠈⠠⢓⡹⣎⠇⣿⠻⣷⡝⣻⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠠⣀⠌⢣⡝⣆⣿⠀⠙⣇⠏⠿⣽⣿⣿⡗⣎⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠐⠠⢘⠡⠞⡤⣿⣧⡀⠘⡌⠑⠄⠛⣿⡟⣌⢻⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⣩⠄⠀⠀⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⢈⠑⢦⣹⡯⢷⡇⠀⠀⠀⠁⠈⣿⠰⢻⣿⣿⣿⣿⣗⣎⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⡟⠀⣀⠀⢉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣥⠞⠉⠀⠀⠀⠀⣌⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠠⠉⠐⠢⢄⡀⢸⣯⡙⡷⠀⠀⠀⠀⠀⢿⢬⣇⡟⢿⣿⣿⣧⠌⣿⣿⣿⣿⡇⡹⣿⣿⣿⣿⣿⣿⣿⠀⠂⢀⠱⠀⢳⡈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣡⡮⠀⠀⠒⠁⠠⠀⠡⠄⡃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠐⠠⠌⣸⡟⢧⡏⠀⠀⠀⠀⠀⢸⢇⠘⠇⠀⠙⣿⣏⢒⢽⣿⣿⣿⡇⡱⣿⣿⣿⣯⢹⣿⣟⡃⠀⠁⠈⠢⠀⢉⠢⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣡⡞⠁⠀⡠⠄⠀⠀⠀⠀⠐⠌⢱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⣿ ⣴⣤⣄⣀⣀⠀⢸⡯⢅⣻⠀⠀⠀⠀⠀⢸⠈⢳⠀⠀⠀⠈⢻⣀⠺⣿⣿⣿⣇⠡⣿⣿⣿⣿⢸⣿⣯⡅⠠⠥⠦⠌⡂⠅⠍⡢⡈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⡴⠋⣄⢌⠋⠀⠀⠀⠀⠀⠈⠉⠂⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿ ⣿⣿⣿⣿⣿⣿⣷⣿⣶⣆⣀⣀⠀⠀⠀⢸⣀⣸⠀⠀⠀⠀⠘⡗⢿⠋⠛⣿⣿⠐⣻⣿⣿⣿⠰⣿⣷⣧⠀⠀⠠⠐⢂⡥⠥⣌⡈⢄⣘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢏⣤⡔⣡⢊⠵⠁⠀⠀⠀⠀⠀⠀⠀⠀⠂⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣯⣿⣿⣿⣷⣿⡿ ⢽⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣧⣂⣉⡀⠀⠀⠀⡯⢼⣠⠀⠈⢹⡖⢸⣿⣿⣿⠘⣿⣿⣷⡀⠀⠐⢒⠢⢀⠀⠈⠷⣟⢏⢙⣻⡿⡯⠟⢯⣹⣿⠟⠻⣏⠈⠛⣥⠿⠻⠛⠻⣯⣽⣯⣻⣛⣻⣩⢻⣁⠕⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⡟⠋⣿⣿⣿⡇⢿⣿⣿⣿⣿⣿⣿⣿ ⣾⣭⢟⣺⣟⡿⣿⣿⣿⣿⡿⣿⢿⡿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣧⣖⣬⣀⡀⠀⡗⠪⡟⢿⣽⠀⣿⣿⣿⡄⠀⡒⠈⠑⠌⢣⣱⡷⠞⠛⡛⣀⣤⡾⠀⠀⠀⠹⣷⡆⣸⣧⣄⢈⣼⡀⣸⡿⠋⠈⠈⢳⣰⣩⠛⠚⢶⣂⣠⠂⠀⠀⢀⠀⠀⠀⠀⠀⣞⢻⣿⣿⣿⢉⣿⣿⣿⡇⣾⣿⣿⣿⣇⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿ ⣿⣞⣯⢶⢯⣟⡿⣿⣿⣿⣿⡽⣮⢷⣳⢿⣿⣿⡿⢏⡟⣿⢿⣿⣯⣤⣤⣿⣿⣷⣦⣥⣬⣽⣿⣼⣿⣿⣷⠤⣀⣁⣦⡛⠯⡃⠀⠀⠀⠈⣿⣿⡆⠀⠀⠀⠈⡟⢋⢠⢋⠿⣎⣉⡽⢿⢁⠀⡀⠀⠀⣿⣿⡇⠀⠀⠈⠙⣷⢀⣀⡀⠀⠀⠀⣠⣾⣯⢿⣿⣿⣿⢺⣿⣿⣿⣏⢿⣿⣿⣿⠾⣸⣿⣿⣿⢇⠰⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿ ⣿⡞⣬⣛⢾⣿⣿⣻⣿⣿⣿⣿⣹⡞⣟⣻⣿⢎⣿⣿⡘⡧⣏⢿⠿⣟⡼⣹⢿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣇⠤⡟⠛⢥⣤⣶⣦⣔⣠⡀⠀⠈⠙⡀⠀⠀⣀⢘⠈⠂⠈⣰⠮⡈⠥⣻⡀⣼⣶⠱⡀⠈⠹⠟⠃⢀⠄⢂⣠⡔⠎⠙⢣⣤⠔⢋⢀⣿⣷⣻⣿⣿⣿⣻⣿⣿⣿⣯⣿⣿⡿⣿⡸⣽⣿⣿⣿⢲⢸⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⡹⢮⡷⣿⣿⡼⣿⣿⣿⣿⣷⣿⣿⣿⡟⠻⢇⣿⢭⡷⣹⢾⣿⠧⣿⢣⣯⢿⣭⢹⣧⢿⡟⠿⣿⡿⠅⠀⠀⣨⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⢝⠢⢂⠈⠐⠨⢄⠠⠪⢀⠔⣭⣿⠠⠁⠀⢀⣤⣴⣿⣿⣿⣿⣿⣿⣿⡆⠀⠩⣧⣾⣿⡷⣟⢯⣟⣽⡟⣿⣝⣯⣳⢻⡾⣽⣿⣡⣿⣿⣽⣿⣬⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⡷⣿⣩⢿⡿⡿⣽⣿⣿⣿⣿⣿⣼⣻⣟⣿⠀⠀⢿⣞⣿⣽⢺⣽⠀⣯⢿⣹⡾⡼⢻⣮⡷⣽⢾⡿⠗⠛⠛⠉⢹⡟⠁⣿⣿⣷⣿⣶⣿⣿⣿⣧⡀⠀⠀⡱⠀⠬⠖⣄⣲⣑⣶⠇⠢⣵⠀⠀⢀⣶⠟⢻⣿⣯⣯⣿⣿⣿⡏⢿⡗⠂⠠⠬⣽⣾⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⡯⣿ ⣿⣿⣷⣟⣿⣿⣧⣻⣼⣿⣿⣿⣿⡯⣷⣿⣿⡆⠈⢸⡿⣼⣿⢿⡛⣆⣿⡺⢭⣿⢷⢸⣷⣽⣯⣹⣙⠢⣄⠀⠀⠘⠳⣄⡙⢿⣿⣿⣿⠟⢁⣼⣿⡇⠀⢠⠀⠀⠀⠐⠉⠐⣗⢲⡄⠀⠘⡀⠀⢸⣷⡀⠘⢿⣿⣿⣿⣿⡿⢁⣼⠏⠀⠀⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢭⣿⣿⣿⡏⠉⣿⣿⣿⣿⡿⣿⣸⣿⣿⣿⣿⢋⣿ ⣿⣿⣽⡞⣯⢿⣳⢿⣽⣿⣻⢯⣿⣧⢽⣟⣿⡇⠀⢛⣿⠴⣛⢯⡇⠌⣿⣯⡓⢾⣿⠘⡿⣿⢸⢇⣸⠶⣁⡙⠩⡒⠤⣄⡈⠉⠉⠉⠀⠈⠉⣹⣻⡷⡊⠀⠀⠀⠀⠀⠀⠈⠂⠀⠈⠳⣀⠜⣶⣿⠿⠟⠂⠠⠽⠿⠿⠛⠒⠋⠁⡀⠠⠔⣀⣴⠏⣱⣿⣿⣿⣿⣻⣿⣿⣿⣟⣿⣿⣿⣟⣬⣿⣿⣿⡇⠀⣿⣿⣿⣿⢹⣿⣿⢹⣿⣿⡏⣸⣿ ⣿⣿⣗⣯⣽⣾⣝⡮⣞⣿⣧⣿⣿⡗⡾⣻⣾⣷⠀⢸⢿⣹⠜⣎⣧⠀⣿⣧⡛⢦⢿⣦⣿⣯⡟⠀⠈⠢⣤⡞⢒⣈⣲⠺⡂⢭⡀⠄⡀⣠⣞⣿⠃⣴⣆⡀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⣽⡸⡙⢿⡹⢤⣀⣀⣀⣀⡘⡛⠛⠉⠐⡤⠽⠛⠡⠀⢭⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣧⢛⣿⣿⣿⡇⠀⣿⣿⣿⡟⣿⣸⠏⣿⢳⣿⢃⣿⡟ ⢹⠟⡿⣏⣿⣿⣽⣧⣿⣯⣿⣿⣿⣷⢧⣛⢿⣻⣦⣬⣼⣻⣔⣯⣻⣴⣯⢟⣱⣪⣾⢿⣽⡟⠁⠀⢄⣀⡙⠳⢜⣛⠉⠢⠳⢜⣇⣂⡥⠭⠹⠏⢲⠟⠙⢓⣤⣶⣢⣄⣀⣀⣀⣠⣀⣀⣀⠉⠑⠃⠈⠷⢾⣝⠛⠽⣋⣑⡓⢶⣀⠀⣁⡠⠀⠀⠀⠈⣿⣿⣻⣿⣿⣻⣿⣿⣿⣿⣿⣿⡯⢼⣿⣿⣿⡇⠀⣿⣿⣿⢡⣏⣿⣰⣿⣸⣿⣸⣿⣇ ⢯⣿⣿⣿⣿⣿⣿⢿⣯⣿⣿⣿⢿⣻⣟⡿⣻⣿⡿⣽⣛⢯⣛⣟⣻⣛⣟⣻⢻⣻⢻⣿⠫⠤⢶⣶⣌⠿⠿⠿⠿⠟⠁⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠺⣿⣟⣉⣁⡀⠉⠀⠉⠀⢉⣁⣉⣻⣿⣴⠀⠀⠀⠀⠈⠓⠄⠈⠱⠚⠁⣶⣋⣁⣤⡤⣀⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣽⣻⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣷⣟⣷⣯⣷⣻⣞⣷⣻⣮⣗⣻⣼⣻⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⣀⣠⡤⠤⠶⠤⠯⠄⠀⠀⠀⠈⠙⠻⣿⣿⠃⢀⡄⠀⣿⣿⡿⠛⠉⠀⠀⠀⠀⣤⠀⣤⡀⢁⡀⠀⢠⡼⠏⠉⠀⠉⠛⠒⠖⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣷⣿⣿⣷⣿⣿⣿⡄⠀⠛⡣⠄⠤⡦⠤⠀⠒⠊⠁⢠⡄⠲⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣶⣿⣿⣶⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠁⣤⢥⣈⠙⠲⢀⡀⠈⣁⠀⡀⠤⠒⠋⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣟⣿⣿⣿⣿⣷⠆⠀⠀⠀⠈⠀⠁⠍⠑⠂⠉⠡⠤⠤⠔⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢀⣀⢠⣠⢉⠂⠤⢀⡂⠍⠙⠋⠳⠦⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢋⡝⡡⠖⣈⣫⡻⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣿⣯⣭⣿⢷⣖⣶⣿⠓⢦⣀⡀⠀⠀⠀⠀⠄⠐⠭⠔⢂⡲⢞⡒⢀⡀⠀⠀⠀⠀⠀⢀⢀⢠⣴⣶⣤⢧⣈⠂⠀⠨⠀⠀⠀⢨⡠⠤⡤⢤⣀⠈⠁⠛⠖⠠⠍⠁⠀⠄⢰⣿⠿⠶⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣯⢻⡏⠴⣀⠰⣘⣴⡽⣷⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣗⣿⣷⣛⠽⣞⠋⠥⠉⠄⠰⠞⠁⣠⠄⠀⠀⠀⠀⠀⢐⠋⠉⠈⠀⠀⠀⠀⠁⠀⠀⠀⠁⠈⠑⢍⢂⠁⠃⠵⠂⠀⠀⠈⠑⠅⠓⠈⠀⠀⠀⠀⠀⠀⠀⠡⢂⠤⢐⣾⣷⣾⣭⣑⣄⠒⣤⠓⠒⠛⢉⣢⡞⢩⠞⠍⢩⠉⠔⣂⣿⣳⣷⣿⣿⢿⡋⣴⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡻⠟⣿⠿⣛⣽⢾⡛⠍⣊⣭⣊⠥⣛⣨⠝⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⡀⡂⠁⠀⠀⡀⠈⢆⠡⠠⡀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠌⣵⢿⡿⠽⢮⣵⣾⣵⣲⣤⣞⣥⣶⣥⣾⣦⠷⣾⡟⣿⣿⣯⠧⡝⡾⢿⡽⣿⣿⢿⣿⣿⣿ ⢽⡿⡿⡽⣞⡽⣻⢿⡹⢟⡺⡑⠮⣱⠊⠁⡦⣛⠥⡿⠝⠂⣡⠔⣋⠯⠛⣉⣵⠼⢂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠀⠀⢜⠎⠀⣸⠀⢼⣯⠀⠸⡦⢅⠈⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢶⣚⠌⡱⠯⣒⢦⣁⡈⣳⣟⣯⣿⣽⣿⠉⢓⣮⣵⡦⣝⣿⣿⠞⡥⢍⡘⡡⠉⡻⢿⠿⡭⡿⣿ ⢺⣻⣝⡳⣌⢷⣹⢳⣍⠦⡐⢄⠣⠆⡀⠚⠊⠓⠉⣠⢴⡮⠓⠈⠀⡠⡾⠋⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡊⠀⠎⠁⠀⠀⠙⣆⠐⡑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣀⣀⡒⠛⠭⠯⠗⣾⣿⡵⢟⢛⠾⢝⡿⣿⣿⣿⢄⠂⢡⠺⣽⣿⣿⣿⢣⠒⠬⠼⣱⢃⡐⢂⡙⠶⢳⣍ ⢸⡵⣊⠔⣨⡚⠬⣡⠂⠅⠠⢊⣑⠁⠂⠀⠠⣴⢟⠖⠉⢀⠀⣤⠮⠏⢐⠒⠂⣠⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⣀⠔⠂⢀⢀⠂⠀⠀⠀⡀⡚⠁⡄⢀⣾⠁⠠⠀⠀⢹⡆⠐⠀⠑⠀⠈⠐⣀⢄⠀⠀⠁⢒⠦⡀⠀⠑⣏⠶⠤⡫⣍⠓⠒⠀⠀⠈⣿⡟⠭⢛⡽⠶⣯⢬⣝⡻⢦⡈⣄⡳⢸⡭⣿⣿⣇⡘⣻⣜⡰⢣⠄⣠⣘⠴⣃⢮ ⣹⢳⣣⠞⣥⡟⢧⢃⠣⣈⣑⢊⡀⢤⠐⠴⢊⠵⠉⠌⠐⠀⠒⠉⠀⢂⣀⡤⠊⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠤⢦⢆⢊⡠⢀⡠⠂⡠⡚⠙⢠⠂⣠⣾⠃⠀⠆⠆⡀⠀⣇⠠⠐⡈⢄⠈⠠⡈⡌⠳⡀⢄⠢⣀⣢⣭⣒⣴⣫⣖⠕⠂⠄⠤⢔⣢⡐⢿⣽⣊⢳⣞⣞⡣⠭⢋⡝⣛⠻⠾⣭⣷⣝⣿⣿⣷⣞⠤⡙⠽⢣⡟⣶⢯⣛⡶⣯ ⢬⣓⡤⣞⡴⣜⣦⡾⢳⠹⣌⠳⡚⠥⠛⠂⠨⠤⠖⢋⣉⠤⠒⠊⠉⠀⠀⠀⠀⠀⢀⡀⠀⠈⠁⣀⣤⣀⡠⠄⢂⠡⠐⠁⠨⡰⣾⠵⣻⡣⣔⢊⢤⢢⠚⣽⢸⠀⣘⠀⡀⡁⢀⢇⢣⢣⠐⣌⣧⢳⣜⣮⢲⣼⣦⣯⡺⣺⣏⠉⣓⠋⡀⠀⠬⠑⠠⢬⣱⣿⠿⣯⣽⣛⢮⠷⣭⣳⢎⣴⢢⣜⣥⣎⣤⡬⢆⡙⠛⠻⠷⢮⢇⡳⠜⡬⢯⡝⡿⣷ ⢾⣯⢿⡽⣛⠭⠅⢊⠁⠡⢈⣁⡐⠀⣁⣠⠖⠒⠉⠁⠀⠀⢤⠂⠀⠀⠀⠀⠀⠀⢭⣁⡀⠀⠈⠉⢑⣋⣭⣿⣷⣒⡮⣄⣮⣋⣤⠮⠛⠑⠑⣋⠖⡡⢪⢄⣼⠔⠏⠖⡰⢡⢿⡸⡀⢦⠳⡽⢟⢿⢿⠿⣧⡟⠛⠟⢏⠠⠄⠈⠂⢄⠀⢨⢖⠤⣙⣢⡴⠌⢭⢿⣿⡽⣞⣿⣺⢵⣻⡼⣯⣟⠾⠽⢲⡙⢫⠍⠽⡉⡬⠤⣌⣉⡙⠙⡶⠽⣼⣹ ⢺⣉⠣⠴⣁⡲⢌⡦⠒⡋⠭⠤⠩⠙⠁⠀⠠⡀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠀⠀⢀⣒⣲⣭⡄⢀⡠⠐⠻⣻⣿⢿⣿⣿⣷⣭⣾⡷⠋⢊⣪⢜⣢⢞⢋⣴⢦⢃⢞⣬⣞⠇⣇⣾⡟⣷⡈⡖⡜⡌⠢⡑⡄⢘⠦⡑⢮⡢⡉⠂⠄⡉⢨⡉⢖⢽⣻⢿⡷⣆⠀⠀⣻⣿⣿⣽⡾⣽⣻⠷⣛⡵⢮⡹⣋⢗⡜⠧⠚⠵⢒⡐⠣⠔⢢⠊⡵⡉⠶⣅⣋ ⣿⣿⣿⣿⣶⣿⣿⡤⠤⠀⠈⠒⠄⠈⢦⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠟⢫⠖⣣⣎⣵⣞⠁⣄⡭⠹⢿⣿⣿⣿⣷⣷⣿⣶⣿⣷⡿⣿⣻⢠⢞⣿⠞⡟⣼⠀⡏⣷⣸⣷⣜⢻⡘⣄⠈⣎⡆⣟⢮⡂⢝⣮⣹⣦⣐⣷⡽⠒⠯⡉⠙⠂⣀⣩⣿⣿⣿⣿⣯⢿⡱⣏⠾⣹⠶⣏⡕⢣⡌⣌⠧⡙⠜⠦⠰⠥⡌⢍⠲⣀⠃⢣⠌⡆ ⣿⣿⣿⣿⡿⠛⠉⢁⠤⣄⡀⠀⠀⠐⠸⠄⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠘⢇⡰⣮⣴⣿⣯⡽⢩⡶⢋⠁⡀⢌⠉⠟⣛⣛⡿⠿⢿⠿⠋⣱⣿⣿⡞⣼⠟⣰⢣⢻⠀⣇⠻⣯⣿⣿⣞⣳⣿⣦⣽⣷⣹⣼⣷⣬⣿⢿⣍⠿⣿⡓⠢⠐⣅⠀⡀⣙⣿⣿⣿⣿⣽⡻⢎⡷⣛⣶⣛⡶⣩⠓⣌⡳⢩⢄⡓⢄⠐⠆⢒⢳⣈⡆⢭⡒⣬⠰⢇ ⣿⣿⣿⠁⠀⠀⠐⠺⠧⣾⣟⣿⣒⢦⡜⣲⣔⡠⡀⠄⠀⠀⠀⠀⠀⠀⠀⠐⡀⠲⢘⣿⣫⣼⠿⣋⣵⣿⣷⣥⣞⡵⣰⠶⢋⠅⡒⣪⠔⢡⠔⡾⠟⣟⢝⢺⠃⡜⡏⡠⠃⠀⠿⢠⡘⡏⢿⣿⣿⣿⠿⢿⣿⡿⣿⡞⠋⠱⠟⢌⠳⡢⠈⡠⣈⠲⠽⣦⣿⣿⣿⣿⣿⣿⡿⣿⣻⣽⢶⣭⠴⡅⣚⡴⢛⡭⣒⠼⠢⠜⢢⠛⠦⠛⡜⣇⠻⣔⠫⢎ ⣿⣿⣿⣷⣦⡄⠀⠀⠀⠀⠬⣧⣽⣻⣽⣱⢮⡱⣃⢎⡰⠤⣄⢠⠀⣀⠀⠠⠀⠭⣙⣻⡿⣿⣿⣟⣯⣽⣶⣭⣞⣿⣷⣫⡴⣎⡶⢋⣴⠟⢀⡴⡪⢋⡾⠁⣸⡝⡔⡁⠀⡆⠀⢈⠷⡐⢠⣦⡈⠀⣍⢆⠳⣹⢎⢳⠈⠢⡁⠀⠣⢝⡬⡢⣝⣷⣾⣷⣽⣿⣿⣿⣿⣯⢿⣷⣟⣯⠟⣦⡟⡶⣇⡘⢡⠒⡎⠡⠀⠉⢢⠙⣈⡝⠘⡤⢓⡸⢉⡏ ⣿⣿⣿⣿⣷⣶⣠⣤⣾⣿⣯⢢⢹⣿⣯⡿⣧⣳⢭⢖⡱⢎⡐⣂⠒⡔⢢⡱⡜⣺⡱⢧⣟⡿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣶⣯⢃⣾⠟⢉⣰⢋⠀⣰⡿⢙⢠⠁⣵⢳⡁⢸⠀⢳⠈⣿⡮⣦⠈⠢⢄⠈⣆⠣⢙⠊⢷⢀⡀⠀⡙⠿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣟⡿⣳⢟⡮⣟⢣⠽⣱⢦⣙⡡⢎⠰⢡⡉⢀⠂⠂⠁⢠⠡⢌⡁⢎⡱⢎ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⢾⡿⣯⣿⣻⡽⣯⢾⡽⣎⠷⣍⡳⣜⡡⢧⣱⢣⡝⣿⣾⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢷⣿⣷⣾⣿⢣⠞⡠⣹⠓⡏⢃⡜⡝⡿⡷⣸⡆⠈⠇⠈⢧⠘⣶⠰⣌⢳⡀⣄⣚⣮⣭⣷⣽⣿⣟⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⢾⣽⣛⣮⠷⣝⣎⢳⢧⠞⣤⠣⢌⡡⢃⠔⡀⠁⢁⡘⡀⠂⠄⡈⠒⠄⠫ ⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣳⡿⣿⣽⣿⣞⣽⡻⣍⡳⡍⢎⡱⢆⡻⢼⣳⣿⣿⣿⣿⣿⣿⣿⣾⣿⣻⣯⣷⡿⣟⣾⣿⣿⣿⣿⣳⣎⠖⣡⠁⠦⠐⢸⠇⣰⣗⣧⡗⡹⢤⠀⣄⣈⣧⣼⣷⣽⣶⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣞⣷⣚⢿⡜⣮⢇⠯⣛⡴⣋⢦⠑⡌⠰⢀⠡⠂⡔⠠⢉⠠⠐⡀⣀⠱ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣟⣾⣳⣏⢷⡹⣎⠵⣣⣝⡾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣽⣿⣿⣿⣿⣿⣿⣷⣚⡝⣲⠍⠂⠡⢈⣶⣻⠶⠛⠛⠛⢷⣮⡐⡈⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣟⣾⣭⢿⣾⡱⣏⡾⣱⢞⡱⣊⠓⣈⢆⣈⡠⠅⠄⡁⠆⣆⠡⣓⠠⡜ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣯⣷⡻⣜⣯⡷⣾⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣷⡹⣎⣱⣒⢤⣤⣋⡞⣡⣢⠄⠐⠒⢣⡻⣿⣶⣤⡀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣟⣾⣻⢾⡽⢧⣛⡥⢯⡳⣍⢪⢅⡶⢢⠎⡘⠀⠒⣈⡤⢳⡼⣧⡷
𓂸⠀⠀⠀⣴⣾⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⢿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⣉⣩⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣼⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣼⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣾⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⣾⣿⣿⠉⣿⣿⣿⣿⣿⡄⠀⢀⣠⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠙⣿⣿⣧⣿⣿⣿⣿⣿⡇⢠⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣷⠸⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⠿⢿⣿⣿⣿⣿⡄⠙⠻⠿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡟⣩⣝⢿⠀⠀⣠⣶⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣷⡝⣿⣦⣠⣾⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⣮⢻⣿⠟⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠻⠿⠻⣿⣿⣿⣿⣦⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⠇⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⡆⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⠇⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠀⠀⠀⢀⣴⣿⣿⣿⣿⣟⣋⣁⣀⣀⠀ ⠀⠀⠀⠀⠀⠀⠹⣿⣿⠇⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣿⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣿⣶⣦⡀⢀⣾⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣀⣤⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⣱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢸⣿⣿⣿⣿⣿⣿⣿⠟⣀⣴⣾⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⣱⣿⣿⣿⣿⣿⣿⠟⢛⣉⣉⣉⣉⣙⣛⣛⠛⣿⣿⣿⣿⢃⡈⣿⣿⣿⡟⡉⣉⣵⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣱⣿⣿⣿⣿⣿⡿⢡⣾⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⡟⣸⣷⠸⣿⣿⢱⣿⣿⣿⣿⣿⣿⣿⡿⠻⢿⣿⣿⣿⣿⣷⣄⠀ ⣀⣤⣤⣤⣤⣤⣤⣤⣤⣴⣿⣿⣿⣿⣿⡟⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢰⣿⣿⣿⣧⣭⣛⣁⣙⣋⣘⠻⣿⣿⣿⣿⣿⠟⠀⠀⠀⠙⢿⣿⣿⣿⣿⣧ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⣸⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⡿ ⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⠟⢹⣶⣶⣝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⡟⢰⡌⠿⢿⣿⡾⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⢸⣿⣤⣒⣶⣾⣳⡻⣿⣿⣿⣿⡿⢛⣯⣭⣭⣭⣽⣻⣿⣿ ⣿⣿⢸⣿⣿⣿⣿⢿⡇⣶⡽⣿⠟⣡⣶⣾⣯⣭⣽⣟⡻⣿⣷⡽ ⣿⣿⠸⣿⣿⣿⣿⢇⠃⣟⣷⠃⢸⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣇⢻⣿⣿⣯⣕⠧⢿⢿⣇⢯⣝⣒⣛⣯⣭⣛⣛⣣⣿⣿⣿ ⣿⣿⣿⣌⢿⣿⣿⣿⣿⡘⣞⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣦⠻⠿⣿⣿⣷⠈⢞⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣗⠄⢿⣿⣿⡆⡈⣽⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⡿⣻⣽⣿⣆⠹⣿⡇⠁⣿⡼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟ ⠿⣛⣽⣾⣿⣿⠿⠋⠄⢻⣷⣾⣿⣧⠟⣡⣾⣿⣿⣿⣿⣿⣿⡇ ⡟⢿⣿⡿⠋⠁⣀⡀⠄⠘⠊⣨⣽⠁⠰⣿⣿⣿⣿⣿⣿⣿⡍⠗ ⣿⠄⠄⠄⠄⣼⣿⡗⢠⣶⣿⣿⡇⠄⠄⣿⣿⣿⣿⣿⣿⣿⣇⢠ ⣝⠄⠄⢀⠄⢻⡟⠄⣿⣿⣿⣿⠃⠄⠄⢹⣿⣿⣿⣿⣿⣿⣿⢹ ⣿⣿⣿⣿⣧⣄⣁⡀⠙⢿⡿⠋⠄⣸⡆⠄⠻⣿⡿⠟⢛⣩⣝⣚ ⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣤⣤⣾⣿⣿⣄⠄⠄⠄⣴⣿⣿⣿⣇ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠛⠿⣿⣫⣾
⣿⣻⢿⣹⢯⣻⢽⣫⠿⣽⢯⡿⣽⡻⣿⣿⣿⣿⣻⢯⢿⣝⡯⣟⡽⣏⡿⣝⡯⢿⡽⢯⡿⡽⣯⢿⡽⢯⡿⣽⣻⢿⣿⣿⠿⣽⢯⣟⡽⣏⡿⣝⣯⠿⣽⢯⡿⣽⣻⣽⣻⣽⣻⢿⣿⣟⣯⠿⣽⢯⣻⢽⣫⢿⣹⢯⣟⡽⣯⣟⣯⠿⣽⣻⡽⣿⣿⣿⣻⡽⢯⣿⣹⢯⣻⢽⣫⠿⣽⢯⣟⣯⠿⣽⢯⣟⣯⣟⣿⣿⣿ ⣟⡷⣯⣛⡾⣝⡾⣭⣟⣳⢯⡷⢯⣽⣳⣿⣾⣟⡷⣯⣟⣮⡽⣞⡽⣞⡽⣞⣽⣛⡾⢯⣷⣻⢽⡾⡽⣯⢷⢯⡽⣿⣻⣾⢿⣝⣯⢾⡽⣞⡽⣽⣚⡿⣽⠾⣝⡷⣽⢶⣛⣶⡿⣿⢻⣾⣭⢿⡽⣳⢯⡷⣫⢷⣛⡾⣞⣽⣳⢾⣭⣟⡷⣫⣽⣻⣾⢷⡯⣽⣻⢶⢯⣳⢯⣏⣷⣻⡽⣾⣹⡞⣿⡽⣾⣹⢶⣻⣾⠟⣾ ⣯⣟⡾⣝⣳⢯⣳⣏⡾⣝⣻⣞⢿⣚⡷⣿⣻⡾⣽⢶⣻⣼⣳⢯⡽⣞⡽⣞⡵⣯⣻⢟⡶⣯⢟⡾⣽⣳⢯⡿⣽⣿⣟⣯⣟⡾⡽⡾⣽⣝⣯⠷⣏⡿⣞⣿⣹⡽⣞⣯⣿⣿⠟⢡⠺⣿⣞⣯⡽⢯⣷⢻⣭⢷⢯⣷⢻⣮⣽⣳⢯⡾⣽⣳⢯⣿⣻⣯⣞⡷⢯⣻⣏⣷⣻⢮⢷⣻⣼⣳⢯⣽⣳⢯⡷⣯⣿⠿⡁⢎⣹ ⡷⣯⡽⣯⡽⣞⣳⠾⣝⣯⢷⣞⣯⢟⡽⣿⣻⡽⣏⣯⢷⣳⣻⢞⣳⢯⣳⢯⣽⣳⢯⣻⡽⣞⣯⠿⣵⢯⣟⣾⡿⢃⢿⣷⣯⣽⢻⣽⣳⢾⣭⢿⡽⣽⡞⣧⢿⣽⣟⡿⣻⣴⣌⣆⠒⢻⣿⡾⣽⣛⣾⣛⡾⢯⣻⣼⣻⢮⣗⣯⢷⣻⣳⣿⣿⠟⡉⢿⣾⣽⢯⡷⣻⣼⣳⢯⣟⣧⢷⢯⣟⣞⣷⣿⡿⠟⢡⢂⡑⢢⣿ ⣿⣳⣻⣵⣻⢽⣫⢿⡽⣞⣯⣞⡾⢯⡿⣽⣿⣽⣛⡾⣽⡳⣯⠿⣭⢷⡯⣟⡾⣵⢯⣷⢻⡽⣞⣻⡽⣾⣻⠟⡁⠆⡌⠹⢿⣾⣟⣶⢯⣟⣞⣯⣞⣷⣻⣽⣿⠿⠋⡔⣿⣿⣿⣿⣿⠠⢻⣿⣷⣻⢮⣟⡽⣯⢷⣳⢯⣟⡾⣞⣯⣿⡿⢋⣴⣾⣦⠡⣛⡿⣿⣽⣷⣳⣯⣟⡾⣞⣯⣿⣾⠿⢛⣱⣿⣿⣦⡆⣌⣿⣿ ⣿⣳⡽⣶⢯⣻⣭⢷⣻⡽⡶⢯⣽⢯⣿⣿⠞⣿⣽⣯⢷⣛⣷⣻⡽⢯⡾⣝⡷⢯⣻⡼⣯⣻⣽⣳⣿⠿⣉⣿⣿⣷⣾⣷⡎⣙⣿⠿⢿⣾⢿⣾⢿⠿⢛⢫⣴⣬⣵⣤⣿⣿⣿⢿⣟⠠⢃⣩⣿⡻⣿⣾⢿⣽⣯⣿⢿⡾⠿⢟⡛⡡⢐⢂⣿⣿⣿⣷⣿⣿⣧⢉⠛⣝⡻⠟⠟⡛⢋⣍⠰⣈⢲⣿⣿⣿⣿⣿⣿⣿⣿ ⠿⣟⣷⣯⣻⡵⣯⣻⢧⣿⣽⣿⣿⠿⢋⠅⢢⡉⠿⣿⣯⡿⣶⣯⡽⣯⣻⡽⣞⣯⢷⣻⣵⣿⣾⢟⣭⣶⣤⣿⣿⣿⣿⡿⣱⠟⠉⠛⢶⣄⣦⣴⡂⠜⡠⣿⣿⣿⣿⣿⡿⣿⣾⣿⣏⣴⣿⣿⣿⣷⡔⢨⠉⣌⣵⣬⣁⠆⡑⣾⣿⣿⣿⣾⣿⣿⣻⣿⣟⣿⣿⣆⣱⣾⣿⣷⠨⣴⣿⣿⣷⣦⣿⣿⣿⣿⣾⣿⣯⣷⣿ ⣷⡘⠫⢟⡷⣿⣟⡿⠿⢛⢋⣵⣶⣬⣆⡘⢤⣿⣷⣶⣽⡇⠀⠉⠻⢷⣯⣷⣿⢾⣿⣿⠟⡋⠔⣺⣿⣿⣿⡿⣿⣷⣿⣶⠏⠀⠀⡀⠀⠉⠻⣿⣿⣷⣰⣿⣿⣿⣾⣿⢿⣿⣿⣻⣿⣿⡿⣿⣽⣿⣿⣆⣱⣿⣿⣿⣿⣶⣭⣿⣿⣿⣻⣿⣷⣿⣿⣟⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⢿⣿⣾⣿⣷⣿⣿⣿ ⣿⡅⢃⠆⣴⣾⣿⣿⣆⠡⢺⣿⣿⣿⣿⣿⣾⣿⣿⣿⡿⡇⠀⠀⠀⠀⠉⠛⠿⣴⣿⣿⣿⣷⣎⣼⣿⡿⣷⣿⣿⣿⣻⡏⠀⠀⡘⠈⠢⡀⠀⠈⠙⢿⣿⣿⣿⣯⣿⣿⣿⣿⣻⣿⡿⣷⣿⣿⡿⣿⣽⣿⣿⣿⣟⣯⣿⣿⢿⣟⣯⣿⣿⣿⣽⣿⣾⣿⣿⣯⣿⣿⢿⣷⣿⣿⣽⣿⣷⣿⣿⣿⣾⣿⣿⣻⣷⣿⡿⣷⣿ ⣿⡇⣬⣾⣿⣿⣿⢿⣿⣧⣽⣿⣿⢿⣾⣿⣿⣽⣷⣿⣷⣧⠀⠀⠀⡀⠀⠀⠀⠀⠉⠻⠿⣿⣿⣿⣟⣿⣿⣿⣯⣿⣿⡇⠀⠀⡅⠀⠀⠈⠂⢄⠀⠀⠈⠛⠿⣿⣿⣷⣿⡿⣿⣟⣿⣿⣿⣻⣿⣿⣿⣯⣷⣿⣿⣿⢿⣻⣿⣿⣿⡿⣿⣾⣿⣟⣯⣿⣾⣿⣟⣿⣿⡿⣿⣾⣿⣿⣽⣿⣿⣾⣿⣿⣽⣿⣿⣻⣿⣿⣿ ⣿⣿⣿⣿⡿⣿⣾⣿⣿⢿⣿⣟⣿⣿⣿⣷⣿⡿⣟⣿⣿⣿⡀⠀⠀⢩⠐⠤⢀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠷⠿⠿⠿⠇⠀⠀⠀⠀⠀⡀⠀⠀⠁⠢⢄⡀⠀⠀⠙⠻⣿⣿⣿⣿⢿⣯⣿⣿⢿⣷⣿⡿⣿⣻⣽⠛⠛⢿⣿⣿⣾⣿⣿⣿⣽⣿⣿⡿⣿⣽⣿⣿⣻⣿⣿⢿⣷⣿⡿⣿⣾⣿⣷⣿⣿⣯⣿⣿⢿⣷⣿ ⣿⣿⡿⣷⣿⣿⣿⣯⣿⣿⡿⣿⣿⢿⣾⣿⣟⣿⣿⣿⣟⣿⣧⠀⠀⠀⢇⠀⠀⠈⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠠⠀⠀⠀⠈⠑⠠⢀⠀⠀⠙⠻⣿⣿⣿⣟⣿⣿⣿⣻⣿⣿⣿⠃⠀⡀⠀⠈⠙⢿⣿⣷⣿⡿⣿⣾⣿⣿⣿⣯⣿⣿⣟⣿⣿⣿⣻⣿⣿⢿⣷⣿⣿⣾⣿⣟⣿⣿⡿⣿ ⣿⣿⣿⣿⢿⣿⣾⣿⣟⣿⣿⣿⢿⣿⣿⣯⣿⣿⣿⣽⣿⣿⣿⣆⠀⠀⠈⢆⠀⠀⠀⠀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠐⠀⠀⠀⡀⠄⠀⠀⠀⠀⠈⠢⢀⠀⠈⠛⢿⣿⣿⣯⣿⣿⣿⣽⡏⠀⢠⠀⠑⠠⡀⠀⠙⢿⣿⣿⣿⣟⣯⣷⣿⣿⣿⣽⣿⣿⣯⣿⣿⣟⣿⣿⡿⣿⣾⣿⣯⣿⣿⣟⣿⣿ ⣿⣿⣿⣾⣿⣿⣯⣿⣿⢿⣿⣾⣿⣿⣷⣿⣿⣷⣿⡿⣿⣾⣿⣿⣷⡀⠀⠀⢁⣤⣬⣀⠀⠀⠀⠀⢀⠈⠀⠀⠄⠀⠀⢂⣤⠟⢻⡀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠂⠀⢀⠀⠀⠑⠤⡀⠀⠙⢿⣿⣿⣷⣿⡿⠀⢀⠇⠀⠀⠀⠈⠢⡀⢠⣿⣿⣯⣿⣿⣿⢿⣷⣿⡿⣿⣾⣿⣿⣽⣿⣿⣻⣿⣿⢿⣷⣿⣿⣯⣿⣿⣿ ⣿⣿⣯⣿⣿⣷⣿⣿⣻⣿⣿⣻⣽⣷⣿⣿⣾⣿⣟⣿⣿⣿⣽⣿⣿⣿⣦⠶⠋⠀⠀⠉⠳⢦⣀⠈⠀⠀⠀⡀⠀⠠⢀⡞⠁⡌⠈⢷⡀⠀⠠⠀⠀⠀⠄⠈⠀⠀⢀⠀⠀⠀⡀⠀⠈⠢⡀⠀⠙⢿⣿⣿⡇⠀⡘⠀⠀⠀⠠⠀⢀⣴⣿⣿⣿⡿⣿⣽⣾⣿⣿⣟⣿⣿⡿⣷⣿⣿⣯⣿⣿⣟⣿⣿⡿⣿⣾⣿⢿⣷⣿ ⣿⣿⣿⣻⣷⣿⣿⣽⣿⣿⣻⣿⣿⢿⣯⣿⣿⣽⣿⡿⣿⣾⣿⣿⣽⠟⠁⠀⠀⠀⠀⠀⠀⠀⠉⠛⢦⣄⡀⠀⠀⢀⡾⠀⡘⠀⠀⠘⢷⡀⠀⠀⠀⠂⠀⠀⠀⠄⠀⠀⠀⠄⠀⠀⠀⠀⠈⢂⠀⠀⢻⣿⠀⢀⠃⠀⠀⠠⢀⣤⣿⣿⣿⣿⡿⣿⣿⡿⣿⣻⣽⣿⣿⣻⣿⣿⢿⣷⣿⣿⣯⣿⣿⣟⣿⣿⣟⣿⣿⡿⣿ ⣿⣿⣟⣿⣿⢿⣾⣿⣿⣽⣿⣿⣻⣿⣿⣿⣽⣿⣟⣿⣿⣿⣷⠟⠁⠀⠀⠀⡠⠤⠀⡀⠀⠀⠀⠀⠀⠈⠙⢶⣄⣸⠁⠀⠇⠀⠀⠀⠈⢳⡄⠀⠁⠀⠀⠐⠀⠀⠀⠀⠂⠀⠀⠀⠁⠀⢀⠀⢆⠀⢸⣿⠀⡘⠀⠀⢠⣴⣾⣿⣿⣿⣿⣻⣿⣿⣟⣿⣿⣿⣿⣿⣽⣿⣿⣻⣿⣿⢿⣾⣿⣿⣽⣿⣿⣻⣿⣿⣻⣿⣿ ⣿⣿⣿⢿⣻⣿⣿⢿⣾⣿⣿⣽⣿⡿⣷⣿⣿⣯⣿⣿⣿⡾⠃⠀⠀⠀⢀⠔⠀⠀⠀⠀⠀⠂⠄⡀⠀⠀⠀⠀⠙⠛⠀⠰⠀⠀⠀⠂⠀⠀⠹⣦⡀⠐⠈⠀⠀⢀⠈⠀⠀⢀⠀⠁⠀⢀⠀⠀⠸⠀⢸⣷⠀⠃⣠⣶⣿⡿⣿⣿⣿⣿⣽⣿⣿⣽⣿⣿⣯⣷⣿⣿⣻⣯⣿⣿⣟⣿⣿⡿⣿⣾⣿⣿⣽⣿⣿⣽⣿⡿⣿ ⣿⣿⣿⣿⣿⣿⣻⣿⣿⢿⣾⣿⣟⣿⣿⡿⣷⣿⣿⣻⠟⠀⠀⠀⠀⡰⠁⠀⠀⠀⡀⠄⠀⠀⠀⠀⠁⠢⠄⡀⠀⠀⠀⠘⠀⠀⢀⠀⠄⠂⠀⠈⠳⣤⡀⠀⠠⠀⠀⠀⠠⠀⠀⠀⠠⠀⠀⠀⠀⠄⢸⣯⣴⡾⠟⠋⠁⠀⠘⢿⣿⣾⣿⣿⣽⣿⣿⣾⣿⢿⣻⣽⣿⣿⣿⣽⣿⣿⣻⣿⣿⢿⣷⣿⡿⣿⣾⣿⣟⣿⣿ ⣿⣿⣷⣿⣿⣽⣿⣿⣻⣿⣿⣯⣿⣿⣟⣿⣿⣿⣽⠏⠀⠀⠀⢠⠊⠀⠀⠀⠀⠄⠀⠀⠀⠐⠀⠀⡀⠀⠀⠈⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡀⠀⠈⠻⣦⠀⠀⠀⠐⠀⠀⠀⠐⠀⠀⠀⠈⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣾⣿⣿⣾⣿⢿⣿⣿⣿⢿⣷⣿⣿⣯⣿⣿⣟⣿⣿⣿⣻⣿⣿⣿⣽⣿⡿⣿ ⣿⣿⣿⣽⣾⣿⣿⣽⣿⡿⣷⣿⣿⣯⣿⣿⢿⣾⠋⠀⠀⠀⡰⠁⠀⠀⠀⠐⠀⠀⠀⠀⠂⠀⢀⠀⠀⠀⡀⠄⠀⢀⠀⠀⠄⠀⠀⠀⠐⠀⠁⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢀⠈⠀⠀⢀⠈⠀⠀⡀⠀⠀⡀⠀⠀⡀⠄⠐⠀⠀⠀⠈⠻⣿⣿⣾⣿⢿⣿⡿⣿⣾⣿⣿⢿⣾⣿⣿⣽⣿⣿⣯⣿⣿⢿⣷⣿⣿⣻⣿⣿ ⣿⣿⣟⣿⣿⢿⣾⣿⣟⣿⣿⡿⣷⣿⣿⣻⣿⠋⠀⠀⠀⡐⠁⠀⠀⠀⠂⠀⠀⠄⠈⠀⠀⢀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⡀⠄⠈⠀⠀⠀⡀⠀⠁⠀⠀⠄⠂⠀⠀⠄⠀⠀⠀⠠⠀⠀⠀⠀⠀⢀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣟⣯⣿⣿⣿⢿⣾⣿⣿⣾⣿⣟⣿⣿⣿⣯⣿⣿⣟⣿ ⣿⣿⣿⢿⣻⣿⣿⣯⣿⣿⣟⣿⣿⣿⣽⣿⠏⠀⠀⠀⡜⠀⠀⠀⠀⠂⠀⠀⠄⠀⠀⠠⠀⠀⠀⠀⠄⠀⠀⠀⠂⠀⠈⠀⠀⠀⠀⠀⢀⠀⠁⠀⠀⠀⠐⠀⠀⠀⢀⠀⠀⠀⠄⠂⠀⠀⢀⠈⠀⠀⣀⣠⡴⠶⠆⠀⠀⠀⠁⠀⠀⠀⡀⠀⠀⢀⣠⣴⣿⣿⣯⣿⣿⣿⣯⣿⣿⣿⢿⣾⣿⣯⣿⣿⢿⣾⣿⣿⣽⣿⣿ ⣿⣿⣿⣿⣿⣿⣯⣿⣿⣯⣿⣿⢿⣾⣿⡏⠀⠀⠀⡜⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⡀⠁⠀⠀⠄⠐⠀⠀⠐⠈⠀⠀⠀⢀⠀⠁⠀⠀⠀⠂⠀⠀⠀⠂⠀⠀⠀⠄⢀⣠⡴⠛⠋⠁⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣟⣿⣽⣾⣿⣟⣿⣾⣿⣿⣯⣿⣿⣻⣿⣿⢿⣾⣿⣟⣿ ⣿⣿⣷⣿⣿⣾⣿⢿⣷⣿⣿⣻⣿⣿⡿⠀⠀⠀⠰⠐⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⢀⠀⠠⠀⠀⠀⠀⠄⠀⠀⠀⠄⠀⠀⢀⠠⠀⠀⠀⢀⠀⠈⠀⠀⠀⠐⠀⠀⠀⣐⣤⠞⠋⠁⠀⠀⠀⠀⠀⡀⠄⠀⠀⠀⠀⢀⣤⠶⣿⣿⣿⣿⣿⣿⣻⣽⣿⣿⢿⣟⣯⣿⣿⣿⣻⣷⣿⣿⣿⣿⣿⣻⣿⣿⣯⣿⣿ ⣿⣿⣿⣽⣾⣿⡿⣿⣿⣯⣿⣿⣟⣿⡇⠀⠀⠀⠀⢀⣠⣴⣶⣾⣿⣿⣿⣿⡟⠁⠀⡔⠁⠀⠀⠀⠀⠀⡀⠐⠀⠀⠀⠐⠀⠀⠀⠈⢀⣀⣠⣤⣤⣤⣄⠀⢀⠈⠀⣴⡿⣦⡾⠋⠀⠀⠀⠀⡀⠄⠂⠈⠀⠀⠀⠀⢀⣠⠶⠋⠁⠀⣿⣿⣿⢿⣷⣿⣿⣿⣟⣿⣿⣿⣿⣿⣯⣿⣿⣿⣯⣷⣿⣿⣿⣿⢿⣷⣿⡿⣿ ⣿⣿⣟⣿⣿⣻⣿⣿⣿⣽⣿⣯⣿⣿⠀⣀⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⢀⠜⠀⠀⠀⠀⠂⠁⠀⠀⠀⠀⡀⢈⣀⣤⠶⠞⠛⠉⠉⠀⠀⠀⠀⠙⢧⡀⢠⡾⣟⡾⠋⢷⡀⠀⠀⠀⠄⠀⠀⠀⠀⢀⠠⠀⠀⣼⢁⣠⣴⠀⢠⣿⣿⣿⣿⡿⣿⣽⣾⣿⡻⣽⢻⣼⣳⣏⡿⣽⣫⣟⣿⣿⣿⣿⣿⣿⡿⣟⣿⣿ ⣿⣿⣿⢿⣻⣿⡿⣷⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣟⣿⣽⣷⣿⠁⠀⡌⠀⠀⠀⠀⠁⠀⠀⡀⢄⣢⡵⠞⠋⠉⠀⠀⣀⠠⠤⡔⠂⠈⠀⠢⠀⠈⠛⢯⡼⠋⡀⢄⠀⠻⣆⠀⠀⣠⡾⢷⡀⠀⠀⠀⠀⢰⣟⠋⢠⠇⠀⢸⣿⣿⣿⣷⣿⣿⣿⡿⠗⠿⣭⣟⡞⢹⡾⡽⣶⣛⣾⣟⣾⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⡿⣿⣿⢿⣷⣿⣿⣯⣿⣿⢿⣿⣻⣯⣿⣾⣿⣿⣿⡿⣿⡏⠀⡘⠀⠀⠀⠐⠀⠀⠠⢠⡾⠋⠁⠀⢀⠠⠔⠈⠁⠀⠀⠀⢳⣰⠀⠀⠀⠑⠄⣴⣿⣿⠈⠀⠀⠣⡀⡘⣷⣼⠋⠀⠀⢻⣆⠀⠀⠂⡿⢻⣄⡞⠠⢄⣾⣿⣿⣟⣿⣿⣿⠟⠁⠐⡄⠀⡙⠀⠀⣿⡽⣶⣻⣷⡿⣾⣽⣿⣿⣿⣻⣿⣿⣿ ⣿⣿⣷⣿⡿⣿⣿⢿⣿⡿⣿⣾⣿⣟⣿⣿⣿⢿⣿⣟⣿⣯⣿⣷⣿⣿⠀⢀⠃⠀⠀⠠⠀⣀⣦⣶⣾⣿⡀⠐⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⡇⠀⠀⠀⠙⢴⡨⢅⠂⣀⠤⡀⠹⣦⠀⣸⡇⠈⠛⠁⠀⣼⣿⣿⣿⢿⣿⣿⣁⣀⡀⠀⠙⣦⠀⢀⣀⠈⣿⣵⣿⢿⣽⣳⢯⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣽⣿⣿⡿⣿⣿⣿⣿⣿⣽⣿⡿⣿⣾⣿⣿⢿⣿⣻⣿⣟⣿⣿⠀⡘⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⣿⣿⣿⣿⣿⠀⢶⡞⠛⠛⢳⣎⠴⠁⠀⠈⢄⢙⣧⣿⣷⡀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⠟⢁⣠⡖⠺⣿⣍⢹⣶⡟⢟⠛⡿⢾⣽⣿⠋⣿⢿⣿⣿⣿⣿ ⣿⣿⣯⣿⣿⣷⣿⣿⣿⣾⣿⣽⣿⣟⣿⣿⣿⣯⣿⣿⣿⡿⣟⣿⣿⣿⠀⣡⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠤⣤⣤⣄⣀⣀⣀⠀⠀⠀⠀⠀⢠⠏⠀⠘⣿⣿⢿⣿⠀⢸⡇⠀⠀⠈⣹⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣄⣰⣿⣿⣿⣿⣯⢿⣿⣿⣿⣾⡿⠿⠃⠀⢻⠈⠉⢻⢡⣼⡞⠙⣦⣜⡿⣼⣿⣿⣶⣾⣿⣿ ⣿⣿⣿⣿⣷⣿⣿⣿⣾⣿⣟⣿⣯⣿⣿⢿⣾⣿⣟⣿⣾⣿⣿⣿⢿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⡞⠛⠀⠀⠀⠈⠛⠋⠁⣠⠟⠀⠀⢐⡶⠃⠀⢀⣴⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣋⠹⣷⣦⣤⣄⣠⡨⡭⡭⢿⣿⠒⠋⢁⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⢿⣻⣿⡿⣿⣿⣯⣿⣿⣟⣯⣿⣾⣿⣿⣿⣿⡿⣿⣿⢿⣟⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⣀⡴⠋⠀⣀⡴⠋⠀⣠⣴⣿⣿⣿⣿⢿⣷⣿⣿⣟⣿⣿⣻⣿⣿⣿⣿⡿⠋⠁⠀⣧⣉⣿⠿⣛⡿⢗⣯⠤⢤⠀⢢⡀⠀⢻⣿⣿⣯⣷⣿⣿⣻⣿ ⣿⣿⣿⢿⣻⣿⣿⣽⣿⣟⣿⣿⣿⡿⣿⣿⣿⣽⣿⣯⣿⣿⡿⣟⣿⣽⣾⣿⣿⣿⢿⣿⣿⡿⠁⠀⠀⠀⠀⢹⠀⡀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠶⠶⠿⠷⠒⠋⠉⠁⣀⡤⣾⣿⣿⣿⣿⣟⣿⣿⣿⣯⣿⣿⢿⣻⣿⣿⣽⣿⣿⠀⡠⢴⠁⢀⢜⣣⡼⡁⠀⠯⢈⠦⠋⠀⢈⡀⠙⣿⣿⣿⣻⣿⣿⣽⣿⣿ ⣿⣿⣿⣿⣿⣿⣽⣿⣯⣿⣿⢿⣷⣿⣿⣿⣾⣿⣟⣿⣿⣽⣿⣿⣿⡿⣿⣿⣾⣿⣿⣿⣻⣷⣄⠀⠀⠀⠀⠀⠓⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠋⠉⠀⣿⣿⣿⣿⣽⣿⡿⣿⣾⣿⣟⣿⣿⣿⣿⣯⣿⣿⣿⣷⣷⣌⡒⢁⣾⣭⣿⣿⣷⣶⣶⣤⣤⣶⢾⡹⢖⣺⣿⣿⣿⣿⣽⣿⣯⣿ ⣿⣿⣿⣿⣽⣾⣿⣟⣿⣿⣻⣿⣿⣿⣽⣾⣿⣯⣿⣿⣻⣿⣯⣿⣷⣿⣿⣿⣽⣷⣿⡿⣿⣿⣿⣷⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⡤⠴⠚⠋⠁⠀⠀⣀⠀⠀⠹⣿⣿⣯⣿⣿⣿⣿⣿⡽⠿⣿⣯⣷⣿⣿⢿⣷⣿⡿⣿⣿⣿⡿⣟⠺⢷⣿⣟⡿⣿⣮⣵⡿⣿⣾⣼⣿⣿⣿⣿⣯⣿⣿⣻⣿ ⣿⣿⣿⣯⣿⣿⣟⣿⣿⣻⣿⡿⣷⣿⣿⣟⣯⣿⣿⣟⣿⣿⣻⣿⣽⣿⣿⣾⣿⢿⣻⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠘⣇⡄⠀⠈⢻⠿⠛⠛⠉⠁⠀⠀⡀⠤⠈⢙⠻⢿⣿⣿⣻⣿⣿⣻⡽⣯⣯⣿⣿⣻⣾⣽⣿⢿⣽⡯⣕⣛⢯⡉⢿⡽⣿⢿⣿⣽⣿⣿ ⣿⣿⣿⣿⣿⣽⣿⣿⣻⣿⣟⣿⣿⣿⣽⣿⣿⢿⣯⣿⣿⣟⣿⣿⣟⣿⣾⣿⢿⣿⣿⡿⣷⣿⣿⣯⣿⣿⣻⣿⣿⣿⣿⣿⣿⠿⠛⠉⠉⠉⠉⠻⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⣴⠏⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠈⠐⢿⣿⣿⣏⠓⠛⠻⠿⠟⣛⣭⣤⣤⣤⣴⢿⣯⢷⡶⣿⣻⣟⣿⡽⠏⣸⣿⣿⣯⣿ ⣿⣿⡿⣷⣿⣿⣯⣿⣿⣟⣿⣿⢿⣾⣿⣟⣿⣿⣿⣟⣯⣿⣿⣯⣿⣿⣟⣿⣿⣿⣻⣿⣿⢿⣷⣿⣿⣻⣿⡿⣷⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⢤⣄⣀⣀⠀⢀⣀⣠⡤⠶⠋⠁⠀⠀⠀⠀⢀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣦⣍⣉⣛⣓⣋⣉⣥⣴⣾⣿⣿⣿⣽⣿ ⣿⣿⣿⣿⢿⣷⣿⣿⣯⣿⣿⢿⣿⣿⣯⣿⣿⢿⣾⣿⣿⣿⣯⣿⣿⣽⣿⣿⣯⣿⣿⣟⣿⣿⣿⣯⣿⣿⣟⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣟⣿⣿⣻⣿⣟⣯⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣾⣿⣿ ⣿⣿⣿⣾⣿⣿⢿⣾⣿⣟⣿⣿⡿⣷⣿⣿⣻⣿⣿⣯⣷⣿⡿⣿⣽⣿⣿⣾⣿⣿⣽⣿⡿⣿⣾⣿⣿⣽⣿⡿⣿⠋⠀⢀⡆⠀⠀⣀⠄⠐⠂⠈⠉⠀⠀⠀⠀⠀⠈⠀⠀⠒⠂⢄⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⢿⣻⣿⣟⣿⣿⣿⣻⣿⢿⣾⣿⣟⣿⣿⣻⣿⣽⣿⣾⣿⣿⢿⣷⣿ ⣿⣿⣯⣿⣿⣻⣿⣿⣯⣿⣿⣟⣿⣿⣿⣽⣿⡿⣷⣿⣿⣟⣿⣿⡿⣿⣾⣿⣷⣿⣿⣻⣿⣿⢿⣷⣿⣿⣻⣿⠏⠀⢀⡞⠁⡠⠊⠀⠀⠀⣀⣤⠶⠞⠛⠛⠛⠳⣦⡀⠀⠀⠀⠀⠑⠄⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⡿⣿⣿⣯⣿⣿⢿⣿⣿⣯⣿⣿⣟⣿⣿⣟⣿⣽⣿⡿⣿⣿⣿ ⣿⣿⣿⣻⣽⣿⣿⣷⣿⣿⣯⣿⣿⢿⣾⣿⣟⣿⣿⣿⣽⣿⣿⣻⣿⣿⢿⣷⣿⣿⣽⣿⣿⣻⣿⣿⣯⣿⣿⡟⠀⠀⣸⠁⠌⠀⠀⢀⣴⠞⢿⡁⠀⠀⠀⠀⠀⠀⠈⢻⡄⠀⠀⠀⠀⠰⡀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣾⣿⣿⣿⣽⣿⡿⣿⣿⣷⣿⣿⣯⣿⣿⣯⣿⣿⣿⣻⣿⣿⢿⣾ ⣿⣿⡿⣿⣿⢿⣷⣿⣿⣾⣿⣟⣿⣿⣿⣯⣿⣿⢿⣾⣿⣿⣽⣿⣿⣻⣿⣿⢿⣾⣿⣿⣽⣿⡿⣷⣿⣿⡟⠀⠀⣤⠏⡌⠀⢀⣴⠏⠁⠀⠈⠻⣆⠀⠀⠀⠀⠀⠀⢘⡇⠀⠀⠀⠀⠀⡁⠀⢸⣇⠀⠀⠡⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠙⢿⣿⣯⣿⣷⣿⣿⣻⣿⣿⢿⣾⣿⣷⣿⣿⣯⣿⣿⣷⣿⣿⣟⣿⣿⣿ ⣿⣿⣿⣿⢿⣿⡿⣿⣾⣿⣯⣿⣿⢿⣾⣿⣟⣿⣿⡿⣿⣾⣿⣿⣽⣿⣿⣻⣿⣿⢿⣾⣿⣟⣿⣿⣿⠟⠀⢀⣴⠋⢰⠀⢀⡾⠁⠀⠀⠀⠀⠀⠹⣦⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⢀⠃⠀⠀⠙⢷⣄⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠈⠻⣿⣿⣿⣽⣿⡿⣟⣿⣿⣿⣯⣿⣿⣾⣿⢿⣷⣿⣿⣽⣿⣿⣯⣿ ⣟⢻⡛⢾⢻⡛⢿⡛⣟⠳⣟⢻⡛⢿⡛⢯⢟⡻⣛⠿⣛⠟⡷⢻⠟⡯⢟⠿⣛⠿⡻⢟⠯⣟⢿⣋⠀⠀⣠⡞⠁⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠹⣧⠀⠀⠀⣠⡿⠀⠀⠀⠀⠀⡈⠀⠀⠀⠀⠀⠙⡷⣄⡀⠀⠁⠒⠀⠀⠐⠊⠀⠀⠀⣠⣾⠿⡿⢿⢻⠿⢿⠿⡿⠿⡷⢿⠿⣯⠿⡿⢿⠿⡿⢾⠿⡿⢾⠿⡿ ⠊⠑⠘⠁⠃⠘⠁⠚⠈⠓⠈⠃⠙⠂⠙⠈⠂⠃⠁⠋⠌⠙⠈⠃⠛⠈⠋⠒⠉⠒⠉⠊⠑⠊⠊⠛⣶⡶⠋⠀⠀⠀⢠⠀⠘⢷⡀⠀⠀⠀⠀⠀⠀⠀⠸⣇⣠⡾⠋⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⢨⡇⠈⠙⠓⠶⢤⣤⣄⣤⣠⣤⡶⠟⠋⠒⠍⠒⠣⠉⠞⠂⠳⠘⠱⠊⠕⠪⠔⠓⠌⠓⠎⠱⠉⠞⠡⠋⠖⠱ ⠀⡎⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠡⡀⠈⠙⠷⢤⣤⣤⣤⣤⡤⠾⠛⠁⠀⠀⠀⠀⢀⠀⠊⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠼⡑⢆⠀⠀⠀⠀⠀⠀⠀⠀⠈⢁⠂⠀⠀ ⢱⠊⣱⠂⠀⠀⠀⠀⠀⢀⠀⢀⠀⠂⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢀⠔⠒⠒⠂⢛⠀⠁⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡘⠤⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⢊⠄⠀ ⡇⢰⠃⠀⠀⠀⠀⠀⠁⠀⢀⠠⠀⡦⠒⢲⡶⠛⠛⠛⠛⠦⣤⡀⠀⠀⠀⠀⠀⠀⠄⣸⠟⠁⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⡀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⢸⠀⠀⠀⠱⠇⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⢹⡀⠀⠹⣄⠀⠀⠂⠀⠁⠀⠀⠌⢠⠀ ⡤⠓⠈⠀⠀⠀⠀⡀⠀⠄⠠⠐⣸⠀⢰⠏⡇⠀⠀⠀⠀⠀⠈⠙⢷⡄⠀⠀⠀⠀⣼⣯⣤⠴⠶⠶⠛⠛⢛⡏⠍⠉⠉⠁⠁⠀⠀⠀⠉⠈⠉⠉⠉⠉⠙⠛⠲⠶⠤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠠⠀⠀⠀⠀⠈⠀⢣⠌⠀⡘⢦⠀⠀⠀⠀⠀⠀⠈⠀⢂ ⠇⠀⠀⠀⠀⠀⠀⠀⠄⠂⢀⠂⢼⡗⢼⡄⢣⠀⠀⠀⠀⠀⠀⠀⠀⠹⡛⢶⣦⡀⡈⠙⢶⣄⡀⠀⠀⠀⢸⡇⠀⠀⠀⢀⠤⠀⠒⠒⠂⠈⠀⠉⠀⠒⠂⠀⠤⢀⠀⠀⠀⠉⠙⠳⢤⣄⡀⠀⠀⠀⠀⢀⡿⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⢦⠁⠀⠌⢧⡀⠀⠀⠀⡀⠀⠀⠀ ⠀⠀⠈⠀⠀⠀⠀⠂⠠⠈⠀⠀⢾⡇⠙⣿⡄⠓⢄⠀⠀⠀⠀⠀⢀⠴⢁⠂⢹⡿⠋⠙⢦⣈⢹⡷⠦⣤⣸⡇⠀⠀⠌⠀⠀⠀⠀⠀⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠢⡀⠠⡄⠀⠈⠙⠳⢦⣀⠀⠀⣿⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠠⠀⠂⡵⡀⠀⠀⠀⠀⠀⠀ ⠂⠀⠀⠀⠀⢀⠀⠄⠀⡁⢈⠀⠘⣷⠠⠘⣻⣧⣄⡉⠑⠒⠒⢊⠁⢂⣤⣼⠞⠧⣄⠀⠀⠙⢿⣄⡀⠀⠉⣇⠀⢸⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⢳⢠⡄⠀⠀⠀⠉⠛⢦⣿⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠘⣄⠂⢀⠈⢵⢂⠀⠀⠀⠀⠀ ⡀⠀⠠⠀⠂⠀⠀⠀⠀⠐⠀⡀⠀⣿⡅⠂⣿⡿⡍⠛⢳⠻⠶⠷⠚⠛⠉⠀⠀⢀⠈⠉⠒⠦⢤⣈⣉⠛⠶⣿⠀⠸⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠈⠉⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠘⡆⢀⠠⠀⢋⣆⠀⠀⠄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠂⠀⠀⢸⣇⠄⢹⡇⢹⡄⠀⠡⠀⠀⠀⠀⠀⠀⠀⠸⣄⠆⠀⠀⠀⠀⠉⠙⠒⠿⢤⣄⣃⡀⠀⠀⠀⠀⠸⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠘⡆⢀⠠⠀⠎⣥⠀⠀⠀ ⠁⠀⠀⠀⠀⠀⢀⠀⠀⠠⠀⠁⡀⠀⠙⠿⠾⣷⠈⢻⡄⠀⢱⣠⠶⠚⠉⠉⠓⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠒⠲⠦⠤⣄⣀⠀⠀⠀⠀⠀⠀⡀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠹⡀⠄⠐⠀⠱⣋⠄⠀ ⠂⠀⠐⠀⠀⠁⠀⠀⠀⠂⠁⡀⠀⠀⠀⠀⠀⠘⣧⠀⠻⣦⠟⠁⠀⠀⠀⠀⠀⢀⡷⠚⠉⠙⠳⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⠀⠀⠈⠉⠓⢔⠂⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢳⡌⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠙⡄⠠⠁⡀⠌⣋⢆ ⠄⠀⠀⠀⠀⠀⠀⠀⢈⠀⠂⠀⠀⠀⠀⠀⠀⠀⠙⢧⣰⠏⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⢳⠴⠖⠶⣄⠀⠀⠀⠀⠀⣆⡼⠀⠀⠀⠀⠀⠀⠀⠁⠄⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⣇⢸⢄⠀⠀⠀⠀⠀⠀⠀⠀⠠⠹⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠱⣀⠐⠀⡀⠈⠌ ⠀⠀⠀⠀⡀⠀⠀⠁⡀⠐⠀⠁⠀⠀⠀⠄⠂⠀⠀⠈⡿⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⡎⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠈⠉⠀⠢⠀⠀⠀⠀⠀⠀⠀⠸⠀⠘⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡄⠂⢀⠀⠀ ⠁⠀⠈⠀⠀⠀⠠⠀⢀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠄⡀⠀⢀⠠⠊⢘⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠠⠀⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠔⠈⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢸⠀⠀⢹⡄⠀⠀⠀⠀⠀⠈⠢⣀⠀⠀⡀⠔⠁⠀⠀⠙⣷⠀⠀⠂⢀⠀⠀⠀⠁⠀⡠⠀⠀⠱⡀⠂⢀⠀ ⡆⣤⠠⣄⠠⢀⠀⡐⢀⠠⠀⠀⢀⠀⠂⠀⠀⠁⠀⠀⢻⣄⠈⠈⠀⠀⠀⠈⢆⠀⠀⠀⢀⠔⠏⠀⠀⠀⢀⠃⢠⡏⠐⠒⠒⠒⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⡆⠀⠀⢀⠄⠂⢉⢠⠀⠉⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠘⢿⡄⠘⠁⠀⡠⠤⢀⠀⠈⠑⣤⢄⡥⢎⡴⢊ ⡱⣈⠓⠬⡙⢎⡱⢚⠲⢆⡳⢌⢦⡰⡄⢦⡐⣄⡀⣄⣀⡙⠷⣤⣤⣶⠀⠀⠀⠁⠐⠀⠁⠘⡀⠀⠀⡠⠁⢀⣾⣁⣀⣀⣀⣀⣤⣤⠀⠀⠀⠀⠀⠀⣰⠆⠀⠀⠀⠀⠄⠆⠀⠀⠘⣧⠀⢠⠃⠀⠀⠀⠁⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⠀⡀⠁⠀⠀⠀⠀⢀⠀⠘⣎⠒⡩⣐⢩ ⡇⢧⢛⢦⡱⢆⣆⢣⡉⢆⠱⣈⠆⣱⠸⣅⢏⡶⣝⢦⡑⢎⠳⣜⢢⡛⣷⣤⣄⣀⣀⣠⣼⡄⠈⠀⠁⠀⢠⣞⣁⡀⣀⣀⣈⣀⣈⣀⣀⣤⡤⠶⠚⣿⠏⠀⠀⡠⠐⠂⠈⠒⠀⢄⠀⠸⣇⠃⠀⠀⠀⠀⠀⠀⡞⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢸⡄⡁⠀⠀⠀⠀⠀⢈⠀⠀⣯⠳⣱⢩⠖ ⡝⢎⡚⣆⠧⠳⣌⢣⡝⢪⡑⢦⣙⢦⣟⣾⣿⣻⡿⣷⡜⢪⡑⢮⡑⡞⣰⠣⣍⢯⡹⣙⠮⢿⣦⣤⡤⠶⠋⠁⠉⠉⠉⣹⠋⠉⠁⠀⠀⠁⢄⠀⠀⠉⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠡⠀⠹⣆⠀⠀⠀⠀⠀⢸⠁⠀⠀⠁⢢⡀⠀⣠⠄⠀⠀⠀⠀⣰⠆⠀⠀⠀⣿⠀⡀⠸⡇⠐⢀⠀⠀⠀⠀⠈⠀⣼⢣⡛⣤⢋⣾ ⡝⣪⠕⣎⠞⡱⢎⡕⣎⢧⡽⣶⡿⣿⣻⣽⡾⣿⣽⣷⣻⣇⠞⡤⡙⢼⡡⢏⡲⢎⡱⢎⡙⢆⣿⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⢢⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠹⡆⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⡙⢳⡏⠀⣀⣀⠀⠀⣿⢀⣠⠀⠤⡿⠁⠀⠀⣿⣤⡀⠈⠀⠀⠀⣠⠞⣥⢣⠳⣬⣿⣻ ⣿⣦⣙⠦⣋⠵⣋⣶⣽⣾⢿⣻⣽⡿⣽⣷⢿⣯⣷⣯⢷⢯⣟⡴⡩⢆⡱⣋⠴⣋⠼⡱⣚⢤⣿⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡷⠀⠀⠀⠀⠈⢧⡀⠀⠀⢀⠆⢸⠁⠁⠀⠀⠈⠑⣿⠁⠘⠚⠀⣿⠀⠀⢀⣿⣿⣿⣿⣶⣾⣿⣥⣛⣤⣯⣿⣟⣷⣿ ⣿⣯⣿⢾⣵⡿⣟⣯⣿⢾⣿⣻⣽⣟⣿⡾⣿⣽⡾⣯⣟⣻⣞⡷⣝⢦⢣⡹⢜⡡⢏⡕⣎⢖⣿⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠡⡀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⣰⠇⠀⠀⠀⠀⠀⠀⠙⠲⢴⣤⣄⣿⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⣿⠀⢠⣼⣿⡷⣿⣞⣯⣷⡿⣞⣯⣿⢾⣷⣻⣟⣾ ⣿⣷⣻⡿⣯⣿⣟⣯⣿⣻⡷⣟⣿⢾⣯⡿⣟⣾⢿⣳⢯⡷⣏⡿⣽⢮⣧⡜⣣⠝⣮⡼⣞⡿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡄⢀⣀⣀⠠⠊⠀⠀⢀⠀⠀⠈⠂⠄⣀⠀⢀⠠⠐⠁⠀⣴⠏⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠁⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⢠⣿⣿⣿⢿⣯⣿⢷⡿⣯⣷⡿⣟⣯⣿⢯⣿⣽⣯⣿ ⣿⡾⣿⣽⢿⣞⣯⣿⢾⡿⣽⡿⣯⣿⢷⡿⣟⣯⣿⢯⣿⣹⢯⣟⣽⣻⢶⣻⣽⣻⢷⣻⡽⣽⣻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡝⠳⠦⣤⣤⣀⣤⣤⣽⠦⣄⣀⠀⠀⠀⠀⠀⠀⣀⣤⠞⠃⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢤⣀⠀⣀⣠⡴⠻⢲⣤⣴⣶⣿⣿⣻⣾⢿⣳⣿⣻⣿⡽⣷⣿⣻⣟⣾⣿⣻⡾⣷⢿ ⣿⡿⣽⣾⢿⣯⣿⢾⣟⣿⣻⣽⡿⣽⣟⣿⣻⣽⣯⣟⡾⣽⣛⣾⣳⢯⣟⣧⢷⡯⣟⣳⣟⣳⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⣻⠿⡿⢿⡿⣿⡉⠀⠀⠀⠀⠀⠰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠡⢻⣿⡿⣽⣾⢿⣽⡿⣯⣷⢿⣳⣿⣟⣾⢿⣽⣷⣻⣷⢿⣻⣿ ⣿⣟⣿⡽⣿⣳⣿⣻⣯⣿⣽⡷⣿⣻⣽⣯⢿⣳⣿⡽⣯⢷⣻⣞⣭⣟⡾⣭⣟⡾⣽⣳⢯⢿⣹⢿⡄⠀⠀⠀⠀⠀⠀⠀⡄⠀⡄⠀⠀⠀⠀⠀⠀⠀⣸⣯⢗⣯⢻⡝⣧⡻⡽⣿⣄⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠘⡆⣀⠀⠀⠀⠀⠀⠀⠀⠣⢿⣿⢿⣽⣿⣳⣿⢿⣽⡿⣯⣷⢿⣯⣿⣻⣾⢿⣽⡿⣯⣿ ⣿⣿⢾⣟⣿⣽⡷⣿⣳⣿⢾⣟⣿⣽⡷⣿⣻⣟⣷⡿⣽⣫⢷⣻⢾⣭⣟⣷⣫⣟⡷⢯⣟⣯⡟⣿⣧⠀⠀⠀⠀⠀⠀⢠⠠⠄⡇⠀⠀⠀⠀⠀⠀⢠⣿⢧⣻⠼⣧⢻⡵⣫⢷⡹⣿⣧⡄⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣻⡾⣿⡽⣿⣳⣿⢿⣽⣿⣳⣿⣽⡾⣿⣳⣿⢿⣽
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pov: ur stroking ur pussy to some good smut/porn dot art in emojicombos.com. couldnt be me 🥸
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⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣾⡿⠋⠀⠿⠇⠉⠻⣿⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣿⠏⠀⠀⠀⠀⠀⠀⠀⠙⣿⣆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣆⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⡄⠀⠀⠀⢀⣤⣀⠀⠀⠀⠀⣿⡿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠻⣿⣶⣶⣾⡿⠟⢿⣷⣶⣶⣿⡟⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⡏⠉⠁⠀⠀⠀⠀⠉⠉⣿⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⡀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀ ⠀⠀⢀⡇⠀⠀⣿⡇⠀⢀⠀⠀⠀⠀⠀⠀⣿⡇⠀⢸⠀⠀⠀ ⠀⠘⡆⠀⠀⠀⣿⡇⠀⠀⢣⠀⠀⠀⢯⡀⣿⡗⢏⠀⠀⢠⠒ ⠒⠒⡕⠄⡀⠀⣿⡇⠀⠀⣸⣿⠀⠀⠐⠆⣿⡇⠀⠓⡤⠈⡆ ⠀⡸⠀⡄⠈⠁⣿⡇⢀⣴⣿⠇⠀⠴⠀⠀⣿⡇⠉⠁⢀⢠⠃ ⠀⠉⠁⢀⣠⣴⣿⣷⣿⠟⠁⠀⠀⠀⠀⠀⣿⣧⣄⡀⠀⠀⠀ ⠀⢀⣴⡿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠄⠀⢀⠈⠉⠙⢿⣷⣄⠀ ⢠⣿⠏⠀⠀⠄⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣆ ⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠐⠀⠀⢹⣿ ⣿⣇⠀⠀⠀⠄⠀⠀⢸⣿⡆⠀⠀⠁⠀⠀⠀⡀⠀⠂⠀⢸⣿ ⢹⣿⡄⠀⠀⠀⠀⠂⠀⢿⣷⠀⠀⠀⠀⠁⠀⠀⠀⠀⢀⣾⡿ ⠀⠻⣿⣦⣀⠁⠀⠀⠀⠈⣿⣷⣄⡀⠀⠀⠀⠀⣀⣤⣾⡟⠁ ⠀⠀⠈⠛⠿⣿⣷⣶⣾⡿⠿⠛⠻⢿⣿⣶⣾⣿⠿⠛⠉⠀⠀
⠶⠶⣶⣿⣆⠀⠐⠙⠛⠛⠳⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠈⠙⠦⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠉⠉⠑⠒⠲⠤⠤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⣠⠔⠉⠀⠀⠀⠀⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⠒⠤⢄⡀⠀⠀⠀⠤⡀⠀⢶⡏⠀⡰⠁⠄⢀⣀⠀⣀⣀⡤⠤⠂⠀⠰⣄⠁⠀⠀⣀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦⣠⣤⣼⣦⣀⣧⠀⡇⢀⣤⣾⣯⣽⣄⠀⢀⣀⡠⢶⡀⠈⣳⠖⠊⠁⠀⠀⠀⠀ ⠓⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣤⣧⡀⠉⠹⠿⣿⡏⠠⣸⣿⠟⠉⠁⠀⠀⣀⡠⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀ ⣷⣶⣾⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠋⠀⠀⣿⣶⣟⣻⣀⠀⣀⡁⠀⠀⢠⡀⠀⣄⣀⣉⡹⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢥⣤⣤⣤⣤⣬⠹⠛⢶⣦⣤⠤⠤⠴⠖⠒⠉⠁⠀⠀⠀⢀⠟⠉⠉⠉⠙⢠⠋⣹⠆⠀⠘⠓⠾⡩⠟⠉⠀⢰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣶⣦⣭⣽⣛⣛⣿⣿⡴⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⢀⡇⡴⠃⠀⠀⣀⠴⠊⠀⠀⠀⠀⠀⠙⠳⢤⣀⣀⣀⣀⣠⣤⣾ ⠉⠻⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣧⠤⠖⠶⠟⠻⠛⠻⢶⠖⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⢹⣿⠟⠛⠉ ⣦⣄⣈⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣎⠀⠀⠀⠀⠀⠀⣠⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠒⠲⠤ ⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠋⢁⡬⠛⠉⠉⢑⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⡀⠀⠀ ⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⢀⠎⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣷⣄⡀ ⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣸⠀⠀⠀⢠⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣁ ⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢠⡏⠀⠀⣠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠹⡿⣿ ⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡸⣿⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠹⠌ ⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⢻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀ ⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀ ⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⠀⠀⠀ ⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀ ⣿⣿⣿⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀ ⠿⠋⠁⢀⣹⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀ ⢀⡤⠖⠉⠀⠀⠹⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⣬⣿⠷⠶⠶⠤⢤⣤⣤⡤⣤⣹⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⡠⠤⠒⠋⠉⠀⠀⠀⠀⢀⡴⠞⠋⣀⡴⠞⠋⠻⢿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀ ⠒⠁⠀⢀⡀⠀⠀⠀⠀⣠⡴⠞⣉⣠⠴⠚⠁⠀⠀⢀⣴⣿⣿⣿⣿⣶⣦⣤⣤⣀⣤⣤⣤⣤⣶⣿⣿⣿⣿⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣴⣾⣿⣿⣶⡄ me⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⢿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⣉⣩⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣼⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣼⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣾⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⣾⣿⣿⠉⣿⣿⣿⣿⣿⡄⠀⢀⣠⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠙⣿⣿⣧⣿⣿⣿⣿⣿⡇⢠⣿⣿⣿⣿⣿⣧⠀you⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣷⠸⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⠿⢿⣿⣿⣿⣿⡄⠙⠻⠿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡟⣩⣝⢿⠀⠀⣠⣶⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣷⡝⣿⣦⣠⣾⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⣮⢻⣿⠟⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠻⠿⠻⣿⣿⣿⣿⣦⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⠇⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⡆⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⠇⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠀⠀⠀⢀⣴⣿⣿⣿⣿⣟⣋⣁⣀⣀⠀ ⠀⠀⠀⠀⠀⠀⠹⣿⣿⠇⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⢀⣴⠟⠉⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣀⢀⣾⠿⠻⢶⣄⠀⠀⣠⣶⡿⠶⣄⣠⣾⣿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢻⣿⣿⡿⣿⠿⣿⡿⢼⣿⣿⡿⣿⣎⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠉⢻⢛⣛⡉⠀⠀⠙⠛⠻⠛⠑⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣧⣤⣼⠿⠿⣷⣤⡤⠴⠖⠳⣄⣀⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣀⣟⠻⣦⣀⡀⠀⠀⠀⠀⣀⡈⠻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠉⡇⠀⠈⠛⠛⠛⠋⠉⠉⠀⠀⠀⠹⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⠀⢦⡀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠃⠀⠈⠑⠪⠷⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣦⣼⠛⢦⣤⣄⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠢⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠲⠖⠛⠻⣿⡿⠛⠉⠉⠻⠷⣦⣽⠿⠿⠒⠚⠋⠉⠁⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣾⠛⠁⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⠀⠀⠀ ⠀⠀⠀⠀⣰⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀ ⠀⠀⠀⣰⣿⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣧⣄⠀⠀⠀⠀⠀⠀⢳⡀⠀ ⠀⠀⠀⣿⡾⢿⣀⢀⣀⣦⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⣫⣿⡿⠟⠻⠶⠀⠀⠀⠀⠀⢳⠀ ⠀⠀⢀⣿⣧⡾⣿⣿⣿⣿⣿⡷⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢿⣿⣧⠀⡀⠀⢀⣀⣀⢒⣤⣶⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⠀⡾⠁⠙⣿⡈⠉⠙⣿⣿⣷⣬⡛⢿⣶⣶⣴⣶⣶⣶⣤⣤⠤⠾⣿⣿⣿⡿⠿⣿⠿⢿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⣸⠃⠀⠀⢸⠃⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⠟⡉⠀⠀⠀⠈⠙⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⣿⠀⠀⢀⡏⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠛⠉⠁⠀⠀⠀⠀⠀⠉⠠⠿⠟⠻⠟⠋⠉⢿⣿⣦⡀⢰⡀⠀⠀⠀⠀⠀⠀⠁ ⢀⣿⡆⢀⡾⠀⠀⠀⠀⣾⠏⢿⣿⣿⣿⣯⣙⢷⡄⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣻⢿⣷⣀⣷⣄⠀⠀⠀⠀⢸⠀ ⢸⠃⠠⣼⠃⠀⠀⣠⣾⡟⠀⠈⢿⣿⡿⠿⣿⣿⡿⠿⠿⠿⠷⣄⠈⠿⠛⠻⠶⢶⣄⣀⣀⡠⠈⢛⡿⠃⠈⢿⣿⣿⡿⠀⠀⠀⠀⠀⡀ ⠟⠀⠀⢻⣶⣶⣾⣿⡟⠁⠀⠀⢸⣿⢅⠀⠈⣿⡇⠀⠀⠀⠀⠀⣷⠂⠀⠀⠀⠀⠐⠋⠉⠉⠀⢸⠁⠀⠀⠀⢻⣿⠛⠀⠀⠀⠀⢀⠇ ⠀⠀⠀⠀⠹⣿⣿⠋⠀⠀⠀⠀⢸⣧⠀⠰⡀⢸⣷⣤⣤⡄⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⢼⡇ ⠀⠀⠀⠀⠀⠙⢻⠄⠀⠀⠀⠀⣿⠉⠀⠀⠈⠓⢯⡉⠉⠉⢱⣶⠏⠙⠛⠚⠁⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⠀⠀⠀⠀⠀⠻⠄⠀⠀⠀⢀⣿⠀⢠⡄⠀⠀⠀⣁⠁⡀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⢀⣐⡟⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⣁⡀⠀⢀⡤⢴⣒⣭⣵⡶⣶⢷⡶⣾⡶⠆⠀⠄⠁⠡⠁⠁⠄⣠⣀⣄⠠⠉⠉⡉⠝⢦⡑⠆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⣠⠴⠋⢡⡶⢋⣩⣩⡶⣳⡿⢻⣙⣎⣶⣩⣜⣻⣿⢟⡟⠀⠡⠈⠄⠡⢈⠐⡈⣹⣿⢿⡡⣃⠌⡄⢡⠀⠌⢂⠀⠀⠀⠀⠀ ⠀⠈⠀⠔⠋⠀⣠⢞⡵⠞⣫⢟⡵⣚⣧⠝⡋⢉⡶⠶⠾⢛⣛⠵⠋⢀⠈⠄⡁⠈⠀⠄⠠⡐⢭⣿⣣⡟⣬⣓⡌⢆⡈⠤⡀⢀⠉⠠⢀⠀ ⠀⠀⠀⠀⠀⣰⣿⣿⡰⢿⣷⣋⣶⣿⠵⠒⢲⣵⣻⢀⠀⣄⠠⣀⡐⣀⠈⣄⣠⢆⡵⣼⣣⠽⡶⣭⡿⣼⣣⢟⣼⢣⡜⢢⢁⠢⢀⠁⢂⠱ ⠀⠀⠀⠀⠀⣷⠏⣿⡾⠋⣹⡿⠁⣯⣥⣴⡿⢥⣛⣮⣽⣾⣷⣷⣽⣞⡿⡼⢭⠻⣜⣣⣭⣷⢿⡟⠛⠉⠙⢾⣽⣣⣏⠷⣌⢢⠡⢈⠄⠀ ⠀⠀⠀⠀⠀⢹⣀⣿⠀⢀⣿⠁⠀⢹⣿⢷⣾⣷⡿⠉⠀⠀⣉⣹⠿⠿⠿⣿⣿⡿⢏⡉⢁⠸⣇⣷⠀⠀⠀⠀⢷⡹⣾⢹⡎⣶⢱⠈⢰⠀ ⠀⠀⠀⠀⠀⠀⠀⠁⠀⣼⡿⠀⣰⠟⠁⣠⠖⠉⠀⢀⣴⠟⠋⡀⠀⠀⠀⢸⣿⡚⡴⣈⣅⢊⣽⣾⡆⠀⠀⠀⠀⠹⣧⢻⡞⡵⣎⡍⢆⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⠿⢥⡼⠁⢀⡴⠁⠀⢀⣴⠟⠁⣠⠞⠁⢀⠜⢡⠏⣿⣿⠉⠉⣏⠉⠸⣿⣷⠀⠀⠀⠀⠀⠹⡕⣯⢳⣝⡞⢦⡐ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⡐⡾⣱⢠⡞⠀⠀⣠⡿⠁⢀⡴⠁⠀⡴⠃⢠⠏⣰⠇⢸⣆⠀⢹⣸⠀⠹⣿⠀⠀⠀⠀⠀⠀⠹⣌⠷⣺⡝⣧⣙ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣼⣳⣧⡏⠀⠀⣰⡟⢀⣴⠏⠀⢠⠎⠀⣠⡏⢰⡟⠀⠀⢿⡄⠀⣿⡇⠀⢻⡄⠀⠀⠀⠀⠀⠀⠘⣎⡕⣻⢼⣣ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⣿⠱⢤⠀⡰⡏⢠⣾⠋⠀⡰⠃⢀⡴⡿⢠⡿⠁⠀⠀⠈⣿⣆⠸⣷⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠈⢆⢣⢛⡼ ⠀⠀⠀⠀⠀⠀⠀⠀⣻⣾⣇⠻⣤⠫⡔⣡⣿⡿⠀⡼⡱⢠⡞⢰⠇⣾⠃⠀⠀⠀⠀⠙⣝⢧⣿⡇⠀⢿⡣⡀⠀⠀⠀⠀⠀⠀⠈⠣⣊⠜ ⠀⠀⠀⠀⠀⠀⢰⣋⣯⣿⢬⠳⣌⡳⢭⣿⣿⠃⠐⣰⣿⢯⠃⣼⣸⠏⠀⠀⠀⠀⠀⠀⠈⠳⣹⣿⠍⣽⣿⢳⠀⠀⠀⠀⠀⠀⠀⠀⠙⢮ ⠀⠀⠀⠀⠀⠀⣿⣿⢻⡗⢮⡙⢦⡙⢾⡟⡍⠀⢰⣿⠳⠁⠀⣿⣿⣄⣀⣀⣀⣀⣤⣤⣶⣶⡤⣼⡏⣼⡜⣺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⣾⣿⡘⢣⣼⣷⣿⣿⣿⣷⣶⣿⣷⠟⠋⠀⣿⠀⠈⠛⣻⣿⠿⣿⠙⠛⢟⣿⣿⡧⣽⣷⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⡇⠌⡡⠘⢻⣟⣟⠀⢿⣯⣿⠷⣆⠀⢰⡇⠀⠀⢰⣏⣻⣿⡿⠥⠴⢿⣵⡾⣿⢸⣷⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠁⠆⢿⣷⣀⣸⡿⢉⣹⡿⣷⣾⣆⣶⣷⡿⠉⠁⠀⠀⠀⠀⠀⠈⣿⣿⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀ ⠀⠀⠀⠀⠀⠀⠀⢹⡄⣼⠀⠈⠀⢸⡁⠈⣽⠋⠉⠀⠀⠀⢿⡟⠯⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⢸⠁⠀⠀⡀⠠⠐⠐⠈⠁⠀⠠⠀ ⠀⠀⠀⠀⠠⢀⠀⠈⣇⣿⡄⠀⠀⣾⠀⢰⡏⠀⠀⠀⠀⢀⡿⠁⠀⠀⠻⣦⡀⠀⠀⠀⠀⢀⣴⠟⡷⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠄⡀⢒⣼⣿⣧⠀⠀⣿⣦⣼⣁⣀⣀⣠⠴⢛⠀⠀⠀⠀⢀⡰⠉⠛⠛⠚⠛⢫⣷⣾⣣⠧⠤⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⠔⠉⠀⠣⣿⡀⠀⣻⠱⣿⠉⠀⠁⠀⠀⠈⠒⠶⡤⠶⠋⠀⠀⠀⠀⠀⡰⠋⠃⣼⡿⢀⠀⠀⠈⠙⢦⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⢸⣧⠀⢹⡄⣯⢓⢤⡀⢠⣤⢤⣤⣤⣔⣲⠾⢿⣿⠛⣷⡞⠁⢀⣰⡿⠋⠀⠀⠀⠀⠀⠀⠑⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⢿⡆⠘⣇⡟⢳⠔⣵⣞⠏⠞⠆⠀⡇⣹⠀⢸⣿⠀⣿⣄⡶⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀ ⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄⢿⣇⠈⠳⡏⣏⢷⡸⠀⠀⡇⣯⠀⠞⠹⣀⣿⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀ ⣷⣄⠀⢼⠀⠀⠀⠀⢇⠀⠀⠀⠈⢿⣜⣿⠀⠀⠉⡟⢧⡹⡄⠀⡇⣽⣈⡇⠱⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢸⠀⠀⠀⠀ ⡳⣏⡿⣯⡀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠳⣽⡄⠀⢸⠇⠘⣹⣞⣆⣷⡿⠀⠳⠀⣆⣿⠀⠀⠀⠀⠀⠀⠀⢀⣰⠁⠀⠀⠀⠀⡞⠀⠀⠀⠁ ⠳⡹⡞⣽⢻⡶⣄⠀⠀⣽⠀⠀⠀⠀⠀⠘⠳⡀⣺⠇⡈⣼⣟⠿⡧⣇⠀⠠⢁⢸⡿⠀⠀⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⠀⠀⣧⡀⠀⠀⠀ ⠰⢇⡹⡎⣷⢹⣏⣷⡸⡏⠀⠀⠀⠀⠀⠀⠀⠈⣹⠎⣸⣇⡿⢸⡷⡏⠀⠁⡎⢶⡇⠀⠀⠀⠀⠀⠀⠀⢹⠇⠀⠀⠀⠀⢀⠇⡇⠀⠀⠀ ⠀⠘⠴⡙⣬⢳⣎⢷⡿⣧⡀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢫⣞⡁⢰⣟⡇⢀⠳⣸⢸⡇⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⢠⠋⠀⣧⣠⣴⢾ ⢸⡟⣷⣛⣧⣟⡬⢷⡹⣝⢿⣦⡀⠀⠀⠀⠀⠀⢻⣿⡟⢤⠓⣾⢏⡟⣌⠳⢤⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⢀⣔⣡⣴⣾⢻⡽⣙⢮ ⢸⠻⢷⣭⣾⠼⡇⣣⢝⡞⣧⢟⡿⣦⡀⠀⠀⠀⣿⠯⡜⣡⢏⡼⢭⡗⢬⠓⠦⣿⠀⠀⠀⠀⠀⠀⠀⠀⢄⣸⣴⣿⡟⣭⢗⢮⠳⡜⡱⢊ ⢸⣤⣽⡤⣤⢴⡇⡘⢎⢞⡱⢯⡽⣳⢿⣄⠆⠀⢹⣗⡼⣡⢞⣜⣣⡛⣬⡙⢶⣹⡀⠀⠀⠀⠀⢀⣠⣶⢿⣛⣧⢷⡹⢞⡺⢌⠓⡌⢁⠂ ⢸⣷⣫⡽⣞⢯⡇⠰⡉⢎⡹⢣⡟⣵⢫⣾⣦⣤⣾⣧⢯⣝⡻⣚⢧⡻⢵⣫⢗⣻⣇⣀⣀⣦⣶⣿⣯⢽⡺⡵⣎⢧⠛⡆⠱⠈⡐⠀⠂⠀
⠀⠀⠀⠀⠀⢀⣴⡾⠿⠿⠿⠿⢶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⣿⠁⠀⠀⠀⣀⣀⣀⣈⣻⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣾⡇⠀⠀⣾⣟⠛⠋⠉⠉⠙⠛⢷⣄⠀⠀⠀⠀⠀⠀⠀ ⢀⣤⣴⣶⣿⠀⠀⢸⣿⣿⣧⠀⠀⠀⠀⢀⣀⢹⡆⠀⠀⠀⠀⠀⠀ ⢸⡏⠀⢸⣿⠀⠀⠀⢿⣿⣿⣷⣶⣶⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀ ⣼⡇⠀⢸⣿⠀⠀⠀⠈⠻⠿⣿⣿⠿⠿⠛⢻⡇⠀⠀⠀⠀⠀⠀⠀ ⣿⡇⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣼⣷⣶⣶⣶⣤⡀⠀⠀ ⣿⡇⠀⢸⣿⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀ ⢻⡇⠀⢸⣿⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⡇ ⠈⠻⠷⠾⣿⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣇ ⠀⠀⠀⠀⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⢸⣿⣿⣿⡿ ⠀⠀⠀⠀⢿⣧⣀⣠⣴⡿⠙⠛⠿⠿⠿⠿⠉⠀⠀⢠⣿⣿⣿⣿⠇ ⠀⠀⠀⠀⠀⢈⣩⣭⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣿⣿⣿⣿⠏⠀ ⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀ ⠀⠀⠀⢸⣿⣿⣿⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⢸⣿⣿⣿⣷⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠛⠿⠿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⢀⣹⣿⣿⣿⡇⠀⠀ ⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀ ⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠁⠀⠀⠀ ⠀⠀⠀⠀⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠉⠉⠁⢤⣤⣤⣤⣤⣤⣤⡀ ⠀⠀⠀⠀⢿⣿⣿⣿⣷⣶⣶⣶⣶⣾⣿⣿⣿⣆⢻⣿⣿⣿⣿⣿⡇ ⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠻⣿⣿⣿⡿⠁ ⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠀⠙⠛⠉⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⢸⠇⢸⠀⡿⡟⡷⡇⠀⢠⣾⣉⣅⣿⣈⣧⡀⠀⢹⡇⠀⠀⠀⢸⣿⣿⣆⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⢸⠀⣼⠀⢿⡇⡇⣧⠀⠸⣿⡍⢩⢿⠈⠉⢻⡝⢻⡇⠀⠀⠀⢸⣿⣿⣿⡜⡆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⢸⡄⣿⡴⢿⡇⣷⣿⣦⠀⢿⡇⣸⠀⠀⠀⠀⠙⣾⡇⠀⠀⢰⢸⣿⡿⡇⣧⢹⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⣿⢫⠘⡇⣿⡇⢸⡧⢹⣿⣯⢊⣿⣇⠋⢀⣀⣀⣀⣀⣺⡁⠀⠀⣼⢸⣿⡇⢷⢸⡎⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣼⣿⠘⡆⢿⢯⣷⡌⠛⢸⡏⢿⠳⣇⠉⠐⠋⣿⣿⣿⣿⣯⢻⡇⢀⡟⣼⡇⡇⢸⢸⣷⢻⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣹⣆⣧⠸⣧⣼⢿⣿⣿⣯⠈⣰⡏⠳⠄⠠⠿⠿⠟⠚⡅⣾⠀⣸⣇⣿⢻⡇⢸⢸⣿⣿⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⠸⡏⡜⡆⠹⡟⢾⣿⠿⡯⠀⢻⠁⠀⠀⠀⠀⠀⢀⣼⢱⠇⢀⣿⠙⣿⢸⡇⣾⢸⡿⢿⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⡇⡜⣷⢻⠹⡄⡹⡄⠑⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠀⣼⡏⢀⡿⣸⡇⣿⢸⣧⢸⣷⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⡇⡇⢻⡘⣇⠹⣎⠻⣲⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢿⣇⣾⣿⣧⣿⠁⣿⢠⡟⠸⡿⠈⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⡇⡇⢸⣧⢿⣶⠿⣦⢮⠉⠃⠀⠀⠀⠀⠀⠀⠀⠘⢁⣾⣿⣿⣿⣿⡟⠀⣿⢸⣷⢰⡇⠀⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⡇⣿⡌⣿⣿⣿⣥⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⢀⡴⣿⡟⣿⡿⣿⣿⠃⢰⣿⣿⣹⢸⡇⠀⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⡇⢻⣷⣿⠿⣿⣿⣾⣿⣿⣿⣿⣿⠲⣤⡤⠞⠉⠞⠉⠰⣿⣣⣿⣿⠀⢸⣿⡏⣿⣸⠀⠀⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣧⢸⣿⣿⠀⣹⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⠘⠀⣿⣿⢹⣿⡏⠀⢰⡟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢹⠸⣿⣿⣼⣿⣿⣿⣿⡿⠿⠋⠀⠀⠙⠒⠒⠒⠛⢀⡴⠀⠈⠛⠷⣦⣿⣯⣿⣿⠃⠀⣼⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡤⠜⠃⠉⠉⠁⠉⠉⠁⠀⠀⠀⣀⣀⡐⡄⠀⠀⠀⢠⣏⡤⠴⠖⠂⠀⠀⠀⠀⠀⠈⠈⠳⣻⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢤⣤⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠱⡄⠀⠀⠀⠀ ⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⠀⢹⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⡀⠀⠀⠀⢸⡇⠀⠀⠀ ⠀⠀⠀⠀⢀⡴⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⣀⠀⢸⡇⠀⠀⠀ ⠀⠀⠀⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⣼⠀⠀⠀⠀ ⠀⢀⠞⠀⠀⣠⠶⠚⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀ ⢀⡟⠀⢠⠞⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀ ⢸⠀⠀⡿⠀⠷⠃⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⢤⡀⠀⠈⢧⠀ ⢸⠀⠀⠛⠀⠀⠀⠀⠘⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⢹⡄⠀⢸⠀ ⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡏⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⢡⡀⠀⢠⡇⠀⢈⡇ ⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⢸⠃ ⠀⠀⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡟⠁⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡤⠚⠁⠀⢀⡞⠀ ⠀⠀⠀⡷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠞⣡⠟⠀⠀⠀⠀⠀⠀⠙⡷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀ ⠀⠀⠀⠃⠀⠙⢷⡶⠤⣤⢤⠤⠴⠖⠋⣩⠴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠳⣌⠳⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢴⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⣦⣿⠀⠀⠀⠚⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠈⠉⠓⠲⢶⡶⠶⣶⠞⠋⠁⢸⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠀⠀⠀⣸⡁⡼⠁⠀⠀⠀⠈⡧⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢟⣛⣛⣛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣡⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣍⠻⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⠟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢋⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠻⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡜⢿⣿⣿⣿⣿⣿ ⣿⣿⣗⡀⠀⢻⣚⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢨⡿⠟⠋⠛⠉⠉⠉⠈⠙⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡘⣿⣿⣿⣿⣿ ⣿⣿⣿⣾⣃⠘⣺⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⢀⣠⣤⣶⣶⡶⠀⠀⢠⣿⣿⣿⣷⡆⠘⢿⣿⣿⣿⣿⣿⣿⣷⢸⣿⣿⣿⣿ ⣟⠀⠈⠙⢟⡀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⢰⣿⣿⣿⣿⣿⠃⠀⣰⣿⣿⣿⣿⣿⣿⣦⠘⢽⣿⣿⣿⣿⣿⣿⡆⣿⣿⣿⣿ ⡿⣗⢶⣢⢆⣀⠀⠘⠛⠛⢛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡘⣿⣿⣿⣿⠃⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⢃⢸⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿ ⣁⣀⣀⣠⣬⠟⣰⡐⢽⣿⣷⣦⡙⢿⣿⣿⣿⣿⣿⣿⣿⣧⡐⢛⠻⠀⠀⠾⠿⠿⠿⠿⠿⢛⠛⢁⣠⣾⣿⣿⣿⣿⣿⣿⣿⠂⣿⣿⣿⣿ ⣿⣿⣿⣿⡟⣸⣿⣿⣆⢘⢿⣿⣿⠒⢉⣿⣿⣿⣿⣿⣿⣿⡧⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠅⣿⣿⣿⣿ ⣿⣿⣿⣿⣇⢺⣿⣿⣿⣿⡾⠛⣠⣾⣶⣌⡛⢿⣿⣿⣿⣿⣗⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡂⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⡌⢿⣿⠟⢉⣴⣿⣿⣿⣿⣿⣿⣦⡙⢿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣌⠀⢴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠹⣿⡧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢁⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣯⠜⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡜⠓⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣘⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠔⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢰⠸⣿⢿⢿⢿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠅⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣬⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣠⣶⣶⣿⣶⣶⡆⠑⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡅⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣬⡛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠘⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⢰⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣠⣽⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⣼⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢁⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠘⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⣼⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⠟⡁⠛⡻⠿⢿⣿⠿⠿⢛⢀⡘⢿⣿⣿⣿⣿⣿⣿⣿⣿⢡⣾⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡙⣛⣛⣛⣋⢜⣣⣿⣿⣾⣾⣾⣾⣾⣾⣿⣿⣦⡈⠻⠟⠛⠻⠛⣋⣴⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣴⣶⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣼⣿⣿⣿⡿⣿⣿⣆⠀⠀⠀⠀⠀⠀⣠⣴⣶⣤⡀⠀ ⠀⠀⠀⢰⣿⣿⣿⣿⠃⠈⢻⣿⣦⠀⠀⠀⠀⣸⣿⣿⣿⣿⣷⠀ ⠀⠀⠀⠘⣿⣿⣿⡏⣴⣿⣷⣝⢿⣷⢀⠀⢀⣿⣿⣿⣿⡿⠋⠀ ⠀⠀⠀⠀⢿⣿⣿⡇⢻⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⣿⣇⢸⣿⣿⡟⠙⠛⠻⣿⣿⣿⣿⡇⠀⠀⠀⠀ ⣴⣿⣿⣿⣿⣿⣿⣿⣠⣿⣿⡇⠀⠀⠀⠉⠛⣽⣿⣇⣀⣀⣀⠀ ⠙⠻⠿⠿⠿⠿⠿⠟⠿⠿⠿⠇⠀⠀⠀⠀⠀⠻⠿⠿⠛⠛⠛⠃
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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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