Meme Sonic the Hedgehog Emojis & Text

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⠶⠟⠛⠛⠛⠻⣷⣶⣤⣤⣤⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⣭⣀⣀⡀⠀⣠⣶⠿⠛⠋⠉⣉⣿⣿⡛⠛⠛⣛⣿⣿⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⣿⣿⣅⠀⠀⣰⡿⠋⠉⣉⣻⣷⡿⠛⠋⠛⠛⣿⡟⢿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣤⣤⣄⣀⣠⣿⠉⠁⠀⠀⢿⣇⣀⣠⣿⠟⠙⢿⡀⠀⠀⢋⣿⠃⠀⠙⢻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣤⣶⣾⣿⣿⣉⣉⣉⣁⡉⠉⠉⠉⢹⡏⠀⠀⠀⠀⠈⠙⠛⠋⣁⣰⣶⣌⠻⠶⠶⠿⠃⠀⠀⠀⠀⠙⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠛⠻⠶⣿⣧⠀⠀⠀⠀⠀⣴⡿⢟⠛⠛⠛⠛⠿⢶⣦⡀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣿⣏⣀⠀⠀⠀⠀⢿⣄⠙⠿⠶⣶⣤⣤⡄⠙⢿⡄⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣠⣴⣾⣿⣿⣯⣭⣭⣭⣭⣽⣿⣯⣽⣯⣭⣿⣿⣤⠀⠀⠀⠈⠻⢷⣦⣄⣀⡀⢀⣀⣠⣾⠇⠀⠀⠀⠀⢠⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠟⠋⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠰⠷⣿⣿⣇⣀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠉⠀⢀⣀⣠⣤⣶⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣀⣤⣴⠶⠿⠛⠛⠛⠛⠛⠛⠛⠛⠷⠶⣮⣍⣙⠛⢻⡿⠿⠶⠶⠶⠿⠿⣿⠛⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⣾⣿⣭⣤⣶⡶⠶⠶⠿⠛⠛⠛⠛⠿⠶⣶⣦⣍⣛⣿⡿⠃⠀⠀⠀⠀⠀⠀⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢿⣫⣭⡷⠶⠾⠛⠛⠛⠛⠛⠛⠿⠶⣶⣤⣀⠀⠉⠙⣿⣿⣠⣤⣤⣀⣀⠀⠀⠀⠈⣿⡄⠀⠀⠀⠀⠀⠀⢀⣤⣶⠿⠛⠛⠛⠻⢷⣄⠀⠀⠀⠀ ⣴⣾⣿⣯⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣽⣷⣦⡾⠛⠛⠁⠀⠉⠉⠛⠛⠛⠶⢶⣿⣇⣀⣀⠀⢀⣤⡾⠟⠉⠀⠀⠀⠀⠀⠀⠀⠹⣷⡄⠀⠀ ⠈⠀⠀⠀⠀⠀⠀⢀⣴⡿⠛⠉⠁⠀⠀⠀⠀⠈⣩⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⢿⣿⣏⠀⢀⣤⣶⠾⠿⠷⣶⣄⡀⠀⠈⢿⣆⠀ ⠀⠀⠀⠀⠀⠀⢠⣿⠋⠀⠀⢀⣤⣦⣤⣤⣤⣴⡟⠁⠀⠀⢠⣾⠿⢿⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⡿⠋⠁⠀⠀⠀⠀⠙⣷⡀⠀⠈⢿⣆ ⠀⠀⠀⠀⠀⠀⣾⠃⠀⢀⣼⠟⠉⠀⢀⣀⣠⣿⠀⠀⠀⢰⡿⠋⠀⠀⠀⠉⠙⠻⢿⣶⣄⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⢹⣇⣠⣤⣼⣿ ⠀⠀⠀⠀⠀⢸⡟⠀⢀⣾⢣⣴⣿⣟⠟⠛⢻⣿⠃⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣇⠀⠀⠀⠀⠀⣠⡿⠀⠀⠀⠀⠀⠀⢀⣴⠾⣿⠉⠉⢹⣿ ⠀⠀⣀⣤⣶⣿⣷⣶⣾⣯⣀⠉⠙⠛⠿⠿⢿⡿⠃⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⢀⣼⠟⠁⠀⠀⠀⠀⠀⠀⢾⡇⠀⠿⠀⠀⠀⠁ ⠀⣰⡟⠁⠈⠉⠀⠙⣿⠉⢻⡇⠀⠀⣠⣴⣾⣷⠀⠀⠀⠈⣿⡄⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⠀⣠⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣄⡀⠀⣀⣀⣴ ⢀⣿⠁⠀⠀⠀⠀⠀⠀⠀⣾⠇⣠⣾⠟⠉⣽⡇⠀⠀⠀⠀⠸⣿⡀⠀⠀⠀⠀⠀⢀⣾⠏⠀⠀⣴⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠉⠁ ⠀⣿⠀⠀⠀⠀⠀⠀⢀⣼⢿⣾⣿⠶⠶⠶⢿⣿⠀⠀⠀⠀⠀⠙⢿⣦⣤⣤⣄⣠⣿⠋⠀⠀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢻⣧⡀⠀⠀⣀⣴⠿⠋⠘⠁⠀⢀⣀⣤⣶⣿⣷⣄⠀⠀⠀⠀⠀⠉⠉⠉⠛⠛⠁⠀⢀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠉⠛⠛⠛⠋⠁⠀⠀⢀⣶⣾⣿⣯⣽⠶⠟⠛⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⢺⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠿⠛⠛⠉⠁⠀⠀⢀⣠⣴⣿⣿⣷⣦⣄⡀⠀⠀⣀⣠⣴⣿⣿⠀⠀⠹⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡶⠟⠋⢉⣀⣤⣾⠿⠻⠿⠿⢿⠿⠛⠉⠀⢻⣿⠀⠀⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠛⠁⢀⣤⡾⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⠀⠀⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⠀⠀⣼⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠇⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠟⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠘⣿⡀⠀⠀⠀⠀⢀⣶⣿⡿⠿⢿⡆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣀⢀⣿⢀⣀⡀⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠙⠷⣶⣷⣴⡶⠟⠋⠁⠀⣠⡿⠃⠀⠀⠀⠀⠀ ⠀⢀⣤⡶⠾⠟⠛⠛⠻⠿⠛⠛⠛⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣦⡀⠀⠀⠀⣿⡇⠀⠀⣠⣴⡾⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⢿⣏⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠷⢶⣶⣾⣷⠾⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⢠⠠⣆⢆⢶⢴⢄⣦⢊⠴⡘⢆⢤⡞⢢⡤⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢦⡝⣇⠻⡘⠄⠀⡸⠊⠀⠀⠀⠀⠀⠀⠀⠐⠁⠒⣤⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣴⡄⠁⡈⠀⡇⡃⡐⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⣀⠀⠻⣧⣄⡀⠀⠀ ⠀⠀⠀⠀⠙⣿⡌⣉⡀⠀⢠⠁⠀⢀⠄⡠⠏⠀⠀⠂⠁⠁⢀⡀⠀⠀⠸⠿⡀⠀ ⠀⠀⠀⠀⠀⣿⠓⢿⣧⣾⠷⢅⠀⠀⠀⠀⣠⡇⠀⢀⠄⠘⠋⠀⠀⠀⠀⠀⠿⠄ ⠀⠀⠀⢀⠎⠀⠀⠄⠈⠁⢁⣅⠇⢀⣀⣨⠁⠀⡠⠋⠀⢠⠴⢂⡔⢦⡈⣑⢄⠀ ⠀⠀⡠⠊⠀⣶⡄⠀⠀⠀⡚⠋⠛⠿⠭⣤⢖⣋⠀⠀⢀⡀⠄⠑⠂⣀⠀⠀⠛⠅ ⣴⡏⠀⠀⠀⠉⠁⠀⠀⠄⠃⠀⠀⠀⠀⠀⠀⠉⠉⠃⠾⠗⣆⣳⡄⠀⠉⠀⠹⢥ ⠀⠃⠠⠤⠀⠀⠀⠐⠋⠀⠀⡀⢀⠀⠀⠀⠀⠀⠰⣦⠀⠀⢀⠙⠻⠂⣸⣧⡱⡂ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠑⠰⠆⡀⢠⣐⠀⢀⠀⠀⠀⠂⡄⠁⢀⢀⠾⠉⠀⠉ ⠀⠀⠀⠀⠀⠀⠀⠺⠭⠤⢢⡄⠂⣀⡠⠉⠉⠀⠉⠒⠚⣶⢃⡠⠞⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠤⠤⠤⠄⠀⠤⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⣶⣾⣿⣿⣿⣿⣿⣷⣶⣶⣦⣤⣄⣀⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣿⣿⠿⣟⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀ ⠀⠀⠀⠀⢰⠶⣶⣶⣶⣦⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠟⠋⠉⡇⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠋⠉⠀⠀⠀ ⠀⠀⠀⠀⢸⣷⣄⣙⣿⣿⣿⣿⣿⣿⣿⣫⣭⠿⣭⣝⢿⣿⣦⣄⡇⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣫⠟⠁⠀⠀⠀⠈⢷⢻⣿⣿⣿⣿⣿⣿⣿⣥⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣾⡟⣷⢻⣿⣿⣿⣿⠃⠀⠀⣠⣤⡀⠀⠘⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⠀⢸⣏⣿⣿⣿⡏⠀⠀⠀⣿⣿⣇⠀⠀⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⢹⠀⠀⣿⣿⣿⡟⠀⠀⠀⠀⣿⣿⣿⠀⠀⣿⣿⠇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀ ⠀⠀⠀⠀⠀⣸⣄⡀⢻⣿⠉⠀⠀⠀⠀⠀⠹⠿⠏⠀⣸⣿⣿⡀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀ ⠀⠀⠀⠀⠀⢿⣿⣿⣷⡖⠒⠦⢄⣀⣀⣀⣀⠤⠒⢉⣀⡀⠀⠙⣿⣿⣿⣿⣟⠛⠉⠉⠉⠉⠛⠛⠻⢿⣷⠀ ⠀⠀⠀⠀⠀⠀⠉⠻⡛⠁⠀⠀⠀⠀⠈⠀⠀⠀⠀⢀⡸⠻⠀⢰⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣄⠀⠀⠀⠀⠀⠠⠒⠚⠉⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠬⠵⣦⠤⣤⠀⠀⣀⣤⣤⣶⣿⠟⠛⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⡞⢀⡔⠒⣼⡞⢁⡔⠂⠉⠉⠉⠛⠧⣄⢀⠟⠛⠻⢿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⠘⠷⠤⢷⡀⠈⠳⠼⡀⠀⠀⠀⠀⠀⢀⠈⢿⣧⠀⠀⠀⠉⠻⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡠⠓⢦⡤⠔⠛⠲⠤⠤⠵⢴⠀⠀⡄⢰⠈⣇⣿⣿⣧⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⠦⠤⠟⣆⠀⠀⠀⠀⠀⠀⢦⣀⣴⣠⣧⣼⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢦⣤⣀⣠⣤⣾⣿⣿⣿⡇⠀⠀⠈⠙⠻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⠻⣿⣿⡏⠻⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡏⠀⢹⣿⣿⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠒⢋⣿⣿⣿⡒⢬⣿⣿⡧⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠀⠈⠉⢉⡟⠉⢥⣿⣿⠿⠒⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⡸⢄⠀⠀⠀⠀⢣⡀⠀⠀⠀⠀⠀⠀⡸⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣤⣾⣿⡦⠀⠙⢶⣶⣤⣼⠀⠀⠀⠀⠀⠀⠀⠀⣨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⣶⣿⠿⠋⣡⣴⣷⡀⠈⣿⣿⣿⣷⣦⣤⣤⠄⠀⠒⠚⠻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣼⡿⢋⣡⣴⣿⣿⣿⣿⡇⠀⢻⣿⣿⣿⣿⡿⠁⣠⣾⠘⣷⣦⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⢿⣾⣿⣿⣿⣿⣿⣿⡿⠧⠤⠚⠛⠉⢿⣿⠃⣸⣿⣿⡀⠹⣿⣧⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣄⣿⣿⣿⣧⠀⢻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣇⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀ ⠀ (\__/) (•ㅅ•) Don’t talk to ＿ノヽ ノ＼＿ me or my son `/　`/ ⌒Ｙ⌒ Ｙ ヽ ever again. ( 　(三ヽ人　 /　 | |　ﾉ⌒＼ ￣￣ヽ ノ ヽ＿＿＿＞､＿_／ ｜( 王 ﾉ〈 (\__/) /ﾐ`ー―彡\ (•ㅅ•) / ╰ ╯ \ / \>

*ੈ✩‧₊˚🔭🦔

⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣿⢿⣿⣿⣷⣶⣦⣤⡀⠀ ⠀⠀⢾⡻⣶⣾⣿⣿⣛⣻⣮⡉⣿⣿⣿⠟⠋⠉⠀⠀ ⠀⠀⢸⢿⢿⣿⡿⠁⣀⠀⢛⣿⣿⣿⣷⣦⣄⠀⠀⠀ ⠀⠀⢸⠈⣿⣿⠁⠀⣿⡇⢸⡏⢻⣿⣿⣿⣿⣷⡄⠀ ⠀⠀⢰⣦⣝⠁⡀⠀⢙⠡⠚⠣⣾⣿⡿⠿⠿⠿⢿⡄ ⠀⠀⠀⠈⠡⡀⠀⠀⠀⠄⠚⣰⣿⣿⣷⡄⠀⠀⠀⠀ ⠀⠀⠀⢀⡔⡈⡲⠂⠰⠶⢟⡉⠿⢿⣿⣧⠀⠀⠀⠀ ⠀⠀⠀⠫⣓⠣⢀⡣⡀⠀⡔⣹⣧⠀⠉⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠑⢄⣀⣀⣶⣶⠟⠛⠿⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⡏⢿⡏⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⠉⠻⠏⣺⣷⠔⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣤⡒⢤⣀⡆⠀⠀⠀⢐⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⡾⣋⣵⣾⡀⣿⣿⣶⢂⡌⣍⠆⠀⠀⠀⠀⠀⠀⠀ ⠘⠛⠛⠛⠛⠃⠉⠙⢏⣾⣧⢹⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣾⡏⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⣰⡄⠀⢠⡀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣄⣿⠦⡜⢻⣴⠃⢸⢦⠋⢣⣼⣿⡠⠖⣿⠀⣀⢤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣄⣻⠦⣿⣄⠁⠀⢱⠈⡇⠀⢸⠀⠀⠈⢻⠋⠁⠀⡟⠉⠀⠰⠗⢙⠇⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⣀⢹⠙⠛⢦⡀⠈⢢⡀⠈⠆⠈⠀⠘⠀⠀⠀⠘⠀⠀⠀⠇⠀⠀⠀⠀⠈⠉⢩⣏⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⡦⠽⠇⠀⠀⣀⡀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋⠽⠥⣤⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠽⠦⠀⢠⠋⠁⠈⢢⡀⠀⠀⣤⣼⣄⢠⢧⣰⣧⡀⣠⣦⣤⡴⠋⠉⠙⢅⠀⠀⠀⢰⣁⡤⠆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣶⡾⠶⣄⡀⠀⢸⠀⠀⠀⠀⡗⢾⠶⠏⠋⠈⠏⠈⠋⠉⠛⠁⠟⠿⠀⠀⠀⠀⣼⠀⠐⠚⣉⣥⠟⠂⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⢁⡶⠞⠁⠀⠈⢣⣀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⡁⠀⠀⠀⠀⠈⠉⣲⠄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣾⣅⠀⠀⠀⠀⠈⣫⣹⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡇⡿⣥⣤⠄⠀⠒⠒⠉⠻⣗⠂⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠺⢯⣭⠉⠁⠀⠀⠀⠈⣇⢹⠀⢀⣴⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣤⡀⢸⠁⠻⣥⡀⠀⠀⠀⠀⠀⠀⣄⣙⣦⣀⠀ ⠀⠀⠀⠀⠀⠰⢞⣉⠀⠀⠀⠀⠀⠘⢯⡍⠈⡆⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⠇⢸⠀⠀⢻⣷⠄⠀⠀⠀⠀⠀⠀⣹⣤⠀⠀ ⠀⠀⠀⠀⠀⣠⣔⣋⣀⡀⠀⠀⠀⣴⠏⠀⠀⠹⡀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⢀⠇⠀⠀⠀⣼⡗⠀⠀⠀⠈⠉⠑⠛⢧⡀⠀ ⠀⠀⢀⡤⠚⡹⠋⠀⠀⠀⠀⢀⣴⣁⡀⠀⠀⠀⠙⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⣽⠂⠀⠀⠀⠀⠀⢠⣤⣹⡦ ⠀⠀⠁⠐⠮⠤⣤⡀⠀⠀⠀⠀⢩⠋⠈⠳⡀⠀⠀⠈⠢⡀⠀⢠⣴⣶⣶⣶⡄⠀⢀⡴⠋⠀⠀⠀⠀⡴⢯⡬⠷⠀⠀⠀⠀⠀⠀⠙⡄⠀ ⠀⠀⠀⠀⣠⣴⡿⠃⠀⠀⠀⠰⢷⡶⠀⠀⢱⠀⠀⠀⠀⠘⠢⣈⠻⢿⡿⠛⣁⠴⠋⠀⠀⠀⠀⠀⡜⠀⠀⢻⡶⠀⠀⠀⠀⠀⠢⣀⣘⡄ ⠀⢀⠴⠊⣡⠋⡀⠀⠀⠀⠀⢠⠏⡀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⣰⠁⠀⠀⣷⡷⡄⠐⠒⠒⠀⠀⠙⢧⡁ ⠖⠁⠀⣴⣷⡾⠃⠀⠀⠀⠀⠋⣹⣃⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃⠀⠀⠀⢻⡇⠀⠀⠀⠀⠲⢤⣀⠀⢻ ⣠⠖⠉⠀⠘⡷⠃⠀⠀⠀⠀⠐⠛⡿⣄⠀⠀⠀⠈⠣⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠁⠀⠀⠀⣰⣿⠛⠃⠀⠀⠀⠀⠀⠙⡍⠐ ⠁⠀⠀⢀⣞⣁⣀⡀⠀⠀⠀⢀⠰⠛⡏⠳⣄⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀⠀⠀⠀⢠⠎⠁⠀⠀⠀⣠⠞⡙⣟⠂⠀⠀⠀⠀⠰⢤⣄⣸⡄ ⠀⠀⠀⢈⡩⡿⠋⡀⢀⡴⠊⠁⠀⠐⢿⣦⠤⠷⠦⢤⣤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠈⢳⣤⠤⠴⠿⠤⣄⡏⠉⠀⠀⠈⠓⠦⣀⠀⠿⠮⡁ ⠀⠀⠴⠋⠀⠛⣽⣡⠊⠀⠀⠀⠀⠀⠈⢻⣧⡀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⡞⠉⠀⠀⠀⠀⢠⡿⠁⠀⢤⡀⠀⠀⢦⡹⡏⠛⠀⠉ ⠀⠀⠀⠀⠀⠀⠓⠻⠇⠀⢀⡴⠀⠀⠀⠀⠹⠗⢷⠀⠀⢠⠿⡷⢦⣶⡴⣿⣷⢷⣇⠀⠀⠀⣄⡞⠛⠀⠀⡀⠀⠈⢦⠀⠸⡿⣧⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⠒⡶⠃⣀⠀⠀⠀⢀⠀⠀⠈⠓⠒⠋⠀⠀⠈⠀⠀⠀⠀⠀⠈⠓⠒⠒⠃⠀⡀⠀⠀⠱⡄⠀⠈⡗⠤⠇⠈⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢰⡧⠚⢻⠀⣠⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣄⢀⡀⢸⢦⣤⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠘⠉⠀⢻⠞⣆⡴⢦⠀⣴⣄⣀⢀⣦⣰⣄⢠⡄⢀⢤⣀⡿⣤⠴⠴⠒⠼⣏⠉⠃⠀⠁⠀⠀⠀⠀⠀⠀⠀ ⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣯⣤⣼⣿⣶⣿⣾⣿⣼⣷⣾⣷⣼⣿⣤⣿⣦⣬⣤⣤⣤⣤⣼⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⡾⠟⠉⢹⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠻⠿⠿⣷⣶⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠾⠟⢫⡿⠋⠀⡀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⠿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⠟⠉⠀⢀⣴⠋⢀⣴⣾⣿⡀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠟⠉⠀⠀⠀⢀⠞⠁⣠⣾⣿⣿⣿⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁⠀⠀⠀⠀⠀⠈⠀⠠⣿⣿⣿⣿⣿⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠻⠇⠀⠏⠀⠀⠀⠠⠤⠤⣤⣴⣿⣯⣥⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣴⣶⡶⠶⠶⠶⣶⣦⣴⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠶⠶⠶⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠻⠿⣷⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢹⣿⠀⠀⠀⠀⠀⠀⠉⡟⠀⠀⠀⠀⠀⠀⠀⣠⠟⠁⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣶⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⢻⣧⡀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⣰⠃⠀⣤⠶⠛⠛⠒⢦⡀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⡀⠀⠀⠀⠀ ⠀⠀⠻⣷⣄⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⡏⢀⡞⠁⠀⠀⠀⠀⠀⠙⡄⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⠀⠀⠀ ⠀⠀⠀⠈⠻⣷⣤⠞⠧⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣦⠀⠀ ⠀⠀⠀⠀⠀⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⡔⠲⣄⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⡀⠀⠀⢻⣧⠀ ⠀⠀⠀⠀⠀⠘⣿⡄⢻⢆⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⣇⡇⢈⡆⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢶⣤⣶⣾⠿⠿⠛⠛⠛⠛⠛⠛⠛⠿⠿⠿⠿⠇ ⠀⠀⠀⠀⠀⠀⠘⢻⣿⡌⢣⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠸⡽⣾⡿⠀⣼⠟⠛⠛⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠈⢷⣾⣄⠀⢀⡟⠀⠀⠀⠀⠀⠙⢽⣃⠟⠁⠠⣦⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⡈⢝⢾⣟⣩⠤⠶⠶⠦⠤⠤⠴⠚⠁⠀⠀⣰⠃⠀⣸⡥⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠿⠿⠷⣷⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⣠⣾⣿⣶⣶⣶⣦⣤⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣶⣶⣾⣿⣿⣄⡀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣴⡿⠟⠉⠀⠀⠀⠉⠉⠉⠉⠛⠛⠻⠿⢿⣶⣦⣤⣀⡀⠀⠀⠀⠀⠻⣿⣆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠛⠻⠿⠿⠿⠿⠿⠿⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⠿⣷⣦⣤⣀⠀⢹⣿⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣷⣦⣿⣷⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⣖⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⡧⠀⠑⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢐⠥⠤⠥⠤⠆⢇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢘⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢘⠀⠀⠀⠀⠀⢘⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⢐⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡃⠀⠀⠀⠀⠀⠨⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⢘⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢘⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⠋⠉⠑⣇⠀⠀⠀⠀⠀⡾⢄⣀⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡆⠀⠀⠀⠀ ⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀ ⠀⠀⠉⠙⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠉⠁⠃⠒⠒⠒⠒⠒⠋⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣠⡆⢀⡀⢀⠀⣤⠀⣄⠀⠀⣴⠀⡠⠞⡽⠁⣼⠀⣰⡄⠀⠀⢀⣠⣤⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠁⣴⠛⡇⡞⣇⣼⣧⡏⢷⣯⢳⣰⣿⡾⠁⢸⣡⠞⢸⣰⠃⢻⡤⢞⣽⣫⠥⠷⢒⣶⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⢸⢹⢰⠇⢠⣷⠃⢸⡗⠘⠁⠀⠉⠀⣿⣴⠇⠀⠘⠋⠀⠘⠋⠀⠈⠁⠈⠉⠀⠀⠀⠀⠀⣠⠴⠮⠥⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢳⣸⠀⢻⣦⠀⠻⢦⠀⠙⢲⠀⠀⠀⣠⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠁⢀⡶⣃⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⢇⠻⣆⠀⠹⡇⠀⠸⡆⠀⡾⠀⠀⢰⠃⢀⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⣩⣞⣭⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⣠⠘⣷⣄⠘⠆⠉⢠⡀⣷⠀⠀⡇⠈⠁⠀⣰⠋⠰⠊⠀⠀⣀⡄⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⠎⠁⠞⢛⣭⠿⢿⣁⣀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⢾⣾⣀⠀⡰⡠⣿⠀⠀⢸⠁⢠⠏⠉⡤⠀⠀⢀⠔⠋⠀⠀⢀⡠⠶⣺⠿⠋⠀⠀⠀⠀⠀⢀⡠⠶⣋⣭⠿⠋⠁⠀⠀⠀⠀⠷⠴⣶⣛⣟⣁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢯⣹⣿⡀⡇⠁⣿⠀⠀⡞⠀⠏⢀⡞⠁⡠⠞⠋⠀⠀⢀⠔⠉⣠⣞⣥⡄⠀⠀⠀⢀⡤⠞⠋⠀⠈⠉⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠟⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣿⡇⡷⢠⣿⣸⣧⠀⠀⣄⣼⠗⠋⠀⠀⠀⠀⠔⠁⠀⣴⠛⠁⠈⠀⢀⣠⠞⠁⠀⠀⠀⠀⠀⢀⣠⢴⡾⠋⠀⠀⠀⠀⠀⠀⠀⠈⠉⣷⠦⠄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣾⡿⢁⣼⣿⣿⣿⢠⣾⣿⣷⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣟⠁⠀⠀⠀⠀⠀⡀⠀⢩⡴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⡭⢿⡆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢿⠋⠁⠋⠈⢈⣿⢿⣾⡿⠿⣛⣛⡛⢶⡄⠀⠀⠀⢀⡄⠀⠀⢀⡿⣫⠞⠀⠀⠀⠀⣤⡾⠁⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠤⠶⠤⠀⢀⠈⠭⠟⠓⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠃⠁⠰⠀⠀⠀⣈⠈⠘⠁⠁⠞⠉⠈⢹⠀⡷⠀⠀⡠⠊⠀⠀⠀⢘⠉⠁⠀⠀⢀⡴⣫⠟⠁⠀⠀⠀⠀⣀⣴⠟⠀⢀⣀⠤⠀⡐⠒⠉⠁⣄⣀⣀⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁⠀⠀⣰⠆⠀⠚⠁⠀⠀⠀⠀⠀⢀⡴⣯⡾⣃⠀⠐⠢⠤⣤⣤⡶⠾⠂⠀⠀⢀⣩⠾⠋⠀⠀⠀⠴⣲⡿⠋⠁⢀⣀⡍⠀⠞⣛⡧⠄⠀⠤⣈⠳⣄⠀⠀ ⠀⠀⠀⠀⠀⠀⣴⠟⠁⠀⠀⢀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡾⠿⠟⣻⣯⣶⣦⠞⠋⠁⠀⢀⣤⣴⣶⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⣀⣀⡄⠀⠤⠄⠀⠀⠀⠘⣻⣟⡻⠀ ⠀⠀⠀⢀⣠⡾⠋⠀⠀⠀⢰⣿⣿⣻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠷⠒⠒⣒⣛⣛⣉⣁⣀⣄⠀⠀⠀⠀⢀⣀⡤⠤⠾⠭⠍⠉⠀⠀⠀⣀⣀⡀⠀⠀⢀⠀⠈⠉⠛⠂ ⠀⣠⡴⠟⢁⡴⠀⠀⠀⠀⠈⠛⠟⠛⠁⠀⠀⠀⠀⠀⠀⣐⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠓⠛⠛⣭⡭⠭⠿⠶⠶⣦⣄⢰⣶⣤⡀⠒⠦⠄⠙⠛⣿⠭⠙⡿⣒⠆⠀ ⣼⣿⢷⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠳⠤⢤⣥⣄⣙⢯⡙⠂⠀⡀⠀⠀⠀⠀⠀⠙⠛⠿⣦ ⠙⢮⣟⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠈⠛⢯⣟⠿⢷⡄⠉⠙⠲⣷⡦⠴⣦⢤⣀⠈ ⠀⠀⠀⠉⠛⠒⢶⣒⠒⠀⠀⠀⠀⠀⠀⠠⠒⠋⠀⠀⠀⠀⠀⢀⡀⠀⠀⢀⣠⣄⣀⠀⠀⠀⠀⡀⠀⠀⠀⠤⣜⣛⣒⠀⠀⠀⠀⠀⢀⠀⠀⠈⠻⠓⠦⢤⣄⣰⣼⣷⣦⣈⢣⡈⠁ ⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠉⠉⠉⠁⠀⠀⠀⠀⠒⠲⢤⣀⣦⣀⠉⠳⡝⠓⠈⠁⠉⠓⢦⣀⠀⠙⢦⣀⠀⠀⠀⠀⠉⢃⡀⠀⠀⡆⠈⢻⣄⠆⠀⠀⠀⠀⢦⡙⣿⢿⣦⠈⠙⢷⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠈⠙⠫⠳⢦⣼⣀⠀⠈⠷⡄⣀⠙⠲⢄⣀⠈⠙⠓⠀⠀⠀⠀⠙⠲⠀⢻⡄⠀⠙⠣⣀⠀⠀⠀⣼⣿⠇⠀⠙⠃⠀⠀⠉ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡇⠀⠀⢀⡠⠊⠁⢈⡟⠀⠀⠙⢾⣷⡗⢄⡈⠑⠦⣀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⢸⡇⢠⡾⠃⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣟⡍⠉⠉⠀⢀⡴⠋⣀⣠⡴⠋⠀⠀⠀⢀⡾⠃⠁⠀⠉⠛⠒⠈⠛⠲⠶⣴⣮⣿⣶⣾⠟⠀⠀⢀⣾⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠓⠋⠀⢿⣏⣀⣀⣀⣀⣤⠴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣅⣠⣤⡶⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⣀⠀⠀⠀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡀⡀⣀⡀⢀⣀⡀⣀⣀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠋⠃⠛⠛⠚⠃⠓⠛⠛⠛⠀⠀⠓⠛⠂⠘⠓⠛⠛⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⠿⠀⠉⠛⠻⢷⠂⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣤⡶⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠃⠺⣧⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣆⠀⠀⠀⠀⠀ ⠀⠀⣰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣷⣀⣴⣾⣿⡄⠀⠀⠀⠀ ⠀⠰⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⡟⠉⠙⢿⣿⣄⠀⠀⠀ ⠀⠀⢸⣇⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣴⣿⣿⣿⣿⣶⣴⣿⣿⣿⣃⣀⠀ ⠀⠀⠀⢿⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠃⠀ ⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⢀⣤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⢤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡼⠋⠀⣀⠄⡂⠍⣀⣒⣒⠂⠀⠬⠤⠤⠬⠍⠉⠝⠲⣄⡀⠀⠀ ⠀⠀⠀⢀⡾⠁⠀⠊⢔⠕⠈⣀⣀⡀⠈⠆⠀⠀⠀⡍⠁⠀⠁⢂⠀⠈⣷⠀⠀ ⠀⠀⣠⣾⠥⠀⠀⣠⢠⣞⣿⣿⣿⣉⠳⣄⠀⠀⣀⣤⣶⣶⣶⡄⠀⠀⣘⢦⡀ ⢀⡞⡍⣠⠞⢋⡛⠶⠤⣤⠴⠚⠀⠈⠙⠁⠀⠀⢹⡏⠁⠀⣀⣠⠤⢤⡕⠱⣷ ⠘⡇⠇⣯⠤⢾⡙⠲⢤⣀⡀⠤⠀⢲⡖⣂⣀⠀⠀⢙⣶⣄⠈⠉⣸⡄⠠⣠⡿ ⠀⠹⣜⡪⠀⠈⢷⣦⣬⣏⠉⠛⠲⣮⣧⣁⣀⣀⠶⠞⢁⣀⣨⢶⢿⣧⠉⡼⠁ ⠀⠀⠈⢷⡀⠀⠀⠳⣌⡟⠻⠷⣶⣧⣀⣀⣹⣉⣉⣿⣉⣉⣇⣼⣾⣿⠀⡇⠀ ⠀⠀⠀⠈⢳⡄⠀⠀⠘⠳⣄⡀⡼⠈⠉⠛⡿⠿⠿⡿⠿⣿⢿⣿⣿⡇⠀⡇⠀ ⠀⠀⠀⠀⠀⠙⢦⣕⠠⣒⠌⡙⠓⠶⠤⣤⣧⣀⣸⣇⣴⣧⠾⠾⠋⠀⠀⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⣭⣒⠩⠖⢠⣤⠄⠀⠀⠀⠀⠀⠠⠔⠁⡰⠀⣧⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⢤⣀⣀⠉⠉⠀⠀⠀⠀⠀⠁⠀⣠⠏⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠒⠲⠶⠤⠴⠒⠚⠁⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⡀⡴⠰⡄⡔⢄⡰⢣⠔⡀⡠⠀⠀⠀⠀⠀⢀⠄⠠ ⠀⠀⠀⠀⠀⡄⠠⢇⠞⠙⣃⠈⠀⠁⠈⢀⡀⣀⢦⢄⠉⢀⠇⢒⠀⠀⠀⡸⣀⠐ ⠀⠀⠀⡤⠀⠱⠁⠀⠀⣀⢉⡂⠑⠢⡒⠀⢈⠀⢈⠀⢦⠼⠉⣈⡀⠈⠁⠀⠀⢘ ⠀⠀⠗⠴⡀⠀⠠⡲⠌⠀⠑⠘⠶⡒⠀⠑⢖⠈⣠⢖⠾⠂⢸⢿⣿⠀⠀⠀⠀⠌ ⢀⠡⠘⠀⠀⡉⠖⢀⠤⠊⠑⠀⡀⠐⠂⢁⡠⠉⠈⢮⣲⠂⠀⠁⠁⠀⠈⡖⠒⠰ ⢬⠯⠁⠐⠛⡀⠈⢉⣭⡒⢀⠭⠀⣀⠤⠈⣉⠆⠐⠢⣉⠀⠀⠀⠀⠀⠀⠀⠀⡘ ⢀⡱⠆⠐⠓⢂⠴⠍⢀⡰⠉⠥⣄⡂⢀⣜⣁⣥⣌⣫⡀⠀⠀⠀⠀⠀⠀⣠⠊⠀ ⠀⢎⡁⢀⠴⠅⡠⠒⠃⢀⡴⡅⢀⢔⠋⡴⢀⠰⡒⠓⠀⠀⠀⠀⠀⠀⡔⠁⠀⠀ ⠈⣹⡥⠀⠀⡜⣨⡂⣔⠥⡞⢂⠎⡅⣄⠰⢼⡉⠑⠀⠀⠀⠀⠀⢀⡜⠀⠀⠀⠀ ⠀⠀⠞⣙⠚⠖⠁⣜⢠⢤⠑⡌⠱⠉⠃⠙⠀⠁⢀⠀⠀⠀⣄⡠⠊⠀⠀⠀⠀⠀ ⠀⠀⠀⠎⢒⡾⡜⠀⡡⠊⠹⡲⠤⢀⣀⣀⣀⡀⠼⠀⠀⠀⢫⡐⢀⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⢄⣀⠀⠈⠡⡒⢾⠂⠀⠀⠀⠀⠀⠀⠳⢄⡀⠀⠈⠓⣄⣳⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠑⠢⠴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⣌⣢⢡⠉⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠐⢶⣶⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀ ⠀⢀⣠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀ ⠰⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀ ⠀⠀⠀⠈⠙⣿⣿⣿⣿⣿⣿⡿⠛⠛⢿⣿⣿⣿⣿⣄⣀⣀ ⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⠁⢠⡄⠈⣿⣿⣿⣿⣿⣿⠟ ⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣷⡋⠀⠀⣿⣿⡿⢻⠟⠁⠀ ⠀⢠⡿⠟⠋⠉⠉⠀⠀⠉⠛⢿⣿⣷⣶⣿⣻⠁⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠃⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠤⠤⢠⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⠉⠁⢀⣀⠀⠀⠀⠉⠙⠓⠶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣶⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣾⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠤⠤⠤⠤⠖⠛⠙⢿⣅⡀⠀⠀⠀⠀⠀⠙⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⣿⡇⠀⠀⠀⠀⢀ ⠀⠀⠀⣿⣿⣿⣿⣿⠀⠂⠀⠀⠀⠀⠀⢀⣾⣭⣤⣤⣤⣤⣄⣀⠀⣀⣀⢀⡟⢹⣶⣤⣀⡀⢀⣀⣠⣼⣳⣄⠀⠀⠀⠀⠀⠀⠀⣼⢻⣷⣦⣾⠀⠀⡄⠀⣠⠟ ⠀⠀⠀⠀⠉⠛⠿⢿⣿⣷⣄⠀⠀⠀⢠⣾⠿⠛⠉⠙⠛⠻⠿⣿⠿⢟⣡⣾⡁⠀⣿⠻⠿⣿⠿⠿⣿⣿⠟⠻⣆⠀⠀⠀⠀⠀⣸⣿⣮⣿⣿⣿⡇⠘⢀⡼⠋⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣶⣤⡴⣿⣿⡆⢚⣻⣿⣿⣟⡿⠛⠺⠟⠉⠈⠀⠘⠛⠀⠀⠰⢾⣿⣿⣿⣷⣦⡌⠷⣄⠀⢀⣼⣿⡿⠛⠛⠉⠉⣷⣴⠋⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⢰⣿⣿⠱⣿⣋⣽⣿⣿⣝⣿⣾⣆⣠⡴⠶⠞⠷⣾⣆⣶⠾⣿⣶⡶⢮⣝⢿⡀⠘⢾⣿⠟⠁⠀⠀⠀⠀⠀⠸⣿⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⠇⠀⠀⠉⠛⠿⣿⣿⡿⠿⠟⠛⠉⣩⡥⠤⠄⠀⠀⠈⠙⠻⢾⣿⣿⣟⣒⠋⠀⠁⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⢀⣴⠆⠀⢠⠞⠁⠀⠀⠀⢶⣆⡀⠀⠀⠀⠐⣬⡉⠉⠁⠀⠀⠀⠈⣷⡀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠱⡄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣤⣶⣶⣤⣤⣀⡀⠀⠈⢻⣧⣄⣀⣤⣤⢸⣿⢶⣤⡀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢀⣤⣶⠿⠟⠉⠀⠉⠉⠙⠿⠿⣿⣿⣿⣿⣾⣿⠿⠛⠋⠙⠻⣿⣷⣿⣿⣶⣄⡀⠀⢹⣆⠀⠀⣀⣀⠤⠞⠋⠀⣠⣴⠆ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⢰⣿⠋⣡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠉⠙⢿⡀⠀⠀⠀⠀⠀⠛⢿⣿⣿⣽⣿⡆⠀⢹⡆⠉⠉⣀⣤⠴⠚⠋⠉⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣼⠏⠀⠀⠀⠘⠏⣸⣿⣴⣦⣤⣤⣤⣤⣤⣀⣷⣀⠀⠀⠀⠀⣘⣃⣀⣀⣀⣀⣀⣀⣈⣿⡏⢿⡇⠿⠀⣸⡷⠚⠋⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡴⠛⣡⡆⠀⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⢻⣿⠉⢻⡿⠛⠿⣿⠿⠿⠿⣿⡟⠻⡿⢿⣿⣿⣿⡟⠷⢸⡇⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣴⠋⣠⠾⠙⣷⠀⠀⠀⠀⠀⠀⠀⠘⢻⣿⣿⣿⣿⣶⣾⣇⣀⣀⣿⣄⣀⢀⣿⣅⣠⣧⣼⣿⠿⠙⠀⠀⠈⠇⠀⠀⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡾⠉⡟⠁⠀⠀⠹⣦⠀⠀⠀⠀⠀⠀⠀⠀⠁⢹⣟⣿⣿⣿⣿⠹⣿⡝⢿⡟⠻⣿⣿⠻⡟⠛⠁⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⡇⢰⠁⠀⠀⠀⠀⠙⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⠶⠶⢶⣶⣦⣤⣶⣶⣾⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⠂⡿⠀⠀⠀⠀⠀⠀⠘⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣧⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣿⢸⠁⠀⠀⠀⠀⠀⠀⠀⠘⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡆⠀⠀⠀⠀⠀⠀⢀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⡇⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣧⠹⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣼⠇⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⡇⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠛⠀⢸⠙⠷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⠀⠀⠀⣀⣠⠴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⣿⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⢠⡟⠀⠀⠀⠉⠛⠷⠦⣤⣤⣀⣀⣀⣀⣀⣀⣀⣈⠛⣦⣴⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⠀⣼⣷⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⢻⡁⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⠀⠈⣿⡀⠀⠀⠀⠀⠀⠀⣸⠇⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⣿⣧⠀⠻⡇⠀⠀⠀⠀⠀⠀⢸⡀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠘⣿⣧⡀⠀⠀⠀⠀⠀⠀⠐⢺⡿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⢡⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠻⠿⠁⠀⠀⠀⠀⠀⠀⢸⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⠀⠀⠀⠀⢠⡤⠛⠛⠀⠈⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁⠀⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠐⠿⢦⣤⣤⣤⣼⣀⣀⣤⣤⠴⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠉⠙⠒⠦⠤⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠳⠶⠦⠤⣤⣄⣀⣀⠀⠠⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡉⠉⠉⠉⠉⠉⠉⠉⠙⠓⠒⠲⠤⢄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠙⢦⡀⠀⠉⠛⠲⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⡾⠁⢠⠶⣄⠙⣄⠀⠀⠀⠀⠈⠑⠦⣄⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⡤⠀⠀⠀⡼⠀⢠⡏⠀⠈⢧⠸⡄⠀⠀⠀⠀⠀⠀⠈⠳⢄⡟⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡶⠚⠉⠁⠀⠀⠀⢸⠁⠀⡼⠀⠀⠀⠘⡆⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⡾⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⡇⠀⣀⡤⠴⠃⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⢦⣀⡤⠤⠒⠒⠒⢲⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣀⣠⣴⣶⡿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠻⠋⠀⣠⡶⠾⠓⠲⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠉⠀⠀⠀⣀⠴⢲⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠻⣿⣯⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢀⡾⠉⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⢠⢧⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠻⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⢀⡴⢤⠀⠀⠹⡄⠀⠀⡤⠚⠀⠀⠀⠀⠈⢧⣤⣯⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡏⠀⠀⠀⠀⠀⢸⠀⢸⠀⠀⠀⠙⣆⠚⠀⠀⣠⣤⠶⢶⣤⣈⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⢿⠀⢸⠀⠀⠀⠀⠘⡷⠒⣿⠀⠀⣠⠴⣾⣿⣿⠀⠀⠀⠀⢀⡴⠚⢻⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⣸⣆⣸⣤⠤⠴⠶⠖⠓⠶⣿⡴⠊⠁⢀⣼⣿⢹⠀⠀⠀⣰⠏⠀⠀⡞⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠉⠉⠉⠉⠉⢀⣦⣀⠀⠀⠀⠀⠀⠀⠀⠿⠤⠤⠶⣏⣡⠇⢸⠀⠀⢰⡟⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⣅⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡟⠀⢀⣿⣁⣠⠤⣏⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣴⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠒⠒⠒⠀⠀⠀⠀⠀⠀⣸⠁⢀⣿⣏⡁⠀⠀⣀⠙⠲⢤⣀⠀⠀⠀ ⠀⠀⠀⠀⢀⣴⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⣼⠛⠉⢹⠖⠉⠁⠀⠀⣠⠈⠳⣄⠀ ⠀⠀⠀⠀⠻⢿⣷⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢟⡴⠚⠁⠀⢠⣿⠀⠀⠀⢠⡞⠁⠀⠀⠈⡇ ⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⠷⣶⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠋⡟⠀⠀⣠⢶⠋⢿⣄⡀⢰⠋⠀⠀⢀⠀⢀⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠿⠶⠤⣤⣄⣀⡀⠀⠀⠙⢲⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠴⠛⠁⠀⣠⣇⠀⠀⠀⠈⡇⠀⠀⠉⠉⠦⠤⢤⠎⢀⡜⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣩⡽⣿⡿⠛⠛⡇⠉⠉⠙⠛⣳⠶⠚⠛⠛⠻⢶⣄⠀⠀⣰⠃⠹⣄⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢀⣰⠏⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠴⠚⠉⣤⠞⠁⠀⢀⡼⠁⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠹⣿⠏⠹⡆⠀⠈⠓⢦⡀⠀⠀⠀⠀⠀⣀⣴⠟⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⡞⠀⠀⠤⢾⣉⣀⡀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠳⠀⠀⠀⠀⠙⠲⠶⢶⣾⠛⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢀⠀⠀⢀⣤⠈⣧⣽⣀⣀⣀⣈⠷⠎⢻⣀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣠⠶⠟⠟⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⣸⠋⢳⡀⠈⢧⠀⠀⠀⠀⠀⠀⠀⢰⢋⣧⡀⠀⠀⢀⡴⠒⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠑⠦⠀⠀⠀⠀⠀⢟⠁⠀⠉⠙⠚⢁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠂⠉⠀⠀⠀⣠⣶⡏⠙⠓⠖⣤⣀⠀⠀⠀ ⣀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠛⠉⠀⠀⠀⠀⠀⣠⣿⠋⢸⣷⣶⠆⠀⠀⢉⣳⠄⠀ ⡿⣯⣖⣠⢄⣀⣠⡾⠋⠀⠀⠀⠀⠀⠀⡠⡺⢋⠊⠀⢸⣿⣟⣀⠴⠚⠉⠀⠀⠀ ⢿⡈⢻⣝⠉⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠤⣀⠀⡎⣟⣛⠤⢀⡀⠀⠀⠀⠀ ⠘⣧⠀⢹⣄⡀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠁⠀⠉⠀⠉⠀⠏⠀⠀⠁⠊⠕⡤⡀⠀ ⠀⠸⣷⢿⣖⠙⠄⠀⠀⠀⠀⠀⠐⣡⠔⠋⠙⢶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠢ ⠀⠀⢧⡼⠀⠱⡀⠀⠀⡀⠀⠀⡸⠁⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠹⣇⠀⠀⠱⡀⠠⡇⠀⢰⠃⠀⠀⠀⣀⠀⢀⡄⠀⠀⠰⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⣿⡀⠀⠀⢳⡄⡇⢠⠏⠀⠀⠀⢸⣥⠀⡜⠀⠀⠀⠀⠘⢣⣤⡀⠤⣤⠤ ⡀⠀⠀⠹⡗⢴⣖⣬⡷⢓⡊⠀⠀⠀⠀⢸⣏⠜⡀⠀⣀⠄⠒⠠⢄⣀⠹⠷⣄⠁ ⠈⠑⠤⡀⠣⡀⠙⠿⠶⠠⢀⠁⠂⠀⠒⢈⠠⠄⣾⠞⠁⢀⣄⡀⠄⠈⠺⡄⠱⠑ ⠀⠀⠀⠈⠗⡌⠢⢄⡀⠀⠀⠀⠉⠅⢊⣀⡴⠞⠁⢀⡴⠋⠹⢿⠐⣄⠜⠀⠀⠀ ⠀⠀⢀⡢⢂⡎⡆⢀⠔⠋⡽⠛⠛⢛⠯⡁⠘⠢⠲⠯⣇⣀⣀⣸⣀⠀⣀⠄⠀⠀ ⠀⠀⠏⠀⣾⠃⡎⠀⢀⠔⢃⠀⠀⠁⠀⠈⠢⡀⠀⠀⢱⡠⠚⡛⠳⣬⠓⠂⠀⠀ ⠂⠊⠀⠛⢁⣼⠥⠒⠁⠀⠈⢢⡀⠀⠀⠀⠀⠱⠀⠀⠸⠗⣹⣥⣀⠘⢄⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⢀⣴⠟⠉⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣀⢀⣾⠿⠻⢶⣄⠀⠀⣠⣶⡿⠶⣄⣠⣾⣿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢻⣿⣿⡿⣿⠿⣿⡿⢼⣿⣿⡿⣿⣎⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠉⠛⢛⣛⡉⠀⠀⠙⠛⠻⠛⠑⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣧⣤⣴⠿⠿⣷⣤⡤⠴⠖⠳⣄⣀⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣀⣟⠻⢦⣀⡀⠀⠀⠀⠀⣀⡈⠻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠉⡇⠀⠀⠛⠛⠛⠋⠉⠉⠀⠀⠀⠹⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⠀⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠈⠑⠪⠷⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣦⣼⠛⢦⣤⣄⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠢⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠲⠖⠛⠻⣿⡿⠛⠉⠉⠻⠷⣦⣽⠿⠿⠒⠚⠋⠉⠁⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣾⠛⠁⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⠀⠀⠀ ⠀⠀⠀⠀⣰⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀ ⠀⠀⠀⣰⣿⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣧⣄⠀⠀⠀⠀⠀⠀⢳⡀⠀ ⠀⠀⠀⣿⡾⢿⣀⢀⣀⣦⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⣫⣿⡿⠟⠻⠶⠀⠀⠀⠀⠀⢳⠀ ⠀⠀⢀⣿⣧⡾⣿⣿⣿⣿⣿⡷⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢿⣿⣧⠀⡀⠀⢀⣀⣀⢒⣤⣶⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⠀⡾⠁⠙⣿⡈⠉⠙⣿⣿⣷⣬⡛⢿⣶⣶⣴⣶⣶⣶⣤⣤⠤⠾⣿⣿⣿⡿⠿⣿⠿⢿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⣸⠃⠀⠀⢸⠃⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⠟⡉⠀⠀⠀⠈⠙⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⣿⠀⠀⢀⡏⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠛⠉⠁⠀⠀⠀⠀⠀⠉⠠⠿⠟⠻⠟⠋⠉⢿⣿⣦⡀⢰⡀⠀⠀⠀⠀⠀⠀⠁ ⢀⣿⡆⢀⡾⠀⠀⠀⠀⣾⠏⢿⣿⣿⣿⣯⣙⢷⡄⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣻⢿⣷⣀⣷⣄⠀⠀⠀⠀⢸⠀ ⢸⠃⠠⣼⠃⠀⠀⣠⣾⡟⠀⠈⢿⣿⡿⠿⣿⣿⡿⠿⠿⠿⠷⣄⠈⠿⠛⠻⠶⢶⣄⣀⣀⡠⠈⢛⡿⠃⠈⢿⣿⣿⡿⠀⠀⠀⠀⠀⡀ ⠟⠀⠀⢻⣶⣶⣾⣿⡟⠁⠀⠀⢸⣿⢅⠀⠈⣿⡇⠀⠀⠀⠀⠀⣷⠂⠀⠀⠀⠀⠐⠋⠉⠉⠀⢸⠁⠀⠀⠀⢻⣿⠛⠀⠀⠀⠀⢀⠇ ⠀⠀⠀⠀⠹⣿⣿⠋⠀⠀⠀⠀⢸⣧⠀⠰⡀⢸⣷⣤⣤⡄⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⢼⡇ ⠀⠀⠀⠀⠀⠙⢻⠄⠀⠀⠀⠀⣿⠉⠀⠀⠈⠓⢯⡉⠉⠉⢱⣶⠏⠙⠛⠚⠁⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⠀⠀⠀⠀⠀⠻⠄⠀⠀⠀⢀⣿⠀⢠⡄⠀⠀⠀⣁⠁⡀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⢀⣐⡟⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢠⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⠀⠀ ⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠉⠀⠀ ⣤⣶⣤⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀ ⢿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⡀⠀⠀ ⠘⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀ ⠀⣿⠁⢻⣿⣿⠇⠀⠀⠀⣴⣄⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠷ ⠀⢻⠀⢀⣿⣿⠀⠀⠀⠀⣿⣿⡄⢸⣿⣿⣿⣿⣿⣿⣿⣟⠉⠀⠀⠀⠀⠀ ⠀⠘⡆⠘⣿⡇⠀⠀⠀⠀⠘⠛⢃⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀ ⠀⢀⣼⣶⣾⣧⣤⣤⣄⣀⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀ ⠀⠀⠉⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠛⠛⠛⠛⠛⠿⠿⣧⠀ ⠀⠀⠀⠀⠀⠀⠈⠙⠛⠻⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠿⠿⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣾⣿⣶⣶⣤⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠘⢿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀ ⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠈⠻⣿⣿⣿⣿⣆⠀⠀⠀⢀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⣀⣤⣶⣶⣌⠻⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀ ⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⠁⣰⣿⣿⣿⣿⣿⣦⣙⢿⣿⣿⣿⠄⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣦⣹⣟⣫⣼⣿⣿⣶⣿⣿⣿⣿⣿⣿⣯⡉⠉⠉⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠐⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⡆⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⢻⣿⣿⣿⣿⣿⡇⠀⠀⠈⠉⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⣠⣴⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⡇⠀⠸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠹⢿⣿⣿⢿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢰⣶⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣧⣄⣐⣀⣀⣀⣀⣀⡀ ⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠁⠛⠛⠛⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

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

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⢀⣤⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣤⡀ ⢸⣿⣿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣿⣿⡇ ⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇ ⢸⣿⣿⠀⠀⠀⠀⠀⣠⣦⡀⠀⠀⢀⣿⡟⠀⢀⣴⣄⠀⠀⠀⠀⠀⣿⣿⡇ ⢸⣿⣿⠀⠀⠀⣠⣾⡿⠋⠀⠀⠀⢸⣿⠇⠀⠀⠙⢿⣷⣄⠀⠀⠀⣿⣿⡇ ⢸⣿⣿⠀⠀⠘⢿⣿⣄⠀⠀⠀⢀⣿⡟⠀⠀⠀⠀⣠⣿⡿⠃⠀⠀⣿⣿⡇ ⢸⣿⣿⠀⠀⠀⠀⠙⢿⣷⠄⠀⢸⣿⠇⠀⠀⠠⣾⡿⠋⠀⠀⠀⠀⣿⣿⡇ ⢸⣿⣿⠀⠀⠀⠀⠀⠀⠁⠀⠀⠿⠟⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⣿⣿⡇ ⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇ ⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇ ⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹⣿⣿⣿⣿⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣼⣿⣿⣿⣿⣧⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠒⠛⢙⣶⡟⠻⣧⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣤⣤⣀⣀⣀⡔⠋⠀⠀⠀⠀⠉⡌⠀⢠⡷⢬⣙⣧⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢻⣏⠁⠢⡁⠀⠀⠀⠀⠀⠀⠀⠈⠑⠚⡇⠀⠉⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠹⣦⠴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⠀⣀⣀⠀⠀⠀⠀⠀⠀⢠⠖⠹⣀⠘⡆⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢻⣧⡇⠈⠳⡀⠀⣇⠀⣠⣿⡄⢰⡽⠀⠙⠻⣖⠒⠾⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢿⢻⣄⠀⠹⣶⣾⣾⣁⡿⠗⢻⠇⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⡄⠻⣓⠋⠉⠉⠁⠀⣠⡾⠏⣀⣤⡴⢿⡙⢢⣸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠹⡄⠈⢙⡖⠒⡖⠻⡝⢷⣾⣿⠛⢳⡀⠑⠄⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⣄⡞⠀⠀⣣⠀⠙⣾⣅⠀⠳⡀⠑⠀⠀⣸⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⢹⠀⠀⣸⣿⠀⠀⠀⠀⣀⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣠⣴⠒⢦⡀⢀⡜⢩⣷⠒⠋⠀⢸⠢⣿⣧⣤⣴⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢰⢫⠞⣋⢷⣤⡏⠻⣴⠉⡇⢸⠓⡆⠸⡷⠧⠄⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠸⣆⡌⢠⠞⠉⣿⡶⠟⢠⡇⢸⠀⢹⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠙⠢⠦⣤⡿⠟⠀⠀⢸⠀⢸⠀⠈⡆⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⢸⠀⠀⢱⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣴⠋⣇⣀⣿⠖⣄⢸⡀⠘⣧⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣸⣗⠂⠀⠀⠐⣿⣏⠓⠒⠛⢁⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣀⡴⡞⠉⠉⢻⠒⠲⠚⡧⣏⣉⣉⣀⣠⣼⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⠞⠁⠀⠘⡄⠀⠀⡇⠀⠀⣷⣼⡟⠁⠀⠀⠈⠹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⡾⠁⠀⠀⠀⠀⢣⠀⣀⣧⣤⣶⠿⡟⢀⠖⠊⠉⠉⠒⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⠛⠷⣶⣶⣒⣶⣿⠿⠟⠋⠉⠀⠀⣧⠎⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣦⣀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢠⣤⣤⣤⡄⣄⣤⣤⠀⠀⣠⣤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠦⠿⠿⠿⠿⠿⠋⠀⠀⠀⠈⣉⠉⠉⠉⠉⣛⡛⠀⠉⢉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠉⠉⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣠⣤⣶⣦⣤⣤⣤⣤⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀ ⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠁⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀ ⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀ ⠀⠀⠀⣽⣿⡿⠛⢿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄ ⠀⠀⠀⣿⣿⠀⠀⠘⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⣴⣶⣦⡀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿ ⠀⠀⠀⣿⣿⠀⠀⠀⢹⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠉⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢹⣿⠀⠀⠀⢀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠘⣿⡆⠀⠀⢸⣿⣿⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⡇⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠹⣿⡄⠀⠘⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠃⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⣿⣄⠀⠹⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣦⣤⣤⣤⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀ ⠀⠀⠀⠀⠘⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠛⠿⠿⢿⣷⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣶⣶⣦⣄⡀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣴⣶⣶⣦⣤⣤⣄⣀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣾⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠉⠉⠙⠛⠿⢿⣶⣦⣀⠀⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⠛⠁⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣏⠀⣠⣴⣾⡿⠟⠛⠋⠉⠁⠀⠀⠀⠀ ⠀⢀⣠⣤⣤⣤⣤⣤⣤⣀⣈⠙⠻⣷⣿⣿⣿⣿⣿⡟⠀⠀⠀⢀⠀⠀⠀⠘⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⡿⠟⠋⣁⣀⣤⣤⣤⣤⣤⣤⣀⡀⠀ ⠈⠉⠉⠉⠉⠉⠉⠉⠛⠛⠿⢿⣶⣄⣿⣿⣿⣿⣿⡇⠀⠀⠀⣾⡆⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⢸⣧⠀⠀⠀⣸⣿⣿⣿⣿⣿⣤⣶⡿⠟⠛⠋⠉⠉⠉⠉⠉⠉⠉⠁ ⠀⠀⠀⣠⣤⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⢿⠃⠀⢀⣼⣿⣿⣿⣿⣧⡀⠀⠸⡏⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣤⣄⠀⠀⠀ ⠀⠀⠊⠉⠁⠀⣠⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣤⣶⣿⣿⣿⠿⠿⣿⣿⣿⣶⣤⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣀⠀⠈⠉⠑⠀⠀ ⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠛⠛⠛⠛⠛⠛⠋⠀⠀⠀⠀⠙⠛⠛⠛⠛⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠻⢿⣿⡿⠟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⣿⣿⠿⠋⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⣴⠂⡄⢠⢀⣄⣤⡀⢰⣄⡴⢻⢃⣼⢀⢦⠀⢀⣠⡤⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢰⡇⡘⢹⣼⠸⣞⠿⠈⠿⢳⡟⣿⠀⠾⠊⢸⠎⠈⠗⠱⠟⠚⠉⠙⠋⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⣷⡀⠸⣇⠈⢷⡀⠣⡄⠀⠀⡠⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠩⠝⢁⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣄⠀⢣⠻⡀⠙⡇⠀⢧⢀⡇⠀⣰⠃⣠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢋⡽⢯⣴⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠠⣶⣘⣷⡀⠁⡀⣦⠃⠀⡜⠀⡀⢴⠃⠈⠁⡠⠔⠀⠀⢀⣠⣤⠀⠀⠀⠀⠀⠀⣀⠤⣤⡴⠂⠈⠉⣽⢛⣫⣤⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⠀⠙⣿⠀⢠⠃⠘⢀⠌⢀⠤⠂⠀⢀⡤⠊⡡⣊⠀⠀⠀⢀⡠⠔⠉⠒⠋⠁⠀⠀⠀⠀⠈⠉⣹⣿⡷⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡆⣿⣴⡄⠀⣠⡼⢒⠁⠀⠀⠠⠋⠀⠞⠋⠉⠀⣠⠔⠉⠀⠀⠀⠀⣠⣤⠞⠀⠀⠀⠀⠀⠈⠙⣶⡤⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠏⣴⡿⣿⣧⣶⣿⣿⣋⡀⠀⠀⠀⠀⠀⠀⠀⣴⢟⡅⠀⠀⠀⣠⠀⠈⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠤⢿⣷⠀ ⠀⠀⠀⠀⠀⠀⠀⣰⠛⢁⠀⠀⠀⠙⠿⠛⡩⠓⠢⡙⡆⠀⢀⡴⠂⠀⠰⠟⠋⠀⠀⡠⣾⠋⠀⠀⠀⢀⣠⠀⠀⢀⡈⠉⠥⠔⠀⠉⠁⠀ ⠀⠀⠀⠀⠀⢀⡼⠃⠀⢠⠄⠀⠊⠀⠀⠀⠀⢠⣴⣵⡃⠀⠬⢤⣤⣤⠴⠀⠀⠀⣪⠞⠁⠀⠀⢤⡶⠛⠁⣀⡊⠩⢶⡦⠀⠠⢘⢯⡁⠀ ⠀⠀⠀⠀⣠⠞⠁⠀⢠⣤⣄⠀⠀⠀⠀⠀⠀⠶⠟⠛⢿⣷⣷⠚⠉⣀⣠⣴⠶⠋⠀⠀⠀⠀⠀⠀⢀⣀⣨⠤⠤⠀⠀⠀⠀⠀⠈⢿⣿⡂ ⠀⠀⣠⠞⠃⠀⠀⠀⢿⣿⡿⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠉⠉⠉⠛⠁⠠⢤⣶⣤⣤⣤⣤⣶⣒⣛⠂⣀⡀⢀⣀⠂⢤⣤⡤⢤⣤⣀⠀ ⣴⣿⠅⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠩⠭⠭⣭⣏⡛⢿⡢⠀⠀⠀⠀⠉⠀⠻⠶⣤ ⠙⠿⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠙⠻⢿⣻⠦⠈⠑⢶⡶⠔⢦⢤⡈ ⠀⠀⠀⠉⠙⠻⢭⣤⡤⢄⠀⠀⠈⢁⣀⠀⠀⠀⠠⣄⣄⡤⢶⢤⣀⠀⠀⣄⠀⠀⠒⠚⠧⡀⠀⠀⡀⢠⡀⠀⠙⠙⠒⡦⢼⣿⡓⠬⣦⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠿⠦⣈⣇⠀⠀⢄⠈⠳⢄⡀⠑⠢⠤⠀⠀⠐⠢⠄⢳⠀⠛⠇⡀⠀⠀⣸⣼⠉⠻⠀⠈⠓ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⠀⣠⠞⠉⣱⠀⠀⠻⡷⡶⢌⡁⠠⣀⠀⠀⠀⠀⠀⠘⡇⠀⠀⢹⢀⡴⠋⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣍⣭⣀⣠⠞⣡⠤⠚⠁⠀⢀⡴⠋⠀⠀⠉⠓⠈⠙⠒⠒⠚⣷⠾⠃⢀⣠⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠒⠒⠒⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠚⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠒⠓⠒⠒⠒⠒⠃⠐⠒⠒⠀⠀⠒⠊⠒⠛⠃⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠊⠉⠀⠀⠀⠀⠀⠀⠈⠁⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠿⠶⣄⡈⠂⠔⠀⠀⠈⠀⠀⠈⠉⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡘⡀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡆⠀⠀⠀⠀⠒⣉⣉⠛⢿⣿⣿⣄⠀⢀⣠⣤⣶⡾⠛⠋⠙⠁⣀⠔⠁⣠⣬⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠐⠁⢞⣯⠎⣸⠿⠛⠉⠀⠘⢿⣟⢭⣭⡅⠀⠀⠀⠀⡠⠚⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣀⡀⠀⠀⢀⣠⣤⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠜⠻⠃⠀⠀⠀⠰⠀⠀⠀⠀⣠⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣀⣀⣤⣼⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⣠⣤⣤⣤⣦⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣶⣶⣿⣿⣿⡀⠀⠀⠀⠀⠀ ⠠⠔⠒⠉⠉⠀⠈⠉⢿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢀⣼⠟⠛⠛⠛⠛⠻⢿⣷⣤⣄⣀⣠⣤⡶⠦⠤⡀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠟⠛⠉⠁⠒ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⠀⠀⢀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠉⠁⠀⠀⠀⠈⢳⣆⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠈⠀⠐⣶⣿⣿⠿⣿⠖⢦⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠻⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠸⣿⣿⣇⣿⣀⡈⠀⠀⠋⠉⠙⠛⠛⢲⣦⠤⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣶⣿⡿⠃⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠻⣿⣄⡉⠙⠛⠛⠛⠛⢻⡿⠋⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠷⠶⠶⠒⠉⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠲⣤⣤⣤⣤⣴⣾⣿⡿⠟⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⠀⠀⠀⠀⠉⠉⠉⠉⠉⢀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠢⠤⠤⠤⠤⠔⠊⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀ ⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀ ⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⠛⠛⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠛⠛⠋⠉⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⣦⡄⣿⣿⡇⢠⣶⡄⢀⣤⡀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⣀⣀⣀⣀ ⢀⣠⡄⣿⣿⣧⣿⣿⣧⣿⣿⣧⣼⣿⣿⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿ ⣾⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿ ⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿ ⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⣿⣿⣿⣿⡄⠀⠀⠀⢠⣿⣿⣿⣿ ⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠸⣿⣿⣿⣿⣶⣶⣶⣿⣿⣿⣿⠇ ⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠈⠻⠿⣿⣿⣿⣿⣿⠿⠟⠁⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠶⡦⠴⠶⠦⠤⢤⣤⣀⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠚⡹⢋⣤⠀⡇⠀⠀⠀⠀⠀⠀⠀⢉⣻⡶⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡴⠋⠁⠀⠈⢰⣿⣿⡆⡇⠀⠀⠀⠀⣠⡴⠚⠉⠀⠀⠀⠀⠀⠀ ⣠⡤⢤⣀⣠⡞⠀⠀⠀⢀⡀⠄⡈⠉⠁⠁⠀⠐⠒⠚⠳⠦⠤⣄⣀⠀⠀⠀⠀⠀ ⢹⡄⠀⠀⡘⠀⠀⠀⡐⢁⡠⠤⡈⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢦⡀⠀⠀ ⠀⠙⢦⡠⠁⠀⠀⠀⢡⠃⠀⠀⠈⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀ ⠀⠀⠘⡇⣄⠀⠀⠀⡌⠀⢰⠕⠀⠀⠀⠀⠀⠀⠀⠒⠤⣀⣠⡤⠴⠶⠦⠤⣼⡧ ⠀⠀⠀⠈⣧⢠⣀⠀⠇⠀⠈⢽⡧⠊⡉⠂⠀⠀⠀⠀⠀⠈⠙⢦⣀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢈⡧⣿⣷⠂⠀⠀⠈⠀⠐⣠⣖⣀⣀⣀⠀⠀⠀⠀⠀⠙⣦⡀⠀⠀⠀ ⠀⠀⠀⠀⠙⠶⠟⠳⠤⣤⡤⠤⠔⠚⠉⠀⠀⠈⠉⠉⠛⠒⠶⣤⣀⠈⢷⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠺⠇⠀⠀

⣿⣿⣿⣿⣿⣿⣿⠀⠀⣀⣤⣤⣄⡀⠀⠀⣤⣤⣤⣤⣤⣀⠀⠀⢠⣤⣤⣀⣀⣀⣀⣀⢀⣀⣤⡄⠀⢠⣤⣤⡄⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⣶⣶⣶⣶ ⣿⣿⣿⣿⣿⣿⣿⢠⣿⣿⣿⣿⣿⣿⣆⠀⣿⣿⣿⣿⣿⣿⣿⣄⢸⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⡀⢸⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿⡏⢸⣿⣿⣿⡀⣿⣿⣿⡏⢻⣿⣿⣿⡞⠛⢻⣿⣿⣿⠿⠿⢸⣿⣿⣿⣧⠘⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢸⣿⣿⣿⠋⠉⠉ ⣿⣿⣿⣿⣤⣤⢠⣿⣿⣿⡇⢸⣿⣿⣿⡇⣿⣿⣿⡇⢸⣿⣿⣿⡇⠀⢸⣿⣿⣿⠀⠀⢸⣿⣿⣿⣿⣆⣿⣿⡇⢸⣿⣿⣿⡇⠀⢸⣿⣿⣿⠀⠀⠈⣿⣿⣿⣤⣤⡄ ⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⡇⢸⣿⣿⣿⡇⣿⣿⣿⣷⣿⣿⣿⠟⠀⠀⢸⣿⣿⣿⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⡇⠀⢸⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⡇ ⣿⣿⣿⣿⠉⠉⠈⣿⣿⣿⡇⢸⣿⣿⣿⠇⣿⣿⣿⡿⣿⣿⣿⡀⠀⠀⢸⣿⣿⣿⠀⠀⢸⣿⣿⡇⢿⣿⣿⣿⡇⢸⣿⣿⣿⡇⠀⢸⣿⣿⣿⠀⠀⠀⣿⣿⣿⡏⠉⠁ ⣿⣿⣿⣿⠀⠀⠀⢻⣿⣿⣧⣼⣿⣿⡿⠀⣿⣿⣿⡇⢿⣿⣿⣧⠀⠀⢸⣿⣿⣿⠀⠀⢸⣿⣿⡇⠘⣿⣿⣿⡇⢸⣿⣿⣿⡇⠀⢸⣿⣿⣿⠀⠀⠀⣿⣿⣿⣧⣤⣤ ⣿⣿⣿⣿⠀⠀⠀⠈⠻⢿⣿⣿⣿⠟⠁⠀⠿⠿⠿⠇⠸⣿⣿⣿⡆⠀⠸⠿⠿⠿⠀⠀⠸⠿⠿⠇⠀⠸⣿⣿⡇⢸⣿⣿⣿⡇⠀⢸⣿⣿⣿⠀⠀⢰⣿⣿⣿⣿⣿⣿ ⢿⠿⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠈⠉⠉⠉⠀⠀⠘⠛⠛⠛⠻⠿⠿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⣉⡙⠛⣉⣉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠸⣿⣿⣾⣿⡿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡘⠻⣿⠟⣡⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣶⣤⣼⠟⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢡⣶⣦⡌⠻⡿⢁⣾⣷⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢻⣿⣿⣦⡀⢸⣿⡏⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠙⢿⣿⣿⣆⠙⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡌⠻⣿⣿⣷⣄⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢡⣴⣤⡘⢿⣿⣿⣧⡈⢿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢋⣁⠘⢿⣿⣿⣆⠙⣿⣿⣷⡀⢻⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠀⣿⣿⣷⣄⠻⣿⣿⣿⣿⣿⣿⣷⠈⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⡟⢠⣶⣤⡈⠻⣿⣿⣷⣿⣿⣿⣿⣿⣿⠏⣰⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⡈⢿⣿⣿⣶⣼⣿⣿⣿⣿⣿⣿⣿⠋⣰⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠙⢿⣿⣿⣿⣿⣿⣿⡿⠟⣡⣾⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣉⠛⠛⠛⢛⣉⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣄⣼⣀⢢⣠⠆⣼⢀⡤⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢢⣰⠸⢍⠁⠇⢇⢸⠀⠘⡏⠁⡐⠈⠘⢲⣀⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⢥⠺⠀⢁⡀⠑⠈⠀⠀⠀⢀⠀⠀⠁⠀⠀⣀⠔⢗⣀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣰⡒⠓⢰⠁⠈⢂⣀⡶⠧⡜⠜⠦⢺⡶⠉⠈⢡⢀⠠⢷⡆⠀⠀⠀ ⠀⠀⠀⠀⠉⡁⠖⠁⠈⡦⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡇⠀⠈⢉⣰⡀⠀⠀ ⠀⠀⠀⠠⢶⡓⠂⠀⠀⡗⡇⣠⣤⠀⠀⠀⠀⠀⣤⣄⠀⠙⢏⠁⠀⠀⠈⣐⣄⡀ ⠀⠀⠀⢘⠇⠀⠀⢀⡵⠂⢡⠛⠻⠀⠀⠀⠀⠀⠟⠛⠸⠀⠘⣦⠀⠀⠠⠴⣗⠀ ⠀⡠⢒⠝⠉⠀⠀⢴⠅⡀⠀⠢⠀⠀⠀⣀⡀⠀⠀⡰⠁⠀⢀⠱⡂⠀⠀⠀⢬⠆ ⠀⠀⣈⡽⠃⠀⠀⢮⠄⠐⡄⠀⠀⠠⣛⣿⣟⠠⠊⠀⠀⢠⠃⠹⠄⠀⠀⠀⢄⣂ ⡠⠊⣔⡥⠀⠀⠠⢧⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⠀⠸⠗⠈⠈⢀⠈⢢ ⠔⠉⢀⠎⠀⠀⠀⢛⣣⡀⠀⠑⢄⠀⠀⠀⠀⠀⢀⠄⠂⠀⢀⣾⡃⠀⠀⡀⠙⡁ ⠀⠀⡩⣖⡁⡠⠂⠁⢲⣬⠶⠤⢤⠃⠀⠀⠀⠀⢐⡤⠤⠮⣴⠚⠀⠐⠢⣈⢛⢅ ⠀⠊⠀⠱⢮⠀⢀⠀⠀⠙⡦⡄⠀⡷⣄⣄⣤⣤⡇⠀⠀⡤⠋⠀⠐⢄⢰⣴⠈⠀ ⠀⠀⠀⠀⠘⣰⡡⠀⢀⠄⠀⠑⠈⠀⠀⠀⠀⠀⠈⠀⠀⠠⡀⠈⢄⢸⠒⠂⠁⠀ ⠀⠀⠀⠀⠀⠉⠀⠂⠹⢲⠔⣄⢤⣀⣠⡤⡠⣀⢄⡦⡤⠔⠱⡁⠃⠉⠀⠀⠀⠀ ⣶⣶⣷⣿⣶⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣶⣶⣶

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣄⣀⣀⣀⣿⣶⣤⣄⡈⣽⣄⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⡿⠛⢉⣠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣼⣅⠘⢿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⡟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠹⣿⣿⣿⣿⣿ ⣿⣿⠏⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠈⠿⠋⠁⠀⢻⣿⣿⣿⣿ ⣿⣏⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⢠⣶⣦⡀⠀⠻⣿⣿⣿ ⣿⣿⡇⠸⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠋⠀⠀⠀⠀⠉⠋⠀⠀⠀⠼⠿⣿ ⣿⣿⣿⡀⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣼⣿ ⣿⣿⣿⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣶⣾⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⢠⣶⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⣿⡟⠹⣿⣆⠀⠀⠀⠀⠀⠀⣰⣿⠏⢻⣿⡄⠀⠀⠀⠀ ⠀⠀⠀⢠⣿⡟⠀⠀⠻⠟⠀⠀⠀⠀⠀⠀⠻⠟⠀⠀⢻⣿⡄⠀⠀⠀ ⠀⠀⢠⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡄⠀⠀ ⠀⢀⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡀⠀ ⠀⣾⣿⣃⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣘⣿⣷⠀ ⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⡟⠛⠛⠛⠛⠛⠛⣿⣿⣿⣿⣿⣿⠛⠛⠛⠛⠛⠛⢻⣿⣿⡇ ⢸⣿⣿⡇⠀⠀⠀⠀⠀⣼⣿⣿⡟⢻⣿⣿⣧⠀⠀⠀⠀⠀⢸⣿⣿⡇ ⢸⣿⣿⣷⣶⣶⣶⣶⣶⣿⣿⡟⠀⠀⢻⣿⣿⣶⣶⣶⣶⣶⣾⣿⣿⡇ ⠀⠛⠿⠿⠿⠿⠿⠿⠿⠿⠟⠁⠀⠀⠈⠻⠿⠿⠿⠿⠿⠿⠿⠿⠛⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⡤⣤⣤⣴⡯⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠋⠁⠀⠀⣀⡼⣻⠏⠀⢹⡏⠳⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣶⣶⣤⠤⣄⣀⣠⠟⠁⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⣼⡟⢶⣄⣙⡷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠹⣷⡈⠓⠦⣈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠒⢻⡇⠀⠈⠙⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠹⣷⣄⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠚⣯⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⡆⠀⠀⠀⠘⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⡇⣤⠤⣄⠀⠀⠀⢰⠀⠀⠀⠀⣰⠟⠁⢹⢰⠄⢧⡀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢻⣧⢿⠀⠈⠳⣄⠀⠀⣧⠀⠀⣴⣿⡇⠀⡞⣼⠀⠈⠛⢿⣟⠒⠦⠼⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⣯⢿⣧⠀⠀⠙⣷⣄⣹⣠⠞⠙⣿⣧⡴⣿⠃⠀⠀⠀⠀⠉⢳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢹⡄⢻⣷⣄⣀⣽⡷⣿⡗⠓⠒⠛⢉⣤⡞⠀⠀⠀⢀⣤⣤⡀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢻⡀⠻⢦⣀⠀⠀⠀⠀⠀⣠⣴⡿⠛⣀⣴⣶⡷⠟⢧⡄⠙⢦⣹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠉⣹⠗⠒⢾⠛⢿⠉⢷⣾⣻⣾⠛⠻⣆⠀⠙⢦⡀⣷⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⢠⡏⠀⠀⢸⠀⠈⠳⣰⡟⠀⠙⢧⡀⠈⢧⠀⠀⠀⣸⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⠀⠀⠀⠸⡄⠀⠀⢳⣷⡇⠀⠀⠓⠀⠀⠀⠀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣇⠀⠀⢀⡇⠀⢀⣴⣿⣇⠀⠀⠀⠀⢀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣀⣠⡶⠒⢦⣀⠀⢀⡼⠋⣽⣷⠶⠋⠀⠀⣿⠲⣜⣾⣧⣤⣶⣶⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣴⠟⣩⠿⢻⣦⣀⣿⠻⣯⣀⡞⢹⠀⠓⡶⢤⠀⣿⣶⢼⣁⠈⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⡞⢁⠔⠛⣉⡿⣿⡄⢈⣻⡄⢸⠀⠀⡇⠘⡆⠈⡏⠉⠉⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠹⣧⡜⠀⡞⠁⣀⣽⣹⠟⠉⠀⣾⠀⢰⠃⠀⢧⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠳⠮⣥⣤⣿⠿⠁⠀⠀⠀⡇⠀⢸⠀⠀⢸⡀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⢸⠀⠀⠀⣧⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⣼⠁⠀⣼⣄⡀⠀⢻⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠾⠤⠤⠿⠒⢙⣦⣨⡇⠀⠸⣗⡒⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⠒⠀⠀⠀⠀⢻⡿⣅⠙⠒⠒⠋⢁⣰⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⣴⠞⠋⠉⠳⡶⠤⣤⠤⢾⣡⡟⠉⠉⠉⠈⢉⣀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣴⠟⠉⠙⢆⠀⠀⠀⢳⠀⠀⠀⢸⡆⢙⣶⡶⠚⠋⠙⠓⠿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣴⠟⠁⠀⠀⠀⠘⡄⠀⠀⢸⡆⠀⠀⣠⣷⣿⠏⠀⠀⣀⣀⣀⣀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⡞⠁⠀⠀⠀⠀⠀⠀⣷⠀⢀⣨⣧⣴⣺⡽⠟⡟⠀⡴⠉⠉⠀⠀⠉⠙⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⠿⣶⡦⠤⠤⠤⠤⣶⣟⣯⣭⠿⠛⠋⠉⠀⢸⡇⡼⠁⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣌⠳⢤⣀⣀⣀⣀⣀⣀⣾⡇⠀⠀⠀⢘⣿⣿⣿⣽⣿⣱⣾⣸⣻⣿⠀⣋⣯⣿⠯ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡈⡛⢲⠶⠶⠶⠶⠾⠟⠋⠀⠀⠀⠀⠀⢀⢁⠀⠀⠀⠀⠀⣉⢉⢉⠀⠀⡀⣀⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡆ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡷ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇ ⠀⠀⣼⣦⡀⠀⠀⠀⠀⠀⣀⣤⠀⣠⣶⣶⣿⣿⣿⣶⣦⡀⠀⢸⣿⣿⣿⣿⡆ ⠀⠀⢻⣿⣿⣿⣿⣿⣷⣿⣿⣧⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢻⣿⣿⣿⣿⠀ ⠀⢀⣾⠟⠙⢿⣿⡟⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⣿⣿⣿⣿⠃⠀ ⠀⢸⣿⣴⣧⡞⢿⣧⣧⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⠏⠀⠀ ⠉⠽⣿⣿⣿⣋⣙⢿⣟⣭⣽⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀ ⠀⠀⠀⠀⠙⠛⠛⠻⣿⣷⣽⣿⣿⡿⠁⠀⢹⣿⣿⣿⣿⣿⣿⠏⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⠁⠀⢀⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡏⠀⠀⠈⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠃⠀⠀⠀⠹⢿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠀⠀⠀⠀⠀⣼⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⣸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⢀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⠀⠀⢠⣾⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⠀⠀⠀⠀⣿⣿⠇⠀⠀⠀⣴⣶⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⠀⠀⠀⠀⠀⣾⣯⠀⠀⠀⠀⣿⣿⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⡀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⣾⣏⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⣹⣿⠀⠀⠀⠀⣿⡟⠀⠀⠀⠀⣠⣦ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣧⠀⠀⠀⠀⢻⣿⠀⠀⠀⢀⣿⠇⠀⠀⠀⠠⣿⠇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡄⠀⠀⠀⠀⠁⠀⠀⠀⠿⠟⠀⠀⠀⢀⣼⡟⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣶⣶⣿⣶⣄⣀⠀⠀⠀⠀⢸⡟⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣤⡈⠀⠀⠀⠀ ⣴⣶⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀ ⠹⣿⣿⣿⡆⠀⠀⠀⠀⠀⢀⣤⣿⣿⡿⠀⠉⠉⢁⣾⣿⣽⣿⣿⡟⠀⠀⠀⠀⠀ ⠀⠈⠻⣿⣧⡄⠀⠀⠀⠀⣨⣿⣿⢿⣿⠀⠀⠀⢨⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠙⠁⠀⣀⠀⣈⣿⣿⣿⣾⣿⣦⡀⠀⢸⣿⣿⣿⣿⣿⡗⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⠿⠿⠿⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡎⣿⢩⠖⠈⠐⠒⠒⠒⠴⠫⢍⢢⠀⠀⠀⠀ ⠀⠀⡼⠁⠀⠀⠀⢀⣂⠀⠀⠀⠈⠐⠼⡜⠀⠀⠀⠀ ⠀⠀⣇⠀⡀⡘⠣⠀⠀⠀⣀⣠⠀⠀⢠⠱⡀⠀⠀⠀ ⠀⠀⢈⠦⢦⠮⣀⠀⠀⠀⣀⣁⠢⡕⣸⠀⢱⠀⠀⠀ ⠀⠀⡜⠀⣠⠀⠾⠅⣀⡀⠩⠬⠀⢃⠇⡆⠀⡆⠀⠀ ⠀⢠⠁⢠⠇⠣⢄⠀⢋⠅⠀⣀⠜⠉⠀⢱⠀⢰⠀⠀ ⠀⡜⠀⢸⠀⠀⠀⠉⠁⠈⠉⠀⠀⠀⠀⠸⡀⠈⡆⠀ ⠀⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢡⠀ ⢠⢀⢐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⢸⠀ ⢸⢁⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡈⡆ ⢗⡕⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢪⡺ ⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣶⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⡿⠿⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠿⢿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠋⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠟⠀⠀⠀⣿⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⣠⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠏⠀⠀⠀⠀⣿⣄⠀⣠⣾⣇⠀⠀⠀⣀⣤⣶⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣀⠀⠀⠀⠀⣼⣿⠃⠀⠀⠀⠀⢰⠟⣿⠿⠋⠘⠿⣿⣿⣿⡟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀ ⣼⡿⠿⢿⣷⣶⣴⣿⠏⠀⠀⠀⠀⠀⣿⣿⡿⠀⠀⠀⠀⣿⣼⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⠀⠀⠀⠀⠀⠀⠀ ⣿⣇⠀⠀⠈⢛⣿⡟⠀⠀⠀⠀⠀⠀⠘⠟⠁⠀⠀⠀⠀⢻⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⢸⣿⣇⠀⠀⠀⠀⠀⠀ ⢹⣿⠀⠀⠀⣼⣿⠃⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣾⠿⠟⠛⠛⠻⣿⣆⠀⠀⢿⣿⠀⠀⠀⠀⠀⠀ ⠘⣿⡇⠀⠀⣿⣿⠀⠀⢸⣷⡀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⡿⠟⠛⢩⣿⣿⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⠿⠛⠉⠀⠀⠀⠀⠀⢀⣿⡇⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀ ⠀⢹⣿⡄⢰⣿⡇⠀⠀⠀⣿⣿⣶⣶⣶⣶⣶⣾⡿⠟⢻⣿⠁⠀⠀⠀⣸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀ ⠀⠀⢻⣿⣼⣿⡇⠀⠀⠀⢸⡇⠈⠉⢹⣇⠀⣸⣧⠀⣼⣿⡆⠀⠀⢠⣿⣧⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠟⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠹⣿⣿⡇⠀⠀⠀⢸⣿⠀⠀⢸⣿⣄⣿⣿⣷⣿⠿⣿⡄⠀⣼⡿⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠋⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠸⣿⡆⠀⣿⣿⣿⡟⠋⠙⠁⠀⠙⢿⣶⣿⠃⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⣿⣿⣾⣿⣿⡟⠀⠀⠀⠀⠀⠀⠈⠙⠁⠀⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⣿⣇⠀⠀⠀⠀⢿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢿⣿⠀⠀⠀⠀⠸⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣷⣶⣶⣶⣤⣀ ⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⢹⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟⠁⠀⠀⠈⣹⣿ ⠀⠀⠀⠀⠀⠀⢻⣿⡄⠀⠀⠀⠀⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠏ ⠀⠀⠀⠀⠀⠀⠈⢿⣷⡀⠀⠀⠀⠈⢿⣧⡀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⠟⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣄⠀⠀⠀⠀⠹⣿⣦⣀⠀⠀⢀⣠⣾⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣦⡀⠀⠀⠀⠈⠛⠿⣿⣿⡿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⡿⠟⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣾⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣶⣦⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣴⣶⣿⡿⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⢀⡠⠔⠒⠒⠒⠂⠴⠊⠉⠉⠒⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡰⠉⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠈⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⣠⠖⠉⠀⠉⠓⣤⡀⠀⠱⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⢀⠜⠕⠒⠀⠀⠀⠀⢀⡬⢦⡀⢣⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠸⠀⠀⠀⠀⠀⢀⠎⢀⡔⠉⠉⠲⡀⢸⢁⣀⣀⣱⠾⡆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸⠀⠾⡤⠒⠒⢚⡇⠘⡧⣀⡠⠾⡄⢱⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⠀⠀⠀⠀⠠⣌⡆⠀⠈⠒⠒⠊⠀⢀⡸⠀⠀⠀⠘⡜⡆⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡀⠀⢀⣠⣶⣶⡄⠀⠀⡇⢣⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⠀⠀⠀⠀⠀⠈⡄⠀⠀⠸⣿⣿⣛⣛⣻⠋⠀⠀⡜⠀⠸⡀⠀⠀⠀⠀ ⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠘⠻⠿⠿⠟⠁⡠⠎⠀⠀⠀⣇⠀⠀⠀⠀ ⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠸⡤⡀⠀⠀⠀⠀⢀⡴⠊⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀ ⠀⠀⠀⢸⠀⠀⠀⡠⠤⠤⣀⠁⣸⠀⠀⠀⠀⢨⢀⣀⣀⠀⠀⠀⠀⠀⠗⠒⣇⡀ ⠀⠀⠀⡸⠀⠀⡜⠀⠀⠀⠈⠋⠀⠑⢄⣠⠤⡜⠋⠀⠀⠙⡄⠀⠀⠀⠀⠈⠁⡜ ⢔⠒⠊⠁⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢧⣀⡜⠀⠀⠀⡀⢱⠀⠀⠀⠀⠀⡴⠁ ⢈⣲⣤⡀⠀⣀⢗⣖⣵⣯⣽⣑⠦⡀⠀⠀⠀⣀⠀⠀⠀⠘⢎⡀⠀⢀⡠⠊⠀⠀ ⠘⢄⠀⠀⠀⢳⣿⣿⠿⠿⠿⣿⣿⣯⣢⢄⣀⣹⣄⣀⣀⡤⣞⣽⠚⠁⠀⠀⠀⠀ ⠀⠀⠑⢤⣀⣿⣿⠁⠀⠀⠀⣿⣿⣿⣿⣷⣿⣮⣥⣿⣶⣿⣿⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣼⣿⣿⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀ ⢀⣀⣤⣾⣿⣿⣿⣷⠀⠀⠀⢻⣿⣿⣿⣿⣿⡿⠟⠛⢻⠉⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⡀⠀⠀⣀⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣦⣾⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀ ⠀⠀⠀⠀⢀⣀⣤⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⡇ ⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⢰⣿⣿⣿⣿⣿⠟⠁ ⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠛⠀⢀⣿⣿⣿⣿⠟⠁⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣀⣀⣀⣀⣀⣤⣴⣿⣿⣿⡟⠁⠀⠀⠀⠀ ⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠙⢿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠻⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⢸⣿⣷⣶⣤⣀⣤⣴⣶⣶⣶⣶⣦⣤⣀⣤⣶⣾⣿⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀ ⠀⠀⠠⣤⣀⡀⠹⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⠃⢀⣀⣤⠄⠀⠀ ⢀⠤⢤⣤⣬⣙⠳⣿⣿⡿⠀⢀⠀⠈⣿⣿⠁⠀⡀⠈⣿⣿⣿⠞⣋⣥⣤⠤⠤⡀ ⠀⢀⡤⠤⢤⣼⣿⣿⣿⣿⡀⠸⠀⣠⣿⣿⣄⠐⠇⢀⣿⣿⣿⣿⣧⡤⠤⢤⡀⠀ ⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⠛⠛⠛⠛⠉⠉⠛⠛⠛⠛⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀ ⠀⠀⠀⠛⠿⢿⣿⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⣿⡿⠻⠛⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣶⣶⣿⣷⣆⠀⠀⠀⠀ ⠀⠀⠀⢀⣤⣤⣶⣶⣾⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⡆⠀⠀⠀ ⠀⢀⣴⣿⣿⣿⣿⣿⣿⡿⠛⠉⠉⠀⠀⠀⣿⣿⣿⣿⣷⠀⠀⠀ ⣠⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⢤⣶⣾⠿⢿⣿⣿⣿⣿⣇⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠈⠉⠀⠀⠀⣿⣿⣿⣿⣿⡆⠀ ⢸⣿⣿⣿⣏⣿⣿⣿⣿⣿⣷⠀⠀⢠⣤⣶⣿⣿⣿⣿⣿⣿⣿⡀ ⠀⢿⣿⣿⣿⡸⣿⣿⣿⣿⣿⣇⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣧ ⠀⠸⣿⣿⣿⣷⢹⣿⣿⣿⣿⣿⣄⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⢻⣿⣿⣿⡇⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠘⣿⣿⣿⣿⠘⠻⠿⢛⣛⣭⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⢹⣿⣿⠏⠀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋ ⠀⠀⠀⠈⣿⠏⠀⣰⣿⣿⣿⣿⣿⣿⠿⠟⠛⠋⠉⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⡿⠿⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

░░░░░░███████ ]▄▄▄▄▄▄▄▄ ▂▄▅█████████▅▄▃▂ [███████████████████]. ◥⊙▲⊙▲⊙▲⊙▲⊙▲⊙▲⊙◤..

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡶⢶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣇⣸⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢩⡿⢿⡍⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁⠈⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣥⣤⣤⣬⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠋⠁⢰⡆⠈⠙⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣾⠟⣷⣄⠀⠸⠇⠀⣠⣾⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⢀⡀⠀⠀⠀⢠⣾⠋⠀⠀⠙⠛⠿⠿⠛⠋⠀⠀⠙⣷⡄⠀⠀⠀⢀⡀ ⠈⠻⣦⣤⣤⣿⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿⣤⣤⣴⠟⠁ ⠀⠀⠀⣰⣿⣉⣉⣉⣉⣹⣏⣉⣉⣉⣉⣹⣏⣉⣉⣉⣉⣿⣆⠀⠀⠀ ⠀⠀⣴⡟⠉⢹⣿⠉⠉⠉⠉⠉⢻⡟⠉⠉⠉⠉⠉⣿⡏⠉⢻⣦⠀⠀ ⠀⠐⠛⠛⠛⠛⠛⠛⢻⣿⠛⠛⠛⠛⠛⠛⠻⣿⠛⠛⠛⠛⠛⠛⠂⠀ ⠀⠀⠀⠀⠀⠀⣤⣤⣸⡏⠀⠀⠀⠀⠀⠀⠀⣿⣤⣤⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠉⠙⠁⠀⠀⠀⠀⠀⠀⠀⠙⠉⠁⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠤⠠⡖⠲⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠶⣴⣶⣄⠀⠀⠀⢀⣴⣞⣼⣴⣖⣶⣾⡷⣶⣿⣿⣷⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⠀⠀⠀⠙⢟⠛⠴⣶⣿⣿⠟⠙⣍⠑⢌⠙⢵⣝⢿⣽⡮⣎⢿⡦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢱⡶⣋⠿⣽⣸⡀⠘⣎⢢⡰⣷⢿⣣⠹⣿⢸⣿⢿⠿⡦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢧⡿⣇⡅⣿⣇⠗⢤⣸⣿⢳⣹⡀⠳⣷⣻⣼⢿⣯⡷⣿⣁⠒⠠⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⣼⣿⣧⡏⣿⣿⢾⣯⡠⣾⣸⣿⡿⣦⣙⣿⢹⡇⣿⣷⣝⠿⣅⣂⡀⠀⠡⢂⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⣿⡟⣿⡇⡏⣿⣽⣿⣧⢻⡗⡇⣇⣤⣿⣿⣿⣧⣿⣿⡲⣭⣀⡭⠛⠁⠀⠀⠈⠀⠉⢂⢄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⢻⣿⣇⣥⣏⣘⣿⣏⠛⠻⣷⠿⡻⡛⠷⡽⡿⣿⣿⣿⣷⠟⠓⠉⠢⢄⡀⠀⠀⠀⠀⠀⠁⠫⢢⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⢸⣾⣿⣽⣿⣏⣻⠻⠁⢠⠁⠀⠀⠀⠘⣰⣿⣿⢟⢹⢻⠀⠀⠀⠀⠀⠈⠒⢄⡀⠀⠀⠀⠀⠀⠀⠑⢄ ⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⢸⣯⣿⣿⣿⢷⡀⠀⠀⠀⠀⠀⠀⠀⠛⣩⣿⣿⢿⣾⣸⠀⠀⠀⠀⠀⠀⢀⡠⠚⠉⠉⠁⠀⠀⠀⢀⠌ ⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⢟⣿⣯⡟⠿⡟⢇⡀⠀⠀⠐⠁⢀⢴⠋⡼⢣⣿⣻⡏⠀⠀⠀⣀⠄⠂⠁⠀⠀⠀⠀⠀⠀⢀⡤⠂⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠈⠊⢻⣿⣜⡹⡀⠈⠱⠂⠤⠔⠡⢶⣽⡷⢟⡿⠕⠒⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⢿⠿⠿⢿⠾⣽⡀⠀⠀⠀⠈⠻⣥⣃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣖⠂⠠⠐⠋⠀⠙⠳⣤⣠⠀⠀⠀⣀⠤⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠵⡐⠄⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⡀⠀⠠⡀⠀⠈⠙⠶⣖⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡥⠈⠂⠀⠀⠀⠀⠀⠀⠀⣼⠉⠙⠲⣄⠈⠣⡀⠀⠀⠈⢻⡦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠈⣷⡄⠈⠄⠀⠀⠀⢧⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⡀⠀⢠⣿⣤⣤⣶⣶⣾⣿⣿⡄⢸⠀⠀⠀⢸⣄⣤⣼⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠇⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢸⠀⠀⠀⣼⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⢀⣼⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠁⠀⠈⠉⠙⠛⠿⠿⠽⠿⠟⠛⡉⠛⠲⣿⣿⠿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⢠⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠀⠀⣠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢔⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠀⠀⠀⠀⠀⣃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡠⣻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢫⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣰⡿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣼⠏⣸⣿⣷⢷⠙⣻⢶⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠾⠉⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠰⣏⠀⣿⣿⡘⣼⡇⠀⠁⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠁⠀⠀⣽⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢙⠓⠛⠘⣧⠾⢷⣄⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⣿⢟⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠸⠀⠀⠀⢸⣧⠀⠹⣆⠀⠀⠀⠀⠈⢻⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⢂⠙⢿⡷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢃⠀⠀⠈⠙⠀⠀⠻⡄⠀⠀⠀⠀⠸⡀⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠐⠠⠀⠻⠬⠄⡒⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠑⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀🎀🎀🎀🎀🎀🎀🎀🎀❤️❤️❤️❤️ 🔥🔥🔥🔥

⠀⠀⠀⢸⣦⡀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣏⠻⣶⣤⡶⢾⡿⠁⠀⢠⣄⡀⢀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀ ⠀⠀⣀⣼⠷⠀⠀⠁⢀⣿⠃⠀⠀⢀⣿⣿⣿⣇⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠴⣾⣯⣅⣀⠀⠀⠀⠈⢻⣦⡀⠒⠻⠿⣿⡿⠿⠓⠂⠀⠀⢂⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠉⢻⡇⣤⣾⣿⣷⣿⣿⣤⠀⠀⣿⠁⠀⠀⠀⢀⣴⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠸⣿⡿⠏⠀⢀⠀⠀⠿⣶⣤⣤⣤⣄⣀⣴⣿⡿⢻⣿⡆⠂⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠟⠁⠀⢀⣼⠀⠀⠀⠹⣿⣟⠿⠿⠿⡿⠋⠀⠘⣿⣇⠀⠄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢳⣶⣶⣿⣿⣇⣀⠀⠀⠙⣿⣆⠀⠀⠀⠀⠀⠀⠛⠿⣿⣦⣤⣀⠀⠀ ⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⠿⠋⠁⠀⣹⣿⠳⠀⠀⠀⠀⠀⠀⢀⣠⣽⣿⡿⠟⠃ ⠀⠀⠀⠈⠀⢰⠿⠛⠻⢿⡇⠀⠀⠀⣰⣿⠏⠀⠀⢀⠀⠀⠁⣾⣿⠟⠋⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⣰⣿⣿⣾⣿⠿⢿⣷⣀⢀⣿⡇⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠋⠉⠁⠀⠀⠀⠀⠙⢿⣿⣿⠇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀ 𐙚 -`♡´-˙✧˖°📷 ༘ ⋆｡˚˙✧˖°📷 ༘ ⋆｡˚˚˖𓍢ִ໋🌷͙֒✧˚.🎀༘⋆˚‧｡⋆🌻⋆｡‧˚⛷🧚‍♀️🛖

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠶⠶⠶⠶⠶⠤⠤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⣠⠖⢬⡉⠑⠢⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⡰⠁⡠⢦⠑⡄⠀⠀⠈⠑⠢⣄⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡹⠔⠀⠀⡸⠁⢸⠁⠀⢳⢱⠀⠀⠀⠀⠀⠈⠑⢮⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⣠⣤⠶⠟⠋⠁⠀⠀⠀⢠⠃⠀⡇⠀⢀⣠⠶⠇⠀⠀⠀⠀⠀⠀⠀⠓⠈⢆⠀⢀⣀⡠⠤⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣀⣤⣴⠶⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠷⠊⢁⡤⠶⠢⠤⣀⠀⠀⠀⠀⠀⠀⠠⠚⠉⠀⢀⡠⢤⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠻⣿⣍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⠀⠀⠈⠑⣄⠀⠀⠀⢀⠀⠀⠀⢰⠉⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠛⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠎⢣⠀⠈⢆⠀⠔⠁⠀⢀⣀⠈⢷⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⢸⠀⢸⠀⠀⠈⢣⠤⠖⠉⠉⣩⣿⣿⡀⠀⠀⠀⣠⠴⣦⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⣀⣀⣀⣆⡼⠤⠤⠐⠚⠒⣶⠔⠉⢀⣽⡟⡇⠀⢀⡞⠁⢠⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠁⠀⠀⠀⠀⣶⡤⠀⠀⠀⠀⠀⠛⠒⠚⠫⢼⣰⠁⠀⡾⠀⠀⡎⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⠤⠤⠤⠀⠀⠀⠀⠀⡟⠀⣼⡗⠒⠉⠓⢤⡀⠀⠀⠀ ⠀⠀⠀⣀⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⣸⠟⠙⡶⠒⠁⠀⡈⠑⢄⠀ ⠀⠀⠀⠻⠿⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣯⠞⠁⢀⣼⠁⠀⢀⠜⠁⠀⠀⢣ ⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠷⠶⣤⣄⣀⣀⠀⠀⠀⠉⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⢁⡇⠀⠒⢻⠈⠓⠤⢾⡀⠀⡄⢀⠇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠓⣒⣶⣴⠾⠿⡒⠒⠢⠤⣤⠤⠴⠶⣯⡉⠀⠀⡞⢧⠀⠀⠘⠃⠀⠀⠀⠉⠉⣠⠎⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋⡡⠚⠁⢀⠜⠀⠀⠀⡜⠁⠀⠀⠀⠀⠻⡶⠉⡇⠀⠑⠦⡀⠀⠀⠀⣀⡤⠞⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⢸⠀⠀⠒⣧⡤⡄⠀⠀⡇⠀⠀⠀⠀⠀⠀⢹⠀⠈⠀⠀⠀⠈⠓⠚⣿⠉⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢂⣠⢴⠋⡰⠛⠓⠒⠒⠉⠁⣽⢢⠀⢳⡀⠀⠀⠀⠀⠀⠸⢦⠀⠀⠀⢀⡠⠤⠞⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢸⠄⠀⠀⠀⠀⠀⠀⠁⠠⠇⠀⠑⠤⠀⠀⠀⠠⡟⠉⠑⠒⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢠⡄⢀⡄⠀⢠⣦⡀⠀⣠⢷⠀⣠⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢶⡀⡞⠳⣄⡞⠡⡜⠙⣦⠎⠀⠳⠚⠁⠘⠋⠀⢱⡠⠜⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢀⡞⢧⡼⠃⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⢳⠦⣄⠀⠀⢀⠸⠖⠊⢙⠀⠀⠀⠀⠀⢀⣇⠀⣀⡞ ⠀⠀⠀⠀⠀⠀⠀⠀⡞⣇⡞⠀⠈⠀⠀⠀⠈⠻⣍⠑⠢⢤⣤⢄⣀⠀⠈⠳⠄⠀⠀⠣⠀⢃⠀⠈⡟⠒⠤⠼⠤⠤⠄⠒⠊⠁⠀⠀⠀⢣ ⠀⠀⠀⠀⠀⢿⠒⠒⠃⠈⠀⠀⠀⠀⠐⢶⣖⠲⠤⡄⠀⠀⠉⠢⡄⠁⠀⠤⢖⡒⠒⠄⠀⠘⣗⠒⠛⠀⣠⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⢨ ⠀⠀⠀⢸⡦⢼⣆⠀⠀⠀⠀⠤⠶⣆⡉⠀⠈⠳⠀⠸⢴⡖⠦⠄⠀⠘⢶⠒⠀⠉⠀⣠⡶⢛⡿⠷⠄⢰⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⢀⠇ ⠀⠠⣄⣀⣧⠀⠈⠀⣀⣤⣖⠒⠒⠀⠈⢠⢤⣄⠀⠀⠀⠉⢦⣀⣀⠤⠀⠉⠢⢴⣊⣿⠀⡁⠀⠀⠀⠈⠣⣹⡿⠃⠀⠀⢠⡀⢀⠴⢃⡀ ⢀⡀⠹⡄⠀⠀⠀⠀⣀⡠⠌⠉⣀⠤⠒⠋⠀⠈⠁⢀⣀⠤⠈⠉⢒⢒⣂⠤⠄⠀⠀⠘⢷⣬⣿⡥⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠉⠉⠁⢸ ⠀⠻⡅⠛⠂⠀⠤⠾⠥⠤⠤⠚⠓⠒⢀⡠⠤⠀⠉⢛⠒⠒⠀⠀⢈⡉⠓⠒⣢⣔⣂⣤⣤⠽⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⡸ ⠙⢷⡉⠁⠀⠀⠀⣠⠤⠒⠀⠀⣠⠾⠥⠄⢀⣴⣊⡁⠀⠠⠶⢎⡁⠄⣠⣴⣛⠀⠀⣀⣈⣳⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁ ⢀⣀⣉⠶⠄⠰⠛⠓⠒⢀⣴⣎⠁⠀⠀⣀⡊⠀⠠⣤⡤⠒⠁⠀⢀⠔⢁⣀⣀⡤⣄⣈⣳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠀⠀ ⠀⢈⣩⠶⠂⠀⠀⢀⡴⠋⠁⠀⣠⣔⣏⠁⠀⣀⠔⠀⠀⠀⠀⣠⠟⢋⡵⠋⠀⣄⣈⡳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠀⠀⠀⠀ ⠀⠈⠳⣤⣀⠀⠴⠛⠈⠉⡤⢊⠁⠀⠀⢀⣴⠗⡺⠃⠀⡴⣊⡄⢠⡾⠋⢡⡀⠙⡌⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀ ⠀⠙⠻⣭⣀⠀⠀⠀⢀⡾⠚⡩⠂⢀⡴⣋⣤⣾⠔⢂⡜⢋⠁⢠⠀⢸⣄⠘⡍⠙⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠛⠛⢤⣤⠀⣀⠞⢀⡼⠒⢉⠟⠋⠁⢸⣇⠀⡾⣇⢸⢦⣸⠣⣜⡌⠙⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠐⠺⠯⣀⡉⠙⢸⡋⡄⢀⣞⠀⣰⢧⡜⠙⢶⠃⠈⠟⠀⠙⠂⠈⠃⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡀⣀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣴⢃⣀⣤⣳⣄⠞⠈⠳⠇⣠⠟⣷⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠈⣟⠉⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠉⠀⢀⡼⠛⠟⠀⠀⢰⣏⠀⠀⠙⠦⣌⠙⠓⠒⠦⠤⠤⠤⠤⠖⠒⠋⢳⡀⠀⠀⠀⠀⠘⠦⣈⠒⠤⢄⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⠀⠀⠀⠉⣑⠒⢿⣦⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⡀⠀⠀⠀⠀⠈⠙⢦⣀⠘⢽⠄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠲⢤⡀⠀⠲⣄⣷⠴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢦⡀⠀⠠⡀⠢⡉⠻⡞⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣄⣸⣦⠼⠞⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠟⠉⠛⣽⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠁⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡎⡇⠀⠀⠀⠀⠀⠹⡿⣧⣀⣀⣴⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⠇⢓⣒⠢⢄⠀⠀⠀⠉⠻⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣞⣬⣂⣼⣿⣿⣷⡀⠀⠀⢠⠛⠛⢛⠃⢀⣀⣠⣤⣶⣶⣶⣶⣤⡀ ⠀⢻⣿⣿⣿⣿⣿⣿⣿⡦⡠⠞⣒⠋⠋⠉⣿⣿⣿⡿⠋⠁⠉⠙⣿⣷ ⠀⡠⠟⠛⠋⠉⠉⠀⠀⠀⠀⠘⠿⢃⣀⠤⠿⢿⣿⡇⠀⠀⠀⢀⣾⣿ ⠞⠄⠤⣤⣤⣤⣶⣶⣶⣿⣿⣿⣿⣷⣦⣄⣀⡈⠻⣿⣷⣶⣶⣿⠿⠃ ⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡉⠉⠉⠀⠀⠀ ⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠿⠿⠛⠋⠁⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⢀⡤⠂⠀⠀⠀⠀⢀⣀⣤⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣤⣀⠀⠀⠀⠀⠀⠐⣤⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣴⡿⠁⠀⠀⣀⣴⣾⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣶⣤⣀⠀⠀⠘⣿⣆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⣾⡿⠁⢀⣴⣾⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣷⣄⠀⠘⣿⣷⡀⠀⠀⠀⠀ ⠀⠀⠀⣰⣿⡿⠁⠀⠸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⠀⠀⠸⣿⣿⡄⠀⠀⠀ ⠀⠀⣸⣿⣿⠃⠀⠀⠀⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⢹⣿⣿⡄⠀⠀ ⠀⢰⣿⣿⡏⠀⠀⠀⠀⠘⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠀⠀⠀⠀⠀⣿⣿⣷⠀⠀ ⠀⣿⣿⣿⠃⠀⠀⠀⠀⠀⢹⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⠀⠠⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠇⠀⠀⠀⠀⠀⢸⣿⣿⣇⠀ ⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣤⣄⢠⣾⣿⣿⠃⠀⠀⠹⣿⣿⣷⠀⢀⣴⣿⣿⣿⣶⣶⣶⣦⣴⣿⣿⡏⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⠀ ⣸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇ ⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⣠⣤⣤⣤⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣤⣤⣄⡀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣧ ⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿ ⣿⣿⣿⣿⣤⣤⣤⣄⣀⠀⠀⠀⣀⣴⣿⣿⣿⡿⠿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⡿⢿⣿⣿⣷⣄⡀⠀⠀⠀⣀⣠⣤⣤⣼⣿⣿⣿⡏ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⣁⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠀⠀⠉⠉⠙⠛⠻⠿⢿⣿⣿⡿⠟⢁⣠⣾⣿⣿⣿⠿⣫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⢿⣿⣿⣿⣦⣄⠙⠻⣿⣿⣿⡿⠿⠛⠛⠉⠉⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢀⣴⣿⣿⣿⠿⢋⣵⣾⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣷⣭⡛⢿⣿⣿⣷⣄⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡿⠟⢁⣶⣿⣿⡿⠋⠁⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠈⠻⣿⣿⣿⣦⠉⠻⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⡿⠋⠀⠀⢸⣿⣿⣿⠁⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠸⣿⣿⣿⡄⠀⠈⠛⢿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣠⣾⣿⣿⠟⠁⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠙⢿⣿⣿⣶⣄⣀⠀⠀⠀⠀ ⠀⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⡇⠀ ⠀⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⡇⠀ ⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀ ⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀ ⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣧⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀ ⠀⢸⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀ ⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⠀⠀ ⠀⠘⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠀⠀ ⠀⠀⢿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⡇⠀⠀ ⠀⠀⠸⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠁⠀⠀ ⠀⠀⠀⢻⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⠇⠀⠀⠀ ⠀⠀⠀⠀⢻⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⠏⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠻⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⣰⣿⣿⡿⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⡄⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⣴⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠂⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⡄⠀⠀⠀⠀⠀⠀⣰⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⠀⠀⠀⠀⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠟⠻⠿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠁⠀⠀⠀⠀⠙⠿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⠁⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣷⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣾⣿⣷⣶⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠿⠿⢷⣶⣦⣤⣤⣀⠀⠀⢀⣠⣾⠿⠛⠉⠀⠀⠀⠀⠈⢿⣧⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣴⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠻⠿⣷⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇⠀ ⠀⠀⠀⠀⠀⣰⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⠀ ⠀⠀⠀⢀⣾⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀ ⠀⠀⢠⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠀ ⠀⢠⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀ ⢀⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⠀ ⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡄ ⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇ ⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿ ⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿ ⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿ ⠈⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣶⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟ ⠀⠈⢻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣤⡀⠀⠛⠉⠀⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠇ ⠀⠀⠀⠙⢿⣦⣀⠀⠀⠀⠀⠀⣴⡿⠟⠉⠉⢹⣿⡄⠀⠀⠀⠀⠀⠀⠀⠙⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⠀ ⠀⠀⠀⠀⠀⠙⠿⣷⣦⣀⢀⣾⡟⠁⠀⠀⠀⢼⣿⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⡟⠀⠀⠀⠀⠀⠀⠉⠙⢿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠏⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⠟⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⡀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠿⠷⣶⣶⣦⣤⣤⣤⣤⣤⣤⣀⣤⣤⣤⣤⣴⣶⡾⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣦⣀⣀⣀⣀⣀⣴⡿⠋⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠙⠛⠛⠛⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠈⡩⢄⠒⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⡜⠐⠑⣡⠀⠀⠈⠢⡢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣀⣠⠴⠒⠉⠀⠀⢰⠀⣇⠀⠕⠂⠀⠀⠀⠈⠊⢆⠠⠤⢠⠀⠀⠀⠀⠀ ⠰⣶⡋⠉⠀⠀⠀⠀⠀⠀⠀⠀⢁⠞⠉⠈⠑⢄⠀⠀⡀⠀⢠⢊⡟⠀⠀⠀⠀⠀ ⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⢘⠀⠀⠈⠁⠀⢂⢊⡠⠤⣌⡟⠀⠀⢀⡀⠀⠀ ⠀⠀⠀⠀⠙⢄⠀⠀⠀⠀⠀⠀⣈⠄⠀⠰⠤⠄⠐⠃⡆⢈⢽⠃⠀⡜⢡⠃⠀⠀ ⠀⠀⠀⠀⡠⠋⠀⠀⠀⠀⠀⡌⠀⠀⠀⠘⠣⢀⣀⣀⠁⠈⠑⠇⡸⠤⠬⡀⠀⠀ ⠀⠀⢠⣞⠁⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⡰⠋⡖⠀⠠⠑⢄ ⠀⠀⠀⠈⠙⠓⠲⠤⢄⣀⡀⠀⠢⢀⠀⠀⠀⠀⠀⠀⡠⠞⡏⠀⠎⠣⠴⡁⡀⡘ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⢍⠳⠋⡏⠁⠠⠒⠈⠳⣄⢼⠑⢄⠈⠀⠀⣠⠔⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠢⡆⠐⣎⢤⠀⡇⠀⠀⠀⠘⠈⠀⠀⠑⢒⠎⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠊⠁⡎⠀⠀⠀⠘⠱⠘⠄⠀⠀⠸⠓⠤⠐⠈⠁⠀⠀⠀⠀

⠀⠀⠀⢠⣾⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣰⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣄⣀⣀⣤⣤⣶⣾⣿⣿⣿⡷ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀ ⣿⣿⣿⡇⠀⡾⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀ ⣿⣿⣿⣧⡀⠁⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⢹⠉⠙⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⠀⣀⣼⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠀⠤⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⠿⠋⢃⠈⠢⡁⠒⠄⡀⠈⠁⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⠟⠁⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠈⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣿⣿⣿⣿⣿⠟⠛⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⣂⣿⣿⡿⠟⣡⡞⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⢋⣴⣼⣿⣥⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⡠⠔⠂⠈⠁⠀⠀⠈⠉⠉⠛⠻⢿⣶⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠿⣿⣿⣿⣎⢃⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣷⣌⠉⠻⣿⡟⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣶⣤⣀⡀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣦⡁⠙⢈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣷⣄⠀⢀⣠⣼⣿⣿⣿⣿⣿⣿⡏⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣦⡄⠀⣸⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡏⠉⢹⣿⣿⣶⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠸⣿⣿⠇⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣏⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⢀⣤⣀⣀⣴⠏⠉⡉⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣆⣤⣶⣾⣿⠿⠿⠿⣿⣿⡖⠛⣿⣦⣀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠟⠁⠙⢿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠙⢿⡿⠿⠟⠋⠁⠀⠀⠀⠀⠉⣻⣦⠸⣿⠏ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡟⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡾⠟⠀⠋⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡏⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⡇⠀⠀⠀⠀⢠⣶⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⡇⠀⠀⠀⠀⣾⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⡿⠿⠁⠀⠀⢀⣼⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣧⠀⠀⠀⣴⣾⣿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⡟⠉⣿⠋⠀⠀⢀⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠇⠀⠹⠄⠀⢠⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣧⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⡿⢿⡿⠻⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⣶⣶⣶⣶⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢰⣿⣿⣿⣿⣿⣿⣿⣿⠿⢃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⡈⠻⢿⣿⠿⣿⣿⣿⠇⣴⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣶⡆⠀⠀⠀⠀⠉⠀⢿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠙⢛⣉⣍⡛⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣄⣉⠛⣛⡉⠁⠀⠀⣀⣤⣶⣦⣤⣀⣶⠄⣿⣿⣿⣿⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⠇⠀⠀⣸⠛⠉⠉⠙⣿⣿⣿⡆⢿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⠟⠀⠀⠀⠁⠀⠀⠀⠀⢸⣿⣿⣿⣮⡻⢿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⢋⣩⣭⣉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⣠⣶⡾⣿⣟⠛⣋⠁⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠛⣩⣤⣶⣤⣄⡀⠀⢀⣼⣿⠟⠁⣩⣿⣿⢿⣿⡿⣽⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⢧⣾⣿⣿⣿⣿⣿⣿⡄⠻⠿⠁⢠⣾⣿⠟⣡⣾⣿⠛⢮⡛⢿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⢳⣾⣶⡄⠀⠈⢿⢸⣿⣿⣿⡟⣩⣶⣿⣿⣿⣷⣄⢿⡿⢫⣾⣿⣿⠏⣠⣼⡿⠾⣻⣽⣤⣶⡶⣦⣄⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣤⣴⣾⡿⠃⠈⠛⢿⣦⣀⣈⠈⢿⣿⡏⣼⣿⣿⣿⣿⣿⠿⣛⣂⣀⡛⢿⠟⣡⣾⣿⡿⢁⣾⣿⣿⣿⣿⡷⢹⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣾⣼⡿⠋⠉⠀⠀⠀⠀⠀⠹⢿⣼⢧⡈⠻⠀⣿⣿⣿⣿⢋⣴⣿⣿⣿⣿⣿⣷⣄⢿⡟⠋⠀⣾⣿⣿⡿⠉⠩⠷⠿⣿⣿⣿⣿⡿⣫⣶⣷⣄⠀⠀⠀⠀ ⠀⠀⠀⠀⣼⣿⠋⠀⢠⣶⣶⣶⣾⣿⣿⣿⣿⣷⡄⣶⣶⣆⣿⣿⣿⢯⣿⣿⣿⣿⣿⣿⣿⣿⣿⡎⠁⣀⣤⣶⣜⢿⠁⢸⣷⡄⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣧⣄⠀⠀ ⠀⠀⠀⠀⣿⡇⠀⢰⣯⣿⠉⠉⢩⣍⣉⣉⣭⣭⣥⣭⣍⣻⣥⣭⣭⣜⠿⣿⣿⣿⣿⣿⣿⣿⠿⢓⠸⢿⣿⣿⡟⠀⠀⠀⢻⣧⣀⡀⠀⠈⠐⣿⣿⣿⣿⣿⣿⣿⣿⡄ ⠀⠀⢀⣼⠿⠁⠀⢸⣿⡇⠀⢸⣿⠿⠟⠿⠿⠿⠿⢿⣿⣟⠛⠛⣻⣥⣴⣶⣄⠉⠛⠿⠟⢱⣿⣿⣿⡄⣀⠈⠀⠀⠀⠀⠈⠉⠛⠁⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⡇ ⣠⡴⠟⠛⠁⠀⠀⢸⣿⡇⠀⣿⣿⠀⠀⢠⣼⣻⣿⣿⣿⣿⣿⣿⠾⣿⠿⠛⠁⣀⣴⣿⣷⠈⣛⠻⠟⠁⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⢿⣿⡇⢀⣾⣿⡃⠉⠙⠛⠋⠁⠀⠀⠀⠀⠀⣟⡛⠻⣿⡁⠀⣿⣇⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡿⠟⠿⠁⠀⢤⣤⣶⠆ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇⢸⣿⡇⠸⣿⣿⡇⠀⠀⠀⣤⠾⠻⣿⣿⣶⣿⣿⣿⣦⠻⠃⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠇⠀⠀⠀⢠⣼⣿⡿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠃⢸⣶⠁⢐⡿⠏⠀⠀⠀⢠⣶⣿⣷⠘⠿⠿⠿⠿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠋⠀⠀⠀⠀⣀⣼⣿⡿⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠜⠉⠀⠀⠀⢻⣧⠘⣿⣦⠀⠀⢠⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢀⣿⣿⠟⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡏⠀⠘⣿⣧⠀⣾⣿⣿⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠉⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠟⠀⠀⠀⣼⣿⠆⣿⣿⣿⣿⣿⢿⣿⣥⣴⣶⣶⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠀⢹⣿⣿⡟⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣠⣤⣤⣤⣤⣶⣦⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⣿⣿⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⠎⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣋⡉⠉⠛⠉⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⣿⣿⣿⣿⠟⠉⢼⣿⣿⣦⣆⢀⣠⣴⣦⣤⡴⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠙⠛⠿⠿⠿⠿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⣴⣾⣿⣿⣶⡄⠀⠀⠀⠀⡠⠔⡆⠂⢒⣆⠤⡄⠀⠀⠀⠀ ⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⣠⠚⢁⡿⣆⡇⣾⡯⠛⡆⡇⠀⠀⠀⠀ ⠀⠀⠈⢿⣿⣿⣿⣿⠏⠘⠥⢄⡀⡇⢩⡇⣿⣑⣼⡟⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⣭⣭⣀⡀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣼⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣼⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣾⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⣾⣿⣿⠉⣿⣿⣿⣿⣿⡄⠀⢀⣠⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠙⣿⣿⣧⣿⣿⣿⣿⣿⡇⢠⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣷⠸⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⠿⢿⣿⣿⣿⣿⣴⣿⠻⠿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡟⣩⣝⢿⠀⠀⣠⣶⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣷⡝⣿⣦⣠⣾⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⣮⢻⣿⠟⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠻⠿⠻⣿⣿⣿⣿⣦⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⠇⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⡆⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⠇⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠀⠀⠀⢀⣴⣿⣿⣿⣿⣟⣋⣁⣀⣀⠀ ⠀⠀⠀⠀⠀⠀⠹⣿⣿⠇⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇

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⠀⠀⢀⣴⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⣿⣿⢿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⡾⠋⠀⣰⣿⣿⠻⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⠀⠀⢠⣿⣿⠃⠀⠈⠻⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣿⡇⠀⠀⠀⣼⣉⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀ ⠀⠀⠀⢹⣿⡇⠀⠀⠀⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⣿⠉⠁ ⠀⠀⠀⠸⣿⣿⣄⠀⠀⠘⢿⣿⡵⠋⠙⢿⣦⡀⠀⠀⣤⣠⠀⣠⣿⡅⠀⣿⠀⠀ ⠀⠀⠀⠀⠈⠻⢿⣿⣶⣤⣄⣀⠀⠀⠀⠈⠻⣷⣄⣠⣿⣿⡼⠋⠛⣡⡼⠋⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠻⠿⠿⠷⠶⠶⠾⣿⡿⠋⠻⣟⠉⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⣤⣴⡶⠿⠛⠛⠛⠛⠛⠛⠷⢶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣴⣾⠛⠉⠀⠀⠀⠀⠀⢀⣤⣤⣄⡀⠀⠀⠉⠛⢷⣤⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠉⠙⠛⠷⣦⡀⠀⠀⠀⣿⡇⠈⠙⠻⠆⠀⠀⠀⠀⠙⢿⣦⣀⣀⣀⣀⡀ ⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦⠀⠀⣿⡇⠀⢀⣠⣤⣄⡀⠀⠀⠀⠀⠙⣿⡉⠉⣿⡇ ⠀⠀⠀⠀⢀⣤⡾⠟⠛⠛⠀⠀⠁⠀⢠⡿⠋⠀⠉⢻⣦⠀⠀⠀⠀⣈⣿⣤⡿⠁ ⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⢀⣴⠀⠀⢿⡇⠀⢀⣾⠟⠻⣿⠁⠀ ⠀⢠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡿⠀⠀⢸⣇⢀⣾⣿⠀⠀⣿⠆⠀ ⢀⣾⣃⣤⣤⣤⣤⣤⣀⠀⠀⠀⠀⣀⣿⡆⠈⠁⠀⠀⠀⠛⠛⠛⠋⠀⣠⣿⡀⠀ ⠘⠛⠋⠉⠀⠀⠀⢩⡿⠋⠀⠀⣿⡏⠙⠛⠻⢶⣤⣤⣤⣤⣤⣴⠶⣿⣿⣿⠏⠀ ⠀⠀⠀⠀⠀⠀⢰⡿⠁⠀⠀⠀⢿⣇⠐⢷⣄⡀⠀⠀⠉⠉⠀⠀⠀⢸⡿⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣿⠃⠀⠀⠀⠀⠈⢻⣦⣀⠉⠛⠿⠷⠀⠀⠀⣀⣴⡿⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣿⢀⣤⣶⠾⠟⠛⠛⠛⠛⠿⠶⣶⣶⣶⠶⠿⠛⠉⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⠀⠀⠀⠀⢸⣿⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣧⠀⠀⠀⠀⢸⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣼⣿⣿⣿⠟⢻⣿⠀⠀⠀⠀⣸⡿⠻⢿⣿⣿⣷⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣴⣿⣿⡿⠋⠀⠀⢸⣿⣀⣀⣀⣀⣿⡇⠀⠀⠙⢿⣿⣿⣦⠀⠀⠀⠀ ⠀⠀⠀⣸⣿⣿⡟⠁⠀⠀⣠⣾⡿⠟⠛⠛⠻⢿⣷⣄⠀⠀⠀⢻⣿⣿⣇⠀⠀⠀ ⣿⣿⠿⠿⠿⠿⠿⠶⣶⣾⣿⠋⠀⠀⠀⠀⠀⠀⠘⣿⣷⣶⠶⠾⠿⠿⠿⠿⢿⣿ ⣿⣿⠀⠀⠀⠀⠀⠀⢀⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿ ⣿⣿⠀⠀⠀⠀⠀⠀⠈⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿ ⣿⣿⣶⣿⣿⣿⣿⠿⠿⠿⣿⣦⡀⠀⠀⠀⠀⢀⣴⣿⠿⠿⠿⣿⣿⣿⣿⣶⣾⣿ ⠀⠀⠀⠘⣿⣿⣿⡄⠀⠀⠈⢻⣿⣷⣶⣶⣾⣿⣿⠋⠀⠀⢀⣾⣿⣿⠏⠀⠀⠀ ⠀⠀⠀⠀⠘⢿⣿⣿⣦⣀⠀⣿⡇⠈⠉⠉⠁⢸⣿⠀⢀⣴⣿⣿⡿⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⣿⣾⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⡇⠀⠀⠀⠀⢸⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⠈⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⢸⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣾⠿⠿⠛⠛⠛⠋⠉⠉⠉⠉⠙⠛⠛⠻⠿⢿⣷⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⡿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⢿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣴⣿⠏⠀⠀⠀⠀⠀⠀⢠⣦⡀⠀⠀⠀⠀⣀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣰⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣄⠀⣠⣾⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣆⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣼⣿⠋⠀⠀⠀⠀⠘⣿⣶⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢀⣀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣧⡀⠀⠀⠀ ⠀⠀⢀⣾⣿⠃⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣷⡀⠀⠀ ⠀⠀⣾⣿⠃⠀⠀⢠⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣷⠀⠀ ⠀⣸⣿⡏⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣇⠀ ⢀⣿⣿⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⡿⠋⠉⠉⠻⣿⣿⠿⠿⠿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡀ ⢸⣿⡇⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⣿⣇⣀⡀⠀⠀⢹⣿⣿⣿⣿⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡇ ⣿⣿⠃⠀⠀⠀⠀⠉⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠉⠀⠀⢀⣀⣤⣤⣴⣶⣶⣦⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷ ⣿⣿⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⠀⢠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿ ⣿⣿⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⢉⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿ ⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠈⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠷⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⢸⣿⡿ ⢸⣿⣧⠀⠀⠀⠀⠀⠀⠀⠠⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⢸⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣾⣿⡇ ⠈⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟⠛⢿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀⣿⣿⣿⡿⠛⠛⠛⠉⠁⠀⣿⡏⠀⠈⠙⠛⠛⠛⣿⣿⡇⠀⠀⠀⠀⠀⢰⣿⣿⠁ ⠀⢹⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣨⣿⣿⣿⣿⣏⠀⠀⠀⠀⠀⠹⣿⣿⣧⡀⠀⠀⠀⠀⢠⣿⣷⡀⠀⠀⠀⠀⢀⣿⣿⡇⠀⠀⠀⠀⢀⣿⣿⡏⠀ ⠀⠀⢿⣿⣧⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⡄⢰⣿⣿⣿⣿⣶⣤⣤⣶⣿⣿⣿⣿⣶⣦⣴⣾⣿⣿⣿⣇⠀⠀⠀⢀⣾⣿⡿⠀⠀ ⠀⠀⠈⢿⣿⣧⡀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠘⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⢀⣾⣿⡿⠁⠀⠀ ⠀⠀⠀⠈⢻⣿⣷⡄⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⣠⣿⣿⡟⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠹⣿⣿⣦⡀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣉⣛⢿⣿⣿⣿⣿⣿⣿⣿⣿⡁⠀⠀⠀⢀⣼⣿⣿⠏⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⢀⣴⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⢠⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⡟⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⡾⠁⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣾⠁⣤⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠉⠙⠳⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⠀⠀⢸⡇⠀⢀⡶⠛⢶⣶⢶⣶⣶⡿⠶⣤⣤⣼⡇⠉⣛⠶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⠀⠀⠘⣧⣀⢸⡇⠀⣼⠁⠀⠀⡟⠀⠀⣤⡀⢉⡹⣟⠉⠀⠈⠻⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣏⠀⠐⠟⠛⠛⢿⡇⠀⣿⠀⠀⢸⡇⠀⠀⢘⣷⡿⠁⢻⡀⠀⠀⠀⠀⠙⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠙⢷⣤⡀⠀⠀⠘⣇⠀⣿⠀⠀⢸⡇⠀⠀⠘⢿⣿⣄⢸⡇⠀⠀⠀⠀⠀⠈⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠛⢦⣄⠀⢿⡀⢹⡄⠀⢸⡇⠀⠀⠀⠀⠙⠿⠿⠷⠶⠶⠦⣤⣀⠀⠀⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣼⡇⠸⣧⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠈⠻⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⣷⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢹⣆⡹⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣤⣀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠷⠶⠶⢤⣤⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣦⣀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠲⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⣤⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢶⣄⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⣄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣦

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⠐⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠂ ⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀ ⠀⢸⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡇⠀ ⠀⠸⣿⣿⣷⣦⣀⡴⢶⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⣴⣾⣿⣿⠇⠀ ⠀⠀⢻⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⡟⠀⠀ ⠀⠀⣠⣻⡿⠿⢿⣫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣻⣥⠀⠀ ⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿⣟⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀ ⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⡹⡜⠋⡾⣼⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀ ⠀⠀⣿⣻⣾⣭⣝⣛⣛⣛⣛⣃⣿⣾⣇⣛⣛⣛⣛⣯⣭⣷⣿⣿⡇⠀ ⠀⠰⢿⣿⣎⠙⠛⢻⣿⡿⠿⠟⣿⣿⡟⠿⠿⣿⡛⠛⠋⢹⣿⡿⢳⠀ ⠀⠘⣦⡙⢿⣦⣀⠀⠀⠀⢀⣼⣿⣿⣳⣄⠀⠀⠀⢀⣠⡿⢛⣡⡏⠀ ⠀⠀⠹⣟⢿⣾⣿⣿⣿⣿⣿⣧⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀ ⠀⠀⢰⣿⣣⣿⣭⢿⣿⣱⣶⣿⣿⣿⣿⣷⣶⢹⣿⣭⣻⣶⣿⣿⠀⠀ ⠀⠀⠈⣿⢿⣿⣿⠏⣿⣾⣛⠿⣿⣿⣿⠟⣻⣾⡏⢿⣿⣯⡿⡏⠀⠀ ⠀⠀⠤⠾⣟⣿⡁⠘⢨⣟⢻⡿⠾⠿⠾⢿⡛⣯⠘⠀⣸⣽⡛⠲⠄⠀ ⠀⠀⠀⠀⠘⣿⣧⠀⠸⠃⠈⠙⠛⠛⠉⠈⠁⠹⠀⠀⣿⡟⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢻⣿⣶⣀⣠⠀⠀⠀⠀⠀⠀⢠⡄⡄⣦⣿⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⣿⣷⣻⣿⢷⢶⢶⢶⢆⣗⡿⣇⣷⣿⡿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣛⣭⣭⣭⣭⣭⣻⣿⡿⠛⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠟⠛⠛⠛⠻⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⠀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠤⠤⠖⠛⠉⠉⢻⡭⢥⣈⠉⠁⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁ ⠀⠀⠀⠀⠀⢀⣀⣠⠤⠤⠴⠒⠒⠚⠛⠛⠛⠛⠛⠛⠛⠓⠒⠦⠤⠤⢤⣄⣷⡀⠈⠛⠦⣄⠀⠀⢀⡤⢴⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⠐⣾⡏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠈⠳⣾⠋⣠⠞⠉⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡉⠀ ⠀⠀⠀⠀⠈⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⣽⣝⡳⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣥⡀⢀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⡃⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⣿⠀⠉⠳⢯⡳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠋⠉⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣆ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢻⠀⢀⣴⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠶⣬⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⢿⠀⢸⣴⠟⠁⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠈⢿⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠒⠂⠙⣦⠀⠀⠀⠀⠸⡆⠀⠁⠀⠀⣠⠶⠛⠉⠉⠙⠲⣤⡀⠀⠀⢰⠃⠀⠀⠀⠀⠸⣟⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⠀⠀⠀⠀⠀⣠⠴⠉⠀⢀⣠⡴⠾⠋⠃⠀⠀⠀⠀⠀⠀⠀⣠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⡼⠀⠀⠀⠀⠀⠀⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷ ⠀⠀⠀⠀⡠⠞⠁⢀⣠⣾⠿⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡇⠀⠀⠀⠀⠀⠀⢸⢻⠀⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿ ⢄⠀⢠⠔⠤⣀⡴⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢀⣀⣀⡤⣴⡦⠖⠛⢻⡟⠛⠉⠉⠉⠙⣿⠀⠀⠹⣄⣠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻ ⠈⠧⠀⣠⡞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣀⡤⠴⠒⠚⠉⠉⠀⠀⠻⠃⠀⠀⠈⠁⢀⡴⣦⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⢀⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣼⣿⡾⢋⣀⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈ ⢰⣿⣦⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣤⣀⣀⣀⣀⣀⡠⠴⠖⠋⠁⠀⠀⠉⠁⠀⠀⠀⠉⠙⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰ ⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠛⠓⠦⢤⡄⠀⠀⠀⠀⠀⠀⣶⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠋⠉⠳⠀⠀⠀⣠⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⣦⣤⠤⠤⣤⣶⡶⠶⣯⣉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⣠⠶⣦⠉⣠⡶⠋⠁⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢀⣀⡤⠤⠖⠚⠛⠉⠉⢀⡴⠟⠁⠀⣠⠞⠁⣴⢃⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠉⠁⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⢀⣶⠋⠀⣼⢁⣼⠥⠤⣄⣀⡤⠴⠒⠛⠙⠒⠒⠓⠛⠲⣄⣰⣋⡀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣤⣀⣀⠀⢸⡇⠀⢀⣿⠟⠁⣠⠖⠋⠁⠀⠀⠀⠀⠀⠹⣤⣤⣶⣿⣿⣿⣿⣿⣷⣧⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⢦⣿⡟⠀⠰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣄⠈⢻⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠈⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⣿⣿⣿⠟⠉⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⣤⣤⣤⠤⠤⠞⠳⡤⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⢧⣀⣀⡠⠖⡟⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠒⠒⠒⢺⠃⢸⡟⢦⡀⠀⠀⠀⠀⠀⠀⢤⣤⣴⣾⣿⣿⣯⡀⠀⠀⣀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⣾⠀⠀⠙⢲⣤⣄⣀⡤⠖⠻⣿⣿⣿⠹⣇⠀⠉⠛⢉⡵⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⢠⡇⠀⠀⠈⢻⠀⣿⠀⠀⠀⠀⠀⠀⠈⠓⠾⠽⠷⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⣸⠀⠀⠀⢀⡏⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠼⠧⢾⡇⠀⠀⠀⣸⡧⠿⠧⠤⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼

⠀⠀⣀⣤⣤⣤⡀⢀⠀⠀⠀⣀⣴⣶⣶⣶⣶⣦⣄⠀⠀⠀⠀⣠⣤⣀⣤⠄⠀⠀ ⢀⣾⣿⡟⠋⠙⣿⣿⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⢸⣿⣿⣿⠀⠀⠀ ⢸⣿⣿⡄⠀⠀⢸⣿⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⣿⣿⣿⣿⡄⠀⠀ ⠘⢿⣿⣿⣦⣤⡈⠉⠘⣿⣿⣿⣿⢿⣿⣿⡿⣿⣿⣿⣿⠃⣸⣿⡏⢻⣿⣇⠀⠀ ⠀⠈⠻⣿⣿⣿⣷⣄⠀⢸⣿⠀⠀⢀⣿⣯⠀⠀⠀⣿⡇⠸⣿⣿⠀⢸⣿⣿⡇⠀ ⢤⣤⣤⠉⠉⢿⣿⣿⡇⢸⣿⣦⣴⣾⡿⢿⣷⣦⣴⣿⡇⢰⣿⣿⣶⣾⣿⣿⡇⠀ ⢸⣿⡇⠀⠀⠀⣿⣿⡇⠈⠛⠿⣿⣿⠁⠈⣿⣿⠿⠛⠁⣼⣿⠇⠀⠀⣿⣿⣇⠀ ⠀⢻⣿⣦⣀⣴⣿⡿⠁⠀⠀⢠⣿⣿⣿⣿⣿⣿⡆⠀⢰⣿⣿⠀⠀⠀⢸⣿⣿⡀ ⠀⠀⠉⠛⠛⠛⠉⠀⠀⠀⠀⠈⠙⠛⠛⠛⠛⠋⠁⠐⠛⠛⠛⠀⠀⠀⠘⠛⠛⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⠀⠀⠀ ⠀⠘⣿⣶⡦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠄⠀⠀⠀⠀⠛⣿⠇⠀⠀⠀ ⠀⠀⠈⠻⠁⠀⠀⠀⢀⠄⠀⠀⠠⡆⣠⠾⠛⠟⠛⠒⠒⠤⢀⠀⠀⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠐⠒⠉⠀⣤⠀⠀⠉⠁⢀⣠⠆⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⣶⣦⣄⠀⠀⣿⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣿⣿⡉⠻⣷⣄⣿⣦⣴⣿⣿⡉⠁⣀⣤⣼⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀ ⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀ ⠀⢴⣿⣿⣿⣿⣿⠁⠈⠙⠟⠁⠀⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠂ ⢴⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠒⠀⠀ ⠀⠙⠻⢿⣿⡿⠂⢀⣀⣀⣀⠀⠀⠀⠀⠀⣼⣿⣿⣿⠿⠿⠟⠋⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠁⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡟⠘⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡿⠀⠀⠹⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⠃⠀⠀⠀⢻⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡏⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢤⣀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣄⣀⣀⣀⣀⣠⣤⠄ ⠈⣿⣿⣷⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀ ⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀ ⠈⠉⠉⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡿⠟⠋⠉⠉⠉⠀ ⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠢⡀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⢀⠔⠀⠀ ⠀⠀⠈⠳⢄⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠟⠋⠀⠀⠀⠀⠀⠀⣀⠔⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢦⣀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠛⠋⠁⠀⠀⠀⠀⠀⠀⢀⡤⠚⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠳⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠒⠤⠄⠀⠀⠀⠀⡀⠀⠀⠀⠀⠠⠐⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢷⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⡶⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⣿⣶⣶⣶⣦⣤⣴⣶⣶⣿⣿⣿⣿⣿⣿⣶⣶⣶⣤⣶⣶⣶⣶⣿⠿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠴⠒⠋⠉⠁⠐⠒⠀⠀⢁⣠⣶⡞⠉⠫⠿⣶⡦⣤⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡚⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡾⣿⣷⠀⠀⡀⠀⠉⠙⠻⢿⣦⣄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠋⠀⣿⣿⣾⣫⣿⠇⠀⠀⠀⠀⠉⢺⣷⡄⠀⠀ ⣿⣷⣶⢤⣀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⢉⠇⠀⠀⣿⢹⣿⣯⡅⠀⠀⢀⣠⠴⠚⠋⠉⠀⠀⠀ ⣿⠻⣿⣷⣮⣝⣲⠦⣤⣀⣠⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢫⠞⠁⣠⠃⠀⠀⠀⡿⣼⣿⣏⣃⡤⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣇⠈⢿⣿⣏⣭⠛⠶⠾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢦⣀⠃⠀⠀⠀⢠⠏⣿⠿⣿⣋⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠹⣿⡄⠀⠙⣷⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠤⢤⣉⠓⢦⣤⡞⠀⣿⡓⠒⠠⢍⣓⠲⢤⣀⠀⠀⠀⠀⠀⠀ ⠀⢻⣷⡀⠀⠈⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠿⠁⠀⠀⠀⠀⠉⠒⠬⣙⠦⣄⠀⠀⠀ ⠀⠀⢿⣧⢀⣴⣟⣛⡻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⣀⣤⣶⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠊⠳⣄⠀ ⠀⠀⠈⢿⡿⠏⣿⢧⡉⠋⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⣴⠞⠋⠁⠀⠀⠹⡿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳ ⠀⠀⠀⢹⡇⢸⡏⠀⠙⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢌⣿⣾⠀⠀⠀⠈⢧⠀⠀⠀⠀⡖⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠈⣧⠀⠀⢸⡇⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠸⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠸⣧⠀⢸⡇⠀⠀⣠⡏⠀⠀⠀⠀⠀⠀⣾⠛⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠈⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⣿⣷⡀⠀⠀⠀⠀⢻⣷⠸⣇⠀⢰⡿⠁⠀⠀⠀⠀⠀⢸⣿⣶⠂⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠈⠹⣗⣿⢏⡉⠙⠻⣟⠛⠓ ⠀⠀⠀⠀⠀⠸⣿⣷⣄⣤⡤⣄⠘⣻⣶⠿⠦⠚⠁⠀⠀⠀⠀⠀⠀⢸⣿⡿⢀⡼⠁⠀⠀⠀⠀⣀⡠⠤⢄⣀⠀⠀⠈⠙⢻⣗⢦⡈⠑⠄ ⠶⣄⠀⠀⠀⠀⢻⡁⠀⠻⣿⣾⣷⡟⠛⠒⠒⠢⢄⡀⠀⠀⠀⠀⠀⢈⡾⠗⠚⠛⢳⡄⢀⣴⠞⠁⠀⠀⠀⠈⠙⠳⢶⡚⢁⠈⠙⣟⣆⠀ ⠀⠈⠙⠲⣄⡀⠈⢳⡀⠀⠈⠻⠿⣿⡷⠠⢄⡀⠀⠈⠒⠠⠤⠐⠊⠁⢀⡠⠠⠔⣺⣷⠟⠁⠀⠀⣠⣤⡀⠠⢀⠀⠀⠉⢾⡇⠀⠈⠀⠁ ⠀⠀⠀⠀⠀⠙⢶⢦⡙⢦⡀⠀⠀⠀⠀⠀⠀⠈⠑⠂⠤⠤⠄⢀⡴⠚⠁⠀⣠⣾⠟⠁⠀⠀⣠⣾⠿⢿⣿⣷⣄⡈⠀⠀⣼⠇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⡆⢹⡄⠉⠳⠤⣄⣀⠀⠀⠢⠄⠀⠀⠐⠊⠁⣀⣠⣴⠿⡿⠋⠀⠀⣠⣾⠏⠀⠀⠘⠻⡟⠀⢑⣦⡼⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡰⢠⠇⢠⡿⣆⠀⠀⠀⣨⠿⠉⣷⣶⠶⠶⠾⢿⣿⡛⠋⠁⠀⢧⣀⣠⣾⣟⣿⠀⠀⠀⠀⠐⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘ ⠀⠀⠀⢠⣾⠴⠁⢠⣿⠀⢹⣠⠴⠊⠁⠁⢀⡟⠃⠀⠀⢀⠴⠊⠙⠢⣀⠀⠀⠀⠀⠉⠉⢻⡷⠶⠖⢶⣶⣿⣷⠤⢤⣤⠖⠃⠀⠀⠀⠀ ⠀⠀⠀⣾⠁⠀⢀⣽⠟⠀⡸⠀⠀⠀⢀⡴⠋⢧⠀⠀⠀⠁⠀⠀⠀⠀⠈⠳⡀⠀⠀⠀⠀⠈⣇⢀⠔⠛⢉⡛⠻⣶⢤⡏⠉⠉⠁⠀⠀⠀ ⣀⠀⣠⠇⠀⣠⡾⠋⠀⢠⡇⠀⣀⡴⠋⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⢻⡏⣀⠴⡿⠀⠀⠈⠻⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡀⠊⠉⠀⢀⣴⣿⠶⠚⠁⠀⠀⠀⠀⠀⠈⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆⠀⠀⠀⠘⠋⢁⣼⣷⣶⣦⣀⠀⠱⣤⡀⠀⠀⠀⠀

⢠⣶⣿⣿⣿⣶⡄⠀⣶⣶⣶⡆⢰⣶⣶⣶⡆⠀⣶⣶⣶⣶⠀⢰⣶⣶⣶⣶⣶⡄ ⣿⣿⣿⠉⣿⣿⣿⠀⣿⣿⣿⡇⢸⣿⣿⣿⣧⢸⣿⣿⣿⣿⠀⢸⣿⣿⡏⢻⣿⣿ ⢿⣿⣿⣦⣉⠉⠁⠀⣿⣿⣿⡇⢸⣿⣿⢻⣿⢸⣿⢻⣿⣿⠀⢸⣿⣿⡇⢸⣿⣿ ⠈⠻⢿⣿⣿⣷⣄⠀⣿⣿⣿⡇⢸⣿⣿⢸⣿⣿⣿⢸⣿⣿⠀⢸⣿⣿⣿⣿⣿⡟ ⣤⣤⣤⠙⣿⣿⣿⠀⣿⣿⣿⡇⢸⣿⣿⢸⣿⣿⣿⢸⣿⣿⠀⢸⣿⣿⡏⠉⠁⠀ ⢿⣿⣿⣀⣿⣿⣿⠀⣿⣿⣿⡇⢸⣿⣿⠀⣿⣿⡇⢸⣿⣿⠀⢸⣿⣿⡇⠀⠀⠀ ⠘⠿⢿⣿⣿⠿⠋⠀⠿⠿⠿⠇⠸⠿⠿⠀⠹⠿⠇⠸⠿⠿⠀⠸⠿⠿⠇⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢔⣫⣭⣭⣒⣒⠦⢤⣀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢊⣵⣿⠿⠋⠀⠀⠉⠙⠓⣶⣬⣙⠲⢄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢊⣴⣿⠟⠁⠀⢀⡴⠶⣤⡀⠀⢈⠑⠊⠿⡆⠑⣄⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⢞⣴⣿⠟⠁⠀⢀⣴⣏⣉⠓⠺⡇⠀⢸⣿⣷⣦⡄⠀⡸⠃ ⠀⠀⠀⠀⠀⠀⢰⢃⣾⡿⠃⠀⠀⣴⠿⢤⣄⣈⠉⠓⢷⠀⠘⣿⣿⣿⣿⠞⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⢸⣿⡇⠀⠀⣼⠧⣤⣀⣀⡈⠉⢻⣟⡤⡀⠙⠟⣹⠋⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⡄⢻⣧⠀⠀⣿⡀⠀⠀⠈⠉⠉⣿⡜⠀⠈⠒⠚⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⡄⢻⣦⠀⠸⣏⠉⠉⠙⠛⠛⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⢻⣆⠀⠹⣤⠤⠤⠤⠤⣿⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⢻⣧⠀⢻⡄⠀⠀⠀⣻⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⢻⣧⠀⢻⡉⠉⠉⠙⣏⡆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⢻⣧⠈⢷⡤⠤⠶⢿⣴⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⢻⣧⠈⣧⣀⣀⣼⣇⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⢻⣆⠘⣧⠀⣀⣹⡽⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⢿⣆⠘⣏⠁⣈⣷⠇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠈⣎⢿⡆⠹⡏⢁⣹⡾⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠔⣉⠠⣬⣑⠢⡀⠀⠀⠀⠘⡜⣿⡀⢻⡉⣈⣧⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⡠⢊⣴⠞⠉⢷⣝⢿⣷⣬⡢⣄⠀⠀⢇⢹⣧⠘⣏⣁⣽⡼⢀⠀⠀⠀⠀ ⠀⢀⠊⠰⣿⡁⠀⡴⠋⠙⣶⣝⠻⣿⣮⣑⢄⣸⢸⣿⠀⣿⣡⢼⢇⣶⣍⡢⣄⠀ ⠀⣀⠇⣀⡀⠉⠛⠦⣤⣞⠀⣸⠛⢳⠾⠿⣧⠉⣼⣿⠀⣿⢤⡾⠘⠛⣛⣡⣎⢢ ⢎⣀⠘⠛⠿⢷⣦⣄⡠⢭⣙⡛⠲⠾⠖⠚⣁⣼⣿⢏⣼⣧⠞⣡⣿⣿⣿⣿⠟⡸ ⠀⠀⠈⠉⠒⠒⠠⠬⠭⠅⢀⣉⣉⣙⣛⣛⣛⣉⠀⠬⠭⠤⠬⠭⠭⠭⠍⠒⠉⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣶⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠈⣿⣿⣇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣷⣄⠀⠀⢸⣿⣿⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠙⢿⣿⣧⡀⠈⣿⣿⣇ ⠀⠀⠀⠀⠀⠀⢰⣿⣿⣦⣄⡀⠀⠻⣿⣿⣦⠸⠟⠛ ⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣷⣤⣈⠛⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⣶⣶⣦⣤⣀⣙⡻⢿⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠉⠙⠛⠿⢿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀ ⢠⣤⡄⠀⣿⣿⣿⣿⣿⣷⣶⣶⣿⠀⣤⣤⡄⠀⠀⠀ ⢸⣿⡇⠀⣉⣉⣉⣉⣉⣛⣛⣛⣟⠀⣿⣿⡇⠀⠀⠀ ⢸⣿⡇⠀⠿⠿⠿⠿⠿⠿⠿⠿⠿⠀⣿⣿⡇⠀⠀⠀ ⢸⣿⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣿⣿⡇⠀⠀⠀ ⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠇⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤ ⣿⡁⠶⢶⡖⠒⠒⠒⠒⠒⠒⠒⠖⣲⠶⠆⣿⣿⡇⠶⢶⣖⠒⠒⠒⢒⡶⠶⠀⣿ ⠛⠛⠻⢦⡙⣦⡀⠀⠀⠀⠀⠀⢰⠡⣾⣿⣿⣿⣿⣿⣶⠘⡆⠀⡴⢫⡶⠛⠛⠛ ⠀⠀⠀⠀⢹⡼⢷⡄⠀⠀⠀⠀⠘⣆⢻⣿⣿⣿⣿⣿⡟⣰⡇⡞⣱⠟⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠹⡌⢿⡄⠀⠀⠀⠀⠘⣆⢻⣿⣿⣿⡿⣱⣿⡞⣰⡟⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠹⣌⢻⡄⠀⠀⠀⠀⠘⣆⢻⣿⡿⢡⣿⡟⢠⡟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠹⣆⢻⣄⠀⠀⠀⠀⠘⢆⠻⢣⣿⡿⢡⡟⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⢻⣆⠀⠀⠀⠀⠈⢦⣾⡿⢡⡟⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⢻⣆⠀⠀⠀⠀⠀⢻⢡⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⢻⣆⠀⠀⠀⢰⢃⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⢻⣆⠀⢠⢃⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠹⠦⠃⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⣠⣶⣿⣿⣿⣿⣶⣤⡀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣶⣄⠀⠀ ⠀⣾⣿⡿⠋⠉⠉⠙⠻⣿⣿⣷⣄⣠⣾⣿⣿⠟⠋⢉⡉⠙⢿⣿⣷⠀ ⢸⣿⣿⠀⢠⣤⣤⣤⠀⠀⠙⣿⣿⣿⣿⠋⠀⠀⣤⣼⣧⡄⠀⣿⣿⡇ ⠘⣿⣿⡄⠈⠉⠉⠉⠀⣀⣴⣿⣿⣿⣿⣦⣀⠀⠉⠹⠏⠁⢠⣿⣿⠃ ⠀⠹⣿⣿⣷⣦⣤⣶⣿⣿⣿⠟⠁⠈⠻⣿⣿⣿⣶⣤⣴⣾⣿⣿⠏⠀ ⠀⠀⠈⠙⠛⠿⠿⠛⠛⠉⠀⠀⠀⠀⠀⠀⠉⠛⠛⠿⠿⠛⠋⠁⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⡞⡏⡏⡏⠻⣦⠴⠶⠶⠶⢦⣤⣤⣤⣤⣤⣀⡀⣠⠶⢛⢟⠷⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢺⡀⡇⣇⠟⠹⢹⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠯⣀⠂⢌⢤⠊⢷⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡾⠋⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⡀⣀⣀⠀⠀⠀⠀⠐⠉⠽⠺⡁⢸⢀⡾⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣸⠗⠉⠉⠁⠀⠀⠀⢠⠀⠀⡤⡠⣀⢤⡤⡀⠀⠀⠀⠀⠀⠀⠃⠱⠚⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡏⠀⠀⠀⠀⢀⠀⠄⢠⠀⠰⡉⠉⠉⠉⢉⠇⠀⠀⠄⠀⠀⠀⠀⠀⡇⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢷⣄⡎⠀⠄⠘⢄⡈⢢⠗⠒⠣⡀⠀⠀⠑⡶⠶⠬⡼⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠹⣧⠀⢈⣒⠖⠊⠁⠀⠀⠀⠁⠀⠀⠈⠀⠀⠘⠠⡄⠤⠃⡀⠀⡆⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⠏⢑⠂⣡⠐⠒⢲⣶⡖⠢⠀⠀⠀⠀⣤⣤⣀⣀⡈⠱⣈⣠⢠⣿⡀⠀⠀⢷⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡟⠀⠈⡄⢸⠀⠀⣀⣙⡓⠊⠀⠀⠀⠀⠘⠿⠤⠜⠀⠁⡦⠌⣿⠸⣇⠀⠀⠸⣇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣼⠁⠀⠀⣸⢿⡀⠀⠉⠉⠉⠀⣀⣠⣤⠀⠀⠛⠛⠓⠀⢰⠁⣰⠇⠀⢿⠀⠀⠀⢿⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⡏⠀⠀⢀⡟⠈⢷⡄⠀⠀⠀⠀⡟⠋⢹⠀⠀⠀⠀⠀⢀⡟⠛⠉⠀⠀⠸⡇⠀⠀⠸⡇⠀⠀⠀⠀ ⠀⠀⠀⣼⠁⠀⠀⣸⠃⠀⠀⠙⠷⣄⡀⠀⠡⣀⠆⠀⠀⢀⣠⡴⠋⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⢿⠀⠀⠀⠀ ⠀⠀⢠⡏⠀⠀⠀⡿⠀⠀⠀⠀⠀⠈⠙⠳⠶⠦⠶⠶⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⢸⡆⠀⠀⠀ ⠀⠀⣸⠃⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣷⠀⠀⠀ ⠀⠀⡿⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⢸⡄⠀⠀ ⠀⢸⡇⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠘⣇⠀⠀ ⠀⢸⡇⠀⢀⢴⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⢄⠀⠀⣿⠀⠀ ⠀⢸⠃⡠⠊⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠑⢄⢹⡄⠀ ⢠⡾⠋⢀⠞⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡏⠢⡀⠙⢷⡀ ⢸⡧⠒⣡⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣶⢌⠒⢼⣇ ⢿⡠⠞⣡⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠑⢤⡟ ⢸⣥⣞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⣤⡇ ⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⣀⣀⡠⠄⠒⢲⠖⡒⠂⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠠⢖⠈⠉⠀⠀⠀⠀⡤⣈⠉⠉⠓⠈⠑⢖⠝⣿⠀⠀⠀⠀⠀⠀⠀⢀⠂ ⠀⠀⠀⠑⢄⠀⠀⠀⢠⢹⠉⣻⠂⠀⠀⠀⠀⠉⣉⠆⠀⠀⠀⠀⠀⠀⠀⢣ ⠀⠀⠀⠀⡀⠑⢄⠀⠘⡀⠊⢀⠠⠤⢄⠀⢀⠊⠀⢹⡀⠀⠀⠀⠀⠀⠀⠘ ⠀⠀⠔⢈⡤⠊⠉⠀⠀⠀⠰⠁⠀⠀⠀⠑⢜⠀⠀⠈⡇⢀⠀⠀⠀⠀⠀⢰ ⠂⡩⠚⠁⠀⠀⠀⠀⠀⠀⢢⠠⠄⠒⠂⠊⠉⢋⣠⠀⡇⠀⠀⠀⠀⠀⠀⢸ ⠾⠤⠀⠀⢀⣀⠀⠀⠀⠀⣈⡦⠤⠤⠤⠒⠀⠉⠁⠀⢳⠀⠀⠀⠀⠀⠀⢠ ⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠣⡀⠀⠀⠀⠀⠂⠐⢀⠔⠁⠀⠀⠀⠀⠀⠀⠸ ⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠈⢑⡒⢒⠖⠒⠫⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠤⠐⠂⠉⢁⠔⢁⡔⣡⡱⢁⡀⠤⠀⠼⠤⣀⣔⢂⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠚⠤⡟⠰⠁⠀⠀⠀⠑⢿⣿⣿⣿⠒⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢤⣤⣘⡴⣄⠀⠀⠀⠀⢀⣿⡿⠤⢰⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢡⠁⢱⢤⠄⠚⠿⢻⣁⠢⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣆⡌⠀⣸⢜⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀

⠀⠀⣀⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢰⣶⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠛⠛⠛⠛⢿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⡿⠛⢻⣿⣿⠀⠉⠛⠛⠿⠿⠿⣿⣿⣿⣿⣿⣿⡟⠉⠉⠁⠀⠈⠉⠉⠛⠛⠿⠿⢿⣿⣷⣶⣶⣶⣤⣤⣤⡴⠶⠂ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⠀⠀⢈⣿⣿⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⢻⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⠀⠀⣸⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠘⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠀⢀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡆⠈⠻⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣷⠀⠀⣸⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⣀⡀⢀⣠⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⢤⠄⠰⠊⠀⠀⠨⡁⣼⢭⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⢧⡱⠀⠀⠀⠀⠀⠀⠈⠀⠈⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⣧⠠⡀⠠⠀⢠⡎⣣⠰⣄⣀⣃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢟⢦⣈⣦⡷⠽⢗⡏⠀⢀⡑⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠌⠒⡤⠤⢖⢯⣶⠿⡑⢌⢾⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⢲⠀⢰⠀⢺⡄⠁⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣠⣔⢤⣀⢜⡦⡊⠀⡫⠧⡤⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⡪⠪⢻⣬⠇⡇⡇⠇⠏⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠑⠓⠛⠁⠀⠃⡇⠸⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢰⡺⠀⠗⣄⡄⢣⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⠔⠫⡤⠤⣿⠂⢀⣈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡴⠋⠀⢡⠀⠃⣀⣷⠏⠠⠤⢙⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⠲⠤⠠⠾⠞⠛⠉⢸⡌⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠢⠤⠤⠾⠀⠀⠛⠛⠓⠺⠇⠐⠒

⠀⠀⠀⠀⡀⠀⠀⠢⠨⣔⠄⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠤⢖⣚⠳⢒⠀⠀⠘⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⡈⢭⠟⠁⣀⣭⢀⠀⠈⠁⢆⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣆⠀⠀⠀ ⠄⢐⡋⡤⠀⠈⢎⠃⠑⠜⠀⢰⣷⣦⠶⠞⠛⠛⠛⠲⠤⠤⣊⣾⣿⢠⣯⣕⢄⠀ ⠐⡯⣴⣤⠀⡐⣼⠕⡀⠘⠀⣿⣿⠃⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣌⣫⠿⢛⠆ ⠘⢴⣻⢷⠠⡷⡟⡈⢣⠀⢀⣿⠃⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠛⢛⠛⠦⠃ ⠈⠈⠻⡌⢑⡝⣴⣿⠌⠃⢸⡇⠠⣿⣿⠿⠿⢟⠻⡛⢿⣿⣿⣷⣴⣿⣷⣿⡆⣹ ⠀⠀⠀⠀⢈⠻⡮⣮⠀⢠⠸⣷⢸⣿⣿⣿⣿⣷⣦⠘⢄⣛⣛⡻⠟⠋⠈⠫⠿⠁ ⠀⠀⠀⠀⠀⢕⢽⣮⢦⣋⢆⣿⡀⣿⣿⣿⣿⣿⣿⡇⠀⠈⠇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⢇⣿⣿⣿⣮⣻⡗⣿⣿⣿⣿⣿⣿⣿⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⢐⣿⣿⣿⣿⣷⣿⣿⣿⣿⠿⢋⡷⠾⣧⣤⣤⣤⣒⣉⡡⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⢉⣉⣉⣉⣋⠑⡆⢙⣢⣤⣤⡬⠤⠍⠉⠉⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠒⠉⠉⠍⠛⠛⠉⠀⠀⠻⢿⠿⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀

⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬛⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬛🟨⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬛🟩🟨⬛⬜⬜⬜⬜⬜⬜⬜⬜ ⬛🟩🟨🟨⬛⬜⬜⬜⬜⬜⬜⬜ ⬛🟨🟥🟥🟨⬛⬜⬜⬜⬜⬜⬜ ⬛🟨🟥🟥🟨🟥⬛⬜⬜⬜⬜⬜ ⬛🟨🟨🟨🟨🟥🟥⬛⬜⬜⬜⬜ ⬛🟨🟨🟨🟩🟩🟨🟨⬛⬜⬜⬜ ⬛🟥🟥🟨🟩🟩🟨🟨🟥⬛⬜⬜ ⬛🟥🟥🟨🟨🟨🟨🟨🟥🟥⬛⬜ ⬛🟨🟨🟨🟥🟥🟨🟨🟨🟨🟨⬛ ⬛🟩🟩🟨🟥🟥🟨⬛⬛⬛⬛⬛ ⬛🟩🟩🟨🟨🟨🟨⬛⬜⬜⬜⬜ ⬛🟨🟨🟨⬛🏾🏾⬛⬜⬜⬜⬜ ⬛🟥🟥⬛⬜⬛🏾🏾⬛⬜⬜⬜ ⬛🟥⬛⬜⬜⬛🏾🏾⬛⬜⬜⬜ ⬛⬛⬜⬜⬜⬜⬛🏾🏾⬛⬜⬜ ⬜⬜⬜⬜⬜⬜⬛🏾🏾⬛⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬛⬛⬜⬜⬜

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⢿⣛⣋⠉⠉⠉⠉⠉⠒⠲⠤⣤⢾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⡤⠴⠒⠒⠒⠒⠒⠦⢤⣀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⡴⡱⣿⠦⡀⠀⢀⠤⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠦⡉⠒⣺⠭⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⡑⠀⡿⠀⠈⠞⠁⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⡰⠁⠸⡇⠀⠀⡀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⣀⣠⠄⠒⠈⠀⠀⠀⠀⠀⠀⢠⠏⠀⠁⠉⠀⠈⠛⢥⣠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⡰⠁⡠⠖⠋⢠⠃⠀⠀⠀⠀⠀⠀⠀⢀⢔⡏⠀⠀⠀⠀⠸⣷⠠⡀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⠔⠋⠉⠀⠀⠀⠈⠉⠙⠒⠦⣄⡀⢠⢣⠊⠀⠀⢀⠆⠀⠀⠀⢀⠊⠀⢠⢁⡎⡸⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡿⣅⠀⠀⠀⡼⠀⠀⢀⡔⠁⠀⣠⡇⡞⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⣒⠄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀⠀⡇⠀⢠⡞⠀⢀⠔⢹⡎⠀⡞⠀⠀⠀⠀⠀⠀⢠⡒⠒⠷⠿⠷⠒⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⠇⢀⢻⢃⣴⠁⠀⢨⠇⣸⠁⠀⠀⠀⠀⠀⠀⢸⠉⠲⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡶⡈⠸⠃⡇⢰⠀⡜⢀⠇⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠙⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠑⢄⠀⠀⢳⠀⠀⣸⢁⢆⡼⡡⡞⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠈⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⠼⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⢣⠀⣼⠰⢠⣇⠮⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡞⠁⠀⠈⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣗⠲⢤⡀⣃⣷⣡⢷⡖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢷⢄⠀⠀⠀⠀⠀⠰⡀⠀⠀⠀⠀⠀⠀⠀ ⠰⡇⠀⠀⠀⠀⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠸⣀⡴⠋⠁⠀⢠⠎⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠸⠀⠁⠢⡀⠀⠀⠀⠘⢄⠀⠀⠀⠀⠀⠀ ⠀⢧⠀⠀⠀⠀⠀⠀⠑⢦⡀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⢸⡠⡶⢀⡜⡰⣡⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠈⠲⣄⡀⠀⠈⠳⢄⠀⠀⠀⠀ ⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠙⠢⣄⠀⠀⠀⠀⠀⠳⡄⠀⠀⠘⠁⠗⠃⢿⡟⠙⣿⡈⡄⠀⠀⠀⠀⡄⡀⣰⡟⠀⠀⠀⠀⠀⠀⠈⢯⡑⠢⠄⣀⠑⠢⢀⣀ ⠀⠀⠈⢦⡀⠀⠀⠀⠀⠀⠀⠀⠈⢿⠦⣀⠀⠀⠀⠙⢦⠀⠀⠀⠀⠀⠀⡇⠀⠐⢣⢹⡀⠀⡆⣼⣴⠗⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡜⠻⣄⠀⠀⠀⠀⠀⠀⠀⠸⡴⠚⡟⠢⢄⣀⠀⠳⣄⠀⡟⢲⠒⡇⠀⠀⠀⢑⡇⡼⠛⠉⠁⡼⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀ ⠀⠀⢸⠁⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⢳⡀⢷⠀⠀⠈⠙⠒⠬⣿⣇⣸⡀⡇⠀⠀⢀⠏⢹⠀⠀⠀⣰⠃⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣇⠀⠀⠀⠀⠀ ⠀⠀⢸⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠳⣸⠀⠀⠀⠀⠀⣠⠃⠀⢨⣧⡇⠀⠀⡼⠀⡟⠀⠀⢠⠇⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢸⠀⠀⠀⠀⠀ ⠀⠀⠈⢧⠀⠀⠀⠀⠀⠈⢳⢦⡀⠀⠀⠀⠙⢆⠀⠀⣀⠔⠁⢀⡠⢛⣿⠀⠀⢰⠃⢀⡇⠀⠀⡞⠀⠀⠀⠀⠹⡢⢀⠀⠀⠀⠀⠀⠀⠘⣼⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⠈⢧⠉⣳⣤⣀⠀⠈⠳⣮⡥⠴⠚⠉⠀⢸⡏⠀⢀⡟⡀⢸⠁⠀⢸⠁⠀⠀⠀⠀⠀⠱⡀⠑⢤⡀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⠢⣄⠀⠀⠀⠈⢿⡁⢀⡏⠑⢢⢤⣈⠳⢄⡀⠀⠀⢸⠇⠀⡼⠀⠑⢿⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠙⣄⠀⠈⠓⠦⣄⡀⠀⠑⢄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠤⣀⣀⠙⢼⡀⠀⣿⠀⠈⠉⠓⠻⠶⣄⣸⠀⢠⣧⡀⠀⠈⡇⠀⢸⠈⢲⢄⡀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠈⠉⠐⠒⠓⠄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⡿⢷⡤⣿⢤⠀⠀⠀⠀⢀⡤⣧⣄⣼⣽⣽⠀⠀⢳⠀⠀⢳⡢⠧⠌⠒⠤⢄⣀⡀⠀⠈⠑⠤⢀⣀⣀⠠⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⡼⠧⠼⠼⠀⠀⠀⠀⢿⣰⡇⢸⡆⣹⠀⠀⠀⠸⡄⠀⢄⢹⠓⡄⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠉⠙⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⠂⢀⡀⠀⢀⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣄⣠⣀⠀⠘⠋⠉⠉⠁⠀⠺⣿⡷⣿⣿⣿⡿⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣛⠛⠉⠀⠀⠀⠀⠺⣷⣦⠀⠀⠀⠙⠛⠉⠀⠀⠈⣿⣦⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣆⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠙⠉⠀⠀⢸⣦⠀⠀⠀⢀⣼⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡆⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣷⠄⠀⠀⠀⠀⠀ ⢠⣾⣷⣦⡀⠘⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⢠⣿⣿⣿⡿⠟⠛⠋⠁⣀⣠⣤⣄⣀⠀ ⠘⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣾⣶⣿⣿⣿⣿⣿⣿⣟⠘⣿⣷⡀⠀⠀⠘⠿⡿⠉⠀⠀⣀⣴⣾⣿⣿⣿⣿⡿⡂ ⠀⠈⠿⢟⣿⣿⣆⠀⠀⠀⠀⢀⣤⣤⣿⣿⣿⣿⣿⣎⠛⢫⣿⣿⣿⣷⡘⢿⣿⣆⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⡿⠛⠋⠁ ⠀⠀⠀⢺⣿⣿⣿⣷⡄⠀⢰⣿⣿⣿⣯⠹⣿⣿⣿⣷⣶⡜⢿⣿⣿⣿⣷⡄⠹⣿⣷⣄⠀⠀⣴⣼⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀ ⠀⠀⠀⠀⠙⢻⣿⣿⣿⣦⡘⢿⣿⣿⣿⣃⠉⢿⣿⣿⣿⣿⡌⢻⣝⠻⠿⢃⡀⣿⣿⣿⣷⣶⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣷⣄⠛⣿⣿⣿⣿⣄⠻⣿⣿⣿⣿⡆⠙⠷⠶⠟⢠⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⡇⠈⠻⣿⣿⣿⣷⠘⠧⣉⣁⡴⠀⢠⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣷⣄⠙⠧⣍⣩⡜⢀⣀⣀⠄⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣷⣦⣄⣀⣤⣾⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠻⠛⠛⠁⠉⠙⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⢀⡴⡒⠒⠲⠶⠒⠒⠛⠓⠲⠶⠒⠒⠚⠓⠶⠶⠤⠤⠤⠶⠶⠦⠤⠤⠴⠶⠦⠤⠤⠤⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⠟⠀⢱⠀⠀⠀⢀⠴⠒⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⢤⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⠶⠋⣀⡀⠸⡆⠀⠀⢏⠀⠀⡠⠃⢰⣄⠀⣸⣇⣀⣴⠇⠀⠀⠀⣶⡀⢀⣿⠀⠀⣤⠀⠸⠤⠊⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣠⠏⠀⡜⠁⢸⠀⠙⡄⠀⠀⢉⢉⠀⠀⡠⠛⠉⠉⠉⠉⠉⠳⣄⢀⠴⠊⠉⠉⠉⠉⠙⢧⡀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣾⠁⠀⠀⢇⠀⡼⠀⠀⢱⠀⠀⠉⠁⠀⡞⠀⠀⠀⠀⠀⡠⠤⣀⠈⡏⠀⢀⣀⣀⡀⠀⠀⠀⢱⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢛⡗ ⣷⡀⠀⠀⠈⠙⠀⠀⠀⢸⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡎⣴⣿⡎⡆⠸⠀⡏⣶⣷⣽⡄⠀⠀⠀⡇⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⡼⢁⡼⠋⠀ ⠈⢳⡄⠀⠀⠀⣀⡀⠀⠘⡆⠀⠀⠀⠀⣧⣀⣀⣀⠀⠘⠪⠭⠛⢠⡇⠀⠑⠭⠭⠞⠀⠀⣀⣸⣀⠀⠀⢸⠃⠀⠀⠀⠀⠀⣴⠚⠺⣟⣩⠷⡄⠀ ⠀⠘⣧⠀⠀⡎⠀⡇⠀⠀⡇⠀⠀⠀⠀⡅⠈⠀⠘⠙⢦⣀⡠⠖⠁⠈⢢⣄⣠⠤⠔⠂⠉⠀⢀⡸⠀⠀⢸⡆⠀⠀⠀⠀⠐⡇⠑⡶⣏⣀⢆⡇⠀ ⠀⠀⠙⣦⠀⠧⠴⢁⣀⣀⢡⠀⠀⠀⠀⠀⠈⢻⡀⠀⠉⠀⠀⠀⠀⠀⠀⠠⢤⣤⣤⡤⠴⠖⠋⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠙⡆⢀⣈⣡⠟⠀⠀ ⠀⠀⠀⠈⡇⠀⠀⢸⠀⠈⡏⡄⠀⠀⠀⠀⠀⢸⣿⣶⣦⣤⣤⣤⣤⣤⣤⣤⡤⠤⣭⠶⠄⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⣰⠃⡞⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⢧⡀⠀⠸⡄⡰⠁⢱⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⢸⣿⡇⠀⠀⡇⠀⠀⢠⠖⠓⢢⠀⢇⠀⠀⠀⠀⠀⣰⠃⡼⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢱⡀⠀⠈⠀⠀⢸⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⠉⠀⠀⠀⠸⣤⠤⠊⠀⣾⣀⣀⡀⠀⣰⠋⡼⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⣧⣄⡀⠎⡐⠈⡆⠀⣰⠆⠀⠘⢏⠉⠙⠛⠟⠛⠿⣿⣿⡇⠀⠀⠀⠀⠀⣀⠤⡄⠀⢸⠋⢠⡶⠗⢚⣡⠾⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⠃⠀⠹⡋⠀⠀⠃⠀⠠⠒⢢⠀⢄⠙⠒⠶⠶⠶⠶⠞⠛⠀⠀⠀⠀⠀⠀⠧⠴⠃⠀⢸⠀⢀⣻⠏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣾⠀⠀⠀⣇⣀⠀⠀⠀⠣⠤⠊⠀⠀⠉⠛⠚⠛⠒⠒⠒⠚⠁⠀⠀⠀⠀⠀⠀⠀⣀⣠⡟⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢦⠤⡴⠋⠉⠉⠙⡟⠛⠉⠙⠛⠻⢟⡉⠉⢉⠟⢖⠒⡻⠻⣍⢉⡽⠛⠉⠉⠉⠉⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⡄⡟⣶⣶⣦⠴⡧⠤⠤⠤⠤⠤⠤⠬⠭⢥⣤⡼⠉⢷⣤⣤⣁⡀⣀⣀⣀⣠⡶⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡇⣿⠀⠉⠉⠀⡇⠀⠛⠛⠛⠛⠀⠘⠛⠛⠛⢧⠀⡸⠛⠛⠛⠁⠙⠛⠛⠛⠃⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⠇⠘⢶⣤⣄⣀⡇⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡞⠀⠀⠸⣆⠸⣏⠉⠉⠉⠉⠉⣹⠏⠉⠉⠉⠉⠙⠯⣍⣉⣉⣀⡤⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣧⣦⠸⡗⠋⠀⠈⠙⡗⣶⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⢸⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠻⠶⠃⠀⠀⠀⠀⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣗⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣷⣿⣦⣄⣀⡀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣶⣾⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠻⠿⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠶⠶⠶⠶⠤⢤⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠤⠶⠶⠦⠤⣄⡈⠙⠲⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄⠈⢳⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⠉⠑⠦⡀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠹⡄ ⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⣠⡀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⢳⣀⡇ ⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠈⠀⠀⠀⠀⠀⣷⠖⠋⠉⠑⠒⠦⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⢧⡀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀ ⠀⠀⣀⡤⠤⢤⣘⢦⡙⠢⠤⢤⡤⠴⠋⡇⠀⠀⠀⠐⠶⠀⠀⠀⢸⠀⠀ ⠀⡼⢁⣴⣶⣶⣌⠑⠉⠑⢠⠞⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⢀⡼⠀⠀ ⢸⠁⣿⣿⣿⣿⣷⠷⣄⠀⣏⣀⡴⠊⠀⠀⠙⠦⢄⣀⣀⣀⡤⠚⠁⠀⠀ ⠸⡄⣿⣿⣿⣿⣿⣿⡏⢳⣄⣀⠀⠀⠀⠀⠑⢦⣀⣀⣀⡄⠀⠀⠀⠀⠀ ⠀⢳⡸⡿⣿⣿⣿⣿⣿⣿⣤⣿⣩⣿⣩⣷⣶⣤⡀⠀⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠱⣝⢿⢻⣿⣿⣿⣿⣿⣿⠻⠿⢿⣿⣿⣿⣿⣦⠹⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠓⠙⢦⣿⠛⣿⣿⣿⣷⣦⠀⠙⣿⣿⣿⣿⡇⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠑⠯⣼⡿⠛⡿⣇⠀⢹⣿⣿⡿⣰⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⢛⣒⢛⣋⡩⠞⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⢀⣴⠀⠀⣴⣿⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⣿⣿⢀⣾⣿⣿⠀⢀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣶⣄⣀⣤⣶⡄⠀⠀⠀⠀ ⢠⣿⣿⣿⣼⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀ ⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣄⣀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟ ⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠛⠉⠉⠉⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀ ⠘⣿⣿⣿⣿⠿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀ ⠀⠀⠀⣴⢛⣠⣤⣀⠀⠀⠀⢀⣠⣤⣀⠀⠐⠿⠟⢻⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀ ⠀⠀⢀⡿⠋⠁⠀⠉⠻⣦⡾⠋⠀⠀⠈⠹⣆⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀ ⠀⠀⢸⡁⣶⡆⠀⠀⠀⣸⠁⠀⠀⣤⡄⠀⢸⡄⢰⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀ ⠀⠀⠘⣧⡀⠀⠀⣰⠞⠹⣆⠀⠀⠉⠀⢀⡾⠀⢸⣿⢟⡻⣿⣿⡿⠋⠀⠀⠀⠀ ⠀⠀⢀⡾⠛⡿⠋⠁⠀⠀⠈⠳⠦⠤⠴⠟⠁⠀⠈⠁⢛⡷⣽⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⡼⠁⠀⠳⢤⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠷⣤⣄⣀⣀⣀⣀⣠⣤⣤⡤⠶⠿⠆⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠉⠉⠉⠙⠧⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠿⣦⣀⠀⣀⠤⣄⣤⠶⠛⠁⠀⢻⣆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢃⣼⣿⣿⣧⣤⠚⠉⠀⠀⠀⠀⣠⣿⡟⢳⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡸⣿⣿⣿⣿⡏⠀⠀⠀⢀⣤⠾⢻⡏⠀⠀⢻⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠟⣿⣿⠛⢿⣤⡴⠾⠋⠁⢴⣿⠀⠀⠀⠈⣧⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢻⡀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⢹⡄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⢀⣼⣇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣻⣇⣀⣷⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣿⡇⠀⠀⠸⣿⣿⠀ ⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣤⣤⣶⣿⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⠃⣨⣿⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⣿⡿⠻⢿⠿⠻⣿⠀ ⠀⠀⠀⠀⠀⠀⠀⠸⣦⣿⣧⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣟⣰⡆⢠⠀⣄⢹⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠻⣼⣿⠉⠛⠛⠻⠶⠶⠶⣦⣴⣶⣼⣿⢿⡇⣸⠀⣿⡼⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠰⢶⣦⣤⡄⠀⠀⠀⠈⠛⢻⡞⠉⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⣸⠃⢸⠃⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⣯⣈⠛⡷⠶⠂⠀⣹⣦⡿⣤⣄⣀⣀⡀⠀⢻⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡏⠛⠛⠛⠛⠛⣏⠈⠳⣦⣍⣉⣉⣡⣤⣾⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⢀⡇⠀⠀⢿⠀⠉⠉⠀⠀⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣶⣄⣀⣠⣼⣿⡀⠀⣸⣄⠀⠀⠀⠀⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣣⣾⣿⣿⣷⣦⣤⣴⣿⣇⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠻⠿⠿⠿⠟⠛⠉⠀⠈⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⠿⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣅⣁⢈⣭⣿⣷⣾⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⣴⣖⣦⣤⣲⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣯⡿⠟⠋⠉⠻⡟⢟⡽⣗⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⢞⢝⣍⢿⣹⡿⠳⣛⣋⣓⣩⣲⡤⡀⠀⠀⠀⠀⠀⣰⡿⣣⠟⠁⠀⠀⠀⠀⠀⠘⢑⡻⣟⡧⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠐⣿⣽⡿⣿⣟⡁⠀⠀⠀⠉⠉⢻⣟⠋⠝⢓⢤⣠⡴⣶⡿⣟⣭⣓⠖⠢⣤⣀⣀⣀⣬⡶⣻⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣹⣫⢿⡇⣃⠴⡀⣀⡠⠤⠶⠒⣺⠿⣟⢸⣯⣃⣳⡾⡲⠷⣮⣥⣼⣮⣤⣥⣾⣿⣿⣻⡿⢯⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢘⠣⣿⣿⣶⣾⣿⣷⣶⡂⢩⡭⢊⣽⣿⡿⠿⠿⢿⣦⣴⣙⠈⠙⠏⠉⠋⠉⠀⠩⠀⠂⠀⢀⣤⢤⣤⣤⣂⣅⠉⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⠀⠉⠉⠙⠟⡟⢛⠋⡵⣻⣿⠏⠀⠀⠀⠘⢿⢯⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⣀⠖⣫⠵⢏⣽⣿⣿⡧⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⣩⢅⡏⠀⠀⠀⠀⠀⠈⠫⣳⠄⢹⡆⠀⠀⠀⠀⣢⣴⣿⣿⣿⠟⠁⠈⢿⢿⡿⠄⠀ ⠀⠀⣰⣾⣏⣩⣉⠰⣄⠀⠀⠀⠀⣠⢖⣴⢟⠎⠀⠀⠀⠀⠀⠀⠀⠀⠉⠷⣾⣿⡀⠀⢠⣾⣿⣿⡿⠟⠁⠀⠀⠀⣸⣾⠣⠂⢀ ⠀⣰⡇⠈⠙⠤⣽⣿⣹⣷⣤⣈⣴⣩⡤⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⠛⠛⡫⠁⠀⠀⠀⣀⣴⣾⡿⠃⠁⠀⠘ ⢰⣿⣹⡄⠀⠀⠀⠉⠛⠻⠿⠛⠋⠉⠂⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⣀⡀⣤⡶⠁⢼⣿⠃⠀⠀⠀⠀ ⢹⡇⠂⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡁⡆⠡⣬⣧⣀⡜⠁⠀⠀⠀⠀⠀ ⠀⠱⡄⢂⠣⠀⣠⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⢶⠃⠙⠋⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠢⢀⣙⠿⣿⡿⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡾⡄⠀⠀⠀⣀⣀⠀⠀⠀⡄⠀ ⠀⠀⠀⠀⠀⠈⠑⠊⠁⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠺⢿⣿⣿⡶⡤⣕⡤⠀⠂⠀ ⠀⢀⠀⣤⠔⠆⢶⣶⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁⠄⠀⠀ ⠁⣠⡎⠀⣀⣠⡾⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠄⠀⠀⠀ ⠀⣿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀ ⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⋆౨ৎ˚⟡˖ ࣪⋆୨୧⋆⋆ ˚｡⋆୨♡୧⋆ ˚｡⋆

⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣶⣶⣶⣶⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀ ⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⢿⣿⣿⣿⣦⠀⠀⠀ ⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠈⠻⣿⣿⣷⡀⠀ ⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⢠⣾⣿⣿⣦⠀⠀⢸⣿⣿⣷⠀ ⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⢸⣿⣿⣿⣿⠃⠀⢸⣿⣿⣿⡄ ⠀⠈⠙⠿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠉⠛⠋⠁⠀⢀⣾⣿⣿⣿⡇ ⠀⣤⡀⠀⠀⠉⢛⡋⠉⠁⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣿⣿⣿⣿⣿⠃ ⠀⢿⣿⣷⣦⡴⣿⣿⣿⣦⡀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀ ⠀⠈⢿⣿⣿⣇⠀⠈⠛⠟⠁⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀ ⠀⠀⠀⠻⣿⣿⣦⣄⣀⣀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀ ⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠿⠿⠿⠿⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⣤⡄⠀⠀⣀⠀⠀⠀⠀⢀⡀⠀⠀⣤⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠻⣧⣀⣀⣿⣧⣀⣼⡟⠀⠀⠀⠀⠹⣧⣀⣀⣿⣇⠀⣰⡷⠀⠀⠀ ⠀⠀⣰⠟⠉⠀⠀⠀⠀⠈⠙⢷⡄⢀⡴⠚⠉⠀⠀⠀⠀⠉⠻⣇⠀⠀⠀ ⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀ ⢸⠁⠀⠀⠀⠀⠀⡴⢋⣭⣽⣷⠀⢷⠀⣰⢚⣭⣽⢣⡀⠀⠀⠀⠘⡇⠀ ⢸⡀⠀⠀⠀⠀⠈⣇⢿⣿⣿⣿⠀⡾⠀⢧⢿⣿⣿⢇⡇⠀⠀⠀⢀⡇⠀ ⢸⣧⣤⣤⣤⣀⠀⠈⠓⠾⠒⠁⣰⣇⠀⠈⠓⠾⠶⠛⠀⠀⣀⡤⠼⢄⠀ ⢸⠁⠈⠠⠄⠛⠳⣄⠀⣀⡤⠞⠁⠈⠳⣄⡀⣀⣠⠴⠖⠋⠁⠀⠀⣰⡇ ⠀⠀⠐⢲⡶⠄⠠⠟⠉⠉⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⢀⣀⣠⡴⠾⠋⠀ ⠀⠀⠀⢸⣿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⣋⡉⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣿⣿⣿⣿⣿⣶⡶⠶⠶⢶⣶⣶⠶⠒⠒⣶⠛⠛⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⣸⣿⣿⣀⣀⣀⡟⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠘⣿⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠙⢷⣄⣀⡀⠉⠀⠀⠉⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠰⣤⣈⣉⣙⡛⠛⠛⠛⠛⠉⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠙⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣾⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⣴⣿⡿⠟⠛⠋⣽⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀ ⠀⠀⢀⣾⣿⠟⠁⠀⠀⠀⣼⣿⣿⠏⢸⣿⣿⡏⠻⣿⣷⡀⠀⠀ ⠀⢠⣿⡟⠁⠀⠀⠀⠀⣼⣿⣿⡟⠀⢸⣿⣿⡇⠀⠈⢻⣿⡄⠀ ⢠⣿⡟⠀⠀⠀⠀⠀⣼⣿⣿⡿⠀⠀⢸⣿⣿⡇⠀⠀⠀⢻⣿⡄ ⣸⣿⠇⠀⠀⠀⠀⣼⣿⣿⣿⠁⠀⠀⠘⢿⣿⡇⠀⠀⠀⠘⣿⣇ ⢿⣿⠀⠀⠀⠀⣰⣿⣿⣿⣇⣀⣀⣀⣼⣦⡙⠇⠀⠀⠀⠀⣿⡿ ⢸⣿⡇⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡦⠀⠀⠀⢸⣿⡇ ⠀⢿⣿⡀⣸⣿⣿⣿⠟⠉⠉⠉⠉⠉⣿⠟⣡⡆⠀⠀⢀⣿⡿⠀ ⠀⠈⠛⣰⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠠⠾⠿⠇⠀⣠⣿⡿⠁⠀ ⠀⠀⣰⣿⣿⣿⡟⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⡿⠋⠀⠀⠀ ⠀⣰⣿⣿⣿⡿⠰⠿⣿⣶⣶⣶⣶⣶⣶⣿⠿⠟⠉⠀⠀⠀⠀⠀ ⠀⠉⠉⠉⠉⠁⠀⠀⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⣤⡀⣀⣴⣾⣿⠿⠟⠛⢛⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀ ⠀⠀⣾⣿⣿⣿⣿⠟⠉⠀⣀⣴⣾⣿⠿⠛⠉⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⢨⣿⣿⠋⠀⠀⣠⣾⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣰⣿⡟⠁⠀⣠⣾⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⣿⡟⠀⢠⣾⣿⠿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣾⣿⠁⣰⣿⡟⠁⠀⠈⠻⣿⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣴⣿⡟⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀ ⠸⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣷⣄⠀⠀ ⠀⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣷⣄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⡿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠋⠀

⠀⠀⢠⣷⣦⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⠿⠿⠿⠿⢿⣿⣿⡿⠃⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠄⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⣴⠞⠋⢀⣠⣤⣴⣶⣶⣾⡿⠶⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⡾⠋⠀⢀⣴⠟⢉⣾⣿⣿⣿⡿⠿⠗⠀⠘⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣾⠟⠀⠀⠀⠸⠏⠀⠛⠉⠉⠁⠀⠀⣀⣤⡀⣴⠶⢶⣶⣲⡶⠀⠀⠀ ⢀⣾⡟⠀⠀⠀⠀⠀⢀⡀⢰⡄⣶⢻⡷⣾⡏⢶⡆⣿⣋⣹⡿⠻⡦⠀⠀⠀ ⣸⣿⠀⠀⠀⣶⣟⡿⢸⡇⣸⡇⣿⠻⠷⠙⠛⠛⠁⠉⠁⠀⣀⣤⣤⣤⠀⠀ ⣿⣿⠀⠀⠀⣿⣯⡿⠘⠛⠛⠀⠀⣀⢀⣤⣄⠀⢰⣿⣦⣾⡿⢋⣉⣉⠀⠀ ⣿⣿⠀⠀⠀⠉⠁⢀⠀⢀⣶⡆⣾⣿⢸⣿⣿⣷⣼⣿⣿⣿⣧⣈⣹⣿⠀⠀ ⢸⣿⡆⠀⠀⠀⢸⣿⣰⣿⠏⠀⣿⣿⢸⣿⡇⠙⢿⣿⠇⠉⠛⠛⠛⠉⠀⠀ ⠈⢿⣿⠀⠀⠀⢸⣿⠻⣿⣷⡄⣿⠟⠘⠛⠁⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀ ⠀⠈⢿⠀⠀⠀⢸⠿⠀⠈⠉⠁⢀⣀⣀⣠⣤⣴⣶⣾⠆⣴⡿⠁⠀⣠⣄⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⢿⣿⣿⣿⣿⣿⣿⣿⣿⠾⠋⠀⢀⣴⣿⣿⠋ ⠀⠀⠀⠀⠀⠀⣤⣴⣤⡀⠀⠀⠈⠉⠙⠛⠉⠉⠉⠀⠀⣠⣴⣿⣿⠟⠁⠀ ⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣶⣤⣤⣤⣤⣤⣤⣶⣾⣿⣿⡿⠛⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⠿⠿⠿⠿⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀

⬜⬛⬛⬛⬜⬛⬛⬛⬜ ⬛⬛⬛⬛⬛⬛⬛⬛⬛ ⬛🌫️🌫️🌫️🌫️🌫️🌫️🌫️⬛ ⬛⬜⬜⬜⬜⬜⬜⬜⬛ ⬜⬛⬜⬜⬜⬜⬜⬛⬜ ⬜⬜⬛🟪🟪🟪⬛⬜⬜ ⬜⬜⬜⬛🟪⬛⬜⬜⬜ ⬜⬜⬜⬜⬛⬜⬜⬜⬜