*Stares into your soul* 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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(\__/) (•ㅅ•) Bulky, Bunny, Deku ＿ノヽ ノ＼＿ `/　`/ ⌒Ｙ⌒ Ｙ ヽ ( 　(三ヽ人　 /　 | |　ﾉ⌒＼ ￣￣ヽ ノ ヽ＿＿＿＞､＿_／ ｜( 王 ﾉ〈 /ﾐ`ー―彡\ / ╰ ╯ \ /\

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⢀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣷⣷⢤⣂⣀⣤⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣄⡀⠀⠀⠀⠀ ⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀ ⠀⣰⣿⣿⣿⣿⣿⣿⡿⠛⠻⠁⠿⠿⠿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀ ⢰⣿⣿⣿⣿⣿⣿⣿⠃⣔⡒⢶⡄⠀⠀⠀⣀⣉⠙⠐⠿⣿⣿⣿⣿⣿⣿⣿⡷⠀ ⠘⢿⣿⣿⣿⣿⢸⠁⠀⠹⢿⡟⢛⠆⢠⠶⣶⣦⣤⡑⠀⢹⣿⣿⣿⣿⣿⣿⣿⡄ ⠀⠈⠻⣿⣿⣿⣄⡁⠀⠀⠀⡠⠈⠀⠘⢇⠈⠋⠉⠀⢀⢸⠋⢸⣿⣿⣿⣿⣿⣷ ⠀⠀⠀⠈⠻⣿⣿⣟⠲⢆⣀⣉⡓⠒⠒⠚⠑⠄⠀⢀⠌⣇⣀⣾⣿⣿⣿⠿⠛⠁ ⠀⠀⠀⠀⠀⠈⠙⠻⣆⠀⠙⠬⢉⣁⣑⣲⡶⠚⢀⠃⣰⣾⣿⣿⣿⠿⠟⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢘⣇⠀⠀⠀⠀⠈⠉⢀⠐⢁⣤⠿⡛⠉⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡴⠋⠞⣦⣀⡀⠀⢀⣀⣤⠖⠉⢻⣳⡼⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣜⡀⣸⠜⠂⢹⡭⠿⢾⣄⠎⠀⠀⠀⡇⢻⣷⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡇⠀⠈⠉⠉⠻⡄⠀⠀⠈⠙⠑⠂⣄⡇⠈⣏⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠑⢤⠀⠠⠤⠐⠊⠢⣀⠀⠀⢀⠔⢫⡄⠀⡿⠀⠀⠀⠀⠀⠀⠀

𓍊𓋼𓍊𓋼𓍊𓆏 𓍊𓋼𓍊𓋼𓍊 𓍯

⠀⠀⠀⠀⠀⠀⠈⠉⠙⣉⡤⠴⢞⠋⠉⠹⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐⠀ ⠀⠀⠀⠈⠙⠒⣲⣤⣾⣯⣤⣄⣿⠗⠀⢄⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⡤⠧⠾⣿⠀⣀⣤⠴⠶⠛⣛⣀⣀⣀⣀⡀⠲⠦ ⠀⠀⠀⠀⠀⣾⠋⠼⢫⠟⢿⣿⠙⣆⣀⡼⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠦⡄⢀⣻⣁⣤⠶⠿⠛⠋⠁⠀⠀⠈⠁⠀⠠ ⠀⠀⠀⠀⣾⠗⠀⠀⠀⠀⠀⣻⠃⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠹⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⠃⠀⠀⠀⠀⡀⠠⡏⡔⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠢⡈⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⢀⠀⠀⢀⡴⠁⡼⠛⠀⠀⠀⠀⢀⡔⢻⣿⣷⣌⠉⢻⣷⡖⠋⣡⣿⣯⡙⠳⣄⠀⠀⠀⠘⠆⠙⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⠈⢸⠀⡞⢣⠸⠁⠀⠀⠀⠀⠀⠈⢧⠈⠻⣿⠟⢁⡼⠀⠹⣄⠹⢿⡿⠃⣠⡟⠀⠀⠀⠀⠘⢆⠘⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⡆⢸⠀⣇⡞⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⢀⣴⣞⠁⠀⠀⠘⡄⠐⠲⠞⠋⠀⠀⠀⠀⠀⠀⠈⠣⡈⢻⡏⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⣇⡾⣠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⠒⡶⢦⡈⣳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠙⢦⡀⠀⠀⠀⠀⠀ ⠀⠀⢲⠿⠏⠰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠿⠿⢿⣿⣀⡷⠾⡿⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠻⣦⡀⠀⠀⢀ ⣿⣶⡿⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠁⠀⠈ ⣿⣿⠃⡎⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⢸⣧⣀⣀ ⣿⣿⢸⣇⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿ ⣿⡿⢸⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡄⠀⢿⣿⣿ ⢿⡇⡾⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠒⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡼⡇⠀⠘⠟⠋ ⡾⢠⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠒⠶⠀⠀⠀⠀⠀⠒⠒⠂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣥⣿⡆⠀⠀⠀ ⡇⣼⢺⣏⣁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⠟⠛⣿⢧⠀⠀⣄ ⡇⠛⣾⢹⠻⢭⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⡿⠉⠀⠀⣧⡾⠃⠀⢸ ⠀⠀⣿⢸⠀⠀⠀⠄⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⡿⠋⠀⠀⠀⠀⢻⠃⠀⠀⠀ ⠀⠀⡿⢸⠒⠂⠀⠀⠀⠀⡏⢻⡀⠀⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠟⠁⠀⠀⠀⠀⠀⠀⠙⡄⠀⠀⠀ ⠀⣰⡇⠨⠀⠀⠀⠀⠀⢘⡇⠀⢸⣿⡗⠙⠓⠦⣄⣀⡀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣤⢾⢻⣷⡿⠋⢰⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀ ⠀⣿⠇⠀⠀⠀⠀⠀⠐⣾⠇⠀⢸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡌⣿⠁⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀ ⠀⢿⠈⠈⠒⠒⠒⠒⠒⠞⠀⠀⣸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀ ⠀⠘⣆⢻⡖⠒⠶⠶⠶⢦⠔⢠⣿⣇⣄⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠐⠒⠒⠒⠂⠀⠇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠀⠀⠀ ⠀⠐⠌⢂⢹⣦⣀⣀⣀⣠⣰⣾⣿⠀⠀⠀⠛⠋⠉⠉⠉⠉⠉⠉⠙⠋⠛⠛⠛⠳⠶⠶⢶⡆⣿⡔⠦⣤⣤⣤⣄⣠⣤⣀⣀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡠⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢄⡀⠀⠀⠀⠀ ⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀ ⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀ ⠀⠀⢸⠀⠀⣀⣠⣤⣤⣤⠄⠀⠀⠀⠀⠴⠶⠚⠛⠓⠒⢦⡇⠀⠀⠀ ⠀⠀⢠⣾⣋⣥⣶⣦⣀⡀⠀⠀⠀⠀⠀⢀⢴⣿⣿⣿⣿⣆⢸⠀⠀⠀ ⠀⠀⢸⣾⣿⣿⣽⢃⡳⠀⠀⠀⠀⠀⠀⠀⠘⠮⢿⣿⣿⣻⠘⡠⢾⠂ ⠸⡛⠼⠳⠭⠟⠃⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀ ⠀⠀⢂⡀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢀⡀⣀⠀⠀⠀⢀⠭⡆⠀ ⠀⠀⡏⠓⡄⠀⠙⠓⠶⠤⠤⠤⠤⠤⠤⠶⠒⠛⠁⠀⠀⢠⠇⢀⡷⠀ ⠀⠀⠫⡂⠗⡄⠀⠀⠀⠉⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠈⠉⠀⠀ ⠀⠀⠀⠀⠀⠈⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⢀⣠⣤⣤⣄⡀⠀⠀⠀⢀⣀⣤⡤⣤⣀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⠞⠉⠀⠈⣉⡓⠒⠚⠉⠴⢶⠀⠈⠉⠉⠂⠉⠉⠀⢠⡶⠶⣌⠙⠒⠒⠒⠋⠉⠉⠙⢷⣆⠀⠀⠀ ⠀⠀⠀⢿⠀⢀⡀⠘⠿⠃⠀⠀⣠⡾⠛⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⣦⠀⠀⠀⠀⠀⠘⢿⡆⠀⢀⡿⠀⠀⠀ ⠀⠀⠀⠈⢣⡈⠁⠀⢀⣠⣴⣾⣏⣈⠉⠒⢄⡀⠀⠀⠀⠀⣀⡤⠖⠛⣳⣦⣄⣀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀ ⠀⠀⠀⠀⢠⠟⢉⣿⣿⣿⣿⣿⣿⡿⢿⣦⡀⠱⣄⠀⢀⠜⢁⣠⣾⣿⣿⣿⠿⣿⣿⣏⠛⢻⡉⡇⠀⠀⠀⠀ ⠀⠀⠀⢠⡏⢰⣿⢋⣿⣿⣿⣿⠋⠁⢾⣿⣿⡀⠸⣄⡎⣰⣿⢻⣿⣿⣿⣿⠛⠻⣿⢻⣷⡀⠹⡇⠀⠀⠀⠀ ⠀⠀⠀⣾⢀⣿⡇⣿⣿⣿⣿⣿⣦⣴⣿⣿⢻⡧⠀⡿⠀⣿⡇⣾⣿⣿⣿⣿⣄⣠⣿⡟⢻⡇⠀⢻⠀⠀⠀⠀ ⠀⠀⠀⣿⠸⣿⣤⢿⣿⣿⣿⣿⣿⣿⣿⡟⣿⡇⢀⣇⠀⣿⡄⣿⣿⣿⣿⣿⣿⣿⣿⣇⣼⡇⠀⣾⠀⠀⠀⠀ ⠀⠀⠀⢹⡄⠙⣿⣦⠿⣿⣿⣿⣿⡿⣏⣳⡟⢀⣼⢿⡀⠹⣿⣉⣿⣿⣿⣿⣿⣿⠟⣩⣿⠁⣰⠇⠀⠀⠀⠀ ⠀⠀⠀⠀⠻⣄⡈⠛⠷⣼⣯⣭⣥⣴⠟⠋⣠⠞⣿⢸⡷⣄⠘⠻⣷⣬⣟⣏⣹⣿⡷⠟⢁⣴⠏⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⠙⠲⠤⣤⣤⣤⣤⣤⠴⠛⠁⠀⡟⢸⡇⠈⠓⠦⣤⣈⣉⣉⣉⣁⣤⠶⠋⣱⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠸⡇⠀⠀⠀⠀⠀⠉⣉⡍⠁⠀⠀⠠⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⠀⠀⢴⡄⠀⠀⠀⠀⠀⢀⡴⣿⡇⠀⡷⣄⠀⠀⠀⠀⡼⠙⢳⡀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⣄⠀⠀⣀⡀⠀⠀⠀⢠⠏⠀⢈⡇⠀⡇⠈⢧⠀⠀⡼⠁⠀⠈⡇⠸⠃⣼⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡼⢻⠀⠘⢿⡿⠆⠀⢴⠛⡄⠀⢸⡇⠠⡇⢠⣈⡼⠀⢧⡘⢾⡷⠃⠀⢸⠛⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⡁⣈⡷⠖⠒⠲⠶⠤⢼⡛⠓⠶⣾⠃⠀⣷⡤⠭⢤⣶⠦⢬⣤⠤⢤⣀⡼⠀⣻⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠙⡟⢻⣤⣤⣤⣤⣀⣀⣈⣓⣊⣽⠀⠀⣇⣙⣖⣋⣀⣀⣀⣀⣀⣀⣹⣿⠛⠉⠀⠀⠀⠀⠀⠠ ⠀⠀⠀⢀⣀⣀⣇⢸⠙⠛⠛⠛⠁⠙⠿⠿⠿⣿⠀⠀⣿⠿⠿⠏⠉⠿⠿⠿⠿⠋⡟⢻⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣼⠸⣦⢤⣄⣀⣀⣀⣀⣤⡤⣬⣿⣾⣁⣀⣀⣀⣀⣀⣀⣠⣤⣀⡇⣾⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⠣⡄⡇⠀⠿⢦⣄⣀⣀⣸⡆⠀⠀⠀⠀⠀⠸⣿⣿⣍⣿⣿⠈⢸⢃⢸⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠸⣧⢻⠇⠀⠀⠀⣧⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣼⠁⠀⠀⢸⣾⣾⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠻⠿⠀⠀⠀⠀⣿⢺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠀⠀⠀⠸⢿⠇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⡃⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⣷⠀⠀⠀⠀⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⣦⣾⣧⣼⡇⠀⠀⠀⠀⠀⠀⠀⢀⣾⣧⣿⣇⣠⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣀⣀⣀⣀⣀⣀⣀⣘⣻⣿⣟⢛⣻⣟⣁⣀⣀⣀⣀⣀⣀⣀⣈⣻⣿⣿⣿⣿⣿⣿⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣳⣄⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡤⡴⠁⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣯⣷⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⡀⠀⠀⠀⠀ ⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠏⠀⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀ ⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠿⢿⡿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⢁⣬⣉⣉⣙⣻⣶⠀⠀⠀⠀⠀⢠⣤⣤⣄⠀⠀⠈⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀ ⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⠈⣿⠃⠀⠀⢻⣿⣿⣿⠟⣿⢷⡆⠀⢀⣴⣶⣦⣤⣄⡀⠀⠳⠄⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀ ⠀⠀⢻⣿⣿⣿⣿⣿⣿⣏⠀⢿⠀⠀⠀⠀⠉⠛⠛⠁⢀⣾⠁⠀⢸⡍⠙⣉⢿⣿⣿⡷⠂⠀⠀⠸⣿⣿⠟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀ ⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣄⣸⠀⠀⠀⠀⠀⠀⢀⡴⠈⠁⠀⠀⠘⣟⠂⠈⠉⠉⠉⠀⠀⠀⠀⢀⣾⠋⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣦⣀⠀⣀⠀⠀⠹⢧⣤⣀⡀⣀⣀⡈⡷⢤⡀⠀⠀⠀⠀⠀⡧⣼⠃⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟ ⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣋⡀⠘⠿⣤⣄⣀⣀⣀⡉⠉⠉⠉⠉⠁⠀⠳⠀⠀⠀⢀⡔⠁⣿⣀⣀⣾⣿⣿⣿⣿⣿⣿⠿⠋⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣷⣷⡀⠀⠀⠻⣍⠋⠛⠛⠓⠚⠲⢶⣶⣤⡤⣷⠄⢠⠃⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡾⠏⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡀⠀⠀⠀⢍⠓⠲⠤⠤⢶⣶⡿⠋⠀⠀⢠⠏⠀⣴⣿⣿⣿⣿⣿⣿⠿⠟⠋⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠢⠄⠉⠉⠁⠀⠀⠀⠐⠁⢀⣼⣿⣟⡛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠞⣻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⢿⣿⣦⣌⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⢀⠇⢹⠿⣦⣄⣀⣀⡀⣀⣀⣠⡴⢶⠟⠉⠀⠀⠹⣯⣽⣧⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⠀⠀⢸⢀⡿⠒⠚⣿⡟⣻⣿⣿⣸⡁⢀⡎⠀⠀⠀⠀⠀⢻⠁⢻⣏⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠖⠒⠒⢾⣍⣀⣀⣠⣿⡟⠋⠁⠉⠓⠧⣞⣀⣀⠀⠀⠀⠀⢸⠀⠀⣿⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠙⠿⣄⠀⠀⠀⠀⠀⠀⠈⠓⠉⠑⢦⣄⣸⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣯⡏⠀⠀⠈⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠤⠤⠤⠖⠒⠉⠁⠉⠉⠑⢦⣀⡀⠀⠀⢀⣠⠞⠁⢳⣷⠀⠀⢠⠇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⣀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢰⠀⠀⠀⢀⣤⡴⠶⠶⠶⠺⠷⡷⠶⠶⠤⣤⣬⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢈⠽⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠿⠯⡉⠉⠀⠀⠀⠀ ⠀⢀⡼⠋⠀⠀⢀⣔⠤⠤⠄⣀⢀⠀⠀⠀⣀⠤⠄⠀⣀⠀⠀⠀⠈⠲⢄⠀⠀⠀ ⠀⣾⠁⠀⠀⠀⣾⠁⠀⢠⣤⡀⠙⢧⡶⠛⠉⣉⣉⠉⠻⡆⠀⠀⠀⠀⠈⠣⡀⠀ ⢰⣿⡀⠀⢀⠾⣿⢠⠀⠘⠻⠛⠀⢀⡅⠀⠘⠿⠿⠂⠀⡿⠀⠀⠀⠀⠀⠀⢣⠀ ⢺⠀⠀⢢⣆⡀⢘⢷⡥⣀⣀⣠⠖⠚⠓⢄⠀⠀⢀⣠⢜⠄⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⡆⠀⠈⣿⣿⣦⡀⠈⠁⡾⣿⠀⠀⠀⠀⢹⣛⣶⠞⠁⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠘⡀⠀⢸⣿⣿⣿⣀⣀⢳⣹⢦⣄⢀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀ ⠀⠀⠑⣄⣾⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣯⣠⣀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⠀⠀ ⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣤⣤⣴⣶⣿⣿⠟⠀⠑⢄ ⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⠿⣿⠿⠿⠿⠿⠿⠟⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠤⠄⠀⠀⠀⠀⠀⠀⠀⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠓⠋⣡⣥⣴⠟⠛⠙⠋⢻⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⢰⠀ ⠀⠀⠀⠀⠴⢦⣤⣤⣀⠀⢀⣴⠟⠋⠀⢰⣿⣄⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⢰⣿⣦⡀⠀⠀⠀⣀⣠⣤⣴⡶⠄⠀⠀⠀⠀⢀⢠⣄⡀ ⠀⠀⠀⠀⠀⠀⠀⣤⣼⡿⣿⡿⣿⣿⣿⣾⣿⠁⠀⠈⢳⣀⣀⣠⠴⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢶⣏⠉⠉⠻⠷⢠⣶⠾⠛⠋⣉⣅⣤⣶⠶⠶⠶⠶⠶⠤⠀⠉⠉ ⠀⠀⠀⠀⠀⠀⢸⡿⠃⠸⠋⠼⠋⠺⣤⣇⠘⣇⣀⣴⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠤⢀⣠⣛⣠⣴⡿⠟⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒ ⠀⠀⠀⠀⠀⣴⡿⠇⠀⠀⠀⠀⠀⠀⠙⣾⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⢻⣿⣋⡭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢰⡿⠁⠀⠀⠀⠀⠀⠀⠀⣾⠇⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀⠹⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⢰⠂⢈⣿⣰⠃⠀⠀⠀⠀⠀⠈⢂⣤⡤⠤⠶⠤⢤⣤⣀⡀⣀⣤⡴⠶⣶⢤⣤⣀⠀⠀⠀⠀⠀⠙⢦⠘⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⠀⡀⢠⠀⠀⣴⠃⢀⡾⠋⠀⠀⠀⠀⠀⠀⢠⡞⠋⣸⣿⣿⣧⡀⠀⠙⡏⣿⠋⠁⣴⣾⣿⣷⡌⠙⠻⣆⠀⠀⠀⠀⠀⠳⠀⠹⣿⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⠀⠀⣼⠀⣼⠹⡇⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢧⡀⠹⢿⣿⡿⠛⠀⣼⠇⠈⢿⡀⠹⣿⣿⣿⠃⠈⣰⠇⠀⠀⠀⠀⠀⠈⢳⡀⠘⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⢰⠀⣿⠀⡟⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⣀⠉⣀⣠⡾⠃⠀⠀⠀⢹⡀⢀⣈⣀⣠⡾⠛⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠈⢿⣶⠖⠒⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⣸⠀⣿⠀⣧⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⢧⣄⡀⠀⠀⠀⠳⣤⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⣦⡼⠃⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⠋⠹⠛⠻⣄⣈⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠘⢿⣄⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠐⢿⣿⠟⢁⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠻⠿⣿⠿⢿⣿⡀⣨⡶⠿⢿⢿⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠛⢷⣄⠀⠀⠀⠀⢀ ⣴⣤⣤⣾⢀⡆⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⠃⠀⠀⠻ ⣿⣿⣿⠃⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⢿⡆⠀⠀⠀ ⣿⣿⡿⢠⡏⠀⡄⠀⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⢸⣷⣤⣤⣤ ⣿⣿⡇⢸⡇⠀⠃⢀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿ ⣿⣿⡇⣸⢻⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣄⠀⠀⢿⣿⣿⣿ ⣿⣿⠃⣿⢾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠸⣿⣿⣿ ⢻⡏⢰⡏⣼⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠙⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣢⣾⢻⡄⠀⠀⠋⠀⠀ ⣾⠁⣼⢰⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠻⠶⠂⠀⠀⠀⠀⠀⠐⠒⠒⠒⠶⠶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣥⣤⣿⡇⠀⠀⠀⠀ ⡟⢰⣿⣼⡟⠢⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣿⡧⣿⣿⣽⣇⠀⠀⠀⡉ ⡇⢸⡇⣾⢷⣶⡾⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⠏⠀⠀⣸⠏⣹⣄⠀⠀⣧ ⠇⠘⢠⣿⢸⠉⠙⠷⠀⠀⠀⠀⠀⠘⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⠟⠁⠀⠀⠀⢠⣿⡏⠁⠀⠀⠙ ⠀⠀⢸⣿⢸⡆⠀⠤⠄⢰⠀⣀⣀⢠⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢞⣿⣽⡿⠉⠀⠀⠀⠀⠀⠈⣻⠁⠀⠀⠀⠀ ⠀⠀⢰⡿⢸⠦⠶⠤⠀⠀⠀⠀⠀⡟⠻⡇⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣦⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠈⢹⠀⠀⠀⠀⠀ ⠀⠀⣸⠇⠸⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠙⣦⣦⣌⡻⣷⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⣴⣶⣄⣤⣼⣿⠃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀ ⠀⢰⣿⠀⠘⠁⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⢹⣿⡿⠀⠀⠈⠙⠛⠥⠤⠤⠀⠀⠀⠀⠀⠀⠀⠈⠣⠤⠤⠤⠴⠿⠛⢻⠉⣿⢿⠏⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀ ⠀⢸⣿⠀⠀⠀⠀⠀⠀⠐⠒⠚⣹⡇⠰⠀⣾⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣾⠀⣿⡎⠀⢀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀ ⠀⢸⡏⠘⠐⠒⠒⠶⠦⠤⠤⢄⣿⠀⡄⠀⣿⣿⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣿⡇⠀⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀ ⠀⠸⣷⠐⣤⣄⣀⣀⣀⣀⣀⣀⣀⠀⡅⢸⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣀⣀⡀⢀⣀⠀⢸⡆⣻⡇⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀ ⠄⠀⡘⣧⡘⣧⣀⡁⠉⠙⠛⠋⢹⠃⡁⣾⣿⠗⠛⠶⠶⣶⣤⣶⣤⣤⣤⣤⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠁⢿⡇⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠿⠃⠀⠀⠀⠀ ⠀⠀⠳⢈⠳⡈⣷⣤⣤⣤⣤⣤⣤⣸⣷⣿⣟⠀⠀⠀⠀⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠘⠉⠉⠛⠃⠛⠛⠻⠟⢻⡷⢸⣷⡘⠷⠤⠤⠤⢤⣤⣤⣤⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠶⠋⠁⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠈⠉⠙⠳⠤⣄⣀⣀⠀⠉⢻⣷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⣠⠄⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠘⣆⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠙⣇⠀⠀⠙⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⣰⠆⠀⠀⢀⣴⠏⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⣿⣆⠀⠀⠀⠈⢇⠀⠀⠀⠀⠀⠀⠀⢸⣧⠤⠶⠼⢿⣿⣖⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⠞⠁⠀⠀⣸⠃⠀⠀⢀⣾⠟⠀⢠⢿⠇⠀⠀⠀⠀⠀⠀⠀⣼⠀⡄⠀⠀⣿⡹⣦⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⡀⠉⣿⣆⠀⠀⠀⠀⠀ ⠀⠀⠀⣰⠋⠀⠀⠀⣸⠃⠀⠀⢠⣿⡟⠀⠀⡞⣸⠀⠀⠀⠀⠀⡄⠀⢀⠇⢀⣇⣀⣠⣿⣿⣾⣦⡀⠀⠀⠙⡄⠀⠀⠀⠀⣄⠀⠀⠙⠦⡾⡇⠀⠈⣿⣇⠀⠀⠀⠀ ⠀⣤⠞⠁⠀⠀⠀⢰⡇⠀⠀⢠⣯⣾⠗⠒⢛⣾⡟⠀⠀⠀⠀⢰⡇⠀⣾⠀⢞⣿⠁⠀⡟⢣⡹⣆⠉⠛⠦⣄⢻⡄⠀⠀⠀⢸⡄⠀⠀⠀⠙⡇⠀⠀⣻⣿⣆⠀⠀⠀ ⠈⠀⠀⠀⠀⠀⢀⡎⠀⠀⢠⡟⢡⡟⠀⠀⣾⡟⡟⠀⠀⠀⠀⡜⠀⢰⠇⠀⣾⢹⠀⠀⡇⠀⢻⡜⣧⠀⠀⠀⠻⣿⡀⠀⠀⠀⢧⠀⠀⠀⠀⣹⠤⠤⢿⣟⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⢸⢇⡞⡇⠀⢀⡿⠀⡇⠀⠀⠀⢸⠃⢠⠏⠀⣸⠇⢸⠀⢸⠁⠀⠀⠹⡞⣧⠀⠀⠀⣿⣷⠀⠀⠀⢸⡄⠀⠀⠀⣧⠀⠀⠚⢿⣬⣇⠀⠀ ⠀⠀⠀⠀⠀⣴⣿⠀⠀⢠⣇⡾⠁⡇⠀⣼⠀⠀⣷⠀⠀⢰⠇⣰⠃⠀⢠⣿⠀⢸⠀⡿⠀⠀⠀⠀⠘⢞⣇⠀⠀⣿⠎⣦⠀⠀⠈⡇⠀⠀⠀⢹⡀⠀⠀⠀⢻⣿⠀⠀ ⢠⠀⠀⠀⢠⠛⣿⠀⠀⢸⣿⠃⢀⡇⢀⡏⠀⠀⢿⠀⢰⣿⡞⠁⠀⢀⣿⠁⠀⣸⢰⠃⠀⠀⠀⠀⠀⠈⢿⡆⠀⣿⢧⢻⡄⠀⠀⢱⠀⠀⠀⠀⠛⣶⡀⠀⢤⣿⠀⠀ ⠞⠀⠀⠀⡄⠀⡏⠀⠀⣷⡇⠀⠈⡇⣸⠀⠀⠀⢘⡴⠛⠁⠀⠀⠀⣸⠃⠀⠀⣿⣿⣠⣤⡤⠄⠀⠀⠀⠀⣷⠀⡿⠈⢷⢷⠀⠀⢸⡄⠀⠀⠀⠀⠈⣷⠀⢀⣿⠀⠀ ⠁⠀⠀⠀⡇⠀⣗⠀⢸⣿⣅⣰⣦⣿⣿⣼⣛⡛⠛⣄⠀⠀⠀⠀⣸⠇⠀⠀⠀⣿⣿⣶⣿⣿⣿⣿⣿⣷⣶⣿⣧⡷⠀⢸⣿⣇⠀⢸⠂⠀⠀⠀⠀⠀⢹⠂⠈⠀⠀⠀ ⠀⠀⠀⠀⡇⠀⣿⠀⠈⡟⣿⠛⠋⠹⡛⢿⣿⣿⣷⣾⡄⠀⠀⢠⡏⠀⠀⠀⢰⠿⠛⠛⠳⣷⣶⣦⣀⠀⠀⠀⢻⣟⠂⠀⣿⢿⡀⠸⠀⠀⠀⠀⠀⠀⠈⡇⢐⡏⠀⠀ ⠀⠀⠀⠀⡇⠀⢻⠀⢠⡇⢿⠀⠀⣶⣄⣼⣿⢿⣮⠻⢳⡀⠀⡾⠀⠀⠀⠀⠀⠀⣴⣷⢶⣿⡿⢿⣿⣧⠀⠀⠼⡿⠀⠀⡏⠈⢧⡐⠀⠀⠀⢀⡀⠀⠀⣷⡿⠀⠀⠀ ⠀⠀⠀⠀⣿⠀⢸⡇⢸⠁⠘⠂⢸⣿⢁⣴⣿⣴⣿⠀⠀⢱⣼⡇⠀⠀⠀⠀⠀⠀⣿⡿⣸⣿⣷⣨⣿⣿⠆⠀⠴⠃⠀⢠⠃⠀⠘⡇⠀⠀⠀⠀⠇⢰⡀⢿⣁⣠⠄⠀ ⠀⠀⠀⠀⢹⡄⢸⣻⣸⡇⠀⠀⠀⢿⣿⠟⠛⣯⣽⠀⠀⠀⠹⠃⠀⠀⠀⠀⠀⠀⠙⣿⡿⢉⡙⣧⣸⡏⠀⠀⠀⠀⠀⣸⠀⠀⠈⠁⠀⠀⠀⢰⡄⣼⠷⡀⢿⣠⠀⠀ ⠀⠀⠀⠀⠀⢷⣸⡇⢻⡇⠀⠀⠀⠀⠙⠦⣤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠶⠾⠟⠁⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢸⣷⠻⡄⠹⣜⣿⠀⠀ ⠀⠀⠀⠀⠀⠀⢿⡁⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⣼⣿⠀⣷⡴⣿⣾⣦⠀ ⠀⠀⠀⠀⠀⠀⠸⣇⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⢸⣿⡋⢀⠿⠁⣿⣿⠙⠂ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⣼⡿⠃⣾⠀⠀⢸⣿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⢠⠀⢸⣏⣡⠞⠁⠀⠀⠘⣿⠀⠀ ⠀⠀⠀⠀⠀⠀⣶⠀⢠⡇⢸⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⣧⣼⠋⠀⠀⠀⠀⠀⠀⣿⠀⠀ ⠀⠀⠀⠀⣤⠀⠋⠀⢸⡇⢸⠋⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠀⠀⠀⠀⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀ ⠀⠀⠀⢀⡟⠀⠀⠀⢸⣧⡏⠀⠀⠉⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢾⣯⣺⣿⠀⠀⠀⣰⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀ ⠀⠀⠀⣼⣷⠀⠀⠀⢸⣿⠁⠀⠀⠀⣀⣤⣙⠳⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠚⠛⣟⣶⡀⠀⣿⠀⠀⢠⡏⢸⣧⡤⠒⠆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡟⢻⡄⠀⠃⢸⡇⣀⠤⠤⣼⠁⠀⠀⠛⢤⡀⢹⡝⠓⠂⠤⡤⢤⣤⠤⠤⠖⠒⠛⠉⠀⠀⠀⣠⡟⠁⢿⣀⣿⠀⠀⣼⢁⡜⣇⣀⡤⣾⣶⣤⣀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢷⠀⠀⢸⣏⠀⠀⠀⡇⠀⠀⠀⠀⠀⢩⣾⡟⠛⣿⣿⠁⠀⡝⣆⠀⠀⠀⠀⠀⠀⢠⡼⠋⠀⠀⢀⢻⣿⠀⠀⣿⣿⡤⠛⠁⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣷⡀⠀⢹⡀⠀⢠⣧⣤⣀⠀⠀⢠⣿⠇⠀⠀⢻⡟⠀⠀⠙⣏⠀⠀⠀⠀⣠⠜⠁⠀⠀⢀⡤⠁⣿⣿⡆⢰⣿⡇⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠁⠀⠀⢀⡿⠳⣔⠸⣇⠀⢧⣀⣀⣀⡙⠛⣿⠃⠀⠀⠀⢸⡇⠀⠀⠀⠘⢦⣠⡴⠋⠁⠀⠀⠤⠚⠁⠀⣼⡿⠈⣿⣿⣿⠀⣠⠴⠚⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣼⠀⠀⠈⠳⣿⣶⠃⠀⠀⠉⠉⢱⣿⠀⠀⠀⠀⢸⡇⠀⠀⣴⣋⣿⣭⣙⣦⠒⠀⠀⠀⠀⠀⣼⡿⠀⠀⠉⣿⡟⠉⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⠏⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⣼⠉⠀⠀⠀⢀⣿⠀⣠⢾⡏⠙⠚⠋⠉⠙⢧⡀⠀⠀⠀⣸⣿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⢰⣞⡁⠀⢀⣀⣀⣿⠀⠀⠀⠀⣸⣏⡔⠁⠀⡇⠀⠀⠀⠀⠀⡾⠱⢆⠀⡸⢻⣟⠀⠀⠀⣰⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸⣰⠃⠀⠀⠀⣸⡟⠀⠀⠀⢈⡿⠁⠀⠀⠀⣧⠀⠀⠀⠀⣼⠁⠀⠈⠛⠁⣼⣏⠀⠀⠀⣹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⡠⠤⠤⢀⡠⢤⡒⠢⠄⠀⠤⠐⣒⡤⢄⣀⠤⠤⢤⡀ ⠀⢸⠀⡄⠚⠃⢀⡴⡃⠀⠀⠀⠀⠘⢱⡁⠀⠀⠐⠆⠀⡇ ⠀⠀⠱⢦⣴⣾⣿⣶⣤⡑⢄⠀⡠⣂⣥⣾⡷⣶⡤⢤⢺⠀ ⠀⢠⢡⡿⣽⣿⣿⣉⣿⣷⠈⡞⣰⢻⣾⣿⡏⢹⡽⣆⢹⠀ ⠀⢸⢸⡥⢿⣿⣿⣿⣿⣺⢀⡇⢿⣸⣿⣿⣿⣿⣧⡟⢰⠀ ⠀⠈⢆⠙⢯⣻⣛⣫⠷⣣⢾⢱⡌⠷⣟⣿⣛⣯⠾⢡⠎⠀ ⠀⠀⢸⠉⠒⠒⠒⠒⠊⠁⡈⢸⠈⠑⠢⠭⠭⠔⠊⣱⠁⠀ ⠀⠀⢸⠀⠰⠄⠀⠀⢀⠴⡇⢸⢄⠀⠀⡔⠳⡀⡀⡘⠀⠀ ⠀⠀⢈⢧⠀⢶⠄⢠⢎⠀⡆⢸⢀⣣⠸⡠⣤⠇⢱⢧⠀⠀ ⠀⠀⠠⣬⡆⠁⠒⠒⠍⡰⡇⢸⢖⡲⠖⠒⠒⠢⣎⠸⠀⠀ ⠀⠀⠠⢇⡟⠛⠛⠙⠛⠿⣇⣸⠿⠟⠹⠿⠿⢹⢻⠀⠀⠀ ⠀⠀⠀⣎⢙⠱⣖⣒⣒⡏⠙⠓⠒⣶⣖⣲⡖⠺⢡⠀⠀⠀ ⠀⠀⠀⢷⡟⠀⠀⣶⠀⠀⠀⠀⠀⠀⣷⠃⠀⢳⡞⠀⠀⠀ ⠀⠀⠀⠀⢀⡀⢀⠉⡀⠀⠀⠀⠀⢀⢿⡀⠀⠀⠤⠀⠀⠀ ⣀⣀⣀⣀⣿⣾⠿⣿⣃⣀⣀⣀⡀⣺⣿⣷⣿⣇⣀⣀⣀⡀

⣿⣿⣿⣿⣿⣿⣿⣿⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣶⣶⣶⣤⣄⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⢿⣭⣶⠿⣟⣛⣿⣿⣷⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣿⣿⣿⣿⣿ ⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⢿⠟⠉⠀⠀⠀⠀⠈⠉⠻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⠀⠀⠀⠂⠀⠈⠻⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣻⣿⣟⡏⠀⢀⣀⣀⣀⡀⠀⠀⣀⣻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡀⠀⠀⠀⠀⠀⠀⠹⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣠⢴⠚⢛⣻⣿⡳⣶⢾⡯⢽⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⠛⣻⣟⠆⢸⠦⠤⠤⠤⣿⡿⠀⢳⠒⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⢶⣖⣛⣛⣛⣿⣿⣿⣭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⠐⠏⢹⣄⠏⠀⠀⢠⣞⣤⣿⠟⠿⢆⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⢸⢻⣤⠤⠤⠤⠤⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⠲⣾⣿⢆⠈⢷⢿⣾⣭⣭⣭⣽⠈⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⣿⢸⢷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⢀⣿⡌⢷⡈⢧⢩⡩⠟⠒⠋⢀⣿⣀⣴⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡟⢠⡇⡿⠈⢷⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⡿⠋⠓⠈⢻⣷⣿⡇⠈⠳⣍⣠⠀⠀⣸⢻⡇⠘⠛⠋⠉⠛⠲⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⢸⢃⡇⠀⠈⢿⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣾⣿⠛⠉⠀⠀⠀⠀⠀⠀⠙⢿⣻⣠⣀⠈⡉⠙⣛⣡⣾⠇⠀⠀⠀⠀⠀⠀⠀⠈⠻⣆⠀⠀⠀⠀⠀⠀⣿⠀⣿⢸⠃⠀⠀⠈⢳⣄⣀⣠ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠷⠾⠿⢻⠛⠁⠀⠀⠀⠀⠄⠀⡄⠀⠀⠀⠘⣦⡀⠀⠀⠀⢐⡇⢰⡇⣾⠀⠀⠀⠀⢸⡟⣿⣬ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠟⠁⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢓⠂⠀⠀⡅⠀⠀⠈⢰⢦⡘⢸⠀⢰⡄⠀⠀⠈⢳⡄⠀⠀⢸⠃⣸⠷⡟⠀⠀⠀⠀⣼⠓⣿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡏⠀⣶⡆⠀⠀⠀⠀⠘⣷⡄⠀⠀⠀⠀⠀⠀⢶⠃⠉⠀⠈⠀⠠⠀⠂⡀⠀⢦⠙⠌⢷⣌⣇⠀⠀⠀⠀⠹⡄⠀⣿⢀⡟⢸⡇⠀⠀⠀⠀⣿⠀⣿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡿⠀⠀⠀⠁⠀⠀⠀⠀⠀⠘⡆⠀⢀⣠⣴⠆⣴⣅⣴⡊⠀⢐⠃⠄⢁⡀⡇⠀⠈⢧⠈⠀⠙⠻⢿⣄⡀⠀⠀⠙⣶⡇⢸⠇⣾⠀⠀⠀⠀⢠⣏⢀⡏⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣀⣾⡽⠁⠀⠀⠈⠓⠀⠇⠦⡀⠀⠀⢰⠇⠀⠀⠈⠳⣤⣄⣀⠀⠀⠙⢦⡀⠀⢨⠇⣾⢠⡏⠀⠀⢀⣴⠟⠉⠛⠛⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⣡⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣨⣤⡤⠖⠒⠋⠁⠉⠙⠾⣶⣄⣸⡗⠀⣸⢀⡟⢸⠃⢀⡾⠋⠁⠀⠀⠀⠀⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⣸⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⡏⢀⣤⣄⠀⠀⠀⠀⠀⠀⠀⢀⡴⡿⠋⠁⠀⠀⠀⠀⠀⣀⣀⡀⠈⠙⠻⣄⠀⡇⢸⠃⢸⢾⣯⣤⡤⠀⠀⠀⠀⠠⣿ ⣧⠀⠀⠀⠀⠀⠀⠀⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⣀⡴⠧⠤⠿⡤⠿⢯⠴⠤⣤⣤⣤⣴⡚⠉⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠘⠺⣷⡾⠶⠶⠷⠶⠶⣶⣶⠶⠖⠒⢚⣿ ⣿⢲⡄⠀⠀⠀⠀⠀⠘⢿⣿⣄⠀⠀⠀⠰⠒⠉⠁⠀⠐⠋⠀⠀⠚⠉⠀⠈⠁⠀⠀⠀⣩⠉⠉⠉⠉⡉⠲⣭⠷⢶⣶⣤⣶⠶⠯⠭⠶⠶⠶⠾⠛⠒⠒⠒⠒⠒⠛⣉⣉⣉⣉⣉⡿ ⣿⣨⣿⣀⠀⠰⣄⠀⠀⣈⣻⣿⣳⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⣀⠳⠖⢦⡀⡀⢳⣙⠲⣷⣌⠛⠿⣦⣤⣤⣤⣤⣤⣶⣶⣶⣶⣶⠾⠿⠿⠿⠟⣛⣛⣛⣻⠇ ⣿⣿⣿⠛⠛⠛⠛⠉⠉⢩⣉⠉⠉⠩⠍⠿⢶⣾⡿⣶⠦⠤⠤⠤⠤⠤⠤⠾⠷⠖⠒⠛⠛⠒⣶⣛⣳⣦⣹⣷⢾⣿⣙⣿⠿⣯⠉⠛⠛⠶⠦⢴⡿⠤⠶⠖⠛⠋⠉⠉⠁⠀⠀⢸⠀ ⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠈⠓⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠒⠚⠚⠻⠿⣖⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠧⠤⣤⠞⣬ ⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠈⠙⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣿⡆⠴⠒⠒⠚⠋⠳⠿⣵⣶⣿⣻⣠⣿⣯ ⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠈

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⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣿⣿⣿⣿⣿⣿ ⣿⣿⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣛⣯⣿⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿ ⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⠟⠃⠀⠀⠀⠉⠙⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡄⠀⠀⠀⠈⠻⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⡟⠀⣠⣤⣤⣄⢀⣤⣽⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠻ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⣿⡗⢹⣉⣉⣉⣽⣏⢫⡹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣬⣥⣤⣤⣤⣤⡴ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⠠⠟⣇⡜⠀⠀⣴⣩⣿⠶⢄⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⢸⢯⣭⣭⡭⠍⠉ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⡲⢿⣧⡈⣿⣿⣿⡭⢽⠈⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⡏⡾⣆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⠇⢼⣧⣵⠘⢔⡀⠉⠉⢰⣷⠾⣷⠤⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⣸⢠⢇⡇⠘⣆⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⠟⠛⠉⠀⠀⠀⠻⣿⣆⣀⠙⠓⠶⢊⣼⠀⠀⠀⠀⠀⠉⠳⣄⠀⠀⠀⠀⢀⡇⢸⢸⠃⠀⠘⣆⣀⣀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠓⠷⠟⠛⠁⠀⠀⠠⡀⠀⠀⠀⠈⢧⠀⠀⠀⢸⠃⡏⡿⠀⠀⠀⣸⢻⡭ ⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏⢀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⢀⡠⡨⠀⠀⠀⠀⠀⠐⠢⡄⣄⢰⡀⠀⠀⠳⡄⠀⡸⢠⣟⡇⠀⠀⠀⡟⢸⠁ ⠀⠀⠀⠀⠀⠀⠀⣾⡏⠀⠛⠀⠀⠀⠀⠘⡇⠀⠀⣀⠀⡀⢁⠄⠀⠄⠈⠄⢰⠀⢳⡈⠈⠲⣧⡄⠀⠀⠹⣄⡇⣸⢸⠁⠀⠀⢀⡇⢸⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⠁⠀⠀⠀⠀⠀⠀⠀⢱⣠⣿⠏⠀⠉⠛⠁⠠⡅⠀⠈⡽⠀⠀⠑⢤⣀⡀⠈⠓⣄⠀⢘⠇⡇⡿⠀⠀⣠⠞⠓⠺⢶ ⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠏⡽⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠤⠒⠊⠁⠉⠙⠷⣦⣼⠂⢸⢰⢇⡇⣠⠞⠁⠀⠀⠀⢸ ⡄⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⣸⠈⣇⢾⡶⣀⡀⠀⠀⣀⠤⠚⠋⠀⠀⠀⠀⠀⠠⠒⠀⠀⠙⢤⣇⣸⣈⣻⣓⣒⣂⣀⣀⣀⣿ ⣧⣄⠀⠀⠀⠀⠸⣿⣆⠀⠀⠀⠤⠒⠊⠉⠟⠉⠩⠟⠉⠛⠉⠙⠓⡂⠀⠒⠒⠶⣲⣤⣤⣀⣤⣤⣶⣦⣤⣽⠿⠤⠤⠤⠽⠟⠒⠂⠐⣿ ⣧⣽⣆⡀⣦⣀⣀⣘⣿⣷⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣘⠷⠦⡀⠙⣔⠺⣦⡙⣿⣤⣤⣤⣤⠴⢶⣶⡶⠶⠾⠿⣟⣻⣻⢿⡏ ⣿⣿⣏⠉⠉⠉⠉⠠⢄⡈⠘⠛⠛⠛⠛⠖⠒⠒⠒⠒⠚⠛⠛⠉⠉⠉⠋⠩⠷⠼⣟⡿⢯⣿⣻⡎⠉⠉⠒⠒⠓⠒⠋⠉⠉⠀⡀⠀⢀⢇ ⣿⣿⣿⣧⡀⠀⠀⠀⠀⠉⠲⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⢷⡄⢀⠀⠤⠤⢤⣴⣺⣭⡝⣫⣾ ⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠈⠒⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠾⠃⠀⠀⠀⠀⠀⠈⣉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⠲⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣴⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣤⣄⣀⡀⠀⣷⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⠀⠀⠀⣀⣤⣤⣶⣶⣿⠶⠶⠶⠂⠀⠀⠀⠀⠀⠀⠀⠘⠿⠛⠛⠉⢉⣉⣉⣉⠉⠛⢶⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⣼⢠⡾⠟⢋⣉⣠⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣭⣽⣿⣿⣿⣷⡌⠹⡇⠀⠀⠀⠀ ⠀⠀⠀⣿⡟⣽⣦⣾⣿⣿⣿⡿⢿⣶⠶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢛⡿⠻⣿⣿⣿⣿⣿⢿⣧⠰⡇⠀⠀⣀⠀ ⠀⠀⠀⢻⣷⣿⣿⣿⣿⣥⣿⠇⢀⣹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⣌⣻⣿⣿⣿⡟⣸⠀⢣⢀⣽⣿⠇ ⢠⣶⠀⢸⣿⣝⠿⢿⣿⣿⣧⠴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠚⠁⠀⠀⠁⠀⣾⠀ ⠸⡆⠉⠛⠀⠙⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀ ⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀ ⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⡇⠀⠀ ⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⣸⡠⢷⡀⠀ ⠀⠀⢀⡿⣙⡄⠀⠀⠀⢠⣤⣤⡀⢀⡤⠐⠊⠉⠀⠀⠀⠀⠀⠀⠀⣀⣀⣭⣶⠞⠋⠁⠀⠀⠀⠀⣾⠉⠀⣸⡇⠀ ⠀⠀⢸⡇⠈⠉⢇⠀⠀⠀⠀⠈⠙⠛⡷⠶⠶⠶⠶⠶⠶⠶⠖⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⡸⢻⠀⢀⣽⠇⠀ ⠀⠀⠘⣇⠢⠀⢾⢦⠀⠀⠀⠀⠀⠀⠈⠓⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠉⠉⠁⠀⠀ ⠀⠀⠀⠈⠓⠚⠁⠈⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠐⠙⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⠛⠉⢿⢣⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠫⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠟⠁⠀⠀⠀⠸⣾⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⡻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠢⡝⢦⡀⠀⣦⣄⢀⢀⣀⠀⠀⠀⢀⣾⡿⠁⠀⠀⡀⠀⠀⠀⡇⢳⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⠃⠹⣌⠳⣄⠀⠀⠀⠀⢀⣀⣤⠿⠷⣄⡀⠈⠷⣝⢶⣇⣹⡿⠿⠛⣆⠀⣰⣿⡿⠟⠛⠛⠛⠻⡆⠀⠀⣿⢸⠀⠀⠀⠀ ⠀⠀⠀⠀⢻⡀⠀⠈⢷⣌⣻⣆⣠⡶⠟⠉⠀⠀⠀⠀⠀⠀⠀⠈⠻⠻⠛⠁⠀⠀⣼⣾⢿⡟⠀⠀⠀⠀⠀⠀⣿⠀⠀⣿⢸⡆⠀⠀⠀ ⠀⠀⠀⡀⠘⣇⠀⠀⣐⣿⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣟⣀⣠⣶⠀⠀⠀⠀⣿⠀⠀⡏⢸⠇⠀⠀⠀ ⠀⠀⠀⣟⠚⠛⠚⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠘⠏⠉⠀⢸⠀⠀⠀⣰⠏⠀⢀⡇⢸⠀⠀⠀⠀ ⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⢠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⢀⣤⠖⠋⠀⠀⠀⠀⢀⡾⠀⣀⣴⣿⣶⠶⣾⠃⣸⠀⠀⠀⠀ ⠀⠀⠀⠈⢻⣦⣀⠄⠀⠀⢰⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⣇⣴⠟⠁⠀⠀⠀⠀⠀⠠⢾⣩⠿⠋⠙⠛⣶⠀⡟⢰⠇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠉⠻⣷⣦⣤⡞⠀⠀⠀⠀⠀⠀⣀⠀⢀⣶⣶⠟⠁⣻⣧⣀⢀⡀⠀⠀⠀⠀⠀⠐⢻⣤⡀⠀⠀⢽⡿⢀⣯⣄⣤⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣾⠋⠀⣸⠁⠀⠀⠀⠀⣀⣾⣧⠶⠟⠋⠁⠀⠀⠟⠛⠋⠉⠉⠉⠙⠒⠶⣄⡀⠀⠉⠁⢀⡴⠿⠃⠈⠡⠀⢹⡆⠀⠀ ⠀⠀⠀⠀⢀⡿⠁⠀⢰⣿⠀⠀⢀⣴⣷⠿⠋⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠁⠀⠀⠀⣴⠆⣸⠃⠀⠀ ⠀⠀⠀⠀⣿⡇⠀⠀⣼⢻⠀⠀⣻⣿⡑⠃⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⣸⣣⠤⠚⠀ ⠀⠀⠀⣸⡿⠀⠀⠐⢿⣿⡆⣰⢿⠟⠁⠀⠈⠓⠒⠦⣄⡀⣼⠃⢀⡀⣀⣀⡤⠤⠤⠤⠤⣤⡀⠀⠀⠀⠀⠀⠀⠘⠳⠦⢭⣁⠀⠀⠀ ⠀⣀⣴⠟⠀⠀⠀⠀⣸⢿⣷⠏⠈⠀⠀⠀⠀⠀⠀⠀⠈⠙⢯⡴⠟⠋⣹⣷⡀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢶⣄ ⢺⡏⠁⠀⠀⠀⠀⢠⡟⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⢰⣿⣿⡇⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠶⠚⠋ ⠀⠙⣦⣄⣀⠀⢀⣾⠳⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⢸⣿⣿⠃⠀⠀⠀⠀⣠⠓⠁⠀⠀⠀⢳⡦⢀⣠⠞⠋⠀⠀⠀⠀ ⠀⠀⠀⠉⢙⣿⠿⢿⣄⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡏⠀⠀⠀⢸⣿⡏⠀⠀⠀⠀⡴⠋⠀⠀⠀⢀⡴⣫⣶⠯⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⣾⠟⠁⠀⠀⠉⠀⠀⠐⠶⣤⠀⠀⠀⠀⠀⠀⣠⡇⠀⠀⠀⠸⣿⠃⢀⣀⡰⠛⠀⠀⠀⠀⠀⠈⠉⠳⢦⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⣰⡿⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡥⠤⠤⣴⠒⠛⣉⣅⡤⢘⠀⠀⠀⠀⣼⣧⠀⠀⡄⠑⠾⣷⣄⠀⠀⠀⠀⠀ ⢰⣿⠋⠉⣹⢻⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣀⠀⠉⠁⢠⡞⣶⠟⠛⠁⠀⢸⠀⠀⠀⠀⠘⣷⡀⠀⢹⠀⠀⠀⠉⠁⠀⠀⠀⠀ ⢸⣯⣤⣰⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⠀⠀⠀⠀⠀⢀⡎⠠⠤⠤⠖⠒⠿⠇⠀⠸⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⢻⣯⡉⣁⣤⣤⣤⣤⣤⣤⣄⣀⠀⠀⠀⠀⢀⣀⡤⢶⡿⠁⠀⠀⠀⠀⠀⢄⡟⠀⠀⣠⡤⠤⠶⠒⠛⠒⠲⠽⢄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠙⠻⢿⡅⠀⠀⠀⢀⣽⣿⠋⠳⣤⡶⠚⠋⢉⡴⠋⠀⠀⢀⣠⠖⢊⣴⣯⣴⡶⣿⡿⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⣿⠃⠀⠀⣿⠛⠲⠞⠋⠀⣀⣤⠶⠗⠒⢛⡋⠉⣾⡿⠞⣋⣴⢞⡥⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡷⠶⠛⠁⢀⣠⣴⠞⠉⠁⠀⠀⠀⢠⠟⠀⣾⡟⠀⠈⠻⣛⣉⣴⣄⡽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡴⠊⠈⠛⣷⣶⡶⢾⣿⣿⡇⠀⠀⠀⠀⠀⣀⣿⣤⠾⠋⠀⠀⠀⠈⠙⠛⠛⠻⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⣶⣟⠁⢰⣿⠟⠀⠉⠀⣠⡤⠶⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⡶⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣴⠋⠀⠀⠀⣀⣤⢿⠛⠁⠙⠛⠛⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣠⠎⠁⠀⠀⢀⣾⠟⢡⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠻⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀

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the shakespearean rickroll 😎😎 We're nay strang'rs to loveth thee knoweth the rules and so doth i (do i) a full commitment's what i'm bethinking of thee wouldn't receiveth this from any oth'r guy i just wanna bid thee how i'm humour gotta maketh thee und'rstand nev'r gonna giveth thee up nev'r gonna alloweth thee down nev'r gonna runneth 'round and des'rt thee nev'r gonna maketh thee caterwauling nev'r gonna sayeth goodbye nev'r gonna bid a forswear and did hurt thee we've known each oth'r f'r so longeth thy heart's been aching, but thou art too dainty to sayeth t (say t) inside, we both knoweth what's been going on (going on) we knoweth the game and we're gonna playeth t and if 't be true thee asketh me how i'm humour bid not me thou art too blindeth to seeth nev'r gonna giveth thee up nev'r gonna alloweth thee down nev'r gonna runneth 'round and des'rt thee nev'r gonna maketh thee caterwauling nev'r gonna sayeth goodbye nev'r gonna bid a forswear and did hurt thee nev'r gonna giveth thee up nev'r gonna alloweth thee down nev'r gonna runneth 'round and des'rt thee nev'r gonna maketh thee caterwauling nev'r gonna sayeth goodbye nev'r gonna bid a forswear and did hurt thee we've known each oth'r f'r so longeth thy heart's been aching, but thou art too dainty to sayeth t (to sayeth t) inside, we both knoweth what's been going on (going on) we knoweth the game and we're gonna playeth t i just wanna bid thee how i'm humour gotta maketh thee und'rstand nev'r gonna giveth thee up nev'r gonna alloweth thee down nev'r gonna runneth 'round and des'rt thee nev'r gonna maketh thee caterwauling nev'r gonna sayeth goodbye nev'r gonna bid a forswear and did hurt thee nev'r gonna giveth thee up nev'r gonna alloweth thee down nev'r gonna runneth 'round and des'rt thee nev'r gonna maketh thee caterwauling nev'r gonna sayeth goodbye nev'r gonna bid a forswear and did hurt thee nev'r gonna giveth thee up nev'r gonna alloweth thee down nev'r gonna runneth 'round and des'rt thee nev'r gonna maketh thee caterwauling nev'r gonna sayeth goodbye nev'r gonna bid a forswear and did hurt thee

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

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

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

⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣀⠤⠶⠶⡛⠉⠉⠙⠋⠙⠛⠒⠶⣤⣤⣄⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢲⣴⣛⣹⣆⣀⠀⠈⠀⠀⠀⣠⣴⣤⣤⣤⣤⣤⠉⠛⢿⣦⣀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⡖⣿⣿⣿⣿⡿⠿⠀⠀⠀⠀⠀⠛⠷⠿⢿⢿⣿⡿⠀⠀⠀⠀⠘⣿⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⣰⠛⠁⠉⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠘⢦⡀⠀⠀⠀ ⠀⢀⣼⠃⠀⠀⡀⣆⣀⣀⠀⡁⣄⠀⢀⢀⣠⣀⣤⣤⣀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣯⡁⠀⠀ ⠀⡼⠏⠀⣤⣪⣿⣿⣿⣿⣿⡷⣖⠖⣷⣾⣿⣿⣿⣟⠙⢿⣾⣦⠀⠀⠀⠀⠀⠀⠀⠀⠻⢷⢀⠀ ⢠⡟⠀⠀⠾⠛⣿⣿⣿⣿⢿⠀⠺⣾⣿⣿⣿⣿⣿⡏⠀⠀⠛⠹⣿⣆⠀⠀⠀⠀⠀⠀⠀⢸⣏⠀ ⣿⠉⠀⠀⠸⣜⠛⠛⠟⠻⠀⠀⣇⣿⣿⠛⠻⠟⠋⠃⠀⠀⠀⢀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀ ⡟⠀⠀⠀⠰⢿⣦⡤⠀⣀⡀⣴⡿⠛⣿⣷⣤⡄⠀⠀⡄⢀⣼⡼⠗⠂⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄ ⡇⠀⠀⠀⠀⠐⠙⢻⣿⠿⠛⠉⠀⠀⠛⠟⠛⠻⠷⠾⠿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⡇⠀⠀⠀⣤⣄⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆ ⣧⡀⠀⠀⠘⠙⠻⠶⣦⣤⣄⣄⣀⣀⣀⣀⣀⣠⣤⣴⢶⠶⠺⠋⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⣸⠆ ⠻⣗⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀ ⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠆⠂⠀⠀⡀⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠏⠀ ⠀⠈⢧⠀⠀⠀⠀⣀⣰⣤⣦⣤⣤⡄⢰⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡏⠀⠀ ⠀⢠⣙⣻⣶⣶⠚⠉⢀⣄⣀⣀⣬⠿⣾⣎⡖⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠃⠄⠀⠀ ⠀⠀⣟⣿⠉⠀⠀⠘⢿⣿⣿⠉⠀⠀⠀⠙⢿⣾⣦⣤⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⡿⠁⠀⠀⠀⠀ ⠀⠀⠹⣧⠀⠀⠦⠴⠴⠏⠟⠀⠀⠀⠀⠀⠈⢿⠨⢿⡶⠀⠀⢀⣀⣀⣀⣼⠟⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠘⠻⣇⣄⠀⠀⣀⢀⣄⡀⠀⠀⠀⠀⠀⢈⣆⣸⣦⣤⣤⡾⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠠⡛⡿⠻⠿⠛⠛⠋⢀⢀⠀⢀⣀⣴⡾⠙⠍⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠽⠿⣄⣀⣠⣤⣶⡾⠋⠀⣸⣟⠉⠁⣤⣴⣶⣶⣶⣴⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⣿⡟⠋⡀⢀⣤⣶⣿⡇⠀⠸⣿⣿⡿⠿⠻⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣀⣀⢀⣀⣤⣾⣿⣶⣿⣿⣿⣿⣿⡇⠀⠀⣿⣷⣀⣰⣲⣼⣿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣠⣿⣿⢿⣿⢿⣿⣿⣿⣿⣿⡉⣿⣿⣇⡀⣠⣿⣿⣿⣿⣟⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣵⣿⠉⠀⠀⠀⠁⠸⣿⣿⠏⠀⣿⣿⣿⣿⣦⣿⡿⡿⠉⠉⠙⢿⣾⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣾⣯⣂⡀⣀⡀⠀⠸⣀⣹⣮⣶⣿⣿⠿⣿⡿⣟⠒⠀⠀⠀⠀⠀⠀⠹⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⢳⣯⡝⠹⢛⡛⠛⢉⣉⣹⠿⠋⠉⠉⢀⣿⣤⣼⡀⠀⠀⢀⢀⢠⣦⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠈⠦⠿⣿⣿⣉⢉⡉⢛⣉⢩⣡⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⢟⠟⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

like if you're at school rn ୧⍤⃝💐☻༘˚⋆𐙚｡⋆𖦹.✧˚ദ്ദി ˉ͈̀꒳ˉ͈́ )✧

∧,,,∧ 　 （ ・ω・） I like milkshake! 　　( つ旦O 　　と＿)_) 　　 ∧,,,∧ 　 （ ・◎・） slrrrp 　　(　ﾞノ ヾ 　　と＿)_) 　　 ∧,,,∧ 　 （ ・ω・） Hmm, tastes like prion disease… 　　( つ旦O 　　と＿)_) 　　 ∧,,,∧ 　 （ ・ω・） 　　( つ　O. __ 　　と＿)_) （__(）､;.o：。 　　　　　　　　　　ﾟ*･:.｡ 　 　　　 _ _　 ξ 　　　 (´ 　 ｀ヽ、　　 　 __ 　　⊂,_と（　 　 ）⊃　 （__(）､;.o：。 　　　　　　Ｖ　Ｖ　　　　　　 　 　 ﾟ*･:.｡

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠤⠤⠤⣄⣀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠉⠲⢄⡠⠔⠚⠉⠁⠀⠀⠀⠉⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⠀⠀⠀⠀⢀⣀⣠⠤⢤⣀⣀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠠⠴⠚⠉⠀⢀⣀⣠⡤⠤⠭⣷⣦⣧⠤⠔⠒⠒⠒⠒⠒⠢⠤⠼⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⣠⠖⠋⣀⣠⠤⠤⢤⣤⣤⣉⣙⢦⡀⠀⢀⣀⣤⠴⢶⡒⠲⠤⠿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡤⢾⠁⠀⠀⠀⠀⠀⠀⡜⢁⡴⠋⠁⠀⠀⠀⠸⣿⣿⣶⣄⠙⢷⣾⡿⠛⠋⠉⠉⢿⣿⣿⣏⡚⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣰⠋⠀⡾⠀⠀⠀⠀⠀⢀⡼⢠⠏⠀⠀⠀⠀⣿⣦⣀⢹⣿⣿⣿⡆⠈⡏⠀⠀⠀⣦⣀⠈⣿⣿⣿⣷⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡰⠁⠀⠀⠁⠀⠀⠀⠀⠀⠿⠴⠛⢦⡀⠀⠀⠀⢻⣿⣿⣿⣿⣿⡿⠁⣸⠁⠀⠀⠀⠹⣿⣿⣿⣿⣿⡿⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⣄⣀⣙⣻⣿⣟⣫⣤⠞⠉⠑⠢⢤⣀⣀⣈⡛⠛⣛⣉⣤⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⢉⡽⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠙⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⣾⡧⠀⣶⣶⠀⢰⣶ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⢋⣉⣁⣀⣀⣀⣈⣉⠉⣉⢉⣉⠉⠉⠛⢦⠀⢠⠏⠀⠀⠀⠈⠀⠀⠈⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣄⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠙⣡⣏⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢉⡵⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠛⢿⣷⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⣠⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠙⠲⢬⣍⣙⠒⠒⠦⠤⠤⠄⠀⠀⠀⢀⣀⠀⢀⣀⣀⣀⡀⠀⣀⣤⠖⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠓⠒⠒⠲⠶⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠞⠋⠉⠙⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠈⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠚⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣴⣿⣿⠿⣟⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣏⡏⠀⠀⠀⢣⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣟⠧⠤⠤⠔⠋⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⣿⡀⢀⣶⠤⠒⠀⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢹⣧⠀⠀⠀⠀⠀⠈⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠈⢿⣆⣠⣤⣤⣤⣤⣴⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣾⢿⢿⠀⠀⠀⢀⣀⣀⠘⣿⠋⠁⠀⠙⢇⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣾⢇⡞⠘⣧⠀⢖⡭⠞⢛⡄⠘⣆⠀⠀⠀⠈⢧⠀⠀⠀⠙⢿⣄⠀⠀⠀⠀ ⠀⠀⣠⣿⣛⣥⠤⠤⢿⡄⠀⠀⠈⠉⠀⠀⠹⡄⠀⠀⠀⠈⢧⠀⠀⠀⠈⠻⣦⠀⠀⠀ ⠀⣼⡟⡱⠛⠙⠀⠀⠘⢷⡀⠀⠀⠀⠀⠀⠀⠹⡀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠹⣧⡀⠀ ⢸⡏⢠⠃⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠸⣷⡀ ⠸⣧⠘⡇⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⣿⠇ ⠀⣿⡄⢳⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠈⠆⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀ ⠀⢹⡇⠘⣇⠀⠀⠀⠀⠀⠀⠰⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⣼⡟⠀⠀ ⠀⢸⡇⠀⢹⡆⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢳⣼⠟⠀⠀⠀ ⠀⠸⣧⣀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⢃⠀⢀⣴⡿⠁⠀⠀⠀⠀ ⠀⠀⠈⠙⢷⣄⢳⡀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⣠⡿⠟⠛⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠻⢿⣷⣦⣄⣀⣀⣠⣤⠾⠷⣦⣤⣤⡶⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀ ⠀⣸⣿⣧⣶⣶⠿⠿⠿⠿⢿⣿⢿⣶⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⣿⡇⣀⣠⣤⣶⣶⡿⠿⠿⠿⢿⣿⢿⣶⣶⣤⣄⡘⣿⡆⠀ ⢸⣿⡏⠁⠀⠀⠀⠀⠀⠀⢻⣧⡀⣠⣿⠉⠙⠛⠀⠀⠀⠀⠀⠀⣿⡿⠛⠉⠉⠀⠀⠀⠀⠀⠀⢺⣯⡀⣠⣿⠉⠙⠛⢻⣿⡄ ⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠁⠀⠀⠀⠀⣿⣧ ⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿ ⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿ ⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿ ⢻⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣦⣤⣴⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡏ ⠘⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠁ ⠀⠸⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠻⢷⣶⣤⣤⣄⣀⣀⣀⣀⣀⣀⣤⣤⣴⣶⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠃⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠛⠛⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣶⢶⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⢛⡼⠋⠈⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢷⣿⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⠛⣻⣇⡀⠀⠤⠙⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣓⣾⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣾⠀⣿⣿⣙⣷⣦⡀⢻⡿⢶⠲⠶⠶⠒⠶⢤⠤⣤⠤⠴⠒⠛⠉⠙⠻⢧⣷⡸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⠀⣿⣿⣿⣿⣿⣿⢯⣿⡌⣳⡄⠀⠀⠀⠀⠀⢦⣀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠸⣷⣿⣿⣿⣿⣄⣈⡛⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠙⠳⡄⠀⠀⠀⠀⠀⠀⠲⣄⠈⠛⠲⢦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢰⣿⡧⡈⢻⣿⣿⣦⣵⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠄⠀⡄⠀⠀⠀⠈⢣⡀⠀⠀⠈⢻⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⡟⢡⡠⠽⣭⣿⣟⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣧⠀⠹⣄⠀⢀⣀⣀⡁⠀⠀⠀⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡾⠀⢸⣿⣿⡌⡀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⡀⠀⠈⠻⣷⡀⠘⢷⣸⣿⣯⣽⣷⡆⠈⢲⡀⣿⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⡃⠀⢾⡿⠋⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⡙⢿⣯⡷⣄⠀⠈⡇⠀⠀⠉⠻⣿⣧⠟⠀⢦⠀⠙⢺⣧⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣼⢤⡄⠈⠧⣾⠋⠀⠈⠉⠉⠉⠉⠉⠱⣄⠈⠻⣿⣿⡿⠁⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠈⢿⡴⠛⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⠈⠁⠀⣠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⣄⡈⠉⠉⠉⠉⠀⠟⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠈⣇⠀⠀⠀⠀⣀ ⠀⠀⠀⢰⡇⠀⠀⢀⣧⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠒⠂⠂⡄⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣿⣿⣿⡆⠀⠀⠀⢸⡷⠶⠒⠚⠛ ⠀⠀⢠⡟⠀⠀⠀⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⢸⣧⣤⣀⠀⠀ ⠀⠀⣸⠇⢀⠀⠀⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⠀⠀⠀⠀⠉⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⡶⢌⣉⠛ ⠀⢀⡇⠀⠹⠀⠀⠀⠉⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠈⠳⣄⡀⠙⠂⣾⣿⣿⣿⣿⣿⡿⠀⠀⠀⢸⠷⣝⠲⢤⡀ ⠀⣸⠀⠀⠀⠐⢆⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣤⣤⣄⣒⣀⣀⣴⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⣸⠇⠈⠓⠈⠁ ⢰⡇⠀⠀⠀⡄⠈⠆⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣾⣭⣽⡟⢻⣿⠿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀ ⢸⠁⢀⠀⠁⠙⣦⡀⢄⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠓⠀⠀⠀⠩⠙⠛⠁⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀ ⣸⠀⠘⣧⠀⠀⢶⡻⣦⡁⠈⡒⠿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀ ⢻⠀⢠⣀⢀⡀⠈⢷⣶⡝⣷⣌⣷⠈⠃⠀⠀⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡾⠩⢧⡀⠀⠀⠀⠀⠀ ⣾⣧⠀⠀⠉⠳⢤⣈⣻⣷⡈⣟⠙⠀⠀⠀⠀⠀⠙⢿⣲⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⢋⡼⠁⠰⣾⠁⠀⠀⠀⠀⠀ ⣿⡟⡆⠀⠀⠀⠀⠀⠀⠙⠻⣾⣦⡀⠀⠀⠀⠀⠀⠀⠈⠓⢬⡉⠓⠒⠒⠢⠤⣤⣤⣀⠀⠀⠀⠠⠴⠖⣋⡵⠚⠁⠀⠀⣿⡄⠀⠀⠀⠀⠀ ⡟⢲⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠲⠶⢤⡀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀ ⣯⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣦⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀ ⠛⠒⠚⠓⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠚⠓⠒⠒⠒⠒⠚⠓⠒⠒⠒⠒⠒⠒⠒⠒⠻⠇⠀⠀⠀⠀

⠀⠀⠀⠀⠀⣾⠓⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⣧⣄⡑⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⢧⡌⠙⢦⡙⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣷⣀⠱⣄⠀⠳⣄⠈⠑⠢⠤⢄⣀⣀⣀⣀⠀⠀⠀⣀⣀⣀⣀⡤⡤⠤⠤⠴⡶⠶⠶⠲⠶⠚⠁⠀⣠⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢻⣟⣷⣌⠳⡄⠻⡃⠰⠀⠀⠀⠀⠀⠀⠀⠙⠛⢿⣻⣉⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⡼ ⠀⠀⠀⠀⠀⠘⡟⠓⠿⡍⠙⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠰⡇ ⠀⠀⠀⠀⠀⠀⢳⣼⡄⢹⡄⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢸⠁ ⠀⠀⠀⠀⠀⠀⣸⠯⠀⠀⠀⠀⢠⡀⣌⢦⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⠀⠀⢀⡟⣧⡐⢄⡐⠀⠀⠈⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆ ⠀⠀⠀⠀⣠⢟⡉⠙⠚⠤⣅⠀⢀⣠⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⠀⠀⣼⣷⠋⠀⠀⠀⠀⢀⣾⡿⠟⢉⣩⣍⡛⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡇ ⠀⠀⣼⡋⠀⠀⠀⠀⠀⠀⣾⡟⢁⣼⣿⣿⣿⣿⣦⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⣿⣿⣍⠉⠻⣦⡄⠀⠀⠀⠀⠀⠀⠃ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠈⠳⣾⣿⣿⣿⢻⣿⣿⢆⣿⠀⢠⠇⠀⣀⠀⠠⡀⠀⠀⣼⠏⣿⣿⣿⣿⣿⣷⡆⢹⣿⠆⠀⠀⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠁⣺⡟⢠⡟⠓⠂⠉⠁⠲⣮⠀⢀⣿⣇⠿⣿⣷⣿⣿⣿⣏⣸⠏⠀⠀⠀⠀⠀⠀⠀ ⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡠⠋⣀⠀⣀⣠⢀⠀⠈⠣⠈⠟⠇⠉⠉⠙⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠀⢠⡏⠀⠁⠈⠙⢷⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠆⠀⠠⠀⠀⢰⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣷⡆⢂⣴⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣧⣼⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢚⡋⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⢀⣀⣀⣴⣿⡿⢿⣦⣐⡠⠄⠀⠀⢀⣀⢄⡒⢾⣿⣺⢽⡒⠭⠀⠀⠀⠀⠀⠀⠀ ⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡿⣿⣿⣿⡿⡿⣯⡝⢧⣄⣀⡈⣽⣿⣶⣤⣶⣤⣤⣽⣿⣦⡈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⡟⢳⠈⢧⣬⡋⣹⣰⠏⣸⢠⡟⣻⣿⡿⠛⠉⠁⠉⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠘⢆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣷⣬⣭⠭⣭⣳⣴⣿⣾⠃⠁⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⡠⠀⠀⠀ ⠀⠀⠀⠀⠉⠲⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠯⠽⣶⣿⠿⠿⢿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠤⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠊⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠤⠤⠤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⣤⣤⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀ ⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢸⡀⢀⣸⣏⠛⢷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡴⢖⣿⣿⣿⣿⣿⠿⠿⠿⢿⣿⣿⣷⣿⣿⣿⡿⣿⣷⣶⣦⣤⣤⣤⣄⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠣⢤⣤⣤⣤⣤⣤⣤⣼⡿⠟⠛⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠉⠙⠻⢿⣿⣻⢿⣶⣦⣤⣀⣠⣤⣀⣤⣄⣀⣀⣠⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡾⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠀⠸⢿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠈⠙⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣼⣿⠟⠁⠀⠀⠀⠀⠀⠀⢀⣤⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⣠⣾⣥⠖⠛⠉⠉⠙⠓⠶⣤⣀⠠⢤⡀⠀⠀⠀⠀⢀⣠⣤⠶⠚⠛⠉⠁⠀⠀⠠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⢰⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢶⣝⢀⢀⣠⣶⣿⣿⠿⠟⠛⠋⠉⠉⠛⠿⢿⣶⣝⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⠀⠀⠀⠀⠀ ⠀⢀⣾⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠁⠀⠀⠀⠀⣰⣿⣿⣶⣄⠀⠀⠀⠙⣿⣿⡿⠛⠁⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠈⢻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀ ⠀⢸⣿⣷⣇⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⡷⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣦⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⠀⠀⠀ ⠀⣸⣿⣿⡇⡀⠀⠀⠀⠀⣰⡟⢻⣿⡿⡄⣧⠀⠀⠀⠀⠙⠛⠛⠋⠁⠀⠀⠀⠀⣿⠆⠀⠀⠀⠀⠹⢿⣿⣿⡿⠃⠀⠀⠀⠐⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡇⠀⠀ ⠀⢿⡇⠙⠟⠁⠀⠁⠀⣰⠟⠁⠀⠹⣷⣳⡌⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣍⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀ ⠲⢾⡇⠀⠀⠀⠈⢳⣶⠟⠒⡂⠀⠀⠙⢷⣝⢦⣱⣄⠀⠀⠀⠀⢀⣤⡶⠛⠛⠉⠙⠻⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⢃⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀ ⠀⢸⡇⠀⠀⠀⠀⠸⣿⣿⣿⣷⡀⠀⠸⡇⠙⠷⣤⣉⡻⠶⠶⣾⣿⡏⠀⠀⠀⠀⠀⠀⠀⠙⢿⡤⠤⢤⡤⠤⠶⠟⢛⣡⡴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀ ⠀⠀⢿⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠈⠛⢛⢻⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠶⠶⠶⢶⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀ ⠀⠐⢸⣦⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣦⣀⠀⠀⠀⠀⠘⣾⠉⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠷⠾⠿⠟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀ ⠀⠀⠀⢻⡄⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠛⢿⡄⢸⣿⣷⡄⠀⠀⠀⠀⠀⠀⢀⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⠁⠀⠀ ⠀⠀⠀⠀⢿⡄⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣦⣴⣶⣶⣤⠈⣿⡌⣿⠏⣻⢷⣄⠀⠰⢄⣀⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡏⠀⠀⠀ ⠀⠀⠀⠀⠈⢿⡄⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣰⣿⣿⣿⣷⣶⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣼⡿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⣦⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣴⣶⣆⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⡁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣽⣶⣴⡾⣿⣭⣽⣛⠿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣄⣶⣶⣾⣿⣿⣿⡟⠀⠙⢶⣄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⣠⣶⣴⣶⣴⣦⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠉⠳⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠈ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠋⡽⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⡟⢹⡛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⢿⠈⡇⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠋⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⡼⠇⠀⠀⠀⠘⡆⠀⠀⠐⠀⠀⠀⢀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠓⠢⢼⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⣠⠎⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠈⣇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⢀⡼⡇⠀⠀⠀⠀⠀⠀⢸⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⢠⠞⠀⢹⡄⠀⠀⠀⠀⠀⠘⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⣰⠁⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⢹⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⡴⠃⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⡇ ⠀⠀⠀⠀⠀⠀⠀⢰⠋⠀⠀⠀⠀⠀⠀⢀⡾⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⢸⡁⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⡇ ⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⡿⣯⡷⡴⢦⣤⡠⣶⡶⠀⢷⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⡾⠀ ⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⣼⣥⣤⣤⣤⣤⣤⣤⣤⣀⣀⣀⣀⠀⠈⢧⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢀⡇⠀ ⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠉⠙⠻⢿⣿⣿⣿⣿⣿⣿⠛⢦⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⡇⠀ ⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⠳⠀⢳⡀⢹⡇⠀⠀⠀⠀⠀⡾⡇⠀ ⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡿⠘⠀⠀⠹⣼⡇⠀⠀⠀⠀⢠⠇⠀⠀ ⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡿⠁⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⡾⠀⠀⠀ ⠀⠀⢠⡏⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠁⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⢸⠁⠀⠀⠀ ⠀⠀⡾⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⡟⠀⠀⠀⠀ ⠀⣴⠓⣾⣳⣀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠃⠀⠀⠀⠀⠀⠀⢸⡇⢀⠇⠀⠀⠀⠀ ⣾⠃⠀⠀⠀⠑⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠈⡇⢸⠀⠀⠀⠀⠀ ⠹⡀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣾⠀⠀⠀⠀⠀ ⠀⢳⡄⠀⠀⠀⠀⠘⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⣿⠀⠀⠀⠀⠀ ⠀⠀⣷⡄⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⡏⠀⠀⠀⠀⠀ ⠀⢀⡇⢹⣄⠀⠀⠀⠀⣀⠉⠓⠶⢄⡀⠀⠀⠀⠀⠀⢀⣠⠴⠋⠣⣄⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⣸⣧⠀⠀⠀⠀⠀ ⠀⣴⣿⠋⠘⣆⠀⢰⠶⠤⢍⣛⣶⠤⠿⣷⣦⡀⠒⠚⡟⠀⠀⠀⠀⠈⠛⠢⠤⡄⠀⠀⢀⡴⢯⠴⣳⠇⠀⠀⠀⠀⠀ ⠀⠀⠉⠀⠀⠘⢦⡈⠻⣖⠤⣤⣉⣉⣹⣯⣭⠉⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠛⣫⣼⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠑⣄⠉⢦⡀⠀⠀⠈⠉⠁⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢿⣷⢚⡝⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢶⣷⠇⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠷⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⡼⠋⠿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠘⢝⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣻⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣷⣄⠀⠀⠀⠀⠀⠀ ⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡘⢿⣷⠀⠀⠀⠀⠀ ⠀⣿⠀⢀⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⣹⡄⠀⠀⠀⠀ ⢠⡏⠀⠀⠀⠀⠀⠈⠉⠉⠈⠉⠛⠛⢳⣦⠀⠀⠀⠀⠀⠀⢷⠘⣇⠀⠀⠀⠀ ⣾⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣂⠀⠀⠀⠀⠈⣇⢿⠀⠀⠀⠀ ⡿⠀⠀⠀⠀⠀⢀⠀⠀⠃⢀⣄⣀⣠⠀⠀⠀⠱⡕⠀⠀⠀⠀⢹⣾⡇⠀⠀⠀ ⢻⣷⣶⡄⠀⠀⠘⠀⢰⣾⣿⡿⠟⠉⠀⠀⠀⠀⠘⣄⠀⠀⠀⠀⠹⡇⠀⠀⠀ ⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠘⡄⠀⠀⠀⠀⣷⠀⠀⠀ ⣀⢰⠰⣇⣀⣾⡦⠄⠀⠀⠁⠀⠤⠠⠽⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⢸⠀⠀⠀ ⢟⣧⠁⠈⠹⡃⠠⠄⠀⠀⡀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢸⠏⠀⠀⠀⢸⠀⠀⠀ ⠀⢿⣶⣾⣾⣿⣷⣶⣧⣤⣤⣴⠾⢟⠋⠉⠉⠀⠀⢀⡼⠀⠀⠀⠀⢸⡆⠀⠀ ⠀⢸⣿⡟⠋⠁⠀⠈⠉⠉⢁⡀⣀⠬⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⢸⡇⠀⠀ ⠀⠀⢷⡽⠤⢄⣠⣀⠩⣶⣔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀ ⠀⠀⠀⠻⣶⡀⠀⠐⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀ ⠀⠀⠀⠀⣇⡃⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀ ⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡏⠀⠀⠀ ⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⢀⠴⣇⠀⠀⠀ ⠀⢀⣠⢞⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡈⠹⢶⣄

⣿⣷⣷⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⢂⡴⠋⢻⣿⣿⡿⢿⠀⠈⠉⢻⡿⣷⣄⣀⡷⠀⢧⠀⢱⠀⠸⡄⣿⣿⣿⣿⣿⣿⣿ ⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⣠⡎⠀⠀⢸⡿⠋⠀⠈⡆⠀⠀⠈⡇⠀⠈⣇⠀⠀⢸⡄⠘⡇⠀⢷⢹⣿⣿⣿⣿⣿⣿ ⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⣠⣾⣿⠀⢀⡴⠻⠀⠀⠀⠀⠃⠀⠀⠀⢻⠀⠀⠸⡄⠀⠈⣇⠀⢷⠀⠸⣾⡿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠴⠊⣠⣾⣿⣿⣿⠴⠋⠀⠀⡄⠀⠀⠀⡇⠀⠀⠀⠸⡄⠀⠀⢧⠀⠀⣹⣤⠼⠶⣀⠉⠙⠢⣍⡻⢿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⡤⠔⠯⣼⣿⣿⣿⣿⡀⠀⠀⠀⡇⠀⠀⠀⢹⠀⠀⠀⣀⣷⣤⠴⠚⠺⣉⠀⠙⠢⣄⡈⠑⠤⣀⠀⠉⠲⢌ ⠀⠀⠀⠀⠀⠀⢠⣶⡿⠟⠁⠀⣠⣾⣿⡿⢋⡼⠋⠉⠁⢉⡿⠛⠒⣶⠚⠙⠻⣍⠁⠀⠀⠈⠳⢤⡀⠈⠑⠦⣀⠀⠙⠲⢤⡈⠙⠢⢄⡀ ⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⢀⣾⡿⠟⢁⡴⠋⠀⠀⠀⣠⠞⠁⢀⡜⠁⠱⣄⠀⠈⠳⣄⠀⠀⠀⠀⠉⠳⢄⡀⠈⠓⢦⣀⠀⠉⠓⠦⣄⣉ ⠀⠀⢈⣠⡾⠋⠀⠀⣠⣴⠟⠋⢀⡴⠋⠀⠀⠀⢀⡜⠁⠀⢀⠞⠀⠀⠀⠈⠣⣀⠀⠀⠙⢦⣀⠀⠀⠀⠀⢉⣲⣤⣀⣈⣷⣦⡒⣂⣩⣿ ⢀⣴⡿⢍⡀⠀⣠⡾⠛⠁⠀⣠⠋⠀⠀⠀⠀⣠⠋⠀⠀⢀⠎⠀⠀⠀⠀⠀⢀⣸⣷⣶⡾⢿⣿⣦⣤⡍⢥⠤⠤⡾⢿⡛⠛⡏⠙⣿⣿⣿ ⣿⣿⣷⣶⡤⡽⢿⣶⣦⣤⣾⣁⡀⠀⠀⢀⡜⠁⠀⠀⢠⠎⠀⠀⣀⡠⢔⡺⢷⣷⣿⣥⣀⣘⣛⣩⣽⡇⢀⠀⠀⠁⠀⡇⠀⡇⠀⠹⣿⣿ ⣿⣿⣿⣯⡴⠃⠀⢸⠉⠉⠓⠲⣬⣭⣉⣿⣷⣶⣶⣶⣟⢒⣊⣩⣵⠚⠉⠠⡌⢟⠛⢿⣿⣿⣿⣿⣿⢷⣜⠀⠀⡄⠀⡇⢰⠃⡄⢆⠹⣿ ⣿⣿⡿⠋⠀⠀⡀⢸⠀⢣⢠⡄⢇⠈⠉⠛⠛⠛⠿⠿⢛⡟⣻⠟⡿⠳⣄⠀⣿⡾⣆⠀⠀⠉⠉⠁⠀⢸⡟⢠⠀⣧⠀⣇⢸⠀⠘⣜⣷⣿ ⣿⡏⠀⠀⠀⡰⠁⠃⢣⡀⠈⢿⣜⡄⠀⠀⠀⠀⠑⠦⣀⠘⠁⠀⡅⠀⠈⠣⡘⡇⠈⠓⠀⠀⠀⠀⠀⠀⣇⡌⣰⠋⢧⣏⠻⡄⠀⠈⠻⢿ ⣿⢀⣤⣶⡞⠁⠀⠀⢠⠙⢷⡈⢿⣿⣆⠀⠀⠀⠀⠀⠀⠙⠢⢤⡇⢸⠀⠀⢱⡟⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠃⠀⠀⠹⡄⠈⠀⠀⠀⣠ ⣿⣿⣟⣁⣀⣀⣀⣠⡟⠀⡄⠑⢬⣻⣮⡑⠀⠀⠀⠀⠀⠀⠀⠀⢧⡀⣆⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⣼⡟⠁⠀⠀⢀⣀⡁⠈⠑⠲⣿⣿ ⣿⠉⠉⠉⠉⠉⠉⡿⢁⣴⡇⠀⢠⠌⣿⣍⠀⠀⠀⣀⠀⠀⠀⠀⣀⣉⣁⣀⣀⣀⣀⣀⡠⠄⠀⢀⣾⠏⠀⠠⣤⣀⣀⣀⣨⣷⣶⣦⣼⣿ ⡏⠀⠀⠀⠀⣰⣾⣵⣿⣿⡇⣠⡏⢠⣿⠈⠓⢄⠀⠀⠉⠻⠿⣉⣉⣉⣋⣉⣉⠩⠝⠋⠀⢀⡴⠋⣸⢮⢣⣄⣈⠻⣿⣿⣿⣿⣿⣿⣿⣿ ⣧⠀⠀⠀⠈⠉⠉⠀⣿⣿⡾⠛⣇⡿⢻⣇⡄⠀⠑⢄⠀⠀⠐⠤⠤⠤⠤⠤⠤⠐⠂⠀⣠⠊⠀⢀⡇⡾⣦⡇⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿ ⣻⣷⣼⣧⣴⠶⣦⣄⣿⡿⠀⣀⣼⣷⣤⣿⣿⠀⠀⠀⠱⣄⠀⠀⠀⠀⠀⠠⡀⠀⢀⠞⠁⠀⠀⢸⣼⠇⠹⠃⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿ ⠁⣸⡿⠛⠁⠀⣨⣿⣿⡿⠛⢹⡟⣼⣿⣿⣧⢣⠀⠀⠀⠈⠳⣄⠀⠀⠀⡐⢁⡔⠁⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿ ⠰⠋⠀⠀⠀⣰⣿⣿⠇⠀⠀⢸⡇⢻⣿⠟⠻⡈⢇⠀⠀⠀⠀⠈⠓⠲⠗⠚⠉⠀⠀⠀⠀⠀⢰⣿⣦⣄⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⣴⣿⣿⣿⠀⠀⠀⠈⡇⠘⣿⡀⠀⡇⠈⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⣿⢿⣿⣦⡀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⣼⣿⣿⣿⡟⠀⠀⠀⠀⣧⠀⢻⣧⠀⠹⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢣⣿⣿⣿⣿⣿⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠘⠻⣿⣿⣿⡇⠀⠀⠀⠀⢸⠀⠘⣿⡆⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣾⣿⠟⢻⣿⣿⣎⢿⡈⠙⠿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⢸⣇⠀⢹⣿⡄⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁⠀⢸⣿⣿⣿⡜⣧⠀⠀⠀⠈⠙⠛⠿

⣷⣇⡴⢡⣿⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀ ⣿⣟⡴⠋⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⣄⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠁⠀ ⣿⠏⠀⢸⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⢀⢎⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⢘⡀⠙⣷⣀⠀⣀⣀⣀⣽⣷⠖⠿⡅⠀⠀⠸⣄ ⡟⠀⠀⠸⠟⣿⣷⡀⢻⠛⢿⣦⣤⣤⣼⠬⣆⣀⣀⢀⠀⢸⢸⡇⠀⠀⠀⠀⠈⠀⠀⠀⠻⡿⣿⠿⠻⢿⡛⠉⠁⣼⠘⣦⠀⢳⠀⠀⠀⣿ ⠁⠀⡖⠀⠀⣿⣧⠇⢸⢸⢸⠀⠉⣿⠛⠳⠿⡿⠿⠿⠅⠀⣇⢷⠀⠀⠀⠀⢸⠀⠀⠀⠀⡤⠔⢦⡇⠈⢷⡀⣀⣿⣴⣾⣷⣼⡷⠂⡀⢻ ⠀⢠⠇⠀⣴⣿⠛⠀⢸⢘⣼⠀⢸⡏⠀⣀⠀⠹⡄⢀⠀⠀⠸⡜⣧⠑⠀⠀⢸⡀⠀⠀⠀⣀⡀⠀⣠⣴⣾⣿⣿⠟⠛⢿⣿⣿⡿⠒⢱⠸ ⠀⢸⠀⠀⢻⡛⢦⣀⣸⣾⣿⣿⣿⣷⣦⣬⣑⠦⠽⣮⡧⠀⠀⠱⣹⡧⠀⠀⢸⡇⠀⠀⢸⣭⣴⣿⣿⣿⣿⣿⣯⠀⠀⣶⣿⣿⡇⠀⠘⠀ ⠀⣿⠀⠀⢸⠳⣦⣼⣿⡟⢹⢠⣿⣿⣿⣿⣿⣿⣦⣌⡻⣦⠀⠀⣳⡁⠀⠀⡟⢹⠀⣠⣾⣿⣿⠿⢿⠟⢙⣿⣿⠀⠀⣿⣿⠟⡇⠀⢹⡇ ⠀⡇⠀⢀⣾⠀⠨⢿⣿⡆⢸⣸⢿⣿⣟⠛⣿⠞⢹⣿⣿⡿⠷⢦⡙⣿⡄⢠⡇⢸⡏⣹⠇⣿⣿⣦⣀⣀⣾⣿⣿⠇⠰⠟⢃⢠⡇⠀⣿⣿ ⣸⠃⣠⡎⢸⠀⠀⢰⡏⢿⣌⣿⢸⣿⣿⣦⠀⣠⣾⣿⡿⡇⠀⠀⢿⣮⣷⣼⠁⢀⣧⠃⡀⢻⣿⣿⣿⣿⣿⣿⠟⠀⠀⢀⣾⢸⡇⠨⢸⢻ ⣿⣾⣿⠀⣾⠀⣠⡏⢱⠈⢻⣿⡄⢻⣿⣿⣿⣿⣿⣿⡷⠃⠀⠀⡞⣸⡿⣿⣷⣿⢃⠎⢀⡴⣻⢿⣿⣿⡟⠁⢀⡤⠼⠘⢛⢸⡇⠀⠀⢻ ⣽⣿⠏⢠⡟⢠⣿⠀⠈⣇⠀⢉⡅⠀⠙⠿⣿⣿⠿⠋⢀⣠⣶⣿⡿⣿⣿⣿⡟⢠⠏⣠⠎⡴⡳⠶⢾⡿⣻⠛⡻⢀⠀⠀⣾⢸⠁⠀⠀⣸ ⣿⡟⠀⣾⣷⣯⣿⡇⠀⢹⡀⠈⠛⠒⣦⣄⣀⣠⣤⣴⢋⣼⢾⢏⣞⣿⢿⡙⣠⠃⡰⢁⠞⡔⢡⡿⣱⡿⢡⡞⣴⣷⢞⡟⢇⣼⠀⠀⠀⢻ ⡿⠀⢰⢿⢟⣿⣿⣷⠀⠘⣧⣇⣴⠊⣼⣟⡍⣱⡟⢡⢮⢎⠎⣾⠋⠁⠈⠁⠀⠀⢡⠋⠜⠀⣝⣀⠟⢠⢏⢾⠏⢪⠋⣴⢻⡟⠀⠀⠀⠸ ⢃⣠⢴⣾⡟⣿⣿⣿⠀⠀⣿⣿⢃⢞⣿⢋⣼⠏⣠⢣⢫⠎⠘⠁⠀⠀⠀⠀⢀⣀⡡⠤⠔⠒⣿⠏⠀⠘⠋⢺⠔⣡⣾⣁⣾⡇⠀⣠⠁⠀ ⣩⣶⣿⣯⣇⠸⣿⣿⡀⢠⣿⣡⢫⡿⢁⣾⠏⠐⠁⠐⠲⣦⣴⣒⣲⢲⠊⣉⣁⠀⠀⠀⠐⣩⠋⠀⠀⠀⢀⣠⣿⣿⣿⣿⣿⠁⢠⣿⡅⠀ ⣿⠟⠘⣿⢿⣆⣤⣼⡇⣼⠙⢻⣿⣡⡞⢃⡀⣜⠒⠁⠀⠙⠛⠒⠚⠾⠭⠤⠤⠐⠒⠒⢆⢹⠀⠀⣀⣴⣿⣿⠏⠀⣾⣿⠛⠀⣼⡟⠚⣄ ⣷⡀⠀⠸⣿⣿⡉⢀⣿⠃⠀⠀⠀⠋⠙⢿⣷⣼⣄⣀⣀⠀⠘⢆⠀⠀⠀⠀⠀⠀⠀⠀⠈⡞⣴⣾⣿⣿⡿⠃⠀⠀⣿⣿⢸⢰⡏⠀⢠⡿ ⠈⢿⣄⠀⢻⣿⢷⡜⠁⠀⠀⠀⠀⠀⠀⠀⣿⠙⢿⣿⣿⣿⣶⣼⠹⣇⠀⠀⣰⡄⢀⣤⣾⣧⣿⣿⣿⠋⠀⠀⠀⢰⣿⣹⡎⣿⡇⢀⡟⣼ ⠀⠀⠻⡆⠀⠙⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢹⣿⣿⣿⣿⡷⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⡟⠳⣄⠀⢠⣿⢸⡄⣧⠘⠧⡾⣱⠃ ⠀⠀⠀⢸⡀⠀⠘⣿⣿⣦⠀⠀⠀⠀⠀⠀⣿⠂⠀⠸⣟⠻⣍⢻⠧⣿⣿⣿⣿⡿⢿⣿⡿⣿⣿⠏⠀⠀⠙⢷⣌⠉⠀⣧⢹⠀⡼⣱⠃⠀

⠀⠀⠄⣀⣉⡩⠒⣪⡉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⢀⣀⡤⠀⠀⠀⡀ ⠀⠀⠀⡞⠙⠝⢿⡹⣠⠔⠂⠉⠀⠀⠀⠀⠀⠀⠈⠑⠀⣑⣫⠵⠒⠋⠉⠉⠁⠀ ⠀⠀⡞⠁⠀⠀⢰⡡⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢜⢯⡀⠀⠀⠀⠀⠀⠀ ⠀⠠⡧⠀⣠⢣⠋⠁⠀⠀⡆⢿⣶⠌⡟⢏⢵⣷⠉⡢⠀⠀⢀⠱⡆⠀⠀⠀⠀⠀ ⠀⠀⣷⡇⢇⠃⠀⠀⠀⠀⠈⠂⣡⣞⡀⠈⢄⠁⠚⠁⠀⠀⠀⠁⡙⣖⠀⠀⠀⠀ ⠀⢤⡗⡑⠁⠀⠀⠀⠀⠀⠀⠾⢿⢿⣇⡭⡶⠷⠀⠀⠀⠀⠀⠀⠈⠊⠳⣀⠀⢀ ⣿⡏⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⡇⠈ ⣿⢹⡀⠰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿ ⣿⡸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡆⠸⠿ ⡇⣿⠇⠀⠀⠀⠀⠀⠀⠀⠈⠉⠂⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⢀⣰⣷⣿⠀⠀ ⠟⢸⡟⠅⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⡿⠋⠀⣷⠃⠸ ⠀⡝⡧⠄⠀⠀⡶⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡼⠋⠀⠀⠀⢃⠀⠀ ⢠⡇⠂⠀⠀⡠⠇⢸⡗⠉⠒⠀⠀⠀⠀⠀⠢⠤⠐⢺⢷⠏⡰⠀⠀⠀⠀⠸⠀⠀ ⠸⣑⡒⠒⠀⠘⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⠀⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⡕⣱⣉⣉⣙⣠⡿⠀⠲⠖⠒⠒⠒⠠⠤⠤⠤⠤⢤⢸⡠⣀⣀⣀⣀⣀⠊⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠴⠒⠚⠉⠉⠉⠉⠉⠙⠒⠲⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠋⠁⢀⣠⠴⠒⠒⠒⠒⠦⠤⠀⠀⠀⠀⠈⠙⠶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⠸⣏⠀⠀⡀⠀⠀⠀⣤⢤⡀⠰⡄⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⢀⡽⠷⢯⣁⡀⠀⠀⠙⣦⣽⣄⣹⡄⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠙⠏⠁⠀⠀⠀⠀⠀⠀⢹⣦⢤⣀⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⣠⠾⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⢀⡴⠋⠀⢀⡤⠛⠲⣄⠀⠀⠀ ⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⣼⠃⠀⢠⣀⣰⠟⠁⠀⠀⠀⠀⠀⠀⠀⠹⡆⠀⠀⠀⢀⡞⠀⢀⡴⠋⠀⠀⠀⠘⣇⠀⠀ ⠀⠀⣠⠶⡟⠀⠀⠀⠀⠀⢸⡇⠀⠀⠿⢿⡇⠀⠀⠀⠀⠐⣿⡷⠀⠀⠀⢿⠀⠀⠀⣸⠁⢠⠏⠀⠀⠀⠀⠀⠀⢹⠀⠀ ⢀⡾⠁⢰⠃⠀⠀⠀⠀⠀⠀⠙⠃⠀⠀⠀⠳⠤⣄⣀⠀⠀⠀⠀⠀⠀⣤⠟⠀⠀⠀⠸⣦⡜⠀⢰⠀⠀⠀⠀⠀⡾⠀⠀ ⣼⠁⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣲⡯⠤⣀⠀⠀⢠⠇⠀⠀ ⠸⣦⣀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠧⢤⡀⠈⣧⢀⡞⠀⠀⠀ ⠀⠀⠈⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠧⠶⠤⠄⠉⢀⢇⡞⠀⠀⠀⠀ ⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠤⠤⣄⠀⠀⠈⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠻⡄⠀⠀⠀⠀⠀⠀⠶⠒⠲⠤⠤⢤⣀⣀⣀⣀⢀⡴⠚⠛⡷⠦⣄⢀⡴⢧⣀⡀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡟⠀⠀⡜⠁⠀⠋⠁⠀⠀⠀⠃⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢤⣀⣀⠀⠀⠀⠀⠀⠀⣧⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⣠⡇⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣹⠿⠶⠶⠶⠶⠿⢦⣸⡀⠀⠀⠀⣼⢃⣠⣾⣟⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠉⠙⣄⠀⠀⠀⠀⣀⡤⠞⠋⣿⠒⣺⡯⠟⠋⠀⠈⠳⣄⠀⠀⠀⠀⠀⣼⠄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣏⠀⣀⣸⡆⢀⡴⢞⣉⠀⠀⢀⡿⠋⢹⡄⢠⠞⠉⣽⠀⠈⠳⢤⡀⠀⣼⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠈⠉⠁⡀⠘⠋⠀⠉⢈⡑⠦⠚⠀⠀⠀⢻⡟⠒⠋⣡⠴⠲⡆⠀⠈⢛⣿⠿⠿⠻⠟

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠠⠶⣿⣷⣶⣤⣄⡉⠑⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⡿⢿⡻⣿⠭⡒⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣽⣯⣼⠷⢶⣕⣚⡖⠊⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⣴⠾⠿⠿⢿⣿⣇⢰⢋⣁⣈⠕⡄⢀⠇⠀⠀⢀⣀⣀⠀⠀⠀ ⠀⠀⠀⠀⢀⣤⣴⣶⣶⣶⣶⣤⣟⣿⣿⣦⣤⣤⣮⠴⠋⢀⣴⣿⠿⠷⢶⣝⢢⠀ ⠀⠀⠀⠀⠀⠈⣙⡿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⡿⠐⢴⡟⠋⠀⠀⠀⠀⢹⡇⠃ ⠀⠀⠀⡠⢖⣩⣶⡾⠿⠿⣿⣿⣿⣿⣿⣿⡿⠛⠓⢄⠈⢦⠀⠀⠀⠀⢀⣼⣇⡆ ⢀⠐⠉⠉⠛⡋⠀⣀⣀⣀⡹⣿⣿⣿⣿⠋⠀⠀⠀⠀⢣⠈⢆⠀⠀⡎⠁⠀⠀⠑ ⠸⡀⠀⠀⢀⠷⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠈⠁⠒⠀⠁ ⠀⠀⠉⠉⠀⠀⠀⠀⠀⠉⠙⣿⣿⣿⣧⠀⠀⠀⠀⠀⢀⠇⣸⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣧⡀⠀⢀⣠⡎⣰⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡿⠟⠿⠿⣿⣿⠿⠟⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡢⢤⡤⢤⣄⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢿⣯⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⠷⠟⠋⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣶⣿⡝⣽⣋⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠈⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⢠⠀⠀⠙⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠸⡆⠀⠀⠈⢳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠶⠛⠛⡉⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⢻⠀⠀⠀⠀⠙⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠶⠛⠋⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠈⠃⠀⠀⠀⠀⠈⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⣀⣠⣤⠤⠤⣤⣐⣹⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠾⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣠⡾⠋⣿⣾⣦⡄⠀⠉⠛⢿⣽⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⡒⡶⣶⣿⣉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠋⢨⣾⣿⣿⣿⣿⣿⣶⠄⠈⢻⣜⣷⡄⠀⠀⠀⠀⠀⠀⣴⢟⣡⣾⣿⣿⣦⡀⠀⠙⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠈⠋⠉⠛⠛⠁⠀⠁⠀⣀⣀⣿⡾⠿⠶⠶⠶⢤⣤⣴⡏⠸⠟⠿⣿⡿⠟⠿⠷⠀⠀⠹⣧⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡷⠲⠒⠒⠒⠒⠛⠛⠛⠛⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⠁⠿⠧⠤⠤⠤⠤⠶⠤⠤⣤⣤⣤⣤⣿⣧⣤⣤⣤⣀⡀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣴⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢻⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡽⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢹⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⡇⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⢾⡇⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣤⡀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⣸⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠈⢷⠀⠀⠀⠀⠀ ⠀⠀⢠⡿⢻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀ ⠀⠀⣾⠇⣸⢹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣄⠀⠀⠀⠀⢿⡀⠀⠀⠀ ⠀⢰⠏⢠⣿⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣦⣤⣤⣤⣤⣤⣤⣀⡀⠀⠀⠀⠀⢻⣆⠀⠀⠀⠘⣧⠀⠀⠀ ⠀⣿⠀⢸⡏⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⢦⣄⡀⠀⢻⡆⠀⠀⠀⢻⡄⠀⠀ ⣼⠃⠀⢸⡇⠈⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢶⣄⣿⠀⠀⠀⠈⣿⠀⠀ ⣿⠀⠀⠸⣧⠀⠈⢿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠾⠋⠀⠀⠀⢀⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣿⠀⠀⠀⢠⢻⡄⠀ ⣿⡄⠀⠀⠙⠛⠆⠀⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠟⠁⠀⠀⠀⣠⡶⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣼⠃⠀ ⠈⢿⣴⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠛⠉⠀⠀⠀⢀⣴⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⡟⠀⠀ ⠀⠀⢻⣿⡃⠀⠀⠀⠀⠀⠀⠈⠙⣿⣦⣤⣤⣤⣤⡤⠶⠚⠛⠉⠀⠀⠀⣀⣤⡴⠞⠋⠀⠀⠀⠀⣰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡾⠛⢹⡇⠀⠀ ⠀⠀⠀⠻⣧⣁⡀⠀⠀⠀⠀⠀⠀⠈⢿⣬⣁⠀⢀⣀⣠⣤⣤⡶⠶⠖⠋⠉⠁⠀⠀⠀⠀⠀⠀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⣠⣾⠟⠉⠀⠀⠸⣇⠀⠀ ⠀⠀⠀⠀⠀⠈⠛⠳⣦⣄⡀⠀⠀⠀⢀⡉⠉⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠾⣿⡟⠛⢛⡅⠀⠀⠀⠀⠀⣿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡉⠉⠉⠉⠻⢦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠁⢰⡇⠁⠀⢰⡇⠀⠀⠀⠀⠀⠈⣇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠘⠓⠲⠦⠤⣤⠤⠤⠀⠀⠀⠀⠀⠀⣰⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⢀⣿⠁⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢹⡆ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢸⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⡀⣼⠋⠀⠀⠀⢀⣾⣃⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⣧

⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿ ⣿⠟⠁⠀⠀⠀⠀⠀⠀⢀⣴⣞⠿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿ ⠁⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠏⢀⣀⠀⣘⡄⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀⠙⢻ ⠀⠀⠀⠀⠀⠀⠀⠀⢿⡿⣿⢘⠭⠭⣯⠫⢇⠀⠀⠀⠀⠀⠀⠀⠀⠠⣥⣤⠤⠔ ⠀⠀⠀⠀⠀⠀⠀⠀⣼⣷⡭⡯⢠⢿⡿⡏⡚⠀⠀⠀⠀⠀⠀⠀⠀⡇⢻⡍⠉⠀ ⠀⠀⠀⠀⠀⠀⠀⣨⡿⠟⠃⢻⣇⠩⢤⣀⢿⠛⠒⠂⢄⡀⠀⠀⢠⢸⡄⠘⡄⠀ ⠀⠀⠀⠀⠀⣠⠞⠋⠀⠀⠀⠀⠉⠓⡒⠒⠋⠀⠀⠀⠀⠑⡀⠀⡘⣆⠇⠀⢸⡯ ⠀⠀⠀⠀⣰⠃⠆⠀⠀⢢⠀⠀⢀⢆⠀⡀⠀⡀⢕⠡⣃⡀⠘⡄⡇⢻⠀⠀⡇⡇ ⠀⠀⠀⠀⡿⠀⠀⠀⠀⢈⢴⠋⠈⠉⠐⠁⠈⠃⣈⠢⢤⡉⢢⢈⢸⡆⢀⠔⠑⢳ ⡀⠀⠀⢠⣇⠀⠀⠀⠀⡌⣇⣦⣀⠀⣀⠤⠚⠁⠀⠀⠄⠈⠫⣘⣄⣳⣁⣀⣀⣸ ⡷⡄⢀⠀⠻⣤⣀⠂⠉⠀⠀⠊⠈⠀⡩⣀⠉⡝⣕⢶⣖⣚⣓⣚⣓⣒⣬⣭⠤⢽ ⣿⣏⠉⠉⠉⢍⠙⠓⠓⠒⠒⠒⠒⠂⠉⠐⠙⠪⠾⠫⢿⣉⡑⠒⠓⠂⠈⢉⣁⣤ ⣿⣿⣧⡀⠀⠀⠈⠂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡽⠀⠀⠉⠙⠛⠓⠛

⠀⠀⠀⠀⢠⠒⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡌⢂⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⡆⠀⠀ ⠀⠀⠀⠀⡇⠈⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠉⠀⠀⠀⡇⠀⠀ ⠀⠀⠀⠀⢇⠔⣿⣧⣌⠙⣧⡀⠀⠀⠀⡠⣶⣖⠺⢅⠀⠀⠀⠀⠀⡸⠀⠀⠀ ⠀⠀⠀⠀⢸⠌⠩⠭⠬⠤⠼⠛⠒⠒⢾⣘⣛⣛⣓⣀⣧⣀⡀⠀⢰⠁⠀⠀⠀ ⠀⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢇⠀⠀⠀⠀ ⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡄⠀⠀ ⠀⣸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⠀⠀⢣⠀⠀ ⢠⢧⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⠀⢣⠀⠘⡆⠀ ⡜⢸⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠊⠀⠀⠀⠀⠀⠉⠒⢤⣇⠀⢰⠀ ⣇⠈⠂⠙⢄⠀⠀⠀⠀⠀⠀⠀⣠⠔⠁⢀⠔⠃⠀⠀⠀⠀⠀⠀⠀⠁⠀⢸⠃ ⠈⢷⠀⠀⠀⠙⣦⠤⠤⠔⠒⣉⡠⠄⠊⠁⢠⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⢻⠀ ⠀⠀⠉⠒⡤⠤⢬⡉⠈⠉⠁⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⡠⠖⠞⢺⠁⠀⠘⡀ ⠀⠀⠀⠀⠹⡀⠀⠀⠀⠐⠒⠀⠀⠀⡠⠃⠀⠀⠀⢠⠊⠀⣸⠀⢸⠀⠀⠀⢡

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⣿⣿⡿⠿⠿⠿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛ ⠉⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⣀⣀⣀⠀⣀⣀⣤ ⠀⠀⠀⠀⠀⠀⠀⠘⢧⣠⣤⠶⠶⠚⠛⠛⠛⠛⠻⠶⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⣀⣠⣤⣶⣶⣶⡾⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿ ⣿⣿⣿⡿⠃⣀⣳⢯⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿ ⣿⣿⡟⠁⠀⠟⢳⣾⡉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⢹⣿ ⣿⣿⠃⠀⠀⠀⠈⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⢀⡆⣀⣿ ⣿⡟⠀⠀⠀⠀⠀⠀⠀⡀⣿⣿⡿⠀⠀⠠⣄⠀⠀⠀⣸⠂⠀⠀⠉⠀⠟⡼⠃⢹ ⣿⣧⠀⠀⠀⠀⠀⠀⣴⢣⡞⠉⠁⠀⠀⠀⠈⠳⢦⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⣸ ⣿⣿⡀⠀⠀⠀⠀⠀⠁⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿ ⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠿ ⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀ ⣿⣿⡿⠿⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠟⠁⠀⠀

⢉⠡⠸⢾⣿⣿⣿⣷⣾⣏⠛⠒⠿⡍⠒⠤⢄⡀⠠⢄⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀ ⠀⠀⠀⠀⡠⡺⠁⡃⠀⢿⣧⠀⠀⠋⠀⠀⠉⠙⣫⣍⢍⠉⠒⠢⢄⡀⠀⠀⠀⠀ ⠀⠀⣠⠊⢰⠁⠀⠱⢄⣀⡽⠀⠀⠀⠀⠀⠉⠉⠉⠉⠓⢍⠢⡀⠀⠀⠀⠀⠀⠀ ⠄⡴⠁⠀⠸⠀⡀⠀⠀⡰⠡⠀⠀⣀⢴⠚⠹⣿⣿⣶⢦⣀⠑⣌⢢⠀⠀⠀⠀⠀ ⢀⠃⠀⠀⠀⢱⠉⠐⠚⠒⠁⢀⠜⠁⠈⠢⡀⠀⠉⠀⠀⡨⠷⣿⣾⡶⠶⠶⠄⠀ ⢺⠀⠀⣸⣷⢄⠀⠀⠀⠀⢠⠋⠀⠀⠀⠀⠀⠉⠀⠉⠁⢀⡼⡏⡻⣿⣛⠳⠶⠦ ⢼⠀⠀⣿⣧⡀⠉⠢⢄⡀⠀⠑⠠⣀⠀⠀⠀⠀⠀⢀⡴⠋⡰⢀⠃⠀⠙⠻⠷⠀ ⠀⡆⠀⣿⣿⣿⣷⣦⣀⠀⠁⠒⠂⠤⠬⠡⢤⠖⠈⠁⠀⡴⢁⠌⠀⠀⠀⠀⠀⠀ ⠀⢳⠀⢿⣿⡿⠿⠿⠿⠿⣷⣶⣤⣄⣀⠔⠁⠀⢀⡠⠊⢠⠊⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⡆⠘⡅⠀⠀⠀⠀⠀⠀⠈⡹⠛⢁⣀⠤⠖⠉⣀⠔⠁⠀⠀⠀⢀⠀⠀⠀⢠ ⠀⠀⠘⡄⠈⠒⠤⠀⠠⠔⠒⠯⣍⠭⠥⠤⠄⠒⠉⠀⠀⠀⠀⠤⠒⠁⠀⠀⡰⢻ ⠀⠀⠀⠘⢄⣀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢒⣢⣤⡤⠴⠒⣒⣉⣀⣀⠤⠴⠊⠀⣸ ⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⢏⠉⠉⣀⣷⣿⣿⣀⡀⠱⢄⣀⠀⠀⠀⠀⠀⠟ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢼⣶⣿⣿⣿⣿⠏⠀⠈⠣⡤⠬⠝⠛⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣋⠝⠉⠻⣿⣿⣿⡄⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿ ⣿⡿⠿⠛⠋⠉⠉⠉⠉⠛⢻⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠠⠀⠐⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣴⣾ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⣀⣠⣤⣴⣶⣾⣷⣶⠶⠶⢶⣶⣶⣾⣷⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣿⣿⡿⠿⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⢀⣠⣤⣶⣶⣾⣿⣿⣿⣿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⢿⣶⣿⠃⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⡿⠁⠀⣷⣦⣾⠋⢙⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿ ⣿⣿⣿⣿⡟⠁⠀⠀⠾⠟⠛⣷⣿⣋⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢹⣿⣿ ⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠘⠏⠉⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣷⡄⠀⣀⠀⠀⣿⣿ ⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⠇⣰⡿⢀⣤⢸⣿ ⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⡆⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⣴⡆⠀⠀⠀⠈⠉⠉⠁⣼⡟⣠⣾⠋⠈⣿ ⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠌⢿⣿⣿⡿⠃⠀⠀⠀⠀⠹⣿⣦⡀⠀⠀⠀⣰⣿⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠻⠁⠀⠀⣿ ⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏⣰⡿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣶⣤⣾⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿ ⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿ ⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿ ⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿ ⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠁⠉ ⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠃⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠟⠁⠀⠀⠀ ⣿⣿⣿⡿⠟⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⡟⠁⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⢀⠂⡠⡌⠀⠀⠘⠒⠀⠀⠀⢈⣤⣀⡉⠄⠀⠀⠀⠀⣠⠴⠁⠀ ⠀⠀⠀⠀⠠⢴⠅⠊⢉⣵⡆⠀⠀⠀⠀⠀⢸⣿⡛⠛⠛⠓⠦⣦⡴⠋⠀⡸⡀⠀ ⠀⠀⠀⠀⠀⠈⠠⠶⠿⡟⣇⣀⣀⣀⢔⣾⣿⣿⢏⡁⠀⠀⠈⠈⢫⡀⠀⢯⠎⡀ ⠀⠀⠀⠀⠀⢀⢀⣠⣤⣼⣿⢻⡿⣿⡿⢻⡙⣻⣿⣏⢀⠀⡤⠂⡎⢻⣆⢆⠘⠃ ⠀⠀⢀⠤⠊⢠⣿⣿⣿⢫⣧⣼⣷⣜⠉⣿⣿⣄⣿⣿⣿⣞⣁⡼⡠⣾⣿⣄⠀⠁ ⠀⠠⠀⢤⡔⢿⡿⣿⡿⣏⠃⠀⣠⢽⣥⠸⡏⡿⣷⡾⠻⣿⣿⣿⣷⣿⡿⠋⠀⠀ ⡄⠀⠀⢼⣇⡸⢃⠃⠙⢷⠲⣦⠙⠋⠟⠀⢹⢔⢟⡿⣿⣀⠈⣻⣿⣷⡏⠀⠀⠀ ⡇⠀⠀⢸⣿⠁⢀⠞⠁⠀⠀⠀⠀⠀⠀⠀⢠⣞⣉⢘⢛⣿⢿⣿⠀⢹⠁⠀⠀⠀ ⠀⠀⠀⢈⣿⡆⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢒⣾⢵⣫⣼⣿⣿⣧⡃⠀⠀⠀⠀ ⡆⠀⠀⠈⣿⣧⠀⠀⡔⠛⠛⢿⣗⡀⠀⠈⢺⡼⡛⠀⢹⢟⣿⠀⠀⠄⠀⠀⠀⠀ ⠻⡀⠀⡜⠀⢿⣆⠀⡇⠀⠀⠀⡟⠀⠀⠀⠀⡆⡇⢲⡟⣻⣿⠀⠀⠀⠀⠀⠀⠀ ⣷⣿⡿⢧⣄⣸⣿⣦⡀⠂⠐⠉⠀⠀⠀⠀⠈⣳⣖⣻⣿⣿⣿⢿⡀⠀⠀⠀⠀⠀ ⠈⢙⣿⣿⡿⢿⡁⠈⢉⡿⠶⢾⠄⠠⢤⣶⣾⠟⢿⠿⣛⠝⡡⠊⠈⠐⠠⠄⠀⠀ ⠺⠭⠁⣶⣶⡸⣯⠴⠈⠀⠑⣄⠀⠀⠈⠁⠈⠑⠖⡊⠀⠀⢰⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⡟⠻⣿⠋⡗⢶⣤⣤⣄⣑⡄⠀⠠⠄⠒⠈⠁⠀⠜⠜⡕⠅⠒⠀⠄⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠴⢶⣚⠛⠉⢉⣛⣿⣿⣿⡖⠶⠤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⣡⠴⠒⠛⠿⢿⣿⡿⠟⠁⠀⢿⣿⣦⣤⣤⣌⠉⠓⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⣠⠞⠁⠀⠀⠀⠀⠀⠈⢳⡄⠀⠀⢀⡽⠟⠛⠛⠋⠙⠲⣄⠈⠳⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⢀⣰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄⠈⠛⣦⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⢸⣻⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣀⠀⠈⢧⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡾⠀⠀⠈⢷⠻⣆⡀⠀⠀⠀⠀⠀⣠⠞⠁⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⡿⠀⠀⠈⣧⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⡴⠋⠁⠀⠀⠀⠀⠀⠀⠈⠙⢲⡶⠶⢶⡿⠷⠶⣶⣦⠤⠽⣦⡀⠀⠀⠀⠀⢀⡴⢏⡼⠃⠀⠀⠀⢻⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡾⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠛⠷⠤⢤⣭⣿⣭⠭⠤⠤⣶⠚⠻⡗⠒⠒⠋⠉⠐⠋⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⠴⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠸⢦⣄⣸⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠒⠒⠒⠦⣼⡆⠀⠀⠀⠀⠀⠀⠀⠀⢉⡏⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠁⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠘⠳⣦⣀⡼⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠹⣆⣴⠿⠃⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⢀⣀⣰⡃⠀⠀⠀⡀⠀⢀⡠⢴⡞⠀⠀⢤⣄⠀⠀⢀⡽⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠙⠒⠶⠖⠒⠛⠉⠉⠉⠉⠲⢄⡀⣉⡉⠉⢀⣠⠇⠀⠀⠈⠙⢷⡤⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⣀⣀⡉⠛⠦⣤⣀⠀⠀⠀⢀⠀⠀⣤⡀⠀⠀⣠⠶⠒⢦⣀⡟⠁⠈⣆⠉⠀⠀⠀⢀⣠⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡾⠷⣤⡾⠋⠉⢻⣧⠀⠀⠀⢻⠀⠀⠀⢸⡤⠴⠒⠋⠉⠀⣼⣿⣿⡿⣿⣿⣿⣶⣶⣶⣶⣶ ⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡿⡇⢠⠀⣼⣇⣼⣠⡖⠀⢳⣀⣤⣼⡇⠀⠀⠀⠀⣰⣿⠀⣿⡇⡿⠿⣿⣿⣿⣿⣟⣿ ⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⡿⠀⢧⣼⣤⠟⠉⠉⠹⡄⠀⠈⢻⡿⢿⣧⣄⣀⣤⣶⣿⣿⣀⣿⡇⠇⠀⣿⣿⣿⣿⡇⡻ ⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠁⠀⡼⠁⠀⠀⠀⠀⠀⠹⡆⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⢸⣿⣿⡗⠇ ⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣴⠃⠀⠀⠀⠀⠀⠀⠀⣿⣦⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆⣾⣿⣿⠇⠀ ⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀ ⡄⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛

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⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠭⠓⠒⠀⡇⡿⠀⠁⢸⡿⡇⠈⣿⣿⣛⠨⣝ ⢻⢿⣿⣿⣿⣿⣿⡿⠟⢩⣟⡟⠈⢀⣀⣀⣴⣷⠷⠒⠒⠛⠒⢻⠤⣿⢹⣿⣷⣮ ⣸⢸⢈⣻⠙⣿⣍⣴⠶⢿⣿⡟⠉⠉⠁⠀⠜⢁⠀⣀⣤⡴⣶⢿⠀⡟⣆⣿⣿⣿ ⣿⡜⠾⠛⠋⠉⠁⠀⣀⠀⠈⠃⠀⠀⠀⠀⠰⠷⣟⣇⣠⠤⢻⣾⠀⣧⢹⣞⢿⣿ ⡿⠆⣀⣲⣴⠶⠶⠶⣶⡖⠻⠄⠀⠀⠀⣀⠔⠚⠻⠗⠃⠀⢾⣿⢠⣿⣼⣿⣮⣻ ⠜⠎⠹⣅⠠⠤⠶⠾⠿⣯⠅⠀⠀⠀⠀⠁⢂⠀⠀⠀⠀⠀⠸⡿⢸⣿⣿⣿⣿⣿ ⠞⢒⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⣿⣿⣿⣿⣿⣿ ⠉⣡⠛⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⣠⡿⡀⣿⣿⣿⣿⣿⣿ ⣿⡏⠙⢷⡽⢦⡀⠀⠠⡤⣀⡤⣤⣤⠴⡶⡯⠋⠀⠀⣴⣿⣱⢹⣿⣿⣿⣿⣿⣿ ⣿⠃⠀⠀⠑⡜⡇⠀⠀⠈⠁⠛⠚⠛⠓⠁⠀⠀⣠⣾⣿⣷⡇⣼⣿⣿⣿⣿⣿⣿ ⣿⠀⠀⠀⠀⡇⢹⣦⣄⣀⠀⠀⠀⠀⠀⡀⠔⠛⠛⠻⠿⢿⢃⣿⣿⣿⣿⣿⣿⣿ ⣿⠀⠀⠀⢰⢠⡇⠈⠻⣿⡿⡷⠒⠒⠪⢀⠀⠀⠀⠁⠀⡞⠌⠉⠛⢿⣿⣿⣿⣿ ⣿⣆⠀⠀⡘⣸⠣⢀⠀⢀⠝⠀⠀⠀⠀⠀⠑⢄⠀⠀⢰⡙⠀⠀⡐⠀⠙⢿⣿⣿ ⠘⢿⡄⢀⢣⡏⠀⠀⠈⠍⠂⠀⠀⠀⠀⠀⠀⠀⠑⢄⡞⠀⠀⠀⠃⠀⠀⠀⠙⣿ ⠀⠘⣿⠮⠋⠀⠀⠀⠈⠀⠘⡀⠀⡐⠀⠀⠶⠲⠒⡞⠓⠀⠀⠀⠀⠀⠀⢀⢠⣼

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢀⣠⣴⠿⠗⠀⠀⠀⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢀⣴⠟⠉⠀⠀⠀⠀⠀⠀⠀⠉⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣄⣄⣀⣀⣀⣇⠀⠀⠀⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠛⠛⠋⠉⠉⠉⠉⠉⠁⠀⠀⠀⣀⣀⡀⠀⠀⣈⣹⣦⣤⣤⣶⣶⣶⣶⣤⣤⣤⣀⣀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣀⣤⡶⠟⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⢷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠪⠿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣾⠃⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡆⠀⠀⠀⠀ ⠀⠀⠀⠀⣾⠇⠀⠀⠀⠀⠀⠀⠀⢀⠏⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⣤⣤⣄⣀⡀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠈⣿⡀⠀⠀⠀ ⠀⠀⠀⢰⡿⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⣿⣿⡿⣿⣿⣿⢿⣿⣿⣿⣿⠇⠀⢸⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⢸⣇⠀⠀⠀ ⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠁⠀⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠈⠙⠉⠀⠀⠀⠀⠈⣿⠀⠀⠀ ⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⢠⣴⣶⣿⣿⣿⣿⣿⣿⣧⠀⠀⢠⣶⣿⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⣿⠀⠀⠀ ⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⢾⣯⣀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠛⠛⠛⠋⠁⠀⠀⠀⠉⠉⠉⠛⠛⠛⠁⠀⠀⠀⠀⠀⣿⠀⠀⠀ ⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⢶⣦⣤⣄⣀⣀⣀⣀⠀⠀⠀⠀⣀⣀⣀⣀⣠⣤⣤⣤⣾⠇⠀⠀⠀⠀⠀⠀⣠⡿⢀⠀⠀ ⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠈⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢉⣉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠇⠊⠀⠀ ⠀⠀⠀⠀⢹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠿⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⢡⡿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠋⢠⡿⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠄⠚⠁⠀⣴⡟⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⢟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⠟⠋⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⡶⣦⣤⣄⣀⣀⣀⣀⣀⣀⣀⣤⣤⣶⠾⠿⣭⣄⣀⣀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠉⠉⠉⠉⠉⢻⣿⣭⣍⣀⡀⠀⠀⠀⠀⢠⣍⢉⠙⠛⠒⠲⠦⠤⣤⣀⣀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠤⠀⠀⠀⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⠴⠋⢠⠔⠂⠀⠀⠒⠀⠀⠀⠙⠢⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡰⠁⠀⠀⠨⠶⠆⣀⣀⣫⢧⣱⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⠞⠀⠀⠀⡠⠀⠀⢀⣀⡀⠀⠀⡁⠀⠀⠀⢠⠜⢀⠲⢄⠀⠀ ⠀⠀⢀⡜⠀⠀⠀⡞⠀⣤⡜⠁⠀⢀⣄⠀⠙⡀⠀⢠⠁⡔⠁⠀⠀⢣⠀ ⠀⡔⢡⠁⠀⠀⠀⠑⠀⠀⠳⠤⠀⠈⠁⠀⠠⠃⠀⠸⣼⢀⠀⠀⠀⡜⠀ ⠈⣅⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⡀⢢⢠⠃⠀ ⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡒⠒⠀⢬⠂⠀⠀ ⠀⠀⠀⢣⠀⠀⠀⠠⠒⠀⠤⠤⠤⢄⡠⠒⡒⢤⡠⠧⢀⠁⠀⠘⡆⠀⠀ ⠀⠀⠀⠀⠑⢤⡀⠀⠀⠀⠀⠀⠀⠰⠀⡜⠀⠀⠀⠀⢸⠀⠀⠀⠸⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠑⠂⠤⣄⣀⣀⣠⣰⠀⠀⢀⠄⣠⡎⠀⠀⠀⠀⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢰⠘⢄⠀⠀⡀⠝⢲⣒⡾⠞⣉⡓⢄⠀⠀⢠⠇⠀ ⠀⠀⠀⠀⠀⠀⠀⡠⠛⠐⠈⠖⠙⠒⠄⠜⠀⠣⠮⠔⡡⢤⠑⠢⣧⠤⠤

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⠀⠀⠐⢰⠀⡶⢰⠀⠀⠐⢆⢂⠀⢆⠀⠂⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀ ⠀⠀⡇⡌⢰⡿⡎⡀⠀⠀⠀⠑⡵⣜⡆⠈⡄⠀⠀⠀⠀⠐⠀⠀⠀⠀ ⠀⠀⣱⡇⢸⡇⢇⢡⠀⠀⠀⠀⢡⠈⡿⡄⢸⡘⢄⠀⠀⡀⢃⠀⠀⠀ ⠀⢰⣿⣴⢼⣀⣘⣄⣧⡀⢢⠀⠀⠦⢴⠽⡄⠿⣌⠻⡅⠀⠈⡆⠀⠀ ⠀⠈⣿⠉⣼⡀⠤⠶⣭⠻⣦⡳⣄⠸⣄⠗⠛⢜⡊⠢⣹⢦⡀⡇⠀⠀ ⠀⠀⣇⣤⣼⣤⣄⣀⣌⣆⠈⠫⠺⠷⠇⣶⣤⣴⣷⣶⣾⣦⣽⣇⢀⠀ ⠀⠉⡟⢅⣀⣯⣿⣽⣿⠃⠀⠀⠀⠀⠘⢭⡀⢰⠾⠣⠿⠇⠈⠉⣸⠀ ⠠⠀⢁⠀⠀⠀⠀⠀⠀⠀⠐⢋⠂⠉⠑⠀⡀⠂⠀⠀⠀⠂⡘⢰⢻⠀ ⠀⢧⡈⡄⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡕⢹⠸⠀ ⢀⢸⣱⣜⡄⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⢸⡇⠀ ⠀⡆⢯⡎⣏⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠀⠀ ⠀⡘⡜⣵⡇⠑⢄⠀⠀⠀⠀⠘⠳⠅⠀⠀⠀⠀⠀⠀⡠⠞⣹⠃⢀⠀ ⠀⢱⡈⢜⢷⡀⠘⣿⠲⢄⡀⠀⠀⠀⠀⠀⠀⡀⠔⠊⠀⢠⠏⢠⡞⠀ ⠀⠀⢷⡀⠑⣟⣤⡈⠢⢼⣿⠑⢢⠤⠔⠂⠉⠀⠀⢀⡴⢃⣴⡿⠁⡀ ⠀⡀⠈⢮⢢⣌⡢⣍⣀⣿⣿⣷⡤⠇⠀⠀⢠⣴⣿⣯⣶⣿⣛⣤⡾⠁

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠛⠛⠻⣿⣿⣿⡟⠛⠛⠛⠛⠋⠉⠉⠉⠉⠛⠛⠛⠛⠛⠛⠛⠿⠿⠛⠻⠿⠿⠟⠛⠛⠛⠛⠛ ⠿⠉⠾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⢨⣿⣿⣿⣿⣯⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠁⠀⠆⠦⠦⠀⠀⠠⠰⠀⠀⠀⠀ ⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠐⠀⠀⠀⢸⣿⣿⣾⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⡀⢸⣿⣿⠙⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀ ⣤⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠐⠀⠀⠂⠀⣿⣿⢘⣿⣿⠇⠈⢿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠒⠐⠂⠀⠀⠀⠀⠀ ⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠖⢀⠀⠀⠀⠀⠀⢹⣿⣿⣿⡟⢀⠀⠈⢿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠅⢀⢄⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠈⠀⠀⠈⢿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⠋⠁⣈⣽⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⢻⣿⣦⡀⢀⡀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠇⠀⢀⣾⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⢹⣿⣧⣭⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣿⣿⣿⠋⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⠀⢠⠀⠀⠀⠀⠀⠄⢹⣿⣿⡄⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣠⣾⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣇⠈⠇⠀⠀⠀⠀⠀⠀⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠂⠀⠀⣈⣿⣿⣆⠑⠀⠀⠀⠀⠀⠀⠈⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⢿⣿⣿⣇⣀⣀⡀⠀⣀⣀⣤⣶⣾⣿⡿⠿⠿⠿⠿⠿⠿⠿⣿⢷⣶⣤⣄⣀⡀⠀⠀⠈⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠙⢻⣿⣿⣿⣿⣿⠿⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⣿⣶⣤⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣤⣄⣀⣀⣠⣤⡆⠀⠀⠀⠀⠀⠀⣠⣤⣴⣦⣾⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⡛⠉⠛⠋⠉⠉⠉⢙⣿⣿⣋⣀⡀⠀⠀⠀⠀⠀⠀⠈⢠⣼⣿⣿⣯⠻⣿⣦⡀⠀⠀⢀⣠⣴⣿⠟⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣴⣶⣶⡶⠾⠿⠿⠿⠛⠿⠏⠀⠀⠀⠀⠀⠀⡄⠀⠈⠉⠉⠉⠀⠀⠙⢿⣿⣦⣴⣿⠿⠛⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⣀⡀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠈⠀⡄⠀⠀⠀⠀⠀⠀⠈⢀⡀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⡁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣴⣾⡿⠛⠛⠛⠛⠿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣦⡀⠀⠀⠀ ⠀⠀⠀⠀⢀⣾⡿⠋⠀⠁⠀⠀⠀⠀⠈⢻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⣰⣿⠋⢉⠻⣿⣦⠀⠀ ⠀⠀⠀⢀⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⠀⢰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⡀⠰⢀⠀⠀⠀⠀⠀⣿⣿⠀⠈⠀⢻⣿⡇⠀ ⠀⠀⠀⢸⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⠀⢸⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⣿⡇⠀ ⠀⠀⠀⠈⢿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⢀⣻⠃⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⠀⢸⠀⠀⠀⠀⠀⣽⣿⡄⠀⠀⢰⣿⠇⠀ ⠀⠀⠀⠀⠈⢿⣷⣦⣤⡀⠀⠀⠀⠀⣠⣾⡿⠁⢰⠃⠀⠀⠀⠀⠀⠀⠀⢰⣿⡏⠀⣹⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣄⢀⣾⡟⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⠛⠿⡷⠶⠶⢾⠿⠟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠶⠿⠾⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⡟⠀⣠⡆ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⠿⠛⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⠏⠙⣿⣆⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡟⠁⠀⠀⠘⣿⣧⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡏⠀⠀⠀⠀⠀⠙⣿⣆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⣿⣿⣧⡀⠀⠀⠀⠀⠀⠘⣿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣏⣽⡿⠀⠀⠀⠀⣠⣼⣿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠿⠋⠀⠀⣀⣴⣾⣿⠟⠁⠀ ⣧⠀⠀⠀⠀⠀⠀⠀⠀⣾⡏⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⢀⣴⣾⡿⠟⠋⠁⠀⠀⠀ ⣿⠀⠀⠀⠀⠀⠀⠀⣸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡄⠀⠀⠀⠀⠀⠀⣸⣿⣾⠟⠉⠁⠀⠀⠀⠀⠀⠀⠀ ⣽⣷⣤⣤⣼⣯⣤⣤⣿⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣤⣭⣿⣷⣦⣤⣤⣤⣤⣴⣿⣿⣥⣤⣤⣤⣤⣤⣴⣤⣤⣤⣦

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⠀⠀⠀⠀⠀⣀⣤⣴⡶⠛⠋⠉⢀⣼⣿⠟⠉⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⠋⣼⠁⣰⠏⠁⣴⡿⠉⠀⠀⠀⠀⣼⡏⢿⡄⠀⠀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀ ⠀⠀⠀⢚⠛⠉⠁⠀⠀⠀⠀⢀⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠟⠁⠀⢰⣇⣾⠋⢀⣴⠟⠁⠀⠀⠀⠀⠀⣿⠀⠈⢿⡄⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠹⡆⠀⣷⡄⠀ ⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣠⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠟⠁⠀⠀⠀⣼⠟⢁⣠⡿⠋⠀⠀⠀⠀⠀⡄⢠⡟⠀⠀⠈⣿⡄⠀⡄⠀⢹⣧⠆⠀⠀⠀⠀⠸⣄⠸⣷⠀ ⠀⠀⠀⡟⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠿⠋⠀⠀⠀⠀⣠⡿⢋⣴⣾⠏⠀⠀⠀⠀⠀⠀⢠⠁⣼⡇⠀⠀⠀⠈⢻⣆⢹⡀⠈⢿⡎⢦⠀⠀⠀⠀⠹⡄⠹⡄ ⠀⠀⢸⡷⠀⠀⠀⣠⠟⠃⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠾⣿⠉⠀⠀⠀⢀⣤⣞⣯⣶⠛⢡⡟⠀⠀⠀⠀⠀⠀⢀⣾⢀⡿⠀⠀⠀⠀⢀⡀⣻⣦⣁⣀⢘⣿⡞⢦⡀⠀⠀⠀⠹⣆⠳ ⠀⠀⢸⠇⢀⣤⢞⣡⣴⣶⠶⠶⠚⢛⣛⣽⡿⠟⠛⠷⠶⣿⣦⣤⣠⣴⡿⠛⠉⢰⡏⢀⡿⠁⠀⠀⠀⠀⠀⠀⣸⣁⣸⣧⡶⠞⠛⠛⠛⠛⠛⠻⣿⡟⠛⠻⣿⡞⢷⣦⡄⠀⠀⠘⣦ ⣀⣠⣾⠿⠋⠉⠉⠁⠀⣀⣤⣶⢿⡿⠋⠁⠀⠀⠀⠀⠀⣿⠀⠉⠉⠁⠀⠀⢀⡿⠀⣼⠃⠀⠀⠀⠀⠀⠀⢠⡿⢛⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣄⠀⠘⣿⡄⠳⠄⠀⠀⠀⠈ ⠛⠉⠀⠀⢀⣀⣠⣴⠿⠋⠁⣰⠟⠁⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣼⠃⣴⡏⠀⠀⠀⠀⠀⠀⢀⣾⠇⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⡀⠙⢿⣄⠀⠀⠀⠀⠀ ⠿⠻⢿⠛⠛⢉⡼⠋⢀⣠⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡀⠀⠀⠀⢠⠏⣰⡿⠀⠀⠀⠀⣰⠏⢠⣼⣿⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠈⢿⣆⠀⠀⠀⠀ ⡄⠀⣿⠀⣰⡟⢁⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢠⠇⠀⠀⢠⣾⢠⣿⠁⠀⠀⢀⣾⠏⢀⡞⢻⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣧⡀⠻⣦⠹⣦⠀ ⡇⠀⢹⣾⣯⠶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⣼⠀⠀⠀⣼⣿⣿⠏⠀⠀⣠⣾⠏⣰⠟⢠⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡙⢷⡈⢷ ⣇⠀⢸⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡏⠀⠀⣰⡿⢋⡟⠀⢠⡾⣿⣥⠞⠁⢀⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⣿⣦ ⢻⡀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⠋⡇⠀⣰⡿⢁⡾⢁⡴⣫⣾⠟⠁⠀⣠⡿⠁⠀⠀⠀⠀⣀⠀⠠⠤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠿ ⠸⣇⢸⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠤⠶⠞⠛⠋⠉⣀⣴⡇⣴⠟⢀⣾⡷⠿⠞⠛⠁⠀⠀⠴⠋⠀⠀⠀⠀⠀⠀⠹⣷⣦⣤⣀⡀⠉⠙⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⣀⣀⣤⡿⠀ ⠀⢻⣮⣿⠙⢿⣶⣶⣶⣦⣤⣤⣤⣤⣤⣤⣴⣶⣶⣿⣿⣿⣼⡿⣶⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠛⠿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⠟⢹⠇⠀ ⠀⠈⢻⣿⡀⢠⣽⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠿⣿⣿⣿⣿⣿⠿⠿⠿⠟⠻⠷⣦⡏⠀⢠ ⠀⠀⠀⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠀⢠⠜ ⡄⠀⠀⠀⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⣰⠏⠀ ⣷⠀⠀⠀⠸⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⢀⣾⡟⠀⠀ ⠹⣷⡄⠀⠀⠈⣿⡻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⢠⡞⣿⠁⠀⡞ ⠀⡾⠻⣶⡀⠀⠈⢷⡈⠻⢶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢋⣴⠏⢰⡟⠀⢠⡇ ⡄⢳⠀⠈⣿⣦⣀⠈⢻⣆⠀⠈⠙⠷⠶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣵⠟⠁⠀⡾⠀⠀⣼⠀ ⢳⡸⡇⠀⢸⣏⠻⣷⣄⡙⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠟⠁⠀⠀⣼⡇⠀⣸⡇⠀ ⠈⣿⣿⠀⠈⣿⡀⠹⣎⠙⠻⠿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠾⠛⠉⠀⠀⠀⠀⣸⢿⠁⠀⣿⠀⠀ ⠀⠘⢿⣷⠀⠸⡇⠀⠹⣧⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢳⡏⠀⣾⠇⠀⠀ ⠀⠀⠈⢿⣇⠀⣿⣤⠶⠼⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⢃⣿⠁⢰⡟⠀⠀⠀ ⡄⠀⠀⢀⣿⣦⠺⣿⡀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠁⣼⠇⢠⡟⠀⠀⠀⣸ ⣧⠀⠀⠀⠻⣟⣷⣿⣷⠀⠀⠈⠻⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠀⢰⡏⢀⡿⠀⠀⠀⣠⣏ ⢻⣇⠀⠀⠀⠙⣿⣿⣿⣷⠀⢶⡀⠈⠙⢷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⠟⠁⠀⢠⡿⢁⡼⠁⠀⠀⣰⣿⡏ ⣆⢻⣧⠀⠀⠀⠙⣿⣿⣿⣦⡈⢻⡄⠀⠀⠉⠻⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠟⠉⠀⠀⠀⢀⣾⢃⡾⠃⠀⠀⣴⣟⡿⣠ ⣿⣆⢻⣧⡀⠀⠀⠘⣯⣿⣿⣿⣦⣿⡄⠀⠀⠀⠀⠉⠛⢷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣯⣤⣄⣀⣀⣀⣀⣾⢡⡾⠁⠀⢠⣾⠟⣿⠃⠙ ⣿⣿⣦⠹⣷⡀⠀⠀⠘⣿⣿⣿⡉⢻⣿⣆⣠⣶⣶⣿⣿⣿⣿⣿⠛⠶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠞⠋⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠏⠀⠀⣰⣿⣁⣾⡏⠀⠀ ⣿⣿⣿⣷⡜⢿⣆⡀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠈⠙⠛⠷⢤⣄⣀⡀⣀⣠⣤⠴⢞⠛⠁⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠃⠀⣠⣾⣿⣿⣿⣿⣿⣷⣦

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⣠⠔⠛⠀⠀⠢⢤⡀⠀⠀⠀⠀⠀⠀⠀ ⣀⣀⣀⣀⣀⠀⠤⠤⠤⠤⢤⡀⠀⠚⠁⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠒⣂⡤⠶⠛⠚⠉⠉⠉⠛⠒⠶⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣦⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣼⠋⠀⠀⠀⠀⠀⡠⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⠀⠀⠀⠀ ⠀⠀⠀⡾⠁⠀⠀⠀⠀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀ ⠀⠀⣸⠁⠀⠀⠀⠀⠌⠀⠀⢠⣴⣶⣶⣶⣦⣤⠀⢠⣤⣤⣤⡀⠀⠈⣇⠀⠀ ⠀⠀⡏⠀⠀⠀⠀⢸⠀⠀⠀⠈⠉⣻⣿⣈⣉⠉⠀⠈⣿⣏⠛⠁⠀⠀⢹⠀⠀ ⠀⠀⡇⠀⠀⠀⠠⣜⠀⠀⠀⠀⠿⠿⠿⠿⠟⠃⠀⠛⠛⠿⠿⠀⠀⠀⢸⠀⠀ ⠀⠀⢧⠀⠀⠀⠀⠈⡛⠓⠶⠤⠤⣤⣤⣤⡤⠤⠤⠶⠶⠛⠀⠀⠀⢀⡾⡀⠀ ⠀⠀⠸⡆⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠐⠒⠚⠁⠀⠀⠀⠀⡠⢹⠃⠀⠀ ⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠊⣰⠋⠀⠀⠀ ⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠳⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠞⡡⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣿⠒⠒⠒⢶⣒⣛⠉⠉⠐⢒⠂⠤⠤⠄⣀⣀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀ ⠀⠀⢀⡀⠀⠀⠀⠀⢀⠶⡄⠀⠀⠀⠀⠀⠀⡠⠊⠁⢻⠀⠀ ⠀⠀⢸⠻⡢⡀⠀⣀⠼⠄⠙⢦⣷⡶⢂⣠⡾⠒⠒⡄⢸⡇⠀ ⠀⠀⣘⣀⡘⠾⠊⠀⠀⠀⠀⠀⠀⠀⢈⣿⠤⡄⠀⡇⢸⡇⠀ ⠀⠀⢇⠀⠀⢀⠂⠀⠀⠀⠀⣠⢀⠔⠀⠀⢠⣡⢼⡖⡆⠃⠀ ⠀⠀⠀⢹⠖⡆⠀⠀⣠⡠⠖⢩⠧⠤⠀⣀⠈⠧⢀⡷⠸⢤⠀ ⠀⠀⢠⠃⢰⠀⣴⠿⠁⠀⠀⡠⠀⠀⠀⠀⠁⠀⠋⠀⡰⣜⡀ ⠀⣀⠎⠀⢹⣧⠋⠀⠈⠑⠢⡡⢤⡖⠒⠒⢢⠀⠀⠀⠁⠂⢄ ⠈⠣⣀⣀⣦⡇⠀⠀⠀⠀⠰⠀⢸⡇⠀⠀⡼⠀⢠⡄⡠⠒⠉ ⠀⢀⡜⠋⠛⠀⠤⠀⠀⠀⡇⠀⢸⣃⡠⠊⠀⡀⠚⢍⠀⠀⠀ ⠀⡟⢲⣦⠀⠀⠀⠀⠀⠄⠉⡩⠖⠚⠡⠀⠀⣇⠘⡈⠑⠀⠀ ⠀⠻⣩⠥⠤⢤⣄⢀⡀⢤⠞⠀⠀⢠⣂⣨⠄⠘⠂⠣⠀⠀⠀ ⠀⠀⠈⠀⢰⣿⣀⠟⢒⡡⠔⠚⡒⣹⠛⡵⢇⠄⠀⠀⠀⠀⠀ ⠀⠀⠀⡠⠊⢹⠖⣾⠏⢀⣀⠤⠖⠁⠀⠈⣉⡆⠀⠀⠀⠀⠀ ⠀⡠⠊⢀⡴⡋⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠈⠑⢄⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠴⣶⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠁⠀⢹⣧⠀⠀⠀⠀ ⠀⠀⠀⣿⣿⣄⠀⠀⠀⠀⠀⠀⢠⣿⠀⠨⡳⣄⠀⣤⣀⣀⡀⠀⠀⢀⣾⠋⠀⢀⡀⠀⠸⣿⡀⠀⠀⠀ ⠀⠀⠀⡇⠈⢯⡳⣄⠀⠀⣀⡤⠾⠛⠢⠀⠈⠺⣿⣿⣿⠋⠙⣄⣴⣿⠛⠉⠉⠉⢳⠀⠀⡇⡇⠀⠀⠀ ⠀⠀⠀⣷⠀⠀⢻⣾⣷⠞⠉⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⢻⣿⠃⢀⡀⠀⠀⢸⠀⠀⡇⡇⠀⠀⠀ ⠀⠀⡶⠾⠖⠒⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠟⠋⠉⡇⠀⠀⡼⠀⢠⢇⡇⠀⠀⠀ ⠀⠀⢿⡀⠀⠀⠀⠀⢠⠋⠀⠀⠀⠀⠀⠀⠀⢀⡆⢀⣠⠖⠃⠀⠀⠀⣰⣃⣠⣾⡿⠶⣾⢸⠁⠀⠀⠀ ⠀⠀⠈⠻⣦⣄⠀⣰⠃⠀⠀⠀⠀⠀⠀⢀⣠⡿⢳⡞⠁⠀⠀⠀⠀⠐⢫⡟⠁⠉⢹⣤⠃⡞⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⠟⠛⡏⠀⠀⠀⢀⣴⣣⡴⠟⠋⠀⡾⠿⠗⠦⠤⠤⢤⣀⠀⠛⠂⢀⣸⠏⠘⠛⠻⡄⠀⠀ ⠀⠀⠀⣸⠏⠀⣸⡇⠀⢠⣶⡿⠋⠁⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠟⠀⠀⠀⡄⢰⠃⠀⠀ ⠀⠀⢠⡟⠀⢀⣿⡇⢀⣿⡏⠁⢀⣀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠠⠧⠒⠁⠀ ⠀⢀⡾⠁⠀⠀⣹⣧⡼⠙⠀⠀⠀⠀⠉⠲⣤⢇⣴⠤⣶⡒⠚⠛⠓⠒⣦⠀⠀⠀⠀⠀⠉⠙⠒⢤⡀⠀ ⣾⠋⠀⠀⠀⢀⠏⣿⠁⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⢰⣿⡇⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⢀⣀⡤⠿⠂ ⠈⠷⣤⣀⣀⣾⢲⡟⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⣼⣿⠇⠀⠀⠀⡰⠃⠀⠀⠘⡶⢀⡴⠋⠁⠀⠀⠀ ⠀⠀⣀⡽⠛⠻⠾⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⢹⡿⠀⠀⢀⠜⠁⠀⠀⢠⣾⡟⠛⠀⠀⠀⠀⠀⠀ ⢀⣼⠏⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⢸⣀⣀⣠⠼⠗⣂⡒⠃⠀⠀⠀⣆⠀⢀⠉⢷⣄⠀⠀⠀⠀⠀ ⣼⠟⠛⣒⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠃⢀⡼⡴⠛⠋⠀⠄⠀⠀⠈⢻⡀⠈⡆⠀⠉⠓⠀⠀⠀⠀ ⣿⣦⠼⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠎⠀⠀⠀⠀⣠⠀⠐⠒⠒⠛⣇⡀⢻⡀⠀⠀⠀⠀⠀⠀ ⠈⠻⣤⡖⠒⠛⠛⢲⣶⠤⣀⣀⣤⠴⢚⡿⠁⠀⠀⣀⠄⣴⣃⣠⣴⡖⠉⠉⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠉⠀⠀⢰⣿⡏⠀⢹⡷⢤⠴⠋⢀⣠⡴⠯⠴⠚⢻⡿⠿⣋⣼⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⡷⠖⠋⢀⣤⡖⠋⠉⠀⠀⢠⠏⣰⡟⠀⠘⣿⣩⣤⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⠞⠁⢈⣽⡟⢛⣿⠿⠀⠀⠀⣀⣤⠼⠞⠋⠀⠀⠀⠈⢉⣉⣃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⠞⠁⠀⢀⣸⠿⠀⠿⠧⠤⠤⠶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢯⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⠔⠁⠀⢀⣴⠟⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣄⠀⠀⠀⠀⠀⠀⠀

⣥⣿⢀⡜⠁⣾⢠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀ ⣽⣏⡞⣠⠾⣿⣯⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠈⢣⠀⠀ ⣿⡟⡴⠃⠀⣿⡞⣷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⢻⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⣀⣠⠀⠀⠀⠀⡄⠀ ⣿⡽⠁⠀⠀⣿⣿⢸⡆⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⡸⣄⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⢀⣸⣀⣀⣙⣷⣀⣀⣀⣀⣤⣤⣼⣿⣿⠯⠛⢷⠀⠀⠀⠀⢳⣠ ⣿⠁⠀⠀⠀⡟⢿⢸⣧⡄⠙⡟⠿⣶⣦⣤⣀⣀⣰⣃⣹⡄⠀⠀⠀⠀⠀⠘⣇⢹⡇⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠘⢿⣟⣿⣻⡿⠿⣿⡿⠛⠋⠉⢨⡇⢹⣦⠀⠘⣆⠀⠀⠀⢸⡿ ⠟⠀⠀⡄⠀⠀⢸⢸⢏⣇⠀⡇⢠⢸⡏⠛⠿⣿⣿⣦⣬⣿⡿⣿⣿⣾⡖⠀⢻⡸⣧⡀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⢸⠀⠉⣁⡀⡆⠘⢿⡄⠀⠀⢸⡇⢀⣻⣧⠀⣿⣀⣀⠀⠈⣿ ⠂⠀⢸⠁⠀⠀⢸⢸⢸⠈⠀⡇⢸⢸⠀⠀⢠⢿⠁⠘⠉⠉⢿⡉⠉⠙⠂⠀⠈⣇⢻⡇⢠⠀⠀⠀⠀⢸⠀⠀⠀⠀⢸⠚⠉⠉⠓⠃⠀⠈⣿⣤⣴⣿⣿⣿⣿⣿⣿⣿⣟⡀⢰⠀⢻ ⠀⠀⡼⠀⠀⣼⣿⢸⠘⠀⠀⡇⠈⣸⠀⠀⡾⡏⢀⣀⣀⠀⠈⣧⠀⢦⠀⠀⠀⠸⡌⢿⡄⠃⠀⠀⠀⣿⡀⠀⠀⠀⢸⢀⣠⠀⢀⣤⣶⢾⣿⣿⣻⡿⠉⠙⢿⣿⣿⢿⡟⠛⠃⡇⢸ ⠀⠀⡇⠀⠀⠸⡟⠲⢦⠀⠀⣧⣿⣿⣿⣽⣿⣷⣶⣄⣉⠳⢦⣈⣷⣨⢧⡀⠀⠀⢱⡘⣿⡄⠀⠀⠀⣿⡇⠀⠀⠀⢸⢋⣤⣾⣟⣿⣿⣿⣿⣿⣿⠀⠀⠀⣶⣼⣿⡿⡇⠀⠘⢣⠀ ⠀⢰⡇⠀⠀⠰⣿⣄⡈⢙⣶⣿⣿⠻⠉⢻⣿⣿⣿⣿⣿⣿⣶⣄⡀⠹⣷⣆⠀⠀⠀⢷⡙⠀⠀⠀⢰⡏⣷⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⡇⠀⠀⣿⣿⣿⣿⡇⠀⠰⣼⠀ ⠀⢸⠇⠀⠀⢠⡇⠙⢿⣍⣿⣿⠃⠀⡇⣿⣿⢿⣿⣿⣿⣻⡻⣟⣿⣶⣬⡻⣧⡀⠀⢼⣷⣄⠀⠀⣾⠇⢹⣠⣴⣿⠟⣿⣿⡏⠛⠻⠃⠀⣼⣿⣿⡇⠀⢠⣿⣿⠟⢠⡇⠀⢀⡏⣆ ⠀⣾⠀⠀⠀⡞⡇⠀⠓⠿⣿⣿⡆⠀⡇⡏⣿⣿⣻⡉⠙⣿⠟⠁⣿⣿⣟⡟⠿⠻⢦⡌⠻⣿⡄⢀⣿⠀⢹⡇⢀⡿⠀⣿⣿⣿⣦⣀⣀⣸⣿⣿⣿⡏⠀⠜⠛⠋⣀⢸⡇⠀⢸⢱⡏ ⢰⡟⠀⣠⡾⠁⡇⠀⠀⢀⣿⠹⣿⡄⣿⡇⢿⣿⣿⣷⡄⠀⠀⣸⣿⣿⣾⡇⠀⠀⠀⢹⣦⡹⣷⣼⠏⠀⢀⣇⡞⠁⠀⢻⣿⣿⣿⣿⣿⣿⣯⢛⡿⠁⠀⠀⠀⣤⡇⢸⡇⠀⡏⣼⢇ ⣿⣡⣾⣿⠃⢸⡇⠀⠀⣼⠻⡄⠘⣿⣽⡇⠈⣿⣾⣿⣿⣦⣾⣿⣿⣿⣏⡇⠀⠀⠀⢸⠏⢻⣾⣿⣶⣤⣾⡞⢀⡞⠀⢈⣿⣿⣿⣿⢿⣿⡿⠏⠀⠀⠠⣴⠸⣧⡇⢸⠁⠈⠁⢸⢸ ⣿⣿⢿⡏⠀⣼⡇⢀⣼⠇⠀⣷⡀⠈⢿⣿⣄⠘⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⣠⣾⣰⣿⡏⣿⣿⣿⠿⣤⠏⠀⣰⠋⣴⢋⡛⣛⣋⣝⣁⣤⣴⡞⠙⠓⠀⠀⡄⢸⠀⠀⠀⠸⣼ ⣾⡿⣾⠁⢠⣿⠀⣼⣿⡀⠀⢸⣧⠀⠈⣠⢆⠀⠈⠙⠻⢿⣷⡾⠏⠀⢀⡠⣾⣿⣿⡿⣻⢟⣾⣿⣿⠃⣰⠃⢀⡾⢁⡾⢩⠿⠛⣳⢿⢟⡿⠋⡽⢃⡀⠀⢀⡼⡇⣿⠀⠀⠀⠀⣿ ⣽⣽⠇⠀⣼⣟⣞⣋⣼⣇⠀⠀⢿⡀⠈⠱⠟⠒⣦⣄⡀⠀⢀⣀⣠⣴⡏⣰⢋⣾⡏⣴⢻⣿⣟⠛⠃⣰⠃⢠⠟⢠⠞⣰⠋⡼⡿⣱⣯⠞⢠⡟⣡⣾⢦⠞⡾⣹⠀⡿⠀⠀⠀⠠⢻ ⣿⡏⠀⢸⣿⣿⢟⣽⣿⣿⠀⠀⢸⣇⡸⠀⣠⡴⠋⣿⡿⣛⠛⣽⡿⠋⣰⢣⠏⡞⣼⣱⠿⠃⠙⠧⠘⠁⠀⠏⣰⠏⡰⠃⢼⡟⠱⣻⠃⢠⠟⡴⣿⢣⢋⠞⢀⣵⣾⡇⠀⠀⠀⠀⢺ ⡿⠀⠀⠏⢹⣃⣿⣿⣿⣿⡆⠀⠀⣿⣇⣾⠟⢁⡞⣟⡵⢃⣼⡟⠁⡼⣱⢃⡞⢘⡟⠁⠀⠀⠀⠀⠀⠀⠀⡴⠁⠐⠃⢀⣾⣤⡼⠁⢠⣏⡜⣽⠁⢠⠏⣠⠾⢃⣿⠃⠀⠀⢠⠃⠘ ⢁⣤⡶⢾⣿⣏⢻⣟⣿⣿⡇⠀⠀⣿⣿⠏⣠⢏⣾⠟⢠⣞⡞⢀⡞⢱⢃⡞⠀⠈⠀⠀⠀⠀⠀⠀⠀⣀⣈⣠⠤⠖⠊⠉⢻⣿⠃⠀⠉⠉⠈⠹⠞⣡⣾⡷⣁⣼⣿⠀⠀⣠⠆⠀⠀ ⣋⣥⣾⣿⣿⣻⠈⢿⣿⢿⡇⠀⢠⣾⡏⡰⢃⣾⠏⢠⢿⠞⠀⠎⣀⠐⢦⣤⣤⠤⠖⢲⡖⢲⠒⠋⠉⠁⠀⡀⠀⠀⠒⢋⡿⠃⠀⠀⠀⠀⣀⢸⣾⣿⣿⣷⣿⣿⡜⠀⢀⣾⣏⠀⠀ ⣯⣼⡟⢻⣻⣿⣦⠈⠛⢛⣿⠀⣹⡟⡿⣥⣿⠏⣠⢿⠏⢀⡀⣄⣸⠀⠀⠻⣿⣗⣒⣒⣧⣶⠒⠚⠉⢉⣀⣀⣠⣄⡀⢻⠀⠀⠀⠀⢀⣠⣿⣼⣿⠋⢹⢹⣿⣿⡇⠀⣼⣿⣝⣆⠀ ⣿⠉⠀⠈⢿⣏⣿⣾⣿⠿⣿⢰⡿⠄⠀⠻⠛⣶⣧⣀⢰⡄⢻⡄⠀⠀⠀⠀⠈⣀⠀⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⠀⢷⢸⠀⠀⣠⣴⣿⣿⣿⡟⠁⠀⠸⣾⣿⢸⡀⢠⣿⡏⠀⢈⣷ ⢿⣆⠀⠀⠈⣿⣽⣷⡀⠀⣿⡿⠁⠀⠀⠀⠀⠁⠈⠛⢿⣿⣴⣧⣤⣤⣀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡏⣷⣿⣿⣿⣿⣿⠟⠀⠀⠀⢠⣿⣿⡌⡇⣾⡏⠀⠀⣼⠟ ⠈⢻⣧⠀⠀⠸⣿⡿⣷⡤⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠙⢿⣿⣿⣿⣿⣶⣤⣄⡏⣾⠁⠀⠐⠄⢢⠀⠀⢀⣠⣾⣇⣽⣿⣿⣽⠋⠀⠀⠀⠀⠀⣼⣿⢹⣇⢹⣸⠃⠀⣸⠏⣼ ⠀⠀⠻⣷⡄⠀⠻⣿⡞⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠙⢿⣿⣿⣿⣿⣿⡇⣿⣿⣶⡦⣼⣼⣤⣾⣿⣿⣿⣿⣿⣿⢟⣿⣦⡀⠀⠀⠀⢰⡿⢸⠈⣿⠀⢿⡆⢰⡟⣰⠏ ⠀⠀⠀⠘⢿⢀⠀⠈⢷⣽⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⢸⣯⣿⡿⣿⣿⣧⢻⣿⣿⣿⣿⢸⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠈⠻⣦⡀⢰⡿⡇⢸⡆⢸⡇⠀⢡⡟⢰⡏⠀ ⠀⠀⠀⠀⠘⣆⠀⠀⠈⣳⣷⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠸⣷⠙⢷⣌⢹⠻⢼⣿⣿⣿⣿⣿⡿⢛⣿⣿⢟⣽⡿⡟⠁⠀⠀⠀⠙⢷⣄⣀⡀⢸⣧⠘⡇⢀⡿⢡⡟⠀⠀

⠛⠋⠁⢀⣿⣶⣽⣿⣿⣿⣿⣿⣷⣴⣶⣾⣋⣯⣥⣬⣭⣿⡓⠶⢤⣀⡀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀ ⠄⠒⠉⠀⠈⠙⠛⠛⠻⣿⣿⠟⡟⠙⢻⣷⣦⡀⠀⠀⠈⠹⣷⠀⠀⠈⢩⣳⣦⣤⣤⣭⣵⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⠴⡿⠃⢸⠀⠀⠘⣿⣿⣷⠀⠀⠀⠈⠋⠀⠀⠀⠀⠈⠉⠓⠲⢤⡀⢀⡀⠈⠭⠟⠲⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⠞⠁⡼⠁⠀⠘⣆⠀⠀⠀⠉⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠤⠶⠶⠿⠿⠿⣷⣍⠳⢤⡀⠀⠀⠀⠉⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡼⠋⠀⢸⠃⠀⠀⠀⠈⠳⢄⣀⣀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⡞⠁⠀⠀⢾⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⡀⠀⠀⠀⠀⢀⣤⡶⠾⢿⣿⣿⣿⣶⣦⣤⣀⠀⠈⠳⣄⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠑⢈⡟⠀⠀⠀⠀⠉⢧⠀⣦⣀⠀⠀⢀⠞⢁⡜⠁⠀⠀⣠⡼⠛⢇⠀⠀⠀⠛⠿⢿⡿⠿⠛⠛⢷⣦⡀⢸⣦⠀⡇⠀⠀⠀⠀⠀⠀⠀⠠ ⠀⣸⠁⠀⠀⠀⠀⠀⠀⢿⠀⠈⠉⠒⠛⠊⠁⠀⠀⢀⡾⠋⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡹⠿⣿⣿⣶⣶⣶⣶⣶⣶⣶⡄⠀⠀ ⣀⣿⠀⠀⠀⠀⣾⣄⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠈⠑⠢⠤⠤⠤⠤⠖⠚⠉⠀⢀⣾⡿⣿⣿⣶⣶⣤⣤⣤⣤⣤⡀ ⠉⣿⠀⠀⠀⢸⣿⣿⠗⢤⡀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⣹⠃⣸⠛⢿⣯⣭⣉⠛⠛⠛⠃ ⢀⣿⠀⠀⠀⣿⣿⡃⠀⠀⠉⠲⣄⡀⠀⠀⠀⠀⠙⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⢠⠏⢀⡟⠀⠀⠙⠻⣿⣿⣶⡆⠀ ⠋⢻⠀⠀⠀⣿⣿⣿⣷⣤⣀⠀⠀⠉⠒⠦⢄⣀⠀⠀⠈⠑⠲⠤⣀⣀⠀⠀⠀⠀⠀⣀⡤⠞⠋⠀⢠⡟⠀⣸⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀ ⠀⢸⡄⠀⠀⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀⠀⠀⠈⠉⠑⠒⠤⠤⣤⣄⣀⣉⣭⡿⠟⠉⠀⠀⠀⠀⣠⠏⠀⣠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀ ⠀⠈⣧⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⣠⠟⠀⠀⠀⠀⠀⢀⡴⠃⠀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢹⡄⠀⢹⣿⣿⣿⠿⠛⠛⠛⠛⠛⠛⠿⢿⣿⣿⣿⣶⣦⣤⣤⠞⠁⠀⠀⠀⠀⣠⡶⠋⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⣷⠀⠈⢿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⡿⠋⠁⠀⠀⣀⣠⡴⠞⠉⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀ ⠀⠀⠀⠘⣆⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣞⣁⣀⣤⠴⠖⠛⠉⠁⠀⢀⣠⠖⠉⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⠀⠀⠀⢠⣾ ⠀⠀⠀⠀⠹⣆⠀⠀⠙⠲⢤⣀⣀⣀⣀⠤⠞⠛⠿⣭⣍⠡⠤⠤⠤⠤⠤⠤⠖⠚⠉⠀⠀⠀⠀⠀⠀⢀⣠⡤⠞⠋⠀⠀⠀⠀⠀⣰⠟⣿ ⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠶⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⠴⠂⠀⠀⠀⠀⠀⢀⣠⡾⠃⠀⣿ ⠀⠀⠀⠀⠀⠀⠘⠦⢤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⣉⣩⣿⣿⣿⠛⠛⠉⠉⣁⣀⣀⣀⣤⡤⠤⠶⠚⠋⠁⠀⠀⢠⡏ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠛⠛⠛⠒⠒⠺⣿⠛⠋⠉⠉⠉⠈⣧⣾⣿⣿⡇⠀⠀⠀⠻⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡷ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⣀⣤⣴⣿⣿⣿⣿⣿⡷⠚⠶⢤⡀⠉⠛⠶⢤⣤⣄⣀⣀⠀⠀⠀⠀⠘⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠹⣦⣀⣤⣤⠶⠞⠋⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡷⠞⣿⠙⢿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣏⣴⠞⠁⠀⠀⠙⢿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠈⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣾⢀⠈⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⡇⠸⠀⠀⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠶⢒⢲⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣇⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠖⠛⠁⠀⠀⠀⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⢘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠛⠉⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⠀⣠⢴⢿⣽⣉⠉⠙⠿⣿⣄⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⢤⣤⣴⡋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⣿⠃⣵⣿⣿⣿⠿⡶⠀⠙⣟⢷⡀⠀⠀⠀⠀⣴⢋⣼⣿⣷⣦⡀⠙⢳⡄⠀⠀⠀⠀⠀⠀⠀⣰⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣯⣀⣈⣀⣉⣥⣤⣤⣤⣤⡾⠋⠉⠙⠛⠲⢾⡇⠈⠉⠛⣛⠉⠛⠀⠀⢹⡄⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣴⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠛⠛⠛⠓⠶⢦⡟⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⢷⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⢷⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀ ⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠲⣄⠀⠀⠀⠀⢿⠀⠀⠀⠀ ⠀⠀⢀⡿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠸⡆⠀⠀⠀ ⠀⠀⣼⢁⡿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠀⠀⢷⡀⠀⠀ ⠀⢰⠏⢸⠿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠒⠒⠒⠲⠶⠦⢤⣄⠀⠀⠘⣦⠀⠀⠘⣧⠀⠀ ⢀⡟⠀⣾⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⣄⣸⡇⠀⠀⢸⡄⠀ ⢸⠁⠀⢹⡀⠘⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋⠀⠀⢀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⡏⠀⠀⠀⣧⠀ ⠸⣧⢀⠀⠉⠑⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠞⠁⠀⠀⣠⠶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡏⠀ ⠀⠘⢿⣠⠀⠀⠀⠀⠈⠻⢶⣄⡀⠀⢀⣀⣀⡤⠶⠛⠉⠀⢀⣀⡴⠛⠁⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⢿⠀⠀ ⠀⠀⠈⠻⣄⡀⠀⠀⠀⠀⠈⢿⣭⡉⠉⣁⣠⣤⡤⠴⠒⠛⠉⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢠⣶⠟⠁⠀⢸⡀⠀ ⠀⠀⠀⠀⠈⠉⠳⢦⣄⣀⣀⣠⡍⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⡿⠋⠉⡅⠀⠀⠀⠈⣇⠀ ⠀⠀⠀⠀⠀⠀⠀⠸⣦⠀⠀⠈⠙⠂⠀⣄⣀⣀⣀⠀⠀⠀⠀⠀⠀⢀⡾⡁⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⣸⠁⠀⢸⠃⠀⠀⠀⠀⠸⡄ ⠀⠀⠀⠀⠀⠀⠀⠐⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⢀⢀⡴⠋⠀⠀⠀⠀⠀⠀⡀⡴⠋⠀⠀⣠⣏⠀⠀⢸⠀⠀⠀⠀⠀⠀⣧

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⢀⣰⠃⠀⠀⠀⠀⠏⠖⠂⠀⠀⠀⠀⠀⠙⣅⠈⠉⠉⠹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡔⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⠀⣠⣉⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣷⣶⣤⣀⠀⠀⠀⢀⡤⠀⣠⡴⠟⢡⣵⠀⠀⠀ ⠂⠀⠀⠀⠀⠀⠐⠤⣠⣾⣠⠔⠋⠀⠉⣨⣷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡟⠻⠛⠛⠿⠿⠷⢦⣴⣯⣴⡿⠋⠀⢠⠈⡟⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠄⠀⣠⣴⣾⣿⣿⣿⠀⠀⠀⠀⠀⠀⢀⣤⣶⣾⣿⣿⣷⡤⠀⠀⠀⠀⠀⠐⠊⠹⣿⠂⠀⠀⠈⣧⠎⣠⠄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠛⠛⠻⡏⢉⣏⣤⣦⣤⣤⣀⠞⣩⣿⣿⣿⣿⣿⣷⣤⡀⢀⠀⠀⠀⠀⠀⠀⠙⣷⣄⠀⡀⢸⠟⠁⣀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⣿⣿⣿⢿⣿⣿⣿⣿⣿⠟⡿⢿⠿⣿⣿⣿⡟⠉⠀⠀⠀⣀⡤⠀⣰⠛⣿⣦⠘⡄⠀⠸⠹⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⠤⠦⣤⣾⣿⣿⣿⣿⣿⡿⠃⣸⣿⠛⣿⣿⣋⢰⣷⣀⡴⠛⣿⣿⣷⣀⣤⠀⣴⡟⠀⢠⡟⠀⠘⣿⣧⠘⠂⠀⢀⠀ ⠀⠀⠀⠀⠀⠠⡔⠁⠀⣰⣿⣿⣿⣿⣿⠋⣸⣧⣀⣧⣿⣦⡟⠀⠈⣿⣿⣿⣧⡀⣹⣿⣿⣿⣿⣿⠏⠀⣠⡟⢠⠄⡆⣿⣿⡆⡀⠀⠀⠀ ⠀⠀⠀⠀⠈⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣼⡏⡿⠉⠉⠉⠻⣿⣧⡀⠹⡟⡿⢿⣿⣏⢉⣻⣿⣿⣿⣿⣾⣿⣰⡟⣸⣷⣿⣿⣷⡿⠀⠀⠀ ⠀⠀⠐⠢⠄⢴⣶⡏⠟⣿⣇⢿⢿⣿⣹⣿⣄⡁⠀⠀⣠⣶⣮⣷⣵⡀⢻⡇⡼⠻⣿⣿⣟⡉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀ ⣄⠀⠀⠀⠀⢸⣿⡇⠀⢻⢿⠈⠆⠙⢿⣿⡬⢶⣤⡀⠘⠿⠟⢸⡿⠀⠘⢿⠁⣰⡿⢿⣿⣿⣿⠁⠀⠙⣿⣿⣿⣿⣷⣾⠃⠀⠀⠀⠀⠀ ⡿⠀⠀⠀⠀⠘⣿⣷⣴⠃⠈⢆⢀⣄⠀⠈⠃⠀⠙⠛⠂⠀⠀⠈⠀⠀⠀⣸⠞⣸⣣⡾⢛⣿⣿⣷⣄⣠⣾⣿⠟⠛⣿⣿⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⣿⣿⡏⠀⠀⢈⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣼⣛⡁⠀⠚⠩⢿⣿⣿⠟⣽⣏⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠸⢻⣿⡇⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣉⣛⡳⢿⣥⠾⠛⣧⣾⣿⣿⣾⢀⡿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⡀⠀⠀⠀⠀⠀⠀⡰⣄⠈⣩⣿⡟⠷⣬⣲⣶⣿⣿⣿⣿⣿⡫⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠘⢹⣿⣿⡇⠀⠀⠀⢀⡴⠾⠿⠿⣿⣿⣗⢄⠀⠀⠀⠀⠁⢼⡆⢳⠽⠇⠀⠙⣿⣿⣿⣿⡏⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀ ⣿⡀⠀⠀⠀⠀⣸⠛⣿⣿⡀⠀⠀⢺⠀⠀⠀⠀⠈⢻⣿⣿⠀⠀⠀⠀⠀⠀⡜⡎⢇⠀⠀⢀⣿⣩⣶⣿⡇⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠻⣧⠀⠀⠀⢠⠃⠀⢹⣿⣧⠀⠀⢸⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⢸⠀⢸⠀⢒⣻⠟⠻⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣦⣼⣷⣶⣤⣏⠀⠀⠀⢿⣿⣷⡀⠈⢡⣀⡀⣠⣤⠶⠃⠀⠀⠀⠀⠀⠀⠠⣾⣚⣁⣠⣾⣿⣶⣿⣿⣿⣷⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢿⣿⣿⣽⣛⢿⣷⣦⣤⣼⣿⢿⣿⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡿⣿⣍⣙⣿⣿⣿⣿⣿⡟⢻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠙⠻⠿⣿⣿⣿⣿⣿⣿⡇⠀⠉⠙⠛⣿⣷⣶⣤⣬⣀⣀⣀⣀⣀⣤⣤⣶⣿⣿⣿⣿⣿⣿⠿⢟⡿⠋⡠⠃⠈⠑⠦⣄⡀⠀⠀⠀⠀⠀ ⠀⣠⣴⣾⠿⠿⠛⠛⠛⣿⣧⡀⠀⠀⣸⠿⠻⡍⠉⠟⠁⠀⠈⠙⣿⡿⠿⠿⣉⠀⠉⠯⢤⡤⠖⠋⠀⣏⠀⠀⠀⠀⠀⠀⠉⠛⠒⠀⠀⠀ ⠛⢯⠥⠒⠀⣹⣿⣿⡇⢹⣿⣥⠼⠏⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠯⡉⠀⠀⠀⠀⠀⢸⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢰⣿⣿⣿⣿⣦⣿⣧⣄⣀⡀⠀⠀⠀⠈⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠬⠂⠀⠀⠀⡄⢸⡿⡝⠦⣀⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢾⡿⠀⠉⣿⣿⠀⠀⡇⠹⣿⣿⣿⣶⣶⣤⣤⣽⡶⠤⠤⠐⠒⢎⡉⠀⠀⠀⠀⠀⢠⡞⢠⠋⢱⠈⢦⡀⠉⠉⠁⠂⠀⠀⠀⢀

⣿⢎⢾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⡀⠀⠀⠀⢠⠀⠀⠀⠁⠀ ⡿⠁⣾⢧⢀⡀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⡀⠀⣸⣙⣆⣀⣀⣸⢧⠲⡀⠀⢆ ⠇⡀⠁⢸⠇⣯⡛⢳⡾⣼⣶⣦⠀⡾⡄⠀⠀⡄⠀⢹⣛⣩⠹⡄⢰⣈⣆⣡⠀⢸ ⠀⠇⢰⣈⠀⣛⣆⣸⡁⢄⡰⡠⡀⠐⣱⠂⠀⡇⠀⢸⢄⣠⣴⣿⡟⠙⢿⣿⠒⡎ ⢰⠀⢸⢤⣵⡿⠋⣿⣿⣿⣮⣝⣧⡀⢱⡁⢀⢿⢀⣼⣿⠿⡟⣻⡇⠀⣿⢿⠀⣆ ⣸⢀⢼⠀⢻⢧⢠⢹⣿⡙⢋⣿⣿⠛⢪⣳⡸⠈⡠⠃⣿⣦⣴⡿⡏⠘⢉⢸⠀⡿ ⣷⡟⢸⢀⠎⡎⢻⡌⢿⣿⣾⣿⠟⠀⣸⣽⣷⣾⡱⢁⢻⠿⢿⣋⡠⠔⠛⢸⠀⢹ ⣿⠃⣯⣾⡄⢸⠀⠶⢄⣉⣛⣁⢖⣿⢫⣿⡟⡑⡰⡑⢝⣭⡯⡫⣳⣠⠾⡄⠀⢸ ⠇⢘⣏⣿⣧⠀⣿⡞⣵⡛⡵⠣⣗⢟⠋⠁⠁⠀⠌⢈⣸⡘⢱⢽⢓⣢⢮⡇⠀⠈ ⣪⣿⣣⢻⣿⢀⣟⢬⢎⡼⠁⠉⢤⣤⣠⡐⣒⡀⠉⠀⡞⠀⠀⣀⣶⣿⣾⠀⣼⠀ ⡏⠈⣿⡶⢺⡜⠈⠛⠮⣥⣪⠁⠀⢩⠈⠁⠀⠀⠉⠡⣇⣤⣾⡟⠁⢻⣿⢰⠋⣱ ⠙⣆⠸⣟⣜⠁⠀⠀⠀⢸⠙⢿⣷⣶⡗⣄⣀⣆⣠⣾⣼⣿⡋⠀⢀⣿⢇⢿⢠⢻ ⠀⠈⡆⠘⣿⣆⠀⠀⠀⢸⠆⠸⡿⡟⣯⣿⣿⣽⣿⣿⣿⠏⠈⢦⡚⢸⣸⢈⢣⠃

⣿⣿⣿⣿⣿⣿⣿⡿⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿ ⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿ ⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢀⣀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢤⣀⣼⠀⠀⠀⢀⡄⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿ ⣿⣿⣿⣿⣿⣿⡿⠀⢀⣠⠴⢚⣩⠤⠤⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠒⠦⢬⣉⡙⠧⣄⠾⢁⡞⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿ ⣿⣿⣿⣿⣿⣿⣇⡤⠏⣤⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⣌⠛⢮⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿ ⣿⣿⣿⣿⣿⣿⠏⢡⠞⠁⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣷⣮⣳⡄⠀⠀⠀⠀⠀⠀⠀⢸⣿ ⣿⣿⣿⣿⣿⡏⢰⡟⠀⠀⠀⣾⠿⠿⠿⢿⡻⣷⠀⠀⠀⠀⣴⠞⣻⢿⣿⠿⠷⠦⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣍⢷⣄⢀⡖⠀⠀⠀⢸⣿ ⣿⣿⣿⣿⣿⠃⣿⠁⠀⢀⣼⣧⣴⣿⣿⣿⡷⠂⠐⠉⢱⠇⠀⢺⣿⠿⣿⣿⣷⣧⠀⠀⠀⠀⠀⠀⠀⠀⠁⢿⣿⣦⠙⣿⡀⠀⠀⠀⣿⣿ ⣿⣿⣿⣿⣿⣸⣿⠀⠠⠟⠉⠁⠀⠿⠿⠋⠀⣰⡀⠀⣟⣷⠀⠀⠉⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠷⡎⢳⡄⠀⠰⠿⠿ ⣿⣿⣿⣿⣿⣿⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠛⢻⡾⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢡⣾⣿⣶⢻⡇⠀⠀⠀ ⣿⣿⣿⣿⡿⠛⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⠾⠶⠶⠶⢽⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⢹⢏⣿⣄⣏⠀⠀⠀ ⣿⣿⣿⡟⠁⣰⣧⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠀⠀⠀⠀⠐⠲⣍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⣼⡟⣿⣿⡄⠀⠀ ⣿⣿⠏⠀⡰⣱⢻⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⠀⠀⠀⠀⠀⠀⠚⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠀⣿⠋⠋⠳⣄ ⣿⡿⠀⣠⡷⠃⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⣸⠀⠀⠀ ⣿⣧⡶⠋⠀⢀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⣱⡃⠀⠀⠀ ⣿⠟⠀⠀⠀⢸⡄⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⣼⡟⠀⠀⠀⠀ ⢅⣀⣠⣼⠛⣽⠛⢿⠉⡷⢦⣄⣤⠤⢴⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⢁⣼⠏⠀⠀⠀⠀⠀ ⡀⢻⢁⡾⠀⢳⠀⣿⠀⡶⡆⢻⠁⣶⡆⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⢠⡿⠁⠀⠀⠀⠀⠀⠀ ⣹⠀⡞⠁⠀⠸⣄⣹⣤⣷⣧⡸⣦⣭⣥⡾⠃⠀⠀⠀⠀⠀⠀⢀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢀⣴⠞⢁⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠶⠚⠁⠀⠀⠀⠀⠀⠀⠀⠉⠙⠮⣍⠛⠛⠻⠶⠶⠦⠤⠥⠤⠤⣷⣬⣤⣤⣤⣤⣤⣤⠤⠶⢶⡚⠫⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⡗⢲⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⢠⣟⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣄⣠⣿⣝⣳⣤⣀⣀⣀⡀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⣴⣶⡿⠿⠿⠿⠛⠛⠛⠉⠛⠻⠿⠿⠛⠛⠛⠛⠿⢶⣶⣶⣧⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠉⣉⣽⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠉⠹⣿⣿⣯⡉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣴⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠙⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⣿⠏⠀⠀⠀⠀⠀⢀⡴⣂⡤⠤⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⡀⠀⠀⠀⠀⠀ ⠀⠀⣼⡿⠁⠀⠀⠀⠀⠀⢠⣿⠟⠁⠀⠀⠀⠀⠉⠛⢦⣽⡄⠀⣠⣴⣾⡿⠶⠶⠒⠲⠶⣮⣵⡄⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀ ⠀⢰⣿⡇⠀⠀⠀⠀⠀⢀⣾⡏⠀⠀⠀⢠⣶⣶⣦⡀⠀⠈⠻⣿⠟⠉⠁⠀⢀⣤⣤⡀⠀⠀⠙⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀ ⠀⣾⣿⡇⠀⠀⠀⠀⢠⣿⣿⡇⢀⠀⠀⠘⢿⣿⣿⠟⠀⠀⠀⣏⠀⠀⠀⠰⣿⣿⣿⣿⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀ ⠀⣿⠻⡗⠀⠀⠀⣰⠏⠈⢿⣷⡜⢆⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠉⠛⠋⠁⠀⠀⢠⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀ ⠒⣿⠀⠀⠀⠸⣦⣓⣒⠀⠀⢻⣝⢦⣦⡀⠀⠀⢀⣤⡶⠛⠋⠙⠳⣤⡀⠀⠀⠀⠀⠀⢀⣴⠟⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀ ⠀⢹⠀⠀⠀⠀⢿⣿⣿⣦⡀⠙⠈⠙⠲⢽⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠹⣶⣖⣒⣒⣛⣩⡴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀ ⠀⠨⣇⠀⠀⠀⠸⣿⣿⣿⣿⣦⡀⠀⠀⠀⠰⣿⢻⣇⠀⠀⠀⠀⠀⠀⠀⣸⣯⣭⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀ ⠀⠀⠹⡄⠀⠀⠀⢿⣿⣿⣿⣿⣿⡀⠀⠀⠐⢿⡘⣿⣦⡀⠀⠀⠀⠀⢀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀ ⠀⠀⠀⢻⡄⠀⠀⢸⣿⣿⣿⣿⣿⣷⣾⣿⣶⣘⣧⣼⢉⣿⣷⣄⣒⣤⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃⠀⠀ ⠀⠀⠀⠀⠹⣆⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣏⣁⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⠏⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣽⣽⠿⣽⣟⣻⠿⣿⡄⠀⠀⠀⠀⠀⠀⢀⣀⣀⣴⣶⣾⣿⣿⠋⠑⢦⡀⠀ ⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠙⢦ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠛⠉⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⣿⣿⣿⣿⠁⠀⠀⣀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⣆⠀⢠⢀⠀⠀⠀⠀⠀⢸ ⣿⣿⣿⣿⡠⢒⠅⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠲⣵⠪⡊⠀⠀⠀⠀⠀⣾ ⣿⣿⣿⡏⡰⠁⢀⣤⣤⣤⣄⠀⠀⢀⣠⣤⣤⡀⠀⠀⠀⠈⠳⣿⢄⠀⢀⠀⠀⣿ ⣿⣿⣿⣱⠃⢀⣾⢴⣶⡿⠃⠂⣒⠁⢾⣿⣷⡦⠀⠀⠀⠀⠀⠸⣧⡙⡇⠀⢀⣿ ⣿⣿⣿⡿⠀⠈⠀⠀⠉⠀⠼⡤⠟⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠘⣩⣬⢦⠈⠉ ⣿⣿⡟⢹⠀⠀⠀⠀⠀⢠⠖⠛⠓⢻⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣽⣼⣾⡀⠀ ⣿⡏⢠⡟⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⡟⠓⠄ ⣿⡠⠋⠁⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⣷⠀⠀ ⠟⠁⣠⣴⣴⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⡹⠃⠀⠀ ⡐⢣⠃⠇⣾⢸⠘⡫⣮⣳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢊⡞⠁⠀⠀⠀ ⡦⠂⠀⠈⠚⠛⠓⢿⠺⠧⣤⣤⣀⣀⣠⣂⣀⣀⣀⣄⣤⠴⠊⠐⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⢳⠂⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀

⠉⠙⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠰⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⡠⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠋⠁⠀⠙⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣷⣍⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠹⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠁⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣆⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⠀⠀⢠⡄⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣧⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡆ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡘⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠹⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠠⣶⡀⠀⣀⡈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⣿⡇⠀⠀⠀⠀⢰⣿⣿⡿⠿⣧⠀⣿⠿⣿⣿⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢀⡿⠉⠀⠀⠀⠘⣿⠁⠀⠀⠈⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⣸⠇⠀⠀⠀⠀⡏⠀⠀⠀⢀⣠⣦⣀⡇⣸⣦⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢰⣿⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⡻⠿⢁⡇⢿⡿⠁⠀⢸⡇⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⢀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠁⠀⠀⠀⠀⠀⠀⠻⣦⣀⠀⣀⡴⠋⠳⠦⠤⢴⣟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⢰⣅⠀⢻⣧⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡏⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢶⡿⠙⠈⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠦⣴⡌⠁⢀⡿⠼⠧⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠒⠛⠁⡀⢩⡷⣤⡤⠀⢀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⠿⣯⣈⣠⡿⣷⡀⢸⠀⢻⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠟⠁⠀⠊⠉⠉⠀⠈⢻⣎⣄⣸⣶⠶⠛⠋⠉⢿⡆⠀⠀⠀⠀⠀⣿⡏⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠶⠚⢿⠁⠀⠀⢠⡀⠀⠀⠘⢿⣀⣀⡀⠀⢸⣿⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣸⠏⠀⠀⠀⠀⠀⠀⠈⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠘⡆⠀⠀⠙⢻⣄⡤⠞⠛⠉⠉⠛⢿⣾⡿⢀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠖⠛⠒⠒⠒⠿⣤⢠⡖⢾⡏⠀⠀⠀⠀⠀⠀⠀⠉⢿⣷⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⢻⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⢨⡇⣳⡾⣧⡀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⣠⡴⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠀⢿⡀⣾⠯⢷⡶⣤⣀⠀⠀⠀⠀⢹⠝⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⢀⣤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⣆⠀⢹⣛⣷⠞⠁⠀⢿⠃⠀⠀⠀⣼⡆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡴⠛⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠿⣀⠀⠀⢹⡀⠈⣋⣁⠄⠀⠀⣼⠀⠀⠀⠼⣿⡇⠀⠀⠀⠃⠀⠂

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⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣩⡤⠤⠆⠀⢻⠃⣿⡏⠀⠘⠀⠈⣿⡟⣿⡇⠉⢹⣿⣿⣿⠾⢇⣉⡛⠻ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⡏⠁⠀⠀⠀⠀⠀⣾⣀⣿⠁⠀⠀⠀⣸⡿⠋⢿⡇⠀⢸⣿⣿⣿⣷⣦⣈⠻⣿ ⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⣼⡟⣾⡇⠈⠁⠀⠀⠀⢀⣀⣴⣿⣛⣿⠿⠛⠛⠛⠛⠛⠛⠒⢷⣄⣈⣿⠀⣿⣿⣿⣿⣷⣬ ⢠⡿⢹⠉⢻⣿⣿⣿⣿⣿⠿⠏⠁⣀⣠⣴⣿⣧⣟⣷⡶⠶⠞⠛⠛⠋⠉⣻⡿⠋⠁⠀⠀⠀⠀⠀⢀⣀⣠⣿⠀⠀⡿⣇⢹⣿⣿⣿⣿⣿ ⣼⡇⣼⠀⢸⣧⣷⠀⢸⢻⣧⣴⣿⠿⠿⠿⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠋⠀⢀⠄⣀⣤⣶⣾⠿⠿⣿⡿⢻⠀⢀⡇⢻⡄⢿⣿⣿⣿⣿ ⣿⡇⡿⣧⣼⣿⠿⠛⠛⠈⠉⠁⠀⠀⠀⠀⠀⠈⠻⠇⠀⠀⠀⠀⠀⠀⠀⢀⣴⣷⣾⡟⡟⠀⠀⢀⣸⣿⣷⣾⠀⢸⣧⠈⢿⣌⢿⣿⣿⣿ ⣿⣷⠇⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠒⠦⠤⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢉⣿⣶⡷⣺⠟⠉⠁⣸⣾⣿⠀⢸⣿⡆⢸⣿⣆⠻⣿⣿ ⡗⠿⠀⠀⠀⣱⣶⣶⣶⣿⠿⠿⡿⣿⣿⣿⠛⠳⠦⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠉⠙⠾⠟⠋⠀⠀⢀⢿⣿⣿⠀⣼⣿⣧⢸⣿⣿⣷⣝⣿ ⠛⣦⡠⢽⣿⠛⠋⠉⠀⠀⢀⣀⣤⣼⣿⣿⣶⠒⠂⠀⠀⠀⠀⠀⠠⠛⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠂⢨⠀⠀⠻⠷⠤⠴⠶⠿⠟⠛⠛⠛⠹⠿⠶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣴⡷⠖⣄⢠⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠃⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣁⣀⠔⢻⣅⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⣠⡟⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢀⣾⣿⠁⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣴⣾⣿⠳⣼⣿⡙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣾⠟⠁⠀⠀⠀⢀⣾⣿⠇⡜⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⡇⠀⠈⠻⣷⡶⠻⣷⡀⠀⠀⠀⠻⣶⠶⣤⣶⣒⣲⣶⡿⠿⢟⣻⢟⡷⠃⠀⠀⠀⠀⣰⣿⣿⢏⣼⠁⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⠀⠀⠀⠀⠈⠳⣄⠾⣿⠀⠀⠀⠀⠀⠑⠚⠭⠭⠭⠽⠶⠯⠽⠚⠁⠀⠀⠀⠀⣠⣾⣿⣿⣿⣾⡏⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⠀⠀⠀⠀⠀⠀⢻⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⡿⠀⠀⠀⠀⠀⠀⢸⠀⣿⡿⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠋⠙⠛⠛⢻⡿⠿⣿⣿⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⡇⠀⠀⠀⠀⠀⠀⡎⢀⣿⠁⠻⣿⣿⣿⣷⣶⣤⣄⣀⣀⣀⣠⠔⠋⠀⠀⠀⠀⠀⠰⠋⠀⠀⢸⡏⡸⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣇⠀⠀⠀⠀⠀⢠⠇⢸⣿⠀⠀⠈⠻⣿⣿⣿⣿⠟⠁⠀⠀⠀⠑⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢡⠃⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⡄⠀⠀⠀⠀⣸⠀⣼⣿⡀⠀⠀⠀⠀⠉⣹⠃⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⢰⣧⠏⠀⠀⠀⢠⠄⠀⠈⠻⣿⣿⣿⣿⣿ ⠻⣿⣷⡀⠀⠀⢀⡇⢰⡿⠀⠉⠲⠤⣀⣠⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⣾⡟⠀⠀⠀⠀⡜⠀⠀⠀⠀⠘⢿⣿⣿⣿ ⠀⠹⣿⣷⡀⠀⢸⢀⣾⠃⠀⠀⠀⠀⠀⡸⠁⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣀⣸⡟⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠙⢿⣿ ⠀⠀⢹⣿⣷⣀⢇⣾⠏⠀⠀⠀⠀⠀⠰⠁⠀⠘⡄⠀⠀⠀⢀⣠⣤⣀⣀⣀⣀⡀⠀⠀⣸⣿⣄⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠈⢻ ⠀⠀⠀⢻⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢣⠀⠀⠀⠞⠀⠠⠤⠄⠒⠊⠛⠉⢩⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣶⣿

⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣄⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⠉⠛⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⣝⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣧⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠐⠂⠀⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡆ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠤⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⣀⣠⣄⠀⣀⣹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⡿⠿⠛⠛⣦⡟⠛⠿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⡼⠀⠀⠀⠀⠸⡀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢸⠇⠀⠀⠀⡇⠀⠀⢠⣤⣤⣇⣶⡄⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⡿⠀⠀⠀⠈⣇⠀⠀⠀⠛⢁⡏⠛⠁⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀⠘⢆⠀⠀⢀⡼⢦⣀⣀⡴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⢴⡀⢻⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡛⠟⢁⣙⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠽⠗⠀⢺⣋⡉⠒⠂⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⢧⣈⣼⢷⡀⡄⢸⠀⠀⠀⣀⡀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠉⠀⠀⣻⡦⠼⠖⠋⠉⠉⢿⡀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠠⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣎⠉⠀⢇⠀⠀⢶⡄⣀⡬⠷⠶⢦⣤⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⠏⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠾⠖⠒⠾⢄⣠⡶⡟⠁⠀⠀⠀⠀⠉⢻⣆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⢀⣠⠔⠊⠁⠀⠀⠀⠀⠀⠀⢠⠏⡿⢷⣤⡀⠀⠀⠀⠀⠀⢿⡆⠀⠀⠀⠀ ⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⢀⣠⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠛⡄⠳⣾⣍⡽⠙⢶⠄⠀⠀⣸⠁⠀⠀⠀⠀ ⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢾⡁⠀⢳⠀⢛⣋⠄⠀⣸⠀⠀⢠⣿⠀⠀⠀⠂⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⠆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠚⣿⣿⠏⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣀⣠⠖⠉⠀⠀⣿⠏⠀⠀⠀⠀⠀⠀ ⢶⣶⣶⣆⠀⠀⠀⠒⠒⠊⠉⠀⠀⠀⠀⠁⠀⠀⠀⣠⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠙⠻⢦⣀⢠⠃⠀⠀⠀⠀⠀⣀⣠⠀⠀⠀⠘⡟⠓⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣈⣽⢹⢮⠀⠀⠀⠀⠚⠑⠂⠀⠀⠀⡇⠀⠸⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣳⡃⠀⠀⠐⠚⠀⠀⠀⠀⡴⠒⠲⡀⡇⠀⠀⢳⠀⠀⣀⠤⠈ ⠀⠀⠀⠀⠀⡏⢹⠀⠀⠠⣾⠗⢦⠀⠈⢏⣀⡠⠃⡇⠀⠀⠸⠖⠋⠁⠀⠀ ⠀⠀⠀⠀⠀⠻⡞⠀⠀⠀⡇⠀⠘⡆⠀⠀⠀⠀⠀⠇⠀⠀⠀⠇⠀⠀⠀⠀ ⠀⠀⠒⠀⠀⠒⠺⡓⠧⠀⢧⣀⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡴⠁⠀⠀⠀⢲⣒⠒⠂⠀⠀⠀⠀⠀⠀⠀⣜⣠⠤⠖⠒⠉ ⠀⠀⠀⣠⠖⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⢧⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣄⣀⣤⠴⠾⠿⠟⠿⣛⡿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣀⣀⣤⠤⠤⠖⠒⠛⠉⢉⣠⡶⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣯⡽⠶⠒⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠘⠋⠉⠀⠀⠀⠀⠀⠀⢀⣴⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠋⠉⠻⣅⠀⠀⠀⣯⠉⠒⠦⣄⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⣴⢿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢤⣀⣀⡼⠙⠳⡎⠉⠙⢢⡀⠀⡈⠙⠛⠲⢤⢠⡀ ⠀⠀⠀⠀⣦⠀⠀⠀⢰⡟⢁⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠙⡶⠟⠳⣄⠀⢀⡇⠀⠙⠢⣄⡿⠁⣠⠇ ⠀⠈⣶⣯⣻⣆⠀⢠⡟⢀⡞⢁⠀⠀⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠐⠿⣶⣦⡤⣾⣄⠀⢀⡿⢷⣾⠀⠀⠀⣤⣿⣛⣴⠏⠀ ⠀⠀⠘⢷⣟⣷⣲⣿⣷⣿⠁⡾⢀⣰⡿⣠⠀⠀⣇⡆⠀⠀⠀⠀⠀⣾⣤⡆⠀⣿⠏⢱⠇⣈⣷⣏⣀⣼⣿⡀⠀⢀⣿⢹⣧⠏⠀⠀ ⠀⠀⠀⠈⣿⣽⣿⣿⡿⣿⣸⠃⣸⣻⡇⣿⡆⢰⣿⡗⡄⠀⠀⢠⠀⣿⣿⡇⢀⣿⠀⢸⣿⡏⠀⠉⠙⣏⣿⣧⣴⣿⣶⣾⠏⠀⠀⠀ ⠀⠀⠀⠀⠘⣿⣿⣿⣧⣿⣿⡄⢿⢿⣷⣿⢻⣼⣿⡇⣿⠀⠀⣿⡀⣿⣿⡇⣾⣿⠀⣸⣿⡇⠀⣶⠀⣿⣾⣿⣿⣷⡾⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⡼⣷⣸⣀⣿⡏⠘⠿⣼⡇⢿⡌⠀⢻⡁⡿⢹⣷⣿⢻⣤⣿⣿⡇⠀⡇⢠⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⣿⣼⣽⣿⣶⣶⣶⣿⣧⠸⣷⡀⠈⣿⠇⢿⣿⣏⣠⣿⡽⠁⣇⣸⢇⣿⣿⣿⣿⠛⠄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡠⠴⣿⣿⡿⣿⣿⣿⣿⣿⠀⢙⣿⣿⣿⡟⠁⠹⠳⣤⣿⠀⢸⣿⣿⣿⣯⠙⢷⣿⣿⣿⣿⣿⣿⣧⠜⠓⠲⠤⣤⣄⠀⠀ ⠀⢤⡞⠁⠀⠀⢹⣿⣿⠛⠻⣿⣿⣇⠑⠘⢟⣛⡿⠀⠀⠀⠀⠈⠉⠀⠈⣿⣿⣿⡟⠀⢿⣿⣿⣿⡻⣿⣿⠁⠀⢀⣠⠄⠞⣋⡠⠂ ⢠⠖⠤⣝⠢⣄⣾⣿⣿⠀⠀⠈⢻⡉⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠋⠀⢠⣿⡿⠋⠉⣷⣿⢻⡆⢀⠎⣡⡶⠉⠁⠀⠀ ⠀⠀⠀⢈⣳⣸⣿⣿⣿⡇⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⡟⠀⠀⣰⣿⣯⡄⣿⡇⣸⣿⣄⠀⠀⠀⠀ ⠀⠀⣴⡿⣻⣿⣿⣿⣿⡇⠀⠀⠀⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠁⠀⣴⣿⣿⣿⡑⣿⣷⣅⣻⣷⠀⠀⠀⠀ ⠀⠀⠙⠻⣿⣧⣿⣿⣿⡇⠀⠠⠔⣻⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⠏⠀⢀⣿⡿⣿⡿⣧⣹⣿⣿⣏⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⡎⣹⣿⣿⣿⠛⠲⠞⠋⠉⠀⠀⠼⣿⠓⠤⣀⠀⠀⠀⣀⠤⢴⣾⣿⣿⣿⣀⣒⣾⣿⣧⣘⠇⠸⣿⣿⣿⢿⣧⡀⠀⠀⠀ ⠀⠀⠀⠀⣿⣿⣯⡿⠛⢹⣷⣿⠀⠀⠀⠀⠀⢹⠂⠀⠀⠉⠈⠉⠀⠀⢸⣿⣿⣿⣥⣈⣉⣩⠘⠋⣻⣧⡠⣬⡿⣿⣷⡙⢿⣦⣀⠀ ⠀⠀⠀⢠⣿⣿⠋⠀⠀⢸⣏⣿⣇⠀⠀⠀⠀⠈⠣⢀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⢹⣿⠉⠹⡇⠀⢈⢻⣿⣎⣻⣮⡉⢻⣾⣙⣿⣗ ⠀⠀⢀⣾⣿⡿⠦⠀⠀⠈⣿⣿⡟⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡘⠀⠀⡇⠀⢨⠀⢹⣮⣿⣿⣿⣶⣍⠻⣯⡙ ⠀⠀⡸⢹⣿⠀⠀⠀⠀⠀⢻⣿⣿⡊⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⢸⣿⢠⣾⠇⠀⡸⠀⠀⣿⣿⣿⣿⣿⣿⣷⡹⣿ ⠀⠀⠀⣾⣿⠀⠀⠀⠀⠀⠀⠻⣧⣷⡘⣿⠂⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠠⣿⣿⣼⡟⠀⢠⠃⠀⠀⢹⣿⣿⣿⡿⣿⡟⣿⡽ ⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⠛⢿⣽⣇⠀⠀⠀⠀⠀⠀⠠⠃⠀⠀⠀⠀⢰⣿⢏⡾⠁⢀⠇⠀⠀⠀⢸⣿⣿⣿⣷⡹⣿⡟⣿ ⠀⠀⠀⠃⢻⠀⠀⠀⠀⠀⠀⠀⡸⠀⠈⣿⡿⠂⠀⠀⠀⠀⠐⠛⠢⢄⣀⠀⢀⣼⣿⠟⠁⠠⠋⠀⠀⠀⠀⢸⣿⣿⡇⢻⣷⡹⣿⠈

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡴⠚⠉⠉⠙⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡼⠁⠀⠀⣀⣤⣴⡧⠤⠤⢤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⠋⠀⣠⣴⠟⠋⣉⣅⢀⣠⡀⠀⠀⠉⠛⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣰⢃⣴⡿⠋⠀⣠⡞⠁⣼⣯⣉⠹⡆⠀⠀⠀⡀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀ ⠀⢰⣷⡿⠟⠚⠛⢻⡟⠀⢸⠷⠦⠬⢭⣿⣀⣠⡤⠿⠃⠀⠹⣄⣀⣀⡠⠤⠤⠖⠚⠉⠁⠈⢳ ⠀⡿⠋⠀⠀⠀⢠⣿⡅⢀⡏⠀⢠⡴⠚⢻⡏⠙⠓⠦⣄⡀⠀⠹⡶⠶⠤⠤⣀⠀⠀⠀⠀⠀⡾ ⣸⠃⠀⠀⠀⠀⣾⣿⣷⡾⠀⢠⡏⠀⠀⡞⠀⠀⠀⠀⠀⠙⠳⣤⣻⠀⠀⠀⠈⠙⢦⠀⢀⡼⠁ ⡧⠤⠤⢤⣄⢸⣿⣿⡿⠁⠀⣸⣷⡀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀⠀⠀⠀⠈⡟⠉⠀⠀ ⡇⢠⣄⣀⣨⠛⣿⠟⠁⠀⢠⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀ ⢹⣆⠀⠀⠀⠀⠀⠸⣆⡴⠃⠻⠟⢁⡐⠊⠉⠉⠉⠓⢦⡀⠀⠀⠀⠀⠀⠀⣠⠜⠁⠀⠀⠀⠀ ⠀⣿⣷⣤⡀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠙⠲⠤⠤⠄⠠⠴⠃⣲⡤⠤⠶⠶⢯⡁⠀⠀⠀⠀⠀⠀ ⠀⢹⡈⠛⢯⣗⡦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠋⠀⠀⠀⠀⠀⠙⠦⣀⠀⠀⠀⠀ ⠀⠈⣧⠀⠀⠈⠙⠓⠺⠭⣽⣶⣒⣲⠶⢶⣶⣶⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀ ⠀⠀⠸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠈⠉⠓⠦⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢳⡀⠀ ⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠓⠶⠤⣤⣀⣀⣀⣁⣼⠇⠀ ⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀ ⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⢳⣄⠀⠀⣺⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⠛⠚⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⢀⡞⠀⠀⠀⠀⠀⡠⠈⠒⠻⠰⡤⡀⢣⢀⡏⣧⠈⢆⠃⠀⡠⠈⠂⠀⠀⠀⠀ ⢡⢳⠁⡠⢄⠀⢰⠏⠀⠀⠸⠀⡤⢠⠀⠀⠁⡷⡇⢣⡈⢆⠀⠀⡠⠜⠀⠀⠀⠀ ⠁⠸⠀⠡⡀⢀⣎⠤⠀⠤⠀⠀⠱⡀⠆⠀⠈⣩⠹⠁⠘⠪⠲⠊⠀⠀⠃⠀⠀⠀ ⠀⠀⠐⢲⠺⡟⠀⠉⠉⠉⠁⠀⠀⠁⠀⡀⠔⣪⡴⠤⣄⡀⢀⠴⠊⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠀⣆⣰⠚⡿⢲⣅⠀⠀⠀⠀⠰⣻⡇⣰⣦⠈⡿⠅⠀⠀⠀⢀⠀⠀⠀ ⡈⠍⠁⡇⠀⠘⡃⢸⠿⠿⡇⠀⠀⠀⠀⠀⢹⠛⠛⠹⠀⠀⡆⠀⠀⠀⠘⠀⠀⠀ ⠀⠉⠐⠁⠀⠀⡇⢔⠓⡖⠁⠀⠀⠀⠀⠀⠀⠉⠙⡵⢳⡄⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡇⢫⠷⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠈⠀⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡄⠀⠀⡆⠐⢑⡤⡀⠀⠀⠀⠀⠀⠀⠀⡀⠔⣿⣟⠀⠀⠀⠀⢸⠀⠀⠀ ⠀⠀⢰⡇⠀⢠⡇⢸⢸⠇⢘⡗⠢⣤⡤⣐⡂⠥⢐⡪⢻⣿⠀⠀⠀⠀⣸⡇⠀⠀ ⠀⠀⣿⡇⠀⠸⠶⠚⠚⠣⠴⣧⣠⣇⢀⡀⠀⡹⡏⣠⡼⡑⡄⠀⠀⢀⠛⠻⠀⠀ ⢾⠷⣿⢿⠀⠀⠀⠀⠀⡠⢊⣔⣏⠿⣇⣇⣴⠻⡘⠕⠀⣦⡇⠀⠀⠌⠀⠀⠀⠀ ⣿⡿⠻⠋⠆⠀⣆⠠⢊⣴⣿⠏⠨⠮⣀⠠⠔⠊⠐⠀⣸⣾⠀⠀⡰⢄⡀⠀⠀⠀ ⠟⠀⣀⠧⢘⡀⠇⣺⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡟⠀⢠⠓⠢⠌⣁⠂⠄

⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⠿⣿⠿⠿⠿⠿⠿⠿⠿⢿⣿⢿⣿⣿⣿⠿⠿ ⠟⠹⣿⣿⣿⣿⣿⡟⠀⠀⢸⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠍⠁⠀⠀⠀ ⠀⢠⣿⣿⣿⣿⣿⡿⠀⠀⢸⣿⢿⣿⣷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣤⣿⣿⣿⣿⣿⡿⠀⠀⠀⠈⣿⣼⣿⠈⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⢿⣿⠇⠀⠀⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡏⠀⣾⣿⠟⠁⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⢻⣶⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣼⣿⠃⠂⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⢻⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣾⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣷⡠⠀⠀⠀⠀⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⢿⣧⣤⣄⣤⣴⠶⠟⠛⠛⠛⠛⠛⠛⠶⢦⣤⣀⠘⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠉⠻⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⢀⡀⠀⠀⠀⠀⣀⣀⣻⣧⡀⠀⠀⠀⠀⠀⣠ ⠀⠀⠀⠀⠀⠀⠀⠉⠍⢉⣉⣉⣽⣿⣥⠀⠀⠀⠀⠉⣽⣿⠯⢻⣦⡀⣀⣴⠞⠃ ⠀⠀⠀⠀⠀⣀⣀⣀⠘⠉⠉⠀⠀⠀⠀⠀⠀⠀⠈⢀⠀⠀⠀⠀⠙⢿⣏⠁⠀⠀ ⠀⠀⠀⣰⡟⠋⠉⠉⠛⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠄⠀⠀⠀⠀⣼⠿⣷⡄⠀ ⠀⠀⣼⠏⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⣀⡐⠀⠀⠀⢸⡏⠈⠘⣿⠀ ⠀⠀⢻⣆⠀⠀⠀⠀⠀⢰⡟⢠⠀⠀⠀⠀⠀⣠⣾⣿⡇⠀⠀⠀⠸⣿⠀⠀⣿⠀ ⠀⠀⠈⠻⣶⣄⣀⣠⣴⠿⠁⠊⠀⠀⠀⠀⢸⣏⣬⡿⠁⠀⠀⠀⠀⠸⣧⣴⠇⠀ ⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⠾⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠿⣆⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠁⠀⠹⣇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣿⣆⠀⠀⠀⢹⡆ ⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠟⠁⢀⣤⡾⠃ ⡆⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⢸⣇⣠⡾⠟⠋⠀⠀ ⣷⣀⣀⣀⣠⣟⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣿⣆⣀⣀⣀⣼⣟⣁⣀⣀⣀⣀⣀

⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡠⠚⠉⠈⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡠⠋⢀⣠⡴⠞⠛⠋⠉⠒⠢⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡜⣡⡶⠋⢁⡴⢋⣷⡋⢳⡀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀ ⠀⣸⡿⠛⠉⢉⡿⠁⡼⠛⠒⢫⣧⣤⡔⠛⠀⠙⣦⠤⠤⠔⠒⠈⠉⠀⢘⡄ ⢀⠏⠀⠀⠀⣼⣷⣰⠃⢠⠊⠁⡟⠀⠈⠙⠢⢄⡘⡏⠉⠑⠢⣄⠀⢀⡜⠀ ⡼⠠⠤⣀⢰⣿⣿⠃⠀⣿⡀⡸⠀⠀⠀⠀⠀⠀⠉⠓⠀⠀⠀⠈⡗⠋⠀⠀ ⢣⠰⠤⠬⠛⠟⡃⠀⡸⣿⡿⢁⣀⡀⣀⡀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⠀⠀ ⠈⣷⣄⠀⠀⠀⠙⠊⠀⠉⠐⢦⣀⡀⠀⠈⡣⣀⣀⣀⣀⡤⠊⠁⠀⠀⠀⠀ ⠀⢹⠙⠿⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁⠀⠀⠉⠲⣄⠀⠀⠀⠀ ⠀⠈⣇⠀⠈⠉⠓⠻⠭⠶⣶⠶⠶⣶⣛⠋⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀⠀⠀ ⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠈⠙⠒⠢⠤⣄⣀⡀⠀⠀⠀⣹⠀⠀ ⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠉⠉⠀⠀ ⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⢦⡀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⠒⠚⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⣀⣀⠠⠤⣀⡤⠔⠒⠛⠛⠩⠛⠢⣤⠄⣀⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠐⠊⠉⠁⠀⠀⣠⠎⠁⠀⠀⠀⠀⠀⠀⠀⡖⠒⢃⣀⢈⣅⠂⠤⣀⡀⠀⠀ ⠀⠀⢠⠀⠀⢠⢎⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⡩⠒⠪⡤⠧⡀⢱⠀⠤⣨⡅⡂ ⠀⠹⣯⣇⣠⢣⠎⡄⢠⠁⠀⣄⠀⠀⠀⣀⠀⢻⡶⡺⢦⡰⢻⡇⠀⢰⢯⡼⠁ ⠀⠀⠹⣿⣿⣿⣼⢸⣻⣾⡀⣿⠄⠀⡄⢿⡿⢸⡇⣇⡏⠉⢻⣿⣴⢽⡞⠁⠀ ⠀⠀⠀⢹⣿⣿⣿⣼⢸⡇⢿⣻⢷⠀⠗⡽⣧⡿⣗⡿⡇⡏⣸⣿⣯⠟⠀⠀⠀ ⠀⠀⠀⣐⣿⣿⣷⣿⡞⢲⣶⣿⠜⣆⢸⠇⣿⣧⣿⣇⣧⣷⣿⣿⣱⣀⡀⠀⠀ ⠠⠔⡉⠀⣿⡟⠻⣿⣇⠘⠿⠏⠀⠀⠉⠀⢻⢿⡏⢸⣿⣿⢿⡏⠀⡠⢜⡫⠄ ⠈⠉⢢⣰⣿⣷⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠉⢠⣟⣸⡌⣴⡃⠀⠀ ⠀⠰⣯⣿⣿⣿⠀⢀⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇⢰⣿⣿⡼⣷⡼⠇⠀⠀ ⠀⠀⢨⣹⣿⣟⡒⡒⠉⠉⢽⠂⢄⣀⡀⠤⣶⣿⡿⣐⡾⣯⡋⠽⣿⡿⣦⡀⠀ ⠀⠀⢸⡿⠊⠀⣟⣇⠀⠀⠈⢄⠀⠀⠀⠀⠙⠛⢳⡖⢢⠀⡻⣦⣯⡛⢮⡻⣦ ⠀⢠⣿⡟⠂⠀⢿⣯⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡁⣸⠀⡆⢱⣿⣿⣶⡝⣮ ⠀⠀⣿⡇⠀⠀⠈⢯⣇⢷⠀⠀⠀⠀⢀⠌⠀⠀⣼⣿⠇⠰⠀⠈⣿⣿⣿⡟⣾ ⠀⠀⠿⡇⠀⠀⠀⠨⠈⢿⠆⠀⠀⠀⠤⢀⠀⢀⣿⠎⠠⠁⠀⠀⣿⣯⢷⢻⡜

⠀⠀⠀⠀⠀⠀⠀⣠⠖⠚⠁⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⢀⠀⠀⢹⠀⠀⠀⠀⠀⠉⠙⠲⠦⠤⣄⠈⠹⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⠞⠁⢀⠀⠀⠀⣰⠇⢀⡾⠀⠀⠀⠀⠀⢸⠀⠀⠘⣧⠀⠀⠀⢦⠀⠀⠀⠀⠀⠘⣧⣀⣞⣿⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡴⠁⠀⢰⠏⠀⢀⣼⠏⠀⣾⠇⠀⠀⠀⠀⠀⣸⢸⠀⠀⣿⣧⡀⠀⠈⢧⠀⠀⠀⠀⠀⢻⡉⠉⢉⠙⣿⡄⠀⠀⠀⠀⠀ ⠀⠀⣠⠎⠀⠀⢰⠏⠀⢀⣾⡟⢀⣼⣽⠀⠀⠀⢠⡆⢀⡇⣸⣠⢤⣿⣿⣷⣀⡀⠘⣆⠀⠀⠀⡄⠀⠙⠲⣿⠀⠘⣿⡄⠀⠀⠀⠀ ⠠⠞⠁⠀⠀⢀⡟⠀⢀⡾⣺⠋⢉⣽⣯⠀⠀⠀⣼⠀⡼⠀⡿⡇⢸⡏⢣⣳⡀⠉⠳⢽⣆⠀⠀⢹⡀⠀⠀⢸⣀⢀⣿⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣸⠁⠀⣼⢠⡟⠀⢸⠏⡇⠀⠀⢰⠇⣰⠃⣸⠇⡇⢸⠃⠀⠳⣽⡄⠀⠘⣿⡄⠀⠀⣇⠀⠀⢸⡁⠉⢿⣎⣇⠀⠀⠀ ⠀⠀⠀⠀⣴⡟⠀⢠⣧⡏⡇⠀⡟⠀⣷⠀⢀⣏⡼⠁⢠⡿⠀⡇⡿⠀⠀⠀⠙⣿⡀⠀⣿⣳⠀⠀⢹⠀⠀⠘⣇⠀⠀⠹⣿⠀⠀⠀ ⢰⠁⠀⠐⠋⡇⠀⣸⡟⠀⣧⢸⠃⠀⢹⢠⡿⠋⠀⢀⡿⠁⢠⣷⠃⠀⠀⠀⠀⠈⢧⠀⡟⣿⣇⠀⢸⡇⠀⠀⠈⠻⡄⠐⣿⠀⠀⠀ ⠊⠀⠀⣼⠀⡇⠀⣿⣃⣤⣿⣾⣰⡶⠾⡁⠀⠀⠀⡼⠁⠀⢸⣿⣯⣿⣷⣶⣶⣤⣼⣦⡇⢘⣿⡄⠀⡇⠀⠀⠀⠀⣷⠴⠋⠀⠀⠀ ⠀⠀⠀⣿⠀⡇⠀⣿⣿⠛⠹⡿⣿⣿⣷⣷⠀⠀⣸⠃⠀⠀⡾⠟⡛⢻⣷⣦⣄⠀⠈⢻⡗⠀⣿⢷⠀⠇⠀⠀⠀⠀⢹⢀⡏⠀⠀⠀ ⠀⠀⠀⢿⠀⣿⠀⡏⢿⠀⣾⠶⣿⡟⣷⠉⢣⢀⡏⠀⠀⠀⠀⣸⣿⢻⣿⠻⣿⣆⠀⢸⠇⠀⡇⠈⣿⠀⠀⠀⡦⠀⢸⡿⠀⠀⠀⠀ ⠀⠀⠀⢸⡄⢸⡆⡇⠀⠀⢿⣷⠿⢿⣻⠀⠀⢻⠅⠀⠀⠀⠀⠸⣧⡟⠿⣟⣻⠏⠀⠉⠀⢸⡇⠀⠘⠀⠀⠀⡅⣸⣆⢻⣛⠁⠀⠀ ⠀⠀⠀⠀⢳⣸⠹⣇⠀⠀⠀⠙⢤⠼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠷⠟⠉⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢀⣧⢿⡌⣮⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⢿⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣸⣿⢢⡷⢻⣿⢧⠀⠀ ⠀⠀⠈⠀⠀⠈⠁⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⢀⣿⡇⣸⠁⢸⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⡄⢸⣋⠔⠁⠀⠘⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⡏⢸⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⢸⣷⡟⠁⠀⠀⠀⠀⣿⠀⠀⠀ ⠀⠀⠀⣼⠁⠀⠀⡇⡟⠈⠳⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⠇⠀⠀⣼⣿⠇⠀⠀⠀⠀⠀⢻⠀⠀⠀ ⠀⠀⢠⣿⠀⠀⢀⣿⠁⠀⠀⣀⣝⡲⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠖⢻⣾⡍⢹⡇⠀⢸⠇⣿⠤⢦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⠙⣇⠈⡰⣯⠤⠒⣺⠁⠀⠈⠲⡄⣯⣹⣷⡶⠲⢶⠒⠚⠋⠉⠀⠀⢀⡼⠁⠻⣼⡇⠀⣿⡔⣿⠤⢺⠿⠦⠤⠀⠀⠀⠀⠀ ⠀⠀⢸⠀⠹⡄⠁⢻⠀⠀⣿⡀⠀⠀⢀⣾⠋⠉⣿⡇⠀⢻⡇⠀⠀⠀⣀⠔⠋⠀⢀⠔⣿⣇⢰⣿⠟⠁⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠊⠀⢠⡟⢶⡸⣇⢸⣉⣉⣙⠒⣾⠃⠀⠀⣿⠇⠀⠀⠳⣄⡴⠚⠁⢀⠠⠚⠁⣼⠟⣿⣾⡟⢀⠤⢲⡞⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡼⠀⠀⠙⠿⡎⠀⠀⠉⢱⡿⠀⠀⠀⣿⠀⢀⣴⣽⣿⣭⣦⠂⠀⠀⠀⣼⡟⠀⠈⣿⠏⠁⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⠇⠀⠀⠀⣤⡿⠀⠀⠀⣼⠃⠀⠀⢰⡟⡴⠛⡇⠈⠁⠀⢈⡷⡀⠀⡼⣿⠀⠀⢀⣿⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣼⠀⠀⠀⠀⢻⡝⠀⠈⢉⣿⠀⠀⠀⣿⠋⠀⠀⣇⠀⠀⠀⡼⠁⠘⠞⢱⣿⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠