Poggers Braille Art Emojis & Text

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿ ⠀⢠⣶⣯⣀⣀⣤⣴⠶⠿⠿⠿⠿⠿⠿⠟⠻⠿⠿⠿⠿⢿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣶⣶⣾⣧ ⠐⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⡿⠉⠉⠛⠻⢿⣿⠋ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⣤⠴⢶⠀⠀⠀⠀⠀⢻⡆ ⠀⠀⠀⠀⢀⣠⠤⣶⣶⣶⣶⣶⣶⣶⣤⣴⣆⡀⠀⠀⠀⠀⣀⡄⠀⠀⠀⠀⠀⠠⣎⣤⣶⣿⣿⠿⠃⠈⠀⠀⠀⠀⠀⡀⡷ ⢀⣤⣶⠿⠿⠟⠛⠉⠉⠉⠉⠀⣨⣿⣿⣿⣿⣿⣤⡤⣲⣦⠟⠛⠁⠀⠀⠀⠀⠀⣿⣿⣿⠉⣁⣠⣶⠶⠿⠿⢿⣿⣿⡿⠁ ⠈⠛⠀⠀⠀⢀⠀⠉⠓⠶⠀⠈⠻⠿⠿⠟⠛⠛⠃⠹⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⡗⢾⣿⣋⣀⠀⠀⢀⣿⣿⣿⡇⠀ ⠀⠀⠀⠀⠦⣤⣷⣤⣤⣤⣤⣤⣤⣴⣶⡾⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⢷⠶⢶⣦⣭⣍⣉⡉⠉⣿⡇⠀ ⠀⠀⠀⠀⠀⠀⠠⣉⣉⣉⣉⣉⣉⠅⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⢠⠛⠛⠛⠿⣿⣿⣿⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠘⠓⠒⠒⠂⠛⠙⠉⢧⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠐⠄⠈⡧ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⡀⠀⢀⣤⠀⠀⠀⠀⢠⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣦⣀⣤⣤⣤⣾⣿⣿⣶⣶⣶⣾⣟⠛⠛⣓⣛⣿⠟⠃⠀⠀⠀⣠⣿⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠻⠿⢿⣿⣾⣿⣿⣿⣶⣾⣿⡏⠀⠀⠀⠀⠀⢐⡿⠃⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⡉⠙⠛⠿⢿⣧⡀⠀⠀⣰⡷⠋⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠉⠛⢷⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⣠⣄⢉⡀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣤⣤⣴⠶⣶⣶⣶⣶⣶⣷⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣁⡀⢠⡤⠴⠚⠋⠁⠀⣀⣠⣴⣶⣶⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣷⣶⣿⣛⣿⠿⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⣶⡀⠉⠙⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡄⠘⠆⠀⠀⠈⠻⢿⣛⣻⣿⡿⠟⢿⣿⣿⣿⣿⣟⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠆⠀⡀⠀⠀⠀⠋⠉⠀⠀⠀⠀⠸⡟⠛⠛⣩⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠀⠀⠀⢧⠀⡀⠠⣤⣄⡀⠀⣀⣀⣀⣀⣤⣾⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⣀⣀⡀⡀⠀⠙⢻⠶⣶⣯⣭⡭⠭⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⣠⡴⠛⢀⡴⠛⠀⠀⠀⣀⠀⢀⡜⠀⢀⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠙⢦⣷⡀⠀⠀⠀⠀⠀⠀⠄⠐ ⠀⠀⠀⠀⠀⡘⠀⠀⣠⡞⠁⢀⡴⠋⠀⠀⠀⠀⣴⠃⢀⡞⠀⢀⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⢀⠀⠀⠀⠀⠀⠀⡉⠁⢱⣤⡀⠀⠀⠀⠀⠀⠰ ⠀⠀⠀⠀⠀⡇⣄⡼⠃⡀⣠⡞⠁⡀⠀⠀⠀⡼⠃⢀⡞⠀⢠⠟⢱⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠀⢸⠀⠀⠀⠀⠀⠀⠻⡄⠀⠫⠳⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⡿⢋⣴⠋⣠⠏⠀⡴⠃⠀⠀⣼⠃⠀⡞⠁⢠⠟⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠃⣟⠀⢸⠀⠀⠀⠀⠀⠀⠀⢷⡀⠀⠀⠘⢂⠀⠀⠀⠀ ⠈⠋⢀⣴⠟⢡⡞⢡⣴⠋⠀⡼⠁⠀⠀⢠⡟⠀⠀⠁⢠⠏⢠⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡾⠁⠀⢸⠸⡿⡄⠀⠀⠀⡄⠀⢸⡘⣧⠀⠀⠀⠀⢢⡀⠀⡄ ⠀⣠⠞⠁⣠⣟⣼⣿⠃⠀⣼⠇⠀⠀⣠⣿⡇⠀⠀⢀⡞⢀⡆⠀⡇⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡟⠁⠀⠀⢸⠀⣷⣧⠀⠀⠀⢿⠀⠀⢧⣹⡄⠀⠀⠀⠀⠀⠀⠀ ⠼⠁⠀⣰⣿⠟⢡⡏⠀⢰⠏⠀⠀⢰⠏⢸⡇⠀⡄⡞⠀⠈⠁⠀⣹⣤⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢾⣿⠿⣤⣤⣀⠀⢸⡇⢿⣿⡄⠀⠀⠘⡆⠀⠘⣏⣧⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣸⡟⠁⠀⡾⠀⠀⡾⠀⠀⢠⠏⡀⢸⡇⢸⣿⢁⣀⣤⣶⠿⢻⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⢀⡾⠋⠀⠀⠈⠙⢷⣤⡇⢸⢻⣇⠀⠀⠀⢷⠀⠀⣸⣿⡆⠀⠀⠀⠀⠀⠀ ⠀⣼⡟⠀⠀⢰⠇⠀⣸⠇⠀⢠⠏⠘⢃⣨⣧⣼⡟⠛⠋⠁⠀⠀⠈⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⡼⠀⠀⠀⠀⠀⠀⠀⠈⢿⣜⡎⣿⡀⠀⠀⢸⡆⠀⢸⣿⣇⠀⠀⠀⠀⠀⠀ ⠘⠋⠀⠀⠀⣿⠀⢠⣿⠀⠀⡾⣠⠖⠉⠁⠹⢧⣷⡀⠀⢀⣠⠤⣄⡘⣷⡀⠀⠀⠀⠀⠀⠀⢰⡇⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⣷⠾⣧⣀⠀⠀⡇⠀⠈⣿⢿⠀⠀⠀⠀⠀⠀ ⢠⠀⠀⠀⠀⣿⢠⡟⢿⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠉⠹⣷⡄⠀⠀⠀⠀⢀⡿⣇⡟⠀⠀⢠⡔⠛⠉⠒⠒⠂⠀⢷⢹⠀⢻⡏⠉⠀⢷⠀⠀⢻⣼⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⡞⠁⣸⡀⡏⠀⠀⠀⠀⠀⠀⠀⠴⠖⠒⠒⠊⠉⠓⠲⠀⠘⢿⢦⡀⠀⠀⣸⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⢷⠀⠀⢸⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠀⢿⡇⠀⡟⢷⣧⠀⠀⣀⣸⣷⣶⣶⣶⣶⣶⣶⣶⣒⣲⣦⠤⠀⠀⠀⠙⠶⢤⡇⢸⡏⠀⠀⠈⠉⠉⠙⢳⡲⠦⢄⣀⡀⠘⢿⡀⠈⣧⠀⢸⠃⠀⢸⡟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⢰⠃⣀⣈⣻⣿⣿⣛⣋⠁⠀⠀⠀⠀⠀⢉⣻⠛⠃⠁⠀⢀⣀⠀⣀⡠⢀⣀⠤⢄⡀⠤⣬⡿⠷⠯⠿⣶⣶⣼⣯⣓⠚⢷⡀⢹⡀⣾⡄⠀⢸⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣸⠠⣽⣿⠋⠙⢋⠉⠉⠙⠶⠶⠒⡀⠠⣴⣯⠄⠀⠀⠒⠉⢀⡭⠝⠀⠉⠀⠀⠉⠀⠀⢬⡔⠲⣤⡀⠀⠈⠉⠙⠻⣷⣶⣽⣤⣿⠏⡇⠀⠘⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡏⠀⠈⠛⠓⢠⣬⠇⠄⠒⠒⠂⠀⠀⠀⠒⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠓⠲⢬⣿⣒⠒⠊⠉⠙⢶⣽⣿⣿⣿⡀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠠⠴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢳⡶⠲⠞⠋⠀⣀⣿⣿⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠮⠷⠯⠉⠁⠀⠀⡞⠀⠀⠀⡤⠀⠀⠀⠀⠀ ⠀⠀⠀⡴⠀⣾⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⣰⠁⠀⠀⠀⠀⠀ ⠀⠀⢀⡇⣸⡟⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇⠀⠀⣼⠃⠀⠀⠀⠀⠀⢰ ⠀⠀⢸⢠⣿⣆⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠶⠶⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠃⠀⣸⠃⠀⠀⠀⠀⠀⠀⢀ ⠀⠀⢸⣿⡇⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠋⣁⣀⣀⣀⣀⣀⡈⠉⠲⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠁ ⠀⠀⣿⣿⣷⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠓⠀⠹⣿⣿⣿⣿⣿⣿⣿⣶⣄⣙⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀ ⠀⢰⣿⡟⡟⠷⣼⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣦⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⣠⠏⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠶⢸⣽⠁⣧⡇⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⢀⡼⠁⣨⡯⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢈⠗⢀⣿⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⣠⡤⣤⡀⠀⠀⢻⣿⣿⣿⣿⡿⠿⢿⣿⡿⠿⠿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⡰⠏⣆⣼⢋⣶⠷⠀⠀⠀⠀⠠⠄⠀⣠⠞ ⠀⢹⣋⡿⢻⠁⠀⠀⠸⣧⠀⠀⠀⡤⠟⠉⠀⠀⠉⡇⠀⠘⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⢈⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⡀⠀⠀⠀⠓⠒⠉⠉⠿⣿⠀⠀⠀⠀⢀⠜⠁⠀ ⠀⢸⣽⠀⢸⡄⠀⠀⠀⣿⣧⡀⠀⠳⣄⠀⠀⠀⢰⡇⠀⠀⠹⣿⣀⠀⠀⠀⠀⢀⣀⣄⣴⡏⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠃⣠⠞⠁⠀⠀⠀⠀⢠⢠⡼⡿⠓⢰⣾⣦⡞⠋⠀⠀⠀ ⠐⢸⣇⠀⠀⣿⠀⠀⣼⣿⣿⣿⣄⠀⠈⠢⠤⠤⠚⠀⠀⠀⢠⡰⠯⣭⣭⣭⣭⣭⡷⠋⠙⠃⠀⠀⠀⠀⠀⠀⣠⡾⠋⢀⣴⠏⠀⠀⠀⢀⠀⠀⢸⡰⢌⠁⢠⣿⡿⠃⠀⠀⠀⠀⠀ ⠀⠀⢿⠀⠀⣿⠀⠢⠟⠁⠙⠙⠻⣷⣄⠀⠀⠀⣠⠤⣄⠀⡜⠀⠀⠀⠀⠈⢧⠀⠇⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⢀⣴⣿⡟⡀⢀⣠⣤⣼⠷⡄⣸⠚⠋⢀⣾⠟⠀⣴⠁⠀⠀⠀⠀ ⣤⠀⢸⡀⢀⡿⣀⠄⠀⠀⠀⠀⠀⠈⠙⣷⣄⠘⠷⠴⠇⢰⠇⠀⠀⠀⠀⠀⢸⣼⠀⠀⠀⠀⠀⢀⣤⠞⠁⢀⡴⠟⢱⠟⠀⠁⠉⢱⡾⢋⠜⡴⠃⠀⠀⣾⡟⢠⡾⠁⠀⠀⠀⠀⡰ ⣜⣆⠀⣷⡾⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣷⣄⡀⠀⠘⠛⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⣀⡴⠋⢁⣠⠾⠋⠀⢀⡞⡀⠀⠀⢠⡼⠆⠁⠀⠀⠀⢀⣼⡿⢡⡞⠁⠀⠀⠀⠀⡴⡇ ⠹⡌⢧⠸⡍⠛⠢⣤⣠⠀⠀⠀⠀⢀⣠⣿⣿⣿⣿⡟⢀⠀⠀⠀⠀⠀⠀⠀⠀⣛⣠⠴⢛⣥⡴⠚⢉⣀⣤⠤⠶⣿⡹⠀⠀⠀⡚⠗⣄⠀⠀⠀⣀⣼⣿⣣⡞⠁⠀⠀⠠⠀⠘⠁⠃

⠀⠀⠀⠀⠀⠀⠀⢀⣀⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⡰⠖⠒⠋⠉⠉⠈⠒⠰⡄⠀⠀ ⠀⡠⠊⠀⠀⠀⠀⠀⠀⢀⣠⠀⠉⢹⠇ ⡰⠀⠀⠀⠀⠀⠙⠀⠀⠉⠀⠉⠙⢿⡀ ⢇⠀⠀⠀⠀⠀⡸⠀⢀⣤⡦⠤⡀⣀⣇ ⢸⣤⣶⡤⡀⢸⠁⠀⠀⠔⢳⠄⢠⢧⡆ ⠀⢫⢗⠿⣹⢸⣆⠀⠀⠀⠉⠀⠀⠀⡇ ⠀⠈⡎⡆⠊⠙⠀⠀⠀⠀⠀⠓⠣⢮⠃ ⠀⠀⠉⢣⠀⠀⠀⠀⠀⠐⠤⣴⣖⠞⠀ ⠀⠀⠀⠀⠑⢀⠀⠀⠀⠀⠀⠈⠝⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠜⠀⠀⠀

⠉⠳⢶⣶⣶⣶⣤⣤⣤⣀⣀⠉⠓⢷⣤⡀⠀⠀⢀⡠⠤⠀⠀⠐⠀⠈⠉⡛⢤⡤⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣹⣿⣿⣿⣿⣿⠿⣿⡟⠒⠦⣿⡿⠦⠚⠋⠁⠀⠀⠀⠀⠀⠑⠢⣌⠢⡉⠪⠢⣈⣙⠳⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣴⡿⠋⠉⠉⠙⢿⡄⢹⠀⣀⣼⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠱⡄⠀⠈⠫⠑⢤⡉⠪⣳⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⠙⠛⠀⠀⠀⠀⠀⢸⣇⣸⡋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢄⡀⠀⠀⠀⠘⠢⣀⠀⠘⣆⠀⠀⠀⠀⠙⢆⡈⠣⡑⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣸⠟⣿⣇⠀⠀⠀⠀⠀⢈⣑⠦⣄⡀⠈⠿⣶⢤⣤⣀⣈⢿⣦⣼⣦⠠⠀⠀⠀⠘⣷⣄⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⡿⢟⣻⣿⡟⢀⡏⠞⡄⠀⠈⢦⢣⠀⠙⢯⡛⠻⢗⣲⢼⡻⡍⠉⠓⢤⡘⣿⠻⣷⣇⠀⠀⠀⠘⣿⢦⠀⢘⣿⣿⣿⡀⠀⠀⠀ ⢿⡿⠛⢉⣴⡿⢿⠏⡇⠈⡇⠀⢘⡄⠀⠀⠻⣧⡀⠀⠙⢾⡉⠈⢠⠞⠻⣦⢤⣢⣽⣿⡷⠿⣿⡄⡇⠀⠀⠈⢇⢣⠀⢻⠿⠿⠿⠦⠀⠠ ⠉⣠⣶⠟⠁⠀⡼⠀⡇⠀⢇⠨⠈⠻⡀⠀⢀⠙⢻⡗⢤⣀⠸⢶⣄⡀⠜⣽⡿⠿⠋⡸⠁⢠⣼⣧⣗⠀⠀⠀⠸⠀⢧⠈⢇⠀⠀⠀⠀⠀ ⢸⠟⠁⠀⠀⠀⡇⠀⠀⠀⠘⠀⡇⠀⢹⡦⣾⣄⡀⠉⠂⠈⠑⠒⠽⠿⣖⠻⠓⠚⢋⣥⢚⡿⠛⣿⣿⠀⠀⠀⠀⠀⡘⣧⠈⡆⠀⠀⠀⠀ ⠁⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡇⠀⢀⣹⡏⠙⡿⢷⣟⡛⠶⠶⢶⣤⣌⠳⡀⡶⣽⡱⠎⠀⠀⢹⣿⠀⠀⠀⠀⠀⡇⡟⣧⠘⣆⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣇⠀⠘⣿⡽⣜⠀⣤⣽⡿⠦⡀⠀⠀⣈⣿⣿⠀⢀⠀⠀⠀⠀⢸⢹⡄⠀⠀⠀⠀⡇⢸⢸⢧⠈⢧⠀⠀ ⠀⠀⠀⠀⠀⠀⡃⠀⠀⠘⣆⠀⢿⠀⣼⢻⠙⠺⣾⣿⡿⠛⠀⡨⢦⣴⢋⡿⠃⠀⢀⣀⣤⣀⡀⠈⡆⣿⠀⠀⡄⢠⡇⢸⣇⠀⠀⠀⠳⡀ ⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠘⢆⠸⡆⢹⠀⡇⠀⣿⠿⠷⠋⢸⢏⣾⡟⠘⠀⢀⣴⣿⣿⣿⠿⢿⡄⢃⢹⠀⠀⢣⣸⡇⢸⣿⡄⠠⡀⠀⢳ ⠀⠀⠀⠀⠀⠀⢸⠀⢠⠀⠀⠈⢧⣻⡎⢳⣿⡸⣇⠀⣠⠶⣧⡞⡏⠀⠀⠀⣾⣿⠛⠛⠁⠀⠀⠱⡈⣼⡆⠀⠀⢻⡇⢸⣸⠷⣤⣿⡌⣆ ⠀⠀⠀⠀⠀⢀⣾⡏⣼⠀⠀⠀⢈⢻⣿⣆⠹⣷⡛⠉⠙⠊⠛⠁⠀⠀⠀⠀⠻⣿⣦⡀⠀⠀⠀⠀⡇⠹⣝⣧⣤⣤⣿⣾⢏⡔⠈⣿⣷⠘ ⠀⠀⠐⠒⠚⠛⠉⣧⣿⡆⠀⠀⠘⣆⠙⠮⠙⠺⣷⣦⣀⣀⡀⠠⠀⢀⣀⠄⠀⠀⠉⠛⠑⠒⢤⡷⠃⠀⢹⣿⣟⠉⡽⠛⣾⣶⣶⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⢠⡿⣽⡇⠀⠀⣧⢿⠃⠀⠀⠠⠭⠟⢛⡿⠯⢍⣉⣀⣀⣀⡀⠀⠀⠀⠀⠀⢸⡇⣇⡠⢿⣧⡜⠑⣶⠊⠈⢿⣿⡝⣿⣌ ⠀⠀⠀⠀⠀⣀⡞⢻⢻⣇⠀⠀⢸⣸⣷⣄⠀⣒⠒⠶⢤⣭⣿⣿⣷⣯⣟⣛⠛⠷⣦⡴⠿⠂⢙⠋⠀⠀⢠⣿⡧⠤⣿⣿⣷⣮⣻⣿⣿⠈ ⠀⠀⠀⠀⣸⣿⡀⠈⢸⣿⣄⠀⠸⣿⣿⣿⣿⣿⣿⠟⠉⠁⠀⠀⠉⠙⢿⡏⠛⠶⣮⣿⣆⣀⠈⠀⠀⣰⡼⠛⢿⣿⣿⣿⣯⡀⠉⢿⣿⠀ ⣄⣠⣤⣾⡿⠿⠇⠀⠘⣿⢹⡄⠀⢹⡿⣍⢻⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢹⢀⣄⠀⢨⣻⢉⣉⣑⢶⡟⢉⡉⠒⠛⢿⣿⣿⣿⣯⣞⠻⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠤⠤⠤⠤⣄⣀⠀⠀⠀⠀⠀⢀⣀⡤⠤⠖⠒⠲⠦⠤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡖⠒⠒⠶⢿⣤⣀⠀⠀⠀⠀⠀⠉⠙⠒⢦⣤⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢦⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣀⡴⠖⠛⠉⢉⣉⣉⠉⠓⠶⢤⣀⠉⠁⠀⠀⣀⣀⣤⣤⡤⠤⠤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢷⣄⠀⠀⠀⠀ ⠀⠀⢠⣾⡵⠶⠛⠉⠉⠉⠉⠉⠉⠙⠳⢦⡈⠙⢶⣴⢋⣉⣠⠴⠶⠖⠚⠛⠓⠶⠦⣍⡙⠲⣦⣀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣧⡀⠀⠀ ⠀⣠⠟⢁⣤⣶⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣠⣟⣋⣡⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣄⠙⠳⣄⠀⠀⠀⠀⠀⠀⢿⣿⣷⡀⠀ ⣼⠋⢰⣿⡿⠿⣿⠟⣿⡆⠀⠀⠀⠀⠀⠀⢀⡾⢹⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⣈⣀⠀⠀⠀⠀⠀⠘⣿⣿⣧⠀ ⣧⠀⠸⣿⣧⣠⣾⢿⣿⡇⠀⠀⠀⠀⠀⠀⢸⠀⢸⣿⡋⠉⢹⣧⣨⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⠀⠀⠀⠀⠀⣿⣿⣿⡇ ⠘⢷⡀⠙⠻⠿⠿⠿⠋⠀⠀⠀⠀⠀⠀⣠⣾⡄⠘⣿⣷⣶⣾⣛⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠚⠋⠁⠀⠀⠀⠀⠀⢹⣿⣿⣷ ⠀⠀⣽⠶⠦⣄⣀⣀⣀⣀⣀⣀⡴⠶⠛⠁⠀⠻⣆⡈⠛⠿⠿⠿⠛⠁⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁⣠⡄⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿ ⠀⠀⠈⠓⠦⢤⡤⣤⡤⠤⠤⠤⠶⠞⠀⠀⠀⠀⢻⣝⠶⢤⣄⣀⣀⣀⣀⣀⣀⣠⠤⠖⢋⣁⡴⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿ ⠀⠀⢠⡴⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣤⣄⣉⣉⣉⣉⣭⣥⡤⠴⠒⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿ ⠀⠀⡇⣠⣤⡤⠤⠤⠦⠦⠴⠶⠶⣤⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿ ⠀⢰⡟⠉⠀⠀⣀⣀⣤⣤⣤⣀⣀⣀⠀⠀⠀⠈⠉⠉⠛⠲⠶⢤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿ ⠀⠀⠙⢧⡀⠸⣏⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣤⣀⣀⠀⠈⠙⠳⠦⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿ ⠀⠀⠀⠀⢻⡄⠙⡇⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⠀⠈⠙⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⡇⠀⣧⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿ ⠀⠀⠀⠀⢠⡇⠀⣧⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⡏ ⠀⠀⠀⠀⢸⡇⠀⡏⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⢁⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡿⠁ ⠀⠀⠀⠀⢸⠀⢰⡇⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⣠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⠃⠀ ⠀⠀⠀⠀⢸⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⢀⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⠃⠀⠀ ⠀⠀⠀⠀⣿⠀⠸⣧⡀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⠟⠋⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⠟⠁⠀⠀⠀ ⠀⠀⠀⠀⠹⡆⠀⠈⠙⠶⠶⢤⣄⣀⣀⣀⣤⡽⠿⠛⠉⠀⢀⣤⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⠟⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠻⣷⢦⣤⣀⣀⣀⡀⠀⠀⢀⣀⣀⣀⡤⠶⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠳⣄⣀⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣾⣿⠿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠒⠲⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠒⠚⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣀⣠⣔⣦⣾⡟⣩⣿⣿⠢⡄⣀⣀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣾⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣬⢧⡀⠀⠀⠀ ⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣍⣱⢦⡀ ⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⣏⣹⠃⠀ ⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠉⠀⠀⠀⠀⠀⠈⠙⠻⣿⣹⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡇⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⣴⠶⠶⠶⠦⠀⠀⣤⣿⡇⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⣀⡤⢶⣾⡶⠀⣴⣃⣸⠁⠀ ⠈⣿⣿⡏⠙⣻⣿⣿⣿⡇⠀⠀⠀⠀⠙⢶⣿⠟⠀⠀⢻⣼⣿⠀⠀ ⠀⠹⣿⣧⠈⠛⣇⢸⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢹⠀⠀ ⠀⠀⢹⣿⣷⣄⣈⠸⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⠆⢸⡀⠀ ⠀⠀⠸⣿⣿⠏⠟⠀⠁⠀⠀⢸⣷⠐⠿⡇⠀⠀⠀⠈⣙⣳⡟⠀⠀ ⠀⠀⠀⠈⣿⠇⠀⠀⠀⠀⠐⠀⠀⠀⠀⢿⣭⣶⣾⣿⣟⡽⠀⠀⠀ ⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢳⣌⠻⠿⣿⠀⠀⠀⠀ ⠀⠀⠰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣀⠈⢷⣿⣷⣾⡇⠀⠀⠀⠀ ⠀⠀⠀⠘⢆⠀⠀⠀⡀⠸⣄⠀⠀⠀⢿⡿⢆⣼⡿⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠑⠦⣀⡀⠀⠉⢙⣶⡆⠀⣴⠿⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠘⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠟⠛⠉⠉⠀⠈⠉⠉⠲⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠀⠀⠀⠀⠀⣠⠖⠒⢦⡀⠘⡆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⢹⡼⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠤⠤⣀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠘⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠇⠀⠀⠑⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⡶⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⢄⣹⣄⠀⠀⠀⠀ ⠀⠀⠀⠀⡰⠋⠀⠀⠀⢀⡤⠒⠈⠉⠉⠉⠑⠒⠤⣀⠀⠀⢀⠴⠋⣀⣀⣀⠈⢿⠀⠀⠀⠀ ⠀⠀⠀⢰⠃⠀⠀⠀⢠⠏⠀⠀⣀⣤⣤⣶⣤⣄⣀⠀⠉⠉⢁⣴⣾⣿⣿⣿⡇⢸⡄⠀⠀⠀ ⠀⠀⠀⡎⠀⠀⠀⢀⡟⠀⢠⣾⣿⣿⡿⠿⠿⠟⠿⣿⣿⡿⠛⠛⠛⠛⠻⢿⡇⢸⠀⠀⠀⠀ ⠀⠀⠀⣇⠀⠀⠀⠈⡇⠀⢻⣿⠋⠀⠀⠀⠀⠀⠀⣠⣽⡆⠀⠀⠀⠀⢠⣾⣿⡟⠀⠀⠀⠀ ⠀⠀⢀⣸⠦⣀⠀⠀⣧⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠿⢿⡇⠀⠀⠀⠀⢀⣹⡿⠁⠀⠀⠀⠀ ⠀⡔⣯⣤⣤⠞⠓⠀⠸⣆⠀⠳⣄⠀⠀⠀⢀⣀⣀⡤⠾⢤⣤⣤⡶⠖⠿⠹⠙⠲⢄⡀⠀⠀ ⢸⠙⠃⠀⠘⢤⡄⠀⠀⠈⣳⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠁⠀⠉⠀⠀⠀⠀⠀⡠⠖⠋⠙⢦ ⢻⡆⠀⠀⠀⡎⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣋⣤⣴⣶⣄⣸ ⠈⢷⡀⠀⣞⢻⠃⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⡟ ⠀⠀⠉⠲⠄⠈⣦⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⠀ ⠀⠀⠀⠀⠀⠀⠘⢆⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣧⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⡻⠿⡿⢛⣳⠃⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠦⠤⠤⣤⣀⣤⣤⣤⣤⠤⠜⠛⠉⠋⠁⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⣦⠘⢲⣺⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣤⣴⣾⢶⣾⣿⣿⣿⣷⣾⣿⣿⣿⣿⣷⣷⣶⣰⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢒⡇⠀⠀⠀ ⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣤⠄ ⠀⢀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⣧⡙⠀ ⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠻⠋⠉⠁⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣇⠀ ⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣻⣿⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣇⣳⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡇ ⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠓⠀⠀⢀⡴⠿⠛⠛⠛⠲⠀⠀⠀⣴⣾⠇ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠐⠈⠀⣀⣤⣀⠀⢀⠇⢀⣤⠏⢨⠀ ⠀⢻⣿⡟⣽⠮⣝⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠎⠩⠰⠿⣿⠊⠀⠸⠑⣉⣿⠀ ⠀⠸⣿⣷⠀⢠⣼⣾⠏⢻⣷⡾⠄⠀⠀⠀⠀⠀⠀⠭⠽⠟⠁⠀⠀⠀⢉⣻⣾⠀ ⠀⠀⠸⣿⣇⠀⠋⢫⠀⢸⣟⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢸⡀ ⠀⠀⠀⢻⣿⣷⣄⠀⣠⢘⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⣀⣤⣤⠄⠄⢸⠁ ⠀⠀⠀⠘⣿⣿⡟⢙⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⠉⠛⢧⣰⠏⠀ ⠀⠀⠀⠀⠛⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡡⠀⡠⠀⣀⣤⣤⣴⡿⠀⠀ ⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢓⠶⣿⣿⣿⢿⠏⠀⠀⠀ ⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⡘⠻⠽⢿⠆⠀⠀⠀ ⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⢴⡶⠉⠀⠀⠀⠀ ⠀⠀⠀⠀⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⠀⠓⢊⡴⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠴⢒⡤⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⠀⠀⠀⠀⠀⠀⠐⢀⡀⠴⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣠⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿ ⠀⠀⢀⣤⠔⠀⠀⠀⠀⣀⣠⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣦⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣼⡛ ⢀⣼⣿⣿⡶⠶⠶⠶⠟⠛⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠈⠉⠉⠉⠉⠉⠉⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣾⣿⡿⣿⣿⣿⣿⣿⣿⣿⡟ ⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢿⡿⠟⠀⠀⠀⠉⠛⢻⣿⣿⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣀⣠⢤⡆⠀⠀⠀⠀⠀⠀⠙⣿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣤⣤⣤⣄⡀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢏⠀⣤⣴⣶⣾⣯⡷⠀⠃⠀⠀⠀⠀⠀⠀⠀⠈⡇ ⠀⠀⢀⣀⣠⣶⣞⣩⣽⣿⡿⠷⠿⠿⠿⠿⣿⣿⣿⣿⣿⣶⡆⠀⠀⠀⠀⠀⢰⣾⣀⡀⠀⠀⠀⠀⠀⠀⢹⣾⣿⣿⣿⢿⠟⠃⠀⠀⢀⣀⣠⣤⣤⣤⣦⣶⣤⡇ ⣠⣶⣿⠿⠿⠿⠛⠉⠁⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⡶⢴⢊⣿⣷⠏⠉⠁⠀⠀⠀⠀⠀⠀⠀⢸⢿⣿⣿⠃⢀⣀⣴⣾⡿⠟⠛⠛⠛⢻⣿⣿⣿⡏⠀ ⠙⠿⠃⠀⠀⠀⠀⠛⠛⠛⠻⠾⠂⠀⠈⠻⠿⢿⢿⡟⠛⠿⠛⠃⠈⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢺⣿⢿⢰⣾⣿⠋⣁⠀⠠⠀⠀⣰⣿⣿⣿⣿⠀⠀ ⠀⠀⠀⠀⢠⣀⣀⠳⣄⡀⠀⣀⡀⠀⣀⣀⣀⣠⣤⣴⣴⣲⠖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢾⣦⣬⣉⣉⣉⣙⠒⠒⠒⠛⠿⠛⣿⣿⡀⠀ ⠀⠀⠀⠀⠀⠙⠛⠛⠿⢿⡿⠿⠿⢿⣿⠿⠿⠟⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⣏⠉⠙⢻⣿⣿⣷⣶⣦⣤⣤⣿⡿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠐⠶⠤⠤⠴⠤⠤⠤⠤⠖⠆⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⠇⢰⡎⠁⠉⠉⠟⢻⣿⡿⣿⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇⠐⠿⠶⠶⠶⠚⠊⠇⠓⠎⢻⣄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠹⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠃⠀⠀⠀⠀⠀⠁⠐⠁⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠠⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣄⣀⠀⠀⢀⣵⠀⠀⠀⠀⠀⠀⢸⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⠀⠀⣀⡀⢀⣠⣴⣶⣶⣶⣤⣤⣤⣤⣶⡾⠿⠿⠿⠮⠽⢶⣶⡿⠟⠀⠀⠀⠀⠀⡸⣿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣟⢿⣿⣿⣿⣿⣀⣀⣴⣶⡶⠟⠋⠀⠀⠀⠀⠀⡐⣦⣿⠇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠙⠛⠛⠿⠿⢿⣿⣿⣿⣿⣿⣿⢿⣿⣧⠀⠀⠀⠀⠀⢀⡀⣡⡿⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣄⣀⠈⠉⠛⠿⠿⣿⣿⣄⠀⠀⠀⢀⣾⡾⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠈⠙⠻⢷⣦⣼⡟⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣠⣝⣙⣿⠂⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡔⠂⠀⠀⠀⠀⠀⣀⣤⡶⠢⠤⠴⠒⠄⠀⠀⠀⣀⣀⣠⣤⣴⣶⣷⣾⣿⣿⣭⣭⣽⣙⣿⠿⠿⣛⣛⣿⣿⣿⣻⠟⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⢀⣤⠤⠶⠛⠋⠁⠀⠀⠀⢀⣠⣴⣶⣾⣿⣿⣿⣿⣿⣿⣯⣭⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⡟⡛⢩⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣷⣤⣤⣤⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣻⡿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠿⣏⢉⡙⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣆⠀⠀⡀⠈⠙⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣤⣼⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⠀⠙⠆⠀⠀⠀⠈⠙⢿⣭⢉⣭⣿⣿⡛⠛⢻⣿⣿⣿⣿⣿⣯⣭⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⢰⡄⠠⠀⠀⠀⠀⠀⠹⠛⠛⠉⠉⠀⠀⠀⠈⣿⠿⠿⠟⠛⢛⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠁⠈⢰⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⣠⡾⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠘⠇⠀⣦⡀⡛⠛⠶⣤⣠⣤⣤⣤⣤⣴⢶⣟⡷⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⢤⢀⠠⡄⢀⠀⠀⠙⠛⡿⠿⢷⣶⠶⢶⠶⠶⢧⡾⠛⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⢀⡀⠤⣀⡰⠭⡉⠉⠐⠂⠄⠂⠉⠀⠉⠁⠂⢄⠀⠀⠀ ⠀⢠⢞⣒⡀⠉⠀⠒⢅⢲⠬⠙⠒⠚⠛⠵⡢⢄⠀⠀⠈⣷⡀⠀ ⢠⠁⣿⣻⣿⠀⠀⠀⡔⣽⠿⣟⣦⠀⠀⠀⠈⠒⢠⠀⠀⢹⣷⠀ ⠀⢑⠌⣉⣁⣀⡠⠔⠳⡘⠷⠿⠋⠀⠀⠀⡠⣊⠁⠀⠀⠘⣿⡆ ⠀⢀⠭⠃⠀⠀⠉⠀⠀⠙⠥⠒⠒⠲⠬⠕⠊⠁⠀⠀⠀⠀⣿⡇ ⠀⢸⡊⠩⠭⢭⣉⣉⣁⡐⠒⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇ ⠀⠀⠘⠘⡀⠀⢿⣿⣿⣿⣿⣷⣶⣤⡉⢲⠀⠀⠀⠀⠀⢸⣿⡇ ⠀⠀⠀⠀⠇⠀⠈⢿⣿⣿⣿⣿⣿⣿⠟⡜⠀⠀⠀⠀⢀⣿⣿⠀ ⠀⠀⢀⢸⠀⠀⠀⠘⣿⣿⣿⣿⠟⢡⠊⠀⠀⠀⠀⢀⣼⣿⠃⠀ ⠀⠀⠘⡈⠒⠤⠄⠀⠸⠟⢋⡡⠒⠁⠀⠀⠀⢀⣤⣿⠟⠁⠀⠀ ⠀⠀⠀⠘⠩⢀⣒⠒⠀⠉⠁⠀⠀⣀⣀⠤⠶⠛⠋⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠒⠒⠦⠤⢄⡀⠀⠀⣀⡤⠔⠒⠒⠒⠒⠤⣄⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣠⠤⠴⠿⠭⣍⣙⠓⠦⠄⠀⠀⠀⠀⠈⠙⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄⠀⠀⠀⠀ ⠀⠀⣠⣾⠥⠖⠒⠒⠒⠒⠒⠬⣙⠲⢤⡴⢒⣉⡭⠭⠭⠿⠿⢭⣒⠦⣄⡀⠀⠀⠀⠀⠀⠘⣷⡄⠀⠀ ⢀⡼⢋⣴⣶⣶⣄⠀⠀⠀⠀⠀⠈⢣⣴⣿⣭⣤⣄⡀⠀⠀⠀⠀⠈⠙⢦⡙⠢⡀⠀⠀⠀⠀⢿⣿⡆⠀ ⣜⠀⣾⡟⠙⣿⣽⡇⠀⠀⠀⠀⢀⠎⢸⣿⠿⢿⠟⣿⡆⠀⠀⠀⠀⠀⠀⠙⠒⠢⣄⠀⠀⠀⢸⣿⣿⡄ ⠹⣄⠘⠿⣿⣿⠿⠁⠀⠀⠀⠀⣸⡄⢸⣷⣤⣼⢿⣿⠇⠀⠀⠀⠀⠀⠀⢀⡤⠴⠋⠀⠀⠀⠀⣿⣿⣇ ⠀⠈⡗⠦⠤⢄⣀⣀⡠⠤⠖⠋⠁⠙⣄⡙⠛⠛⠛⠉⠀⠀⠀⠀⠀⣠⠔⢁⡤⠀⠀⠀⠀⠀⠀⢹⣿⣿ ⠀⠀⠈⣙⡶⠒⠒⠒⠒⠛⠋⠀⠀⠀⠹⣍⠓⠢⠤⠤⠤⠤⠔⢒⣉⡤⠞⠋⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿ ⠀⢰⠋⣁⣀⣀⣀⣀⣠⣤⣀⣀⣀⠀⠀⠀⠉⠓⠒⠒⠒⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿ ⠀⢸⡋⠁⢀⣀⡤⢤⣤⣀⣀⣀⠈⠉⠉⠓⠒⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿ ⠀⠀⠙⢦⠘⣄⠀⠀⠘⣿⣿⣿⣿⣿⣿⣶⣶⣦⣤⣄⣈⠙⠒⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿ ⠀⠀⠀⠈⡆⢸⡀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿ ⠀⠀⠀⢀⡇⢸⡀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇ ⠀⠀⠀⢸⠃⣸⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⢠⠞⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⡿⠀ ⠀⠀⠀⢸⠀⡟⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⡿⠏⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⡿⠁⠀ ⠀⠀⠀⢸⠀⢷⣀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⠟⠋⢀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⠟⠁⠀⠀ ⠀⠀⠀⠘⣆⠀⠉⠓⠒⠦⠤⠤⠤⠞⠛⠉⣀⡠⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⠟⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⢯⡛⠒⠒⠲⠤⠤⠖⠒⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⠟⠋⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠑⠒⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠖⠚⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⣀⡤⠶⠒⠒⠒⠒⠒⠒⠒⠒⠲⠦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡴⠞⠉⣀⣠⠦⠴⠆⠀⠀⠀⠀⠀⠀⠐⠛⠛⠛⡻⣿⡶⣦⡀⠀⠀ ⠀⠀⣴⠋⣠⣶⠟⢋⡤⠶⠶⠶⢶⡀⠀⠀⠀⠀⠀⢀⡴⠛⠉⢉⣿⡶⡍⠀⠀ ⠀⣼⠁⠚⠛⠁⢠⠏⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⢠⡏⠀⠀⠀⠙⠛⠁⣇⠀⠀ ⢰⡇⠀⠀⠀⣠⣼⠀⣾⣿⡆⠀⠀⢸⡇⠀⠀⠀⠸⣆⠀⠀⠀⠀⣀⡼⢻⡀⠀ ⣸⠀⠀⠀⠈⠉⠎⠳⢭⣉⣀⣀⣠⠞⠁⠀⠀⠀⠀⠈⢙⡿⠛⠉⠉⠛⢾⡇⠀ ⡏⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠤⠤⠤⠤⠤⢲⡟⢁⣴⠋⠛⢳⡄⠹⡆ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢠⡿⠀⣾⣹⣋⣏⣟⣷⠀⡇ ⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⡏⠀⠀⠀⠀⣹⢠⠇ ⢹⡄⢣⠀⡆⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡇⠀⠀⠀⢠⠇⡾⠀ ⠈⣧⠈⢃⢹⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡇⠀⠀⠀⣿⠀⡇⠀ ⠀⠸⡆⠀⢇⢃⠀⠈⡆⠀⠀⠀⠀⠨⢕⣄⠀⠀⠀⡟⢸⣃⡀⠀⠀⢿⠀⢹⠀ ⠀⠀⢻⡄⠈⡌⣆⠀⢡⠀⠀⠀⠈⠉⠓⢬⡑⠀⣸⠁⣾⠀⠈⠙⢦⢸⡇⢸⠀ ⠀⠀⠀⢳⡀⠘⠌⢄⠀⠑⢄⠀⠈⠉⠓⠦⡉⠂⣿⠀⣿⠒⡖⡖⡖⢻⠃⢸⠀ ⠀⠀⠀⠀⠻⣄⠈⠢⣑⠢⢄⠑⠤⡀⠀⠀⠈⠳⣿⠀⠹⣏⠙⠓⣷⠟⠀⣼⠀ ⠀⠀⠀⠀⠀⠙⠳⣄⡀⠑⠂⠍⣂⠤⠀⢀⣀⠀⠹⣄⠀⠈⠛⠛⠉⣀⡼⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢦⣄⣀⠈⠁⠐⠒⠀⠀⠉⠙⠒⣶⠶⠚⠉⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠳⢤⣤⣠⣤⠾⠛⠋⠁⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⠀⣠⣤⣾⣶⣶⣄⣀⠀⠀⠑⢢⣀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⡿⠿⠿⠿⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⢻⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢛⡇⠀⠀⠀⢀⣤⣶⣾⣿⣷⡆⠀⠀⣾⣷⣾⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠸⣿⣿⣿⣿⣿⠿⠋⠁⢀⡞⠁⠀⠀⡴⠋⠁⠀⠀⠘⣿⠁⠀⠀⣿⡋⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⢷⣿⣿⣿⠋⠀⠀⠀⢀⡞⠀⠀⠀⠘⠁⢰⡟⠉⣭⣷⣿⣄⡀⠀⡏⢉⣿⣿⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⣀⣄⡉⠈⠙⡆⠒⠛⢻⠛⠒⠲⠶⠤⠤⢄⣉⣻⡿⠁⠉⢸⣷⠶⠒⢼⠏⢿⢦⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⡟⠀⣹⡆⠀⢹⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⣠⡏⠀⠀⢸⡄⢸⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠒⠒⠦⢼⣸⡄⢰⡿⡇⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠚⠋⠀⠀⠀⠀⢙⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠸⣷⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠐⣴⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⣀⠈⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⠿⠛⠛⣶⡴⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⠟⠋⠑⢶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⡀⡽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠠⣴⠂⠀⡟⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢧⠀⠀⢀⣀⣠⣤⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⠷⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣀⠀⠀⠀⠙⠻⠿⠿⠛⠛⠛⣿⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡿⠁⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠛⠛⠻⠿⠷⣶⡶⠾⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⡇⠀⣾⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⣴⣿⠶⠖⠚⢹⣷⠾⠁⢠⠃⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡎⠻⢿⡿⢷⢼⣿⣿⣿⣿⣧⣀⣀⠀⠀⠀⠀⠀ ⠉⠀⠀⠀⢀⣿⢃⠀⠀⣼⠐⡇⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣤⣤⣿⠀⠀⠉⠛⠻⢿⣿⣿⣿⣿⣷⣦⡄ ⠀⠀⠀⠀⣼⣯⠀⠀⠀⢹⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢸⡜⢿⣷⣄⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿ ⠀⠀⠀⢸⡿⠀⠀⠀⠀⠈⣆⠀⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⡀⢀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠻⣿⣆⠀⠀⠀⠀⠀⡈⠛⠭⠙⠻ ⠀⠀⢀⣿⠃⠀⠀⠀⠀⠀⠘⠆⠀⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⣥⣀⣀⣠⣤⣶⣿⠟⠀⠀⠀⠹⣿⣆⠀⠀⠀⠀⠀⢦⡀⠀⠉ ⠀⠀⣸⡟⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠙⢄⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⠟⢻⠏⠀⢸⡇⠀⠀⠀⠀⠀⠹⣿⡆⠀⠀⠀⠀⠀⢳⠀⠀ ⠀⣀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠙⠦⠀⠀⠀⠀⠀⠀⠀⠀⠠⠼⠃⠀⢀⡞⠂⠀⠀⠀⠀⠀⠀⠹⣿⡄⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⠹⢶⣤⠴⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⠀⠀⣀⣶⣤⣄⣠⣶⣿⠏⢠⡄⣿⣾⣿⣿⣧⣠⡆⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣀⣼⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⡶⢀⡆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡇⠀⣠⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡀⠀⠰⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢉⣿⢀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣣⣿⣿⡀⠀⠠⢀⣀ ⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠶⣿⡏⠀ ⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣀⣹⠀⠀ ⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠟⠛⠛⠁⠀⠀⠈⠉⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀ ⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡍⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣿⣧⠀⠀ ⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢟⣿⣿⣿⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢿⡄⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣌⣿⣿⡇⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⣻⣷⠈⢿⡄⠳⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣿⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⢿⡀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⠀ ⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠉⠉⠀⠀⠀⠀⣠⣾⠿⠟⠛⠉⠉⠉⠉⠙⠷⠄⠀⠀⠀⠀⣾⣿⣿⡟⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⡤⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣲⠀⠀⠀⢀⣿⠁⠙⡇⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⣀⣴⡶⠶⣶⣤⣀⠀⣤⠏⠀⢠⣶⠟⢉⣀⣠⡇⠀ ⠀⠸⢿⣿⣿⣿⢏⣰⣶⣤⣙⢿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠾⠛⢁⡠⢴⣿⡿⠿⡼⠋⠀⠀⢸⣣⡴⠛⢹⣿⡇⠀ ⠀⠀⢸⣿⣿⣿⡘⠿⠁⠘⠻⢷⠻⣿⣿⣿⣿⡏⠹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣤⣤⣉⣴⣾⠟⠀⠀⠀⠀⠀⠳⣤⣑⣙⣿⡇⠀ ⠀⠀⠘⣿⣿⣿⣧⠀⠀⣴⣶⣿⣷⡿⠀⠹⣿⣷⣿⡟⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠶⠿⠒⠁⠀⠀⠀⠀⠀⠀⠀⢤⣉⣿⣿⡅⠀ ⠀⠀⠀⠈⢿⣿⣿⡄⠀⠘⡿⠋⣿⠀⠀⠀⣿⠿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡈⠉⢸⡇⠀ ⠀⠀⠀⠀⠘⣿⣿⣿⡀⠀⠀⠀⠹⡄⠀⠀⣿⣧⣿⣷⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠘⣇⠀ ⠀⠀⠀⠀⠀⢻⣿⣿⣿⣦⡀⠀⠀⠀⡇⠀⢾⣿⣿⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡀⠀⣀⣀⣀⣀⡀⣸⠀⢸⡍⠀ ⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⢶⣤⣴⡇⠀⠙⠛⠛⠻⠿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠻⢿⣿⣿⣛⣯⡍⠁⢀⣾⠃⠀ ⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⡟⠁⠈⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠈⡙⠻⣧⡀⣿⠋⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⠁⠀⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣻⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠈⣿⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⠦⣀⡴⠂⣀⣠⣶⣾⣿⣿⣿⣿⡿⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢿⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⠛⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢲⡌⠙⢿⣿⣿⣿⣿⣽⣇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣄⠈⠛⠻⢦⡿⢟⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⠀⣀⣀⣠⠾⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠠⡄⠀⣹⡟⢖⡶⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⢻⠰⠞⢃⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠰⡆⠸⢰⣠⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⣜⣛⣛⣣⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⢐⢠⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⠑⠒⠤⠤⡀⠀⠀⠀⠤⢀⠀⠀⠉⠀⣀⣤⠴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡄⠀⠀⠀⠀⠀⠀⠀⠀⠐⣆⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠟⠁⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠏⠛⠿⣖⡤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀⣀⡤⣤⣶⠿⠛⠁⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⢀⣠⠴⠚⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡴⠚⠉⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣄⡀⠀⠀⠀⠀⠀ ⠀⠀⢀⠐⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠋⠙⠲⠶⠄⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⠤⠴⠒⠒⠚⠒⠦⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⣐⣲⣶⣤⣄⣸⣗⣦⣴⣖⣶⠤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠒⠲⣶⠤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠐⣿⣿⣿⡿⢻⡋⠋⠉⠉⠉⣙⡛⠻⡟⢿⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣶⣶⣶⣤⣿⣷⣦⣬⣽⡖⠦⣄⠀⠀⠀⠀⠀⠀⠀ ⢀⣻⣷⣾⠟⣿⠈⠓⠒⢶⣀⣘⣾⠟⢉⣈⡿⠁⠀⠀⠀⣠⠄⣀⡀⠀⢀⡀⠔⠀⠀⠀⠀⣴⢛⣿⣶⣀⡉⣩⣝⡻⠿⣿⣶⣍⡂⠀⠀⠀⠀⠀ ⠀⠙⠿⠷⠄⠈⡻⢶⣶⡾⣠⠆⠀⠿⠿⣄⣽⢀⡠⣖⡯⠐⢺⣿⠗⠚⠁⠀⠀⣀⡤⠖⣀⡼⢯⣠⡀⠻⣿⣿⣿⡻⠶⢦⣉⠻⣿⣶⣤⣄⠀⠀ ⠀⣠⣖⠥⠺⣏⣣⠼⢋⡠⣔⡯⠖⠀⠀⢀⡠⠔⠊⠁⠀⠀⣸⣶⣀⡀⢄⡒⠍⠀⠀⢀⡾⡔⠈⢛⠛⠛⠛⠷⢤⣥⣀⢀⣽⠿⠋⠙⣿⣧⣿⣀ ⣠⡾⢝⣮⣴⢿⡯⠂⠌⠊⠋⠀⠀⠠⠚⠉⠀⠀⠀⠀⠀⠀⠻⠉⠉⠀⠈⠀⠀⠀⠀⢸⡿⣖⠬⠉⠀⡀⠀⠀⠀⠙⢫⡈⣡⠀⠠⠶⠟⠛⠉⠉ ⢨⡾⠛⡁⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⠀⠁⠀⠀⠀⠀⠀⠀⠀⠩⠋⢒⡬⠔⠒⠋⠁⠀ ⠉⠀⠀⠀⠀⠀⠀⣀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠒⠛⠛⠛⠒⠶⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠉⢠⣤⣤⣤⣤⣤⣤⣀⡈⠙⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢰⣾⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡉⠁⠘⢿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣌⡳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣦⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⢠⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠘⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡿⠯⠁⠀⠀⠀⠀⠀⡀⠅⢨⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡅⠐⠢⠀⠀⠀⠀⣈⣁⡾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣉⣭⣛⡒⣒⣒⣚⣭⡿⠋⢳⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠁⠀⠀⠀⠀⢫⡀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣷⠀⠀⠀⠀⠀⠀⢱⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠿⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠀⠀⠀⠀⠀⠀⢾⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠈⠁⠀⠀⠀⠀⡰⠒⣄⠀⠉⠁⠀⠀⡠⠮⠏⠑⠒⠒⠇⠴⣖⡂⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢈⡴⠁⣈⣋⢳⢅⣀⠀⠔⠑⠀⠀⠀⠀⠀⠀⠤⠮⠤⡰⠖⠈⢆⠀ ⠀⠀⡰⠀⠀⢰⠁⡡⠂⢀⡀⠡⠑⢒⠀⠉⠁⠀⠚⠣⢅⣂⢔⠞⠛⣳⣁⠀⠈⡀ ⠀⠀⠀⠉⢈⡟⢘⡖⡆⠁⠀⡐⡰⠁⠀⠀⠀⠀⢀⠄⡀⠀⢇⡀⠀⠀⣔⠁⠀⢃ ⠀⠀⠀⠀⢸⡥⢪⠊⠀⡌⠌⡜⠁⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⡐⢄⢀⢰⠀⠀⢸ ⠀⠀⠀⢠⠊⣠⢣⠁⣸⠀⡜⢸⠀⠀⠀⠀⠀⢠⠎⢀⡆⠀⡀⣧⠀⠃⠺⡀⠀⠈ ⠀⠀⣔⢡⠋⠆⡆⡐⢸⣰⡠⠼⡀⠀⠀⠀⢠⠋⠐⢼⡹⠀⢃⢸⡄⠀⠀⠃⠀⠀ ⠀⣺⢣⡇⢰⡰⢠⠃⠉⠓⠀⠒⠳⡀⠀⣸⠇⠠⠠⠀⣯⢃⠸⠘⡇⠀⠀⠀⠀⠀ ⠘⠃⢘⠃⠘⢥⠪⣠⡶⠴⠶⢦⠄⠉⠲⠹⠀⣀⣲⣠⡘⡌⣄⠀⡇⢀⠀⠀⠀⢰ ⠀⠀⡘⠀⢠⡈⠛⠹⡀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠵⢴⢹⡿⣏⡆⠀⡌⠀⠀⠀⢸ ⠀⠀⠁⠀⢆⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠃⡐⠀⢀⠀⠀⣸ ⠀⢰⠀⢸⡾⡇⠀⠀⠀⠀⠀⣠⠄⠠⢄⠀⠀⠀⠀⠀⠀⠀⡎⡰⠀⠀⡼⢂⠀⣿ ⠀⡟⠀⣸⣧⡇⠀⠀⠀⠀⢸⣌⣿⣿⣷⣧⡆⠀⠀⠀⢀⢌⠔⠀⠀⠠⠀⡌⠀⢿ ⢸⢡⡞⢿⣷⠘⡀⢀⠤⠠⠸⡿⠛⠛⠛⡿⠀⠀⠀⡠⠂⠀⠂⠂⠠⢒⠝⠀⠔⠀ ⠘⠘⣇⢸⢸⣠⢷⣌⠢⠜⠀⠱⠶⡶⠒⠁⠀⢀⢎⡜⠀⡀⠀⢠⢟⠅⠀⣼⠀⠀ ⢐⠀⢸⡜⣼⠃⠀⠈⢱⣄⠀⠀⠀⢹⠀⡠⡂⠔⣹⠋⠝⠀⢀⣮⠃⠠⢼⢻⡄⠒ ⠄⠀⠀⠹⠧⠑⠢⣶⣿⣿⣔⠤⠄⠌⠙⠑⠂⠉⠃⠘⡣⢠⣾⡟⢰⣟⠸⠄⠛⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⢶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠔⠊⠁⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⠦⠤⠀⠀⠀⠀⠀⠀⠉⠉⠒⠢⢤⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠑⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄⡀⠀⠘⢆⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠋⠉⠐⠒⠲⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣋⠀⠀⠀⠉⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠐⠉⠀⠀⣀⡠⢴⣾⣿⣿⣷⣶⣦⣤⣀⡀⠀⠀⠀⣠⡖ ⠀⠀⠀⠀⢀⣠⣴⣶⣿⣿⣿⣿⣕⣲⠤⣀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠠⢖⣩⡶⠾⣿⣿⣉⣉⡉⠙⢿⡟⠿⢿⣿⣶⡿⠋⠀ ⠐⠶⣶⣶⣿⠿⠛⠋⢩⢿⣥⣄⣩⠻⡟⠦⢅⡀⠘⡿⠀⠀⠀⠀⠀⠀⠖⠉⠀⢀⣸⣁⣀⣉⣛⣋⣀⣀⣵⣤⣾⣿⡿⠂⠀⠀ ⠀⠀⠀⠙⠻⢷⣤⣠⣧⣤⠬⣭⠭⠴⠓⣆⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠉⠉⠉⣉⠋⠉⣙⠉⠏⢹⢈⣭⣤⡀⠀⠀ ⠀⠀⠀⠀⠀⢸⡿⠋⣀⠁⢀⡁⠤⠒⠉⣁⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠉⠉⠓⠈⠁⠀⠀ ⠀⠀⠀⠀⠖⡩⠔⣩⠔⠊⢁⡠⣴⠾⠛⠉⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠔⠋⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠊⠁⠀⣀⣉⡉⠉⠒⠲⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣦⣴⣾⣀⡠⣶⣿⣿⣿⣿⣿⣿⣷⣶⣶⣄⣼⣿⡗⠀⠀⠀⠀⠸⡿⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡿⠿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⢻⣏⡴⠃⠀⠘⡿⠉⠀⡰⣩⠟⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⢰⠃⠀⣴⡵⠃⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦⣀⠀⢤⡤⡾⠋⣀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢌⣉⡤⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡞⠙⡄⠀⠀⠀⠀⠀⠀⠘⠾⠓⢶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⠀⠀⢀⣠⣤⣶⠾⠛⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡠⠔⠊⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠒⠢⠤⠀⠀⠀⠈⠁⠒⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠒⠒⠒⠒⠲⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⣤⣴⣿⡷⠶⠿⠿⢾⣿⣷⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣉⣉⠙⣿⣒⠢⣤⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⣤⡾⢿⠛⠥⢥⣀⣠⡴⠚⢲⡎⠈⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠈⡽⣿⣿⠛⠛⡿⠿⣶⣵⡢⠀⠀⠀⠀⠀ ⠀⠙⢻⠆⣈⡷⣶⡾⠥⡀⠐⠺⠭⠆⢠⡶⠏⢰⡿⠀⠈⠀⣀⠤⠖⢠⠿⣥⣌⣻⣿⣿⠓⠢⣍⣻⣷⣦⣄⡀⠀ ⠀⣰⣗⠋⣯⡴⠉⢔⠾⠋⠁⣀⠴⠚⠁⠀⠀⢸⡯⠄⠂⠄⠀⠀⢠⣟⡁⠨⠉⠉⠉⠓⢶⡄⠞⠋⢀⣹⣿⠧⠄ ⠘⣻⠟⠻⠟⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠁⠀⠀⠀⠀⠀⠀⠑⠖⢀⠉⠥⠄⠀⠀ ⠈⠁⠀⠀⠀⠀⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⢀⡤⠊⣁⣀⣀⣀⡈⠙⠲⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⣿⠃⠀⠀⠀⠀⠀⠀⣿⡁⠀⢿⣿⣿⣿⣿⣿⣷⣦⣹⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠿⠉⠀⠀⠉⢉⢸⢹⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⣀⣀⣀⣀⣠⣤⢼⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⠚⠓⠒⢲⡒⢻⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣆⠀⠀⠀⠀⢱⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠃⠀⠀⠀⢰⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

➖➖➖🟩🟩➖🟩🟩 ➖🟩🟩🟩🟩🟩🟩🟩🟩 🔲⬛⬜🟩🔲⬛⬜🟩🟩 ⬛🔲⬜🟩⬛🔲⬜🟩🟩 ➖🟩🟩🟩🟩🟩🟩🟩🟩 🟧🟧🟧🟧🟧🟧🟩🟩🟩 ➖🟥🟥🟥🟥🟧🟧🟩🟩 ➖🟥🟥🟥🟥🟧🟩🟩🟩 ➖🟥🟥🟥🟧🟧🟩🟩🟩 ➖🟧🟧🟧🟩🟩🟩🟩

⠀⠀⠀⠀⣀⢠⢄⣴⣖⣼⣦⢄⢀⠀⠀⠀ ⠀⠀⢠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣏⡇⠤⡀ ⠀⣴⣿⣿⣿⣿⣿⣿⠿⠿⠛⠻⢿⣿⡍⠀ ⢠⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠹⣷⠀ ⠈⣿⣿⣿⣿⣿⡿⠁⠀⠊⣉⣭⠀⡔⡛⠀ ⠀⢹⣯⢹⡿⢿⡇⠀⠀⠙⠾⠋⠀⠯⠇⠀ ⠀⠀⢿⣦⣐⢺⠷⠀⠀⠀⠀⠠⣤⡄⡀⠀ ⠀⠀⠘⢿⠈⠀⠀⠈⠃⠙⣤⣀⣤⢭⠁⠀ ⠀⠀⢠⠋⠀⠀⠀⠀⠠⠀⣙⣝⣛⠇⠀⠀ ⠀⠀⠘⢄⠀⢀⠠⡀⠀⢴⠌⣿⠟⠀⠀⠀ ⠀⠀⠀⠀⠑⠂⠤⠌⠷⠶⠛⠁⠀⠀⠀⠀

⣼⣇⠄⠚⠉⠁⠀⠀⠀⠀⠀⢀⠐⣾⠃⠀⣿⠀⠀⠀⠀⠀⠀⠀⣾⠘⠀⠀⢸⡇⠀⠀⠀⠀⠀⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢹⡀⣄⠀⠀⠀⠀⡀⠉⠈⠛⠦⢀⣧ ⢫⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣼⠃⠀⠀⣿⠀⠀⠀⠀⠀⠀⣰⡏⠀⠀⠀⠈⣧⠀⠰⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠈⣷⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙ ⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢱⠏⠀⠀⠀⣿⠀⠀⠀⠀⠀⣸⣿⠇⠀⡆⠀⠀⢻⡄⠀⠀⠀⠀⢼⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣿⡄⣿⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀ ⠇⠀⠀⠀⠀⠀⠀⠀⠀⣴⣧⡟⠀⠀⠀⠀⠹⢤⣀⣀⣀⣰⡷⢿⡀⠀⢧⠇⠀⠸⣿⠀⠀⠀⠀⡾⣷⣀⣀⣀⣠⡤⠤⢴⡞⠛⠉⠁⠀⠀⠀⠀⠸⢶⠇⠷⠤⢤⣄⣀⣀⣀⡇⠀⠀ ⠤⣤⠤⠤⠤⠤⠶⠒⢻⠅⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⠋⠀⠈⠉⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠡⠤⠔⠒⠒⠒⠲⠒⠒⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⠖⠒⠒⠒⠒⠒⠒⠢⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠊⠳⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⣴⠯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀ ⣀⣠⢽⣷⣶⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⣠⡆⠀⠘⠁⠀⠀⠀⠀⢀⣀⣠⣴⣶⣶⣿⣿⣿⣶⣶⣶⣶⣶⣟⡁⠀ ⣤⣾⣿⣿⣿⠿⠟⠛⠛⠛⠛⠛⠛⢻⣿⡿⢿⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠁⠀⠀⢀⣠⣤⣴⣾⣿⣿⣿⣿⡿⠟⠛⠛⠛⠛⠻⠿⢿⣿⣿⣿⣿ ⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣶⣬⡉⠛⠿⣿⣗⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⣫⣿⡿⠛⣫⣵⣾⣿⣿⣿⣦⣤⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿ ⣏⠀⠀⠀⠀⠈⠁⠀⢀⣴⣿⣿⣿⣿⠿⠿⣿⣿⣿⣶⡠⠈⠝⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠿⢃⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠒⠀⠀⠀⠀⠘ ⡿⠀⠀⠀⠀⠀⠀⠀⣿⠋⢹⡿⣿⠧⣄⡤⠼⡿⡇⢈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡿⠿⣿⣽⠿⣿⢻⣧⣼⡆⠀⠀⠀⠀⠀⠀⠀ ⣷⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡀⢻⡀⠈⠀⣰⠇⣹⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠈⣇⢷⡀⠀⠁⠀⡸⢻⡇⢸⡇⠀⠀⠀⠀⠀⠀⢐ ⣿⡆⠀⠀⠀⠀⠀⠀⠻⣆⠘⢧⡀⠙⠲⠔⠁⡴⠃⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠙⣆⡙⠶⠴⠋⢁⡼⠀⣸⠃⠀⠀⠀⠀⠀⠀⣸ ⠘⠿⠄⠀⠀⠀⠀⠀⠀⠙⢦⡈⠉⠀⠀⠀⠀⢀⣴⠟⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠶⣂⣄⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣆⠈⠉⠀⠀⠀⠉⣀⡼⠋⠀⠀⠀⠀⠀⠀⠀⠿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⠒⠒⠛⠋⠁⠀⠀⠀⢀⡤⠂⣠⠴⠏⢊⣵⡾⠛⣁⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠒⠒⠒⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⢀⡴⠚⢁⠴⠋⣁⣥⣾⠟⠋⠀⣻⠿⠋⠁⠀⠀⣀⠀⠀⣀⠀⣀⣴⡾⠗⠁⣀⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⢞⠿⠛⣩⠿⣟⠿⢋⡠⠞⢉⡠⠚⢁⡠⣾⡿⠋⠁⣠⠴⠋⠀⣀⡦⡊⠐⢋⡠⠔⣫⢴⡺⠟⢉⣠⠴⠛⠁⠈⠉⠙⢛⣳⠶⠃⠀⣠⡤⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠊⠀⣀⠴⣛⡵⢋⡥⠞⠉⡠⠒⠙⠀⢀⡤⠚⠁⣀⡴⠟⠁⢀⣤⠾⠛⣋⡤⢒⣡⢔⡫⠟⣋⣤⠖⠋⠀⠀⠀⠀⠀⠠⠚⠉⢀⣠⠴⠛⣡⡤⠊⠀⢀⠠⠀⠀⠠ ⠀⠀⠀⠀⠀⠀⢀⡴⢞⣽⢞⣩⠶⠋⠀⠀⠀⠀⠀⣠⠖⠋⢀⣤⠞⠉⠀⣠⡶⠛⢁⡴⢚⡭⠖⣩⠖⣉⣴⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠚⢉⣠⡴⠊⠉⠀⠀⠀⠀⠀⠀⠀⡀ ⢈⠄⠀⠀⣠⠖⣫⠴⣫⠖⠋⠁⠀⠀⠀⠀⣀⡴⠚⠁⣠⠶⠋⠀⢀⣴⠟⢉⡴⣾⠿⢊⣡⠖⣩⡴⠚⠁⠀⡀⠒⠉⠀⠀⠀⣀⡤⠖⠋⠁⣠⠶⠋⢁⣤⠔⠀⠀⠀⠀⠀⠀⠀⠀⡀ ⡇⠀⠐⢉⣴⣿⠷⠋⠀⠀⠀⠀⠀⠀⡠⠞⠉⣠⡴⠋⠁⣀⣴⠞⢋⣤⣾⠟⠋⡡⠖⣉⡴⠛⠉⠀⠀⠀⠀⠀⠀⢀⣠⠴⠋⠁⠀⠀⠐⠋⠀⡠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣟⠀⢾⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠚⠁⠀⠠⠞⠋⠁⠀⠈⢉⡤⠔⠀⣠⠾⠟⠛⠛⠳⢤⡀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢠⡞⠉⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⢿⡗⣶⠒⠲⠖⠶⠶⠶⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰ ⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣸⡇⣿⢨⣅⠀⠀⠀⠀⢠⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼ ⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠛⠙⡇⠻⠷⣤⠷⠞⠛⠛⠛⠷⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢿ ⣿⡟⠻⣦⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⠀ ⢻⡁⠀⢹⣷⡀⢣⡀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠃⠀⠀ ⠘⡇⠀⠀⠙⢿⣦⡉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⠀⠀⠈⠳⡄⠀⠀⠀⠀⠀⠀⠀⣠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁⠀⠀⠀ ⠀⣧⠀⠀⠀⠈⢿⣿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠻⣆⠀⠀⠀⠱⠀⠀⠀⠀⠀⢀⣴⠋⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡿⠋⠀⠀⠀⠀⠀⠀ ⠀⣿⠀⠀⠀⠀⠈⢿⣿⣿⢿⡿⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠈⠑⢦⣀⡀⢀⠀⠀⣀⡴⠟⠁⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢹⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣟⠿⣶⣄⣀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠈⣹⠛⡟⠛⠉⠀⠀⠀⢙⠃⠀⠀⠀⠀⠀⢀⣠⣤⣾⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠊⠉⠙⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡧⣄⠀⠀⠀⣸⠾⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢡⣶⣸⢠⣤⡄⣧⣶⣬⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣮⠟⢃⣴⣾⣧⣼⣿⣵⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣾⢶⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢽⣶⣌⠻⠿⢛⣽⣿⣯⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⢀⠀⠙⠻⣿⣿⣿⣿⠿⠃⢀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⢠⣾⠁⠀⠀⠀⠈⠛⠛⠋⠀⠀⠘⢧⡀⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⢰⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⡀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⣰⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⡄⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⣰⡟⡹⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⢻⣄⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⣸⡟⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⢻⡆⢱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⣰⡿⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠈⢿⡄⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⣰⡿⠁⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠈⢿⡄⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡜⣰⡟⠁⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠈⢻⣦⢧⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣼⣼⡟⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠀⠀⠀⠀⢻⣆⢳⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣾⣿⠏⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡇⠀⠀⠀⠀⠀⠹⣧⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠀⠀⠀⠀⠀⠀⠀⠘⢷⣽⣄⠀⠀⠀⠀ ⠀⠀⢀⣴⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣧⣄⠀⠀⠀⠀⠀⣀⣀⣀⣤⣶⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⡀⠀⠀ ⢀⣴⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠿⠿⠿⠿⠿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣢⣄ ⠉⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣉⡉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠛⠛⠛⠛⠛⠛⠛⣲⣶⣶⠾⠿⠿⢿⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣰⣿⠋⠀⠀⠀⠀⠀⣠⠔⠋⠁⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣼⡟⠁⠀⣠⣤⣦⡀⠐⢁⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣷⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣾⡟⠀⢀⣾⠟⠛⠛⠓⠚⠋⠉⠻⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⠀⠀⠀⠀ ⠀⠀⠀⢠⣾⡟⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣦⠀⠀⠀ ⠀⠀⣰⣿⠏⠀⠀⢸⣁⠀⠀⠀⠀⠀⠀⠠⠔⠒⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣧⠀⠀ ⠀⣰⣿⠏⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡆⠀ ⢰⣿⠏⡼⠀⠀⢰⣧⠾⠷⣦⡀⠀⠀⠀⣠⠾⡛⠛⠦⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⠀ ⣾⡟⣰⡇⠀⠀⠸⣧⡶⠦⣤⡄⠀⠀⠀⢀⣴⠾⢦⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡄ ⢹⣃⣿⠃⠀⠀⣰⣿⡟⠒⠀⠁⠀⠀⠀⢘⡿⡷⠀⣱⡜⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇ ⠸⣿⣿⡀⢠⣸⣧⠴⠿⠿⠛⠀⠀⠀⠀⠀⠉⠙⠉⠁⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇ ⠀⠸⢿⡇⢸⡇⠘⣆⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷ ⠀⠀⠘⣧⣸⣿⡄⠘⠷⡄⠈⠉⠁⠘⡄⠀⠀⠀⠀⠀⢠⡾⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿ ⠀⠀⠀⠘⣿⣿⣧⡤⠞⠁⠀⠀⠀⠀⠹⡀⠀⠀⠀⢠⠟⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿ ⠀⠀⠀⠀⠈⠋⠳⣦⣀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⡿⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⣿⣿⣿⠗⠀⠀⠹⡄⠀⡇⠀⠀⠀⣿⡄⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡏ ⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⡿⠃⠀⠀⠀⠚⠁⢰⠁⠀⠀⠀⣿⣿⢷⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⣼⣿⠃ ⠀⠀⠀⠀⠀⠀⠀⣾⣿⣛⡿⠁⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⢸⣿⣾⣇⡀⠀⠀⠀⠀⠀⣼⢀⣿⣿⠏⠀ ⠀⠀⠀⠀⠀⠀⠀⢻⣍⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢾⣿⣿⣿⣿⠀⣤⣂⠀⣠⣿⣾⣿⠏⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠁⢸⣿⣿⣿⣿⣶⣿⣿⣾⣿⣿⣿⠏⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⠀⢨⣿⣿⠟⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⣠⡞⠁⠀⠀⠀⠀⣸⡿⠁⢀⡿⠛⠋⢰⡟⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⡀⠀⢀⣴⠾⢿⡇⠀⠀⠀⠀⠀⠋⠀⢀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠋⠉⠀⠀⢸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⠶⠶⠖⠒⠒⠒⠒⠶⠶⠶⠶⢶⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⠿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣛⣿⣷⣦⣤⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠋⠀⠀⣀⣠⣴⣶⡶⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠉⠉⠉⠉⠛⠿⣿⣿⢿⣷⣦⣄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⡾⠛⠁⣀⣴⣾⡿⠟⠋⢁⣀⣤⣤⣀⣀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⠿⠿⠿⠿⣷⣮⣝⠻⠷⠀⠀⠀ ⠀⠀⠀⢠⣾⠏⢀⣴⣾⣿⡿⠋⢀⣴⡾⠟⠉⠉⠉⠉⠙⠻⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠀⠀⠀⢠⣾⣿⣿⠻⣷⠀⠀⠀⠀ ⠀⠀⢠⣿⠃⠴⠛⠛⠛⠁⠀⢀⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡆⠀⠀⠀⠀⠀⠀⢠⣿⠋⠀⠀⠀⠀⠀⠈⠛⠛⠋⠀⣿⠀⠀⠀⠀ ⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⣸⡏⠀⢀⣤⣄⣀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⢸⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣆⠀⠀⠀ ⠀⢰⣿⠀⠀⠀⠀⠀⠀⢤⣶⣿⡇⠀⣿⣿⣿⣿⠇⠀⠀⠀⠀⣸⡟⠀⠀⠀⠀⠀⠀⠘⣿⣄⠀⠀⠀⠀⠀⠀⠀⣀⣴⡿⠙⣿⠀⠀⠀ ⠀⣸⡇⠀⠀⠀⠀⠐⠚⠋⢉⡟⢿⣦⡙⠛⠋⠁⠀⠀⠀⠀⣠⡿⠃⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠿⣿⣿⠿⠛⠛⠛⠿⢷⣤⣿⠀⠀⠀ ⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠚⠁⠀⠉⠛⠿⢶⣶⣦⣴⣶⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⠟⠁⢀⣀⣀⣀⣀⠀⠉⠻⣧⡀⠀ ⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⣤⠶⠾⢿⣿⠋⠀⣴⣿⠋⠉⠉⠛⢷⡄⠀⠘⣿⡀ ⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⣰⣿⠃⠀⣼⡿⢿⡿⢳⡶⣦⣼⣿⡀⠀⣿⡇ ⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡏⠀⢰⣿⣀⣼⣥⣼⣇⣼⣇⣽⡇⠀⣼⡇ ⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡁⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⢹⡇⢀⣿⠁ ⠀⣿⡆⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇⠀⢸⡇⠀⠀⠀⠀⠀⠀⢀⣿⠃⣸⡏⠀ ⠀⢸⣧⠀⠸⣆⠀⢸⡀⠀⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⣼⡏⢠⣿⠁⠀ ⠀⠀⣿⡆⠀⠹⡄⠘⣇⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢸⡇⠀⠀⠀⠀⠀⢸⡿⠀⢸⣿⠀⠀ ⠀⠀⠸⣷⡀⠀⠹⡄⠹⡀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣸⡇⠀⠀⠀⠀⠀⢸⡇⠀⠸⣿⠀⠀ ⠀⠀⠀⢻⣇⠀⠀⠹⡄⢳⠀⠀⠀⠈⢷⠀⠀⠀⠀⠀⠀⠀⠀⠎⢍⡲⣄⠀⠀⠀⠀⠀⣼⡏⢀⣿⠁⠀⠀⠀⠀⠀⢸⣧⠀⠀⢿⡆⠀ ⠀⠀⠀⠈⢿⡆⠀⠀⢱⠀⢣⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠐⠒⠶⣤⣉⠛⠷⣄⠀⠀⢰⡿⠀⢸⡿⠛⠛⠓⠶⣤⡀⠀⣿⡆⠀⢸⡇⠀ ⠀⠀⠀⠀⠘⣿⡄⠀⠀⢧⠈⣧⠀⠀⠘⣇⠀⠀⠀⠀⢀⣀⣀⠀⠀⠉⠳⣤⡀⠀⠀⣿⠇⠀⣸⡇⠀⠀⠀⠀⠈⠻⣆⢸⡷⠀⢸⡇⠀ ⠀⠀⠀⠀⠀⠘⣿⡄⠀⠈⢧⠘⢆⠀⠀⠈⠳⣄⠀⠀⠀⠈⠉⠛⠳⢦⣄⡈⠙⠦⢠⣿⠀⠀⣿⡷⠶⣶⠶⣶⢶⡶⠿⣿⡇⠀⢸⡇⠀ ⠀⠀⠀⠀⠀⠀⠘⣿⣄⠀⠈⠳⡌⠳⣄⡀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠈⠻⢦⡀⢸⣿⠀⠀⣿⣧⣠⣿⣄⣿⢈⣧⣠⣿⠁⠀⣸⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⢿⣦⡀⠀⠈⠦⣀⠉⠓⢤⣀⠈⠙⠦⡀⠀⠀⠀⠀⠀⠀⠙⣾⣿⠀⠀⠘⣿⣏⠀⠈⠉⠛⣿⣿⠃⠀⢠⣿⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⠈⠑⠦⣤⣈⠓⠦⣀⡈⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆⠀⠀⠈⠛⠿⠶⠶⠾⠟⠁⠀⢠⣾⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣶⣤⣀⠀⠀⠈⠑⠒⠠⢍⣑⡒⠒⠒⠶⠤⠄⠀⠈⣻⣧⣄⡀⠀⠀⠀⠀⠀⢀⣠⣶⠿⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣶⣤⣄⡀⠀⠀⠀⠈⠉⠛⠒⠲⠄⠀⠀⠀⠈⠙⠛⠿⢿⣶⣶⠿⠛⠋⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠿⣶⣦⣤⡀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣶⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣶⣤⣤⣤⣶⠾⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⢀⠴⠋⣠⠞⠁⠀⢀⠀⢠⠎⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠈⠳⡼⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡔⠁⢠⠞⠁⠀⠀⢠⠋⢠⠋⢀⡾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡏⢀⠀⠀⠀⠀⠰⡄⠘⡷⡀⠀⠀⠀⠈ ⠀⠀⠀⢠⡿⢋⠔⣰⠃⣠⠂⠀⢠⠏⢀⠏⢀⠞⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢻⠃⢸⠀⠀⠀⠀⠀⢱⡀⠀⠙⠆⠀⠀⠀ ⠈⠀⣴⠋⡴⣣⡾⠁⣰⠃⠀⢀⡞⠀⠀⢠⠎⡀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡾⠁⠀⡇⣾⡀⠀⠀⡀⠀⢆⢇⠀⠀⠀⠠⠀⠀ ⣠⠞⢁⣼⡷⢻⠁⢠⠏⠀⢀⠞⡇⠀⢀⡎⠰⠇⢸⡀⠰⠀⠀⠀⠀⠀⠀⠀⠠⣀⣴⡟⠀⠀⠀⡇⣿⣇⠀⠀⢳⠀⠘⣿⡄⠀⠀⠀⠀⠀ ⠀⢀⡾⠋⢀⠇⠀⡏⠀⢀⠎⠀⡇⢰⡿⢀⣠⣤⠾⡏⠀⠀⠀⠀⠀⠀⠀⢀⠀⣸⠏⠉⠙⠳⣦⣥⢹⢿⡀⠀⠈⡆⠀⢹⣧⠀⠀⠀⠀⠀ ⢀⡾⠁⠀⡼⠀⣸⠁⢀⡎⠉⣀⣷⣾⡟⠉⠉⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⡏⣰⠁⠀⠀⠀⠀⠀⢹⣼⡞⣇⠀⠀⢣⠀⢸⣿⡀⠀⠀⠀⠀ ⠈⠀⠀⠀⡇⢠⣿⠀⡸⠐⠉⠀⠈⠛⠳⠀⠐⠒⠒⠮⢷⡀⠀⠀⠀⠀⣸⣧⠇⠀⠀⣠⠤⢀⣀⠈⣇⡏⢻⡦⠄⢸⠀⠈⣿⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⣧⠏⢸⢀⠇⠀⠀⠀⠀⠀⠠⠤⠤⠄⠠⠤⠈⢿⣆⠀⠀⢠⠟⡿⠀⠀⠈⠀⠀⠀⠀⠀⠸⣵⠀⢧⠀⢸⡄⠀⣿⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⢿⡀⡿⢾⣄⣀⣠⣶⣶⡶⠶⠶⣶⣶⣶⣦⡄⠀⠀⠑⠦⠼⠸⡇⠀⠀⢉⡁⢲⡖⠤⢄⣀⠙⣇⠈⡆⢀⡇⠀⢸⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⠃⣤⣼⢿⡯⠭⢤⣀⣀⠀⠀⢠⠏⠉⠀⡠⠄⠠⠄⠢⠔⠂⠄⠒⠾⣛⠛⠛⠻⠿⢷⣬⣙⣦⢸⣸⡇⠀⠘⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⠈⠻⠧⢀⣴⠀⠠⠭⠁⠀⠀⠹⠃⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠘⠥⣙⣦⡤⠄⠐⠬⣿⣿⣿⡇⢳⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠳⡖⢒⡛⢁⣨⣿⢿⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠁⠀⠀⡼⠀⠀⡰⠀⠀⠀⠀ ⠀⠀⡄⢰⡟⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⡰⠁⠀⠀⠀⢀ ⠀⠀⣷⡿⣤⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡗⠀⡸⠁⠀⠀⠀⠀⠈ ⠀⢀⣿⡇⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡞⢡⣤⣤⣤⣤⣤⣉⠓⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⡼⠁⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⡿⣄⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣄⣀⣻⣿⣿⣿⣿⣿⣿⣶⡟⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⢠⠞⠀⠀⠀⠀⠀⠀⠀⠀ ⠦⢿⠿⣷⠈⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⡴⢃⣴⢥⠀⠀⠀⠀⠀⠀⠀ ⠀⣌⣤⣿⠀⠀⢧⠀⠀⠀⠀⣠⠖⠢⣄⠀⢸⣿⣿⡿⠛⠛⠿⠟⠛⠻⣿⠃⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⠚⠱⢞⣵⣞⣀⠀⠀⠀⠀⡠⠚ ⠀⣾⠏⢹⠀⠀⠈⣧⡀⠀⣏⠀⠀⠀⢸⠀⠈⣿⡏⠀⠀⠀⠀⠀⢀⣴⠋⠀⠀⠀⠀⠀⠀⣰⠏⣠⠆⠀⠀⠀⠀⡀⣼⠏⢠⣄⣠⠖⠀⠀ ⠀⢿⠀⠈⡇⠀⢸⣿⣿⣄⠈⠳⠤⠤⠊⠀⠀⣈⠽⢒⣒⣒⣲⡿⠋⠇⠀⠀⠀⠀⠀⣠⠞⢁⡴⠃⠀⠀⠀⠀⢠⡌⡃⢠⣿⠟⠁⠀⠀⠀ ⠀⠘⡄⠀⡇⠐⠋⠈⠉⠛⢷⣄⠀⢀⡖⣢⢀⠏⠀⠀⠀⠙⡄⠃⠀⠀⠀⠀⢀⡠⠞⢁⡴⣿⠃⣠⡤⢶⡿⡆⡜⠉⢁⣾⠃⡰⠁⠀⠀⠀ ⣷⡀⢇⣰⡧⠂⠀⠀⠀⠀⠀⠘⣷⣄⠉⠉⠸⠆⠀⠀⠀⠀⢿⠀⠀⠀⢀⠴⠋⣠⠴⠋⢰⠃⠀⠀⢸⠋⠚⠋⠀⢀⣾⢇⡼⠁⠀⠀⠀⡜ ⢻⠳⠸⡟⠢⢄⣀⠀⠀⠀⢀⣰⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀⣙⣠⠴⣊⡥⠖⢋⣁⡤⢴⣻⠂⠀⠐⠇⡀⠀⠀⢀⣾⣟⡞⠁⠀⠀⠀⠀⠀

⡏⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠘ ⠁⣾⠿⣦⠀⢠⡞⢻⣆⠀⢠⡶⠲⠆⠀⣴⠖⠶⠀⢰⠶⠶⠀⣾⠛⣶⣴⠟⠷⢀ ⠀⣿⠀⣿⠁⣿⠀⠀⣿⠀⣾⠀⠀⠀⢸⡇⠀⠀⠀⢸⠀⠀⠀⣿⣦⡿⠹⣧⠀⢸ ⠀⣿⡴⠋⠀⣿⠀⠀⣿⠀⣿⠈⠛⣷⢼⡇⠙⢻⡆⢸⣷⠶⠀⣿⠿⣧⠀⠘⣷⢸ ⡇⣿⠁⠀⠀⢻⡄⢀⣿⠀⢻⡄⢠⡏⠸⣧⠀⣼⠃⢸⡇⠀⠀⣿⠀⣿⢀⡀⢹⢿ ⡇⠻⠀⠀⠀⠀⠛⠚⠃⠀⠈⠛⠛⠁⠀⠙⠛⠋⠀⠘⠳⠖⠀⠿⠀⠉⠘⠳⠋⢸ ⣧⣤⣤⣤⢤⡤⢤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⠀⣠⣤⡤⠤⢤⣤⠤⣤⣤⣤⣼ ⠀⠀⠀⠀⡼⢰⡞⠁⣈⠤⠭⢭⣉⣉⡡⠖⠚⠛⠓⢦⣘⡒⠒⢦⡉⢦⠀⠀⠀⠁ ⠀⠀⠀⠀⠃⢸⡴⠋⠤⠒⠂⠀⣙⡯⠠⠒⡯⠟⣋⣉⣀⠩⠷⡄⢳⠘⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⡀⠀⢀⣠⣶⠟⣿⣶⣦⠈⢲⠊⢱⣿⣿⣿⣀⣸⣿⠀⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⡇⠀⠀⠻⢅⣈⣿⣿⡿⠗⠛⠒⠒⠛⢉⣩⠿⣷⡇⠀⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣧⢰⡚⠉⣍⣙⣛⡒⣒⣒⣒⣒⣊⣩⡭⠴⣾⣿⠃⢀⠇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢿⣄⠉⠛⠒⠲⠮⠭⠭⠭⠽⠿⠿⠒⠒⣚⣟⠁⣠⠎⠀⠀⠀⠀ ⠀⠀⠀⠀⠰⡄⠈⢻⡟⠶⣤⣤⣀⣤⣤⣤⡤⣤⠴⠞⠋⠉⢿⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠿⢦⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠹⡆⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢴⣶⣶⠒⠒⠶⡦⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⠽⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠋⠀⠀⠀⠀⠀⠀⠀⣠⡤⠖⠶⣄⠀⠈⢳⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠟⠀⠀⠀⠀⠀⠀⠀⠀⢸⠏⠀⠀⠀⠈⢳⠀⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⢸⣿⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⣖⠒⠶⢤⣀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⣀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡇⠀⠀⠈⠳⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡾⠋⠁⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠶⠶⢤⣻⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⠏⠀⠀⠀⠀⠀⢀⣤⠖⠛⠉⠀⠀⠀⠉⠛⠲⢤⣀⠀⠀⠀⠀⣠⡶⠋⠀⠀⠀⠀⠀⠙⣷⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⣀⣀⣠⣀⣀⠀⠀⠈⠙⠓⠒⠚⠁⣀⣴⣿⣿⣿⣿⡆⠀⢹⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⣸⡏⠁⠀⣠⣶⣾⣿⣿⣿⣿⣿⣿⣶⣦⣤⣤⡤⣴⣾⣿⣿⣿⣿⣿⣿⣿⠀⢸⠃⠀⠀⠀⠀ ⠀⠀⠀⢰⠇⠀⠀⠀⠀⢠⣿⠀⠀⣠⣿⣿⣿⡿⠟⠛⠛⠛⠋⠙⠻⢿⣿⠞⠋⠉⠀⠀⠀⠉⠙⠻⣇⠀⡿⠀⠀⠀⠀⠀ ⠀⠀⠀⢨⡇⠀⠀⠀⠀⠈⡏⠀⠀⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⣽⡖⠀⠀⠀⠀⠀⠀⢰⣿⣾⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⣿⠀⠀⢻⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠀⠀⠀⠀⠀⠀⠈⠻⣻⡟⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⡴⠚⠉⠑⣦⣀⠀⠸⣇⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣩⠃⠀⠀⠀⣀⣀⣀⣶⣿⣿⣀⡀⠀⠀⠀⠀⠀ ⢀⡞⣹⡷⠒⢶⠏⠁⠉⠁⠀⠻⣦⠀⠈⠳⣤⣀⣀⣀⣠⣤⣤⡤⠴⠚⠛⢳⢻⣽⣟⠿⠋⠉⠛⠘⠀⠉⠙⠲⣄⡀⠀⠀ ⣸⡇⠋⠀⠀⠈⠦⣤⡀⠀⠀⠀⠈⣻⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⠉⠉⠙⢦ ⣿⡇⠀⠀⠀⠀⣠⠏⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠋⣀⣠⣦⣄⠀⢸ ⢸⣳⠀⠀⠀⢀⣻⣤⡄⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⡾ ⠀⠙⢧⡀⠀⠿⢄⡝⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃ ⠀⠀⠀⠙⠒⠢⠀⢹⡶⠂⢘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠻⡀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠞⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⢿⠖⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣍⡛⠿⢿⡟⢋⣹⠏⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠲⠶⣤⣤⣀⣀⣀⠀⢀⣀⣀⣠⡤⢤⣀⣩⠷⠒⠛⠛⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠛⠛⠛⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣾⠅⠚⠉⠁⠀⠀⠀⠀⣀⡞⠀⢸⠀⠀⠀⠀⠀⢸⠏⠀⠀⣿⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⡀⡄⠀⠀⠀⠈⠈⠛⠂⢷ ⡄⠀⠀⠀⠀⠀⠀⠀⠠⡽⠀⠀⢸⠀⠀⠀⠀⣰⡿⠀⠀⠀⢸⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣇⢻⡄⠀⠀⠀⠀⠀⠀⠀ ⠇⠀⠀⠀⠀⠀⠀⣴⣼⠁⠀⠀⠸⣄⣀⣀⣠⡿⡇⠀⣤⠀⠘⣧⠀⠀⠀⣿⣄⣀⣀⣀⣠⢤⡴⠚⠃⠀⠀⠀⠻⣼⢳⣄⣀⣀⣀⣰⠀⠀ ⠶⠤⠴⠖⠒⠒⢻⠁⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠁⠀⠀ ⠀⡀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⢙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⢀⡔⠉⠉⠉⠉⠉⠉⠁⠒⠀⠀⠀⠀⠀⠀⠀ ⢀⣱⣦⣤⣶⣶⣶⣶⣶⣦⣤⣄⣀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⠀⠐⠋⠀⠀⠀⠀⣀⣠⣤⣴⣶⣶⣤⣤⣤⣤⡞⠀ ⣵⣾⣿⡿⠟⠛⠉⠉⠉⠙⣻⣿⡿⢿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⣀⣤⣴⣾⣿⣿⣿⡟⠛⠛⠛⠛⠻⠿⣿⣿⣷ ⡿⠋⠁⠀⠤⠀⠀⣠⣶⣿⣿⣿⣿⣶⣌⡙⠻⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣽⣿⢋⣵⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠉⢻ ⡇⠀⠀⠀⠀⠀⣸⠛⣿⣿⣏⣈⣹⣿⡛⣳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣻⣿⡿⣯⣱⠀⠀⠀⠀⠀⠀ ⣇⠀⠀⠀⠀⠀⣿⠀⡇⠸⡀⠁⣠⠏⡇⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⣏⢧⡀⠁⣀⠗⡏⢸⡇⠀⠀⠀⠀⢀ ⢿⡆⠀⠀⠀⠀⠘⣇⠙⠦⠈⠙⠁⠚⢠⡟⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡈⠦⠝⠋⠁⠔⢁⡾⠀⠀⠀⠀⠀⢸ ⠀⠁⠀⠀⠀⠀⠀⠈⠑⠦⠤⠤⠤⠞⠋⠀⠀⢀⡀⢀⡠⠾⣛⣵⠞⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⠤⠤⠤⠔⠋⠀⠀⠀⠀⠀⠀⠈ ⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⢀⣀⡀⢀⡠⠚⡡⠖⣉⣵⡾⠋⢑⡿⠛⠁⠀⢀⠀⢀⡀⣀⣴⠺⠋⣠⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠴⠛⣋⣽⡻⢟⡩⠔⣉⠔⠋⢀⡾⠟⢁⡠⠚⠁⣠⡶⠃⡈⢀⣀⣵⠞⢋⡡⠖⠋⠀⠀⢈⡩⠟⠋⣠⠴⢂⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡤⣪⠕⣫⠖⠉⠀⠈⠀⣠⠖⠋⣠⠖⠉⢀⡴⠋⣡⢔⡫⢖⠝⣊⡤⠚⠁⠀⠀⠀⠀⠀⢀⡤⠒⢉⡤⠚⠁⠀⠀⠀⠀⠀ ⡀⠀⠀⠠⢖⣭⡾⠗⠉⠀⠀⠀⣀⠴⠊⣡⠴⠋⢀⡤⢞⣡⣶⠿⣋⠅⣊⠴⠊⠁⠀⠀⠀⠀⢀⡠⠔⠊⣁⠴⠚⣡⠄⠀⠀⠀⠀⠀⠀⠀ ⣇⠀⣠⣾⠟⠉⠀⠀⠀⠀⠀⠚⢁⡴⠊⢁⣤⠞⠋⡴⠟⠉⠄⣊⣴⣏⡀⠀⠀⠀⠀⠀⠴⠊⠁⠀⠀⠈⠁⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡷⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠉⠀⠀⠀⠐⠊⢠⠞⠉⠀⠀⠉⠓⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣶⡶⠶⠶⠶⠶⠾⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀ ⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣧⣿⣿⡩⢀⣀⣀⣠⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼ ⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠉⠀⢸⠈⠙⠋⠉⠀⠀⠈⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋ ⢿⠀⠹⣦⡀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀ ⢸⡄⠀⠘⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣄⠀⠀⠱⡀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠋⠀⠀⠀ ⠀⡇⠀⠀⠈⢻⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡙⠢⣀⠀⠁⠀⠀⠀⣠⠞⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡿⠋⠀⠀⠀⠀⠀ ⠀⡇⠀⠀⠀⠈⢻⣿⣿⣿⣿⣷⡶⣤⣀⡀⠀⠀⠀⠀⢣⠀⠀⠙⣶⢲⠒⠋⠀⠀⠙⠀⠀⠀⠀⠀⣀⣤⣶⣾⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀

⠀⠀⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢦⡀⠀⠀⠙⠓⠋⠁⠀⠀⠀⠀⣠⣖⣻⡋⠑⠦⠤⠤⢤⡆⠀⣨⣥⣤⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢤⠎⠀⢠⣿⣦⡀⠄⡀⠀⠀⠀⠀⢀⡜⠉⠉⠀⠀⠀⠐⠀⠀⠀⠀⠀⠉⠙⣷⠖⠀⠀⢀⡀⣀⣀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⠋⠀⠀⠀⣻⡉⢻⡓⢤⣠⡀⠀⡠⠞⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠾⠷⠶⢄⣠⠿⠋⠁⠙⢆⠀⠀ ⠀⠀⠀⠂⣄⠀⠀⠀⠀⢨⠏⠴⠋⣭⠁⠀⠈⠀⠙⡄⠙⢤⡾⠥⠤⠚⠿⠤⠤⠤⢬⣓⡂⠚⠧⡀⠀⢠⣠⣴⢾⣿⠦⡴⠀⠀⠀⠘⡄⠀ ⠀⠀⠀⠰⢏⡀⠀⠀⢀⡟⠀⡠⠞⠁⠀⣀⠤⠒⠂⠃⠀⠀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⠤⠚⣩⠞⠁⠈⠀⠾⠤⠤⣀⠀⠀⢱⠀ ⠀⠀⠀⠀⠀⠈⠉⢉⢹⡇⠘⢋⡾⣱⡊⠁⠀⠀⢀⠔⢁⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⠀⠀⠘⣅⠀⠀⠀⠀⠀⣤⡎⠁⠀⠀⠈⡆ ⠀⠀⠀⠀⠀⠀⠀⠚⡿⠁⡠⠊⣠⠋⠀⠀⡄⢠⠋⣠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⢠⠆⠀⠀⠀⠈⠉⢆⠀⠀⠀⠙⣏⠀⠀⠀⠀⣷ ⠀⠀⠀⠀⠀⠀⠀⢀⣷⠏⢀⠞⢁⠀⠀⡜⠀⠃⡰⢋⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢿⠀⠂⠀⠀⠀⢣⠈⠓⣄⢀⡀⣾⠀⠀⠀⠀⣿ ⠀⠀⠀⠀⠀⠀⢠⠞⠁⣠⠎⣰⠃⠀⣼⠀⠀⡰⠁⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⢸⢰⡃⠀⠀⠀⢼⡆⠀⠈⠦⠱⣯⠀⠀⠀⠀⠘ ⠀⠀⠀⠀⢀⡔⢁⣤⠾⡏⢠⠃⠀⡼⢻⠀⣰⠁⠂⢸⡀⠀⠀⠀⠀⠀⠀⠀⣤⣿⣁⠀⢸⢼⡇⠀⠘⡄⠘⣿⡀⠀⠀⠀⠈⣧⠀⠀⠀⠀ ⠀⠀⠀⣠⣯⢀⡾⠁⡸⠀⡎⠀⡜⡀⢸⣰⣇⡤⠖⠻⡄⠀⠀⠀⠀⠀⢠⢠⠟⠀⠈⠙⢮⣇⣿⡀⠀⢱⠀⢹⡇⠀⠀⠀⠀⠉⠀⠀⠀⠀ ⠀⠀⣴⡿⢃⡾⠀⠀⡇⣸⠁⣸⠡⠐⠛⢿⡄⠀⠀⢀⣹⡀⠀⠀⠀⢀⣾⡎⠀⠀⠀⠀⠀⢻⡟⣧⠀⢸⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣤⡿⠁⣾⡇⠀⢸⣷⢻⣠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣄⠀⠀⡼⣿⠀⠀⠈⠀⠁⠀⠘⣧⠘⡄⠈⡇⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠌⢻⠃⠀⢹⠇⠀⠈⠯⡸⠻⣄⣀⣴⡶⠶⠶⠶⢶⣴⡆⠀⠈⠓⠲⠇⠇⠀⠈⣉⣰⣂⡤⣀⠙⡆⠱⡀⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⣾ ⠁⠀⠀⠀⡜⠀⠀⠀⠀⡅⣶⡾⠻⡛⠀⠠⠀⠀⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⠫⢭⡉⠙⡛⢶⣽⣶⣿⢃⠀⠁⠀⡸⠀⠀⠀⠀⠀⠀⣿ ⠀⠀⠀⢠⠇⠀⠀⢰⢡⡇⠈⠉⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠛⠿⣍⢹⠿⠛⣷⣼⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⣿ ⠀⠀⠀⡘⠀⠀⢀⡇⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⡸⠀⢀⠏⠀⠀⢀⠇⠀⠀⠀⣿ ⠀⠀⠀⠄⠀⠀⣼⢰⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⢀⡎⠀⠀⠀⣼⡀⠀⠀⢸⣿ ⠀⠀⢠⠀⠀⠀⣿⡿⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢤⠒⠒⠒⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⢀⠎⠀⠀⠀⢰⠇⠁⡀⠀⢸⣿ ⠀⢀⣿⠀⠀⢰⣿⣧⣸⠀⠀⠀⠀⠀⠀⠀⠀⢸⡓⠘⣿⣿⣿⣷⣶⣍⣢⡀⠀⠀⠀⠀⠀⠀⠀⣠⠋⣠⠏⠀⠀⠀⠀⠀⠀⢀⠃⠀⢾⣿ ⠀⣼⠿⠀⢠⣾⡿⣿⠛⡆⠀⠀⠀⠀⠀⠀⠀⢸⣿⣶⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⡴⠁⠜⠁⠀⠀⠀⠀⠈⢀⣄⡞⠀⠀⠀⠟ ⠀⡏⢰⣾⠸⢿⣧⣿⠀⠹⡄⠀⠀⣠⠴⠢⡀⠘⣿⣿⠟⠛⠛⠛⠛⢿⠏⠀⠀⠀⠀⠀⣠⠞⠀⠀⠐⠁⢈⡀⠀⡴⠒⡽⠋⠀⢠⠏⠀⠀ ⠀⡇⠸⣿⠀⢰⡏⢹⡆⠀⣿⣄⠐⢇⠀⠀⡌⠀⠻⢇⣀⣀⣀⣠⣴⠋⠀⠀⠀⠀⢠⠞⣡⠂⠀⠀⠀⠠⠀⠀⣴⡶⠋⠀⠀⢀⡾⠀⠀⠐ ⠀⠀⠀⢻⣧⠘⡇⠈⣧⣼⠟⠿⢧⡀⠉⠉⠀⠀⠀⠉⠛⠻⣋⠉⠀⠀⠀⠀⢀⠔⢁⣼⡃⠀⣀⣀⠀⠨⠀⣼⠋⡜⠀⠀⢆⣿⡇⠀⠀⠀ ⠀⠆⠀⠀⣿⡄⢳⣰⡿⠀⠀⠀⠀⠙⢦⣀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⡠⠞⣁⠔⢹⣿⠋⢩⣟⠀⠀⠀⣸⣏⡟⠀⢀⢂⣾⠻⣳⠀⠒⠶ ⠀⠂⠀⠉⠙⣿⣼⡟⠢⣄⡀⠀⢀⣠⣾⣿⡗⢀⠀⠀⠀⠀⠸⣤⣴⠿⢒⣉⠠⠴⡿⠃⠀⣿⠀⠀⠀⣼⣿⣿⠀⢠⣧⠏⣿⠀⠹⣧⡀⠀ ⠂⠀⠀⠀⠀⠈⠛⠿⠂⠀⠉⠲⣿⣿⣿⣿⣿⣧⠙⠒⠢⠤⠒⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⣉⡓⢀⣾⣿⣾⠃⠐⣿⣿⠤⠟⠒⠉⠉⠉⠉

⠀⣀⠄⠀⢀⣠⣤⣴⣶⣶⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣈⣿ ⠐⠋⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠰⠟⠉⠛⢻⡏ ⠀⠀⢀⡀⢠⣤⣤⣤⣄⣠⠀⠀⠀⢀⠀⠀⠀⠀⢄⣤⣴⠮⠁⠀⠀⠀⢡ ⢴⠞⠛⠋⠩⣀⠀⣼⣿⣿⣷⢲⠶⠊⠁⠀⠀⠀⣿⣏⣠⠶⠚⠛⣻⣿⠃ ⠀⠀⠢⠴⣤⣤⣤⣤⠴⠶⠂⠀⠀⠀⠀⠀⠀⠀⠈⠓⡯⢬⣥⣌⣛⣿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠲⠤⠭⠟⠿⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢐ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⣀⡀⠀⢀⣀⡠⣀⣀⠄⠀⠀⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠶⠿⢿⣿⣿⣿⣤⣴⡗⠁⠀⠀⡾⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠌⠙⠛⢧⣀⡴⠋⠀⠀ ⠀⠀⠀⠀⠠⠀⠀⢀⡠⠄⠤⠀⢀⣀⣠⣤⣤⣄⣀⡴⢦⣶⣾⡿⠀⠀⠀ ⠀⠀⠀⣴⣶⣶⣬⣥⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠉⢦⡈⡍⠛⠻⣿⠿⣿⣿⣿⣿⣭⢿⣯⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡇⠠⢀⠀⠈⠛⠉⠀⠈⠟⢛⣻⠏⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⠀⡀⡈⠀⢬⢵⣖⣒⢲⠶⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⠴⠋⠁⠀⠀⠀⠀⠀⠀⠉⠓⠶⠤⣀⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠉⠀⠒⠢⢀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠈⠑⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⠤⠄⠀⠡⠀⠀⠀⠀⢀⠠⠐⠂⢐⣒⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⣀⣤⣼⣷⣂⡄⣀⠀⢃⠀⠀⠀⠀⡠⣲⠬⣿⣛⠛⢿⠷⣶⣤⡴⠃ ⠲⢾⡟⠉⡝⠷⠼⢹⡓⠀⢸⠀⠀⠀⠀⠉⠀⠸⠤⢭⠥⠤⡳⠾⠟⠁⠀ ⠀⠀⢹⠟⡙⣉⠡⢐⣀⡄⠁⠀⠀⠀⠀⠄⠁⠀⠀⠁⠀⠀⠐⠛⠛⠀⠀ ⠀⠈⠠⠕⠈⠔⠘⠉⠀⠀⣠⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⢀⡄⢊⣡⣤⣭⣍⣐⡂⢤⣄⠀⠀⢀⣺⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⡾⡿⣿⣿⡿⢿⡿⢿⡏⠀⠀⠀⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇⠓⠁⢈⠇⢠⡑⢁⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⢄⠠⡴⢋⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⢹⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⣠⣜⠫⠭⠭⠍⣓⠲⢤⡉⢃⠤⠟⠙⣛⡛⠥⠤⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠞⣩⣤⣤⣄⠀⠀⠀⠉⠢⣍⠕⣈⣁⠀⠀⠀⠈⠁⠢⣉⠻⣿⣿⣿⠟⠉⣀⠜ ⠘⣼⡏⠙⣿⣿⠀⠀⠀⠀⠰⢁⣾⠿⣿⣷⠀⠀⠀⠀⠀⠀⠑⠋⢭⠏⢠⠞⠁⠀ ⠠⡘⢿⣿⡿⠋⠀⠀⠀⢀⡇⠘⣷⣤⣿⡿⠀⠀⠀⠀⠀⠀⡠⠒⡟⢠⠏⠀⠀⠀ ⠀⠫⠖⣒⣒⡒⠲⠶⠆⠁⠈⢢⠌⣉⠉⠀⠀⠀⢀⡀⠔⠊⡠⠂⡇⣸⠀⠀⠀⢰ ⠀⡤⠒⠥⠤⠤⠤⠤⠴⠃⢦⣄⡓⠤⠄⠉⠉⠭⠤⠒⠊⠉⠀⠀⡇⡇⠀⠀⠀⡿ ⠀⡖⠂⣉⡩⠭⠭⠭⢭⣍⣐⣒⠂⠭⢍⣁⠀⠀⠀⠀⠀⠀⠀⠀⡇⢹⠀⠀⠀⡇ ⠀⠙⢆⠳⡄⣭⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣉⠑⠒⠤⡀⠀⠀⠀⢣⠸⣄⣀⣠⡇ ⠀⠀⢸⠀⢿⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⢱⠀⠀⠀⢸⡀⢻⠀⠀⠀ ⠀⠀⢸⠀⡆⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢁⠎⠀⠀⠀⠀⢇⢸⠀⠀⠀ ⠀⠀⢸⠀⡇⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⡡⠋⠀⠀⠀⠀⠀⠘⡌⡆⠀⠀ ⠀⠀⢸⠀⡇⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⠟⣫⠞⠁⠀⠀⠀⠀⠀⠀⠀⠈⢿⢄⡀ ⠀⠀⠸⣄⠉⠒⠂⠤⠤⠤⠒⢒⣚⠭⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠁⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠥⡶⠋⠉⠉⠉⠒⠂⠀⡌⡝⢺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡆⠈⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⠀⠀⠀⠀⠀⢠⠏⡏⢰⠃⠀⠀⠀⠀⠀⠀⠀⠆⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣣⠴⢾⠒⠦⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⠃⠀⠀⠀⠀⢠⠏⢰⢁⠏⠀⠀⠀⠀⠀⠀⠀⢸⢠⠁⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⡇⠀⠀⠀⠀⢀⠎⠀⣼⡞⠀⠀⠀⠀⡀⠀⠀⠀⡟⠈⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⡇⠀⠀⢰⡄⠀⠀⠀⠀⠀ ⠀⠸⣿⠀⠀⠀⣠⠋⠀⢠⣟⣠⠔⢚⣉⣉⠛⠁⠀⡼⢱⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⡌⡀⠃⠀⠀⠀⡇⠀⠀⢸⡇⠀⠀⠀⠀⠀ ⠀⠀⡇⠇⢀⡼⠁⠀⣴⣿⣿⣿⣿⠿⣿⣿⣶⣤⠆⠁⡼⠀⠀⣀⣷⠀⠀⠀⠀⠀⢀⣴⠟⣠⣴⣖⣦⣶⠃⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⢡⣴⠊⠀⣠⣾⣿⣿⣿⣿⣿⣧⡀⣈⣙⣯⡓⢠⣇⠴⠋⠉⡟⠀⠀⠀⠀⢒⠞⠁⣴⣿⣿⣿⠛⢿⣦⡴⠋⣽⡇⠀⠀⠀⠀⠀ ⠀⠀⠘⡇⠀⢨⣿⣿⣿⣿⣿⣿⣿⡿⡏⠀⠈⢻⡷⠋⠁⠀⠀⠀⠃⠀⠀⠀⠀⣎⡠⢞⣿⣿⣿⣿⠠⣄⣿⡏⢉⡏⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⢹⠖⠿⣿⣿⣿⣿⣼⡿⠿⣶⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⣾⡿⣿⣿⠛⠀⠈⣿⠁⣸⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⣇⠀⠘⢿⣿⠇⠈⠀⢤⣘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠙⠙⢿⡟⠀⢰⠃⢀⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⡄⠀⠀⠙⠷⣄⣀⣀⡽⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⣀⡟⠀⠀⠁⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀ ⠠⠤⠤⠤⠤⣤⠗⠤⠤⠄⠀⠀⠀⠀⠤⠤⠤⠤⠤⠤⠤⠤⠤⣤⠤⠤⠤⠤⢤⣤⠤⠤⠤⣤⠤⠤⠤⣤⣤⣤⣿⡤⠀⠀⠀⠀⠀⢠ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣤⣤⣤⣄⣴⣾⣿⣿⣿⣿⣷⣶⡄⢀⠀⠈⠉⠉⠋⠀⠀⠀⠀⠀⠀⣾ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠙⠛⠻⠿⠿⢿⣿⣿⣿⣾⡗⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠳⠾⣦⡀⠀⠀⣀⣴⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢾⣿⡟⢻⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣤⡤⠶⠂⠀⠐⠒⠒⠂⣀⣀⠲⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣶⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣴⠛⢉⣭⣶⣿⣿⣿⣿⣿⣧⣤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⡿⠿⢶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢋⣤⣾⣿⠛⢻⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣄⠀⠈⠉⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣉⠉⠀⢾⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠀⠀⠀⠙⠿⡅⠀⠽⠿⠟⠻⠿⠿⠭⠁⠀⡄⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡸⣡⣿⣋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⢊⣡⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣶⠶⠶⠶⠶⠶⣾⣿⠋⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠤⠤⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⠁⠀⠀⠀⠀⢈⢙⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⢿⠶⣄⠀⠀⠀⠀⣼⠷⢿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⣼⡦⣿⢠⣴⣄⠀⣇⣴⣦⣹⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢧⣀⣻⣿⠏⢈⣭⣽⡁⢳⣿⡟⣹⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⢻⠏⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣽⣷⣦⡙⠿⠿⠿⠟⣱⣿⣿⣥⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠛⠁⠀⠙⢿⣿⣷⣶⣶⣿⣿⣿⣿⠉⠉⠳⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⢁⣠⡾⠀⠀⠀⠙⢻⣿⣿⣿⣿⠋⠀⠀⢰⡀⠈⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠃⢠⣾⠏⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠈⢻⣆⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃⢠⣿⢏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣶⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⣰⡿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣦⡀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⣰⣿⢹⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡝⣷⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠃⣴⣿⠃⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠹⣷⡀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⣸⣿⠃⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠹⣿⡀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⣠⣿⠃⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡇⠀⢻⣷⡀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⣠⣿⠏⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠻⣧⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⢠⣿⠏⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢻⣧⡘⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⣰⣿⠃⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠻⣷⡞⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⣴⣿⠃⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠹⣷⡌⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣼⡿⠃⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠀⠀⠀⠀⠀⠀⠙⣿⡆⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣰⣯⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠇⠀⠀⠀⠀⠀⠀⠀⠘⢿⣞⠻⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣼⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣝⣦⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⣾⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣾⢷⣄⠀⠀⠀⠀ ⠀⠀⣠⡾⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣝⣷⡀⠀⠀ ⢠⣾⣵⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣯⣷⡄ ⠈⠉⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣉⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡿⠛⠛⠛⠿⣦⣄⠀⠀⠀⢀⣾⠟⠁⢠⣿⠁⠀⣠⣶⠾⠛⠛⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁⠀⠀⠀⠀⠀⠈⠙⣳⣦⣰⠟⠁⠀⠀⠸⣿⣦⣼⢫⣥⣤⣄⠀⠀⠹⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣼⣿⡁⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣆⠀⠀⠀⠀⠀⠉⢿⣿⠷⠿⢿⣦⣤⣾⡿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣼⡟⠉⠻⢷⣦⣄⣀⣤⣶⣿⡿⠉⠁⠀⠛⠛⢷⣦⣀⣀⣀⣴⣿⠟⠛⠿⣶⣿⡉⠛⢿⣿⣷⣤⣤⣤⣶⣤⣄⠀⠀⠀⠀ ⠀⠀⠀⠀⣾⡟⠀⠀⠀⠀⢀⣽⠟⠉⢠⠟⢀⣠⣶⠶⠶⣶⣦⡀⠉⠉⢿⣿⣶⣆⠀⠀⠈⠻⣷⣤⣾⡟⠀⠀⠀⠀⢉⣼⡿⠀⠀⠀⠀ ⠀⠀⠀⢰⣿⢀⣠⣤⡶⢞⣿⠃⠀⠀⠀⣰⡿⠋⠀⢠⣾⣿⣿⣿⡀⠀⣿⣿⣿⣿⡇⠀⠀⠀⠹⣿⣿⠀⣀⣠⣴⣾⠿⠋⠁⠀⠀⠀⠀ ⣠⣤⣶⡿⠿⠛⠉⠁⠀⣼⡏⠀⠀⠀⣼⡿⠁⠀⠀⢼⣿⣿⣿⣿⡇⠀⢹⣿⣿⣿⠇⠀⠀⠀⢀⣿⠿⣿⣟⣻⡿⣷⡄⠀⠀⠀⠀⣀⡀ ⡟⠁⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⢸⣿⠁⠀⠀⠀⠘⣿⣿⣿⣿⠁⠀⠀⠹⣿⣄⣀⣀⣀⣤⣾⠏⠀⠹⣿⣇⠀⠈⠻⣷⣶⣶⠿⢿⡇ ⠿⣶⣤⣀⣀⣀⣀⣀⣸⣿⠀⠀⠀⠸⣿⡀⠀⠀⠀⠀⠈⣽⡿⠃⠀⠀⠀⠀⣀⣉⠛⠛⠛⠉⠀⠀⠀⠀⠈⣿⣧⠀⣰⡇⠀⠀⠀⢸⡟ ⠀⠀⠉⣿⡟⠛⠛⠋⢹⣿⡀⠀⠀⠀⠈⠻⣷⣦⣤⣴⡾⠟⠁⠀⠀⣠⣾⠟⠛⠛⠻⣶⡀⠀⠀⠀⠀⠀⠀⢘⣿⣰⡿⠁⠀⠀⠀⣾⡇ ⠀⠀⠀⢻⣿⣤⣤⣶⠾⠻⣷⣄⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⢀⣿⡇⠀⠀⠀⠀⠀⢀⣾⡿⠟⠁⠀⠀⠀⣴⡿⠀ ⠀⠀⠀⠘⣿⡆⠀⠀⠀⠀⣹⣿⡷⢾⠟⠛⠛⣿⣶⠀⠀⠀⠀⠀⠘⣿⣄⡀⢀⣠⣾⠏⠀⠀⠀⠀⣀⣴⡿⠋⠀⠀⠀⠀⣠⣾⠟⠁⠀ ⠀⠀⠀⠀⢹⣷⡀⠀⠀⠀⠀⠀⠀⣸⡇⣠⣴⣿⣥⣀⣀⡀⠀⠀⠀⠈⠙⠛⠛⠋⢁⢀⣀⣤⣾⣿⣿⣭⣤⣤⣤⣤⣶⠾⠟⠁⠀⠀⠀ ⠀⠀⠀⠀⠈⢿⣇⠀⠀⠀⠀⠀⣰⣿⣿⡟⠁⠀⠈⠉⠙⠛⠿⠿⠿⠶⠶⠾⠿⠟⠛⠛⠉⠉⠀⠓⢦⣌⡉⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢿⣧⣄⣀⣴⡾⠟⠉⡽⠻⣷⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⣼⣧⡾⠿⠋⠀⠀⠀⠀⠀⡀⢀⣀⢀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣻⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⣠⣼⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⡶⠞⠋⠁⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠉⠻⣿⣦⣤⣤⣀⠀⠀⠀⣀⣀⣀⣠⣤⣴⢾⡟⠛⠉⠁⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⡿⠟⠿⠿⢿⣷⣦⣀⠀⠀⠀⠀⠀⣠⣾⡿⠋⠀⢠⣿⠋⠀⠀⢀⣴⣶⡿⠿⠿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⡿⠟⠁⠀⠀⠀⠀⠀⠈⠛⠻⣷⣄⡀⢀⣰⡿⠋⠀⠀⠀⣿⣿⣀⠀⣴⡿⢟⣁⡀⠀⠀⠈⠻⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣿⣿⣾⠋⠀⠀⠀⠀⠀⠙⠻⢿⣿⣧⣼⣟⠻⣿⣦⠀⠀⠀⢸⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⡿⢿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠙⣿⣟⠻⠿⠿⣿⣷⣤⣼⣿⡟⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⣿⡿⠙⠻⢿⣷⣤⣀⠀⠀⣠⣴⣾⣿⣿⠋⠁⠀⠀⠻⠟⢿⣷⣤⡀⠀⠀⣀⣠⣾⣿⠿⠛⠿⣿⣮⣿⠉⠙⠻⣿⣿⣿⣧⣤⣤⣤⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣿⡟⠀⠀⠀⠀⠀⠉⢛⣿⣿⠟⠉⢰⡟⠁⠀⣀⣤⣤⣤⣤⣄⡈⠉⠛⠿⠿⣿⣿⣏⣥⡀⠀⠀⠀⠙⣿⣷⡀⠀⣼⣿⠋⠉⠉⠉⠉⠙⠛⢛⣿⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣼⡿⠀⠀⠀⠀⢀⣠⣤⣾⠋⠀⠀⠀⠛⠀⣴⣾⡿⠛⠉⣁⣽⣿⣿⣤⠀⠀⠀⣿⣿⣿⣿⣷⡄⠀⠀⠀⠈⢻⣿⣿⣿⠏⠀⠀⠀⠀⠀⣠⣾⣿⡿⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⣇⣠⣤⣶⠾⠟⢩⣿⠏⠀⠀⠀⠀⣠⣾⡿⠋⠀⠀⣴⣿⣿⣿⣻⣿⡄⠀⠀⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⢿⣿⣿⣄⣠⣤⣴⣶⣿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀ ⢀⣠⣴⣾⣿⠿⠟⠛⠉⠀⠀⢠⣿⡟⠀⠀⠀⠀⣰⣿⡟⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣷⠀⠀⢸⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⣽⣿⢿⣿⣿⣛⣫⣽⣿⣦⡀⠀⠀⠀⠀⠀⠀⣀⠀ ⣿⠟⠉⠁⠀⠀⠀⠀⠀⠀⠀⣾⣿⠁⠀⠀⠀⢰⣿⡟⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⡏⠀⠀⠀⢻⣿⣇⠀⠀⠀⠀⠀⢀⣴⣿⠏⠀⠻⣿⣿⡋⠀⠘⠻⣷⣤⣄⣀⣠⣾⣿⣿⠀ ⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠀⠀⠀⠀⢼⣿⡇⠀⠀⠀⠀⠀⠈⠻⠿⣿⣷⡟⠀⠀⠀⠀⠀⠙⠻⢿⣶⣶⣶⣾⡿⠟⠋⠀⠀⠀⠙⢿⣧⡄⠀⠀⢨⣟⠻⠛⠛⠉⢸⣿⡀ ⠛⠿⣷⣶⣦⣤⣤⣤⣤⣤⣤⣿⡇⠀⠀⠀⠀⠈⢿⣷⣀⠀⠀⠀⠀⠀⢀⣴⣿⡟⠀⠀⠀⠀⠀⣀⣠⣤⣔⣈⡉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣷⡄⢀⣾⡇⠀⠀⠀⠀⢸⣿⡁ ⠀⠀⠀⠉⣿⣿⠛⠛⠛⠉⠉⣿⣿⡀⠀⠀⠀⠀⠀⠙⢿⣷⣦⣄⣤⣶⣿⠿⠋⠀⠀⠀⠀⣠⣾⡿⠛⠋⠛⠻⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣅⣾⡿⠁⠀⠀⠀⠀⣼⣿⠀ ⠀⠀⠀⠀⢿⣿⣆⣀⣀⣠⣤⣾⣿⣷⡀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠋⠁⠀⠀⠀⠀⠀⣿⠛⠁⠀⠀⠀⠀⠀⢻⣿⠆⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠟⠁⠀⠀⠀⠀⣰⣿⠏⠀ ⠀⠀⠀⠀⠸⣿⣏⠙⠛⠋⠉⠀⠘⢿⣿⣦⣀⣠⣤⣤⣤⣤⣦⣄⡀⠀⠀⠀⠀⠀⠀⠘⣿⣆⠀⠀⠀⠀⠀⣰⣿⠟⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠋⠁⠀⠀⠀⠀⢀⣴⣿⠟⠀⠀ ⠀⠀⠀⠀⠀⢿⣿⠀⠀⠀⠀⠀⠀⣤⣿⡿⠟⢻⡏⠉⠉⠉⣹⣿⠇⠀⠀⠀⠀⠀⠀⠀⠹⣿⣦⣤⣠⣤⣾⡿⠋⠀⠀⠀⠀⠀⣠⣴⣾⡿⠋⠀⠀⠀⠀⠀⢀⣴⣿⡿⠋⠀⠀⠀ ⠀⠀⠀⠀⠀⠸⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⢀⣠⣾⣿⣯⣤⣀⡀⡀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠉⠀⠀⠀⣀⣴⣾⣿⣿⣿⣥⣤⣤⣤⣤⣤⣴⣶⠿⠟⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⣿⣧⠀⠀⠀⠀⠀⠀⠀⣰⣿⣷⣿⠟⠋⠉⠉⠙⠛⠛⠿⠿⣿⣶⣶⣶⣴⣶⣦⣾⣶⡶⠿⠿⠟⠛⠋⠁⠙⢦⣍⡉⠙⠋⠙⠉⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢹⣷⣄⠀⠀⠀⠀⢀⣴⣿⠟⠻⣿⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣷⣦⣶⣿⡿⠛⠁⢀⣼⠋⠛⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⣼⣯⣴⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⣀⠀⣀⡀⢀⢀⢀⣀⣀⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠛⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣾⠟⠛⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡏⢿⣿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣶⡿⠟⠛⠉⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠈⢻⣿⢿⣶⣦⣤⣄⣀⣀⠀⠀⣀⣀⣀⣀⣤⣶⣶⣿⢿⣛⡋⣉⣀⡀⠀⠀⠀⠀⠀⠀⢘⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣄⣄⡀⣠⣼⣿⣷⣄⠀⠀⠀⣀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣄⣿⡆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⠆ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⣿⣿⣿⣿⣿⣿⡏⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⡇⠀ ⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⡇⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⢀⣀⠀⠒⠂⠀⠀⠸⣿⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⢸⠿⠛⠻⠿⠆⠈⠢⡆⣼⡿⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡟⣻⢿⣿⣿⣿⣿⡿⠀⠀⠀⠠⠀⢀⢤⣆⠀⠠⠂⣰⠃⢩⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡄⣉⡧⠻⢿⣿⣿⡇⠀⠀⠀⠀⠀⡘⠻⢿⡇⠀⢰⡟⣞⣿⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⠿⣄⡎⠸⣿⣿⡄⠀⠀⠀⠀⠁⠈⠑⠉⠀⠀⡀⢧⠈⢿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣍⣹⡾⣿⣿⣇⠀⠀⠀⠀⢠⠀⢦⠀⡀⠀⠁⢈⣧⠘⡆⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠛⠋⠀⠻⠟⠁⢸⣀⠑⠀⠀⠃⣨⡏⠣⢶⡆⢀⠞⣰⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠋⣿⣿⠃⢠⠃⠀⠀⣦⢀⠀⠀⠙⠆⠀⠰⠃⠀⠀⠀⢙⣧⡴⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃⠀⠋⠀⠀⠀⢸⢱⡧⡁⠈⢢⠰⣤⡤⠤⠒⢉⣩⣄⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡠⠒⠉⠀⠀⠀⠀⠆⠀⠀⠘⠀⠃⡄⠀⡜⠀⠘⡟⢿⣿⣿⣿⠟⠁⠀⠀⠀⠀ ⠀⢀⣀⠤⠚⠁⠀⣀⠴⠃⠀⠀⠀⠠⡀⠀⠀⠀⠀⠁⠸⡀⠀⡀⢡⡈⠻⠿⡿⠀⠀⠀⠀⠀⠀ ⠘⡇⠀⠀⠀⠀⡸⠋⠀⠀⠀⠀⡄⠀⠈⣧⠀⠀⠀⢄⠁⠹⡄⢧⣀⠙⢛⠟⠀⠀⠀⠀⠀⠀⠀ ⠀⠹⡀⠀⠀⠘⠀⠀⠀⠀⠀⣼⠃⠀⠀⠈⢧⠀⠘⢆⡁⠈⠪⠀⣀⡽⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠱⡄⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠳⣄⣀⣉⣷⡶⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠲⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⣠⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⠠⠀⢀⠀⠀⠀⠀⠀⢀⠏⠀⣰⠁⣠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠐⠒⠚⠓⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⡸⠗⠎⠁⠉⠀⠀⠈⢡⠀⠀⠀⠀⠀⠀⠆⣱⣀⠀⠀⠀⠀⠀ ⠀⣠⠃⠀⠀⡰⢰⡜⠀⠀⠀⠀⠸⡄⢸⠀⠀⠀⠀⠀⠀⠋⠈⡀⠁⠀⠀⠀⠀ ⠀⢧⠀⠀⡐⠁⣞⡠⢄⣒⠆⢀⢣⠀⢨⠀⠀⠀⠀⠰⡸⠀⠀⡇⠀⡇⠀⠀⠀ ⠀⢀⢂⠎⣠⣾⣿⣿⡛⠻⣷⡊⡌⡠⢼⡆⠀⠀⡠⢎⣴⣮⣶⡁⡰⡇⠀⠀⠀ ⠀⠀⡅⣨⣿⣿⢿⣿⠿⠉⠙⠒⠉⠀⠘⠀⠀⢰⡡⣺⣿⣷⠤⣿⢰⠑⠀⠀⠀ ⠀⠀⢩⠉⢿⢿⠛⢉⢻⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡯⢻⡆⢀⠇⡎⠀⠀⠀⠀ ⠀⠀⠀⢃⠀⠙⠢⠄⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠜⡁⠈⠀⡇⠀⠀⠀⠀ ⠠⠠⠤⠬⠢⠄⠀⠀⠠⠤⠤⠤⢤⠤⠤⠤⢤⣤⣄⡤⠤⠤⢤⣤⣥⠀⠀⠀⢠ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠓⠿⠿⢿⣿⣷⣴⠄⠀⠀⠀⠀⣠⣼ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣀⣤⣾⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠤⠤⠂⠐⠒⢒⣀⢖⣿⣶⣿⠿ ⠀⠀⠀⠀⠀⠀⠶⡦⢤⣤⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⢟⣡⡴⢿⣿⣿⣿⣶ ⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠈⠉⠻⣿⠟⢿⣿⣿⣿⠭⠁⢸⣿⣿⣾⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢌⣿⣹⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡤⠤⠤⣭⡖⠛⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣯⣾⣯⣤⣾⣿⣇⣈⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠐⣿⣿⡏⠉⢹⣿⡛⠛⢿⠿⢿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⣥⣀⡼⣯⣀⣀⡜⠀⠀⠸⣿⠏⠙⣻⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣾⡿⠿⠿⣦⣤⣑⠊⠐⠂⠀⠀⢀⡟⢀⣰⣿⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠻⣿⣦⡄⡀⣿⣿⣿⣶⡄⠀⠀⠘⣿⠟⣿⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⠘⢟⢿⣿⣿⠃⠀⠀⣰⢏⣼⡿⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠈⣿⡇⠀⢀⣾⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀ ⣀⣤⣤⣤⣀⠀⣀⡀⣻⡿⠶⠶⢾⡿⠶⠶⢿⣯⣠⣤⡶⠶⠶⣦⣤⣤⣤⡄ ⢿⡇⢠⡌⢹⠟⠛⠻⡏⠀⣠⣤⡎⠠⣤⣦⠾⠿⠭⣤⡇⠺⠀⣿⡉⠒⠼⣧ ⢸⡇⠀⣤⡆⠠⣶⠀⡇⠀⠻⠄⡠⡰⠻⠖⠀⢰⠃⠘⢃⣸⣆⡌⠙⠃⢀⣿ ⠸⠿⠛⠛⠻⣶⣤⣶⠿⣦⣄⣠⣴⣷⣤⣤⣴⠟⠛⠛⠛⠉⠛⠛⠿⠿⠟⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⡞⠉⠀⠀⠀⠔⠛⠉⠉⠉⠛⠳⣤⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⣰⠏⢀⣴⠶⢀⠤⢤⡀⠀⠀⠀⠀⠀⠈⠛⢦⡀⠀⠀⠀ ⠀⢀⣼⠏⢠⠏⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠈⢻⣆⠀⠀ ⢀⣾⠃⠀⡸⠂⠀⠀⠀⠈⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢿⡆⠀ ⣼⢣⠃⠀⡗⣛⢆⠀⠀⢔⣉⡑⠇⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀ ⢟⣾⠀⢀⠿⣒⡙⠀⠀⢸⣖⡱⢴⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀ ⠘⢿⢸⡟⡏⠉⡁⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄ ⠀⠘⣾⣷⢈⡳⠈⠁⠡⠀⠀⠀⡔⠇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇ ⠀⠀⠈⠙⡥⣀⣀⣀⠀⢡⠀⠸⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⣸⡇ ⠀⠀⠀⠀⢡⣿⣿⠟⠁⠠⠃⡄⠀⠀⣧⡆⠀⠀⠀⠀⡀⣀⣿⠀ ⠀⠀⠀⠀⢾⠯⠋⠀⠀⠀⠀⠀⠀⢀⣿⣿⣄⠀⠀⢀⣇⣿⠇⠀ ⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⢀⠔⠉⣿⣿⣿⣾⣧⣿⡿⠃⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡴⠁⠀⠀⡾⠋⡹⠟⢻⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⠦⠠⠔⠛⡇⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⢀⡀⠠⠤⠤⠤⠤⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠂⠁⡠⡀⠀⠀⡀⢀⡀⡀⡭⠖⠠⢀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡠⠺⠊⠛⠙⠵⠃⠘⠀⢩⠄⠀⠑⡑⡀⡀⢖⢬⢢⡀⠀⠀⠀⠀ ⠀⠀⠰⠁⣆⢄⠀⠠⠀⡄⣄⢀⢂⣳⡀⠀⠈⣸⡸⡀⠹⡣⡙⢄⠀⠀⠀ ⠀⠀⣧⢄⠕⡞⡄⡀⣇⢳⣽⢻⣀⡙⠿⣃⣄⣽⡉⣿⢎⢾⣶⡈⠀⠀⠀ ⢀⡔⠑⠅⠐⠠⠑⡠⢉⠪⣞⣀⡵⢾⡦⠀⢈⡿⢶⣿⢸⢸⡇⠇⠀⠀⠀ ⠀⠣⡀⢀⠐⡁⠀⢛⠛⡢⡛⠡⢤⡼⠇⠀⢽⡆⠿⢟⡿⣧⣄⡀⠀⠀⠀ ⠀⠀⡈⢓⢡⠸⡌⠢⡢⣘⠢⣀⠀⠀⠀⠀⠀⢜⠠⣿⣇⣀⠠⠃⠀⠀⠀ ⢠⠐⠐⠙⠈⠐⠽⣄⠈⢓⢇⠲⠁⠒⠀⡀⢄⣢⣽⡏⢯⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢻⡨⠹⡟⡄⠢⣎⢧⡀⡇⡀⠩⢝⠛⡫⣆⠀⢣⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⠇⡇⡇⠈⢣⡀⠑⡱⡁⢁⠀⠀⢺⢇⠈⢧⡀⢣⠀⠀⠀⠀ ⠀⠀⠀⠀⠸⡄⡇⠁⠀⠀⠙⢄⠈⢴⣉⢶⡎⠱⣄⠉⠀⠿⢄⠷⣄⠀⠀ ⠀⠀⠀⢀⢆⠃⡿⠀⠀⠀⠀⠀⠑⠄⠙⢿⣿⣀⠙⢟⠤⡀⠀⠑⠨⣳⡀ ⠀⠀⢀⢪⠎⢠⡯⠩⠁⠂⠌⡢⠀⠈⢢⡌⠳⣌⠓⠠⠍⠀⠀⠀⠀⠀⠀ ⠀⠀⠰⠋⠀⠈⠀⠀⠀⠀⠀⠈⠁⠒⠶⢿⠚⢦⠱⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠣⠜⡆⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠾⢄⠀⢠⠾⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡼⢏⣿⣞⣿⣽⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣗⡻⣿⡿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⡡⠈⠻⣶⣿⠟⢉⡑⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⢊⡾⠁⠀⠀⠀⠀⠀⠀⢱⡌⢆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⢂⣞⠇⠀⠀⠀⠀⠀⠀⠀⠈⡟⡌⢆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⢎⡟⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠸⡌⠄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢎⡞⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠹⡌⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣬⡞⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠙⣟⠄⠀⠀⠀⠀ ⠀⠀⠀⢀⣾⠏⠀⠀⠀⢱⡀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠘⢾⣆⠀⠀⠀ ⠀⠀⣠⡿⠁⠀⠀⠀⠀⠀⠻⢄⣀⣀⣀⣀⣀⣤⠾⠁⠀⠀⠀⠀⠀⠻⣧⡀⠀ ⠐⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⡆

⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠐⠉⠀⠀⠀⠀⠀⠀⠈⠑⠢⠀⠀⠀⠀⠀ ⠀⢀⣀⣀⠔⠀⠀⠀⠀⣀⠤⠀⠒⠒⠀⢄⠀⠰⡀⠀⠀⠀ ⠀⠀⠢⡀⠀⡐⠒⣚⢉⡁⠀⠀⠈⡁⠐⡀⠐⡀⠘⠀⠀⠀ ⠀⠀⣶⣾⢶⢶⣶⣶⣶⣶⣶⢶⡿⣶⢶⣶⣷⣶⣶⣶⡆⠀ ⠀⠀⠙⢻⣷⣵⣿⣿⣿⣿⠇⠈⢿⣿⣷⣿⣿⣿⣿⠛⠁⠀ ⠀⠀⠀⠣⣩⠉⠉⠉⠉⠁⠐⠈⠀⠉⡉⠉⠉⢹⡠⠃⠀⠀ ⠀⠀⠀⠀⠈⢢⠀⠀⠻⣿⣿⣿⣿⡿⠓⠀⠠⠂⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠥⠦⠄⢀⣀⣀⣀⡀⡤⠦⠅⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⠀⢠⠓⠚⢳⣲⠻⠐⠱⡀⢰⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⢠⠀⠱⠂⢿⠹⠇⠰⡉⢠⠸⠀⠀⠀⠀⠀ ⠠⢤⣠⢤⡀⡀⢸⠀⠈⠢⠘⣼⠤⡮⡤⢺⢀⠀⣠⡄⠀⠀ ⠠⣾⣿⢀⣿⣷⢳⡆⡖⢲⠣⡡⢡⡟⡇⠈⢲⠛⣿⠀⣖⡦ ⠠⢼⣿⠦⠟⠻⠼⠃⢧⠸⡄⠀⠠⠿⠴⠤⠸⠄⠿⠄⠧⠄ ⠀⠈⠉⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠀⣠⣄⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⣰⣏⠁⠀⠀⠠⠤⠶⠦⠦⠤⠀⠀⠀⠀⠀⢸⣿⣿ ⠀⠀⠀⠀⢠⣀⡀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡆⢀⡇⠀⠀⠀⠀⠀⠀⠀⢠⣿⣀⡤⠂⠀⠀⠀⠶⣖⠀⠠⠄⠀⠀⠀⠀⠈⢿⣿ ⠀⠀⠀⠀⣸⣿⣷⡀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⡇⠀⠀⠀⠀⠀⠀⢠⠊⠁⠀⣀⣀⣀⡀⠀⠀⠈⠉⠑⠀⠀⠀⠀⠀⠀⠀⠹ ⠀⠀⠀⠀⠙⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣧⠤⠤⠤⠤⠤⣴⡋⢈⣠⣤⣬⣀⣀⡀⣤⣀⡀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢁⠀⠀⠀⠀⠀⠙⠳⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⣠⢏⣽⡷⠶⠶⠶⠶⠶⢾⡏⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣠⣤⣶⣶⣶⣶⣶⣿⣿⣷⢀⡴⢳⣿⣿⡇⠀⢠⡄⢠⡄⢸⡇⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀ ⣀⣀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⢫⡎⠀⢸⣿⣿⡇⠀⠸⠇⠸⠇⢸⡇⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀ ⠙⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⢫⡟⡇⠀⢸⣿⣿⣇⣀⠀⣀⣀⣴⡿⠃⠀⠀⡏⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀ ⠀⠀⠈⠙⢿⣿⠿⣿⣿⣿⣿⢁⠀⣾⠁⡇⠀⢸⣿⣿⣿⣿⣴⣿⡿⠋⠀⠀⠀⠀⡇⠘⡟⢻⣿⣿⣿⣿⣿⣿⣿⣿⢁⡄⠀⠀⠀ ⠀⠀⠀⠀⠈⠻⠄⠀⠀⠀⠀⠻⠇⢸⠀⡇⠀⠀⠀⠀⣿⠟⠁⠀⠀⠀⠀⠀⠀⡀⡇⠀⣧⠀⢹⣿⣿⣿⣿⣿⣿⠃⣼⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡺⠀⠙⠦⣀⣀⣀⣁⣀⣀⣀⣀⣀⣀⣀⡠⠞⠁⠀⢹⣀⣠⣿⣿⡿⠟⠱⠋⣸⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠟⠿⠁⢀⠄⠀⡼⠁⠀⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢖⠂⠔⣀⣠⣞⡱⢃⣼⠃⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢤⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢧⠹⡉⠉⣉⢰⣢⠶⠾⠵⠾⠼⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢘⡧⢱⢀⠟⠉⢀⡠⠒⠈⠀⠀⠀⠈⠑⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⡴⠛⢧⡜⠁⠀⡰⠁⠀⠀⡐⠰⠀⠀⢀⠀⠀⠙⡓⢄⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠳⣄⢀⠁⠀⢠⠁⠀⣠⠞⠁⠁⢨⡧⢤⢂⠀⣧⢰⡀⢣⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⢻⠀⠀⢸⡠⠊⠁⠀⠀⡠⢃⣷⠏⡜⣰⢿⢯⠈⣮⡆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⡀⠀⢠⠒⣢⠀⢀⠔⠕⠁⢈⣶⠵⡃⠺⣼⠀⡇⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠇⠀⠘⢄⣼⢪⢁⠀⠀⠀⠈⠁⢀⡒⢼⣇⡔⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⠀⠀⠀⢏⢆⠛⡷⠄⠀⠀⡖⢻⠋⢈⢯⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⠋⠀⡐⠂⢌⣳⢯⠶⢗⡀⠐⢌⣚⡤⠊⡌⠛⠀⠀⠚⡏⠢⠀⠀ ⢤⡀⠤⠒⠁⡠⠊⠀⡞⣸⡿⢼⡔⢚⣯⠙⢋⠁⠱⡉⢀⡄⠀⣀⣁⣃⠁⠀⠀ ⠀⠁⢒⢆⠉⢄⠀⠸⢠⡏⠀⠎⠙⣾⠏⠀⠘⡄⠄⡋⡕⢁⣰⣿⣿⣿⣿⣞⠁ ⠀⠀⡎⡆⡠⡼⠉⡇⣾⠁⡘⠀⣸⠧⡀⠄⠔⣰⠭⠝⠃⠘⣿⡏⠉⠉⢻⣿⠀ ⢀⡀⢇⡿⡶⠁⡰⢰⡯⢄⡃⢀⣿⠀⣇⢊⠎⣜⢠⠀⠀⠈⣹⣷⢢⢴⣾⡟⠀ ⠘⠓⠘⠒⠓⠒⠁⢘⣃⢈⢈⢚⣳⢚⣁⢒⡺⢚⢚⢒⣆⠐⠛⠛⠈⠙⠛⠃⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⠒⢹⣀⢺⣐⡾⣐⣼⣒⢸⢺⢙⣶⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢴⢺⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⡟⠛⡟⠒⠒⠒⠒⠦⢤⣄⠀⢀⣀⣤⡶⢫⣄⣸⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⢿⡄⠘⣆⠀⠀⢠⣄⣉⣺⠿⠟⠛⠃⠙⠉⠉⠙⠚⠛⠲⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⣿⣄⠘⡄⠀⣨⠟⠉⠀⠀⠀⣀⠤⠒⠉⠀⠀⠀⠀⠀⠀⠀⠉⠳⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⣴⣿⠇⠀⣧⠎⠀⠀⠀⢀⡴⠊⠁⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣴⡿⠋⠉⠛⢷⣶⠃⠀⠀⠀⢰⠋⠀⠀⠀⠀⢀⡼⠀⡼⠀⢀⠀⠀⢠⠀⠀⠀⠀⠙⡌⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠙⢿⣦⠀⠀⢠⠇⠀⠀⠀⢀⠇⠀⠀⠀⠀⣠⠞⠃⠜⠁⠀⢿⣧⠀⡈⢣⠀⠀⢰⡀⢘⡆⠈⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠹⣷⣦⣼⠀⠀⠀⠀⣸⠀⠀⢀⣤⠞⠁⠀⠀⠀⠀⢰⢿⣿⢙⣷⠈⡆⠀⣸⣷⡘⡗⢦⡀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠛⢿⠀⠀⠀⠀⣇⣀⡴⠋⠀⠀⠀⠀⠀⠀⣰⠋⣸⣿⡾⠉⡇⠃⣰⣿⡿⣿⡄⠀⢳⣌⣧⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠈⣁⣀⡀⠀⠀⠀⠀⢀⠜⣡⠞⠉⠙⢧⣠⡇⣰⠟⣠⣷⠈⡇⠀⢸⡟⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⢀⣼⠁⠠⣜⡆⠀⢀⡴⠃⢐⣁⣀⣀⡀⣾⠿⠟⠁⠊⠀⢹⣷⡇⠀⣸⠃⠘⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⢻⡀⠀⣼⡵⠚⢹⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠤⢬⣿⡟⠀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠙⢲⡟⡆⠸⣦⢧⡀⠀⠀⠀⠀⠀⠀⢐⣩⣕⣲⠀⢸⡿⣞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠈⢧⠹⣄⠈⠻⡿⠦⠄⠀⠀⠀⢿⠉⠻⡟⠁⠀⢸⠳⣼⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠃⠀⠀⢀⣄⡀⠈⠳⣌⡳⠦⣬⣲⡤⠀⠀⠠⡄⠑⠤⢇⠀⣠⠏⢰⠛⣿⠀⠀⠀⢀⡴⣾⡛⢦⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⢀⡴⠁⠀⡈⠲⣴⣾⠟⡏⠉⠙⢢⣤⣀⡀⠈⣲⣶⠾⡏⠁⣠⠟⠀⠀⠀⠀⠀⢸⡀⠸⠀⣸⠁⠀⠀ ⢦⣄⣀⣀⣀⡤⠞⠁⠀⠀⣠⠋⠀⠀⣼⠃⣸⣿⣧⣴⣷⡴⠒⠋⣻⣤⠽⠻⡅⠀⡀⠻⡏⠁⠀⢀⡀⠀⠀⡀⠀⠉⠛⠉⠀⠀⠀⠀ ⠀⠙⠻⢥⣀⣀⣠⠴⢾⡉⠀⡀⠀⣼⠃⢰⣿⠋⠀⠸⠿⢷⣀⣾⣿⠎⠀⠀⢰⠀⠐⠀⣷⡤⠞⣩⠇⠀⢀⣽⣿⣿⣿⣿⣶⣤⣤⡤ ⠀⠀⠀⠀⠀⡽⢡⠀⠀⠳⣄⣈⠀⡏⢀⣿⡏⠀⢀⠃⠀⠀⣿⣿⠋⠀⠀⠀⠈⣧⠔⢊⣁⠴⣾⠁⢀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀ ⠀⠀⠀⠀⣼⠁⠇⠀⢀⣤⡟⠉⢹⠇⣼⣿⠀⠀⡆⠀⠀⣸⣿⡇⠀⢀⣐⣠⡞⢁⣴⣋⣉⣿⠟⠀⠙⢻⣿⣿⠋⠛⠛⠛⢻⣿⣿⠀ ⠀⠀⠀⠀⡏⠈⠀⡴⢋⡜⠀⠀⡼⢠⣿⠇⠀⢰⡀⠀⢀⣿⡇⠙⡾⠉⢠⠎⣠⠞⡟⠉⡏⠀⠀⠀⠀⣾⣿⣇⠀⠀⠀⠀⢀⣿⣿⡀ ⠀⢀⣤⣤⣽⣰⡿⠛⡿⠀⠀⡰⠁⢸⡿⠲⢄⡈⠀⠀⣼⣿⠁⠀⣇⡴⠃⡔⠁⣼⠁⢀⡇⠀⠀⠀⠀⢀⣿⣿⡟⢳⡖⢾⣿⣿⡟⠁ ⠀⠹⠿⠦⠠⠯⠧⠼⠤⠤⠴⠃⠀⢾⠧⠀⠸⠉⠓⠤⢿⠿⠤⠼⠟⠠⠼⠤⠼⠭⠧⠼⠤⠤⡄⠀⠠⠾⠿⠿⠷⠾⠿⠿⠿⠿⠧⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠖⢦⣠⡖⢶⠀⡴⠛⡆⢠⠖⢲⠀⡶⠒⠲⡖⢲⣀⣶⠳⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡶⠚⢹⡀⢸⠿⣇⠰⣶⢾⡀⢶⠀⡟⠂⠀⡷⢾⠁⡙⣳⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠈⠓⠛⠀⠙⠚⠛⠈⠓⠛⠂⠛⠒⠒⠃⠘⠃⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⢀⣴⠞⠋⠉⠓⢦⡀⢠⠞⠁⣼⡁⣠⢞⠉⠻⣦⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⣞⠁⠀⠀⠀⢀⣴⣿⣧⡀⠀⠈⠙⣷⡿⢷⣄⣼⣧⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⡾⠉⠙⢲⡶⠞⡿⢁⣠⣍⡛⠲⠶⣾⣋⠉⠻⣇⣉⡿⠓⠒⠒⣶⠀⠀ ⠀⠀⣼⣡⡤⢖⡟⠀⠀⣴⠛⢡⣾⣿⡆⠰⣿⣿⡆⠀⠘⣿⣁⣤⣴⠞⠃⠀⠀ ⡞⠛⠉⠀⠀⣾⠁⠀⣼⠃⠀⠸⣿⣿⡏⠀⠻⣏⠁⢀⣰⠏⢻⣖⠙⢷⣤⣤⣶ ⠳⢦⣤⣤⣤⣿⠀⠀⠻⣄⠀⠀⣨⠟⠀⠀⣠⣬⣉⠉⠁⠀⠀⠹⡇⣰⠃⠀⢸ ⠀⠀⣿⣤⣤⠿⣆⠀⠀⠈⠙⠋⠁⠀⢠⡚⠁⠀⢸⡆⠀⠀⠀⣰⡿⠋⠀⢀⡟ ⠀⠀⢸⡆⠀⠀⠹⠛⡏⢉⣽⠇⠀⠀⠀⠳⣤⡴⠟⠀⣀⣤⡾⠋⢀⣀⣴⠟⠀ ⠀⠀⠀⢿⡀⠀⠀⣰⣷⡛⠉⠙⠛⠒⠶⠴⠶⠖⠒⠛⠉⠺⣍⡉⠉⠉⠀⠀⠀ ⠀⠀⠀⠈⠳⠶⠟⠉⣔⣩⠿⠂⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⢻⡆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⣟⠁⠀⠀⠀⠀⠉⠙⠛⠉⠉⠀⠀⢀⣠⢾⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢿⠙⢶⣄⣀⡀⠀⠀⣀⣀⣠⠴⠖⠛⠉⠀⠘⣆⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠉⠉⠉⠒⠒⠦⠤⣀⣀⠀⠀⢀⡇⠀⠈⠓⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠾⠀⠀⠀⠀⠀⠙⢄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⣏⠉⠑⠒⠲⠤⢄⣀⡸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠔⠊⢹⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⣀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠸⠃⠀⡼⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢰⡒⠉⠁⠀⠈⠓⢤⣀⡀⠀⠀⢿⠢⢄⡀⠀⠀⠀⢿⠢⣄⡀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣷ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄⠀⠀⠀⠀⢸⠀⠉⠉⠒⠺⠄⠀⠈⠉⠒⠢⠼⠆⠀⠈⠙⢲⠦⢼⡄⠀⣠⣶⢦⠀⠀⠀⠀⢸⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⢀⡼⠊⠉⠑⢦⠀⠀⣠⣖⠋⠉⠙⠒⠦⣄⠀⠀⠘⡄⠀⠀⡼⢹⣟⠃⣇⠀⠀⢾⠾⠆⠀ ⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈⠳⡀⢾⠀⢰⡄⠀⠈⡇⠀⢏⠻⠆⠀⠀⠀⠀⢸⠄⠀⠀⢳⠀⢰⠃⣾⡿⡆⣿⠀⠀⢸⡆⠀⠀ ⢰⠤⣤⡞⠳⣤⠿⡋⠀⠀⠀⠀⠀⠈⢻⡀⠀⠀⢀⡼⠁⠀⠈⠓⠤⠤⠤⠄⠒⠋⠀⠀⠀⠘⣆⡎⢠⣿⢀⣷⠏⠀⠀⡼⠁⠀⠀ ⠘⡟⠉⣇⠀⣿⢆⣻⡿⠁⠀⠀⠀⠀⠀⣹⠶⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠚⠀⠀⠘⢃⡞⠈⠉⠀⠀⠀⣼⣁⠀⠀⠀ ⠀⢹⡦⠘⠛⠁⠀⠁⠀⠀⠀⠀⠀⠀⠘⠓⠒⠤⡤⣤⣤⣤⣤⠤⠤⠴⠒⠊⠉⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⢀⡠⠞⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡉⠙⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠘⠓⣤⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠋⠀⠀⠀⣀⣀⣀⡠⠔⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠢⠤⠤⠤⠤⠤⠄⠒⠚⠉⠁⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⠒⠲⠶⠤⢤⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠛⠲⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠒⠶⠤⣄⣀⡀⠀⠀⢀⡿⠀⠀⠀⠉⠳⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠦⣼⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡷⠦⠤⣤⣀⣀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠈⠉⠙⠓⠲⠤⣼⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⣠⡴⠶⡆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣯⡁⠀⠀⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⢀⣼⠃⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡶⠚⠋⠁⠀⠀⠙⠷⣤⡀⠀⠀⠀⠀⠈⡟⢦⣄⠀⠀⠀⠀⠀⠈⣟⢦⣀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢳⣦ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡄⠀⠀⠀⠀⠀⠀⢸⠍⠛⠒⠦⢤⣀⣻⠀⠈⠙⠒⠦⣤⣀⡀⢹⡄⠉⠙⠒⠦⣤⣀⠀⢻⡀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⣶⡶⠛⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⢸⣀⣀⣀⣀⠀⠈⠉⠁⠀⠀⢀⣀⣀⣈⣉⠙⠃⠀⠀⠀⠀⠀⣏⠙⠚⠗⠀⢠⢞⡿⣏⢷⠀⠀⠀⠀⣀⢸⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠀⠀⠀⢀⡾⠋⠁⠀⠈⠳⣄⠀⠀⣠⢞⣋⠁⠀⠀⠉⠉⠳⢦⡀⠀⠀⠀⢹⠀⠀⠀⢠⡏⣼⣧⡉⠸⡇⠀⠀⠸⣿⠻⠇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⣾⠀⢀⣤⡄⠀⠀⢹⡄⠀⢻⠘⣿⡄⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠈⣇⠀⢀⡾⢠⣿⣻⣧⠀⣧⠀⠀⠀⢸⠀⠀⠀⠀ ⣀⣀⠀⢠⡴⣦⡀⣠⡶⡷⠂⠀⠀⠀⠀⠀⠈⠳⣿⠀⠀⠙⠁⠀⢀⣾⠃⠀⠈⢷⣉⠀⠀⠀⠀⣀⣠⡴⠏⠀⠀⠀⠀⢹⡀⣸⠃⢘⣿⠋⣸⣠⡇⠀⠀⠀⣼⠀⠀⠀⠀ ⣿⡉⣻⢿⠀⠈⣷⡏⢸⣆⣀⡀⠀⠀⠀⠀⠀⠀⠘⣦⡀⠀⢀⣠⠟⠁⠀⠀⠀⠀⠈⠙⠛⠛⠉⠁⠀⠀⠀⠀⣀⡀⠀⠀⢧⡟⠀⡿⣽⣤⡿⠟⠁⠀⠀⣰⠇⠀⠀⠀⠀ ⢹⣏⠀⢸⣆⠀⢹⠻⣄⣩⣿⠃⠀⠀⠀⠀⠀⠀⠀⢀⡿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠋⠁⠀⠀⠘⠃⣼⠁⠀⠀⠀⠀⠀⠀⣴⣏⣠⠀⠀⠀⠀ ⠀⢹⣦⡀⠛⠓⠋⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠦⠤⢤⣤⣄⣀⣀⣀⣀⣠⣠⡤⠤⠤⠖⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⢀⣴⠏⠀⠀⠀⠀ ⠀⠘⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠲⠯⠿⣶⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠶⣯⣀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠞⠁⠀⠀⠀⢀⣀⣀⣤⣤⠴⠚⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠧⠤⣤⣀⣀⣀⣀⣀⣠⠤⠤⠖⠒⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⣤⡀⠀⠀⠀⠀⠀⢀⠯⡀⠀⠒⡒⠒⡀⠀⠀⠸⣿ ⠀⠀⠀⢸⣷⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⢠⠊⠁⣀⣀⡀⠈⠐⠀⠀⠀⠀⠙ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⡜⢀⣀⣀⡀⢀⡀⠀⠀⠄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣇⣀⣀⣀⣙⣾⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀ ⠀⠀⠀⢀⣤⣶⣶⣶⣾⣷⡠⢳⣿⠀⣤⢠⢸⡇⢻⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀ ⠐⠶⣾⣿⣿⣿⣿⣿⠿⡝⠀⢸⣿⣀⠉⣈⡼⠃⠀⣻⣿⣿⣿⣿⣿⣿⠇⠀⠀ ⠀⠀⠈⠻⡟⠻⠿⢧⠰⠃⠀⠸⠿⣿⠾⠟⠀⠀⠀⠀⡟⢿⣿⣿⣿⡿⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠢⠀⠈⠁⠀⠀⠀⠠⠞⠀⢃⣬⡿⠟⠓⠡⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢎⠁⢀⣔⠁⡔⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡴⠊⠁⢣⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠆⠁⠀⠀⠀⡀⠀⠎⠀⠀⠀⣀⡑⠤⠊⣧⠀⠀⠀⠀⡀⠀⠀⠀ ⡀⠀⠉⠈⠀⠀⡠⠤⠀⠼⢀⠄⢂⡭⢒⡢⠭⠶⠶⣥⠢⡒⢹⠁⠀⠀⠀ ⠀⡩⠂⠀⣀⠊⠀⠀⡠⢂⠥⡪⠕⠈⠀⠀⠀⠀⠀⢘⣷⡧⠃⠀⠀⠀⠀ ⢰⠁⢠⠊⢸⠀⡠⢊⣴⠿⢘⠒⠠⡀⠀⠀⠀⠀⠀⠈⠛⠇⢀⠄⠀⠀⠀ ⢸⠀⠀⠀⢸⣪⣾⡟⠏⠀⣀⡰⠆⠛⢓⡠⠤⡤⠀⠀⣀⠫⡑⡀⠀⠀⠀ ⠈⠀⠀⠀⠀⠝⡇⣿⢸⠀⠉⢢⢀⡀⠛⠚⢀⡧⣀⡘⢿⣃⡇⢡⠀⠀⠀ ⠀⡇⡄⠀⢸⢸⠁⠙⢮⣆⡐⠠⠭⠜⠿⠟⠋⠈⢪⠥⠂⢎⠘⠄⢂⠀⠀ ⠀⠇⠃⠔⠐⢺⠀⠀⠹⡀⣬⢉⡐⠂⠤⠤⠤⠤⠤⠤⢐⣪⡎⠚⠲⠥⠄ ⠀⠒⠁⠀⠀⠘⢦⡀⠀⠈⠪⣑⠪⠭⣛⣭⣉⡽⠉⣉⠆⠢⠉⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠲⢄⣀⠀⠉⠒⠢⠤⠌⠒⢒⡒⠎⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠋⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠻⣆⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⠉⠢⣄⡀⠀⠀⠀⠀⠀⠀⠀⠄⠂⠀⠀⢀⣼⠋⠀⠀⠀⠀⠀⠀⠀⠙⣧⡀⠀⠀⢀⣼⡿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣠⠋⠀⢐⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⠙⢄⡀⠀⠀⠀⠀⠀⠀⠀⢀⡖⠃⠀⣸⠇⠀⠀⠀⠀⠀⠀⣀⡤⠴⠖⠒⠋⠋⠉⠉⠉⠙⠻⢤⡀⠀⠀⠀⠀⠀⢀⣠⣾⠀⠀⠀⠀⠀⠀ ⠀⠀⠐⠉⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⣀⣄⣀⣀⣀⡟⠀⠀⠀⣀⡤⠖⠋⠁⣀⣤⠶⠞⠛⠛⣛⣻⣿⣶⣦⣄⡙⠳⢄⡠⠤⠖⠛⢸⡏⠀⠀⠀⠀⠀⠀ ⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⠁⠀⠀⠀⠈⠁⢀⡴⠛⠁⢀⡤⠶⠛⢃⣠⡤⠶⠛⠉⠉⠀⠀⠀⠉⠙⣿⣷⠀⠻⡄⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠉⢳⡦⠖⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⣠⠞⠋⢀⣤⠞⠋⣠⡴⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣽⣷⡄⢳⢀⡜⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⡼⠋⠀⠀⠀⠀⣀⣴⠏⠀⠀⠀⠀⠀⠀⣠⠞⠁⣤⠶⠋⣈⡴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠘⣿⣷⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⡾⠁⠀⠀⠀⣠⠞⠉⢸⠀⠀⠀⠀⠀⣠⠞⢁⣠⣾⢏⡤⠞⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⠁⠀⠀⠀⣸⠁⠀⠀⡏⠀⠀⠀⣠⠞⢁⣴⡿⣿⡷⠟⠈⠉⢉⠉⠙⡲⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⠃⠀⢠⣤⠄⠀⠀⠀⠀⠀ ⢾⠀⠀⠀⢸⠃⠀⠀⠀⢹⠀⣠⠞⢁⣴⣿⣿⣿⠟⠀⠰⠚⠉⠁⠀⠀⢀⣀⣙⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠠⠤⣶⡟⠁⠀⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠸⠀⠀⠀⠀⣸⡞⢁⣴⣿⣿⡟⠙⡏⠀⠀⠀⠀⠀⢰⣒⣩⠵⠶⠖⠋⠙⠳⠦⣤⣀⣀⣀⣀⡀⠀⠀⠀⠀⣀⡲⢾⣧⠀⠸⡄⠀⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠀⠀⠀⠀⠀⢹⣶⣿⣿⡿⣿⣧⠀⢹⡄⠀⠀⢸⡏⠉⠉⠀⠀⠀⠀⢀⣶⣿⢿⡆⠀⠀⢻⡀⠉⠉⠉⠉⣰⣿⣿⡍⠈⣧⠀⢳⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡿⢻⡄⢹⣿⡇⢀⡇⠀⠀⠈⠙⠳⣄⠀⠀⠀⠀⠈⠿⠿⠾⠇⠀⠀⢸⣇⠀⠀⠀⠀⠙⠿⠾⠃⠀⣿⠀⠈⣇⠀⠀⠀⠀⠀ ⠀⢠⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⣼⠇⢸⣿⡇⢰⡇⠀⠀⠀⠀⠐⠮⣙⠲⠤⣄⣀⣀⠀⠀⠀⣀⣠⢾⣉⠓⡦⠤⣄⣀⣨⡥⠤⢜⣿⡄⠀⠹⡄⠀⠀⠀⠀ ⠀⠀⡇⠀⡀⠀⠀⠀⠀⣾⠀⣼⡟⠀⠈⠻⣿⣄⠹⣄⠀⠐⠦⣄⡀⠈⠙⠒⠦⠭⢉⡉⣉⣩⠽⠋⠀⠙⢦⣌⡉⠓⢲⣒⢐⣶⠛⠁⢹⡀⠀⢳⡀⠀⠀⠀ ⠀⠀⡇⠀⣿⠀⠀⠀⠰⢻⠀⣿⡇⠀⠀⠀⠈⢛⡷⣿⣀⣀⠀⠀⠉⠙⠛⠒⠒⠲⠖⠚⠋⠁⠀⠀⠀⠀⠀⠹⣟⠋⠉⠀⠈⢻⡆⡀⠀⠹⣄⠀⠱⣄⠀⠀ ⠀⠀⡇⠀⡟⠀⠀⣰⢦⣘⣆⣿⡇⠀⠀⠀⢰⠋⡾⠉⠀⠉⠉⠓⠲⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⢀⣠⠿⣝⠲⣤⣙⢷⡀⠈⠣⡀ ⠀⢰⠃⡌⠀⢀⡴⠃⠀⠈⠉⣿⡇⠀⠀⠀⠀⠀⢻⡄⠀⣿⣧⣤⣀⠀⠀⠈⠉⠉⠒⠒⠒⠲⠤⠤⠤⠤⠔⠒⠒⠒⠒⠋⠉⣠⡶⢻⡄⠀⠈⠉⠙⠓⠒⠒ ⠀⠋⠀⣠⡴⠋⠀⠀⠀⠀⠀⣿⡇⡀⠀⠀⠀⠀⠀⠙⢦⡈⠻⢦⣈⣉⣻⣶⣶⣦⣤⠤⢤⣤⣤⣤⣤⣤⡤⠤⠤⠦⣄⡀⠹⣍⠙⢿⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠘⢿⣮⣀⠄⠀⠀⠀⠀⠀⠙⢦⡀⠉⠛⠷⢤⣄⣉⠙⠳⢦⣄⡀⠀⣔⣿⠀⠀⠀⠀⢈⣷⠀⢸⡄⠘⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣷⣄⡀⠀⠀⠀⠀⠀⠉⠳⠤⣄⡀⠀⠈⠉⠛⠒⠺⠭⠿⠯⠥⠤⠤⠖⠚⠋⠁⣀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⠦⣄⣀⣀⣀⡤⠴⠶⠶⠒⠒⠒⢚⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠶⣦⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡤⠤⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⡿⠛⠋⠉⠉⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣯⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⢀⠟⠀⠀⠀⠀⠀⠀⢠⣆⢸⣿⣿⣿⣿⣿⣿⣿⣗⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠃⣾⠤⡄⠀⡤⢶⣜⡀⠈⠓⢺⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⠟⠐⢆⠀⡰⠒⠢⡍⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡷⠄⡴⠘⡄⠀⠀⡹⠶⢶⣿⣿⣿⡿⣫⠽⡹⣿⠟⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣇⡎⣀⠀⠈⠉⠉⠀⠀⠨⣿⡿⠟⢺⡿⠀⣵⠟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣋⠈⠛⠁⠀⠀⠀⠀⠀⣸⣿⠀⠀⠫⠀⣼⠏⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⡜⣿⣶⣤⣀⠀⠀⠀⠐⠿⠋⠀⠀⣠⣾⢣⣤⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠇⢟⣛⡩⠎⠀⠀⣀⣀⣠⣤⠴⠚⠋⡡⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠠⠼⣏⠀⠀⠀⢸⡁⠀⠀⠀⢀⣠⣪⣾⣿⣿⡇⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠑⣄⣉⣷⡶⣖⣟⣁⣤⣴⣾⣿⣿⣿⣿⣿⣿⣷⣦⣄⣀⢀⠀⠀ ⠀⠀⠀⠀⣀⣴⣾⣿⠈⣿⣿⣷⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴ ⢀⣴⣾⣾⣿⣯⣿⣿⣾⣿⣿⣏⡭⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣾⣿ ⣿⣿⣿⢯⣿⣯⡟⣿⡿⢹⣿⣿⣴⣿⣿⣿⣝⣿⣿⣫⣿⣿⣿⣷⣿⣿⡟⣿⣿⣿ ⢫⣿⣟⣿⣿⣿⣿⣿⡤⡾⢺⣿⣿⣿⣿⣷⣿⣿⡾⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿ ⣾⣿⣿⣿⣿⣿⣿⣿⡇⢤⣾⣿⣿⣿⣿⣿⣿⣯⣾⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⡠⠖⠋⠁⠀⠀⠉⠁⠒⠤⡀⢀⡀⠤⠐⠒⠒⠒⠂⢄⠀⠀⠀⠀⠀⠀⠀⠀ ⡰⠋⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠈⢇⠀⠀⠀⠀⠀⠀⠀⠀⠑⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠠⠒⠉⠁⠀⠀⠀⠈⠉⠒⢬⣆⠤⠤⠤⠀⠀⠠⠤⠤⢼⣀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⢄⣒⣒⣀⡼⠦⡀⠀⠀⠀⠠⠤⠤⠤⠤⠭⢒⡄⠀⠀ ⠀⠀⠀⢀⠤⠐⣈⠤⠒⠉⠀⠀⠀⠀⠀⠉⠚⣶⠒⠂⠉⠉⢁⣀⣀⣈⣉⡚⣧⡀ ⠀⠀⠰⠍⣈⣉⣀⡀⠤⠔⣲⡞⣿⣧⣄⠀⠀⠹⠒⠀⠉⢁⣴⣛⣿⣷⣆⠀⠈⠃ ⠀⠀⠀⠀⠀⣑⠢⣄⠀⠸⣿⣟⣿⣤⣿⠧⠔⡧⠤⠀⢀⣸⣿⣽⣷⠼⠿⢦⡶⠁ ⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠙⢴⠖⢒⣉⠁⢐⣒⢤⡠⠐⠊⠉⠐⠲⢇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠄⠒⠒⠒⢠⠋⠀⠀⠀⠀⠀⠀⠀⠑⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⠊⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠊⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠀⣼⣿⣁⣵⡖⠛⠉⠉⠉⠙⠒⢦⠀⠀⣍⢙⠂⣯⠀⠀⠀⠀⠀⠀⠀⠁⠉⠀⠈⠈⠈⢩⡇⠄⠻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠎⠀⠀⠀⠀⠀⠀⢰⡟⡿⠁⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣀⣿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡎⠀⠀⠀⠀⠀⠀⢠⡟⢀⡇⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⡇⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡷⠏⠉⢿⠀⠈⠓⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⢠⠟⠀⠀⠀⠀⠀⠀⢠⡿⠀⣼⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⡇⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⠀⠀⠀⠀⠀⠀⢀⡞⠀⢀⣏⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⢰⠁⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⣼⠀⠀⠀⠀⡷⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⡄⠀⠀⠀⠀⢠⠟⠀⠀⢸⡿⠁⣀⣤⠴⠲⠒⠺⡾⠀⠀⠀⡞⢰⠈⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠂⠀⡇⠀⠀⠀⠀⣧⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣇⣧⠀⠀⠀⣰⠋⠀⠀⢠⣿⢶⣞⣭⣤⣶⣶⣖⣋⡀⠀⢀⢸⠁⣸⠀⠀⠀⠀⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⡼⠀⠁⠀⡀⠀⢀⣿⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣿⠘⠆⢀⡾⠃⠀⢀⣼⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⣿⣦⠆⠀⢠⡏⠀⠀⣀⣀⡟⡄⠀⠀⠀⠀⠀⠀⢀⣼⠞⢁⣴⣾⣏⣭⣶⣟⠁⠀⠀⣠⣿⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠸⣄⣴⠟⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⢉⡻⣯⠛⠢⡼⢁⡴⠞⠁⠘⡇⠇⠀⠀⠀⠀⠐⢢⠟⠀⣰⣿⣿⣿⣿⠿⠿⣿⣷⣠⠞⠉⣽⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⠁⠀⠀⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠋⠉⠹⣟⢷⡴⠛⠋⠀⠀⠀⠀⡧⠀⠀⢀⡀⠀⢠⠏⠀⣴⣿⣿⣿⣿⣿⣆⡀⠈⣿⣟⠓⢲⡏⠿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠸⡆⢀⣰⣿⣿⣿⣿⣿⡿⢿⣿⣿⡟⠉⣻⠀⠀⠀⠘⠇⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⠀⠀⣏⡴⠋⢱⣿⣿⣿⣿⣿⡇⠉⢳⣸⡇⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢿⠋⠹⠻⣿⣿⣿⣿⣿⣾⡏⠛⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠁⠀⣿⡏⣻⣿⣿⣉⠀⠀⠀⣿⠃⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠸⡆⠀⠀⠻⣿⡿⣿⠀⠀⠀⣠⣀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡙⠋⠙⣿⣿⠁⠀⢰⠏⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢹⡄⠀⠀⠈⠻⣷⣄⠀⠀⠀⠛⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠀⢀⣾⠃⠀⢀⠏⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠈⠙⠓⠒⠒⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢾⡃⠀⠄⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⣷⡀⠀⠀⠀⠀⠓⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⢀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠠⠤⠶⠤⠤⠤⣤⡼⠷⠤⠤⠤⠤⠴⠦⠶⠶⠶⠤⠤⠤⠤⠤⠤⠤⢤⡤⡤⠤⣤⡤⠤⢤⣤⡤⠤⢤⣤⡤⠤⠤⠤⠤⡤⠤⠤⠤⠤⠬⠤⢤⣤⢷⡤⠀⠀⠀⠀⠀⠀⠀⣠ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣄⢀⣉⣁⡀⢀⣠⣶⣾⣿⣿⣿⣿⣶⣤⣌⠀⠀⠉⠉⠛⠛⠛⠻⠟⠁⠀⠀⠀⠀⠀⠀⠀⣼ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣿⣿⣷⣀⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⠻⠿⣿⣿⣿⣿⣿⠁⢱⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⢾⣷⣀⠀⠀⠀⢀⣠⣾⣿⣿⣾⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠷⣦⣴⣿⣿⠿⢾⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⣀⣀⣀⣀⡀⠀⠀⣀⣠⣽⣿⣿⣤⣾⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣴⣶⡾⠿⠿⠟⠉⠁⠀⠀⠀⠀⠀⠀⣠⣤⣦⡶⢉⣽⣿⣿⣿⣿⣿⡿⠿⠿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣿⣿⣿⣿⣿⣿⣷⣶⡾⠋⠁⣨⣶⣿⣿⣿⣿⣿⣿⣿⣧⣤⣤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢉⣠⣶⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⣀⡀⠉⠙⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠟⠁⣰⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⡀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡤⠄⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠈⠳⢧⠀⠀⠰⡿⠛⠛⠻⠿⡿⠿⠶⠀⠀⢠⣄⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢀⣿⡟⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠋⣡⣾⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠒⠒⠒⠀⠚⢉⣠⣴⡿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠹⣿⠿⠿⠿⠿⠟⠛⠿⣿⣿⠋⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⡿⠟⠛⠛⠛⠛⠛⠛⠛⠛⣳⣦⣶⣶⣿⣿⠿⢿⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡿⠉⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⠋⠉⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⢿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠀⠀⠀⠀⠀⠀⠀⢀⡖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠋⠀⠀⣠⣶⠾⢿⣶⠀⢈⣀⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⣿⣿⠃⠀⠀⣼⡿⠛⠋⠙⠛⠓⠛⠉⠉⠉⢻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⣿⣿⠃⠀⠀⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣦⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣴⣿⡿⠃⠀⠀⢸⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠘⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣧⠀⠀⠀⠀ ⠀⠀⠀⣼⣿⡿⠁⠀⠀⠀⣾⡤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠋⠁⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣧⠀⠀⠀ ⠀⠀⣼⣿⡿⠀⠀⠀⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡄⠀⠀ ⠀⣸⣿⡿⢀⡟⠀⠀⠀⣾⢃⡾⢷⣦⣀⠀⠀⠀⠀⠀⠀⣴⠿⠿⠿⣶⣤⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣧⠀⠀ ⢀⣿⡿⠀⣾⠀⠀⠀⠀⣿⠉⣠⣄⠉⢛⡃⠀⠀⠀⠀⠚⢁⣬⣤⣄⠀⠉⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡀⠀ ⠸⣿⡇⣼⣿⠀⠀⠀⠀⢸⣿⣯⠈⠛⠟⡇⠀⠀⠀⠀⠰⣯⣥⡈⠻⣦⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡇⠀ ⠀⣿⢡⣿⡏⠀⠀⠀⢠⠿⢿⡛⠉⠀⠀⠁⠀⠀⠀⠀⠀⣝⣻⠟⠀⣠⡿⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇⠀ ⠀⢸⣿⣿⡇⠀⡄⣰⣏⣤⠴⠭⠭⠴⠛⠁⠀⠀⠀⠀⠀⠈⠙⠛⠋⠁⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀ ⠀⠈⢻⣿⣿⠀⣧⡏⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⠀ ⠀⠀⠈⢸⣿⠀⣯⣧⡀⠘⣷⣄⠀⠐⠶⢶⡄⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠀ ⠀⠀⠀⠈⢻⣧⣿⣿⢧⠀⠈⠙⣳⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⣼⠏⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀ ⠀⠀⠀⠀⠀⠻⣿⣿⣼⣦⣴⠟⠁⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⣾⠃⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠀ ⠀⠀⠀⠀⠀⠀⠘⠍⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⣾⠃⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠆ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⣿⣦⣤⣤⣤⣤⣤⡀⠀⠀⠹⡄⠀⠀⣿⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⣹⡆⠀⡏⠀⠀⠀⠀⢸⣿⡄⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⣾⣿⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠈⠉⠀⢸⠁⠀⠀⠀⠀⢸⣿⣷⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⢰⢰⣿⣿⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡿⢿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠈⣿⣿⢸⣷⠀⢀⠀⠀⠀⠀⠀⠀⢀⣾⠀⣼⣿⣿⠏⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠙⠳⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣰⢸⠀⠀⣤⢀⠀⠀⢸⣏⣸⣿⣿⠟⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡶⠋⢿⣿⣿⣿⣿⣿⠀⣼⡇⣾⢀⢴⣿⣿⣿⣿⠟⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠋⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠁⠀⠀⠀⠀⢸⣿⣿⡿⢹⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠃⠀⠀⠀⠀⠀⠀⡾⣿⠋⠀⢸⣿⠯⠿⠋⣹⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡀⠀⠀⠀⠀⠀⠀⣀⣴⣿⡁⠀⠀⠀⠀⠀⠀⢸⠿⠁⠀⢀⡾⠃⠀⠀⠀⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣦⣀⠀⣀⣴⠾⠛⠹⣿⡇⠀⠀⠀⠀⠀⠀⠈⠀⠀⠠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⣿⡇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⠃⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀

⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⠾⠿⠟⠛⠛⠛⠻⠶⣶⣤⣀⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣤⡾⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣦⣀⠀⠀⠀ ⠀⠀⣴⡟⠋⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣬⣿⣆⠀⠀ ⢀⣾⠋⢀⣴⡾⠟⣹⣿⣿⣿⣆⠀⠀⣠⣶⣦⣄⠀⣸⡏⠀⢀⣽⣿⣧⠀ ⣼⡏⠀⣾⠃⠀⢸⣿⣿⣿⣿⣿⡆⢰⣿⣿⣿⣿⣆⢿⡇⢀⣿⣿⣿⣿⡄ ⣿⠃⢸⡇⠀⠀⢸⣿⣿⣿⣿⣿⠁⣾⣿⣿⣿⣿⣿⡼⣷⠈⣿⣿⣿⣿⣷ ⣿⠀⠸⣧⠀⠀⠀⠙⠿⣿⡿⠃⢸⣿⣿⠋⠉⠉⢿⡇⠙⣷⣜⢿⣿⡿⣿ ⣿⡆⠀⠙⢷⣤⣀⣤⡾⠛⠁⠀⠘⣿⠁⠀⠀⠀⢸⡇⠀⠈⠙⠻⠶⢾⡟ ⠸⣷⡈⠀⢀⠉⡉⢉⠀⠉⠢⡀⠀⢿⡇⠀⠀⠀⢸⡇⠀⡞⠸⠀⢢⡿⠁ ⠀⠘⣷⡀⠛⠐⠃⠘⠀⠀⠀⠈⡄⠈⢿⣄⠀⢀⡿⠑⠀⠀⠀⣰⡟⠁⠀ ⠀⠀⠈⠻⣷⣄⡀⠀⠀⠀⠀⠀⢰⠀⠀⠙⠻⠟⠁⠀⠑⣠⡾⠋⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⠻⣶⣤⣀⠀⠀⡌⠀⠀⠀⠀⠀⣀⣴⡾⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠿⠷⠶⠶⠶⠿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣶⡿⠿⠿⠟⠿⠻⠿⠷⣶⣦⣄⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣴⣿⠟⢫⡉⠔⠢⡅⠓⡌⢣⠙⡌⠱⡠⢉⠛⠿⣷⣄⠀⠀⠀ ⠀⠀⢀⣼⡿⢋⠴⣈⣥⣌⣩⡑⠬⡑⡘⢢⠱⣈⠓⡰⢉⣼⣴⣭⣿⣦⠀⠀ ⠀⢀⣾⠏⢴⣽⡾⠛⣻⣿⣿⣿⣶⠡⡑⣦⣷⣶⣍⡔⣿⡟⠀⢠⣿⣿⣧⠀ ⠀⣼⡟⢬⣾⠋⠀⢸⣿⣿⣿⣿⣿⡇⣽⣿⣿⣿⣿⣶⢿⡇⢠⣿⣿⣿⣿⡆ ⠠⣿⣇⢾⡇⠀⠀⢸⣿⣿⣿⣿⣿⢡⣿⣿⣿⣿⣿⣿⡾⣷⡈⣿⣿⣿⣿⣿ ⠘⣿⡌⢻⣧⠀⠀⠀⠙⠿⣿⣿⠃⢾⣿⣿⠻⣭⡙⣿⡇⣻⣷⣝⢿⣿⡿⣿ ⠈⣿⡇⢎⡹⣷⣦⣀⣤⣾⠟⡡⢚⢸⣿⣇⠻⡴⣙⢾⣷⠱⣎⢻⠿⣶⣾⡿ ⠀⠸⣿⣎⠳⣥⢯⡽⣩⢇⢯⠳⣌⢂⣿⣏⣳⠱⡭⢾⣏⠳⣿⢻⢳⣧⡿⠁ ⠀⠀⠙⣿⣵⢛⡞⣳⢛⡭⢎⣝⠺⣆⠜⣿⣶⢫⢵⡿⠻⡱⢎⠧⣿⡟⠁⠀ ⠀⠀⠀⠈⠻⣿⣼⣡⢏⡜⣣⢎⡳⣹⠰⡈⡝⠻⠟⡡⢃⠽⣭⡿⠏⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⠻⣷⣾⣱⡎⡵⡝⠰⠡⠜⣡⢚⣤⣿⡿⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⠿⠷⠿⠾⠿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣶⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠾⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⠶⣶⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠚⠉⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣶⠦⠤⠄⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠒⠲⣤⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠉⠙⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠲⠦⣄⡀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠖⠚⠉⠀⠀⠀⠀⣀⣉⠉⠑⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣮⡁⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠀⠀⠀⢀⣤⠴⢶⣟⣻⣿⣿⣿⣿⣷⣶⣦⣤⣀⠀⠀⠀⠀⠀⣤⣞ ⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⣿⣽⣿⣽⣓⠲⢤⣄⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⢋⣩⣶⡶⢿⡿⡛⠉⠙⢻⠛⢿⣿⠿⣿⣿⣿⣷⣶⣶⣿⠟⠁ ⣤⣤⣤⣤⣤⣴⣿⣿⡿⠟⠛⣻⢿⠛⠛⠛⠿⣶⣦⣍⠓⠀⠀⢀⣿⡄⠀⠀⠀⠀⠀⠀⠀⢀⡵⠖⠋⠉⠁⣰⠋⠈⠛⠿⣿⢾⠆⠀⠈⢧⡀⢈⣽⣿⣿⢟⠅⠀⠀ ⠀⠉⠛⢿⣿⣿⡍⠁⠀⠀⡼⠛⠻⢭⣵⣶⠇⠹⡆⠉⠙⠲⠄⠀⡏⠁⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠐⢒⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣞⣭⡽⢿⣻⠟⠁⠀⠀⠀ ⠀⠀⠀⠀⠈⠛⢿⣷⣤⣴⣧⣶⡶⠶⣶⠖⠒⠚⠉⣹⡄⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠄⠀⠀⠀⠀⢀⡠⠅⠀⢀⠨⠤⠃⠀⣧⢤⣖⣶⣦⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢘⡟⣽⠋⢀⣉⠀⠂⣁⡠⠶⠊⠉⢀⣀⡤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠂⠀⠀⠀⠀⠀⡀⠤⠂⠀⠀⠀⠠⠐⠒⠋⠭⠿⠒⠈⠉⠀⠀⠀ ⠀⠀⠀⠀⠀⣤⠞⣉⡤⠚⣉⡤⠖⠉⠀⣀⡠⣶⡪⠟⠊⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠀⢊⣁⠴⠊⠁⢀⡠⠖⠋⠑⠉⠁⠀⠀⠀⠀⠀⢠⣆⠀⢀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀⠈⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣽⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡄⠀⠤⢤⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠞⠋⠀⠀⣀⣀⣀⣀⣀⡀⠈⠙⠛⠲⠤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣤⣤⣾⣏⠀⠀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣶⣤⢀⣽⣿⣿⠃⠀⠀⠀⠀⠀⢸⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡿⣿⠟⢻⡟⠛⠿⣿⣿⠿⠟⠛⢻⠿⢧⠀⠙⢿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⠸⣧⠴⠋⠀⠀⠀⢹⡇⠀⠀⢠⢇⡴⠋⠀⢀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣆⠀⠀⠀⠀⠀⢀⡾⠀⠀⣰⣫⠞⠁⠀⣠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢤⡀⠀⠀⢀⣀⣠⣾⡟⠁⠀⣠⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣄⠘⠻⠕⠋⣠⡴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠲⠖⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠙⠻⢶⣖⡶⢤⣤⣤⣤⣤⣀⣀⠀⠀⠈⠙⠶⣗⢄⡀⠀⠀⠀⠀⠀⣀⣀⡤⠤⠤⠤⠐⠒⠉⠙⠛⢯⣤⣄⣀⣀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠ ⠀⠀⠀⠙⢻⣿⢿⣿⣿⣿⣿⣿⣿⣟⢷⢦⣤⣈⢳⣿⣦⣀⣠⠶⠯⠅⠀⠀⠀⠀⠀⠀⠒⢤⣀⠑⢦⡙⠪⣐⢬⡉⠓⠲⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠘ ⠀⠀⠀⢀⣾⣿⡿⠿⠿⣿⣻⣿⠙⣿⡟⠀⠈⢉⣿⠿⠋⠁⠀⠀⠁⠀⠀⠐⠀⠀⠀⠀⠀⠀⠈⠓⢄⠳⡄⠈⠂⠙⢾⡲⣄⠙⠻⢗⡦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣀⣠⣿⠟⠁⠀⠀⠀⠀⠹⣿⡆⠘⡇⣀⣠⡾⠥⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠙⣆⠀⠀⠀⠙⠄⠙⢦⡀⠙⢦⡙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠙⠛⠋⠀⠀⠀⠀⠀⠀⠀⢹⠃⣀⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠘⠶⣄⠀⠀⠘⢧⡀⠀⠀⠀⠀⠀⠙⢦⡀⠙⢦⡙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⡿⣻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠒⢤⣀⠀⠀⠉⠓⣶⣤⣀⡀⣀⠀⠈⠻⣦⣄⣈⣷⡀⢠⠀⠀⠀⠀⠈⢿⣄⠀⠁⠈⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣤⣄⣀⣤⣠⣠⣄⣤⣤⣤⣶⡿⠀⡏⡏⡆⠀⠀⠀⢆⠰⡄⠑⠿⣶⣬⣛⣶⣤⣀⠈⠙⣯⣩⠷⢷⣿⡉⠙⠿⣷⣾⣿⣄⢇⠀⠀⠀⠀⠘⣿⡷⡀⠀⠀⢧⣤⣤⣤⣴⠀⠀⠀⠀⠀ ⣿⣿⣿⡿⣿⠿⢛⣩⡿⢿⢿⠃⢠⡇⠈⠸⡆⠀⠀⠈⢧⢳⡀⠀⠈⠳⣄⠉⢙⣪⣽⠛⢯⣙⢦⠀⠈⠙⠲⣄⢻⣎⠻⡝⡾⡄⢠⠀⠀⠀⠸⣽⡹⡄⠀⢪⣹⣿⣿⣿⣄⠀⠀⠀⠀ ⡿⣻⠗⠋⢁⣴⣿⡿⢚⡟⢸⠀⠈⡇⠀⠀⣹⣄⠀⠀⠀⠳⣿⣄⠀⠀⠈⠻⣅⠀⠀⠁⡴⠋⠻⢷⣠⢖⣪⣼⣿⣿⡟⠻⣿⣧⠈⡇⠀⠀⠀⠀⢷⠘⣆⠀⢷⣻⣿⣿⣿⣷⡀⠀⢠ ⠊⠁⣀⣴⡿⠚⠁⠀⣸⠁⢺⠀⠀⣇⠀⡇⠘⢿⡆⠀⠀⠀⠙⠿⣟⠦⣄⠀⠈⢷⣦⣈⠀⠀⣰⢫⣷⣿⣿⠟⠉⡧⠃⠀⣘⣿⢠⡧⠀⠀⠀⠀⠘⡆⢹⡄⠈⢧⠀⠀⠀⠀⠀⠄⠀ ⣠⢞⡵⠋⠀⠀⠀⢠⡏⠀⠸⠀⠀⠸⡄⢹⠀⠀⢳⣄⠄⣼⠀⠀⠙⢧⡈⠙⠳⣤⣉⠻⢷⣦⣁⣾⣿⣬⣤⣤⠞⢁⣴⣾⣏⣿⡿⣧⠀⠀⠀⠀⠀⠁⠀⢿⡄⠈⣇⠀⠀⠀⠀⠀⠀ ⣴⠋⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠁⢸⠀⠀⠀⢻⡳⣿⣻⢤⣀⡠⢤⣀⣀⠀⠉⠉⠛⠙⢮⡉⠉⠀⡀⣠⣶⠏⣹⠛⠀⢺⣿⣿⠀⠀⠀⠀⠀⠀⢰⠸⣿⡄⠘⣆⠀⠀⠀⠀⠀ ⠁⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢸⠀⠀⢠⣄⣿⡁⠈⢙⠿⣿⣯⣙⠚⠻⠿⠿⢷⣦⣤⡙⢦⢠⠻⣽⣁⠞⠃⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⢸⠀⡇⢻⣆⠘⣦⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⡃⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⢿⣧⠻⡴⠁⠀⣠⣙⣿⣶⣄⠀⠀⠀⠀⠉⣝⠿⡏⠀⢀⠁⠀⠀⠠⠀⠀⣿⢻⣀⠀⠀⠀⠀⠀⢸⠀⢻⡘⡟⣆⠈⢧⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⢳⡀⠀⢸⣿⠀⡀⣼⣟⠷⣝⣦⣾⣿⣿⡿⡄⠈⠓⣤⡀⣠⠿⣻⣶⠁⠀⠈⠀⠀⠀⠀⠀⠀⢸⠈⣿⡄⠀⠀⡀⠀⢸⠀⢸⣇⢻⠘⠀⠀⢳⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⢳⡄⠀⣿⡀⢳⡇⢻⠀⠈⢻⣿⣿⡏⣀⡆⢠⣾⢉⣿⡟⢠⠏⠀⠀⠀⣠⢖⣿⣿⣿⣶⡀⠈⡆⢿⠁⠀⠀⣇⠀⣾⠀⠘⣿⡌⠀⠀⠀⠀⠹⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠈⡀⠀⠀⠻⣄⢹⣇⢸⢇⠘⡇⠀⣾⡟⠣⠟⠋⢀⡼⢡⣾⣿⠃⠈⠀⠀⡰⣪⣿⣿⣿⡿⠛⠻⢷⠀⢣⢸⡇⠀⠀⠹⣄⢿⠀⢸⢿⣿⠀⠰⣆⠀⡄⢹ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⡇⠀⠀⠀⠙⣦⣻⣼⠘⣆⣿⡌⣿⡃⠀⢀⣴⠞⡅⡏⡿⠁⠀⠀⠀⢰⣳⣿⠟⠛⠋⠁⠀⠀⠈⢧⠘⣌⣷⠀⠀⠀⠹⣾⡀⢸⢨⣿⠷⡄⣿⣆⠹⣆ ⠀⠀⠀⠀⠀⠀⠀⢀⣼⣧⢂⣷⠀⠀⠀⠀⠘⢷⣽⣦⠈⢯⣷⡸⠷⠒⠻⠤⢺⢻⠁⡇⠀⠀⠀⠀⢺⣿⣯⣄⠀⠀⠀⠀⠀⠀⠈⡆⠹⡜⣿⣦⣀⡀⣙⣧⣸⣿⢃⡤⠙⣿⣿⡄⢹ ⠀⠀⠀⡀⠀⣀⣤⣾⡿⣿⣸⢹⠀⠀⠀⠀⢲⡈⠳⣝⢷⣤⣙⣷⡀⠀⠀⠀⡀⠀⢸⠁⠀⠀⠀⠀⠀⠙⠫⢝⣳⡦⣄⡀⠀⢠⢠⡇⠀⠹⣮⣿⣿⣿⡿⠿⣿⣩⣞⠀⢀⣽⣿⣿⣀ ⠀⠀⠀⠈⠉⠉⠉⠁⠀⣿⡿⣸⠀⠀⠀⢀⡈⣧⡀⠈⠃⠈⢉⢛⡿⠷⣦⣤⣤⠀⣘⣂⣀⡤⠴⠒⠀⠀⠀⠀⠀⠁⠀⠉⢹⢸⠋⡁⠀⢀⣾⡿⢿⣄⠰⠋⢉⡽⣿⣿⣿⣿⣿⠿⢿ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⢣⣿⡄⠀⠀⠈⡇⢻⠻⠀⠀⠀⠠⠬⠭⣝⠛⠻⠿⢭⣭⣤⣄⣀⣀⢀⡄⠀⠀⠀⢠⠀⡀⠀⠀⣿⠀⣇⣠⠾⣿⣷⣸⠉⠳⣶⠋⠀⠸⣾⣿⣍⢻⣷⣌ ⠀⠀⠀⠀⠀⠀⠀⢀⡾⢻⡟⢸⡆⠀⠀⠀⣷⢸⡟⣂⠀⠀⠲⠶⣤⣤⣀⣉⣙⣳⣦⣿⣽⣝⡟⠻⠿⣷⣶⣤⣠⣤⣧⠖⠚⠿⠉⠉⠀⠀⢰⣟⣏⣀⡸⣿⣷⣶⣤⡘⢿⣿⣽⣧⠙ ⠀⠀⠀⠀⠀⠠⣴⣿⠀⠘⠇⢸⣷⠀⠀⠀⢸⣮⣷⣺⣷⣴⣶⣶⣶⣤⡾⠛⠛⠉⠙⠛⢿⣿⣿⠷⣶⣦⣌⡙⢿⣄⠀⠀⠀⡄⠀⠀⠀⡄⣾⣿⣿⣶⣚⣿⣭⡭⠭⠝⠺⣿⣿⡇⠀ ⢀⡄⠀⢠⡑⣼⣿⣿⡄⠀⠀⢸⡿⣿⠀⠀⠈⣿⣿⡿⣿⡿⣿⣿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⣷⡀⠉⠛⠻⠷⣿⣷⣤⣄⣀⠀⠀⣼⣽⣍⣉⡙⢿⣿⣿⣿⣿⣦⣄⣠⢸⣿⡇⠀ ⣮⣠⣶⣾⣿⣏⠟⠻⠃⠀⠀⢸⣧⠙⣧⠀⠀⢸⣿⠻⣌⢻⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⢰⢀⠆⢑⣄⡹⢀⣀⣈⣙⣛⣟⣁⣀⡐⡉⠒⢛⡻⣿⣿⢟⣵⣶⣾⣙⠣⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠤⠐⠀⠀⠠⠤⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢖⣪⣵⣶⣿⣿⣿⣿⣿⣿⣿⣷⣶⣍⡲⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣋⣴⣿⣿⠿⠛⣛⣋⣙⣛⠻⢿⣿⣿⣿⣿⣿⣦⡱⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣀⡞⣴⣿⡟⠉⠖⣛⣋⣉⣛⡻⢿⣿⣷⣮⡙⢿⡿⣿⣿⣷⡜⢆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡴⣪⣭⣾⠿⠿⠿⢿⣙⠛⢿⣍⠉⣉⣿⣶⣬⣭⣍⣉⣀⣻⣝⢿⣿⣿⡌⣆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⢫⣿⡿⢋⣀⡀⠀⠀⠀⠈⠑⣦⡽⠛⠋⠉⠓⠲⣤⡉⠻⣿⠙⢿⣦⢻⣿⣷⠘⡆⠀⠀⠀⠀⠀⠀ ⠀⢠⢃⣿⣿⢱⠋⠛⣿⣦⠀⠀⠀⣼⣡⡷⣶⣤⡀⠀⠀⠈⠻⡄⠘⡇⠀⢿⣇⣉⣿⣧⣙⡒⢤⡀⠀⠀⠀ ⠀⢸⢸⣿⣿⡈⠷⣾⣽⠟⠀⠀⢸⡇⢿⣄⡼⣿⡇⠀⠀⠀⠀⢹⠀⡟⣠⣿⣿⣿⡿⠉⠙⠛⢳⡝⢦⠀⠀ ⠀⣸⢸⣿⡿⣟⢦⣄⣀⣀⣀⡤⠾⢷⡈⠙⠛⠋⠀⠀⠀⣀⡴⢋⡼⢡⣿⣿⣿⡿⠀⢠⡶⣤⣤⣿⡌⣇⠀ ⣠⢣⣿⣭⣤⣬⣵⣞⣉⡀⠀⠀⠀⠀⠙⠲⠤⠤⠴⠒⢋⣁⡴⠋⠀⢸⣿⣿⣿⣠⣾⡟⠀⠈⣷⠟⣷⢸⠀ ⣧⡟⢁⣠⣤⣤⣄⣀⡉⠉⠙⠓⠶⠦⣤⣀⡐⠒⠒⠛⠉⠁⠀⠀⠀⠈⣿⣿⣿⣿⡿⣧⣤⣶⠟⢀⡿⢸⡇ ⢧⠻⣾⡏⠻⢿⣿⣿⣿⣿⣷⣶⣶⣤⣄⣈⠉⠛⠶⢤⣀⡀⠀⠀⠀⠀⠘⣿⣿⣿⣿⡀⠈⠁⣠⡾⢃⣿⠁ ⠈⠳⢮⡙⠶⣄⡉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⡈⠙⠶⣄⡀⠀⠀⢨⣿⣿⣿⣿⣿⠟⣋⣴⡿⠃⠀ ⠀⠀⠀⠉⠓⢮⢹⡗⢀⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡈⠻⣆⠀⣾⣿⣿⡟⣹⣶⠾⠟⠋⠀⠀⠀ ⠀⠀⠀⠀⠀⡏⣼⠁⣼⣿⠟⠉⠀⣰⠞⠋⠀⠉⠛⠿⣿⣿⣿⡇⢀⣿⣾⣿⢿⡟⣰⡿⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢰⢻⡇⢠⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠟⢀⣼⠁⠉⣵⠟⣴⡿⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⢸⡇⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⣠⡾⠁⣠⡾⢣⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣸⢸⡇⢸⣿⠀⠀⠀⣀⣤⣤⣤⣄⣠⡶⢏⢠⣴⣟⣤⠞⣫⣴⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡴⡿⠿⠿⢬⣳⣾⣿⣖⡶⢞⡟⠋⠉⠉⢳⠖⠚⠉⠙⠺⣍⣴⣞⣫⠷⠶⠶⢿⠦⣤⣤⣶⡦⡀⠀⠀⠀ ⠀⢇⡇⠀⣶⠀⠙⠉⠀⠀⢙⡟⠃⢠⣴⣶⣏⣀⣠⣴⣦⣤⣿⡁⣀⣽⠀⠸⠂⣸⡟⠉⠡⣤⡿⣿⠀⠀⠀ ⠀⢸⡇⠀⠀⣠⡄⠀⣾⡦⠘⡇⠀⠸⣿⣏⠀⠀⣸⣿⣉⠉⠁⣹⠨⠿⠀⢰⡄⠈⠻⢷⣤⠀⠉⡾⣇⠀⠀ ⠀⢺⢹⣀⣸⣿⣝⣦⣀⣠⢴⣻⣶⡀⠀⠀⢀⣴⠁⠉⠁⢀⣼⡥⢤⣤⣤⣾⣿⣾⣄⣀⣀⣀⣴⣣⣿⠀⠀ ⠀⠈⠻⣿⡿⠿⠋⠛⠿⠿⠟⠋⠳⣯⣭⣭⣵⣾⣭⣿⣯⣵⡿⠟⠛⠛⠛⠋⠉⠉⠛⠶⣶⣾⠿⠟⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠤⠤⠀⠀⠤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⢞⣩⣥⣶⣶⣶⣶⣶⣶⣶⣶⣦⣭⣙⠓⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⣋⣴⣾⣿⣿⣿⣿⣿⣿⣭⣟⣿⢿⣿⣿⣿⣿⣿⣦⣍⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⣡⣾⣿⣿⡿⠟⢛⣉⣩⣤⣤⣭⣉⡛⠻⢦⣝⡻⣿⣿⣿⣿⣷⡌⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢋⣼⣿⡿⠟⠡⠶⠟⠛⣛⣛⠛⠻⢿⣿⣿⣿⣦⣈⠻⣮⡻⣿⣿⣿⣿⣦⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣠⠖⣚⣽⣧⣾⣿⣿⠷⠶⢶⣶⣾⡛⠛⠛⠛⢷⣦⣍⠛⠛⠛⠿⠷⠈⢻⣮⢻⣿⣿⣿⣧⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣴⢏⣴⣿⡿⠟⠋⠉⠉⠉⠉⠳⢶⣄⠙⢿⣦⣠⣶⣿⣟⡛⠛⠻⠿⣶⣶⣶⣦⣿⣧⡹⣿⣿⣿⣇⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⡞⣰⣿⣿⠏⣀⣀⣀⡀⠀⠀⠀⠀⠀⠙⣷⡶⠛⠉⠁⠀⠀⠉⠙⢷⣄⠈⠻⣷⡄⠙⢿⣷⡘⣿⣿⣿⡄⢻⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡟⢱⣿⣿⠏⡼⠛⠻⣿⣿⣆⠀⠀⠀⢀⣾⢫⣼⣶⣦⣤⡀⠀⠀⠀⠀⠙⢷⡀⠈⢿⠀⠀⣿⣧⡈⣛⣻⣷⣘⣓⠲⢤⡀⠀⠀⠀⠀ ⠀⠀⢠⠇⣾⣿⣿⡀⢻⣦⣤⡟⣿⡿⠀⠀⠀⢸⠃⣿⡁⠈⣻⣿⣷⠀⠀⠀⠀⠀⠘⢷⠀⢸⡧⢠⣾⣿⣿⣿⢟⡫⠭⣟⡳⣦⡙⢦⡀⠀⠀ ⠀⠀⢸⡀⣿⣿⣿⣷⡄⠙⠛⠛⠋⠁⠀⠀⠀⣸⡆⠹⣿⣾⣯⣽⡟⠀⠀⠀⠀⠀⢀⣼⢀⡾⢀⣿⣿⣿⣿⣱⠏⠀⠀⠀⠉⠈⢷⡎⢳⡀⠀ ⠀⠀⢠⠇⣹⣿⠟⢷⣝⠷⢦⣄⣀⣠⣤⠶⠟⠋⢻⣄⠀⠉⠉⠀⠀⠀⠀⢀⣠⡶⠋⢁⡾⠁⣼⣿⣿⣿⡇⡇⢀⣠⡿⠻⢶⠟⣿⣿⡈⢷⠀ ⠀⣠⠏⣼⣟⣁⣀⣀⣉⣛⣒⠒⠀⠀⠀⠀⠀⠀⠀⠉⠻⠶⠤⣤⠤⠶⠞⠋⢁⣠⡴⠋⠀⠀⣿⣿⣿⣿⡇⣥⣿⣿⠁⠀⠘⣷⡼⢹⡇⢸⡆ ⢰⢇⣾⠟⠁⠀⠀⠀⠈⠉⠉⠛⠛⠻⠶⠦⣤⣄⣀⡀⠀⠀⠤⠤⠤⠤⠶⠛⠋⠁⠀⠀⠀⠀⢹⣿⣿⣿⣇⣿⣿⣿⠀⣀⣠⣽⠇⢸⡇⢸⡇ ⢸⡘⣿⡀⣶⢿⣿⣿⣿⣷⣶⣶⣦⣤⣄⣀⣀⠉⠉⠛⠳⠶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣼⣯⠛⠛⠿⠟⠀⢀⣾⠇⣼⡇ ⠀⢳⡈⠻⣮⡀⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣄⠀⠉⠙⠛⢶⣤⣄⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣮⣅⣀⠀⢀⣠⣾⠏⣼⣿⠃ ⠀⠀⠙⢶⣌⠙⢷⣦⣀⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣄⡀⠀⠙⠻⢶⣄⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠿⢋⣡⣾⡿⠃⠀ ⠀⠀⠀⠀⠈⠛⠶⣬⡛⢻⡦⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠙⢿⣦⠀⠀⣼⣯⣿⢿⡿⢹⣥⣤⣾⣿⠿⠋⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢈⠇⣾⠇⢀⣿⣿⣿⡿⠟⠛⠉⣫⣿⠿⠛⠿⣿⣽⣯⣿⡿⣿⣿⡆⠀⢹⡆⣰⣟⣾⢿⣿⢃⣾⡿⠋⠉⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣾⢰⡟⠀⣸⣿⡿⠋⠀⠀⠀⠾⠋⠁⠀⠀⠀⠈⠉⠹⣿⣼⣿⣿⠇⢀⣾⢱⣯⡿⢣⣿⢃⣼⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⡏⣼⠃⢠⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⣿⠃⠀⣾⠇⠀⠉⣴⡿⢁⣾⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⠀⣿⠀⢸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⣴⠟⠁⢠⣾⠋⠀⣠⣾⠋⣠⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⠀⣿⠀⢸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠿⠋⢀⣰⡿⠃⣠⣾⠟⣡⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣀⣀⣼⡀⣿⡀⢸⣿⡇⠀⠀⢀⣠⠴⣖⣛⣓⣲⠦⠶⠟⣓⣒⡲⠿⣏⣴⠾⢋⣠⣾⡿⠫⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣰⢻⠿⠿⠶⠶⣭⡳⣶⣿⣿⣟⠶⡞⣵⠚⠉⠉⠉⠉⣳⠖⠋⠉⠉⠉⠳⣮⡡⠶⢛⣋⡷⠒⠒⠒⠶⣝⢦⢤⢔⣒⣒⡲⣄⠀⠀⠀⠀ ⠀⠀⢻⢸⠀⠀⣤⡄⠈⠻⠋⠁⠀⠈⠻⡾⣵⠁⢀⣠⣤⣼⠋⠀⠀⣀⣤⣄⢀⣨⡟⠉⠉⠉⡇⠀⣿⡆⠀⣸⣷⠋⠉⣉⣉⣿⢺⡇⠀⠀⠀ ⠀⠀⢸⢸⡇⠀⠙⠁⠀⠀⠀⣀⣤⡀⠀⡇⠁⠀⣾⣿⡿⠟⠒⠒⠚⣿⡿⠿⠿⠟⠛⣶⠛⢿⣧⠀⢈⡀⠐⢿⣷⣄⡀⠉⠙⠻⣌⢳⡀⠀⠀ ⠀⠀⢸⢸⡇⠀⢀⣴⣿⡄⠀⠿⠿⠇⠀⣧⠀⡀⠘⠿⠷⠆⠀⠀⣴⠿⣷⡤⠀⠀⢠⡟⠘⠛⠋⠀⠘⣷⡀⣠⠌⠛⠿⠗⠀⠀⢸⠏⡇⠀⠀ ⠀⠀⠘⡌⣇⣀⣤⣷⣳⣙⠦⣤⣤⡤⢞⣫⢷⣗⠀⠀⠀⠀⣠⣾⠃⠀⠀⠀⢀⣠⣯⠤⠤⠶⣶⢒⣚⣿⣿⡳⢦⣀⣀⣀⣀⣴⢏⣼⡇⠀⠀ ⠀⠀⠀⠳⣿⣯⣿⣿⣿⠏⠳⢶⣶⣶⣿⠟⠳⣭⣝⣒⣒⣋⣭⣬⣑⡒⠖⣚⣫⣵⣶⡶⠿⠿⠟⠛⠛⠛⠉⠛⠲⣮⣭⣭⣽⣶⣿⠿⠁⠀⠀ ⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠋⠉⠉⠛⠻⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⣴⡞⠁⠀⠀⠀⠀⢼⠃⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⣽⠀⠀⠀⣀⠤⢶⣾⠷⣶⣲⣦⣤⣀⢀⡤⢊⣿⣠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣰⠏⡄⠒⠉⠀⣠⠋⢹⠀⠐⠉⠛⢯⣽⡟⢉⣽⣥⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁⠀⠀⠀⠀⠀⠰ ⠀⠀⠀⠀⠀⢀⡟⠐⠛⠲⣾⣿⣿⣤⣾⣄⡀⠀⢀⡾⠃⠉⢉⡟⣸⡇⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⢠⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⠇⠀⢀⣴⣿⣿⠿⠟⢿⡿⣿⣷⣿⠀⠀⢀⣀⢷⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡄⠄⢠⠞⠀⠀⠸⡀⠀⠀⡀⠀⠀ ⠀⠀⠀⠀⠀⢸⣠⣶⣿⣿⠋⠀⠀⠀⢸⣄⣿⡟⠻⣷⣄⠀⢹⡟⡟⠠⠤⠀⠀⠀⠀⠀⠀⣠⣀⣠⣧⣦⣾⡋⠁⠒⠒⠴⣇⣰⠞⠁⠀⠀ ⠀⠀⠄⡀⠀⣸⡿⢻⣿⠍⠀⠀⠀⠀⠸⡏⡟⠀⠀⠈⣿⣧⣸⠿⡇⠀⠀⠀⠙⠖⢂⡖⠋⠁⣠⡟⠁⡼⡁⠉⠉⠉⠉⠉⡟⢿⣦⣄⠀⠀ ⠀⠀⡆⣳⠀⢻⡄⠈⣿⡀⠀⠀⠀⣀⣀⣴⠃⠀⠲⢄⣹⢻⣿⠀⡗⠀⠀⠀⠀⢰⠋⠀⠀⣰⡿⢀⡞⠃⠀⠀⠀⠀⠀⠀⡇⢸⠙⠉⠛⠶ ⠀⠀⢀⣿⡆⢸⣿⣠⠛⡇⠀⠈⠙⢯⡉⢻⡛⡗⢲⢄⠈⠑⠛⠀⢃⡞⠀⠀⠀⢠⠀⠀⡼⣱⣡⠋⠀⠀⠀⢀⡀⠀⠀⢀⠇⣿⡄⠀⠀⠀ ⠀⠀⣼⢸⣧⣼⣿⣟⠀⠘⠄⠀⠀⠠⡄⠀⠣⡴⠃⠰⣧⡀⠀⠀⢹⣧⠀⠀⢀⣿⠀⡸⣰⠟⠁⢀⣭⣉⣹⣉⣉⠐⠒⢶⣼⣹⡇⠀⠀⠀ ⠀⠀⠇⠈⣿⣿⢿⣿⡀⣖⣛⡆⠀⠀⠘⠦⠄⠤⠤⠊⠉⠓⠀⠀⠈⣟⡆⠀⡜⢸⢠⠛⠁⠐⠉⠙⠛⠛⠻⠿⢿⣿⣷⣾⣃⣼⠇⠀⠀⠸ ⠀⠀⠀⠀⢸⣿⡎⣿⣧⡀⠈⢏⠓⠶⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢳⢀⠃⢸⡎⠀⠀⠀⢀⠤⠒⠒⠒⢤⡀⠀⢹⠿⣿⣿⣦⡀⠀⠀ ⠀⠀⠀⠀⣾⠏⢿⣿⣿⣿⡿⡜⣷⡸⣦⢀⢣⠰⡄⠀⠀⠀⠀⡇⠀⠀⠀⢿⠀⠸⠀⠐⢲⡶⠃⠀⣾⣆⠴⣶⠹⠴⠋⠀⢘⣿⣿⡝⡿⠄ ⠀⠀⠀⣸⣿⠀⠸⣿⣧⣿⣿⡱⡘⣷⣻⣿⣎⣇⣿⣷⣶⠂⢠⠸⣄⠀⠀⠈⠀⠀⠀⠀⠀⠹⠄⠀⠇⣁⠔⠉⢳⣄⠀⠀⣼⠋⢿⣿⠁⠀ ⠀⠀⢨⣿⣿⠀⠰⣿⠃⠀⠉⠁⠀⠀⠀⠙⢿⣟⢿⣿⣿⣆⠸⣇⢫⡀⠸⡀⠀⢀⠀⣀⠈⠑⠒⢄⣈⣀⣀⠼⠓⠿⣑⡸⠁⠀⠘⣿⡆⠀ ⠀⠀⢸⡇⢸⠀⢠⣽⠀⠀⠀⠀⣠⡀⠀⠀⠈⠋⠀⠈⠈⢿⡇⠘⡎⢧⣀⣇⣆⡈⠂⠈⡙⠢⣄⡀⠀⠀⠀⠀⠀⠀⠈⠁⣀⣴⣾⣿⡇⠀ ⠀⠀⢸⡇⠈⣇⠀⠀⠀⠀⠀⢠⣿⠓⢄⠀⠀⠀⠀⠀⠀⢸⠿⠀⠘⡜⣿⣾⣼⣷⣴⢇⣷⠀⣄⠙⠢⣤⣄⡀⠀⠀⠒⠉⠉⢁⡟⢿⠁⠀ ⢁⠀⢸⣧⠀⠸⡄⠀⠀⠀⠀⢸⣿⣄⡀⠑⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠏⢿⣿⡟⣼⡄⢸⡇⠀⠳⣄⠈⢱⠄⠀⣠⢣⡞⠀⠈⠀⢸ ⠘⡄⠈⣿⢧⣰⡻⡄⠀⠀⠀⠘⡧⠛⡍⠢⣀⠀⠉⠲⡄⢀⣀⣀⡀⠀⠀⠀⠀⠈⠻⣗⢻⢧⢸⣿⢿⡄⣏⠉⠙⢀⡼⣡⠏⠀⠀⠀⢀⡟ ⠀⢱⠀⡿⣎⣿⣇⠹⣄⠀⠀⢀⢀⡤⠚⢄⡈⠑⠢⢄⣘⡋⠀⠀⠉⠉⠉⠉⠉⠉⠉⢻⠂⠘⣏⣿⡟⣿⣻⣀⣰⣠⣾⡏⠀⠀⠀⣠⠞⠀ ⠀⠀⢣⣧⠘⠓⢮⡓⠚⢦⠀⣸⡏⠀⠀⠀⢏⡒⠢⢄⡀⠈⠉⠐⠲⣄⣠⠤⠤⡤⠴⡟⠀⠀⠈⠹⢧⡿⡍⠏⢉⣻⣟⣧⣤⡶⠞⠁⠀⠀ ⠀⠀⠀⠉⠀⠀⠀⠈⠑⠒⢷⣿⠀⠀⠀⢸⣷⠇⠀⠀⠈⠑⠲⠚⠦⠄⠐⡤⠲⢏⠏⠀⠀⠀⠀⠀⠀⠑⢛⣿⠿⠿⢿⡿⠉⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄⠀⠀⣞⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡷⢚⣿⠀⠀⠘⠒⢁⣠⡶⠚⠉⠀⠀⣠⢿⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡎⣦⡀⢉⠄⠀⠀⠀⠀⠀⠀⠀⢀⢼⡏⠀⢘⣛⣠⣤⠖⢚⠉⠁⠀⠀⠀⢀⣾⣷⡞⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠋⠉⠀⠱⠞⠉⠉⠒⠒⠒⠒⢒⣚⣡⠞⠉⠉⠀⠀⡰⡇⠀⣿⠶⠀⣀⡤⢾⣛⣹⠋⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⢀⣀⣤⣷⣦⣤⣤⣀⡀⠀⠀⠈⠒⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣶⣶⣿⣧⣶⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣾⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠉⠉⠉⠁⠀⠀⠉⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⢿⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣄⠀⠀⠀⢀⣴⣤⡙⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⢁⣽⠆⠀⠀⠀⢀⣴⡾⠿⠿⠿⢿⣿⣿⠇⠀⠀⢸⣿⡿⢿⣾⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢻⣿⣿⣿⣿⣿⡿⠟⠋⠀⠀⠀⣼⠁⠀⠀⠀⢠⠟⠉⠀⢀⣀⡀⠀⢻⡇⠀⠀⠀⢸⣟⣁⠈⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣷⣼⣿⣿⡿⠟⠋⠠⠀⠀⠀⢀⣾⠃⠀⠀⠀⢰⠏⠀⣼⡗⠋⢉⣍⣷⣼⣷⣀⠀⠀⢸⠋⢉⢻⣿⣇⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⣼⠋⠀⠈⠉⠛⠛⠓⢶⡄⢤⠶⠶⢾⡷⣦⣤⣤⣤⣄⡀⠀⠉⠙⠲⢼⣿⠟⠹⠋⣹⣧⣠⣬⣆⣸⡿⢻⣧⣉⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣾⡟⠙⢶⡄⠀⠈⣧⠀⠀⠀⡟⠀⠀⠀⠀⠀⠉⠉⠉⠉⠛⠛⢻⠃⠀⠀⠀⢛⣿⠁⠀⠀⢹⠁⠈⡏⠙⢻⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⡿⠀⢀⣾⣿⠀⠀⢸⡄⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⡀⠀⣀⣾⠇⠀⠀⠀⢹⣆⠀⣇⣠⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠛⠓⠲⠦⢼⣌⣧⠀⣾⣿⣿⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⡛⠀⠀⠀⠀⠀⠀⢉⢻⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⢢⣀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠺⣿⠀⠈⠻⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣄⣤⣶⣶⣶⢤⡀⢀⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣷⢦⣄⠈⠓⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠁⠴⡿⢋⢹⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣴⣶⠟⠉⠃⢈⡛⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⡀⣼⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⢀⣤⡾⠀⠀⣿⠃⢴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢿⡀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⡟⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣾⣾⣿⣤⠶⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣁⠀⠂⠒⠶⢦⣤⣤⣤⣤⣤⣤⣶⣿⡇⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣾⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣤⣀⣀⣀⣀⡈⠉⠛⠛⠛⣉⣉⣉⣀⣴⠇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡟⠀⠀⣴⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠉⠛⠛⠻⠿⠿⢿⣿⠿⠿⢿⣿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣿⣿⣿⡇⠀⣸⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣴⣶⣶⣶⠶⠖⠛⣹⣧⣴⠟⠁⢀⡆⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⠈⠿⣿⣿⣿⢷⣠⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠛⠋⠉⠀⠀⠀⢰⣿⡏⠀⠀⠀⣸⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡀⠈⢉⢀⣼⠀⠉⠛⠻⢿⣿⣿⣿⣿⣿⣶⣦⣤⣤⣄⡀⠀ ⠀⠀⠀⠀⠀⢠⣿⡟⠠⠀⠀⠀⣿⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⠿⡟⣿⣿⣄⠀⠀⠀⠀⠈⠉⠛⠻⢿⣿⣿⣿⣿⣿⣿⣯ ⠀⠀⠀⠀⠀⣼⣿⠱⠃⠀⠀⠀⢸⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠘⢿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⢰⣿⠇⡄⠀⠀⠀⠀⠀⣇⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠹⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠈⠳⢮⣉⠻⠿ ⠀⠀⠀⢀⣾⡟⠰⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣷⣮⣙⠄⠀⠀⠀⣀⣀⢤⣷⣿⠇⠀⠀⠀⠘⣿⣿⡄⠀⠀⠀⠀⠀⠈⠑⣄⠀⠀⠉⠒ ⠀⠀⠀⣸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣿⣿⣿⣿⣷⢿⡿⠛⠛⣿⣿⠁⠀⠀⠀⠀⠀⠘⣿⣿⡄⠀⠀⠀⠀⠀⠀⠙⢧⠀⠀⠀ ⠀⠀⢀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⢁⡼⠁⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡀⠀⠀⠀⠀⠀⠀⠨⡇⠀⠀ ⠀⡀⣸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡄⠀⠀⠀⠀⠈⠓⠤⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡠⠴⠞⠁⠀⠀⣰⠃⠃⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣷⡄⠀⠀⠀⠀⠀⠀⡇⠀⠀

⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠄⠀⠀⠀⠐⠖⠢⣤⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡂⠄⠒⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⡀⠀⠀⠀⠀ ⠀⠀⠁⠀⠀⠀⣀⣀⣉⡀⠀⠀⠀⠀⠀⠠⠖⠐⠂⠀⠀⠁⠀⠀⠀ ⠀⠀⣤⣴⡶⠴⠶⡶⣶⠄⠀⠀⠀⠀⠀⣬⣀⣲⣂⣤⢀⠀⠀⠀⠀ ⠐⠿⠙⣬⡽⡚⠯⣺⢀⡤⢢⡆⠐⢀⠠⣰⣟⢢⣾⡭⢛⢦⣄⡀⠀ ⠠⣧⢽⠎⠖⠋⠠⠂⠁⠀⠘⠓⠐⠀⢰⡯⠐⠁⠉⠲⣘⢡⠽⡛⠂ ⠈⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀ ⠀⠀⡄⠀⠀⠀⠀⡠⠐⣂⡒⠂⢄⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀ ⠀⠰⠃⠀⠀⠀⢸⣅⣸⣿⣿⣿⣷⣾⡢⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⣿⣿⡿⢿⣿⣿⣿⠃⠀⠀⠀⠖⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢻⣋⠀⢀⣀⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡐⠁⠀⠆⠇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠗⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠤⠤⠤⠤⢤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣒⡫⠭⠭⠭⠭⠭⠭⠭⠤⠄⠀⠈⠉⠙⠒⠢⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢞⡩⠔⠋⠀⠀⠀⠀⠀⠛⠛⠓⠢⠤⢄⡀⠀⠀⠀⠀⠀⠈⠙⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠗⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⣄⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠴⠚⠋⠉⠛⠛⠒⠧⢄⣀⠀⠀⠀⠀⠘⢆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣴⠥⠔⠒⠋⠉⠉⠓⠦⣄⣠⣤⠤⣤⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⠀⠀⠀⠳⡀⠀⠀⠀ ⠀⠀⢀⡠⠶⣻⠃⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⡖⠀⢸⠀⠀⠀⠀⠀⣀⣤⠶⠶⢤⣄⡀⠀⠀⠀⢻⠷⣄⠀⠀⠱⡄⠀⠀ ⠀⡰⠋⠀⢰⠃⠀⣀⣤⣶⣶⣶⣤⡀⢰⣧⡿⠁⢰⣾⠀⠀⢀⣴⠛⠉⠀⠀⣠⣶⣤⣝⠳⣤⠀⠈⡇⠹⣆⠀⠀⠹⡄⠀ ⣾⠃⠀⠀⡇⢰⠛⢉⣿⣿⣿⣷⡌⢻⣿⠋⠀⠀⢸⢸⠀⠀⣼⠁⠀⠀⠀⣾⣿⣿⣿⣿⣷⡈⣧⠀⡇⠀⢹⣆⠀⠀⢳⠀ ⢿⡄⠀⢸⠁⢾⠀⣼⣿⣿⣿⣿⣷⣿⠁⠀⠀⠀⠀⣿⡀⠀⠹⣧⣀⠀⢸⣿⣿⣿⣿⣿⣿⡇⢸⢰⠃⠀⠀⢻⡄⠀⠘⡆ ⠸⣇⠀⣾⠀⠸⣤⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⣄⠀⢣⡀⠀⠈⠻⢷⣤⣿⣿⣿⣿⡿⠿⣿⡿⠋⠀⠀⠀⠀⢻⡀⠀⡇ ⠀⢻⠲⠿⣤⣀⣀⣀⠁⠀⠈⠁⣿⠀⠀⠀⠀⠀⠋⠳⠬⣟⣲⠦⣤⣄⣉⣉⣉⣭⡶⠶⠛⠉⠀⠀⠀⠀⠀⠀⠀⢳⠀⡇ ⠀⠀⢳⡼⠁⠀⠈⠉⢉⣷⠶⠟⠁⠀⠀⠀⠀⣤⣤⣀⠀⠈⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⡇ ⠀⠀⢸⠃⠀⠀⠀⠘⠿⣄⢰⣦⣶⣦⡄⠀⠀⠻⣿⣿⣧⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃ ⠀⠀⡞⠀⠀⠀⠀⠀⠀⠈⠳⠬⠭⠅⠀⠀⠀⠀⠀⠐⠒⠒⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀ ⠀⢸⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀ ⠀⠈⣇⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀ ⠀⠀⢹⣷⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡀⠀⠀⠀⠀⠀⠀⢀⣿⡁⠀ ⠀⠀⢸⣿⠀⠀⡇⠳⣤⣀⣀⡀⠀⠀⠀⣀⣠⣤⣤⣦⣤⣤⣀⣀⣀⢀⣀⣀⣀⡴⠚⠉⢹⠃⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀ ⠀⠀⠈⣿⡄⠀⡇⠀⠀⠙⢿⡙⡿⠿⢿⠛⠛⢻⣿⣿⣿⠛⠛⠻⣿⣻⡿⠛⠁⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀ ⠀⠀⠀⠹⣷⠄⢻⠀⠀⠀⠀⠉⠛⠶⢾⣤⣄⣀⠹⣿⣿⣤⣴⠾⠛⠉⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⢰⣿⠇⠀⠀ ⠀⠀⠀⠀⢻⡆⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⣾⡟⠀⠀⠀ ⠀⠀⠀⠀⠘⣿⣁⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠀⠀⠀⠀⠀⠀⠀⣰⡿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠸⣷⢀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠀⠀⠀⣠⣿⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠻⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠁⠀⠀⣰⡟⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠀⠀⢀⣼⡿⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡘⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⣴⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣦⠉⠻⢶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡿⠛⠀⠀⢠⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣶⡀⠀⠉⠛⠛⠿⠳⠶⠶⠺⠿⠻⠛⠉⠀⠀⣠⣶⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠾⡶⣶⣶⣦⣶⣶⣾⠻⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣀⢀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠋⠉⠉⠐⢀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠀⠀⠀⡔⠉⠑⣤⠂⠀⠀ ⠀⠀⠀⠀⠀⠀⢲⠂⢄⡇⠀⠀⠀⠀⠑⢄⠀⠁⠀⠀⠀ ⠀⠀⠀⠀⢀⡴⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⠀⠀⠀ ⠀⠀⠀⡰⠋⠀⢀⠤⠐⠒⠠⢄⡀⠀⡠⠔⠀⠐⡆⠀⠀ ⠀⠀⢰⠁⠀⢰⠃⣠⣴⣶⣶⣤⣄⣭⡴⠿⣿⡧⠰⠀⠀ ⠀⠀⢠⠀⠀⠋⠐⡟⠉⠀⠀⠀⣩⡇⠀⠀⢠⣷⠇⠀⠀ ⠀⡠⣚⡱⠤⠸⡀⢇⡀⠀⠀⢀⡩⢃⣀⡤⠴⠮⢄⡀⠀ ⠠⡏⠀⢐⠆⠀⡨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢒⣉⠑ ⠀⠣⡀⠞⠂⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⡟ ⠀⠀⠈⠀⠩⡘⡀⠀⠀⠀⠀⠀⠀⠴⣾⣿⣿⣿⣿⣿⠃ ⠀⠀⠀⠀⠀⠈⠓⢄⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⢿⠂ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠠⠤⠤⠤⠤⠬⠒⠓⠁⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⣶⣶⣶⣶⣶⣶⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⠟⣩⣿⡿⠋⠉⣩⣿⣿⣿⠛⠛⢿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣿⣿⣿⣤⣤⣸⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣟⣁⠈⠉⢉⣿⣟⡛⠛⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣧⡯⠟⠀⠀⢸⣯⡯⠟⠀⠀⠀⣸⡇⠀⠈⠉⣿⣿⣿⡿⠿⢿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⣿⣿⣿⣶⣤⣴⡾⢻⣷⣦⣄⣠⣴⠟⠀⠀⠀⠀⠈⢻⣿⠃⠀⠀⢨⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣯⣽⣶⣀⡀⠈⠳⣤⣈⣡⡴⠂⠀⠀⠀⠀⠀⣾⡟⠀⠀⢀⣾⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣏⠉⠉⠉⠛⠿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣇⣠⣴⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣷⣦⡀⢀⠀⣿⣿⣿⣿⣿⣷⣦⡄⠀⠀⠀⠀⠈⢻⣿⡟⢻⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⡘⣧⢻⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢀⣾⡿⢀⣾⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠃⠈⠳⡝⠿⣿⣿⣿⡟⠁⠀⠀⠀⢀⣾⡿⣡⣾⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡟⠀⠀⠀⠀⠉⢻⣿⡿⠀⠀⠀⠀⣼⣿⣿⣾⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣇⠀⠀⠀⠀⢀⣼⣿⠇⠀⠀⢀⣾⣿⣿⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣀⣀⣤⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⠷⠶⣿⣿⣿⣿⠶⠶⠾⢿⣿⣿⣁⣀⣤⣴⣾⣿⣿⣿⣿⣷⣄⣠⣤⣤⣤⣤⡄⠀ ⣿⣿⠛⠛⠛⠻⢿⣿⣶⣾⣿⣿⣶⣿⡟⠉⠀⠀⠀⠀⣽⠟⠁⠀⠀⠀⠀⣸⣿⡿⠿⠛⠛⡏⠀⣠⡄⠀⣿⡿⠟⠛⡛⢻⣿⡇⠀ ⣿⣿⠀⠀⣿⠆⠀⢹⠋⠁⠀⠉⠛⡏⠀⠀⢠⣾⣿⣾⠧⠤⠴⣶⣿⡿⠿⠿⠿⠓⣶⢶⣿⡇⠀⢹⠁⠐⢿⣧⣀⠀⠉⠙⢻⣿⡄ ⢿⣿⠀⠀⢈⠀⣠⡄⠀⣠⣤⡄⠀⡇⠀⠀⠸⣿⣀⠀⠀⡀⣠⢿⣿⣤⠀⠀⢠⡴⠟⠀⠾⠷⠀⢸⣧⠀⢀⠙⠛⠿⠆⠀⠀⣿⡇ ⢸⣿⣆⣀⣸⣿⢿⣇⠀⠙⠿⠃⠀⣽⣄⠀⠀⠉⠉⠰⠈⣠⠇⠀⠉⠁⠀⠀⣰⣷⣠⣤⣤⣤⣴⣾⣿⣷⣿⣄⣀⣀⣀⣠⣾⣿⠃ ⠸⠿⠿⠟⠛⠛⠛⢿⣷⣶⣤⣶⣿⡿⣿⣷⣄⣀⣀⣤⣾⣿⣷⣤⣤⣤⣴⣿⡿⠿⠛⠛⠛⠛⠋⠉⠹⠋⠛⠻⠿⠿⠿⠟⠋⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠈⠙⠛⠿⠿⠛⠋⠉⠙⠛⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⡟⠈⠁⠀⠀⢠⠃⢸⠀⠀⢀⡇⠀⢃⠀⠀⠀⠀⠀⠀⠀⢸⠀⠈⡴⠀⠀⠀⠉⠘ ⠃⠀⠀⢀⣴⠎⠀⠸⠄⠀⠾⠀⠄⠸⣄⣀⡴⢀⠀⠤⠄⠚⠀⠀⢣⠣⠤⠀⡠⠀ ⢉⠉⠉⠀⠂⠀⠒⠒⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠤⠀⠀⠀⠀ ⣬⣶⣶⡶⠶⠶⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠁⣀⣤⣴⣶⢶⣶⣶⣶⣅ ⡟⠉⠠⠀⣠⣶⡿⣷⣯⡛⠷⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⣫⣿⣿⣷⣤⠀⠀⠉⠻ ⡇⠀⠀⢰⠁⠻⠑⢺⠃⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢻⢏⠓⢹⡗⡇⠀⠀⠀ ⠳⠀⠀⠀⠣⣑⠈⢁⡡⠃⠀⠀⢀⡤⣄⠤⠀⠀⠀⠀⠀⠣⣑⠉⢐⠱⠃⠀⠀⠸ ⠀⠀⠀⠀⢀⡀⣀⡠⢀⢄⠪⣂⡵⢋⠱⢒⢀⠀⠀⣠⠔⡂⠤⣀⣀⠀⠀⠀⠀⠀ ⠀⠀⠀⢈⣅⢞⠌⠊⠐⡡⠜⡡⠒⡡⢒⢥⢢⢗⡫⠐⠉⠀⠀⣂⠅⡢⠕⠀⠀⠀ ⠄⠠⣪⠾⠋⠀⢀⠄⡊⠔⣁⢔⡭⢞⢯⠪⠂⠁⠀⢀⠠⠐⠩⢐⠥⠂⠀⠀⠀⠀ ⡇⠋⠁⠀⠀⠀⠀⠈⠀⠈⠀⠀⢂⠔⠉⠉⠒⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⡍⠉⣉⣹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰ ⡿⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⢠⠉⠉⠀⠈⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋ ⢡⠈⢳⣅⡀⠀⠀⠀⠀⠀⠀⢸⡄⠈⠂⠀⠀⢀⠜⠀⠀⠀⠀⠀⠀⠀⣠⠔⠁⠀ ⢸⠀⠀⠻⣿⣷⣦⣤⣀⠀⠀⠀⠎⠐⢤⡤⠔⠁⠆⠀⠀⢀⣀⣤⣶⡿⠁⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣀⣀⣴⠿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣦⣤⣠⣿⡷⠿⠙⠻⠟⠋⠠⠿⠶⣶⡴⣦⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣸⣿⡟⠁⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⡷⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣼⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠺⢿⣧⣴⣤⠀ ⠀⠀⠀⣠⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡗⠀⠀⠀⠀⠀⢀⡼⠛⠀ ⠀⢀⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠳⠦⣄⣀⣀⢀⣀⣠⣴⠿⠛⠳⠶⠦⢤⣤⣀⡼⡧⠀⠀ ⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠙⢻⣄⢧⠀⠀ ⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡇⠀ ⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡧⠀⠀⠀⠀⢀⣠⣦⣤⣀⠀⠀⠀⠀⠀⠘⡇⠀ ⠙⣻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⡏⠀⠀⠀⢠⣿⠟⡛⣏⠉⠉⠙⠓⠀⢰⡾⠻⡿⠇ ⠀⣿⡇⠀⣠⣤⣤⡀⠀⠀⠀⢠⣾⠟⠂⠀⠀⠀⠀⠀⢀⡼⠿⣯⡀⠀⠀⢀⡼⢇⡰⡇⠀ ⠀⠹⣿⢰⣿⣿⣷⣯⡳⢦⡀⠘⣿⡀⠀⠀⠀⠀⠀⠰⠉⠀⢸⣿⡟⠀⠀⢸⡷⠻⢿⣟⠂ ⠀⠀⢹⡌⢫⣳⢰⣿⣿⠸⣿⡌⢛⣏⠀⠀⠀⠀⠀⠀⠀⠈⠹⠟⠀⠀⠀⠀⠃⠀⢾⡇⠀ ⠀⠀⠀⢳⡜⣏⠘⠟⢹⣄⣿⡁⢙⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣗⠀ ⠀⠀⠀⠈⣧⠘⢣⡄⠀⢹⠿⣷⣾⡟⠟⠀⠀⠀⠀⠀⠀⠀⠀⠠⣦⠀⣤⡄⢀⣰⣤⡿⠀ ⠀⠀⠀⠀⢸⡇⠀⣼⡓⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠙⢾⣁⡾⠃⠀ ⠀⠀⠀⠀⠸⢧⢼⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⠤⣤⣤⣶⣶⠊⣽⠟⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣟⢰⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢠⡞⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣀⣴⣾⣶⣦⣤⣤⣦⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣇⠀⠀⠀⠈⠉⠛⠛⠛⣷⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡠⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠘⢥⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡟⣿⣿⣿⣿⠿⢋⠇⠀⣠⠖⠚⢿⠆⠀⡾⢾⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡷⢿⣿⡋⠀⣀⡎⠀⠐⠁⢖⣠⣾⢦⠀⠏⣺⡧⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⢰⠀⣆⠘⡀⠸⠀⠉⠉⠁⠐⢎⠀⢸⠋⠉⡁⡏⡗⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠚⢴⢸⡛⠀⠁⠀⠀⠀⠀⠀⠀⠈⠩⠁⠀⠀⢹⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢹⣀⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠖⠒⡦⠻⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠐⠒⢋⡄⢺⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢆⠀⢀⣀⡀⠀⠀⠀ ⠀⠀⠤⣤⣤⣤⡼⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⠟⠊⠁⠀⠀⠀⠀⠀ ⢓⡒⢶⣶⢶⠶⡊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⢠⣿⣦⡀⠀⠀⠀⠀ ⠛⠉⠀⡾⠉⢠⢸⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠣⣙⣩⡙⠛⠿⢿⣶⣤⣤⣀ ⠀⠀⣼⠃⠀⠘⡈⢄⠀⠀⠀⠀⠀⠱⣤⠀⠀⠀⠀⠀⢹⠘⢷⡄⠀⠀⠈⢻⡿⣿ ⠀⢠⡏⠀⠀⠀⠡⠀⠢⡀⠀⠀⠀⠀⠈⣷⣦⣀⡤⢴⠞⠀⠈⢿⡄⠀⠀⠱⡀⠀ ⠀⡼⠀⠀⠀⠀⠀⠡⠀⠈⠢⠀⠀⠀⠀⠉⠉⡕⠀⡼⠀⠀⠀⠈⢿⡄⠀⠀⢘⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⣿⣿⡿⠟⢁⣴⣿⡿⠋⠀⠀⣼⣿⣿⣿⡟⠙⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣦⣤⣤⣾⣿⣿⣿⣿⣧⣀⣀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣻⣿⣿⣿⠟⢁⠀⠉⠉⠉⣻⡿⣛⠛⠛⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡏⣟⣿⠀⠀⠀⢸⣟⢻⢛⣷⠀⠀⠀⠀⠈⣿⠈⠉⠉⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣮⡁⠀⠀⠀⢈⣿⣮⡉⠉⠀⠀⠀⢀⣼⡟⠀⠀⠀⠀⠀⢿⣿⣿⣿⡇⠉⠙⠻⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣽⣿⣿⣿⣿⠿⠿⠿⠟⠋⣿⡿⢷⣶⣶⣶⡿⠋⠀⠀⠀⠀⠀⠀⠀⢹⣿⡏⠀⠀⠀⠀⣾⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣧⣭⣭⣭⣄⡀⠀⠘⠻⣦⣌⣀⣤⡴⠟⠀⠀⠀⠀⠀⠀⠀⣿⣿⠁⠀⠀⠀⣼⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠉⠉⠉⠛⠛⣿⣿⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡟⠀⢀⣠⣾⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣷⣄⡀⠀⠀⡀⠈⣿⣿⣿⣿⣿⣷⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣾⣿⡿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⣿⣿⣿⣦⠀⣦⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⣸⣿⡿⠁⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⡇⠸⣷⡹⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⢰⣿⣾⠃⢠⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡇⠀⠈⢳⣌⠻⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⣠⣿⣿⢃⣴⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠁⠀⠀⠀⠈⠐⠲⢿⣿⣿⡟⠀⠀⠀⠀⠀⢰⣷⣿⣿⣵⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠃⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣄⡀⠀⠀⠀⣀⣠⣿⣿⡟⠀⠀⠀⣀⣴⣿⣿⣿⠟⠛⠉⠀⠀⢀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣀⣠⣤⣤⣤⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⡿⠿⠿⢿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣽⣅⣀⣤⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣤⣤⣤⣤⣤⣶⡆⠀⠀ ⢸⣿⣿⠿⠟⠛⠻⠿⢿⣿⣷⣶⣶⣶⣶⣾⣧⣾⣿⡿⠋⠁⠀⠀⠀⠀⢈⣽⡿⠋⠀⠀⠀⠀⠀⠀⣹⣿⣿⠿⠿⠿⠟⢿⠉⠀⢀⣠⠀⠈⣿⣿⡿⠿⠟⠛⠛⣿⣿⡇⠀⠀ ⢸⣿⣿⠀⠀⠀⣶⣄⠀⠙⣿⡿⠟⠛⠛⠻⢿⣿⡟⠀⠀⠀⢠⣴⣦⣄⣾⡏⢀⣀⣀⣠⣶⣶⣤⣾⣿⣿⣿⣠⡄⣤⣤⣾⠀⠀⢹⡟⠀⢠⣿⣏⠀⠀⠐⠲⠶⢿⣿⣷⡄⠀ ⠀⣿⣿⠀⠀⠀⡿⠋⠀⠀⠛⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⣿⣿⠟⠛⠛⠋⠉⠉⠉⣿⣿⠛⠋⠉⠉⠉⠁⠈⡇⠛⠛⣿⡇⠀⢀⣧⠀⠈⠙⢿⣷⣦⣤⡀⠀⠀⠹⣿⣿⡆ ⠀⣿⣿⡆⠀⠀⣤⣀⣢⣾⠀⠀⢠⣾⣶⡦⠀⢸⡆⠀⠀⠀⢻⣿⣤⡄⠀⢠⡄⢰⠞⢻⣿⣶⠆⠀⠀⠐⣾⠛⠉⠀⠛⠛⠃⠀⢸⣿⣆⠀⣠⡄⠈⠙⠛⠃⠀⠀⢀⣿⣿⡇ ⠀⣿⣿⣧⠀⣀⣸⣿⡿⣿⣄⠀⠈⠿⡿⠇⠀⢈⣷⡄⠀⠀⠈⠉⠉⠱⠶⠈⢠⡿⠀⠀⠉⠁⠀⠀⠀⣠⣿⣆⣀⣀⣠⣤⣤⣶⣾⣿⣿⣾⣿⣄⡀⠀⠀⠀⢀⣠⣾⣿⡟⠀ ⠀⢹⣿⣿⣿⣿⣿⠿⠷⢿⣿⣷⣤⣄⣀⣤⣶⣿⣿⣿⣦⣀⠀⠀⠀⠀⣀⣴⣿⣷⣄⡀⠀⠀⣀⣠⣾⣿⣿⣿⡿⠿⠿⠿⠿⠟⠛⠛⣿⠟⠿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠿⠿⠿⠿⠋⠉⠻⢿⣿⣿⣿⣿⣿⣿⡿⠟⠿⣿⣿⣿⣿⣿⡿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠘⣿⡿⠟⠛⠛⠛⠷⢦⣤⣈⠉⠙⠻⠿⡟⠋⠀⢻⣿⡿⣿⣿⣿⣿⠟⠋⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⣠⣴⣋⡥⠴⠒⠒⠒⠒⠢⠤⣈⡙⠻⢶⣤⡀⢀⣤⠞⠛⠋⢉⣉⣉⣉⣉⠛⠒⠶⢤⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿ ⠀⢀⣾⠟⢉⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠉⠒⢤⡈⠛⣫⠤⠒⠋⠉⠉⠀⠀⠀⠉⠉⠙⠒⠦⣄⠉⠻⢿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠀⢀⡾ ⠀⡼⢁⣴⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⢙⠞⢁⣤⣶⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢄⡈⢿⣿⣿⣿⣿⠟⠀⠀⣠⡼⠋⠀ ⢰⠃⣿⣿⠋⠉⢻⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢠⠃⢠⣿⣿⠿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⢯⣽⠇⠀⢠⡾⠋⠀⠀⠀ ⢸⠀⢿⣿⣷⣤⣾⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⡏⠀⢸⣿⡅⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡏⠀⢰⠏⠀⠀⠀⠀⠀ ⠈⢧⡈⠛⠿⠿⠿⠿⠋⠀⠀⠀⠀⠀⠀⠀⣰⣇⠀⠘⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⣾⠀⢠⡟⠀⠀⠀⠀⠀⠀ ⠀⠀⣟⠲⠤⠤⠤⠤⠤⠤⣤⣤⢤⡴⠒⠋⠁⠘⢦⣄⠈⠙⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⠉⠀⡴⠂⡇⠀⣸⠇⠀⠀⠀⠀⠀⢠ ⠀⠀⠈⠙⢒⣶⠖⠒⠒⠒⠚⠋⠉⠉⠀⣀⢀⠀⠀⢻⡉⠓⠲⠤⢤⣄⣀⣀⣀⣠⠤⠴⠒⠉⢀⣠⡴⠊⠀⢰⡇⠀⣿⠀⠀⠀⠀⠀⢠⣿ ⠀⠀⡠⠖⠋⠤⠤⠤⠤⣤⣤⣤⣤⣴⡾⠋⠘⢷⣄⡀⠙⠳⢤⣄⣀⣀⣀⣀⣠⣤⠤⠴⠖⠚⠉⠀⠀⠀⠀⢸⡇⠀⣿⠀⠀⠀⠀⠀⢸⡿ ⠀⢸⣁⣀⣤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⣤⣉⣛⡛⠒⠲⠶⠦⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⣿⠀⠀⠀⠀⠀⣾⡇ ⠀⢸⣏⠀⠀⣠⣤⠶⠶⠶⠶⠶⠶⠶⢶⣦⣤⣤⣀⣈⠉⠙⠓⠲⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⡀⠀⠀⠀⠀⢸⡇ ⠀⠀⠹⣦⠀⠻⣄⠀⢘⣘⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⣀⠉⠙⠒⠦⠤⣤⣀⠀⠀⠀⠀⠀⠀⠀⢿⡀⢸⡇⠀⠀⠀⠀⣸⡇ ⠀⠀⠀⠈⢳⠀⠙⣦⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣀⠀⠈⢻⡄⠀⠀⠀⠀⠀⠸⡇⠀⢻⡷⠶⠾⠿⠿⠇ ⠀⠀⠀⠀⢸⠀⠀⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⡇⠀⠀⠀⠀⠀⠀⣷⠀⠈⣧⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⠀⠀⣿⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢀⡇⠀⠀⠀⠀⠀⠀⢹⡄⠀⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⠀⠐⣿⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⢷⠀⢿⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⠀⢸⡇⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⣠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⢸⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⠀⢸⡇⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢁⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⢿⡀⠀⠀⠀ ⠀⠀⠀⠀⢸⠀⢸⡇⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⢁⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣷⣀⠀⠀ ⠀⠀⠀⠀⢸⠀⠈⠷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠈⣉⣛⣯⡽⠾⠛⣉⣤⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠈⠙⠲ ⠀⠀⠀⠀⠘⢷⣄⠀⠀⠉⠉⠙⠛⠛⠛⠛⠋⠉⢉⣁⣀⡤⠶⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠉⠀⠀⠀⠀⠀

⠀⠀⠀⣠⠔⠒⠊⠉⠙⠒⠒⠒⠦⠤⣀⢲⢤⡀⠀⠀⠀⠀ ⠀⢀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠙⣆⡤⠔⡲ ⢠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢧ ⡈⢱⡄⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⣀⣄⠀⠀⠀⣀⡤⠂⢸ ⡏⠙⣣⡴⢻⡠⠚⠁⠸⡄⢀⡤⠊⠁⠈⠲⠔⠋⠈⢣⠀⡼ ⠘⠤⣌⠀⠀⢀⣤⠀⠀⠈⠁⠀⠀⢿⠀⠀⠀⠀⠀⢸⢰⠁ ⠀⠀⠸⡀⠀⠀⠛⠀⠠⡴⠒⠒⡟⠂⠀⠀⠀⠀⠀⡼⠃⠀ ⠀⠀⠀⠱⣄⠀⠀⠀⠀⠙⠢⠴⠃⠀⠀⠀⠀⠀⡔⠀⠀⠀ ⠀⠀⠀⠀⠈⠓⢤⣀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠎⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⡩⠥⢤⡀⠀⠀⠀⢸ ⠀⠀⡏⠁⢉⡇⠀⠀⣀⣀⠀⠀⠀⢸⠁⠀⠀⣧⠀⠀⠀⢸ ⠀⠀⢏⠉⠁⠀⢠⠏⠀⠀⢱⡀⠀⠈⠣⠤⠚⠁⡆⠀⠀⠀ ⠀⠀⢸⠀⠀⠀⠘⢆⡀⣀⡼⠀⠀⠀⠀⠀⠀⣰⠁⠀⠀⡄ ⠀⠀⠸⠄⠀⠀⠀⠀⠈⠁⠀⠀⠀⠑⠤⠤⠖⠁⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢀⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣶⣿⣦⣠⣾⣿⣿⣿⣿⣷⣄⠀⡀⠀⣴⡆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣿⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣀⣠⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠤⠤⠀⠀⣀⡹⣿⣿⣿⣿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠉⠙⣿⣿⡏⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠉⢉⠀⠀⠀⢸⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⢸⣿⠿⠿⠿⠿⠿⠆⠈⠇⣾⢀⣾⣿⠆⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⢹⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⢀⠀⠁⠀⣤⠤⠀⠀⢠⠄⠀⡼⠘⠛⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⡏⢰⠿⡍⢿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⢰⣏⣽⣿⣦⠀⠋⠀⣼⢃⣤⢼⣏⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⢸⣠⡟⠋⡙⣿⣿⣿⣿⠀⠀⠀⠀⠀⢠⡀⢨⡉⠙⣻⡟⠀⠀⢸⡏⢹⣄⣿⠟⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡞⠿⣄⢸⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠑⠀⠉⠉⠉⢀⠀⢸⡀⢷⡀⠀⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠛⢻⣿⣿⣿⣷⢾⡝⠟⣦⣼⣿⣿⣿⡀⠀⠀⠀⠀⠀⢀⠀⠦⡀⠀⠈⠀⠈⠇⠈⢳⠀⠸⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⣝⡿⠟⠁⣿⣿⣿⠃⣤⠀⠢⡄⠀⠈⣇⠀⢹⣀⡞⠀⣀⠒⠛⢛⡇⢀⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡿⠈⢉⠉⠀⠙⠛⠁⠀⠻⠤⣤⡈⠀⠀⠈⢀⡼⡇⠙⠛⢻⡇⣠⠞⢀⡼⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣿⣿⣿⠃⢠⡎⠀⠀⠀⢷⡄⡀⠠⡀⡀⠹⠆⠀⠀⠞⠁⠳⠀⠀⠀⢈⣻⣶⠟⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡿⠁⠀⡜⠁⠀⠀⠀⠈⡟⡼⣄⠱⠌⠲⡄⠠⣄⣀⣀⣀⡠⠶⠚⠉⡉⢹⡆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠋⠀⠀⠀⠀⢠⠀⠀⠀⢠⠃⢸⠈⠓⠀⠀⢸⠀⠘⣿⢥⣤⣤⣶⣾⣿⣿⡿⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣠⠖⠋⠁⠀⣠⠀⠀⠀⠀⠸⠀⠀⠀⠈⠀⢈⠀⢳⠀⣠⠋⠀⠀⠘⡆⢿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⡤⠖⠋⠀⠀⠀⣠⠾⠃⠀⠀⠀⠀⠀⣦⡀⠀⠀⠀⠘⠀⠸⠀⢳⠀⠀⡐⠀⢧⡀⠛⠿⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⢾⠉⠀⠀⠀⠀⠀⢀⡿⠋⠀⠀⠀⠀⠀⣠⠀⠀⠹⣦⠀⠀⠀⠀⣄⠈⠎⢷⡀⢹⡀⠈⠻⠶⣶⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⣧⠀⠀⠀⠀⣠⠎⠀⠀⠀⠀⠀⠀⣠⡇⠀⠀⠀⠛⢇⠀⠈⢦⡈⠣⡀⢠⡑⠦⠙⠳⣶⡶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢻⠁⠀⠀⠀⠀⠘⣦⠀⠀⠙⠦⣀⠀⠙⢓⣠⡴⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠘⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠀⠀⠀⠀⠀⢸⠈⠳⣄⣀⣀⣈⣽⡶⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠑⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠉⡉⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⢠⠞⠁⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠠⠤⣀⡀⠀⠀⠀⠀⢀⡏⠀⣠⣏⡤⠤⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠉⠉⠉⠉⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠤⠤⠤⢤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣤⠶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠦⣄⡀⠀⠀⠀⣀⣤⠴⠖⠒⠋⠉⠉⠙⠓⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢶⡖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⠴⠒⠋⠉⠉⠀⠀⠀⠀⠉⠉⠙⠲⠦⣄⡀⣧⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣟⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠉⠉⠉⠉⠛⠲⠤⣄⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠤⠔⠒⠒⠒⠒⠶⠤⢼⣧⣀⠀⠀⠀⠀⠀⢀⣀⣀⣤⠤⠤⠤⠤⠤⣤⣄⣉⣳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⢉⣀⡤⠖⠚⠋⠉⠉⠉⠉⠙⠒⠶⢬⣳⣄⠀⢀⣀⣠⠤⠤⠤⠒⠒⠒⠒⠒⠒⠒⠦⢬⣝⣶⣄⠀⠀ ⠀⠀⠀⠀⠀⠀⡠⠖⠊⢉⣠⠴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣈⣻⣿⡉⠀⠀⠀⠀⢀⣀⣀⣀⣀⣤⣤⣄⣀⣀⣀⣉⣻⣄⠀ ⠀⠀⠀⠀⣴⡟⠓⠒⠋⠉⠀⠀⠀⠀⢀⣀⡤⣴⣶⣾⣿⣭⣍⣉⠀⠀⠀⠀⠈⣿⡥⠴⠒⠊⠉⠉⠁⣰⡾⠿⣿⣿⣶⣤⠀⠀⠈⠉⠻⡇ ⠀⠀⠀⠀⠙⠓⠒⠲⢶⡒⠒⠒⠒⠋⠉⠀⣠⣾⣯⣀⣿⡿⠿⢿⣷⡄⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⣾⣿⣷⣤⣿⠛⠻⣿⣷⠀⠀⠀⣠⠇ ⠀⠀⠀⠀⠀⠀⠀⠀⣄⠉⠲⢤⣀⣀⣀⣀⣿⣿⣿⠛⣿⣧⣀⣼⣿⣿⣤⠴⢻⡦⢤⣀⣀⣀⡀⢸⣿⣿⣥⣽⣿⣶⣾⣿⡿⠧⣴⣾⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠖⠚⠉⠁⠀⠀⠈⠉⠙⠻⢿⣟⠛⠉⣉⣁⣤⡴⠾⢥⣤⣀⡀⠀⠉⠉⠉⢉⣩⣭⠽⣭⣄⣀⢀⡴⠋⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡟⠉⢀⣀⡤⠤⠤⠤⣤⣉⡙⢲⡴⠚⠉⠀⠀⠀⠀⠀⠈⠙⠳⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣏⣉⣠⠤⠴⠤⠤⢤⣀⡽⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠞⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢒⣾⠟⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠟⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠶⠟⠋⠉⠉⠉⠉⠛⠛⠶⢶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣀⣴⡾⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⣤⡀⠀⠀⠀⢀⣀⣤⠴⠾⠛⠉⠉⠁⠀⠀⠀⠈⠉⠛⠶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⡴⠞⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠶⠶⠶⠖⠒⠶⠶⠶⢦⣤⣀⡀⠀⠀⠀⢹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⢶⣄⡀⣿⠀⠀⠀⢀⣀⣀⣀⣀⣀⣤⣤⣤⣀⣀⣀⣀⣀⣀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣟⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠶⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣤⣤⣤⣄⣀⣀⣙⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⢦⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠖⠚⠋⠉⣉⣠⣤⣤⣤⣤⣤⣭⣍⣉⠛⠛⢶⣄⡀⠀⠀⠀⠀⠠⠴⠒⠒⠛⠛⠋⠉⠉⠉⠉⠉⠙⠛⠒⠒⠶⢿⣆⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠞⠋⠁⣀⣤⠶⠞⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠶⣮⣿⡀⣀⣀⣠⡤⠶⠶⠖⠚⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠛⠳⠶⣬⣛⢦⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠟⠉⠁⣀⣤⠶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡿⣯⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠉⡻⣧⡀⠀ ⠀⠀⠀⠀⠀⣀⣤⣾⢤⣤⠤⠞⠛⠁⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⡴⡶⡞⣛⠛⠛⠋⠉⠉⠉⠉⠉⠻⣿⣃⣀⣠⠤⠴⠖⠚⠛⠋⢉⣭⣶⣶⣶⣶⣦⣤⡀⠀⠉⠉⠙⠛⠻⣿⠂ ⠀⠀⠀⠀⠀⢿⣿⣄⣀⡀⠀⠀⠀⠀⢀⣀⣠⣤⡴⠶⠚⠋⣹⣿⡟⠛⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⢀⡟⠋⠉⠀⠀⠀⠀⠀⠀⣠⣾⣿⠁⠈⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠘⡆ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠻⢯⡉⠉⠉⠉⠁⠀⠀⠀⠀⣼⣿⣿⣷⣤⣿⣿⠟⠛⢻⣿⣷⡄⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣷⣾⣿⡏⠉⢹⣿⣿⣧⠀⠀⠀⣠⡼⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠉⠳⠦⣄⣀⠀⠀⠀⢰⣿⣿⣿⡿⠛⣿⣿⣄⣀⣰⣿⣿⣷⣤⡴⠞⣿⣤⣄⣀⣀⡀⠀⠀⠀⣼⣿⣿⣧⣠⣿⣿⣷⣶⣾⣿⣿⣿⠶⣶⣾⡏⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⣤⠤⠞⠛⠋⠉⠉⠉⠉⠛⠛⠿⣶⣿⡿⠿⠿⠛⠛⠋⠉⢀⣀⣴⠿⠁⠀⠀⠈⠉⠉⠉⠛⠛⠛⠛⠛⣛⣛⣛⣛⣉⠉⠁⠀⢀⡴⠟⠋⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣦⣤⣤⡶⠶⠛⠛⠛⠉⠉⠙⠛⠛⠲⠦⣤⣀⠀⢀⣠⡴⠞⠛⠛⠋⠙⠛⠛⠳⢦⣞⡁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣧⠀⣀⣤⠴⠖⠚⠒⠒⠒⠲⠶⣤⣄⣩⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⠁⣀⣤⡤⠶⠶⠶⠶⢦⣄⣀⣼⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠉⠀⠀⠀⠂⠒⠀⠀⠀⣽⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⣴⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠴⣶⠞⠋⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⢀⠔⢊⠔⠁⠠⢠⠂⣴⠁⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠈⠒⣄⠀⠀⠀ ⠀⠀⡴⡫⡰⠡⠂⢠⠁⠂⠌⡄⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀⢡⠈⠁⠀⠀ ⡠⢊⡬⡞⢠⠃⠠⡇⠀⠌⠆⡇⠀⠀⠀⠀⠀⣀⣰⠋⠀⣼⡇⠀⠆⢡⡆⠀⠀⠀ ⢀⡞⢠⠁⡆⢠⠅⢇⡶⠤⠖⢫⠀⠀⠀⠀⠀⡘⠁⠉⠳⣇⣿⠀⢰⠀⣿⠀⠀⠀ ⠈⠀⠈⡼⠀⠇⠈⠙⠓⠀⠐⠨⢧⠀⠀⢀⣧⠁⡀⠤⠀⠸⡟⢧⠄⡀⢹⠀⠀⠀ ⠀⠀⢸⢠⢾⠀⣠⣤⣤⣭⣥⣍⠈⠓⠄⡌⡏⠀⠀⢤⠄⣀⠻⡘⡄⡇⢸⠀⠀⠀ ⠀⠀⠀⡈⢶⡛⣛⠂⠤⠀⢼⠉⠀⠂⠖⠐⠐⠀⣯⢭⡉⢛⡺⣵⣥⠇⠈⠀⠀⠀ ⠀⠀⢀⡇⠀⠀⠕⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠲⣘⡋⠹⢶⠀⠀⠀⠀ ⠀⠀⡼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⢠⠂⠀⠀ ⠀⣷⠳⠀⠀⠀⠀⠀⠀⠀⡠⠐⢒⠒⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢠⠃⠀⠀⠀ ⢀⣿⠦⡀⠀⠀⠀⠀⠀⢸⣅⣹⣿⣿⣿⣶⣗⠀⠀⠀⠀⠀⢀⠌⡰⡁⠀⠀⠀⠀ ⢉⣹⡇⠡⡀⠀⢀⡤⢀⠈⣿⡿⠿⠿⠿⢿⡏⠀⠀⠀⠀⡰⠁⠮⢔⣥⠀⠀⠀⡠ ⢰⠏⠇⠀⣷⡀⠧⡀⠠⠀⠻⡄⠀⢀⡤⡎⠀⠀⠀⡠⢊⠔⠀⠀⢠⠞⢡⡦⠊⠀ ⠀⡇⠀⠐⠉⠙⠦⡀⢄⡄⡊⠈⠉⣭⠀⠀⠀⡠⢊⢴⠏⠠⡴⣂⠞⢡⢏⡔⠀⢀ ⠷⣰⠯⣀⠀⠀⢀⣿⣦⠀⠁⠀⠀⢹⡀⣔⠭⢒⣁⣬⠀⠰⡊⠀⢠⣟⠎⠀⠀⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⣴⣶⢶⣒⡂⠤⠤⢀⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡔⠍⠋⠀⠀⠀⠒⠂⠠⠄⡀⠀⠀⠁⠢⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠉⠀⠀⠀⠀⠀⠀⢀⠠⠄⠒⠀⠷⠀⣀⠀⠈⠢⡀⠀⠀ ⠀⠀⠀⣀⡴⠃⠉⠁⠈⠑⠒⡖⢲⠁⠀⠀⢀⣀⣀⠀⠀⠑⣄⠀⠐⡄⠀ ⠀⡠⠉⡐⢀⣤⣶⣶⢤⣰⠞⠀⡎⠀⡠⠊⠁⣠⣶⣭⡲⡄⠁⢳⡀⠘⡀ ⠘⡇⠀⠇⡇⣼⣿⣿⣷⠋⠀⠀⢿⠀⢳⣀⠀⣿⣿⣿⣿⢰⡄⠀⢳⠀⢱ ⠀⢹⢴⣀⡑⠛⠛⠛⡏⠀⠀⠰⢦⣣⣄⣉⣓⣛⣛⣿⠽⠋⠀⠀⠀⢣⢸ ⠀⠀⢳⠁⠈⢩⠗⣊⣁⠀⠀⣤⣤⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾ ⠀⠀⡆⠀⠀⠀⠑⠩⠏⠁⠀⠈⠉⠓⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄ ⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃ ⠀⠈⡀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀ ⠀⠀⢷⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣣⠀⠀⠀⠀⣸⠀ ⠀⠀⢸⡅⢠⠉⠲⣶⡤⢶⠖⢿⣿⡟⠲⣶⡶⠖⠉⠀⡄⠀⠀⠀⠀⡏⠀ ⠀⠀⠀⢷⠸⠀⠀⠈⠉⠛⠲⠬⠿⠗⠚⠉⠀⠀⠀⠰⠁⠀⠀⠀⣸⠇⠀ ⠀⠀⠀⠘⣧⠀⠀⠀⠀⠠⠀⣀⡀⠀⠀⠀⠀⠀⠠⠃⢀⡀⠀⢠⡟⠀⠀ ⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⢠⡟⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⣎⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⢀⣴⠟⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⢷⡙⠳⢦⣀⣀⣀⣀⣠⠴⠟⠁⣠⠞⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠻⢶⣄⡀⠀⠁⠀⠀⣀⣴⠞⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⡿⠿⠿⠿⠿⠶⣦⣤⣄⣀⠈⠉⠛⠿⢿⣿⡿⠛⠉⠀⢻⣿⣻⣿⣿⣿⣿⣿⣿⡿⠟⠛⠛⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⢀⣴⠞⠋⣁⣀⣤⣤⣤⣤⣀⣀⠉⠙⠛⢿⣶⣤⡀⠀⠈⠉⠀⣠⣴⡾⠿⠿⠾⠿⠿⠿⠿⠿⢶⣤⣤⣄⡀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⣠⣾⣿⠷⠞⠉⠉⠀⠀⠀⠀⠀⠀⠉⠉⠓⠶⣄⡀⠉⠻⣷⣦⣰⠾⠋⢁⣀⣤⠤⠶⠶⠶⠶⠶⠦⢤⣤⣀⠉⠙⠻⢶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠋⢙ ⠀⠀⣼⡿⠋⠀⣀⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣄⡀⠉⣡⡶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠳⢦⣀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⢀⣴⡟ ⠀⢸⠟⢀⣴⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⠞⠁⣀⣤⣶⣶⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣄⠀⢹⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⢀⣴⠟⠋⠀ ⢀⡏⢠⣿⣿⡿⠛⠛⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⣼⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠦⣭⣛⣛⠛⣿⠋⠀⠀⢀⣼⠟⠁⠀⠀⠀ ⢸⠀⢸⣿⣿⡄⠀⠀⣼⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⣼⣿⡿⠋⠉⢻⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢻⡏⠀⠀⣰⡟⠁⠀⠀⠀⠀⠀ ⠸⡄⠈⣿⣿⣿⣷⣾⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⣿⣿⣧⡀⠀⣰⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⢶⡟⠀⠀⣸⡟⠀⠀⠀⠀⠀⠀⠀ ⠀⢳⡄⠈⠻⠿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣇⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⣼⠇⠀⢰⡿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢹⠶⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⠴⠟⠋⠙⢦⡀⠀⠈⠻⠿⠿⠿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠟⠁⢀⣤⠀⣿⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⢀ ⠀⠀⠘⠦⣤⣍⣉⣉⣉⣉⣉⣉⣉⣩⣭⣭⣽⡧⠄⠀⠀⠀⠀⠀⠹⣷⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠞⠋⠀⠀⣠⡞⠁⢠⣿⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣾ ⠀⠀⠀⠀⠀⢀⣬⠟⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⢀⣤⢠⡀⠀⠀⠻⣆⠈⠉⠙⠒⠒⠶⠤⠤⠤⠤⠤⠶⠒⠚⠋⠁⠀⣀⣤⡴⠞⠁⠀⠀⢸⣿⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⣸⣿ ⠀⠀⢀⣴⠞⠋⢡⣤⣤⣤⣤⣤⣤⣤⣤⣀⣠⣴⣾⠿⠃⠘⢿⣦⣀⠀⠉⠻⠶⣤⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⠶⠶⠞⠛⠉⠁⠀⠀⠀⠀⠀⢸⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣿⣟ ⠀⢠⡟⠁⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣈⣉⣉⣉⣀⣀⣀⣀⠀⠙⠻⠿⠶⠦⢤⣤⣤⣍⣉⣉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⢸⣇⠀⠀⠀⠀⠀⠀⢠⣿⡇ ⠀⢸⣷⡾⠛⠛⠋⠉⠉⠉⠀⣀⣀⣀⣀⣀⣀⣀⣉⠉⠉⠉⠛⠛⠛⠳⠶⢤⣤⣀⣀⠈⠉⠙⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠈⣿⠀⠀⠀⠀⠀⠀⠸⣿⡇ ⠀⠘⢿⣤⠀⠀⢠⣶⠟⠛⠛⡛⣛⣛⠛⢛⠛⠛⡛⢻⣿⣷⣶⣶⣦⣤⣄⡀⠀⠉⠙⠛⠶⢦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⣿⡄⠀⠀⠀⠀⠀⠀⣿⡇ ⠀⠀⠈⠻⣧⡀⠘⢿⡄⠀⢠⣁⡙⣏⣻⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⠀⠀⠉⠙⠳⠶⢦⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⢻⡇⠀⠀⠀⠀⠀⠀⣿⡇ ⠀⠀⠀⠀⠈⢷⡄⠀⢻⣦⠀⢿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣀⡀⠀⠀⠈⠙⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠘⢿⣶⣶⣶⣶⣶⣿⣿⡇ ⠀⠀⠀⠀⠀⠀⡇⠀⠀⣿⡇⣸⢧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⣿⠀⠉⠉⠉⠉⠀⠀ ⠀⠀⠀⠀⠀⠀⡇⠀⠀⣾⡇⢸⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡇⠀⢀⣼⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡇⠀⠈⣿⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⢀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⢹⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡇⠀⠀⣿⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⢸⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡇⠀⠀⣿⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⣰⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⢻⡆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡇⠀⢰⣿⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⢠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡘⣿⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡇⠀⣸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣻⣿⡿⠋⣠⡴⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣧⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡇⠀⠸⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢿⣿⣟⠟⣛⣿⣷⠿⠛⢁⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠟⠛⠶⣤⣀ ⠀⠀⠀⠀⠀⠀⣇⡀⠀⠙⠻⠷⣦⣤⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⡴⠶⠿⠛⠉⣀⣤⠶⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠉ ⠀⠀⠀⠀⠀⠀⠻⣧⣤⡀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁⠀⠀⣀⣀⣠⣤⠶⠛⠋⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⠟⠁⠀⠀⠀⢀⠀⢀⠀

⠀⠀⠀⠀⢴⠁⠀⢀⣸⣅⣀⠀⠀⢀⢴⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⠎⡐⢈⡰⢹⠈⠛⠻⣕⣁⣯⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀ ⠀⠀⠀⣸⠀⣩⣿⡿⢿⣶⣤⡎⠀⣰⣽⠃⠀⠀⠀⠀⠀⢀⠀⢀⠜⠀⡇⠀⠠⠀ ⠀⠀⠀⣧⣾⡿⠁⠀⠘⣼⠎⠻⣆⢸⡝⠐⠀⢀⢀⡤⠂⡾⢲⠯⠥⠤⢦⣞⠁⠀ ⠀⡆⡆⣯⢘⡇⠀⣀⣀⣜⡒⠠⢙⣿⠘⠀⠀⢠⠋⢀⠾⡠⠋⠀⠀⠀⠘⡏⠙⠲ ⠀⣿⣇⣿⡞⠱⠀⠀⠂⠰⡡⠃⣆⠈⢰⡇⠀⣰⢀⢮⠗⢐⣒⣖⠂⠤⣆⣻⠀⠀ ⠀⠃⢹⣟⣿⠨⢵⢄⡈⠒⠒⠊⠉⠀⠀⠷⢀⢹⠌⠁⠈⣉⠉⣛⠛⢷⣯⣞⠀⠘ ⠀⠀⣸⠹⣾⢿⣥⢧⢲⠙⡠⣀⠀⠈⡀⠀⢻⠈⠀⠢⡎⢰⡦⢰⠣⠊⢈⣿⣕⠆ ⠀⢰⣿⠀⡿⠛⠗⠋⠋⠻⡷⣿⣯⠰⣱⠀⡀⢀⢀⠀⠥⢈⠂⡀⠵⡠⡞⠈⣿⠀ ⠀⢸⠸⠀⠟⠀⠀⣴⡀⠀⠁⠀⠙⡆⠡⢦⣡⣄⣀⠍⠂⢄⠀⠀⠀⡀⠤⢾⣿⠀ ⠀⢸⡄⢣⠀⠀⠀⡿⣈⠂⠄⡀⠀⠁⠀⠈⠙⢻⣷⢹⢸⣄⠫⣁⡢⢀⢔⠎⠘⢰ ⠘⡸⢟⣷⠣⠀⠀⢉⠱⡑⠠⢈⠢⠒⠒⠀⠀⠀⠸⡌⢟⣯⣷⡆⢀⣡⠃⠀⢀⠎ ⠀⠑⠎⠑⠡⢑⣤⠃⠀⢼⡅⠂⠤⢉⣀⠂⣒⡲⡾⠁⠈⠙⠛⢬⣭⣯⡶⠒⠁⠀ ⠀⠀⠀⠀⠀⠀⠸⣄⠀⡞⠀⠀⠀⠀⠀⢀⠓⣺⠀⠐⣂⠤⠒⠉⢀⢾⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡠⠃⠢⠄⠀⠤⠤⢤⣔⠝⠐⠒⣸⠉⣦⠀⣀⡴⡻⠃⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣤⠶⠛⠋⠉⠉⠉⠙⠛⠛⠙⠛⠓⠶⠶⣦⣤⡀⠀⢷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠳⣾⣧⠈⠻⣆⠀⠀⠀⢀⣀⣤⡄ ⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⣾⠞⠋⠉⣾⠁ ⠀⠀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⠀⣧⠀ ⠀⢸⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆ ⠀⠀⠈⢻⣆⠀⠀⢀⡀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⣀⣠⡴⠞⠀⢸⡇ ⢸⡟⠶⣬⣿⠀⢀⣰⣧⠀⠀⣠⡴⠛⠹⣆⠀⠀⠀⠀⢀⣠⠞⠋⠙⢧⡀⠀⢀⣤⠾⠛⣿⡄⠀⠀⣸⡇ ⠘⣇⠀⠈⢱⣦⠟⠁⢸⡶⠟⠁⠀⠀⠀⠻⣆⠀⣠⠶⠋⠁⠀⠀⠀⠀⠙⠚⠋⠀⠀⠀⠨⡇⠀⢀⡿⠁ ⠀⢻⣄⣀⢸⠃⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠙⠛⠁⠀⠀⠀⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⣼⠃⠀ ⠀⠀⠉⠋⢻⡦⠀⠀⠀⠀⢾⣿⠇⠀⠀⠀⠀⠀⠀⠀⢠⣄⠉⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣼⠃⠀⠀ ⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠈⠛⠀⠀⢠⣤⡶⠖⠚⠛⠛⡟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⠀⠀⠀⠀⠀⢸⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠶⢤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⠤⠖⠛⠁⠀⠀⠀⠀⠀⠀⣾⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⠀⢀⡤⠤⢤⣀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⠀⣤⠶⠒⠒⠶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⢼⠀ ⠀⠀⠀⠀⣧⠀⠀⠀⣠⡿⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣼⣧⠀⠀⠀⠀⠀⣿⠀ ⠀⠀⠀⠀⢻⠚⠛⠋⠁⠀⠀⠀⣴⠋⠁⠀⠀⠙⣧⠀⠀⠀⠀⠙⢷⣀⣀⣤⠾⠃⢸⡀⠀⠀⠀⠀⠈⠀ ⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⢷⣀⡀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⢀⡄⠀ ⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠉⠉⠒⠛⠋⠀⠀⠀⠀⠰⣆⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠛⠀ ⠀⠀⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠒⠒⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣰⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣾⣿⣿⣷⣦⣾⡀⠀⠀ ⠀⠀⠀⠀⠀⢀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠄ ⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠛⠻⣿⣿⣿⠀ ⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠈⢻⡿⠀ ⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠁⠀⣤⠶⠦⠄⢤⢠⡇⠀ ⠀⠀⠀⠀⣿⣿⠩⣻⣿⣿⡇⠀⠐⠀⣲⡄⠀⣘⢠⡇⠀ ⠀⠀⠀⠀⣿⣿⣾⣥⢸⣿⡀⠀⠀⠊⠒⠁⢀⢣⠹⠀⠀ ⠀⠀⠀⠀⢸⣿⣿⠵⠙⠿⠃⡐⠄⠡⢰⠐⣤⢐⢆⠀⠀ ⠀⠀⠀⠀⠈⢻⠋⡌⠀⢰⢄⠄⠁⠀⠁⣀⠠⠷⡃⠀⠀ ⠀⠀⢀⠠⠒⡁⠀⠠⠀⠘⠘⠅⡘⠈⠗⣶⣾⠟⠁⠀⠀ ⠔⠊⠁⢀⠎⠀⠀⡀⠢⡀⠀⠀⠡⡰⡘⢬⠝⠀⠀⠀⠀ ⠘⠄⠀⠁⠀⠀⢜⠁⠀⠐⡀⠀⢌⣂⠄⠃⠀⠀⠀⠀⠀ ⠀⠈⠢⢀⠀⠀⠀⠀⠀⢰⠈⡩⠹⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠐⠂⠀⠤⠮⠔⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⣶⣾⣿⣿⣾⣧⣴⣾⣿⣿⣶⣿⣿⣶⣿⣷⣶⣾⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡿⠛⠋⠁⠀⠀⠀⠀⠀⠉⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡙⠛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠆⢠⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⢯⠁⢴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⣾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣿⣿⡯⠆⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠋⠀⢸⣿⣤⣄⡀⠀⠀⠀⠀⠀⣀⣚⣛⠛⠛⠋⠀⠀⠈⠑⠷⠶⠖⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⢸⡟⠛⠛⠿⢧⠀⠀⠘⠟⠛⠛⠻⠿⢿⣶⣄⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡷⠖⠲⢶⡀⠀⠀⠀⢀⣤⣤⣤⣤⣄⡉⠙⠓⠀⠀⠀⢀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡏⠀⠀⠀⠀⢿⣄⣀⣠⡾⠋⠉⠀⠈⠙⣷⡄⠀⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⠀⠀⣠⡿⠙⣯⠀⠀⠀⠀⠀⠀⠘⢿⣦⣤⣤⣬⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⢉⡙⢿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠛⠒⣴⡿⠁⠀⢸⣧⠀⠀⠀⠀⠀⣠⡞⠓⠛⠛⢿⣫⣽⣿⣿⣿⣿⣿⣿⠟⢋⣴⡾⠛⢿⡤⢻⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⢀⣾⠋⠀⠀⠀⠀⠉⠻⠶⠶⠶⠟⠋⠁⠀⠀⠀⠹⢿⣿⣿⣿⣿⣿⣿⢃⣴⣿⣿⣆⠀⠸⠃⣸⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣇⢠⣾⠇⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⠟⠁⠈⢹⣿⡯⠃⠀⢀⣾⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⣿⠃⣠⠞⣻⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⣿⠏⠁⠀⠀⢠⡿⠋⠀⠀⠀⣾⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠁⠀⠘⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣾⣿⡿⠀⠀⠀⠀⠙⠧⠄⠀⠀⣼⣿⠏⠀⣰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⢳⣶⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣾⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⠋⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠙⢿⣿⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⣽⡿⠋⠁⠀⠀⠀⠀⠀⢀⣴⣿⣿⢿⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣸⣿⣿⣿⣿⣿⣿⠟⣶⠀⠀⠀⠀⠀⠀⠀⠘⠉⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⡿⠁⣼⡟⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠰⡿⠿⠿⠿⠛⠁⣠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣴⣿⠿⠟⠋⠁⠀⣠⣿⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠙⣶⣶⣶⣶⠟⠋⠁⠀⠀⠀⠀⢀⣤⣤⣤⣶⠶⠾⠿⠿⠟⠋⠉⠀⠀⠀⠀⣠⠞⣱⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⣡⣼⣿⣿⣿⣿⣿⡇⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⡖⠛⠛⠛⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⣼⣇⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡴⣛⣵⣿⣿⣿⣿⣿⣿⣿⣿⣇⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠈⠻⢷⣦⣄⣀⣀⣀⣀⣴⡿⠟⠀⠀⠀⢀⣀⣴⣶⡿⢟⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣍⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣷⣄⣤⢶⣾⣿⣿⠿⣿⣭⣟⣀⣀⣤⡴⢞⣫⣿⢟⣫⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⠀⢀⣀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢼⣿⣿⣿⠈⢿⡿⠛⠒⣒⣚⣋⣭⣿⣿⣿⣾⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣯⣝⣒⠂⢀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⢧⣿⣿⣿⣿⠀⠀⣿⣿⣿⡿⣟⣿⣿⣿⣯⣵⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣿⣿ ⠀⠀⠀⠀⣀⣤⣤⣠⣴⣿⣿⣿⡟⣾⣿⣿⣿⡟⣠⣾⣿⣿⣿⣿⣿⣿⡿⠟⢋⡡⣴⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢡⣿⣿⣿ ⠀⠀⣀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣹⣿⣿⣿⣿⣿⡟⣽⡿⣿⣯⣿⣯⠀⣠⡶⠋⣼⣿⣿⣣⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣡⣿⣿⣿⣿ ⢠⣼⣿⣿⢟⣿⣿⣿⣟⣿⣿⢯⡿⣿⣿⢳⣿⣟⣾⣿⠃⣿⣿⡟⣿⣿⠋⢀⣼⣿⣟⣽⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢋⣴⣿⣿⣿⣿⡿⢻⣵⣿⣿⣿⣿⣿⣿⢣⣿⣿⣿⣿⣿ ⢸⣿⡿⢫⣿⣿⣿⠇⣼⣿⣿⣾⣥⣿⡇⣾⣿⣿⣿⠏⠸⣿⣿⣿⣿⣿⢀⣾⣿⣫⣾⣿⣿⣿⣦⡙⢿⣿⣿⣿⣿⡿⢋⣴⣿⣿⣿⣿⡿⣫⣾⣿⣿⣿⣿⣿⣿⡇⢧⣿⣿⣿⣿⣿⣿ ⢸⡿⣱⣿⣿⣿⡏⣸⣿⣿⣿⣿⣾⣿⢰⣿⣿⣿⠁⠀⢠⡿⢿⣿⣿⣯⣿⢟⣿⣿⣿⣿⣿⣮⢿⣿⣮⡻⣿⡿⢋⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢀⣾⣿⣿⣿⣿⣿⣿ ⢸⢃⣿⣿⣿⡿⢱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣠⢯⡴⠚⣿⣿⣿⣻⣿⣿⣿⣿⣿⡿⣻⣾⣿⣿⣿⣮⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⣼⣿⣿⣿⣿⣿⣿⣿ ⢈⣼⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⢻⣯⣽⣿⣿⣿⠘⡵⠋⠀⠀⣽⣿⣿⣿⣿⣿⣿⣟⣭⣾⣿⣿⣿⣿⣿⣿⣿⢛⣵⡿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣸⣿⣿⣿⣿⣿⣿⣿⣿ ⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣈⣀⡀⢀⣼⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⢟⣴⡿⣫⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢡⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣯⣿⣿⡇⠾⢃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣷⡿⢋⣾⢟⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠴⠒⠒⠛⠛⠋⠋⠓⠢⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡤⠒⠉⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠈⠑⢄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣰⠋⠀⠀⠒⠒⠀⠐⠒⠒⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⠀⠀⠀⠀ ⠀⠀⢀⣴⡿⡄⢀⡀⠀⠀⡠⠔⠂⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀ ⠀⢠⡿⠛⠓⠂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀ ⠀⣼⠃⠀⠀⠀⠀⢀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡰⠁⠀⠀⠀⠀⠀⢹⠀ ⣸⣏⡎⠀⠀⠀⠈⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡏⢆⠀⠀⠀⠀⠀⠀⠀⣇ ⣿⠏⣷⣤⠤⠤⢀⢸⠀⠀⢀⣀⣤⣤⣤⣤⣤⡶⠚⠋⠀⠀⠠⠀⠀⠀⠀⠀⠀⢸ ⣿⣦⠼⣿⣄⣿⣾⡿⠍⠉⣿⣿⣿⡿⢫⡥⠙⡇⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⢹⣿⣄⠙⠻⢿⣿⡆⠁⠸⡟⡻⢿⣤⣈⣉⣸⣧⠞⠁⠸⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⠈⣿⣿⣷⡄⣠⣿⡣⠀⢠⠆⡿⠷⢭⡉⠓⠛⠁⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣸⠀ ⠀⠹⣿⣿⢿⣿⡖⣿⢀⠟⠊⣉⠉⠱⡌⢆⠀⢀⣠⠤⠂⠀⠀⠀⠀⠀⠀⢠⠇⠀ ⠀⠀⠙⣾⣿⣯⢣⠈⠻⡆⠀⠀⡇⠀⢡⠘⠶⡿⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀ ⠀⠀⠀⠀⠙⢿⣆⠱⡀⢰⠀⠀⠘⣄⠀⡆⠀⡃⠀⠀⠀⠀⠀⠀⢀⣼⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⠧⣅⣼⡏⢹⠉⣯⡕⡎⡰⡍⣮⠥⠀⢀⣠⠔⠉⠀⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠾⠶⣛⣃⣓⣘⣓⣷⠶⠒⠉⠀⠀⠀⠀⡇⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣴⣦⣦⣦⣶⣤⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠟⠋⠉⠀⠀⠀⠀⠀⠀⠙⠉⠁⠈⠉⠛⠛⠻⠿⠿⢶⣦⣀⡀⠈⢿⠿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢷⣼⣇⠈⠙⢷⣄⠀⠀⠀⠀⠀⠀⣀⣀⣀ ⠀⠀⠀⠀⠀⣴⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠈⠀⠀⠀⢻⣆⢠⣦⣤⡶⠛⠋⣿⠇ ⠀⠀⠀⢀⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠟⠁⠀⠀⢸⡇⠀ ⠀⠀⣰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⢸⡇⠀ ⠀⢰⣟⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡆ ⠀⠈⠉⠻⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠄⠀⢹⡇ ⣠⣤⣀⠀⠿⣿⡀⠀⠀⢐⡆⠀⠀⠀⠀⠀⢀⣤⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣷⣄⠀⠀⠀⠀⠀⠀⣀⣴⣶⡟⠋⠁⠀⠀⢸⡇ ⣿⣯⠙⠻⣷⣿⠃⠀⣠⣾⢿⡆⠀⢀⣤⡾⠟⠁⠘⢿⡀⠀⠀⠀⠀⠀⣀⣴⠿⠉⠀⠀⠹⣷⣄⠀⣀⣴⠾⠋⠉⢹⣿⡀⠀⠀⠀⣿⡇ ⠙⣿⠀⠀⠀⢠⢞⣼⠟⠁⠀⣧⣴⠟⠁⠀⠀⠀⠀⠘⣷⡀⠀⢀⣴⡾⠋⠀⠀⠀⠀⠀⠀⠈⠛⠿⠋⠁⠀⠀⠀⠀⣹⡇⠀⠀⢰⡿⠁ ⠀⢹⣆⠀⠀⢸⡿⠃⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠘⢿⡴⠟⠁⠀⠀⠀⢀⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⢀⣿⠁⠀ ⠀⠈⠻⢷⣶⣼⣇⠀⠀⠀⠀⠀⠀⣤⣤⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⣾⠃⠀⠀ ⠀⠀⠀⠀⠀⠙⣿⠁⠀⠀⠀⠀⠀⢻⣿⡟⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣦⣀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣾⠇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⢠⣶⣶⠶⠾⠟⠛⠉⠙⣿⠙⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠏⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⢿⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣆⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣤⣀⣠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⠀⠀⠀⠀⠀⠀⢀⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠃⠀⠀⠀⠀⠀⠀⠀⣿⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠶⣦⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⠾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠻⠶⠶⠶⠶⠶⠾⠛⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠛⠛⠳⢶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⠀⠀⠀⠀⣤⡶⠛⠛⠛⠻⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠀⠀⠀⠀⠀⢹⣧⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣨⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⠀⠀⠀⠀⠀⠀⠀⣿⣇⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⠀⠀⠀⠀⣿⢀⣤⣤⡶⠾⠛⠁⠀⠀⠀⣠⡶⠟⠛⠛⠻⢷⣄⠀⠀⠀⠀⠀⠘⢿⣄⡀⠀⠀⠀⢀⣾⠋⢻⠀⠀⠀⠀⠀⠀⠀⠟⠀ ⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⠀⠀⠀⠀⠀⠀⢹⣧⠀⠀⠀⠀⠀⠀⠹⢧⣤⡴⠾⠛⠁⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⢿⣆⠀⠀⠀⠀⠀⠀⣸⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠠⠀⠀⠀⠀⠀⢀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠶⢄⣤⣴⠾⠏⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⠀⠀⠀⠀⠀⠸⣧⠀ ⠀⠀⠀⠀⠀⠀⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢷⣄⡀⠀⠀⣀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢉⢉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⡙⠛⠛⠋⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠒⠒⠒⠒⠒⠒⠒⠒⠦⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠣⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⣤⣀⣀⠔⠁⠀⠀⠀⠀⠀⠀⢀⣠⠴⠒⠉⠉⠉⠀⠉⠉⠑⠢⣀⠀⠀⠳⡀⠀⠀⠀⠀⠀ ⠀⠀⠈⢣⠀⠀⠀⠀⢠⡤⢤⡶⠖⠛⠛⠀⠀⠀⠀⠀⠀⠑⠒⠢⠤⡀⠈⢢⡀⠀⠙⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠱⢄⠀⢀⠎⠀⣀⠔⠒⠒⠒⠤⡀⠀⠀⠀⣠⠔⠒⠐⠒⠢⣀⠀⢣⠀⠀⡇⠀⠀⠀⠀ ⠀⠀⠀⣶⣶⣾⣿⣾⣶⣾⣷⣶⣶⣶⣶⣶⣾⣶⣶⣾⣷⣶⣶⣶⣶⣶⣾⣷⣾⣷⣶⣿⣶⡆⠀⠀ ⠀⠀⠀⠛⣿⣿⣴⣻⣶⣛⣿⣿⣿⣿⣿⣿⣿⡇⠀⢿⣿⣜⣻⣶⣻⣿⣿⣿⣿⣿⣿⣿⡿⠛⠀⠀ ⠀⠀⠀⠀⠈⢹⢿⣿⣾⣿⣶⣿⣿⣿⣿⣿⠟⠁⢀⠘⢿⣿⣷⣾⣿⣾⣿⣿⣿⣿⠿⡏⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⣏⠘⡏⠉⠉⠉⠉⠉⠉⠉⠁⠀⢠⣀⣱⠀⠈⠉⠉⠉⠉⠉⠉⠉⡿⠀⡽⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠒⢾⡀⠀⠀⠀⠀⣠⣤⣄⣀⣀⢀⣀⣀⣤⣤⣤⠀⠀⠀⠀⢠⠗⠚⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠃⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣀⠀⠀⠈⠉⠛⠛⠛⠛⠛⠉⠁⠀⠀⣠⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠛⠛⢲⠤⢤⣀⣀⣀⣀⣀⡠⠤⡖⠛⠛⠲⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⢠⠟⡦⠶⣿⡧⠤⣼⣿⠓⢤⠟⡄⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⡀⢾⡀⠀⠀⢣⢱⢴⡏⡞⠀⠀⢀⡵⡄⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢈⡇⠀⡇⠀⢈⡱⠂⠘⣾⡀⣿⠃⠀⠾⡁⠀⣸⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⡇⠀⠈⠢⡀⠀⢹⠀⡞⠀⢀⡴⠃⠀⣻⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀ ⠐⠚⣷⣤⡶⢷⣤⡀⢸⠀⢰⠇⠀⠀⠀⠑⡄⠈⣯⠗⡾⢿⡖⣶⠋⢹⠀⣶⡇⢀⣴⣶⠀⠀⠀⠀ ⢀⡤⣿⣿⣇⣀⣽⡿⣯⡴⣶⣤⣀⣴⠶⣦⣼⣆⠛⣰⢁⣿⠾⣿⠀⠘⢲⣷⠿⢾⣿⠖⢀⣤⢶⣄ ⠈⠻⣿⣿⡇⠀⢼⡇⢸⡇⠀⣿⠀⣿⠀⢸⡇⠘⠒⠁⠨⣿⢠⡟⠀⠀⠀⣿⠀⢸⣿⠀⠀⣿⠴⠋ ⣠⡴⣿⣿⣿⣶⡾⠃⠸⢷⣤⠿⠀⢿⡦⢺⣇⠀⠀⠀⣠⡿⠿⢶⣶⡤⠀⣿⠄⠸⢿⡤⠠⢿⣦⠴ ⠀⠀⢿⢿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠾⠷⠶⠿⠃⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⠁⠀⠒⠂⠠⠄⣀⠀⡘⠉⠢⢀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡤⠤⠀⣀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠈⠢⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢱⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⢲⠀ ⠀⠀⠀⠀⠀⠀⠤⠀⠦⡀⠀⠀⢤⡀⠀⠀⢠⡀⠀⠀⢠⠀⠀⠀⠀⠀⠁⠮⡀ ⠀⠀⠀⠀⠀⠘⠄⠀⠀⢘⠁⠒⠘⠈⠁⠒⠨⠀⠁⢲⠬⠆⠠⣶⡄⠀⠀⡎⠁ ⠀⠀⠀⠀⠀⠀⠈⠢⢠⠊⡀⠈⡆⢸⢧⠀⠈⠑⡄⠀⡆⢠⢹⣧⢡⠀⢩⠁⠀ ⢰⡲⡊⣶⢋⡀⠀⠀⠈⢄⣀⠔⠁⠀⠒⠀⠒⠊⠀⡀⠰⡆⡾⠼⠂⢀⠎⠀⠀ ⠈⡦⠓⠂⠉⠁⠀⠀⠀⠊⠤⣤⣤⣤⠤⠤⠐⠂⠁⠀⠀⡜⠀⠀⠀⡈⠆⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠉⠁⠀⠀⠀⠀⠀⢀⠜⠀⠀⠀⢀⡩⠂⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠒⠈⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⡀⣄⣲⣦⣤⣴⣂⡠⢀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⢔⣵⡿⣛⣻⣿⣛⡻⣿⣿⣷⣕⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⣰⡮⠿⢷⡮⢖⠒⣪⣝⣛⣒⡹⡿⣿⣎⠄⠀⠀⠀⠀ ⠀⢀⢮⡿⡡⣤⡀⠀⢈⢶⣉⠉⠁⠲⡙⢯⠹⡞⢿⡞⢄⡀⠀⠀ ⠀⠘⣿⣇⠳⠾⠇⠀⣎⢯⣽⡇⠀⠀⢸⢸⣠⣿⠿⠉⠑⢪⢆⠀ ⢀⢜⣟⣙⣫⡖⠒⠈⠉⠢⠄⠀⠤⢒⠕⠁⣿⣿⣧⡞⠙⡽⡇⡆ ⢸⢏⠴⣶⣦⣤⣭⣉⡒⠢⠬⣉⡉⠁⠀⠀⢻⣿⣽⡓⠶⢁⣇⡇ ⠀⠳⢕⡦⣙⠻⣿⣿⣿⣿⣶⣦⣍⡓⠤⡀⠀⣿⣿⣷⢖⣫⠾⠁ ⠀⠀⠀⢨⡸⢰⡿⠛⢋⠽⠛⠻⢿⣿⡦⢸⣰⣟⣟⡾⠉⠁⠀⠀ ⠀⠀⠀⡌⡇⣾⠁⠀⠀⠀⠀⠀⢀⡽⢡⠏⣨⢎⡾⠁⠀⠀⠀⠀ ⠀⢀⣀⡁⡇⣿⠀⢀⣤⣤⡄⢴⣯⢴⡧⣞⡵⠋⡀⠀⠀⠀⠀⠀ ⠀⢊⠉⡍⠻⠛⠛⡿⠁⣤⡜⢁⣠⣉⡞⣓⠉⡍⣹⠟⣛⣷⠀⠀ ⠀⢸⡀⢠⣆⠸⢃⣇⡈⠻⠀⡸⠯⠀⡘⢚⣃⣧⣈⠓⠂⢱⡃⠀ ⠀⠘⠿⠿⠛⠛⠓⠛⠷⠶⠮⠵⣶⡮⠗⠚⠛⠛⠛⠫⠭⠿⠃⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠁⠀⠈⢷⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡎⠒⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠈⠳⣄⠀⢀⡼⠿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⣠⠀⢠⡏⠀⠀⠀⠀⠀⠀⣀⣀⠨⠷⠮⠤⢬⣇⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀ ⠀⠀⠀⠐⠂⠀⠈⠂⠀⠀⠀⠀⠀⣈⣁⠀⡸⠀⠀⢀⣠⠴⠚⢉⣠⡤⠔⠒⢲⣦⣤⣌⡑⠦⣀⣀⠤⠖⣿⠁⠀⠀⠀⠀ ⠠⠄⣀⡀⠀⠀⠀⠀⠀⢀⡤⠚⠉⠁⠀⠈⠁⣠⠖⠉⣠⠴⠚⣋⠤⠖⠒⠉⠉⠉⠉⠉⢿⣶⡈⢧⠀⢀⠇⠀⠀⠀⠀⠀ ⠀⠀⢀⡽⠚⠁⠀⠀⣠⠎⠀⠀⠀⠀⢀⡤⠊⣠⠴⢋⡡⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣷⣸⡤⠊⠀⠀⠀⠀⠀⠀ ⠀⢠⠎⠀⠀⢀⡤⠚⡏⠀⠀⠀⢀⡴⠋⣠⣾⣡⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡞⠀⠀⢀⠎⠀⠀⡇⠀⢀⡴⢋⣴⣿⣿⠟⠉⠀⠨⠕⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠃⠀⣠⡄⠀⠀⠀⠀ ⠀⡇⠀⠀⠘⠀⠀⠀⣁⡴⢋⣴⣿⣿⡟⠁⠀⠉⠀⣀⠠⢤⣚⣳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣂⡂⠛⡅⠀⠀⠀⠀⠀ ⠀⢃⠀⠀⠀⠀⠀⠀⣿⣴⣿⣿⣯⠀⢇⠀⠀⣤⠶⠒⠋⠉⠀⢀⣤⣬⡍⠑⠲⡖⠒⠒⠒⢠⣶⡟⠛⡄⠸⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⡹⢿⡈⣿⡇⢸⠀⠀⠈⠓⢄⡀⠀⠀⠘⠿⠷⠏⠀⠀⣧⠀⠀⠀⠙⠷⠟⠀⣷⠀⢣⠀⠀⠀⠀ ⠀⠀⡆⠀⠀⠀⠀⠀⡜⢀⡾⠁⢿⣇⠸⡀⠀⢀⠀⠙⠮⣑⠲⠤⠤⠀⠠⢤⠞⢧⡉⠶⣒⣤⠖⢒⣺⠿⡄⠈⡆⠀⠀⠀ ⠀⠀⢠⠀⡆⠀⠀⢠⡇⢸⡇⠀⠀⠙⢷⣽⡀⠀⠑⠒⠤⠤⠬⢥⠴⠶⠒⠉⠀⠀⠙⢶⠤⠚⠂⢸⡅⠀⠱⡄⠘⢄⠀⠀ ⠀⠀⢸⢀⠇⠀⣠⢄⣱⣼⡇⠀⠀⠰⢫⡞⠉⠉⠒⠢⠤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢀⣀⠽⡗⠤⣘⣦⡈⠓⠀ ⠀⠀⠇⠀⢀⡴⠁⠀⠀⢹⡇⠀⠀⠀⠈⢳⡀⢿⡶⠤⣄⣀⡀⠈⠉⠓⠒⠒⠒⠒⠒⠒⠈⠉⠁⣠⣞⣹⠀⠀⠈⠉⠉⠂ ⠀⠀⠤⠒⠉⠀⠀⠀⠀⠸⣷⡀⢀⠀⠀⠀⠙⠢⡉⠓⠶⣟⡛⠛⠿⣅⡒⠒⠒⣶⠋⠉⠉⠓⡄⠑⡄⠹⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣄⠀⠀⠀⠀⠉⠲⠤⣀⠉⠙⠒⠊⠻⠶⠾⠯⠤⠤⠔⠚⢁⡤⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢦⣄⡀⠀⠀⠀⠀⠉⠓⠢⠤⠤⠤⠒⠒⠒⠂⠀⣩⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠒⠲⠦⠤⠤⠤⠤⠤⠐⠒⠒⠒⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢠⣄⡤⢷⣶⠿⢹⣄⣀⣀⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣼⣿⠛⠉⠙⠁⠀⠀⠀⠀⠀⠉⠉⠹⢿⠄⠀⠀⠀⠀ ⠀⠀⠀⠀⣼⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠿⢴⣶⠀ ⠀⠀⢠⠖⠁⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢀⣴⣋⣀⠀⠀⠀⣰⠋⠀ ⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⢹⠑⠒⠒⠚⠉⠀⠀⠈⠉⠻⢿⢹⡁⠀ ⢀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣷⠀ ⠸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣱⠇⠀⠀⢀⣤⣶⣶⢤⣀⠀⠀⣠⣹⡀ ⠀⢸⡇⠀⡀⡀⠀⠀⠀⢀⣾⠃⠀⠀⠀⠛⠉⣼⣤⠀⠀⠀⣸⡋⣝⠁ ⠀⠘⣷⢸⣿⣿⣗⢦⡀⢘⣇⠀⠀⠀⠀⠰⠊⠀⣿⠗⠀⠸⡷⠺⣞⠂ ⠀⠀⠹⡘⡽⢰⣿⡏⢻⣌⣻⠀⠀⠀⠀⠀⠀⠉⠛⠀⠀⠀⠃⠐⣏⠀ ⠀⠀⠀⢳⠹⣌⠁⠳⣾⣆⣿⢲⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⣄⣸⠀ ⠀⠀⠀⠈⡇⠈⡷⠴⠃⠙⠋⠀⠀⠀⠀⠀⠀⠀⠈⠙⠚⠳⣴⢫⠏⠀ ⠀⠀⠀⠀⠷⢼⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⣈⡽⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠶⣶⣿⡇⡿⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⣢⠇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡴⠃⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣠⣀⣀⣤⣄⣠⣄⣠⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣴⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠟⠋⠁⠀⠀⠀⠀⠀⠉⠙⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢠⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⢀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣿⣿⠆⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠏⠀⢸⣷⣤⣄⠀⠀⢀⣠⣾⣿⣍⣉⠀⠀⠈⠛⠒⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣤⣉⠃⠀⠀⠁⣀⣉⣉⠛⠷⠄⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⡟⠁⠀⠘⣆⣀⣠⠾⠋⠉⠉⢳⣄⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⡀⢀⣼⠉⢷⠀⠀⠀⠀⠀⢻⣷⣤⣤⣿⣿⣿⣿⣿⣿⣿⡿⢛⣉⣍⢻⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⢠⡿⠃⠀⠘⢧⣄⣀⣀⡴⠏⠉⠉⢹⣷⣿⣿⣿⣿⣿⢋⣴⣿⠉⢹⠏⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣠⡟⠀⡀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⣸⣿⣿⣿⠿⠁⢻⣿⡿⠁⠀⣶⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⠟⠠⣞⣻⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⡟⠁⠀⢀⡼⠋⠀⠀⣼⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣁⣀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⣿⣿⠃⠀⠀⠀⠙⠂⢀⣴⡿⠃⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡜⢿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠟⠀⠀⠀⠀⠀⣠⣾⣿⣁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢀⣿⣿⣿⣿⡷⢶⡆⠀⠀⠀⠀⠀⠚⠉⠁⠀⠀⠀⠀⣠⣾⣿⠟⢰⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⢸⡛⠛⠛⣁⣴⠏⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⡶⠿⠛⠉⠀⣠⣾⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡟⠉⠀⠀⠀⠀⠀⣾⠛⠛⠛⠉⠉⠉⠁⠀⠀⠀⣠⠞⣱⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡤⠒⠚⣿⡄⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢀⣀⣤⣾⣷⣿⣿⣿⣿⣿⣿⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠈⠻⣶⣤⣤⣤⣤⣾⠟⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡶⢾⣿⣿⣟⣻⡾⢧⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣤⣦⣄⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⡇⠀⢻⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶ ⠀⠀⠀⣠⣤⣤⣴⣿⣿⣿⣿⣿⣿⣇⣴⣿⣿⣿⣿⡿⠿⢛⡥⣴⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣵⣿⣿ ⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣤⡴⢋⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣼⣿⣿⣿ ⣼⣿⡿⣿⣿⡿⣹⣿⣿⣟⣿⣿⣿⣿⣿⠁⣿⣿⣿⣿⢀⣾⣿⣿⣿⣿⣟⢿⣿⣿⣿⣿⡿⣫⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿ ⣿⡏⣾⣿⣿⢣⣿⣿⣿⣿⣿⣸⣿⡿⠁⢀⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣷⣽⣿⡿⣫⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢰⣿⣿⣿⣿⣿ ⠿⣼⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣧⣠⣿⠞⠹⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢡⣿⣿⣿⣿⣿⣿ ⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠖⠁⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣫⡾⣫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣾⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠹⠗⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⢏⡾⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⠶⠶⠶⠿⠿⠿⠛⠻⠛⠳⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠶⠚⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠋⠀⠀⣀⣀⣀⡀⠀⠀⣀⣀⣀⣀⣀⠤⠄⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣾⠋⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⣾⣿⣇⠀⡀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠒⠒⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀ ⠀⠀⠀⣠⣾⣿⣿⣋⣙⠉⠉⠑⠂⠀⠀⠀⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣄⠀⠀⠀ ⠀⠀⢠⣿⡿⠉⠙⠉⠉⠑⠤⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀ ⠀⠀⣼⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠀⠀⣠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀ ⠀⣼⣿⡇⢠⠀⠀⠀⠀⠀⠠⣀⣠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀ ⢰⣿⡏⣴⠋⠀⠀⠀⠀⠀⠀⠀⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀ ⣾⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⢘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⣿⠏⠀⠈⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿ ⣿⣿⠇⢻⣿⣷⡶⠒⠒⠦⢤⡀⠀⣇⠀⠀⠀⢀⣀⣤⣴⣶⣶⣶⣶⣶⣿⣿⣿⠟⠋⠉⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿ ⣿⣿⡄⠀⢻⣿⣧⡀⢿⣿⣤⣿⣿⡏⠛⠉⢹⣿⣿⣿⣿⣿⣿⡿⢛⣁⠉⠙⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿ ⢹⣿⣿⡏⠙⣿⣿⣿⣾⣿⣿⣿⠋⣭⠀⠀⣼⣿⣿⣿⣿⡿⠋⠀⢸⣿⣹⠀⣿⠀⣀⣠⡴⠶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏ ⢸⣿⣿⣧⡀⠈⠙⠿⢿⣽⣿⣿⡀⠈⠁⠺⠿⠏⠉⠿⢿⣷⡦⣄⣀⣉⣁⣼⣿⣶⠟⠋⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀ ⠈⢿⣿⣿⣿⣷⡄⠀⠀⢸⣿⣿⡷⠀⠀⠀⢀⠛⢻⣶⣮⣙⠻⠿⠯⣬⣩⢿⠟⠁⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀ ⠀⠈⣿⣿⣿⣿⣿⣆⢠⣾⡿⢿⣿⠀⠀⢀⡿⢁⣼⣟⣛⣛⠻⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀ ⠀⠀⠹⣿⣹⣿⣿⣿⣿⣿⡧⢤⣿⠀⢀⡾⠿⠋⠉⠉⠉⠉⢻⣄⠙⢦⠀⠀⠀⠀⠀⣀⣠⠴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡇⠀⠀ ⠀⠀⠀⠻⣿⠟⣿⣿⣿⡿⣇⠀⢿⣦⣾⡃⠀⠀⠈⢳⡄⠀⠀⢹⡆⠈⣧⠀⣠⡶⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠏⠀⠀⠀ ⠀⠀⠀⠀⠘⣿⣿⣿⣿⣧⠙⣧⠀⠈⢻⡧⠀⠀⠀⠀⣇⠀⠀⠀⢷⠀⠘⠛⢻⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⡆⠘⢧⡀⠀⢹⡀⠀⠀⠀⠈⣆⠀⠀⠘⡆⠀⠀⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣦⠈⢣⠀⢸⣧⠀⠀⠀⢀⣘⣷⣄⠀⢳⡀⠀⣣⡀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠻⣇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣬⠇⣸⣯⡏⠉⢹⠉⠈⣯⢨⠿⡏⢩⣹⢡⠙⡏⣭⣱⠀⠀⠀⠀⢀⣤⠾⠋⠀⠀⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⣭⡇⣄⢸⣀⢀⣿⣸⠀⣇⣰⢣⣘⣀⣇⣃⣈⣀⣠⡴⠞⠋⠁⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠳⠶⣤⣤⣤⣤⣤⣤⣤⣤⣴⣿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢘⡇⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠀⠀⣀⡀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡛⠁⠀⠀⠀⢀⡤⢤⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⢈⣟⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⠉⢀⡀⠀⠀⠀⠀⣀⣤⡄⠀⣀⣀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿ ⠀⠀⠀⠀⠀⠀⠘⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠟⠛⠀⢺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠿⠓⠒⠋⠀⠀⠀⠀⠀⠀⠙⠰⣤⣄⣉⠁⠀⠀⠀⠀⠀⠀⠀⠻⣿ ⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⢤⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘ ⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⣀⣀⣀⣀⣀⣀⣀⣴⠓⠐⢀⣀⣀⣐⡀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⡏⠀⠀⠀⠀⠀⠀⠹⣿⣤⣐⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣷⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⣧⣀⣀⣀⣀⣀⣀⣀⣀⣨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⣰⢏⣴⣿⡟⠛⠛⠛⠛⠛⠛⠛⢿⡏⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣶⣷⣶⣶⣶⣿⣿⣿⣿⡆⢀⡴⠋⣿⣿⣿⡇⠀⠀⣤⡄⢠⣤⠀⢸⡇⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣷⠏⠀⠀⣿⣿⣿⡇⠀⠀⣿⡇⢸⣿⠀⢸⡇⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀ ⠐⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣼⣿⠀⠀⠀⣿⣿⣿⡇⠀⠀⠈⠁⠀⠉⢠⣾⡧⠀⠀⠀⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀ ⠀⠈⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⣴⡇⣿⠀⠀⠀⣿⣿⣿⣷⣶⡆⢀⣴⣶⣶⡿⠋⠀⠀⠀⠀⣷⠸⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⢻⣿⡿⠿⢿⣿⣿⣿⣿⡇⡄⠰⣿⠁⣿⠀⠀⠀⣿⣿⣿⣿⣿⣷⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⣿⠀⢻⡏⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⢠⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠛⢷⠀⠀⠀⠀⠀⠀⠚⢿⠀⣿⠀⣿⠀⠀⠀⠀⠀⠀⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡟⠀⢸⣧⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⡏⢀⡾⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠘⢦⣀⠀⠀⠀⠘⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⡾⠁⠀⠘⣿⠀⠀⣿⣿⣿⣿⣿⡿⢫⠟⢀⡾⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠉⠛⠓⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠚⠋⠁⠀⠀⠀⠀⢸⡞⢷⢿⣿⠟⠛⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠛⠈⠁⠀⢠⠞⠀⢠⡞⢀⠀⢠⡆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⠈⠐⠈⣀⣠⣶⣏⡴⢋⡴⡿⠀⠀⠀⠀⠀