Totoro Sundae Emojis & Text

Copy & Paste Totoro Sundae Emojis & Symbols ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣀⠀⠀⠀⠀⠀⣴⣄⡰⣶⠀⠀⠀⠀⠀⠀⢠⣄⣠⣶⣼⣿⣷⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣀⠀⠀⠀⠀⠀⣴⣄⡰⣶⠀⠀⠀⠀⠀⠀⢠⣄⣠⣶⣼⣿⣷⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⣿⠟⠉⠻⣿⣷⣴⣶⣿⣷⣿⣷⣿⣷⣶⡄⠀⢀⣴⣿⣿⣿⣿⣿⣿⣋⣿⣿⣤⣀⣀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⣷⣄⢀⣠⣿⣿⣿⣿⢏⠩⣉⠍⣿⣿⣿⡇⣠⣿⣿⡟⢫⢹⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣧⣀⣠⣶⣶⣿⣿⣿⣿⠿⠿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⡎⠐⠁⠈⠙⣿⣿⣷⣿⡿⡓⣌⢣⢺⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⣹⣿⣿⣧⠀⠀⣼⣿⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⢛⠛⣻⡇⠀⠀⠀⠀⣿⣿⣿⣿⣿⡷⢌⢶⣿⡇⣾⡽⣿⣿⡛⢿⣿⣏⣼⣿⡟⠀⠀⠀⣧⣿⣿⣿⣷⣾⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡇⠎⠐⠁⢁⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⡞⠻⠻⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠌⠐⣼⣿⣿⣿⣿⡿⠛⣽⣿⣿⣷⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⠀⠀⠀⠀⣴⢀⢣⠐⣻⣿⡿⠛⠋⠁⠀⢀⠀⠀⠉⠉⠉⠈⠉⠉⠉⠁⠘⠀⠠⠘⠠⢥⣞⣿⣿⣿⣿⣷⣤⡙⣿⣽⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⢻⣿⣿⣷⣦⡐⢮⡹⡆⣠⣾⡟⠃⠀⡀⠄⠂⠈⠄⡐⠈⠀⠄⠀⠂⢀⠐⢄⠂⠡⠌⠄⠡⠐⣾⣿⣿⣿⣿⣿⣆⢻⣿⣿⠟⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⣾⠿⠿⣿⣿⣿⣿⣿⣿⣿⡔⠡⢋⣵⡿⢋⠜⠿⠿⠿⠷⠈⢀⠐⣴⡄⠂⠰⣬⣤⣄⣀⠀⠈⡐⠈⠄⠃⠸⣝⢦⢻⣏⣿⣿⡏⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⣾⣿⣷⣄⣠⣼⣿⣿⣿⣿⣟⣿⣷⣤⣿⠟⡱⢨⠘⠠⠀⠀⢀⠠⠀⡀⠀⠀⡀⠄⠉⠛⠿⢿⣶⣥⣀⡠⠀⢁⢿⣩⠞⣷⡏⠙⢿⣷⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⣽⣿⣿⠏⠀⣁⡎⠐⠀⡀⠂⢬⠤⠦⠁⢦⣠⠁⠀⡀⠀⢀⠨⣿⡟⠿⣷⣆⡸⡬⢏⣶⣿⠁⠀⠸⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣾⣿⣼⣿⠛⣻⣿⣿⣿⣿⠁⣛⣮⣽⣻⣿⠏⠀⠀⠄⠙⢣⣴⠀⠁⠀⠀⠀⠀⠀⠈⠙⢤⣶⡷⠀⠱⣿⡇⠀⠈⠻⣿⡿⠟⠉⠋⠀⠀⢠⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⢿⣿⣡⣼⣿⣿⣿⣿⣏⡽⣳⣼⣳⣿⡿⠁⠀⠌⠈⢀⢠⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠁⢹⣿⡆⠀⠀⢁⠀⠀⠀⠀⠀⣠⡄⠑⢿⣷⣦⣄⡀⠀⠀⠀⠀⠀ ⠀⠀⢹⣿⣿⣿⡿⠋⣿⢮⣷⣻⣞⣧⣿⡇⠀⠈⠀⡐⠤⠞⠁⠀⠀⠀⠀⠀⠐⣤⣀⣰⣿⣇⣀⣈⣄⣼⣿⠁⠀⠀⣼⣷⡄⠀⠠⠀⠿⠿⠀⠀⠹⣟⠻⢿⣶⣄⠀⠀⠀ ⠀⠀⠀⣿⣿⡏⠀⢸⣿⣻⣞⣷⣹⣾⣿⠁⠀⠁⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠹⣿⣴⡟⠟⠉⣹⣿⠇⠀⠀⠀⠈⠋⠁⠀⠀⠀⠀⠀⠀⠀⠠⢹⣧⠈⠙⣿⣷⡀⠀ ⠀⠀⠀⣿⣿⠀⠀⠀⣿⣷⣻⣞⡷⣿⣿⠀⠈⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀⠀⠀⠀⠀⠀⠐⣿⣯⠀⠐⠠⠀⠀⠀⠀⠀⠀⠐⠀⠀⠂⠀⠀⢀⣿⡇⠀⠘⣿⣧⠀ ⠀⠀⠀⢸⣿⡀⠀⠀⠈⠻⣿⣾⣿⣿⣿⣇⣤⣦⣤⣤⣤⣤⣄⠀⠀⠀⣾⠋⠀⠐⠂⠀⠀⢠⡄⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠈⠁⠀⣿⣿⡆ ⠀⠀⠀⠀⢻⣷⣆⡀⠀⠀⠀⠈⠉⠙⠛⠛⠋⠉⠉⠉⠉⠉⠛⠛⠷⣾⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣷⣶⠷⡾⢷⣦⣤⣤⣤⣤⣤⣤⣤⣴⠾⠋⠁⠀⠀⣰⣿⡏⠀ ⠀⠀⠀⠀⠈⡟⣿⣷⣶⣤⣤⡀⠀⠀⠀⢀⣀⣤⣤⣤⣄⣀⡀⠀⠀⠈⠙⠻⢶⣤⣄⣀⣤⣤⣴⡾⠛⠉⠁⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⣀⣾⣿⡏⠀⠀ ⠀⠀⠀⢠⣶⡿⠋⠻⣿⣿⣆⠁⠀⠉⠉⠁⢀⠀⡀⠀⠈⠙⠛⢷⣦⡀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⡤⠤⢶⣾⣿⠟⠋⠀⠀⠀ ⠀⠀⠀⠘⢿⡄⠀⠀⣿⡿⣿⣦⡀⠀⠀⠀⠘⡦⢑⠪⡝⠶⣤⡀⠈⠛⢷⣦⣀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠾⠛⠋⣉⢀⡀⠀⠤⠠⡄⠀⠀⠀⣤⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠻⠶⠟⠋⠀⠈⠻⣿⣄⠀⠀⠀⢣⠈⠐⠈⠒⢉⡙⠶⢦⠄⡈⠙⠛⠶⢶⠶⡶⠶⠛⠋⠉⡠⡐⣌⠲⢡⠀⠀⠥⠀⡱⠇⠀⢀⣾⣿⡿⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣦⠀⠀⠀⠉⠑⠂⠈⠀⠁⠢⠜⣨⢙⣓⠢⢤⠀⡄⠠⢄⣲⠈⣁⠀⠑⠀⠧⠁⠈⠠⢤⡜⠁⠀⢀⣿⣿⠛⡛⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠀⠋⠜⠉⠚⠀⠁⠀⠀⠀⠉⠐⠀⠀⠀⠀⠀⠀⢰⣾⣿⠏⣼⣷⣦⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⡏⣤⣽⣿⣦⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣆⠀⠀⠡⠃⢀⡀⣀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣧⣄⠟⠃⣼⡿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣄⠀⠀⠐⠀⡰⠡⢒⢌⠲⢄⡒⠤⠣⢜⡠⢃⠞⠤⡋⡔⢢⡑⠮⠑⠀⠀⣀⣾⣿⣿⣿⣿⣿⣿⣶⡿⠟⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣧⡄⠀⠀⠁⠤⣀⡄⡠⡐⣌⠣⡙⢤⢊⠥⣊⠅⠆⠉⠐⠈⠀⠀⣠⣴⣿⠛⣛⡛⠛⣛⠛⢻⣿⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⣀⠀⠀⠀⠘⠱⠰⣌⢡⠓⡌⢆⢣⢀⡈⠖⠀⠀⠀⢀⣰⣿⣿⣿⣶⣿⣶⣶⣿⣤⣼⣿⠇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣷⣤⣀⡀⠀⠀⠀⠀⠉⠀⠈⠀⠁⠀⠀⣀⣤⣶⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⡿⢿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠿⣧⣤⣀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣻⣿⠿⠛⠻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⣿⡙⢿⣄⠘⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣽⣿⣆⠀⠀⠀⠀⠀⣾⣿⣿⣷⡾⠿⢿⣦⡀⣠⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⢻⣷⣀⢉⣶⣿⣿⣶⣄⠀⠀⠀⠀⢠⣴⣶⣿⠿⠛⠛⠉⠏⠀⠀⠀⠀⠸⠀⠘⠛⠻⡿⠿⣷⣿⣿⡿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⣿⣿⠿⠛⢷⣶⣴⣾⠟⠋⠁⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⢽⣷⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣏⠀⠀⢨⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣧⡾⠟⠙⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⠻⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⡿⠟⢿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠷⢶⣶⣦⣤⣤⣤⣤⣤⣤⣤⣶⣶⣶⠿⠿⠻⣿⣅⡠⢶⠮⣹⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠙⠋⠉⠁⠀⠀⠀⠀⠙⣷⣦⣾⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⣀⣀⢀⡀⠀⣀⡀⢀⣀⠀⠀⠀⢀⣀⣀⡀⡀⣀⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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

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