Wolf Furry Big Tit Emojis & Text

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