Even Emojis & Text

⋆ ˚｡⋆୨♡୧⋆ ˚｡⋆─── ⋆⋅☆⋅⋆ ──

⠸⣷⣦⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⠀⠀⠀ ⠀⠙⣿⡄⠈⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠊⠉⣿⡿⠁⠀⠀⠀ ⠀⠀⠈⠣⡀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠁⠀⠀⣰⠟⠀⠀⠀⣀⣀ ⠀⠀⠀⠀⠈⠢⣄⠀⡈⠒⠊⠉⠁⠀⠈⠉⠑⠚⠀⠀⣀⠔⢊⣠⠤⠒⠊⠉⠀⡜ ⠀⠀⠀⠀⠀⠀⠀⡽⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⡔⠊⠁⠀⠀⠀⠀⠀⠀⠇ ⠀⠀⠀⠀⠀⠀⠀⡇⢠⡤⢄⠀⠀⠀⠀⠀⡠⢤⣄⠀⡇⠀⠀⠀⠀⠀⠀⠀⢰⠀ ⠀⠀⠀⠀⠀⠀⢀⠇⠹⠿⠟⠀⠀⠤⠀⠀⠻⠿⠟⠀⣇⠀⠀⡀⠠⠄⠒⠊⠁⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⣿⡆⠀⠰⠤⠖⠦⠴⠀⢀⣶⣿⣿⠀⠙⢄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢻⣿⠃⠀⠀⠀⠀⠀⠀⠀⠈⠿⡿⠛⢄⠀⠀⠱⣄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⠈⠓⠦⠀⣀⣀⣀⠀⡠⠴⠊⠹⡞⣁⠤⠒⠉⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⠃⠀⠀⠀⠀⡌⠉⠉⡤⠀⠀⠀⠀⢻⠿⠆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠰⠁⡀⠀⠀⠀⠀⢸⠀⢰⠃⠀⠀⠀⢠⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢶⣗⠧⡀⢳⠀⠀⠀⠀⢸⣀⣸⠀⠀⠀⢀⡜⠀⣸⢤⣶⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠻⣿⣦⣈⣧⡀⠀⠀⢸⣿⣿⠀⠀⢀⣼⡀⣨⣿⡿⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠻⠿⠿⠓⠄⠤⠘⠉⠙⠤⢀⠾⠿⣿⠟⠋

𓇢𓆸🤞

nobody is even fighting the hell wth are yall blabbering bout there is anything yall 🤷🏾‍♀️,

⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣼⡀⠀⠀⠀⠀⠀⠀⣀⣴⣱⠁ ⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠛⠛⢿⣷⣤⣤⣤⡴⣯⣾⠏⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠁⠀⠀⠀⠀⠀⠉⢻⣮⣗⡿⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠐⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣈⡤⢶⠶⠶⣖⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠀⠀⣸⣿⣻⣶⣋⣓⣆⡀⠀⠀⠀⠀⠀⠀⢀⡠⣴⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⡴⠶⠾⠛⠛⠛⠿⣽⡁⠀⠀⠀⠉⠛⢙⣲⣦⣤⠴⠾⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣶⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

🤫

😂🤣😠⛅🙂😆😛😾😄😶😨💢💢💢💢🤣✌️💯🌈⏰ℹℹ👎❌🌟👍🔥🌟🚀

⢀⠀⠀⣀⠀⠀⠀⢀⡀⡀⠀⠀⠀⢀⡀⣀⣀⣀⣀⣀⠀⢀⡀⠀⠀⠀ ⢻⡜⢰⢇⡃⠀⠀⣽⠟⢁⡚⠀⡂⣤⢀⠉⠙⠚⠿⡣⢹⠀⠙⠀⠀⠀ ⠻⠠⣏⠎⠀⠀⢰⢙⡺⣌⠰⠖⣤⣄⡈⠸⡷⢦⠰⠀⣄⠀⠀⠀⠀⠀ ⠁⣺⣌⠃⠀⠀⠄⣻⣷⣟⢿⣤⡀⣍⣫⣲⣿⣭⢶⣠⢤⡭⡜⠀⢂⡄ ⣠⠗⡌⠀⠀⠐⢡⣿⡿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣷⣄⣀⣀⣤⠜⢤⡂ ⣽⢚⠀⠀⠀⠂⣸⣿⢡⣳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣶⣿⡀ ⢾⠀⠀⠀⠐⢁⣿⢿⡀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡇ ⣻⠀⠀⠀⠐⣸⡇⠀⠈⠈⣿⣿⣟⣉⠑⢾⣿⣿⣿⣿⣿⣿⣿⠿⣿⡇ ⢧⠀⠀⢠⢀⡿⠀⠀⠀⠀⠘⣿⣿⢿⡟⠈⠛⠛⠛⠛⢿⣯⣽⠭⣿⡧ ⠇⠀⠀⡄⣸⠇⠀⠀⠀⠀⠀⣷⠀⠠⣃⣀⣄⠀⠐⣴⣿⡗⠂⠡⣿⡇ ⠀⠀⢠⠀⣿⣀⣤⣤⣤⡁⠀⠈⣷⣴⣿⡿⢿⡼⢗⣹⣿⠁⢨⡁⢾⡅ ⠀⢀⠆⣨⣿⣿⣿⣿⣿⣿⣦⡀⠘⣿⡿⣖⡚⢋⣾⣿⣧⡀⢃⠔⢺⡇ ⠀⠐⢰⣿⣿⠿⢿⠿⢠⣼⣿⣧⣀⣼⣿⣿⣿⣿⠿⣙⣿⣿⣶⣮⣼⡇ ⠀⢋⣼⣿⠑⠰⠖⢀⠚⠾⢿⣿⣿⣿⣿⣿⣿⡉⢖⣡⣗⣿⣾⣿⣿⡧ ⢀⣺⣿⡟⠀⠀⠤⣉⠤⠀⣸⣿⣿⣏⡿⣋⠳⢜⣧⢻⣏⣯⣽⣾⣿⣧ ⢹⣿⣿⣿⣷⡄⣀⢀⣠⣴⣿⣿⠿⣿⣵⣇⣠⣿⣶⣿⣿⣿⣿⣿⣿⡧ ⠘⠛⠿⠛⠉⢒⢍⠍⠛⢿⠿⢏⢮⣷⢿⣿⣿⣟⣿⣹⣸⣧⣿⣿⣿⡗ ⠀⠀⠀⢁⡀⠀⠀⠀⠀⣀⠀⢬⣿⢻⣿⣿⣿⣭⣿⣽⣯⣏⣿⣾⣿⡗ ⠀⠀⢀⣤⣤⣤⡀⠀⠀⠀⢰⣻⣟⠼⣿⣾⣿⣿⡯⣽⣿⣿⣟⣿⣽⡇ ⠀⠀⣯⡊⠁⠚⠁⠀⠀⠙⠀⢻⣇⠉⣻⣾⣿⣿⣿⣿⢿⣿⣿⣿⣿⣇ ⠀⠀⠀⠁⠈⠘⠀⠀⠀⠘⠀⠠⢻⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

🍄🍓🧸🧺🪞🌌🌅🌌🌅

🥰

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣴⡿⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⡿⠁⠀⠀⠀⠀⠀ ⠀⠀⢀⣤⣤⡤⠤⠤⠤⢀⣀⡤⠒⠂⠈⠉⠁⠒⢡⡀⡔⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠉⠛⠿⢦⡀⠀⠀⠀⢀⢄⡀⠀⠀⠀⢠⣲⡙⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠁⠖⠀⠸⠾⠃⠀⠠⠄⠈⠋⠁⡵⣠⠤⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡤⣐⡀⠔⠉⢢⠀⠢⠔⠳⡆⠁⠀⢄⠇⢀⠇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠻⡀⠈⠑⢌⠒⠊⠀⠀⠁⠈⠀⠀⡠⠊⠀⡘⠀⠀⠀⠀⠀ ⡖⠒⠢⠤⠤⠤⠤⢵⡀⠀⠀⠑⠀⠀⠀⠂⠒⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠠⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡃⠀⠀⠀⠀⠀⠀ ⡄⠀⠀⣀⡀⠀⣠⡣⡆⡘⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀ ⠉⠉⠁⠀⡆⠀⣩⠠⡗⡇⣸⠟⢣⡀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠓⠉⢸⡰⣧⠽⡈⡄⢸⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠑⠴⢜⣀⠀⠤⢄⣀⠀⢀⠜⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⠆⠀⠠⡤⠄⠤⣦⠀⠠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠿⠟⠛⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠤⠶⠶⠒⠛⢻⣿⣿⣿⣿⣿⡿⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠴⠖⠚⠉⠁⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⠟⠉⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⢀⣀⡤⠿⠶⠒⠒⠒⠒⠒⠲⠶⠶⠶⢤⣀⣀⠀⠀⣀⣠⠶⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣀⡴⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣽⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠶⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠶⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⣠⡤⠶⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⣠⣶⡶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⠤⠶⠶⠶⠶⠒⠒⡷ ⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⢸⣿⣿⣀⣼⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡏⠉⣿⣶⡄⠀⠀⠀⠀⣿⠀⠀⠀⠀⣀⣠⠤⠶⠖⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇ ⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠘⣿⣿⣿⡿⠏⠀⠀⢠⣤⡄⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⢿⣠⡴⠖⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀ ⠀⠀⠀⠀⠀⠀⢀⣼⠁⠀⠀⠀⠉⠉⠀⠀⠀⢀⣤⣍⣀⠀⠀⠀⠀⠀⠀⠉⠻⠿⠛⠉⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀ ⠀⠀⠀⠀⠀⠀⣸⡏⠉⠳⣆⠀⠀⠘⢷⡶⣶⠛⠉⠈⠉⠳⠦⣄⣀⣤⠖⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣹⡄⠀⠀⠀⣿⠋⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⣶⠋⠁⠈⠙⢶⡀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣇⣀⣴⡟⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠐⣇⠀⠀⠀⠀⢠⣏⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠻⣏⠁⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⣴⠃⠀⠀⠀⠀⠀⠙⠦⣄⣀⡴⠟⢰⠇⠀⠀⠀⠀⣶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡀⠀⠀⠀⠀⠀⠀⢳⣄⠀⠀⢀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⣦⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⢦⣀⠀⠀⠀⠀⠀⠙⠳⠶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠿⡇⠘⢷⡀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠉⠳⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡴⠞⠁⠀⣿⠀⠀⠻⣄⠀⠀⠹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠉⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⢹⣦⠴⠞⠋⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⣀⣠⠶⠖⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣀⠀⠀⠀⠀⠀⢰⡏⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠘⣾⠋⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣾⣿⣿⡄⢀⣴⠶⠛⠓⠶⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⣠⠶⠿⠷⠶⣄⣠⣾⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡿⡟⣯⢻⡏⠁⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠁⠀⠀⠀⠀⣼⢧⣿⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣧⠛⠛⠉⣧⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⣼⠋⠈⠈⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢿⡆⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⣧⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠸⣇⠀⢰⣆⠀⠀⠀⠀⠀⠀⠀⠈⢳⣄⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⣀⡾⠁⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠓⠛⠉⠉⠉⠉⠓⠒⠒⠒⠲⠿⣽⣼⣤⣦⡴⣾⡯⣄⣰⣀⣤⣠⣹⣶⠶⠶⠶⠦⠤⠤⠤⠶⠾⠷⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠀⠀⠀⠈⠉⠉⠉⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⣠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣰⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⠋⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡆⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⠁⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠀⠒⣶⣶⡶⠂⠀ ⠀⠀⠀⠀⢸⢀⠠⠔⠒⠒⠒⠒⠂⠤⣀⠤⠒⠉⠀⠀⠀⢀⡠⠟⠉⠀⠀⠀ ⠀⠀⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⣀⠠⠐⠊⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⢃⣖⢢⠀⠀⠀⠀⠀⣠⢤⣄⠀⠈⡄⠀⠀⣀⠠⠄⠀⠒⠒⠀⠇ ⠀⠀⠀⡜⠈⠛⠛⠀⣐⠂⠀⠀⠻⠿⠏⠀⠀⡗⠊⠁⠀⠀⠀⠀⠀⠀⡜⠀ ⠀⠀⢰⠉⢱⠀⠱⠞⠁⠉⠒⡖⠀⢀⠔⠢⡄⡇⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀ ⠀⠀⠀⢶⠊⠀⠀⢣⠀⠀⢠⠃⠀⠘⢄⣀⢾⠃⠀⡤⠤⠤⠤⠤⠔⠀⠀⠀ ⠀⠀⠀⠀⢱⢄⠀⠀⠢⠔⠃⠀⠀⠀⠀⢀⢎⢢⠀⠰⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣌⠀⠁⠂⠀⠀⠀⠀⠀⠐⠈⠁⢸⡤⠓⢀⡇⠀⠀⠀⠀⠀⠀⠀ ⣄⡀⠀⣰⢸⠀⠀⠀⠀⢀⢀⠂⠀⠀⠀⠀⠄⢳⡈⢁⡀⠀⠀⠀⠀⠀⠀⠀ ⢿⣷⠁⠀⠈⡄⠀⠀⠀⠈⡞⠀⠀⠀⠀⡰⠉⠀⢈⠻⠿⠀⠀⠀⠀⠀⠀⠀ ⡇⠈⡆⠀⠀⠱⡀⠀⠀⠀⡇⠀⠀⠀⢠⠁⠀⠀⠈⢀⠇⠀⠀⠀⠀⠀⠀⠀ ⠘⡄⢀⠀⠀⠀⠱⡀⠀⠀⠁⠀⠀⡠⠁⠀⠀⢰⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠉⠉⠉⠀⠐⠛⠶⠒⠣⠦⠤⠗⠒⠒⠒⠚⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀

⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣠⣤⣶⣶ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢰⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⣀⣾⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⡏⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿ ⣿⣿⣿⣿⣿⣿⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠁⠀⣿ ⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠙⠿⠿⠿⠻⠿⠿⠟⠿⠛⠉⠀⠀⠀⠀⠀⣸⣿ ⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣴⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⢰⣹⡆⠀⠀⠀⠀⠀⠀⣭⣷⠀⠀⠀⠸⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠉⠀⠀⠤⠄⠀⠀⠀⠉⠁⠀⠀⠀⠀⢿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⢾⣿⣷⠀⠀⠀⠀⡠⠤⢄⠀⠀⠀⠠⣿⣿⣷⠀⢸⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⡀⠉⠀⠀⠀⠀⠀⢄⠀⢀⠀⠀⠀⠀⠉⠉⠁⠀⠀⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠒⠊⠉⠀⢀⠴⠊⠉⠋⠙⢿⡖⠦⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠊⠁⠀⠀⠀⠀⡠⠚⠁⠀⠀⠀⠀⠀⠀⠹⡄⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⠔⠋⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠈⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⢀⣾⠶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢻⣆⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠠⡇⠀⠀⠀⢀⣴⢿⠁⠀⠈⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⢸⣿⠀⢀⡴⠋⢣⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢾⣧⣘⡀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⢸⣿⠖⠁⠀⠀⠀⢣⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣇⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀ ⠀⠀⠀⣀⣤⣶⠟⠋⠓⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣦⣶⣿⠤⠖⠚⠉⠙⡆⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀ ⠀⢠⣾⣟⠁⠃⠀⠀⠀⠀⠀⠈⠉⠉⠓⠒⠒⠒⠒⠒⠒⠒⣶⡶⢿⠉⠉⠀⠈⢆⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀ ⠀⠀⠙⣿⢿⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣴⡖⣻⡟⠀⢸⠀⠀⠀⠀⠈⡆⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⣨⠇ ⠀⠀⠀⢹⡀⠀⠉⠉⡿⠲⣶⠒⠒⠒⣿⡏⠉⠁⠀⠀⠉⢉⡴⠒⢺⠀⠀⠀⠀⠀⢹⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⣬⠃⠀ ⠀⠀⠀⠀⠳⡀⠀⠀⢧⠀⡾⠀⠀⣀⣠⡀⠀⠀⠀⠀⠀⠸⣦⣀⣸⡇⠀⠀⠀⠀⠈⡆⠀⣰⣿⡇⠀⠀⠀⠀⢀⡴⠁⠀⠀ ⠀⠀⠀⠀⠀⠱⡀⠀⠈⢯⡀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠉⠛⠛⢳⠀⠀⠀⠀⠀⣷⣴⣿⣿⡇⠀⠀⠀⢀⡟⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣱⡀⠀⠀⠑⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⣿⠛⠿⣿⡇⠀⠀⢠⡟⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⣿⢦⡀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⣹⠀⠀⠈⠁⠀⢠⠎⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⠁⠀⢙⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⢦⡀⠈⢣⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣀⡀⠀⠀⣀⠤⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣴⣿⣷⠾⠃⠀⠀⠀⠀⠀⠀⠀ ⡼⠟⠳⣀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠟⠋⢁⣀⡀⢀⣀⡀⠀⠀⠀⠀ ⡇⠀⡀⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠿⠟⠳⡀⠀⠀⠀⠀⠀⠀⢸⣤⡞⠉⠀⠀⠰⡟⠙⠳⣄⠀⠀ ⢹⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⢳⠀⠀⠀⠀⠀⢀⣼⣿⡿⠀⠀⠀⠀⠹⣄⠀⢹⣇⠀ ⠘⡆⢰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡇⠀⠀⠀⣠⣾⣿⣿⠇⠀⠀⠀⠀⢀⠈⠙⣿⣿⠀ ⠀⠸⡄⢹⠆⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⠀⠤⠊⢁⠟⣿⢿⣦⣀⣀⣾⣿⠟⣧⣴⠿⡯⠀ ⠀⠀⠉⠉⠳⢄⡙⠢⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⠀⢸⠀⢀⡠⠊⠀⠘⢦⣢⡈⠉⠻⢿⠿⠋⢀⠔⠁⠀ ⠀⠀⠀⠀⠀⠀⠈⠙⠒⠒⠶⠒⠒⠒⠈⠉⠉⠉⠉⠉⠉⠒⠒⠪⠷⠒⠛⠊⠉⠀⠠⠄⠀⠤⣌⠛⠳⠦⠤⠴⠒⠁⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠋⠉⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣤⣤⣤⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠴⠒⠊⠉⠉⠀⠀⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢀⡠⠼⠴⠒⠒⠒⠒⠦⠤⠤⣄⣀⠀⢀⣠⠴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⣼⠿⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣇⠔⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡟⠀⣠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⡤⠤⢴ ⠀⠀⠀⠀⠀⠀⣸⠁⣾⣿⣀⣽⡆⠀⠀⠀⠀⠀⠀⠀⢠⣾⠉⢿⣦⠀⠀⠀⢸⡀⠀⠀⢀⣠⠤⠔⠒⠋⠉⠉⠀⠀⠀⠀⢀⡞ ⠀⠀⠀⠀⠀⢀⡏⠀⠹⠿⠿⠟⠁⠀⠰⠦⠀⠀⠀⠀⠸⣿⣿⣿⡿⠀⠀⠀⢘⡧⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀ ⠀⠀⠀⠀⠀⣼⠦⣄⠀⠀⢠⣀⣀⣴⠟⠶⣄⡀⠀⠀⡀⠀⠉⠁⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀ ⠀⠀⠀⠀⢰⡇⠀⠈⡇⠀⠀⠸⡾⠁⠀⠀⠀⠉⠉⡏⠀⠀⠀⣠⠖⠉⠓⢤⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀ ⠀⠀⠀⠀⠀⢧⣀⡼⠃⠀⠀⠀⢧⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⣧⠀⠀⠀⣸⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠘⣆⠀⠀⠀⢠⠏⠀⠀⠀⠀⠈⠳⠤⠖⠃⡟⠀⠀⠀⢾⠛⠛⠛⠛⠛⠛⠛⠛⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠈⠦⣀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠙⢦⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⡇⠙⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠋⠸⡇⠈⢳⡀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡼⣀⠀⠀⠈⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⣷⠴⠚⠁⠀⣀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡴⠁⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⡴⠚⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣼⢷⡆⠀⣠⡴⠧⣄⣇⠀⠀⠀⠀⠀⠀⠀⢲⠀⡟⠀⠀⠀⠀⠀⠀⠀⢀⡇⣠⣽⢦⣄⢀⣴⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡿⣼⣽⡞⠁⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠈⣷⠃⠀⠀⠀⠀⠀⠀⠀⣼⠉⠁⠀⠀⢠⢟⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣷⠉⠁⢳⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⣻⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠏⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠹⡆⠀⠈⡇⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢳⡀⠀⠙⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⢀⡄⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢳⡀⣰⣀⣀⣀⠀⠀⠀⠘⣦⣀⠀⠀⠀⡇⠀⠀⠀⢀⡴⠃⠀⠀⠀⠀⠀⢸⡇⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠉⠉⠀⠀⠈⠉⠉⠉⠙⠻⠿⠾⠾⠻⠓⢦⠦⡶⡶⠿⠛⠛⠓⠒⠒⠚⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛🟨🟨⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛🟨🟨⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛🟨🟨🟨🟨⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛🟨🟨🟨🟨⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛🟨🟨🟨🟨🟨🟨⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛🟨🟨🟨🟨🟨🟨⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛🟨🟨🟨🟨🟨🟨⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛🟨🟨🟨🟨🟨⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛🟨🟨🟨🟨🟨⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛🟨🟨🟨🟨⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛⬛🟨🟨🟨⬛⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛⬛🟨🟨🟨⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛🟨🟨🟨⬛⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛⬛⬛🟨🟨🟨⬛⬛⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛⬛⬛🟨🟨🟨🟨⬛⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬛⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛🟨🟨🟨⬛⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛⬛ ⬛⬛⬛⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛🟨🟨⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛⬛⬛⬛ ⬛⬛⬛⬛⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛🟫🟫⬛⬜⬜⬜⬜⬜⬜⬜⬛⬛⬛⬛⬛ ⬛⬛⬛⬛⬛⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛🟫🟫⬛⬜⬜⬜⬜⬜⬜⬛⬛⬛⬛⬛⬛ ⬛⬛⬛⬛🟨🟨⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛🟫⬛⬜⬜⬜⬜⬜⬜⬛🟨🟨⬛⬛⬛⬜ ⬜⬛⬛🟨🟨🟨🟨⬛⬜⬜⬜⬜⬛⬛⬛⬛⬛⬛⬛⬛⬜⬜⬜⬜⬛🟨🟨🟨🟨⬛⬛⬜ ⬜⬛⬛🟨🟨🟨🟨🟨⬛⬜⬛⬛🟨🟨🟨🟨🟨🟨🟨🟨⬛⬛⬜⬛🟨🟨🟨🟨🟨⬛⬛⬜ ⬜⬜⬛🟨🟨🟨🟨🟨🟨⬛🟨🟨🟨⬛⬛⬛⬛⬛⬛🟨🟨🟨⬛⬛🟨🟨🟨🟨🟨⬛⬜⬜ ⬜⬜⬛🟨🟨🟨🟨🟨🟨⬛⬛⬛⬛🟨🟨🟨🟨🟨🟨⬛⬛⬛⬛🟨🟨🟨🟨🟨🟨⬛⬜⬜ ⬜⬜⬜⬛🟨🟨🟨🟨⬛⬛🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨⬛⬛🟨🟨🟨🟨⬛⬜⬜⬜ ⬜⬜⬜⬛🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨⬛⬜⬜⬜ ⬜⬜⬜⬜⬛🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨⬛⬜⬜⬜⬜ ⬜⬜⬜⬛⬛🟨⬛🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨⬛🟨⬛⬛⬜⬜⬜ ⬜⬜⬜⬛🟨⬛🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨⬛🟨⬛⬜⬜⬜ ⬜⬜⬜⬛🟨⬛🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨⬛🟨⬛⬜⬜⬜ ⬜⬜⬛⬛⬛🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨⬛⬛⬛⬜⬜ ⬜⬛⬛🟨⬛🟨🟨🟨🟨⬛⬛🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨⬛⬛🟨🟨🟨🟨⬛🟨⬛⬛⬜ ⬛🟨⬛🟨⬛🟨🟨🟨⬛⬜⬛⬛🟨🟨🟨🟨🟨🟨🟨🟨⬛⬛⬜⬛🟨🟨🟨⬛🟨⬛🟨⬛ ⬛🟨🟨🟨⬛🟨🟨🟨⬛⬛⬛⬛🟨🟨🟨🟨🟨🟨🟨🟨⬛⬛⬛⬛🟨🟨🟨⬛🟨🟨🟨⬛ ⬜⬛🟨⬛🟨🟨🟨🟨🟨⬛⬛🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨⬛⬛🟨🟨🟨🟨🟨⬛🟨⬛⬜ ⬜⬛🟨⬛🟨🟨🟥🟥🟨🟨🟨🟨🟨🟨🟨⬛⬛🟨🟨🟨🟨🟨🟨🟨🟥🟥🟨🟨⬛🟨⬛⬜ ⬜⬜⬛⬛🟨🟥🟥🟥🟥🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟥🟥🟥🟥🟨⬛⬛⬜⬜ ⬜⬜⬜⬜⬛🟥🟥🟥🟥🟨🟨🟨⬛🟨🟨⬛⬛🟨🟨⬛🟨🟨🟨🟥🟥🟥🟥⬛⬜⬜⬜⬜ ⬜⬜⬜⬜⬛🟨🟥🟥🟨🟨🟨🟨🟨⬛⬛🟨🟨⬛⬛🟨🟨🟨🟨🟨🟥🟥🟨⬛⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬛🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨⬛⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬛⬛⬛🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨⬛⬛⬛⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬛🟨⬛⬛⬛🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨⬛⬛⬛🟨⬛⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬛🟨🟨🟨🟨🟨⬛⬛⬛⬛⬛⬛⬛⬛🟨🟨🟨🟨🟨⬛⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬛🟨🟨🟨🟨🟨⬛⬜⬜⬜⬜⬛🟨🟨🟨🟨🟨⬛⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬛⬛🟨🟨🟨⬛⬜⬜⬜⬜⬜⬜⬛🟨🟨🟨⬛⬛⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬜⬛🟨⬛🟨⬛⬜⬜⬜⬜⬜⬜⬛🟨⬛🟨⬛⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛⬛⬛⬜⬜⬜⬜⬜⬜⬜⬜⬛⬛⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠛⠻⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡁⠀⠈⠁⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⢀⣴⣦⠀⠀⠀⠀⠘⡇⠀⠀⠀⣠⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⡤⢤⡿⠉⠙⣦⠀⠀⠀⣠⣿⣿⣿⠀⠀⠀⠀⠀⢻⡴⠞⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣿⠁⠀⠁⠀⠀⢸⠀⠀⢰⣿⡿⢟⡿⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠻⣆⠀⠀⠀⠀⣿⠀⠀⡟⠋⠀⢸⠃⢀⣠⠴⢺⡇⢀⠔⠋⢹⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠙⠶⣄⡘⣿⠀⢸⡇⠀⢀⡿⠚⠉⠀⠀⣼⡷⠁⠀⢀⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⠛⠀⣸⡇⠀⣼⠗⣺⡉⠉⠙⠻⢤⣠⠴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⣇⣄⠀⠘⠉⠙⠂⢀⡂⠉⠙⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠈⣻⣄⡀⠀ ⠀⠀⡀⠀⠀⠀⢀⡜⠁⠀⣴⠋⠘⣿⣿⡆⢸⣿⣿⣿⡆⢸⣿⣧⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠈⠀⢹⡆ ⠀⠘⠿⢭⣽⣶⠘⠢⡀⠀⣿⠀⠀⠘⡿⠃⠈⣿⣿⣿⠇⠘⠿⣿⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⣀⡼⠃ ⠀⠀⣤⣖⣻⡿⠀⠀⠈⠢⣿⠀⠀⠀⣷⠀⠀⢻⣿⡟⠀⠀⣰⠷⠶⠒⢶⡄⠀⠀⠀⠀⠛⠛⠛⠋⠉⠀⠀ ⠀⠀⠉⠉⠁⠀⠀⠀⠀⢀⠿⡄⠀⠀⣹⠀⠀⠀⠉⠀⣠⠔⠁⠀⠀⢀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣠⣄⣠⠖⠒⣦⠀⢴⣃⠀⢷⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣾⠁⠀⠋⠀⠀⢸⡇⠀⠈⠙⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢧⣀⣀⠤⣶⠀⠀⢰⣿⣽⠭⠿⠀⠀⠀⠀ ⢿⡀⠀⠀⠀⢀⡾⠃⠀⢠⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⡿⠀⠀⠈⠻⣭⣲⡄⠀⠀⠀⠀ ⠈⠳⣄⡀⠀⡾⠁⠀⠀⠈⠉⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⢀⡼⠁⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀ ⠀⠀⠈⠙⠛⠁⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⣠⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⣀⣀⣀⣤⠴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠈⠉⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⢀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡴⠒⠚⣻⠇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠓⠒⠒⠒⠒⢤⣤⠴⠚⠉⠀⡸⠁⣠⠞⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⣠⠖⠋⠀⠀⠀⠀⢀⡧⠞⠣⠤⣀⡀⠀⠀⠀⠀ ⢀⣤⠔⠒⠚⣏⠉⠉⠉⠉⠉⠉⠉⠒⠒⠲⠤⠒⠋⠉⠉⠉⠉⠉⠒⠒⠻⢴⠋⠀⠀⠀⠀⠀⣠⠔⠋⠀⠀⠀⠀⠀⠉⠑⠲⢤⡀ ⠈⠙⠒⠤⢄⣘⣦⡀⠀⠀⠀⠀⠀⠀⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠤⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼ ⠀⠀⠀⠀⠀⠀⠈⢉⣿⣗⡒⠒⠒⡾⠁⣠⣶⠒⡆⠀⠀⠀⠀⠀⠀⠀⣀⣄⡀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀ ⠀⠀⠀⠀⠀⠀⢠⡎⠀⠀⠙⢦⣀⠇⠀⠻⣼⡿⠁⠀⠀⢠⡄⠀⠀⠸⣷⣼⣷⠀⢸⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⣏⠀⠀⠀⠀⡿⠖⠲⣄⠀⠀⣤⡀⢀⣤⣀⠀⠀⢀⠈⠋⠁⠀⢸⣿⡉⠓⠦⣀⡀⠀⠀⠀⠀⢀⡴⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⡇⠀⠀⣸⠀⠀⢸⣯⠟⠛⠛⢿⣿⠋⠀⢰⠟⠉⠹⡇⢷⠀⠀⠀⠉⠓⠦⣄⣠⠎⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠹⡦⠴⠋⠀⠀⠀⢹⡄⠀⢀⡼⠁⠀⠀⣇⠀⠀⢠⡇⣀⣧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠙⢆⠀⠀⠀⠀⠀⠹⠤⠋⠀⠀⠀⠀⠈⠓⡶⠋⠙⠳⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠑⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠖⠋⠀⠀⠀⠀⠀⠀⠉⠲⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⢀⣷⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠤⣤⠤⠴⠒⠒⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡆⢀⣠⠤⠒⠒⠒⠂⠀⠀⠐⠒⠒⠒⠒⠲⢦⡀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⡟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠘⣿⣶⡖⠤⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠔⣶⣿⠟ ⠀⠀⠀⠀⠀⠀⠈⠻⣷⠀⠀⠈⠳⠤⠔⠒⠉⠉⠉⠑⠒⠤⠔⠉⠀⠀⢀⠟⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠁⠀⠀⠀ ⢋⠒⠒⠤⠤⣀⣀⠀⠀⠀⠀⡘⢀⣤⢀⠀⠀⠀⠀⠀⢀⣤⣀⠈⡄⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠀⠀⠀⠉⠉⠒⢲⠇⠈⠛⠛⠀⠀⢀⠀⠀⠈⠛⠋⠀⢃⠀⠀⠀⠀⠀ ⠀⣇⡀⠀⠀⠀⠀⠀⠀⠀⢸⢸⣿⡇⠀⠠⢠⠤⡄⠀⠀⢠⣾⣷⢸⠀⠀⠀⠀⠀ ⠀⠀⠈⠉⠉⠉⢹⠂⠀⢀⠎⢆⠉⠀⠀⠀⠈⠂⠁⠀⠀⠀⠉⢉⠎⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⠃⠀⢠⠃⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⠃⠀⠀⠣⢄⡸⢠⠀⠀⠀⢣⠀⠀⠀⢀⠄⠀⠀⢠⢱⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠉⠒⠢⠤⣀⠀⠇⠀⠣⡀⠀⠀⢆⠀⠀⢸⠀⠀⢀⠞⠈⡆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠰⢅⣸⠀⠀⠀⠙⢤⠴⠚⠂⠀⢮⣤⣤⠎⠀⠀⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠗⠂⢤⠤⠤⠤⠤⢤⡤⠤⢤⡊⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠤⠒⠁⠀⠀⠀⠀⠀⠈⠒⢤⣷⠀⠀⠀⠀⠀⠀

⢸⣿⠀⢸⣦⠀⠀⠀⠀⠀⣀⡧⠄⠒⠒⠒⠉⠉⠉⠑⠒⠂⠤⢄⣀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⡆ ⢸⣿⣇⣸⣿⣧⡒⣤⠄⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠽⠗⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙ ⢸⣿⠉⠉⠉⠉⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴ ⠘⢿⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠫⣝⣷⠒⠒⠒⠒⠒⠒⠒⠒⠋⠉ ⠀⠈⠀⠀⠀⡇⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⠀⠀⣤⣿⣧⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⢶⣄⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⠀⠀⡼⠀⠀⠀⠻⠿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣶⣾⣿⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⢸⠀⢰⠗⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠈⠙⠛⠁⠀⠀⠀⠀⠸⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⠀⠸⡆⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⡀⡧⣀⠀⠉⠓⠢⢤⣀⠀⠀⢰ ⢸⣿⠀⠀⠹⡄⠀⡇⠀⠀⠀⠀⠀⠀⠀⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⢠⡟⠀⠀⠈⠑⠒⠤⣀⠀⠉⠓⠲ ⢸⣿⠀⠀⠀⠙⣾⡁⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⣸⠀⠀⣀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⢄ ⢸⣿⠀⠀⠀⡰⠁⠉⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣤⠔⠁⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⠀⠀⢀⠇⠀⠀⠀⠀⠈⠓⠢⢤⣀⣀⣀⣀⣀⣀⣀⣠⡤⠖⠋⠀⠀⠀⢸⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢣⠉⠓⠤⢄⡠⠔⢊⠕⠀⠀⠀⠀⠀⠀⠘⡟⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⠀⠀⠀⢸⣦⢄⡀⠀⠀⠀ ⢸⡟⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⣿⡀⠀⠀⢸⠹⡆⠈⠓⢤⡀ ⢸⡇⠀⠀⡜⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⣇⣇⠀⠀⢸⠀⠀⠀⠀⠀⠉ ⣸⡇⠀⢠⡇⠈⣦⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⡇⠀⢹⡛⠀⠀⢸⠀⠀⠀⠀⠀⠀

⢷⣿⣿⣿⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣧⣿⣿ ⣿⣿⣿⣿⣿⡿⠛⠷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠾⠻⣿⣿⣿⣿⣿⣿⣙ ⣿⣿⣿⣿⡟⠀⠀⠀⠈⠙⠻⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣄⣴⣿⣿⣷⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⠋⠁⠀⠀⠘⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠉⠻⣦⡀⠀⠀⠀⠀⠀⠀⢀⣠⣶⠿⣛⣭⡿⠋⠉⣏⠉⠻⢿⣝⡻⢷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠟⠁⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⠟⠁ ⠈⠻⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⢀⣴⡿⠋⢀⣼⠟⠋⠀⠀⠠⣻⠀⠀⠀⠙⠻⢧⣌⠙⠿⢷⣄⡀⠀⠀⢀⣴⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡿⠃⠀⠀ ⠀⠀⠈⠛⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣾⣛⠋⠀⣰⡿⠁⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠙⠻⣦⣀⣙⣷⣄⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠿⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⠷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⣮⣤⣠⡟⠀⠀⠀⣀⣀⡀⠀⢹⡆⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⡟⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⣄⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⠿⠿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⡇⠀⠀⠀⠀⠀⠀⢀⣤⡾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⢤⣄⡤⠶⠖⠊⢿⣿⣿⡿⠿⠟⠋⠉⠀⠀⣀⣀⣀⣀⣀⣈⡉⠻⢿⡿⠿⠿⣿⣿⡁⠀⢻⡀⠀⠀⣀⡤⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⠞⢶⣟⣩⣄⣀⣠⣤⣶⡾⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣶⣤⣄⣀⣀⣈⣹⣷⢾⣿⠞⠛⠁⠀⠀⠀⠀⠀⠀⠀⣀⣤⠞⠛⢷⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣯⡼⠿⠛⠉⠉⠉⠉⠒⠶⠤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁⠀⣹⣧⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠈⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠓⠦⢤⣀⣀⡀⠀⠀⢀⣀⡤⠞⠉⠙⠋⠉⠹⡆⠀⠀⠀⢀⣴⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠰⣴⣤⡀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠰⠚⣿⠁⠀⣸⠻⣼⡿⠀⠀⢸⠃⠀⠀⣀⣤⣶⣾⣟⣛⡛⠶⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢻⣤⣤⠯⠟⠛⠀⠀⠀⣼⠀⢠⣾⣫⡵⠛⢉⣁⣉⣙⠛⢦⡟⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣄⡀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠭⢭⠀⠀⠀⠀⠀⠘⣿⢠⣿⣿⠋⠀⣠⣿⡏⠀⠈⣧⠀⠹⣄⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠈⣿⣿⣆⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⠛⠛⢛⣶⠆⠀⢠⡟⣿⢻⡇⠀⢸⡿⣿⣧⣤⡤⣿⠀⠀⣿⣾⣇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣤⣴⣿⣿⣿⡤⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢰⣿⡅⠀⠀⣼⡥⣿⠸⣇⠀⠘⣇⠀⠘⣿⣰⡟⠀⠀⣿⣻⡏⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣷⡿⠀⠀⠀⣠⣼⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠛⠃⠀⢰⡇⠀⠹⣆⠻⣆⠀⠈⠙⠚⠛⠉⠀⢀⣴⣿⡿⠁⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠉⠀⠀⣠⠟⠁⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠹⣷⣈⢳⣤⣄⣀⣀⣠⣤⣾⣽⡿⠁⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢀⡴⠂⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡄⡀⡄⢻⠙⠳⢾⣿⣿⣿⡿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢰⡟⢤⡀⠀⠀⢀⣤⠾⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣄⣠⡿⠖⠚⠛⠛⠻⢿⡀⠀⠀⠀⠀⠀⠀⣴⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⢀⣴⠏⠀⠀⢙⣦⡾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⠁⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠻⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⠟⠁⠀⣠⣶⣿⣍⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠛⢻⡄⠀⠀⠀⠀⠈⠉⠉⠉⣿⠇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡏⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠁⠀⠛⣯⡐⠒⠒⠒⠒⠲⠖⠲⠂⠀⢐⣶⠞⠁⠀⠀⠀⠀⠀⠀⠀⢻⣤⣂⡀⠀⠀⠀⢤⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢸⡇⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⡆⠀⠀⠀⠉⠓⠶⢄⣀⣀⣀⣀⡤⠖⠋⠁⠀⣠⠀⠀⠀⠀⠀⠀⠀⠈⣿⣩⡿⠁⠀⣰⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠤⣤⡤⠤⠖⠛⠛⢿⡿⠟⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠁⢀⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣧⡀⣀⠀⠀⠀⠀⠀⠀⣼⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠛⠷⠿⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡿⣦⡤⠀⠀⠀⠀⣠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣦⡀⠀⣠⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠈⠳⢤⣤⠴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣅⣴⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⢻⡄⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠟⠉⢸⡇⠀⠀⠀⢸⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠶⣄⣀⣀⣀⡤⠶⠾⣉⣀⡀⢀⣼⠃⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⣀⠉⠉⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⠋⠉⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡣⣀⣀⠀⠀⠀⠀ ⠁⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣜⣀⠈⠁⠈⠇⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢹⠉⠓⠠⠤ ⠀⠀⠀⠀⡀⠀⠀⢰⠁⠈⡆⠀⠀⠀⠀⡙⠀⠀⠀⠛⠉⠳⠄⠀⠀⠸⠀⠀⠀⠀ ⠀⠀⠀⡰⢛⠒⠤⡸⡄⣠⠃⠀⠀⢹⠟⠳⢤⡠⠂⠀⢀⠤⠤⣄⠀⡄⠀⠀⢰⠂ ⠀⠀⠀⠷⠉⠁⠀⠈⢫⠁⠀⠀⠀⠘⠀⠀⡜⠀⠀⢠⡇⠀⠀⢸⢠⠁⠀⠀⠀⠀ ⠀⠀⠀⠸⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠧⠜⠀⠀⠀⠀⠳⣈⡠⢞⠂⠀⠀⠀⠀⡄ ⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠈⠀⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠣⢄⠀⠀⠀⠀⡇ ⠀⠀⠀⠀⠈⢆⠀⠀⢠⠀⠀⠀⠈⠪⠭⠕⠂⠀⠀⠀⠀⢀⡀⠤⠄⠈⠲⡒⠒⠃ ⠀⠀⠀⠀⠀⠈⢷⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠈⢆⢀ ⠀⠀⠀⠀⠀⠉⠈⢣⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡦⡀⠀⠀⠀⠀⢸⠀ ⡇⢀⣔⣀⣀⠀⠀⡹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡮⣑⡢⢤⣴⢾⡶

⠀⠀⠀⠀⠀⠀⠀⡠⠐⠂⠁⡀⠔⠉⠁⠙⡗⠂⢄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⠔⠁⠀⠀⡠⠊⠀⠀⠀⠀⠀⠘⡄⠀⠑⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⠀⠀⢀⣼⠋⠳⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⡆⢀⠔⡀⠀⠀ ⠀⠀⠀⠀⢸⠀⠀⠻⠬⠤⠤⠀⠀⠀⠀⠀⠀⠁⠀⠀⢸⠇⠀⠀⠐⡀⠀ ⠀⠀⣠⠴⠞⠒⠤⢀⣀⠀⠀⠀⠀⠀⠀⣤⡤⢮⠔⠒⠙⠀⠀⠀⠀⠐⡀ ⠀⠘⢧⣄⠀⠀⠀⠀⠀⠀⠈⣉⡭⣽⠋⡇⠀⠀⠂⠀⠀⡇⠀⠀⠀⠀⣰ ⠀⠀⠐⡀⠉⡟⢻⠉⠉⠛⠉⠀⠈⢱⠈⡇⠀⠀⠘⠀⢀⣇⠀⠀⠀⠰⠃ ⠀⠀⠀⠐⡀⠘⢎⠀⠈⠁⠀⠀⠀⠈⠛⢳⠀⠀⠀⣧⣿⣿⠀⠀⡴⠁⠀ ⠀⠀⠀⠀⣷⣄⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⡃⠉⠋⠀⡜⠀⠀⠀ ⠀⠀⠀⠀⠁⠀⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⠀⡎⠀⠀⠀⠀ ⠀⣀⠀⡠⠔⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣼⡶⠖⠀⠀⠀⠀ ⢸⢁⢓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⠄⠀⠀⠀⠀⣡⠔⠂⢰⠶⢄⠀ ⠸⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠘⡀⠀⠀⣴⣿⠃⠀⠀⠣⢤⣇ ⠀⢣⣱⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⠃⠄⢊⠻⡿⢤⣠⣶⣣⠼⡋ ⠀⠀⠀⠁⠂⠥⠤⠤⠤⠀⠀⠀⠀⠤⠵⠤⠦⠐⢁⠀⢑⠳⠤⠉⠥⠊⠀

░░░░░░░░▀████▀▄▄░░░░░░░░░░░░░░▄█ ░░░░░░░░░░█▀░░░░▀▀▄▄▄▄▄░░░░▄▄▀▀█ ░░▄░░░░░░░░█░░░░░░░░░░▀▀▀▀▄░░▄▀ ░▄▀░▀▄░░░░░░▀▄░░░░░░░░░░░░░░▀▄▀ ▄▀░░░░█░░░░░█▀░░░▄█▀▄░░░░░░▄█ ▀▄░░░░░▀▄░░█░░░░░▀██▀░░░░░██▄█ ░▀▄░░░░▄▀░█░░░▄██▄░░░▄░░▄░░▀▀░█ ░░█░░▄▀░░█░░░░▀██▀░░░░▀▀░▀▀░░▄▀ ░█░░░█░░█░░░░░░▄▄░░░░░░░░░░░▄▀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡀⠈⠙⠲⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢸⡿⠟⠛⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣶ ⡍⢳⣤⣀⠀⠙⠲⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠘⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⡏ ⠙⠻⢦⣈⡛⡦⣄⡀⠉⠲⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠛⠙⠻⣿⡟⠀ ⣄⠀⠀⠈⠙⠲⢬⣛⠲⣤⣀⠉⠳⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⣷⠤⠤⠤⠤⢤⣀⣀⠀⣠⠞⠁⢀⠄⠀⠀⡜⠁⠀ ⠈⠙⠦⣄⡀⠀⠀⠉⠓⠶⣍⡓⢦⣄⠈⠓⢤⣀⠀⠀⠀⠀⠀⠀⠀⠸⣵⠄⠀⢀⡰⠄⠀⠀⠀⠀⠀⠀⠉⠛⢣⣤⠔⠉⠀⠀⡾⠁⠀⠀ ⣦⣀⠀⠀⠉⠒⢦⣀⠀⠀⠈⠉⠳⢮⣛⡶⣄⡈⠓⢦⣀⠀⠀⠀⢀⡾⠁⠀⣰⣿⣿⠆⠀⠀⠀⠀⠀⣴⣶⣤⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀ ⢷⣽⡛⠶⣄⣀⠀⠀⠙⠲⢤⣀⠀⠀⠈⠛⠲⢿⣳⢦⣈⠙⢦⣴⠋⠀⠀⣀⠘⠋⠁⠰⠖⢧⡄⠀⠀⠻⣿⠿⠃⠀⠀⠀⠿⣄⠀⠀⠀⠀ ⠀⠈⠙⠳⠦⣍⡛⠦⣄⣀⠀⠈⠓⠦⣄⡀⠀⠀⠉⠛⠯⣿⣾⠃⠀⢰⠋⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠘⡆⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠙⠒⢤⣍⡛⠦⣤⣀⣴⠟⠲⢤⣀⠀⠀⠈⢹⠀⠀⠘⠷⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⣞⣉⣈⣷⠀⠀⠀⠀⠀⢹⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⢦⣍⡛⠶⣤⣄⠈⢹⣦⣄⡘⣆⠀⠀⠀⠀⠀⠰⣄⠀⠀⠀⠀⠀⠀⠙⠳⠟⠋⠀⠀⠀⠀⠀⠀⣧⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠳⠶⣍⡻⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⡆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠯⣿⣿⣷⣿⣟⡿⠶⢤⣀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⡿⠯⣍⡛⠲⢤⣍⠛⠦⣄⡀⠙⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡁⠀⠀⠉⠓⠦⣍⡛⠶⣭⣉⠓⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠉⠓⠦⣍⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠢⣄⠀⠀⠀⠀⠀⢦⡀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⠤⢄⣀⡀⠉⠀⢀⣀⣤⡤⢶⡒⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠀⢱⠀⠱⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠠⣏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⡀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠈⠂⠄⢳⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⢈⣷⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠖⠊⠉⠉⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⠀⠀⠀⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣤⣤⣤⣀⣀⣀⡴⠋⠀⠀⠀⠀⣠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀⣀⠀⠀⠀⣠⣴⠖⠚⠋⠉⠉⠁⠀⠀⠀⠈⠉⠉⠛⠀⢀⡀⠀⠀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠉⠉⠉⠉⠙⠛⠷⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⣶⣄⠙⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠷⣤⣀⡀⠀⠀⠀⠀⠀⠀⣴⠋⢹⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⣷⣤⣾⣿⡆⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⡖⠆⠀⠀⠘⣿⣷⣿⣿⡇⠀⠀⠀⢀⣀⣀⣀⠀⠙⠻⠟⠋⠀⠀⢻⣆⠀⣄⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠈⠛⠛⠋⠀⠀⠀⠀⠈⠛⠛⠁⠀⠀⠀⠀⠀⠀⢠⠟⢻⣦⡏⠉⠙⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣼⠀⠀⢀⣤⠖⠒⠦⣄⠀⠀⢤⡀⠀⠀⣀⣾⢦⣀⡴⠖⠀⠀⠀⢸⠀⠀⣿⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡞⢦⣀⢹⡄⠀⢸⠁⠀⠀⠀⠘⡆⠀⠀⠉⢻⡋⠁⠀⠙⣾⠁⠀⠀⠀⠀⠈⠧⣼⠏⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠋⠀⠀⠉⠻⢷⣄⠈⢧⣀⣀⣀⡼⠃⠀⠀⠀⠀⠳⣄⣀⡼⠁⠀⠀⠀⠀⠀⠀⣴⠟⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣄⠀⠀⠀⠀⠀⠙⢷⣄⠍⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠃⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠙⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⠛⠛⠻⠶⠶⠶⠶⠶⠶⠶⠶⣶⣶⣦⣤⣽⣆⠀⠀⠀⠀⠀⠀⠈⠙⠀⠀⠀⠀⠀⠀⠐⠒⠶⠒⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⣰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠹⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠈⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⢀⣼⠀⢰⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠠⡇⠀⠀⠀⢀⣀⣠⡤⢾⠂⠀⠀⠠⣾⣣⠶⠋⣼⠀⣸⠁⠀⠀⢀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⠿⠖⠚⠛⠛⠉⠀⠀⢸⠀⠀⠀⠘⠟⡁⠀⢠⣇⡼⣿⠀⠀⣶⣻⣾⠻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣠⣴⡇⠀⣾⡏⠀⣿⠀⢠⣿⠛⠈⠀⢿⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⣴⠞⠉⢸⡇⠀⣨⡧⠈⢻⣧⠋⢹⡄⠀⠀⢸⡄⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⢸⢁⡼⠛⣷⣠⡾⢿⡄⠀⣧⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟⠁⠀⠟⠋⠀⠈⢿⣄⠘⣇⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣬⣳⣼⠁⠀⠀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⢀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠋⠉⠉⠉⠉⠉⠙⣷⠒⠀⣤⣤⡴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣤⣄⣼⠀⠀⠀⠀⣀⣀⣀⢀⢀⣀⢀⣠⡄⡀⠀⠀⢀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠟⠉⠀⠀⠀⠀⠽⣿⡾⠅⠠⣼⡃⣼⢤⡧⠠⢠⣜⣃

⣿⣿⡿⠿⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⣝⠿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢌⢷⣄⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠉⠉⠉⠉⠉⠉⠙⠓⠒⠒⠶⠶ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⡀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⣼⣶⠟⠲⣦⣴⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢹⣽⣶⣤⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠉⠀⠀⢠⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣾⠀⠉⠉⠛⠲⠶⢤⣄⣀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠟⠙⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⣶⣯⣧⣤⣄⡐⢀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠭⠇⠀⠀⠀⠀⠀⠀⠙⠓⠂⠀⢉⡻⣶⡀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡀⠀⠀⠀⠀⠀⣿⡃⠀⠀⠀⢸⡇⠀⠀⠀⠀⠰⣦⡀⠀⢀⣰⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠋⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣴⡿⠇⢟⠦⢤⣀⠀⠀⢻⡇⠀⠀⢀⣼⠇⡀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣦⡀⠀⠀⢀⡴⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⡤⠔⠒ ⠀⠀⠀⠀⠀⠀⠀⡿⢃⣀⡶⠀⠀⠈⠓⢦⡀⢿⡀⣄⣿⡟⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠉⠛⣷⠖⠋⠁⠀⠀⠀⢀⣴⠾⠋⠉⠉⠙⢷⣄⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⡇⣴⠟⠗⠂⠀⠀⠀⠁⠙⠺⣟⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⢱⡟⠀⠀⠀⠀⠀⠀⣼⣯⠀⠀⠀⠀⠀⠀⢻⡀⠀⡏⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⢿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⢰⡿⠓⠀⠀⠀⠀⠀⠀⣸⠇⣸⠁⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠀⢠⡿⠁⠀⠀⠀⠀⠀⠀⠈⢿⣆⡀⠰⠆⠀⠀⣰⡿⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠘⢧⠴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷⣤⣤⣤⠶⠛⣱⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠛⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡛⠲⠶⠤⢤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢮⣉⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⠤⠤⠤⠖⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⡀⠉⠳⣶⠒⠚⠛⠋⠉⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡖⠛⠉⠉⠁⠀⠀⠈⠉⠁⠀⠀⠈⢳⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣳⣄⡀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣬⣷⡍⠳⣦⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡦⠤⠒ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠋⠁⠀⠀⢿⣦⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣮⡙⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀ ⣏⡀⠀⠀⣀⣤⡄⢀⡀⠀⠀⠀⠐⠒⠀⠘⣻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣆⠈⠛⠶⣄⡀⠀⠀⠀⢀⣤⣾⣷⣰⣶ ⣯⠀⠀⢤⣭⣬⣤⣠⣤⣀⣠⠀⡀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⡛⢦⣤⣀⣉⡉⣛⣛⣽⠿⠣⣿⡟⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠛⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠼⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡴⠋⠳⣄⠀⠀⢀⢎⣔⠀⠀⠀⠀⠉⠳⣄⠀⠀⠀⠀⠀ ⠀⢠⠞⠁⠀⠀⠀⠹⣶⢛⠘⡋⠀⢠⣎⣦⠀⠀⠈⠙⠲⢤⡀⠀ ⣰⠏⠀⠀⠀⠀⠀⠀⢰⠀⠰⡤⡀⠀⢛⣋⠀⠀⠰⣄⣀⣠⣿⣆ ⠛⠒⠶⠶⢶⡶⠄⢀⣨⢦⡀⠢⠃⠀⠸⣿⠇⠀⢰⠃⠉⠉⠉⠉ ⠀⠀⠀⠰⠿⣤⣀⠛⢧⣌⡇⠀⠀⠀⠀⠀⠰⠉⠙⢳⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣼⣣⣞⣽⣇⠀⠈⠑⢄⠀⠐⢄⣀⣸⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠛⣿⣿⠁⠉⠠⡀⠀⠀⡆⠀⠀⠀⢹⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠹⡿⠇⠀⠀⢈⠁⠊⠀⠀⠀⠀⠈⣇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣸⠗⠀⣀⣦⣀⣤⣤⠴⠾⣄⡀⠺⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⠀⠹⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠿⠃⠀⠀⠐⠚⠻⢷⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⣰⠟⢁⣀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⣾⠟⠁⠀⠀⠙⢿⣦⣄⠀⠀⠀⠀⣼⠏⣼⣧⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣴⡿⠃⠀⠀⠀⠀⠀⠀⠉⠻⣷⣤⣤⡾⢿⠐⣿⡿⠃⠀⠀⠀⢀⡖⠒⣦⡀⠀⠀⠀⠀⠈⠙⠛⠷⣦⣄⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡿⠁⢸⠀⠀⣤⡄⠀⠀⠀⢸⣧⣤⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣶⣄⠀⠀⠀ ⠀⠀⣰⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⡠⠃⠀⣀⡈⠀⠀⠀⠀⠘⢿⣿⣿⠟⠀⠀⠀⠀⠠⣄⠀⠀⠀⠀⠀⠈⢻⣷⣄⠀ ⠀⣰⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⢹⡟⠓⣶⠀⠀⠀⠀⣨⣤⣤⡀⠀⠀⠀⠀⢸⣿⣶⣦⣤⣶⣾⣿⣿⣿⣆ ⢠⣿⣷⣶⣶⣶⣶⣤⣤⣤⣤⣄⣀⡀⠀⠀⠀⠀⠘⣧⠀⠀⠈⣄⠀⡏⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⣸⡟⠀⠉⠙⠛⠛⠿⠿⠿⠛ ⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⣹⣿⠟⠋⠀⠀⣠⣴⡿⠿⣷⣄⠀⠈⠓⠁⠀⠀⠀⠈⠿⣿⡿⠏⠀⠀⠀⢀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡟⠁⠀⠀⠀⢾⣿⣯⡀⠀⢸⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠒⠛⠛⠿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⢿⣶⣦⣤⣀⠈⠙⢿⣶⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠈⣿⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⡿⠃⣠⣿⢋⣽⣷⠀⠀⠀⠀⠉⠳⢦⡀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣷⣶⣿⣧⣾⣿⣿⡆⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠈⠻⢦⣤⣤⣴⡟⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⣿⣿⣿⣿⠋⠉⠛⠃⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⢹⣧⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣧⡀⠀⠀⠀⠈⠳⣤⡀⠀⠀⠀⢀⡗⠀⠀⠀⠀⠀⠀⠀⠈⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣿⣿⣿⣷⡄⠀⠀⠀⠀⠈⠙⠓⠶⠶⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠛⠋⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⡀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣤⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⣀⣠⣤⣾⠁⠀⠀⠀⣸⣿⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣉⣀⣀⣀⣤⣾⣿⣷⣶⣶⣶⣿⡿⠿⠿⠛⠛⠿⣷⣤⣄⡈⠀⠉⣿⡆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠛⠁⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠻⢿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠁⠀⠀⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣧⣄⣀⠀⢻⡇⠀⠀⠀⠀⠀⢀⡀⠀⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⠿⠻⢿⣷⣤⣤⣤⣤⣭⣭⣥⣼⣿⣡⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⡇⠀⠀⠀⠀⠉⠛⠻⢿⣭⣉⠉⠉⣿⡎⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠛ ⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⢷⣿⣷⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠀⠀⠀⠀⠀⠀ ⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠙⠻⣿⣿⣿⣿⠿⠟⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠿⢿⣿⣿⣽⣿⠿⠿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠴⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠ ⠀⠻⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿ ⠀⠀⠈⢻⣷⣤⡀⠀⠀⠀⠀⠀⠀⢀⣾⡟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣽⡿ ⠀⠀⠀⢸⡏⠈⣹⣦⡀⠀⠀⠀⣰⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⡷⠀ ⠀⠀⠀⢸⡇⠀⠈⣿⠹⣶⣄⣰⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⣿⠏⠀⠀ ⠀⠀⠀⣼⡇⠀⠀⣹⠀⠈⢻⡿⠁⠀⠀⠀⢀⣤⣴⡶⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⣾⣿⣿⣿⡿⠋⠀⠀⠀⠀ ⠀⠀⠀⣿⠇⠀⢀⣿⠀⢀⣿⠇⠀⠀⠀⠀⣿⣿⠀⠀⣰⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡏⠉⠉⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠹⢹⣿⣿⡿⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⠀⠀⢸⣿⠀⣼⡟⠀⠀⠀⢠⡀⣿⣿⣷⣿⣿⣿⣿⡿⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇⣀⣴⣿⣿⣿⡇⢲⠀⠀⠀⠀⠀⠀⠀⣿⣯⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⠀⠀⢸⡏⢰⡿⠀⠀⠀⠀⠀⠣⠙⢿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⡿⠁⠀⠧⡀⠀⣄⡀⠀⠀⠘⣿⣿⣦⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⠀⠀⣸⣧⣾⡷⠶⠿⠗⠀⠀⠀⠀⠄⠈⠻⠍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠿⠿⠛⠁⠀⠀⠀⠀⠀⠉⠛⠿⣶⣄⢸⣿⣿⣿⣦⡀⠀⠀⠀ ⠀⠀⠀⡿⢀⣾⣿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣷⣶⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣦⡀⠀ ⠀⠀⠀⢡⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⡛⢋⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⢸⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⡆ ⠀⠀⢀⣿⠏⠀⣀⣤⣴⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⠊⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣀⡀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿ ⡆⠀⣼⠏⢠⣾⡿⠃⠀⠀⠀⠹⣷⡄⠀⠀⠀⠀⠀⢠⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠇⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠉⠀⠀⠙⠻⣷⡀⠀⠘⣿⣿⣿⣿⣿⣿ ⠀⠀⣿⠀⣼⡟⠀⡆⠀⠀⠀⠀⣿⡇⠀⠀⢀⣠⣶⣿⡏⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣌⠀⠀⠀⠀⠀⠠⠄⣴⡿⠁⠀⠀⠀⠀⠀⠀⢿⣷⠀⢀⣿⣿⣿⣿⣿⣟ ⠀⠐⣿⠀⣿⣇⠀⠀⠀⠀⠀⢀⣿⡇⠀⠀⠈⠉⠁⠉⣷⣧⣤⣤⣶⠾⠿⢶⡶⢶⣶⣦⣤⡀⠀⠀⣀⣼⣿⣷⣶⣄⠀⠀⠐⠀⢸⡇⠀⠀⠀⠀⠀⠀⡄⢸⣿⠀⣸⣿⣿⣿⣿⠿⡇ ⠀⠀⢹⣆⠘⣿⣧⣀⠀⠀⣠⣾⠟⠀⠀⠀⢀⣀⣴⣶⠿⠋⠁⠀⠀⠀⠀⢸⡇⠀⠀⠈⠙⠛⠿⣾⣿⣅⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡄⠀⠀⠀⠀⠀⣠⣿⠇⢰⡟⢿⣿⡟⠁⠚⠃ ⠀⠀⠘⣿⡄⠀⠉⠉⢛⠛⠋⠀⠀⢀⣠⣶⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠄⠉⠻⢿⣶⣄⣀⠀⠀⠀⠀⠀⠈⢿⣷⣦⣤⣥⣾⠿⠃⢠⣿⠁⣸⡟⠀⠀⠀⠀ ⠀⠀⠀⠙⣿⣦⠀⠀⠀⢠⠀⣀⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠙⠿⣷⣦⡀⠀⠀⠀⠀⠀⠈⠉⠉⠀⣠⣴⡿⠁⠀⢸⣷⣀⠀⠀⠀ ⠀⠀⠀⠀⠈⣿⡳⣄⠀⠀⠉⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁⠈⣿⡀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠛⣿⣆⠀⠀⠀⠀⠀⠀⣠⣾⡿⠋⠀⠀⠀⢈⣯⠿⣆⠀⠀ ⠀⠀⠀⠀⠀⢿⡋⣽⣷⡇⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⠁⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡓⠀⠀⠠⢶⡿⠛⠃⠀⠀⠀⠀⠀⠘⡿⠒⣨⣤⠀ ⠀⠀⠀⠀⠀⢸⣷⡏⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠀⠀⠀⠀⠀⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⣇⡀⠙⠋⠀ ⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⡛⠃⡀⠒⠀⠀⠀⠀⠀⠀⠤⠀⢻⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠛⠀⠀⠘

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⡶⠶⠛⠛⠛⠛⠛⠛⠓⠶⠶⢶⣦⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣷⣶⣶⣦⣤⣤⣤⣤⣶⣶⣶⠶⠿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⠷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣦⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⣦⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡾⠟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠾⠿⣷⡶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⡿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠋⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢀⣠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣴⡏⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢠⣾⣿⠋⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⣾⣿⣷⡀⠀⠀⠀⠀⠀⣸⣿⡀⠀⠀⢰⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡄⠀⠀⠀⠀⠀ ⠀⠀⣴⣿⣿⣿⣿⣷⡀⠀⠀⠀⣴⠟⠁⠀⠀⢠⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⢶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀ ⢀⣾⣿⣿⣿⣿⣿⣿⣿⣦⣀⣼⠏⣀⣀⠀⠀⢸⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣤⣼⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⡀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⠀⠀⠉⠳⣄⠀⠙⠿⠟⠋⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆⠀ ⣿⣿⣿⣿⣿⡿⠿⠛⠋⠁⠀⢻⣆⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⡇ ⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⢿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣄⣰⠇⠀⠀⠀⠀⡀⡀⠀⠀⠸⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⠷⠶⠟⠁⣀⣀⠤⠤⢄⣀⠀⠀⠀⠀⠀⠀⢠⡿⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠿⣄⡀⠀⣠⠞⢻⠾⣆⠀⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠈⠻⣆⠀⠀⠀⣰⡿⠁⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡾⠁⠀⠀⠀⠙⠳⣆⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣠⡾⠋⠀⠀⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⣀⣼⠾⢿⣦⠀⠀⠀⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⣀⣠⠶⠞⠋⠁⠀⠈⢿⣆⠀⠀⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠐⣿⣆⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣇⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⡏⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⡄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀ ⠀⢸⣿⢷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⣿⡇⠀ ⠀⠈⣿⡀⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣿⢀⣿⠃⠀ ⠀⠀⠸⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⠇⠀⠀ ⠀⠀⠀⠙⣿⣿⣿⣿⣿⣷⡀⠀⠀⣀⣀⣀⣀⠀⠀⢀⣾⣿⣿⣿⣿⣿⠋⠀⠀⠀ ⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⣿⣿⠟⠋⣿⣿⣿⣿⣿⣿⣿⣿⠙⠻⣿⣿⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣿⣿⡇⠀⠀⠛⠛⣻⣿⣿⣟⠛⠛⠀⠀⢸⣿⣿⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣾⣿⣿⣷⣄⣀⣀⣴⣿⣿⣿⣿⣦⣀⣀⣠⣾⣿⣿⣷⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠛⢿⠟⠻⡿⠛⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢿⣅⠀⠉⢻⣿⣿⣧⣤⣤⣤⣤⣼⣿⣿⡟⠉⠀⣨⡿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠻⣷⣄⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣠⣾⠟⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⣀⣀⠀⠀⢀⣀⣀⣠⣤⡴⠶⠛⠉⠉⠁⠀⠀⠉⠉⠉⠙⠛⠲⠶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⡉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢦⣄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢦⣀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣯⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡶⠋⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⡇⠀⠀⠀⠀⣠⣶⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⣾⣧⠀⠀⠀⠀⠀⣿⠀⠀⢀⣾⣿⣷⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀ ⠀⢀⣴⣿⣿⣿⣆⠀⠀⢀⡾⠋⠀⠀⣾⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢶⣦⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀⠀ ⢀⣾⣿⣿⣿⣿⣿⣷⣦⣾⠡⠤⣀⠀⢿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣷⣾⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀ ⢸⣿⣿⣿⣿⣿⠿⠟⠉⣿⠀⠀⠈⢣⠀⠈⠁⠀⠀⠀⠀⠀⢶⠂⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠙⢇ ⠈⠋⠉⠉⠁⠀⠀⠀⠀⠈⢷⡀⠀⢸⡆⠀⠀⠀⠀⠀⠀⣼⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡹ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡞⠀⠀⠀⣠⣀⡀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠋⣠⠤⠒⠒⠢⢄⠀⠀⠀⠀⣼⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⣴⠋⠀⠉⠣⣄⠻⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠁⠀⠀⠀⠀⠀⢣⠀⣠⡾⠁⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⢀⣼⠾⣯⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠤⠀⠤⠔⠚⠉⠀⠀⠙⣧⠀⠘ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⡉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠈⠉⠙⠉⠘⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣾⣿ ⣿⣿⣿⡿⠉⠉⠓⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠋⠙⣿⣿⣿⣿⣿ ⣿⣿⣿⡇⠀⠀⠀⠀⠈⠙⢦⡄⠀⠀⠀⠀⠀⢀⣠⡴⣞⣿⠟⢻⡟⠻⣿⣳⢶⣄⡀⠀⠀⠀⠀⠀⠀⢀⣠⠾⠋⠀⠀⠀⠀⢸⣿⣿⡿⠋ ⠈⠻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠈⢲⡄⠀⢀⣴⠟⢁⡼⠛⠉⠀⠀⡇⠀⠀⠙⠷⣌⡙⠳⣦⡀⠀⢀⡴⠛⠁⠀⠀⠀⠀⠀⠀⢸⣿⠟⠁⠀ ⠀⠀⠈⠻⢄⡀⠀⠀⠀⠀⠀⠀⠀⠙⣾⣿⠁⢠⡞⠁⠀⠀⠀⠀⣷⠀⠀⠀⠀⠈⣹⣦⣬⣿⣶⠏⠀⠀⠀⠀⠀⠀⠀⢀⡤⠛⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⠲⣄⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣦⣤⣶⣾⣶⣦⣿⣤⣶⣶⣶⣾⣿⣿⣿⡿⢹⠀⠀⠀⠀⠀⠀⣠⠶⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢤⣤⠤⠐⠺⣿⣿⠿⠿⠛⠉⣁⣀⣀⣀⣈⣉⡙⠻⠿⠿⠿⣿⣁⠈⣄⠀⢀⡠⠔⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣹⣟⣿⣵⣦⣤⠶⠾⠛⠛⠛⠛⠛⠛⠛⠛⠻⠶⠤⠤⠤⠽⠗⢻⡏⠉⠀⠀⠀⠀⠀⢀⡴⠊⠉⠣⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠟⠉⠁⠀⠀⠀⠀⠈⠉⠑⠒⠤⢄⣀⡀⠀⠀⠀⠀⢀⡠⠖⠦⠖⠻⡀⠀⠀⠀⣠⠞⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⠀⠀⣤⣄⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠒⠉⠁⠀⠀⠀⠀⠀⢇⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠊⣿⠀⢠⣟⡿⠂⠀⣼⠀⢀⣤⣶⣿⡿⣯⣛⡶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠘⢶⠋⠁⠀⠀⠀⣏⢠⣿⠟⠉⣠⡶⠒⢄⠙⢯⢳⡀⠀⠀⠀⠀⠀⠀⢀⡴⠒⢶⣦⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠸⠓⠒⡦⠀⠀⡟⣿⡟⠀⣾⣿⣧⣀⣼⡆⠈⣿⣇⠀⠀⠀⠀⠀⠀⢸⣧⣠⣼⣿⣧⠄⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⡅⠀⣼⠷⡏⢧⠀⠹⣄⢈⣿⡞⠀⢀⣿⡏⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣷⠏⠀⢀⡴⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠀⠀⡇⠀⠹⣎⠳⣀⠀⠉⠁⢀⣠⣾⡿⠁⠐⠆⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⣰⠋⠀⢸⡄⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡀⠀⢹⠓⠾⣿⣿⣿⡿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣼⢀⠀⠀⠀⣠⠔⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣤⠼⠒⠂⠙⠛⢧⠀⠀⠀⠀⠀⣴⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣇⢀⡼⠁⠀⣹⡶⠟⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡏⠀⠰⠾⠿⠦⠤⣤⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣼⠁⠀⠀⠀⠀⠀⢀⣾⠃⠠⣆⠠⠤⠤⠤⠤⠤⠄⠀⢤⡴⠀⠀⠀⠀⠁⠀⢳⣀⠀⠀⠀⠀⣠⠟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⢀⣠⣾⣿⡆⠀⠈⠙⠲⠤⣄⣀⣠⠤⠖⠉⢀⡠⠀⠀⠀⠀⠀⠈⣏⡽⠃⢀⣼⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢿⡖⠶⠒⠚⠉⠙⠟⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⠀⠀⠀⠀⠀⢸⠁⣠⣞⣁⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣦⣄⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⡀⠉⢩⡟⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠙⠦⠤⠴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⢀⣴⠿⡆⠀⠀⢻⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠀⠀⠀⣀⣠⡴⠋⠁⢀⡇⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠈⠉⠐⠋⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⡶⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢴⣾⣿⣿ ⣿⣿⠀⠀⠈⠓⢤⡀⠀⠀⢀⡤⣶⠞⠟⠲⣲⢤⣀⠀⠀⠀⢀⠴⠊⠀⠀⢹⣿⠟ ⠈⠻⢄⠀⠀⠀⠀⠙⢤⠖⢁⠞⠁⠀⢸⠀⠈⠑⣮⣑⣄⠔⠁⠀⠀⠀⢀⠜⠁⠀ ⠀⠀⠀⠑⠠⣀⠀⠀⢸⣿⣾⣶⠶⠶⠾⠶⢶⣾⣿⣿⠻⠀⠀⢀⡠⠒⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⡳⣲⠯⠭⢤⠖⠒⠛⠒⠲⠯⠭⠭⠶⢗⠂⠁⠀⠀⡠⠔⠂⠀ ⠀⠀⠀⢀⡀⠀⢰⠋⠀⠀⠀⠀⠈⠁⠒⠠⠤⠀⠤⠒⠀⠉⠆⠀⡴⠊⠀⠀⠀⠀ ⠀⠂⡇⡼⠟⠀⡄⢠⣴⠶⠦⢖⣄⠀⠀⠀⠀⠀⢀⡀⠀⠀⢸⠊⠀⠀⠀⠀⠀⠀ ⠀⠀⠹⠤⡄⠀⣧⡟⢡⣾⣈⡆⢱⡆⠀⠀⠀⢠⣇⣹⣦⠀⠈⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠸⠇⠸⠺⡱⡘⠠⠗⠁⣸⡇⡀⠀⠀⠀⠻⠿⠋⢠⠒⡆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⡀⢱⠹⣶⣶⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠃⢀⠇⡀⢀⠤⠂⠀⠀ ⠀⠀⠀⠀⠀⢀⠕⠊⠁⠈⠱⠀⠀⠀⠿⠀⠀⠀⠀⠀⠀⡣⠊⠠⢞⣁⡀⠀⠀⠀ ⠀⠀⠀⠀⢠⡇⠀⠀⠀⣰⡃⠲⣀⠀⠀⠀⢀⠔⠀⠀⠈⠘⡤⡀⠀⡴⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⣧⠤⠐⠚⠿⡇⠀⠀⠉⠀⠉⢀⠔⠁⠀⠀⠀⢱⢁⣞⣁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢨⠲⡀⣀⠜⠁⠀⠀⠀⠀⢀⠊⠀⠀⠀⠀⠀⠈⡆⣠⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢀⡴⢷⠀⢸⡷⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠂⠛⠠⠊⠀⢸⠇⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠒⠊⠉⠉⠀⣠⠶⠋⠉⡏⠉⠻⣷⡶⢦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠚⠉⠀⠀⠀⠀⠀⢀⡤⠞⠁⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠉⠻⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠞⠁⠀⠀⠀⠀⠀⠀⣀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⢹⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⣼⣧⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢠⣾⡟⠉⠀⠙⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠨⣿⡇⠀⠀⠀⣠⠚⢦⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣰⡿⠁⡇⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⣿⡇⢀⡴⠊⠁⠀⠈⣆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠘⢿⣧⣄⣁⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⣿⡗⠋⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⣴⣿⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⣤⣶⡿⠻⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣠⣀⣏⢀⣠⣤⠴⠖⠛⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀ ⠀⠀⠀⣠⣴⡿⢿⠟⠉⠀⠀⠀⠉⠛⠲⠦⢤⣤⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡾⣿⣿⠝⠏⢻⡉⠉⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡄⠀ ⠀⠀⢸⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⢉⣿⠿⠋⡇⠀⠀⠀⠀⠈⢷⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄ ⠀⠀⠀⠙⢿⢾⣭⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⡶⠟⣿⡿⠀⠀⡇⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡿ ⠀⠀⠀⠀⠸⡀⠀⠉⠛⠓⢶⣦⣤⣤⡤⠤⠤⠤⢴⣷⡶⠚⠛⠋⠁⠀⠙⠛⠛⣡⡤⠤⡇⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⢀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⣘⡿⠁ ⠀⠀⠀⠀⠀⢣⡀⠀⠀⠀⢸⡇⠀⢹⡇⠀⠀⠀⠘⠛⠁⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⣸⣿⡇⠀⠀⠀⠀⠀⠀⠀⢀⠟⠀⠀ ⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠘⢷⣀⣼⠃⠀⠀⣠⡤⢦⣀⠀⠀⠀⠀⠀⠀⠀⢹⣖⣦⣤⣿⡇⠀⠀⠀⠀⠀⠀⢸⠀⠠⣰⣿⣿⡇⠀⠀⠀⠀⠀⢀⣤⠟⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠈⢯⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠉⣧⠀⠀⠀⠀⠀⠀⢸⣷⣴⣿⣿⣿⡇⠀⠀⠀⠀⢠⣻⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⢸⢸⠿⣿⣿⣿⡇⠀⠀⠀⠰⡿⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣄⠀⠀⠀⡾⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⢸⢸⠀⠀⠙⠿⠇⠀⠀⢀⡟⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠟⠳⡄⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⢡⣿⠀⠀⠀⠀⠀⠀⣄⡞⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢉⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣯⠀⠀⠀⠀⠀⣰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡷⣄⠀⠀⠸⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠈⣳⣤⣄⣈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣠⣴⡄⠀⠀⢀⡴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣾⣿⣿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢰⠿⠛⠹⡆⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠿⠋⠁⢀⣠⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀ ⢸⠀⠀⡀⠹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⡟⠿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢀⡴⠟⠉⠁⠀⠀⢰⡾⠛⠷⣦⡀⠀⠀ ⢸⡄⠀⡇⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡆⠀⠀⠀⠀⠘⢷⡀⠀⠈⢿⣄⠀ ⠀⡇⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⠃⠀⠀⠀⠀⠀⠈⠳⢤⣀⣸⣿⡀ ⠀⢳⡀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⣧⠀⠀⠀⠀⢠⣴⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⢀⡀⠈⠛⣚⣿⡇ ⠀⠈⢷⠀⠙⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠸⡄⢀⣠⠞⠉⣰⠛⣿⣿⣧⡀⠀⠀⣠⣾⣟⠿⣧⣀⣤⣿⢿⠁ ⠀⠀⠈⠳⠴⢷⣄⠈⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⡇⠁⠀⠀⣰⠏⠀⠹⡌⢩⠛⠻⠿⢿⣿⣿⣶⣽⠛⠉⢠⠟⠀ ⠀⠀⠀⠀⠀⠀⠙⠳⢤⣀⡉⠁⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠹⣄⡀⠀⣸⠁⣀⡤⠞⠁⠀⠀⠀⠙⠦⣳⣄⡀⠀⠙⠛⠛⠁⣀⡼⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡉⠙⠛⠛⠛⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠓⠚⠛⠛⠛⠉⠁⠀⠀⠠⠤⠀⠐⠲⢤⡈⣙⡛⠛⠒⠒⠒⠛⠁⠀⠀⠀⠀

⠀⢰⣿⣿⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢻⣿⣿⣿⣿⣿⠿⠟⠛⣆⢀⣀⡤⠴⠖⠒⠒⠛⠛⠒⠒⠤⠤⣀⡀⠀⠀⡼⢿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠸⡅⠀⠀⠀⠀⠀⠀⠰⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠶⠁⠀⠀⠈⠉⠉⠛⠛⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡼⠀⠀⠀⢠⣤⣤⡄⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⠇⡤⠤⢤⡘⢿⠿⠃⣀⣠⣾⣿⣿⣿⣿⣿⣦⣀⠀⠀⠘⢿⡿⠃⣠⠤⠤⣀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⢀⣀⣀⠀⠀ ⢸⠀⠀⠀⠀⢹⠀⠀⠀⠙⠿⠿⠿⠟⠻⠿⠿⠿⠋⠀⠀⠀⠀⠀⢘⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠸⡗⠋⠉⠉⠀⠀⠀⠙⡇ ⢸⠳⣄⣀⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⣀⣀⡼⠃⠀⠀⠀⠀⠀⢀⣠⡇⠀⠀⠀⠀⠀⠀⠀⡇ ⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠖⠛⠉⠉⠙⠒⢦⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣇ ⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⣷⣟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡇⠀⠀⡤⠤⠖⠒⠚⠃ ⢸⠀⠀⠀⠀⠀⠀⠀⠘⢦⡽⢆⠀⠀⠀⠀⢀⣾⣛⡿⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣆⠀⠀⢧⠀⠀⠀⠀⠀ ⠘⣷⠀⠀⠀⠀⠀⠦⠤⣾⣀⠈⠑⠒⠒⠒⠋⣀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢩⡟⠋⠀⢀⣸⠇⠀⠀⠀⠀ ⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⣶⠚⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⡦⠟⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠳⣄⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠔⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠉⠉⠀⠈⠉⠉⠉⠉⠙⠓⠒⠒⠒⠒⠒⠒⠒⠲⢦⡤⠞⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⡀⢀⠀⠠⠀⠉⠳⢦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀ ⣆⡐⠀⠀⠈⡀⠐⠀⠐⠚⠛⠛⠛⠶⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣉⣿⠷⠚⠁⠀⡈⠀⠌⠀⠄⢀⠀⠐⠂⢌⠙⠾⣶⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠟⠁⠀⠠⠀⠁⡀⢁⠠⠁⡈⠀⠄⠁⠠⣿⣿⣦⡈⠛⠿⣵⣦⡀⠀⠀⠀⠀⠀⠀ ⠀⠐⠈⢀⠂⢀⠐⠀⡀⠐⢀⠐⠠⠈⠀⠿⣿⣿⡷⣮⡙⢶⡙⣯⣦⠀⠀⠀⠀⠀ ⠀⠌⣀⣠⠐⠀⡈⢀⠠⠈⢀⣤⡄⠀⡁⠰⣎⠉⠁⢳⣭⢷⣽⠾⠿⠶⣦⣀⡀⠀ ⠀⣺⣿⣿⣿⣆⠐⠠⢀⡀⠙⠛⣃⣀⣠⡼⠃⠀⣰⣴⣿⣿⣣⣟⡿⣷⢮⡝⣧⠀ ⠀⣿⣿⣿⣿⡿⠐⢦⣀⣀⣤⠞⠉⠁⢁⣠⡴⢟⣋⣥⡾⣟⡷⣿⣿⣿⣿⣿⣹⡄ ⢀⣈⣛⣛⠋⠁⠤⣠⣍⠉⠀⢀⣤⣶⣿⣽⣾⣿⢿⣻⣧⣿⢿⣿⣿⣿⣿⣿⣼⣇ ⠽⣀⡩⣝⡳⡄⢀⣿⣿⣷⣾⣿⣿⣿⣿⡿⣿⡿⣿⣻⣭⢿⣟⣿⣿⣿⣿⣟⡾⣇ ⡟⡴⢳⣌⢳⣻⣾⣿⣿⣿⣿⣿⣿⣿⣻⣿⢿⣽⣟⡷⣟⣾⡿⣽⢯⣟⣿⢾⣽⡿ ⡿⣜⣣⢎⢧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢿⣟⡿⣿⣯⣟⣿⣿⣯⡟⠃ ⣿⣓⣭⣛⢭⠰⢿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣷⣿⠿⢿⣿⣿⣿⣿⣟⣾⣽⣾⠃⠀ ⠙⣻⡿⢉⢦⡙⣚⢿⣿⣿⣿⣿⡿⠗⠛⢻⣿⣿⡖⡈⢳⣯⠉⠙⠛⠛⠛⠁⠀⠀ ⣾⡟⢁⠎⢦⠱⣌⢺⣿⣿⡿⠋⠀⠀⠀⢰⣿⣿⠣⢍⠆⢹⡷⠀⠀⠀⠀⠀⠀⠀

⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠻⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠂⠈⢻⣆⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣧⣤⣀⣻⠀⠀⠀⠀⠀⠀⢸⣿⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⠟⠉⠛⠻⢶⣶⡶⠶⠶⢾⣷⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⠀⠀⠀⠀⠀⠀⠉⠻⠶⣤⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠉⠁⠀⠀ ⣿⡀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠛⠿⢿⡿⠟⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⠿⣿⣿⠿⠟⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠻⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸ ⠀⠙⢻⣦⡀⠀⠀⠀⠀⠀⢀⣾⠟⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿ ⠀⠀⢸⡏⠉⣷⣄⠀⠀⣠⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⡿⠁ ⠀⠀⢸⡇⠀⢸⡟⢷⣤⡿⠁⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⡿⠟⠀⠀ ⠀⠀⢸⠇⠀⢸⠇⢠⡿⠀⠀⠀⢰⣿⠉⢹⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠛⣿⣶⡀⠀⠀⠀⠀⠘⠟⣿⣿⡿⠋⠀⠀⠀⠀ ⠀⠀⢸⠀⠀⣿⠀⣾⠃⠀⠀⢄⢸⣿⣶⣿⣿⣿⠆⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣤⣤⣿⣿⡷⢤⠀⠀⠀⠀⠀⢹⣯⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⠀⠀⣿⢸⣇⣀⡀⠀⠈⠈⠛⢿⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⣿⣿⡿⠃⠀⠃⠀⠠⣄⣀⠀⢻⣷⣦⡀⠀⠀⠀ ⠀⠀⠸⠀⣴⡿⠟⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠍⠀⠀⠀⠀⠀⠀⠀⠙⠷⣾⣿⣿⣿⣦⡀⠀ ⠀⠀⢀⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣆ ⠀⠀⣾⠁⣠⡶⠖⠲⢦⣄⠀⠀⠀⠀⠀⢰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⣠⣤⠴⠶⣤⣀⠀⠀⣿⣿⣿⣿⣿ ⠀⢸⡇⣸⡟⢁⠀⠀⠀⢹⡆⠀⠀⢀⣤⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠁⠀⠀⠀⠀⢀⣾⠋⠀⠀⠀⠈⢻⣆⠀⣹⣿⣿⣿⣿ ⠀⢸⡁⣿⡄⠀⠀⠀⠀⣼⡇⠀⠈⠛⠉⢻⣦⣠⡤⠶⠶⣶⠦⢤⣤⣄⠀⠀⣠⡿⣶⣤⠀⠀⠀⢸⡇⠀⠀⠀⠀⢀⢨⡿⢀⣿⣿⣿⠿⡿ ⠀⠈⣧⠘⠿⢦⣄⣠⡾⠋⠀⠀⣠⣤⠾⠛⠉⠀⠀⠀⠀⣿⠀⠀⠈⠉⠛⠿⣧⣄⡀⠀⠀⠀⠀⠈⢿⣄⡀⠀⠀⣠⡾⠃⡾⠹⣿⠏⠈⠁ ⠀⠀⠹⣧⡀⠀⠀⠀⠀⢀⣴⠟⠉⠀⠀⠀⠀⠀⠀⠀⢀⣿⣆⠀⠀⠀⠀⠀⠀⠙⠛⢷⣤⡀⠀⠀⠀⠙⠛⠿⠟⠋⢁⣼⠃⠸⣇⠀⠀⠀ ⠀⠀⠀⠙⣷⣄⠀⠁⠺⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠁⢻⡀⠀⠀⠀⠀⠀⠂⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⣠⣾⠟⠁⠀⠀⣿⢷⡀⠀ ⠀⠀⠀⠀⣿⣸⠿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢏⠀⠀⠰⠟⠋⠁⠀⠀⠀⠀⡟⢡⣤⡄ ⠀⠀⠀⠀⣿⡏⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡿⠁⠀⠀⠀⠀⠘⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡆⠀⠀ ⠀⠀⠀⠀⠿⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠾⠋⠀⠀⠀⠀⠀⠀⠄⠘⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠋⠀⠐

⣄⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠈⠱⡄⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣷⠒⠧⣤⡤⠤⢼⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡇⠀⠀⠀⠈⠓⠺⢿⣿⣿⣿⠿⠿⠛⠛⠛⠛⠿⠿⢿⣿⣿⣿⡿⠿⠟⠋⠉⠀⠀ ⢻⣀⠀⠀⠀⠀⠀⣀⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⢰ ⠀⢸⠓⣄⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡟ ⠀⢸⠀⣻⢓⡞⠀⢀⡤⢤⡀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣀⠀⠀⠀⢠⣴⣾⠿⠋⠀ ⠀⢸⠀⡇⡼⠀⠠⢸⣷⣾⡷⠀⠀⠀⠀⠀⠀⢰⣧⣤⣿⡆⡀⠀⠀⢹⣅⠀⠀⠀ ⠀⢸⢠⡷⠗⠒⠀⠀⠉⠋⠀⠀⣀⣀⠀⠀⠀⠀⠙⠛⠋⠀⠀⠈⠒⢦⣿⣷⣄⠀ ⠀⢰⠋⣀⣀⠀⠀⠀⠀⢀⠀⠀⠉⠉⠀⠀⠀⡀⠀⠀⠀⠀⠀⣀⣀⠀⠙⣿⣿⣷ ⠀⡇⡞⠅⠀⢹⡀⢀⣠⡞⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⢰⠋⠁⠈⢳⡀⣿⣿⣿ ⠀⣇⢷⣀⣀⠼⠀⢀⡠⠟⠒⠉⢹⠉⠙⠲⢴⣋⠙⠀⠀⠸⣄⠀⢀⡼⢡⢻⡿⠙ ⠀⠘⢆⠀⠀⣤⠞⠁⠀⠀⠀⠀⡼⢇⠀⠀⠀⠈⠙⠲⣄⠀⠈⠙⢋⡵⠋⢸⣄⠀ ⠀⠀⢸⡕⠆⠂⠀⠀⠀⠀⣠⠞⠁⠘⡄⠀⠀⠀⠀⠀⠘⠆⠀⠒⠋⠀⠀⢸⠪⠄ ⠀⠀⠸⠁⠀⠀⠀⠀⣀⠴⠃⠀⠀⠀⠙⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢹⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⢸⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠤⠤⠤⢤⣤⣠⠔⠁⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣴⣶⣶⣶⡖⠒⠒⠒⠒⠶⠦⠤⢤⣴⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⣠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⣄⠙⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⠦⣄⣀⠀⠀⠀⠀⣰⡋⣻⣦⠀⠀⠀⠀⠀⠀⢿⣦⣿⡇⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠁⠀⠀⠹⢿⣿⠟⠀⠀⠀⢶⣴⠀⠈⠉⠉⠀⠀⣿⣄⣰⠤⢤⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡠⠤⢄⡀⠀⣀⠀⠀⢀⣤⣀⣀⠤⠀⠀⢸⠀⢹⡃⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡼⠦⣄⣇⠀⢸⠀⠀⠀⢱⠀⠀⠑⢞⠉⠉⢻⠃⠀⠀⠀⠈⢦⡾⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣏⠀⠀⠈⠙⢦⡈⠳⠤⠴⠋⠀⠀⠀⠈⠓⠖⠃⠀⠀⠀⠀⣠⡞⠁⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠙⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠖⠁⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣾⠛⠒⠒⠶⠤⠤⠤⠤⠤⠤⠤⠼⣆⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠒⠒⠒⠊⠀⠀⠀⠀⠀⠀⠀⣰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣤⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠏⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⢀⣶⠀⡟⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣄⣀⣀⣤⠤⠒⢻⠀⠀⢐⡿⠞⢁⡏⣠⡇⠀⣀⣄⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⠉⠀⠀⠀⠀⠀⢸⠀⠀⢀⣠⠀⣸⡟⢻⡇⢠⡿⠟⠙⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⣠⠴⠋⢹⠀⣨⡇⠛⣇⠋⢧⠀⠀⢳⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⢸⡼⢻⣷⠞⢻⣄⠘⡄⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁⠀⠀⠙⢦⣙⣄⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠓⠒⠒⠛⠉⠉⠑⢲⡤⠀⣄⡠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠛⠀⠀⠀⠸⣿⠇⠃⠔⢚⣇⡇⠀⠀⢒

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣷⣶⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣶⣾⣿⡟ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⠉⠉⠛⠳⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠚⠋⠉⠁⢸⣿⣿⣿⠏⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⡆⠀⠀⠀⠀⠈⠙⠷⣄⡀⠀⣀⣠⡤⠶⠖⠛⠛⠛⠛⠛⠓⠶⠦⣤⣀⠀⢀⣴⠞⠋⠀⠀⠀⠀⠀⠀⣼⣿⠟⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠋⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢻⡟⠛⠶⠶⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⢀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⣇⠀⠀⠀⠀⠀⠉⠉⠛⠛⠲⠶⢤⣤⣀⣀⠀⠀⠀⠀⠀⣼⠃⠀⢰⣿⣿⣤⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣧⣤⣧⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠶⠶⣤⡟⠀⠀⠈⠻⠿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠿⠟⠃⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⢀⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⣿⣿⣿⡄⠀⠀⠀⣄⣀⣀⣤⣤⣀⡀⣀⠄⠀⠀⠀⢠⣾⣿⣿⣦⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠻⠶⠶⠦⢤⣤⣤⣤⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⢀⣿⡄⠻⣿⣿⠟⠁⠀⠀⠀⠀⠈⢏⠉⠉⢹⠃⠀⠀⠀⠀⠀⠸⣿⣿⣿⡿⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣹⠇⠀⠀⠀⠀⢠⡟⠉⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠴⠃⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⢀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⠀⠀⠀⠀⣠⡟⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⣰⠏⠀⠀⠀⣰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⣰⠏⠀⠀⠀⢰⠏⠀⠀⠀⠀⠀⠀⠠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠻⢦⣄⣀⢠⡟⠀⣄⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⢀⣶⠀⠀⠀⠀⠀⠀⣠⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠰⣯⣀⡀⠀⠀⠀⠀⠀⠀⠀⠉⣿⠁⠀⠹⣆⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢀⡿⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠶⢦⣤⣀⡀⠀⢰⡇⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠈⢷⡄⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⢀⡾⠁⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠃⢀⣼⠁⠀⠀⠀⠀⠈⠻⣦⠀⠀⠀⣀⣨⣿⡄⠀⠀⠀⢠⡟⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⢦⣄⣈⣿⠀⠀⠀⠀⠀⠀⠀⠘⢷⣼⡷⡿⠛⠋⠁⠀⠀⠀⠿⣿⣤⣦⣴⣦⡟⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠈⠉⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠉⠉⠉⠛⣻⠷⠒⠶⠶⠶⠶⠶⠶⠶⢶⣶⠶⠶⠒⠛⢿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡫⢀⠀⣠⡴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣦⣀⢀⡠⣹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡾⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠾⣾⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⡆⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣷⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⠿⠻⡇⠀⠀⣀⣤⠦⠶⠶⠶⠦⢤⣄⣀⡀⠀⢠⢿⣿⣿⣿⣿⣿⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣧⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠏⠀⠀⠉⠉⠁⡿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣟⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⢀⣀⡀⢻⡆⠀ ⠀⠀⡀⡀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣠⠞⠋⠑⢦⡀⠻⠿⠀⠀⠀⠀⠀⢀⣤⡀⠀⠀⠀⠙⢯⠎⠉⠙⡞⣇⠀ ⠀⣸⠟⠛⠛⠛⠳⢶⣿⠀⠀⠀⠀⢧⢸⢾⣦⢠⡷⠀⠀⠀⠀⠀⠀⠀⠸⠿⠇⠂⠀⠀⠀⠘⣷⣻⣤⠇⢻⠀ ⠠⣿⠀⠀⠀⠀⠀⠠⣿⣿⣧⠀⠀⠘⠳⠤⠽⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⢸⠄ ⠠⣿⣀⡀⠀⠀⠀⠀⣿⣭⣝⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇ ⠀⠀⠉⠉⢛⡾⠀⠀⣿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⢠⠀⠀⠀⢸⡇ ⠀⠀⠀⠀⢸⣇⡀⠙⠿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣤⣼⠆⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⠞⠀⠀⠀⣼⢸ ⠀⠀⠀⠀⠀⠉⠙⠲⣮⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠏⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠳⠿⢿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⣴⠋⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠳⠶⠶⣶⣄⣠⣤⣤⣤⡤⠤⠤⠤⠶⠶⠶⠶⠞⠛⠛⠙⠻⠿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠤⠤⠤⠤⢄⣀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⣟⠓⠚⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⢤⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⡤⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⡀ ⠀⠀⠀⠀⠀⠀⠚⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃ ⠀⠀⠀⠀⠀⢠⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡴⠁⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣰⠋⠀⠀⣇⠀⢀⣴⣲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣾⣿⣇⠀⣠⠋⠀⣾⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣄⠀⠀⠀⠈⢆⠀⠀ ⣿⣿⣿⡿⠟⡏⠁⢢⠙⠛⠀⠀⠀⡄⠀⠀⠀⠀⢀⣿⣿⣿⠀⠀⠀⠀⠈⠳⡀ ⠉⠁⠀⠀⠀⠘⢆⣠⠀⠀⠀⠀⣞⠁⠀⠀⠀⠀⠈⢿⣿⠏⢀⣀⠀⠀⠀⢠⠃ ⠀⠀⠀⠀⠀⠀⠀⠙⢢⠊⠉⠢⡳⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⠀⠈⣄⡴⠃⡆ ⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠐⢄⡀⠠⠒⠉⢣⠀⠇ ⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⠀⠀⠀⠀⠀⠀⠀⠈⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠃⠀⠀⠀⠀⠀⠀⠄⠡⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⠴⢴⣷⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⣀⣤⠴⠚⢛⡏⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠈⠉⠉⠙⠛⢓⣶⠴⠛⠁⠀⠀⠀⡼⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⢀⣤⠞⠋⠀⠀⠀⠀⠀⠀⣸⣧⠾⠷⠤⣄⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣀⣠⡤⠤⣤⠶⠶⠶⠶⠶⠶⠦⠤⠤⠤⠤⣤⣀⣀⣀⡤⠴⠚⠛⠓⠒⠶⠤⠤⠤⠤⣼⣆⣠⠾⠋⠀⠀⠀⠀⠀⠀⠀⣠⡼⠛⠁⠀⠀⠀⠀⠈⠙⠲⠤⣄⡀⠀⠀ ⠺⣿⣇⠀⠀⠀⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠟⠀⠀⠀⠀⠀⠀⣠⡴⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢦ ⠀⠀⠈⠙⠳⠶⣤⣙⣦⣄⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⡶⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⣿⣟⣛⠛⠒⠓⢺⡏⠀⢀⣴⡗⠓⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠈⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠀⠈⠉⠳⡄⠀⢸⠁⠀⢾⡁⢗⣾⠃⠀⠀⠀⢀⠀⠀⠀⠀⠀⣿⣅⣽⢿⡀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠿⡦⠀⠀⠀⠀⠈⢳⣯⣀⣀⠈⠉⠉⠁⠀⠀⠀⠀⠘⠛⠀⠀⠀⠀⠙⢿⣶⠿⠁⠀⣿⣿⠲⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⣿⠋⠉⠙⢷⡀⠀⠀⢶⣤⣤⣴⠷⢶⣄⡀⠀⢰⡄⠈⠀⢀⣀⣀⣸⡘⣇⠀⠈⠙⠲⣤⣀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⣿⠀⠀⠀⢸⡇⠀⠀⠀⣷⡶⠛⠛⠛⠻⣿⡿⠛⠀⠀⣴⠟⠁⠈⠹⡇⠻⡆⠀⠀⠀⠀⠈⠙⠲⢤⣀⣰⠏⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠹⣧⣄⣤⠟⠁⠀⠀⠀⠸⣧⠀⠀⠀⢀⡾⠁⠀⠀⠀⡇⠀⠀⠀⢠⡇⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⣠⠟⠁⠀⠀⠀⠀⠳⣄⣀⣰⠿⠷⣶⣊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠘⠛⠁⠀⠀⠀⠀⠀⠀⠀⣀⠽⠋⠀⠀⠀⠉⠓⠦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠈⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣤⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⣀⣀⣀⣀⣀⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠋⣹⡏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⡀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣀⣀⣀⣀⣀⠀⡀⠀⠀⠐⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣡⢿⣠⡤⠖⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠦⣄⣀⠈⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⡿⣛⠉⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢉⡙⢒⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⢸⡶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢳⣌⢻⠏⠈⠐⠄⣠⣴⠶⠛⠉⠉⠀⠀⠀⠀⠉⠉⠒⠤⣀⠀⣠⣾⡆⠀⠀⠀ ⠀⠀⠙⣾⡀⠀⠀⠀⠈⠓⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⠟⠋⢳⠀⠀⠀ ⠀⠀⠀⢈⣧⡀⠀⠀⠀⠀⠀⠑⢄⠀⢀⣀⡀⠀⠀⠀⠀⠀⠸⠁⠀⠀⣠⠀⠀⠀ ⠀⠀⢠⡞⠁⠉⠢⣄⠀⠀⠀⠀⠐⠉⠁⠀⠈⠉⠉⠒⠠⣄⡇⠀⠀⢀⠇⠱⡀⠀ ⠀⢀⡟⠀⠀⠀⡷⡄⣩⠖⡊⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠑⡀⠀⡜⠀⠀⠱⠀ ⠀⣸⠀⠀⠀⠀⠈⠲⠃⠀⠔⡀⠀⣿⣿⣬⡏⠀⠀⢠⡄⠀⠀⠘⡴⠁⠀⠀⠀⡇ ⠀⡇⠀⠀⠀⠀⢠⠃⠀⠀⠈⠈⠄⠀⠀⡉⠐⠒⠒⢢⠄⢸⣹⣇⡇⠀⠀⠀⠀⠀ ⠀⡇⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠘⣤⣀⣀⣀⠉⠈⠙⠁⢇⠀⠀⠀⠀⠀ ⠀⢰⠀⠀⠀⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣌⠙⣿⠋⠀⠀⠀⢀⡠⢀⠀⠀⠆ ⠀⠀⢇⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⡠⢠⠒⠁⠀⠁⡘⠀ ⠀⠀⠈⢆⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣈⠔⠁⠀⠀⠀⡐⠀⠀ ⠀⠀⠀⠀⠳⣖⠒⠒⠂⠤⡤⢀⡀⠀⠀⠀⠀⠀⠀⠑⢎⠀⠀⠀⠀⠀⠎⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠓⢤⠤⠴⠥⠀⠘⠀⠀⠀⠀⠀⠀⠀⠈⢢⠀⡠⠒⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠠⠄⠀⠀⢂⠀⠀⠀⠀⠠⠄⠒⠁⠀⠀⠀⠀⠀⠀⠀

⢸⣿⡇⠀⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⣧⡤⠤⠶⠒⠒⠚⠋⠉⠛⠛⠒⠲⠦⢤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢠⡇ ⢸⣿⣧⠀⣿⡿⣧⡠⣄⡀⣀⣠⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⣶⣤⠶⠶⠛⠛⠛⠉⠉⠉⠉⠉⠉⠉⠙⠛⠛⠛⠺⠧ ⢸⣿⡿⡧⡿⠿⢿⣷⣤⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⡇⠀⠀⠀⠀⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⡇⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⢤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾ ⠸⣿⡇⡀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢯⣉⢻⣶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠾⠛⠋ ⠀⠸⠃⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⣠⣶⠖⢦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⡇⠀⠀⣾⣿⣿⣶⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠛⢻⣷⡄⠀⠀⠀⠀⠀⢸⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⠀⠀⠀⣼⠀⠀⠀⠀⠻⠿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣶⣿⣿⡟⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⢺⠀⠀⢰⡧⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠛⠿⠿⠛⠁⠀⠀⠀⠀⠀⣹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣾⡀⠀⢼⡅⠀⢹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠉⠙⠒⠦⣄⣀⠀⠀⠀⠀⠀⠀⢀ ⢸⣿⡇⠀⠘⣧⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠉⢷⣸⠋⠒⠦⣄⣀⠀⠈⠉⠓⠦⢤⣀⡀⢘ ⢸⣿⡇⠀⠀⠘⢧⡀⢘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠃⠀⠀⢀⣾⠃⠀⠀⠀⠀⠈⠙⠓⠦⣄⣀⠀⠀⠉⠛ ⢸⣿⠇⠀⠀⠀⠈⠳⣟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⢀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢤⣀ ⢸⣿⠀⠀⠀⠀⢀⡼⠉⠓⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣄⣀⡴⠋⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⠀⠀⠀⠀⣼⠁⠀⠀⠀⠈⠓⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠞⠁⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠈⢙⠳⢶⡶⠶⠶⠶⠶⠶⠶⣶⡶⠟⠋⠁⠀⠀⠀⠀⠀⠈⣧⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢿⣿⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠉⠓⠦⢤⡤⠖⠋⣡⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⢻⣸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣼⣿⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡏⣧⠀⠀⠀⠀⢸⣷⣤⣀⠀⠀⠀⠀⠀ ⣸⣿⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢿⢻⡀⠀⠀⠀⢸⠺⣇⠉⠓⠦⣄⠀⠀ ⣿⣿⠀⠀⠀⣸⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠸⡞⡇⠀⠀⠀⢸⠀⠙⠀⠀⠀⠈⠙⢦ ⣿⣿⠀⠀⠀⡏⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⣧⣻⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⠀⠀⢸⡇⠀⢹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣳⠀⠀⢹⡝⠃⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⣠⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡀⠀ ⠀⠀⠀⠀⠀⢰⣿⣿⣿⡇⠀⠀⣀⣀⣀⣀⠀⠀⢀⣼⣿⣿⣧⠀ ⠀⠀⠀⠀⠀⡎⠉⠉⠀⠰⠂⠉⠀⠀⠀⠀⠉⠙⠊⠈⠉⠉⡇⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀ ⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⣤⡄⠀⠀⠀⠀⠀⠀⣴⣄⣀⢷⠀ ⢀⠤⠤⢤⣸⠃⠀⢰⢩⣌⢱⠈⠁⠀⠀⠠⣶⠀⠀⠈⣧⣌⣿⡀ ⢼⠀⠀⠀⢸⠷⡆⠀⠓⠚⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⡇ ⠈⠒⢲⡄⢸⡟⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡇ ⠀⠀⠸⠤⣙⣧⠀⠀⠀⠀⠀⠀⠳⠖⠀⠀⠀⠀⠀⠙⠋⠀⢰⠁ ⠀⠀⠀⠀⠘⠻⠷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣰⠃⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠾⠒⠒⠀⠈⠉⠉⠉⠀⠀⠉⠀⠀

⠸⣿⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢿⣮⠻⣿⣿⣿⣶⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⡴⠶⠶⠶⠶⠤⢤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠈⢿⣷⠈⠻⣿⠃⠀⠀⠙⠲⢤⡀⣀⣤⣶⣟⡛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠳⠦⣄⡀⠀⠀⢀⣴⣿⣿⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠻⣿⡀⣿⠀⠀⠀⠀⠀⠀⠉⠻⢿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣤⣾⣟⣭⣽⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠋⠁⠀⠀⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣾⡿⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢳⣤⣤⡤⠤⠤⢤⣤⣄⣀⡀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢰⠛⣆⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⡿⠉⠀⠀⠈⠻⢦⣀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠲⢤⣀⢀⡏⠀⠀⠀⠀⠀⡾⠀⠘⢆⠀⠀⠀ ⠀⠀⠀⢠⣿⠃⠀⠀⠀⢀⣤⡀⠉⠳⢦⣀⢠⡤⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣇⠀⠀⠀⠀⢰⠇⠀⠀⠈⣆⠀⠀ ⠀⠀⠀⣾⠃⠀⠀⠀⠀⠘⣯⠻⣄⣀⣴⠋⠉⡄⠀⠀⠀⠀⢀⣴⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀⠀⢀⡏⠀⠀⠀⠀⠘⡄⠀ ⠀⠀⢸⠏⠀⠀⠀⠀⠀⠀⠘⠳⠌⡴⠁⠀⠐⠘⡄⠀⠀⠀⣿⣿⣏⠈⢹⡟⠃⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠱⣀⡞⠁⠀⠀⠀⠀⠀⢳⠀ ⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⢡⠹⡄⠀⠀⠿⠿⠿⢿⣿⠁⠀⠀⠀⠀⠐⠛⠀⠠⡤⣀⣀⠀⢿⠁⠀⠀⠀⠀⠀⠀⠸⡄ ⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠣⠈⣆⠀⠀⠀⠀⣀⡈⠈⠋⠉⠉⠑⠲⣤⠀⢠⣏⣩⣿⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠠⠄⠀⠀⠀⠉⠀⠀⠀⠈⠙⣄⠀⠀⠀⠀⠀⠘⠷⠆⠘⠿⣿⣿⠃⡏⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⠀⣇⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣤⣄⣀⣠⣤⡀⠈⠀⢀⠈⠁⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠁ ⠀⠀⢸⡀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠉⠙⢿⣯⣿⠓⠒⠊⠀⠀⠀⠀⠈⢀⠀⠀⠀⠀⠀⢰⠀ ⠀⠀⠈⣇⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣄⣠⠟⠁⠀⠀⠀⠀⠀⠀⢀⢒⡋⠁⠰⣄⠀⢀⡎⠀ ⠀⠀⠀⠹⡄⠀⠀⢀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⣠⠟⠋⠀⠐⠲⠾⠀⡸⠀⠀ ⠀⠀⠀⠀⢻⡄⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠞⢁⡴⠃⠀⠀⠀⠀⠀⠀⣰⠁⠀⠀ ⠀⠀⠀⠀⠀⠻⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⠀⠀⠊⣀⠴⠋⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⢶⡶⠶⠤⠤⠤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡴⠚⠁⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠹⢦⡤⠀⠀⠀⠀⠈⢩⡟⠙⠲⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⡤⠤⠤⠤⠯⠤⠤⠤⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠤⣄⡀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣻⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠒⠢⠤⠄⠀⠈⢆⠀⠀⠀⠀⠀⠤⠤⠖⠒⠉⢁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⢀⣴⣶⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣾⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢷⡀⠀⠀⠀⣀⣤⣤⣤⡤⠤⠶⠶⠦⠤⣤⣄⣀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⡟⠛⠛⠛⠛⠛⠉⠁⠀⠀⣈⣷⠴⠚⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠲⢦⣄⢠⡟⠈⠉⠛⠛⠿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣼⠃⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⡟⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⣠⣶⣶⣄⣤⣶⣦⣄⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⠃⠾⠋⠉⠳⣄⠙⠿⠋⠀⢰⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⡆⠀⠀⠀⠙⠿⠋⢀⡴⠞⠉⠓⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣀⣀⣀⣠⣤⣤⣄⣀⡀ ⣼⠀⢠⠀⠀⠀⠈⡇⠀⠀⠀⠈⠛⠿⠿⠿⠿⠟⠻⠿⠿⠿⠿⠋⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠋⠉⠉⠀⠀⠀⠀⠀⠀⠘⣷ ⡟⢳⣄⠀⠁⢀⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣆⠀⠀⠀⣰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿ ⡇⠀⠉⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡴⠶⠶⢶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠉⠀⠀⠀⠀⠀⠀⣶⣶⣶⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠉⠀⠀⠀⠀⠀⠀⠉⠛⣿⢶⣴⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⠟⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⣾⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠇⠀⠀⢠⠖⠒⠛⠛⠛⠛⠉ ⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⣀⣿⣄⠀⠀⠀⠀⠀⠀⢠⣾⠟⣻⡟⠚⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣿⣿⣿⣿⡄⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀ ⢸⣦⡀⠀⠀⠀⠀⠀⢠⣀⡀⣠⡏⠁⠘⠷⠤⠤⣤⣤⡴⠏⠉⢛⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⢻⡷⠟⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀ ⠈⢿⡄⠀⠀⠀⠀⠀⠀⠉⠉⠙⠷⢦⣤⣤⣀⣀⣀⣀⣤⣴⠶⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⢀⣀⣤⠶⠛⠁⠀⠀⠀⠀⠀ ⠀⠈⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠀⠸⣏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣶⡤⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠾⠟⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠳⠶⠚⠓⠒⠶⠦⠤⠤⠤⠤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣄⣀⠀⠀⢀⣤⠤⠴⠖⠒⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢰⡄⠀⠀⠀⠀⠀⠀⡄⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⣼⣿⣤⡤⠤⢲⡶⠶⠒⠒⠀⠀⠀⠀⠠⢤⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢻⡀⠀⢀⣤⣤⣶⠾⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠳⢶⣮⢥⣶⢤⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⣷⣾⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢻⣿⠤⠤⠄⠨⠏⠉⠙⠻⠶⠶⠶⢦⣀⣀⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣾⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠠⢤⣀ ⠀⠀⠀⢀⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉ ⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⢿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣿⡻⣶⢤⣴⣠⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣸⣿⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠋⠁⠀⠀⠀⠉⠙⠷⣄⣀⡀⠀⠀⠀⠀⠀⠀⢈⣿⣿⡀⠀⠈⠉⠛⠛⠻⠷⣶⣶⣖⡄⠠⠄⠀⠀ ⠀⠀⣿⡇⣦⡾⠛⠛⢉⣉⣿⣷⣶⣤⣄⠀⠀⠀⣤⣤⡴⠾⠿⠤⠦⢤⠤⠤⣄⡀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛ ⠀⣠⣿⢷⣿⠷⢤⣤⡾⢹⣤⣀⣀⣈⣙⣶⡴⠺⣟⣁⣠⣀⣀⣤⡦⠼⣤⣤⣤⡥⠤⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⠃⠀⠈⠀⠀⠈⠛⢾⣿⣿⣿⣿⣿⡟⠃⠸⣿⣯⣿⣿⣿⣿⠷⠛⠉⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠓⢯⡝⠛⠉⠀⠀⢀⢿⡝⠛⠋⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠈⠙⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠙⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢻⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⡇⠹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠁⣽⠀⠙⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠙⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⠀⠀⠀⢀⢆⣼⠇⠀⠁⠀⢰⠘⠽⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠘⢧⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⣀⠄⠀⠀⠀⣩⣾⣵⠃⠀⠀⠀⠘⠀⢨⣿⣷⡀⣤⣤⡀⠀⠀⠀ ⠀⠀⠀⠈⠳⡆⣀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣋⡠⠚⠁⠀⢀⢀⣶⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠈⢻⣷⣄⠙⢷⣤⣄⠀ ⠀⠀⠀⠀⠀⠙⣎⡙⠒⢬⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⡾⠟⠋⠁⠀⠀⢀⣠⣾⡿⠫⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣧⡀⠹⠟⠁ ⠀⠀⠀⠀⠀⢠⣿⡻⢦⣄⠀⢈⡙⠻⠷⣦⣄⣀⣀⣀⣀⣀⣀⣀⣀⣠⡶⠾⠛⠋⠉⠀⠀⠀⠀⣀⣴⢿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣆⠀⠀ ⠀⠀⠀⠀⠀⢸⢸⡇⠀⠈⠻⠶⢶⣤⣀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡴⠶⠛⢋⡀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀ ⠀⠀⠀⠀⠀⣾⣸⡇⠀⠀⠀⢰⣆⠀⠉⠙⠛⠳⠶⣤⠄⠀⠀⠀⠠⠤⠚⠛⠛⠋⠉⠀⠀⢀⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⢿⣿⠀⠀⠀⠘⠙⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣧⣸⠘⠀⠀⠀⠀⠘⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢹⢿⡆⠀⠀⠀⠀⠀⠀⠐⠲⠎⡻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⠼⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠈⢿⡇⠀⠀⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠈⢸⣿⡿ ⠀⠀⠀⠀⢀⡀⢀⡘⢇⠀⠀⠀⢃⠀⠀⣀⣀⣒⠒⠒⠒⠀⢀⠔⠁⠀⠀⣼⠟⠁ ⠀⠂⠤⡀⠀⠀⠀⠀⠈⢢⡀⡀⠈⠈⠀⠀⠀⠀⠈⠁⠒⠴⠁⠀⠀⠀⡠⠋⠀⠄ ⠀⠀⠀⠀⠉⠫⢁⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠄⠊⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠑⠠⡸⠀⣀⡤⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⡄⠸⠷⠞⠀⠀⠀⠀⠀⠐⣭⣿⡇⠀⡆⠀⠀⠀⠀⠀ ⡀⣀⡀⠀⠀⠀⠀⠀⢰⠀⠸⡄⠀⠀⣀⡀⠀⡀⠀⠀⠈⢡⠂⠐⡇⠀⠀⠀⠀⠀ ⠀⠉⠙⠫⡔⠢⡄⢀⠊⣆⣰⠁⠀⠀⠀⠀⠀⠀⠁⠀⠀⡇⠀⢠⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠰⠁⠰⢠⠂⢠⠚⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢐⠏⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⡇⠀⠇⢓⢤⠃⠀⠈⠐⢄⠀⠐⠄⠀⠀⠀⠀⠀⠐⠁⢂⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠉⢲⣀⡇⠀⠀⠀⠀⠀⠁⠐⢢⠀⠀⡐⠂⠀⠀⠀⠈⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⢃⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠉⢻⠀⠀⠢⢀⠀⠀⠄⠈⠀⠀⠀⠀⠢⢀⡀⡀⡎⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠸⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⣲⣤⣤⠄⠀⢀⣀⣀⣀⣀⣀⣰⠶⢞⢇⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠸⡟⠈⠙⣰⡯⠭⠖⠒⠒⠒⠒⠛⠓⠒⠑⠋⠀⠀⠀⠀⠀⠀

⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀ ⢷⡤⣑⠢⡀⠀⠀⠀⠀⠀⠀⢸⠀⠐⡀⠀⠀⠀⠀⠀⡠⢴⡟ ⠢⣈⠑⠣⢢⢅⡢⢀⠀⠀⠀⠘⡄⢀⠒⠒⠒⠠⢔⡠⠀⡰⠁ ⢶⢄⡁⠂⠄⡈⠛⠶⣭⡂⢄⠌⢀⠛⠣⢄⠀⢾⠆⠀⠰⠀⠀ ⠀⠈⠐⠡⢒⡬⣱⠢⢄⠉⠃⠀⠴⠂⠀⠀⠀⣔⣲⠀⠀⢡⠀ ⠀⠀⠀⠀⠀⠈⠑⠫⢶⣿⣾⣤⣀⠀⠢⡀⠀⠀⠀⠀⠀⠈⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⠫⠗⡥⣢⠌⡀⠀⠀⠀⠀⢠⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠑⠻⠟⠀⠀⠀⢀⠆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠄⢀⠂⢀⢀⠤⠐⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠈⡆⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⢂⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⡀⠨⠀⠀⠀

⠀⣠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣇⠀⠀⠀⠀⠀ ⠀⣿⣿⣿⠿⠟⢆⣀⠠⠤⠄⠀⠀⠤⠄⣀⠀⡴⢿⣿⣿⣿⡏⠀⠀⠀⠀⠀ ⠀⢣⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠈⢉⠇⠀⠀⠀⠀⠀ ⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀ ⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀ ⠀⡆⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀ ⢸⠐⠒⢜⠛⠠⣴⣿⣿⣿⣷⡄⠀⠙⠋⠔⠒⢄⠀⠀⠀⠀⡇⠠⠤⠤⠤⡄ ⠘⠢⠤⠎⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠢⠤⠜⠀⠀⣀⣠⣤⠀⠀⠀⠀⠃ ⢀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠈⣷⠂⠀⠀⠀⠀⠀⠀⠀⠉⠉⡝⠀⡠⠤⠤⠃ ⢸⡀⠀⠀⢀⣈⠚⠢⠀⠠⠞⣻⠉⠀⠀⠀⠀⠀⠀⠀⠻⢿⠷⠀⢱⠀⠀⠀ ⠀⢳⠀⠀⠀⠀⠉⠉⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣎⢰⠈⠁⠀⠀⠀ ⠀⠀⠑⣄⡀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠠⠐⠋⠉⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿ ⣿⡇⠀⡈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⢁⠀⢸⣿ ⣿⣷⠀⢿⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⠀⡿⠀⣼⣿ ⣿⣿⣇⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⣸⣿⣿ ⣿⣿⣿⣦⠀⠀⠀⠀⠀⠈⢿⣿⣿⠿⠿⠿⠿⣿⣿⡿⠁⠀⠀⠀⠀⠀⣴⣿⣿⣿ ⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⠀⠀⠀⣠⣴⠀⠀⠀⠀⠀⠀⠀⠀⣦⣄⠀⠀⠀⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⡟⠀⠀⢸⣿⣿⣤⣤⠄⠀⠀⠠⣤⣤⣿⣿⡇⠀⠀⢻⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⠁⠀⠀⠈⠻⠿⠿⠋⠀⠀⠀⠀⠙⠿⠿⠟⠁⠀⠀⠈⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣤⡀⣠⣄⢀⣤⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⡀⠺⣿⣶⡄⠀⠀⠘⠛⠛⠛⠛⠃⠀⠀⢠⣶⣿⠗⢀⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣷⣄⠈⠻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟⠁⣠⣾⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⣀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⡀⠈⠀⠀⠀⡀⠀⠀⠀⠈⠙⠿⣶⣄⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀ ⡀⠐⠀⠁⠂⠈⠄⠐⠈⠈⠐⠀⠀⠀⠈⠛⣿⣯⣷⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀ ⡜⢤⠐⠈⠀⠁⠈⢀⠐⢀⠁⠂⠐⠀⠛⠛⠛⠛⠛⠛⠛⠿⢿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀ ⠻⣷⣮⣱⡄⣌⡤⠒⠈⠀⠠⠐⢀⠂⠄⠀⠠⠀⡀⠀⠄⡀⢀⡀⠉⠙⠿⣷⣤⡦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀ ⣠⣔⣿⠿⠛⠁⠀⠀⢀⠂⠡⢀⠀⠄⠠⠈⠄⠠⠀⡐⠀⢀⠀⠈⠁⠒⣆⠀⠙⠿⣮⣻⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀ ⣿⠟⠁⠀⡀⠄⠡⠈⡀⠐⠀⢂⠐⠈⢀⠂⠌⠀⢁⠠⠈⡀⠐⠠⢐⣿⣿⣿⣶⣄⠈⠙⠿⣯⣟⣳⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠁⠀⠄⠂⢀⠐⠀⡁⠀⠠⠈⡀⠄⠐⠀⠀⠂⠈⠄⠀⠂⢀⠂⠁⠀⣿⣿⣿⣿⣿⣦⠀⣀⣀⣉⡛⢷⣯⣻⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⠂⢈⠀⠠⠁⡀⢀⠁⠐⠀⠐⠀⡈⠐⠠⠁⠂⢈⠐⠀⡀⠂⠀⢻⣿⣿⣿⣿⣿⣧⡯⡜⣭⢛⣦⡘⢿⣞⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⠐⠠⠀⠁⠄⠐⡀⠠⢈⠐⠈⢀⠀⠈⠄⠂⠐⠀⠀⠒⠀⢂⠀⡀⣌⠛⠿⠿⠛⠸⣷⡙⢦⣋⡖⣿⣬⣿⣾⣧⣀⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⠌⣀⢠⣀⣆⡀⢀⠂⡀⢂⠈⢀⠠⠁⠀⣐⣬⣶⣷⠀⠀⢂⠀⠀⢻⣷⠂⢀⠠⠀⠹⣿⣲⣝⣾⣿⠿⣛⢛⡛⣛⠻⣷⣤⣤⣀⠀⠀ ⠀⠀⢾⣽⣿⣿⣿⣿⣦⡐⠀⠄⢈⠀⡀⠀⠐⠛⠿⢿⠇⠀⢀⠀⢀⣤⡿⠏⠀⠀⠐⣀⣢⣽⣷⣿⣿⢇⣳⣼⡶⣷⣮⣵⣉⠏⣿⣯⠀⠀ ⠀⢨⣿⣿⣿⣿⣿⣿⣿⣧⠀⠈⠀⠀⠄⡁⢂⠀⠀⣠⣴⡶⡶⠾⠟⠋⠁⠀⢀⣤⣷⣿⠿⢛⣿⣿⣟⣾⣻⢾⣽⣷⣯⣿⡽⣿⡸⣿⡆⠀ ⠀⠒⣿⣿⣿⣿⣿⣿⣿⡿⠀⢻⣧⣄⠀⢀⢀⣠⣾⠛⠀⠀⡀⠀⢀⢠⣠⣾⡿⢛⠍⣰⣬⣶⢻⣿⣞⣷⣻⣿⣿⣿⣿⣿⣿⣟⡗⣿⣇⠀ ⠀⠈⠻⢿⣿⣿⣿⣿⠟⠁⢀⠀⠘⠻⠿⡿⠛⠋⠀⠀⠀⠁⣠⣴⣾⠿⣛⣵⣬⣷⣿⡿⣯⢿⡘⣿⣟⡾⣿⣿⣿⣿⣿⣿⣿⣿⣯⢽⣿⡀ ⢀⣠⣤⣤⣬⣉⡍⠀⠀⠂⠜⢀⣾⣾⣄⠀⠀⠠⠐⣈⣴⣿⢿⣯⣷⣿⣿⡿⣟⣯⣷⣟⣯⣿⣵⣿⣿⡽⣿⣿⣿⣿⣿⣿⣿⣿⣟⢾⣿⡇ ⣎⡓⠀⠈⢩⡛⠿⣷⣄⠀⠈⢰⣿⣿⣿⣷⣾⣶⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⢿⣿⢻⣟⡟⣿⣽⢿⣿⣿⣿⣿⣿⣿⣿⣻⣞⣿⠃ ⣜⡹⣒⢖⡫⣜⡳⣜⢻⣆⡈⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣷⣿⣟⣿⡿⣽⣾⢿⣞⣿⣾⡇⣿⣯⣟⡿⣿⣿⣿⣿⣿⢯⣷⢯⣿⣷ ⣮⠱⡭⣎⠵⣪⠕⣮⡙⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣯⣿⣯⣿⢿⣽⣯⢿⣞⣿⣣⣿⣿⢾⣽⢯⡿⣽⣻⣞⡿⣽⢯⣿⡿ ⣷⢋⢶⡩⢞⡥⣛⠴⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⢿⣾⡿⣷⣿⣯⣿⣷⣿⣿⣿⡿⣿⢿⣿⣻⢾⣻⣽⣿⣿⣿⡽⣯⣿⣿⠀ ⣟⢯⣶⣙⣎⠶⣩⣞⡿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣟⣿⣽⣳⣯⢿⣽⣯⣿⣿⣯⣷⣻⣿⣿⣾⣟⣿⡇⠀⠀ ⣿⢞⡶⣏⠾⡿⢟⠫⡔⡹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣯⣿⣿⣾⣿⣿⣿⣿⣿⣿⢿⣿⣿⣷⣻⢾⣽⣻⣞⣿⠂⠀⠀ ⣿⣿⣶⣮⣷⣼⠾⡱⢌⠳⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢛⣿⣿⣿⣿⣿⣯⣉⠉⢻⣯⣿⣿⣿⣿⣿⣿⣿⣯⣿⣾⣷⣿⠏⠀⠀⠀ ⠉⠙⣿⣿⡿⢃⢎⡱⢊⡕⢢⡝⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠉⢙⣿⣿⣿⣿⣧⢃⡄⠘⣿⣽⡄⠀⠉⠉⠙⠛⠛⠛⠋⠁⠀⠀⠀⠀ ⢠⣾⣿⡟⠁⣘⢎⡱⠣⡜⣡⠚⣼⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀⠠⠀⣿⣿⣿⢾⣿⠰⡘⡄⠘⢷⡿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣻⣿⠏⠀⣌⢣⠒⣌⠳⡘⢤⠓⣬⣿⣿⣿⣿⡿⠁⠀⡀⠀⠐⠈⠀⠠⢽⣿⣿⡿⢣⠱⡱⣘⢃⠈⣿⣏⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠉⠳⢄⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠛⠛⠓⠲⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⣳⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠙⠦⣒⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣦⡈⠙⠺⢵⡢⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⡷⡀⠀⠂⡙⢮⢦⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⣆⠉⠁⠱⡀⢀⣴⠾⠿⠶⢦⣀⡀⠀ ⠀⢠⣾⣿⣿⡄⠀⠀⠀⠀⠉⠛⢁⣀⣀⠴⠃⠀⣀⣤⢷⡿⠁⠀⢂⠂⠀⠉⣧⠀ ⠀⢸⣿⣿⣿⡿⠀⢦⡀⠀⣠⠔⠁⠀⠀⣀⡴⠞⢉⣠⡸⡇⠀⣰⣿⣿⣷⡄⢹⠀ ⠀⢈⣙⡛⠛⠁⠀⣠⣍⠉⠀⢀⣠⠴⣊⣡⠴⠚⠁⢀⣀⣧⠀⣿⣿⣿⣿⣧⢸⡇ ⠀⠀⠀⠈⠓⡄⠀⣿⣿⡷⣖⣿⣷⣿⣿⡀⣶⠿⠟⠛⠉⢹⠀⢻⣿⣿⣿⠏⠀⡇ ⡀⠀⠀⠀⠀⢸⣴⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⢀⣘⣼⡇⠀⠉⢉⡉⠀⢠⡿ ⠃⠀⠀⠀⢀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣧⣴⡶⠶⠛⠛⠋⠉⣿⣄⠀⣿⣿⠆⡟⠃ ⣦⣀⣀⣚⠁⠀⢿⣿⣿⣿⣿⣿⣿⣿⢿⣾⣶⣶⠶⢿⢿⣿⣿⣿⣆⠈⠉⣰⠁⠀ ⠙⣻⡿⠁⠀⠀⠈⢿⣹⣿⣿⣿⡿⠗⠚⢻⣿⣿⡄⠈⠳⣫⠉⠛⠛⠛⠛⠁⠀⠀ ⢼⠟⠀⠀⠀⠀⠀⠘⣿⣿⡿⠋⠀⠀⠀⠀⣿⣿⠁⠀⠀⠱⡇⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣿⣿⣿⣿⣿⣿⣿⣧⠈⢷⡀⠀⠀⠀⠀⢀⡴⠒⠲⡆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⣿⠿⠛⠛⠛⠻⣿⣿⣿⡘⢷⣀⣠⠖⠲⠾⠀⠀⠀⡇⠀ ⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⡏⠀⠀⠀⠀⠀⠀⠙⢿⣧⠸⣿⣿⡀⠀⠀⠀⠀⠈⠻⡆ ⣿⣿⣿⣶⣄⡳⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⣿⣬⡳⣄⠀⠀⠀⠀⢠⣿ ⣿⠿⠛⠉⠉⠻⣦⡳⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣤⣤⣤⣬⣤⣿⣇⣀⠀⠀⠀⠀⠀⠀⠈⣧⣿⣿⢻⣿⢀⣤⣶⣾⣿⣿ ⠁⠀⠀⠀⠀⠀⠈⠻⣮⡙⢦⡀⠀⢀⣠⡴⠖⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠓⠶⣄⡀⠀⠀⠀⢻⢹⡏⣾⣿⣿⡿⠟⠉⠉⠉ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣾⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢰⣄⣸⣿⡹⢟⡽⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣷⡏⠀⠀⠀⠀⠀⠀⠀ ⡄⠀⢢⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣧⡻⣆⠀⠀⠀⠀⠀⠀ ⣷⡀⠀⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢳⡿⣆⠀⠀⠀⠀⠀ ⣿⣷⡄⠀⢹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡙⣆⠀⠀⠀⠀ ⣤⣷⣿⣷⠏⠙⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡙⣆⠀⠀⠀ ⣯⡟⣿⠃⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠿⡿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣧⠀⠸⣷⡁⠀⠀⠀ ⣿⣿⠇⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣶⣤⣤⣀⠀⢀⣤⠄⠀⠈⠉⠀⠀⠀⠀⠀⢠⣀⣀⣤⣾⣿⣿⣿⡿⠃⠀⠀⢹⡇⠖⠀⠀ ⢸⣿⠀⠀⠀⠃⠀⠀⢀⣀⣀⡀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⢸⣇⠀⠄⠀ ⢾⣿⠀⠀⠀⠀⣠⡾⠋⠉⠉⠙⠳⢤⡀⠀⠀⠈⠉⠛⠻⠿⠋⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠈⢙⡟⠉⠀⠀⠀⠀⣠⡴⠀⠈⢻⣦⢲⡄ ⢿⣿⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠻⢦⣀⠀⠀⠀⢀⣤⡀⠀⠀⣴⠟⠀⠀⠀⠀⠀⣼⠋⠀⠀⠀⠀⠹⣆⡇ ⣿⣿⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⣤⡾⠛⠉⠛⢶⣾⠃⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⣿⣦ ⣿⣿⣇⠀⠀⠀⠙⢷⣤⣀⡀⣀⣀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⡧⠀⠀⠀⠀⠀⠀⠀⠀⠻⣆⣀⣀⣀⣤⣿⣇ ⣿⣿⠿⠀⠀⠀⠀⢤⡈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⣿⣿ ⠛⠁⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⣟ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⣼⡋ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⢋⡼⡏⠠ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⣋⡾⠋⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠹⣧⠀⢀⠀⢀⠀⠀

⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤ ⣿⡿⠷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠾⠿⣿ ⠋⠀⠀⠈⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁⠀⠀⠈ ⣇⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⣀⣀⣀⣀⣀⣀⡀⠀⠀⢠⣾⠏⠁⠀⠀⠀⠀⣠ ⠻⣷⡀⠀⠀⠀⠀⠀⢹⣶⠿⠋⠉⠉⠁⠈⠉⠉⠙⠻⢶⣟⠁⠀⠀⠀⠀⢀⣴⣟ ⠀⠈⠻⢷⣄⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⣠⣶⠿⠛⠉ ⠀⠀⠀⠀⠙⢿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣟⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⠀⠀⣠⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⠀⠀⢻⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⢰⡟⠀⣾⣧⣼⣿⡇⠀⠀⠀⠀⠀⠀⢰⣿⣷⣼⣷⠀⢸⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⡇⠀⠻⠿⠿⠟⠀⠀⠀⢻⢿⠀⠀⠀⠙⠿⠿⠟⠀⠸⣇⠀⠀⠀⠀ ⠀⠀⠀⠀⣾⠟⠛⠲⡄⠀⠀⠀⠀⢀⡼⢮⡀⠀⠀⠀⠀⢀⡴⠛⠻⣿⠀⠀⠀⣀ ⠀⠀⠀⠀⢹⣇⠀⠀⣹⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⢸⠀⠀⢰⣿⠶⠞⠛⠉ ⠀⠀⠀⠀⠈⢿⣶⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⡿⣷⡀⠀⠀⠀ ⠀⠀⠀⠀⢀⣾⠋⠙⡛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⠋⠉⢷⡈⢻⣆⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⠁⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋⠘⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠊⠁⠀⠀⠀⣿⣿⣿⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣿⡀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠂⠀⠀⠉⠉⠉⠉⡠⠊⠀⠀⠀⠀⠀⢰⣿⡟⠁⠀ ⠠⢄⣀⠀⠐⠒⠚⠉⠉⠉⠀⠉⠀⠀⠱⡄⠀⠀⠀⠀⠀⠣⠔⠒⠊⠉⠉⠉⠉⠉⠁⠒⠠⢄⡀⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⣿⠋⠀⠀⠀ ⠀⠀⠈⠑⠲⢤⡀⠀⠀⠀⢀⣀⣀⣀⣀⣈⣢⡀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠧⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠈⠓⠢ ⠀⠀⠀⠀⠀⠀⠈⠙⠯⣉⠉⠁⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⢀⡤⠚⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠦⣀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⢀⡇⠀⢀⣀⣴⡦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠈⣿⣿⣄⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡴⠚⢻⣶⡄⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠛⢦⠀⠙⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣶⣾⣿⠃⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠉⠉⣠⠖⠓⢦⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠛⠴⢶⣶⣦⡤⣀⡀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⣿⠀⠀⠀⠀⠑⠀⠒⠀⠉⠑⠤⠤⠄⠀⠀⠀⢠⠃⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠑⠲⣏⠉⠒⣤⠀⢀⡜⠈⣧⣄⣸⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⣰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣰⠃⠀⢠⠃⢀⠞⠀⠀⡼⢆⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⣀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⠃⠀⢀⠏⢀⠎⠀⠀⡜⠀⠈⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⡇⠀⠀⣾⡀⠙⢄⣀⡜⠀⠀⠀⠀⠙⠢⣀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⠹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⠓⠦⢤⣀⠈⠁⠲⡾⠀⠀⠀⠀⠀⠀⠀⠈⠣⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡄⣠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡄⠀⠀⠀⡰⠋⠁⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⡸⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⡇⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠠⠚⠁⠀⠀⠀⠀⠀⠀⠈⠢⣄⠀⠀⠀⠀⣴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠒⠉⢸⠀⢰⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢦⠀⠻⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠚⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⣦⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣶⣶⠿⠛⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠛⠛⠿⡒⢒⣶⠶⠶⢛⠉⠉⣉⣉⣉⣉⣉⣻⣟⣦⣄⣀⠐⠌⣻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⢿⡳⠂⠀⠀⣠⣾⡷⠶⠒⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡇⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠚⠁⢻⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠃⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠈⣿⣿⣿⣿⠏ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⡆⠀⠀⠀⠀⠀⠀⠈⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⡠⠤⠀⣠⠟⠁⠀⠀⠀⠀⠀⢰⣿⣿⣿⠏⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣙⣿⡇⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠒⠂⠒⠛⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠠⣼⣿⡿⠁⠀⠀ ⠠⣀⡀⠀⠀⠐⠖⠒⠒⠛⠛⠛⠋⠉⠉⠉⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⢸⣄⠤⠔⠒⠛⠛⠉⠉⠉⠉⠛⠓⠒⠤⢄⣀⠀⠀⠀⢀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠋⠀⠀⠀⠀ ⠀⠈⠉⠓⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⣶⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠁⠀⠐⠦⣄⣀ ⠀⠀⠀⠀⠀⠀⠉⠓⢦⣄⣠⣤⣤⠤⠤⠤⠒⠒⠒⠒⠒⠻⢦⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋⠀⠀⠀⠀⠀⠀⠈ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣄⡀⠀⠀⠀⠀⠀⠀⠀⠶⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⠀⢀⡴⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⣄⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣠⠄⢀⡟⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣸⠁⠀⠀⢦⣾⣿⠋⠙⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⢸⣿⣿⣦⣤⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣞⠉⠙⣿⣿⡇⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠟⠛⢧⡀⠀⠙⠻⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣶⣾⣿⣿⠇⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠈⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠋⠉⣠⠶⢦⣄⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠠⠄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣺⡆⠀⠀⠀⠀⠠⣄⡀⣀⣀⠤⠤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁⠀⠀⠙⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠉⠙⠲⠾⢭⣛⣳⠶⠤⣄⣀⠀⠀⠀⠀⠀⠀⠀⣼⣇⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⠚⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⠑⠲⢬⠉⠙⠲⣤⡄⠀⠀⡼⢁⣸⣤⡀⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⢀⡟⠀⢀⡾⠀⠀⠀⣿⡉⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀⣰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⢀⡾⠀⢠⠞⠀⠀⢀⡼⠁⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠶⢾⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⣼⠃⣠⠋⠀⠐⠀⡞⠁⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢯⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⣴⣇⠀⠙⠦⣄⠀⡼⠁⠀⠀⠀⠀⠈⠙⠧⣄⠀⠀⠀⠈⠻⢧⣀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠰⠋⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡿⢦⣀⡀⠀⠈⠉⠒⠦⣈⣹⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀⠈⠁⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⣤⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠒⠚⠷⣄⠀⠀⠀⠀⠀⠀⣠⡶⠢⠤⠐⠒⠃⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢻⣇⢠⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠡⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⠿⢿⡇⠀⠀⠀⠐⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠁⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⢰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠙⢦⣄⣀⠀⠀⣀⡠⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣄⠀⠀⠀⢀⡴⢿⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠋⠉⠀⢸⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢸⣄⠀⠷⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⣹⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣦⣤⣀⡀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⣴⣾⡿⠛⡲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣷⣿⠥⣍⣁⣀⣀⣀⣀⣤⣤⠴⠶⠶⠶⠶⠶⠶⠶⠶⠶⣾⣝⡋⠝⠉⠰⣄⡙⢮⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⢃⠀⠈⠙⠦⠀⣰⣿⠛⠉⠉⣠⣄⣤⣤⣤⣤⣤⣤⣴⣦⣬⣽⣬⣿⣷⣦⣤⣄⣙⣦⡷⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⢃⠞⠀⠀⠀⢀⣼⣿⡿⠾⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠒⠂⠀⡤⠔⠊⢩⢁⠔⠁⠀⠀⠀ ⢀⡀⠤⡤⠤⠤⠤⠤⠤⠀⠠⠄⠀⠠⠤⠬⣄⠔⠁⠀⠀⡠⠊⠉⠁⠂⠤⣀⠀ ⠈⠑⠂⠼⠤⣀⣀⣀⡰⠀⣀⡀⠀⠀⠀⠀⠀⠀⢆⠂⠁⠀⠀⠀⠀⠀⠀⣠⠃ ⠀⠀⠀⠀⡔⠉⠑⢄⠇⠨⠷⠁⠀⡄⠀⠰⣽⡆⢸⣀⠀⠀⠀⠀⠀⠀⡔⠁⠀ ⠀⠀⠀⠀⢸⠀⠀⠘⠉⢢⠀⢢⡴⠶⣤⠄⢀⠤⢼⢣⠉⠒⠤⣀⢀⠌⠀⠀⠀ ⠀⠀⠀⠀⠀⠆⠀⠘⡖⠋⠀⠈⢆⢀⠎⠀⠸⡀⡰⣠⠆⠀⠀⠀⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⡄⠀⠈⠢⠄⠀⠈⠁⠀⢀⠤⠊⠀⠀⠉⠒⠄⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⣀⣀⡀⠠⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢾⠗⠒⠉⠁⠀⠀⠀⠀⠀⠉⠑⠢⠵⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠸⣿⣧⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢻⣿⡻⣿⣿⣿⣷⣶⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠘⣿⣇⣈⠻⣿⣿⣿⣿⠋⠙⠲⣄⣀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣶⣾⠟⠿⠿⠟⠉⠉⠉⠉⠉⠉⠉⠙⠛⠳⠶⢦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠘⢿⣿⣄⠈⠻⣿⡇⠀⠀⠀⠀⠉⠳⢦⣀⣠⣴⡾⢿⣋⠯⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠷⣦⣄⡀⠀⠀⢀⣼⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⢻⣿⡇⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣦⣤⣾⣿⣟⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⣿⡟⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡿⠟⠛⠉⠉⢻⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⢻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠋⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⡿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣀⣀⣤⣤⣤⣤⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⢰⡟⢷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢰⣿⠛⠃⠀⠉⠙⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠳⢶⣤⣀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣸⠇⠈⢳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⣿⠃⠀⠀⠀⠀⠀⠀⠉⠻⣦⣄⠀⠀⠀⠀⠀⠀⣠⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢦⣄⣿⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⢻⡄⠀⠀⠀ ⠀⠀⠀⠀⢰⣿⠇⠀⠀⠀⠀⠀⢠⣶⣦⡀⠀⠉⠛⣶⣤⣰⠖⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⢻⡀⠀⠀ ⠀⠀⠀⢀⣿⡏⠀⠀⠀⠀⠀⠀⠘⣿⡝⢷⡀⣀⣤⠟⠁⠀⣀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠈⢧⠀⠀ ⠀⠀⠀⢸⡟⠂⠀⠀⠀⠀⠀⠀⠀⠘⠷⣄⠙⣭⡏⠀⠀⣀⠘⡄⠀⠀⠀⠀⢠⣿⣿⣿⠋⠓⢶⣶⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀ ⠀⠀⢀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣰⠏⠀⠀⠀⠀⡄⠻⡄⠀⠀⠀⢸⣿⣿⣿⣷⣤⣾⡇⠀⠀⠀⠀⠀⠀⢀⣧⡄⠀⠀⠀⠀⠀⠀⠸⣶⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀ ⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠘⣄⠻⣄⠀⠀⠈⠻⠛⠻⠿⠿⣿⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠰⣶⣄⣀⣄⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆ ⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠘⢀⠈⣧⠀⠀⠀⠀⠀⢀⣀⠈⠁⠉⠉⠉⠉⡉⠓⠶⣤⠀⠀⢠⡏⢀⣿⣿⡆⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇ ⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠚⢿⠁⠀⠀⠀⠀⠀⠀⠀⠸⣿⣭⠀⠼⣿⣿⣿⣿⠇⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇ ⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣄⡀⠀⠀⠀⠀⠀⠀⠉⠉⠄⠀⠈⠛⢿⠁⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇ ⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠿⢶⣶⣶⣶⣶⣿⣦⡀⠀⠀⢠⠀⠀⠀⠀⠘⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀ ⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⠀⠀⠙⠿⣿⣷⣿⠏⠓⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀ ⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⣀⠀⠀⢙⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠛⠀⢠⡄⠀⠀⠀⢠⡇⠀ ⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⢠⡆⠀⣴⣤⠶⠂⠀⠀⠉⡃⠀⠀⡞⠀⠀ ⠀⠀⠀⠀⠘⣷⡀⠀⠀⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⢀⡼⠋⠀⠀⠀⠀⠈⠛⠃⠀⣼⠃⠀⠀ ⠀⠀⠀⠀⠀⠘⣧⡀⠀⣸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⢧⣰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⠀⠀⠀⠐⠋⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⢿⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⣠⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣯⣉⠉⠉⠉⠛⠛⠛⠲⠶⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣧⡴⡀⠀⠀⠀⠀⠀⠀⣠⡿⠉⠉⠛⠶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣄⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⢿⣇⣀⣀⣀⣀⣠⣟⣁⣀⣀⣀⣤⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⠀⠀⠀⠀⢀⡴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣍⡉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⣀⣠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠴⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠓⠲⠶⠦⠀⠀⠀⠻⡀⠀⠀⠀⠀⠀⠀⠤⠶⠶⠚⠉⠉⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣿⣇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⡆⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠿⠿⠿⠿⠟⠋⠀⢹⡇⢀⣠⠴⠾⠛⠋⠉⠉⠉⠉⠉⠉⠛⠛⠷⠶⣤⣀⣸⠟⠛⠿⠿⠿⠿⠿⣿⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠸⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣦⠀⠀⠀⠀⢿⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⠀⠀⠀⠀⠀⠀⣀⣤⣤⣄⡀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣷⠶⠶⣦⡈⣷⠀⠀ ⠀⠀⣠⣤⣄⣀⣀⣀⡀⠀⢸⡷⠀⠀⠀⠀⢀⡾⠋⡀⡀⠀⠙⣦⠀⠙⠉⠀⠀⠀⠀⠀⠀⠀⣠⣾⣷⣄⠀⠀⠀⠀⠈⢹⡏⢀⡀⠈⣿⢹⡆⠀ ⠀⢰⣿⠉⠉⠉⠉⠙⠛⠳⣾⡇⠀⠀⠀⠀⠀⣧⠠⡷⣿⣇⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠟⠘⠀⠀⠀⠀⠀⠘⢿⣜⣧⣶⠟⢸⣿⠀ ⢀⣼⡏⠀⠀⠀⠀⠀⠀⢀⢸⣿⣶⣦⠀⠀⠀⠙⠷⣤⣤⣿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠁⠀⢸⣿⠀ ⠀⣿⣇⠀⠀⠀⠀⠀⠀⢨⢸⡟⠛⢿⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀ ⠈⠸⠿⣤⣤⣀⣀⡀⠀⠀⣼⣿⣿⣷⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⠀⠀⠀⠀⠉⣽⡇⠀⠀⣹⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⠀⢀⡄⠀⠀⠀⢸⣿⠀ ⠀⠀⠀⠀⠀⢰⣿⠁⠀⠙⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣆⣀⣼⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣷⡾⠃⠀⠀⠀⢸⣿⢸ ⠀⠀⠀⠀⠀⠈⠛⠿⣷⣤⣤⢾⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠈ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⣿⣿⣿⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠏⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⠿⢷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣄⠐⣿⠉⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠶⢶⣤⣴⣄⠀⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠤⠤⠶⠶⠞⠛⠛⠛⠋⠛⠿⠿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠿⠿⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠙⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀ ⡖⣤⡀⠙⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⠃ ⠙⠳⢬⣳⠦⣀⠉⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠉⠙⢿⠏⠀ ⠦⣄⠀⠈⠑⠺⢝⡲⢤⡈⠒⢤⡀⠀⠀⠀⠀⠀⠀⢸⣄⠀⠀⠐⠓⠀⠀⠒⠒⠠⣤⡎⢁⠔⠀⢀⠎⠀⠀ ⣄⠀⠉⠒⢄⡀⠀⠉⠓⠮⣷⣦⣈⠓⢤⡀⠀⠀⠀⡸⠋⠀⣴⣶⠀⠀⠀⠀⢀⣤⡀⠉⠁⠀⢠⠎⠀⠀⠀ ⠯⣟⡲⢤⣀⠈⠑⠢⢄⡀⠀⠉⠛⠿⣶⣌⡑⢦⡜⠁⣀⡀⠋⠁⠐⠲⠄⠀⠘⠿⠟⠀⠀⠀⠷⡀⠀⠀⠀ ⠀⠀⠉⠓⠮⣝⠲⢤⣀⠈⠑⢦⣀⠀⠈⠙⠻⣿⠀⢸⣁⣼⠀⠀⠀⠀⠀⠀⢀⠤⠤⡄⠀⠀⠀⢱⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⠓⠮⣝⡚⠧⣄⡉⠒⣤⣀⢸⠀⠀⠉⠁⠀⡀⠀⠀⠀⠀⠸⢶⡾⠃⠀⠀⠀⠀⣇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠦⣍⣻⣿⣿⣿⣧⣄⡀⠀⠀⠘⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⡄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⠿⣟⡓⠦⣄⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠉⠙⠲⢍⣓⠦⣝⠒⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠈⠑⠲⢽⣶⣿⠇⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠤⣀⡀⠀⠓⠀⠀⢀⣀⣀⠤⠒⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠒⠉⠁⢹⠈⢦⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⢸⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⠀⢱⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆⢀⣀⡠⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡆⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⡄⠀⠀⢀⣀⣼⡿⠖⠒⠙⠛⠉⠉⠀⠀⠀⠈⠓⠚⠒⠲⢤⣤⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⣧⣴⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⢿⣿⣉⡉⠐⠖⠒⠶⠤⢤⣤⣀⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉⠉⠁⠀⠠⢄ ⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣶⣄⣠⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣿⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠊⠉⠀⠈⠉⠓⠦⣄⡀⠀⠀⠀⠀⠈⢿⣧⠀⠉⠉⠛⠒⠲⠶⣦⣄⣀⡀⠀ ⠀⢸⣏⣰⡋⠉⢠⠴⠟⠛⠶⣆⡀⣰⡶⠞⠛⠛⠚⢒⠒⠒⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉ ⠀⡿⠉⠉⠉⠙⠻⣼⣷⣶⣶⣾⠏⢸⣷⣶⣶⣶⣿⠽⠟⠉⠉⠉⠉⠉⠓⠂⠀⠀⠀⠀⠀⠀⠈⠿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣼⠃⠀⠀⠀⠀⠀⠈⠻⣝⠛⠉⠀⣈⣿⠟⠋⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢈⣅⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⢿⡂⠀⠀⠀⠀⠀⠀⠀⠀ ⠸⣯⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⣸⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⠀⠀⠠⣢⣟⠀⠀⠀⡇⠙⣧⡀⠀⠀⠀⠀⠀ ⠀⠀⠘⢦⠀⠘⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠴⠁⠀⢀⣴⠟⠋⠀⠀⠀⠀⠀⠻⣷⡜⠻⣄⣀⠀ ⠀⠀⠀⠀⢳⡙⠂⠽⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡾⠛⠉⠀⠀⣠⣼⠿⠅⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⣧⡈⠿⠃ ⠀⠀⠀⠀⢸⡏⠳⢤⣀⠉⠙⠳⠦⠤⠤⠤⠤⠤⠤⠤⠒⠛⠉⠁⠀⢀⣀⡴⢾⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⡄⠀ ⠀⠀⠀⠀⡏⣿⠀⠀⠉⡝⠓⠲⠤⣤⣀⡀⠀⠀⠀⠀⠠⠤⠤⠖⠋⠉⣡⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀ ⠀⠀⠀⠀⡗⣿⡀⠀⠀⠛⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣧⡇⠁⠀⠀⠀⠀⠙⠷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢏⣿⠀⠀⠀⠀⠀⠈⠉⢎⣳⡀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀

⣿⡿⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠞⠲⠶⠶⠦⠤⠤⠤⣀⣀⣀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⣤⣤⣔⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⣦⣀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠉⠁⠈⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠋⠙⠓⠦⠤⣄⣀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⠙⣦⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⢰⣾⡷⢦⣤⡀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢸⠇⠀⠀⢸⡄⠀⠀⠀⢀⠀⠀⠀⣀⠁⠀⠀⠀⠀⠀⠁⠀⠀⠈⠟⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣾⠿⠦⢄⡀⠀⢸⡆⠀⠀⣸⠃⠀⠀⠀⠈⢳⣶⣾⣿⣦⡀⠀⠀⡠⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⡞⠀⠀⠀⠀⢀⡤⠤ ⠀⠀⠀⠀⠀⣸⢣⣰⡂⠀⠈⠳⢄⣿⣠⣼⠟⠀⠀⠀⠀⠀⢸⡏⠀⠀⠈⢛⡗⠋⠁⠀⠀⢠⡾⠋⠉⠉⠛⣦⠀⢨⠃⠀⠀⠀⠀⠈⡇⠀ ⠀⠀⠀⠀⠀⢧⠟⠉⠉⠀⠀⠀⠀⠙⢏⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⡼⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⢸⡆⡼⠀⠀⠀⠀⠀⠀⡇⠀ ⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⢧⠀⢀⡼⠁⠀⠀⠀⠀⠀⢿⡀⠀⠄⠀⢀⡾⡰⠃⠀⠀⠀⠀⠀⠀⡇⠀ ⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠀⠀⠀⠀⠀⠘⠶⠚⠀⠀⠀⠀⠀⠀⠀⠈⠛⠦⠤⠶⠛⡱⠃⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⢄⡀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⠦⠤⠄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⢤⡂⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠈⠳⠤⠤⠒⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⠤⠤⠀⠀⠈⠳⣖⠚⠉⠉⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣄⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣹⣯⠳⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡤⠤ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠘⢧⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠄⠀ ⡤⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣌⠳⢤⡀⠀⠀⠀⠀⢀⣼⡀⣀ ⣏⠀⠠⣼⣭⣀⣁⣀⡀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡷⢤⣈⣑⡒⣲⣶⠿⢻⣿⠟

⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠁ ⣧⡀⠀⠀⠀⠀⠙⠿⠿⠿⠻⠿⠿⠟⠿⠛⠉⠀⠀⠀⠀⠀ ⣿⣷⣄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴ ⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣴⣿⣿ ⣿⣿⡟⠀⠀⢰⣹⡆⠀⠀⠀⠀⠀⠀⣭⣷⠀⠀⠀⠸⣿⣿ ⣿⣿⠃⠀⠀⠈⠉⠀⠀⠤⠄⠀⠀⠀⠉⠁⠀⠀⠀⠀⢿⣿ ⣿⣿⢾⣿⣷⠀⠀⠀⠀⡠⠤⢄⠀⠀⠀⠠⣿⣿⣷⠀⢸⣿ ⣿⣿⡀⠉⠀⠀⠀⠀⠀⢄⠀⢀⠀⠀⠀⠀⠉⠉⠁⠀⠀⣿ ⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹

🤫🧏‍♂️

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⣴⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⠀⠁⠀⢹⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⡄ ⠀⠀⠀⠀⠀⢀⠔⠁⠀⢀⣀⠆⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⢤⣶⣶⣶⠖⠀⠀⠀⠀⠀⣀⣠⣤⣶⣾⣿⣿⣿⣿⣿⡇ ⠀⠀⠀⠀⢀⠎⠀⠀⠀⠈⠙⡀⠀⠀⠀⠀⢀⠤⠒⠉⠀⠀⠈⣿⠟⠁⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇ ⠀⠀⠀⢀⠌⠀⠀⠀⠀⠀⠀⠈⠀⠠⡄⠊⠁⠀⠀⠀⢀⠠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⡟⠋⠉⠀⠀⠀⠀ ⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣷⡀⠀⠀⠀⠀⠀ ⠀⢰⠁⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠡⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣶⣾⣿⣿⣧⠀⠀⠀⠀⠀ ⢀⡎⠘⠋⠀⡄⠀⠀⠀⢠⣈⣵⠀⢠⣆⢠⣶⡕⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⠛⠉⠁⠀⠀⠀⠀⠀ ⠸⡀⠀⠀⠀⢤⣀⢀⣾⡿⠿⠇⣾⠀⣿⡄⡏⢀⣿⢣⡷⠂⢳⣦⣀⠀⠀⠀⢀⣤⣴⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⠑⢄⠀⠀⠸⣄⣀⣀⣥⣤⣷⣿⠀⢹⡷⠀⠘⠁⣿⠇⠀⢸⣿⠈⣷⣦⣄⠈⢿⣿⣿⡿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠑⢢⢄⡘⠉⠉⠙⠻⣿⡿⠄⠀⠀⠀⠀⠰⠋⠀⠀⢸⠇⠀⣿⣿⠉⢦⣼⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡏⠀⠈⠉⠁⠀⠀⠀⠁⣠⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀⢸⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⠀⠀⠀⠀⠀⢀⣀⠀⣰⣷⢳⣤⣤⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⠀⠀⠀⠀⡠⠊⠀⢻⡥⢻⣾⢿⠅⢀⠎⠀⠀⠀⠀⠀⠀⢀⣼⣿⣷⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡄⠀⠉⠀⠀⡔⠋⠀⠀⡀⠏⠁⠈⠁⠀⡠⠊⠀⠨⡀⠀⠀⠀⠚⠛⠉⠉⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠖⢡⣤⡞⡼⠀⠀⠀⠰⣀⢰⠀⡀⡀⠞⢉⡡⠔⣋⠩⠭⠽⢷⡾⠇⠀⡠⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠴⠗⠣⠎⠁⠠⣊⣠⣐⣀⣠⣀⡤⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢻⣿⡗⢶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣄ ⠀⢻⣇⠀⠈⠙⠳⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠛⠋⣹⣿⡿ ⠀⠀⠹⣆⠀⠀⠀⠀⠙⢷⣄⣀⣀⣀⣤⣤⣤⣄⣀⣴⠞⠋⠉⠀⠀⠀⢀⣿⡟⠁ ⠀⠀⠀⠙⢷⡀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀ ⠀⠀⠀⠀⠈⠻⡶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣠⡾⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣼⠃⠀⢠⠒⣆⠀⠀⠀⠀⠀⠀⢠⢲⣄⠀⠀⠀⢻⣆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢰⡏⠀⠀⠈⠛⠋⠀⢀⣀⡀⠀⠀⠘⠛⠃⠀⠀⠀⠈⣿⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⣾⡟⠛⢳⠀⠀⠀⠀⠀⣉⣀⠀⠀⠀⠀⣰⢛⠙⣶⠀⢹⣇⠀⠀⠀⠀ ⠀⠀⠀⠀⢿⡗⠛⠋⠀⠀⠀⠀⣾⠋⠀⢱⠀⠀⠀⠘⠲⠗⠋⠀⠈⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⢷⡀⠀⠀⠀⠀⠀⠈⠓⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⡏⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿ ⠀⠀⠀⠀⠀⢹⠀⠀⠀⠈⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠁⠀⣿ ⠀⠀⠀⠀⠀⣿⣧⡀⠀⠀⠀⠀⠙⠿⠷⠿⠻⠿⠿⠟⠿⠛⠉⠀⠀⠀⠀⠀⣸⣿ ⠀⠀⠀⠀⠀⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿ ⠀⠀⠀⠀⠀⢾⣿⣿⣿⠏⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⢸⣿⣿⡟⠀⠀⢰⣹⡆⠀⠀⠀⠀⠀⠀⣭⣷⠀⠀⠀⠸⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⣾⣿⣿⠃⠀⠀⠈⠉⠀⠀⠤⠄⠀⠀⠀⠉⠁⠀⠀⠀⠀⢿⣿⣿⣿ ⠀⠀⠀⠀⠀⢹⣿⣿⢾⣿⣷⠀⠀⠀⠀⡠⠤⢄⠀⠀⠀⠠⣿⣿⣷⠀⢸⣿⣿⣿ ⠀⠀⠀⠀⠀⣸⣿⣿⡀⠉⠀⠀⠀⠀⠀⢄⠀⢀⠀⠀⠀⠀⠉⠉⠁⠀⠀⣿⣿⣿ ⠀⠀⠀⠀⠀⣸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿ ⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿

⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣇⠀⠀⣀⡾⠤⠠⠆⠀⠀⠀⠤⠤⢀⣀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠘⡶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⡏⠉⠋⠐⠒⠢⠤⠄⠀⠀ ⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠈ ⠀⡇⠀⢀⡀⠀⠀⠀⠀⠀⣀⠔⠒⠒⠠⣀⠀⠀⠈⢹⣇⠒⠲⠤⢤⣀⠀⠀ ⢸⠧⠯⢰⣚⣉⣲⡤⣖⣉⣩⢵⡤⠦⠤⠄⡀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀ ⡎⠀⠀⠀⠙⠟⠋⢀⠿⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀ ⣇⠀⠀⠀⠀⠀⠠⠂⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢧⠀⠀⠀⠀⠀ ⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⡰⠹⢈⢦⠀⠀⠀⠀ ⠀⠡⡀⡢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠡⠂⣀⡼⠋⠀⠈⠘⢳⣔⢄⡀ ⠀⠀⢸⠢⣉⠓⠤⠄⣀⠀⠀⠀⠤⠒⠉⢀⡠⡾⠋⠀⠀⠀⠀⠀⠀⠈⠢⠁ ⠀⠀⣌⡇⠀⣭⡑⠒⠠⠀⠀⠀⠒⠒⠉⢱⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁ ⠀⠀⢧⡁⠀⠀⠙⡦⡀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀ ⠀⠀⢸⡇⠀⠀⠀⠈⠚⡄⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀

⠀⣧⢸⣆⡀⢀⠠⠓⠀⠉⠉⠉⠁⠐⠂⠤⣀⠤⠤⠤⠤⠤⠤⠤⠤ ⠀⡏⠘⠛⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡇⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢠⢤⠄⠀⣀⠀⠠⠼ ⠀⠁⠀⠸⠀⣀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⡀⠀⢿⡿⠀⠀⠀⠀⠀⠀⢠⣯⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡇⢰⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠰⠢⢄⡀⠀⠀⠀ ⠀⡇⠀⢂⢡⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⢠⠊⢹⠎⠑⠂⠄⣁⠒⠠ ⢠⡇⠀⠀⠡⡀⠀⠀⠀⠀⠁⠀⠀⠀⠀⣆⡠⣾⠀⠀⠀⠀⠀⠉⠒ ⠀⡇⠀⠐⠀⠀⠁⠂⠤⡀⠀⠀⢀⡤⠔⠊⠀⢨⡄⠀⠀⠀⠀⠀⠀ ⢸⡇⠀⠀⠀⠀⠀⠀⠈⠈⠐⠂⠕⠁⠀⠀⠀⠈⣡⠀⠀⣄⡀⠀⠀ ⢸⡇⠀⣄⠀⠀⠀⠀⠀⠠⠀⠌⠀⠀⠀⠀⠀⢠⠟⠀⠀⡅⠈⠐⢄ ⢸⡇⠀⠁⡀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⢀⡆⠸⠇⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠲⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠠⠌⠀⠀⠀⠀⠀⢶⡶⠂⠀⠀⣤⣶⣶⣿⣿ ⠀⠀⠀⠀⠀⠀⠂⠄⠀⠀⠀⠈⠀⠀⠀⠀⠘⣿⡋⠉⠁ ⢠⠡⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣾⡷⠀⠀ ⠀⠀⠀⣀⣶⢮⡆⣷⠁⢿⠆⣦⢀⠀⢠⣾⣿⡧⠀⠀⠀ ⠀⠀⠀⠟⠙⠻⠇⡋⠀⠚⠀⠟⢸⡗⢼⣿⠇⠀⠀⠀⠀ ⠀⠀⠁⠀⠀⢀⢼⣣⠄⠀⠀⠀⠀⢀⣾⠁⠀⠀⠀⠀⠀ ⠠⡀⢀⠀⠀⠼⠑⠃⣀⣀⣀⠀⢐⠛⠏⠀⠀⠀⠀⠀⠀ ⠈⠉⠉⠀⠀⠢⠤⠨⠂⠁⠈⠉⠉⠀⠁⠀⠀⠀⠀⠀⠀

⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣧⠀⠀⠀⠀⠀⠈⡄⠀ ⠀⠀⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⠿⠟⠋⠉⠁⠀⠀⠠⣖⠁⠀⠀⠀⠀⠀⠀⠘⡀ ⠀⠀⠀⠀⠀⠀⠈⠙⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠆⠀⠀⠀⠀⠀⠀⢸ ⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠒⠊⠉⠉⠉⠉⠒⢺ ⣿⣿⣦⣄⠀⣰⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⣀⣤⣶⣿ ⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣀⣽⣷⣾⣿⣿⣿⣿ ⣿⣿⣾⢿⣿⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠿⣿⣿⣿⣿⡆⢠⣾⣇⣀⣿⡄⠀⢀⣀⢀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁ ⡒⠚⠋⠉⠉⠉⠉⠉⠉⢉⣽⡿⢛⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀ ⠑⠢⣄⡠⢤⠀⠀⠀⣴⡿⢋⣴⣿⣿⣿⡿⠛⠛⠛⠻⠿⣿⣿⣿⣿⠟⠁⠀⠀⠀ ⠀⢠⠎⠀⠟⣦⢤⣾⢏⣴⣿⣿⣿⣿⠟⢀⠴⠒⠒⠤⠤⠴⠃⠀⠀⠀⠀⠀⠀⠀ ⢠⠃⠀⠀⠀⠘⣆⠈⠙⠛⠿⠿⠟⠃⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠀⠈⢯⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣸⡀⠀⠀⠀⠀⠀⠉⠛⠦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀

⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛⬛ ⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛⬛⬛⬛ ⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛⬛⬛⬛⬛⬛ ⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛🟨🟨🟨⬛⬛⬛ ⬜⬜⬜⬛⬛⬛⬛⬛⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛🟨🟨🟨🟨⬛⬛⬜ ⬜⬜⬜⬛⬛⬛🟧🟧🟧⬛⬛⬛⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛🟨🟨🟨🟨🟧⬛⬛⬜ ⬜⬜⬜⬜⬜⬛⬛🟫🟨🟨🟨🟨🟧⬛⬛⬛⬛⬜⬛⬛⬛⬛⬛⬛⬛⬜⬛⬛🟨🟨🟨🟨🟧🟧⬛⬜⬜ ⬜⬜⬜⬜⬜⬜⬛⬛🟫🟧🟨🟨🟨🟨🟨🟨🟧⬛🟨🟨🟨🟨🟨🟨🟨⬛🟧🟨🟨🟨🟨🟧🟧⬛⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬛⬛🟧🟧🟧🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟧🟧🟧⬛⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬜⬛⬛🟧🟧🟧🟧🟧🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟧⬛🟧⬛⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛⬛🟧⬛🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟧⬛⬜⬜⬜⬜⬜⬜ ⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨⬛⬜⬜⬜⬜⬜⬜ ⬛⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛🟨🟨🟨⬛⬛🟨🟨🟨🟨🟨🟨🟨🟨⬛⬛🟨🟨⬛⬜⬜⬜⬜⬜⬜ ⬛🟧⬛⬜⬜⬜⬜⬜⬜⬜⬜⬛🟧🟨🟨⬛⬛⬜⬛🟨🟨🟨🟨🟨🟨⬛⬛⬜⬛🟨🟧⬛⬜⬜⬜⬜⬜ ⬛🟨🟧⬛⬜⬜⬜⬜⬜⬜⬜⬛🟨🟨🟨⬛⬛⬛⬛🟨🟨🟨🟨🟨🟨⬛⬛⬛⬛🟨🟨⬛⬜⬜⬜⬜⬜ ⬛🟨🟨🟧⬛⬜⬜⬜⬜⬜⬜⬛🟨🟨🟨🟨⬛⬛🟨🟨🟨🟨🟨🟨🟨🟨⬛⬛🟨🟨🟨⬛⬜⬜⬜⬜⬜ ⬛🟨🟨🟨🟧⬛⬜⬜⬜⬜⬛🟨🟨🟥🟥🟨🟨🟨🟨🟨🟨⬛⬛🟨🟨🟨🟨🟨🟨🟥🟥🟨⬛⬜⬜⬜⬜ ⬛🟨🟨🟨🟨🟧⬛⬜⬜⬜⬛🟨🟥🟥🟥🟥🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟥🟥🟥🟥⬛⬜⬜⬜⬜ ⬛🟨🟨🟨🟨🟨🟧⬛⬜⬜⬛🟨🟥🟥🟥🟥🟨🟨⬛🟨🟨⬛⬛🟨🟨⬛🟨🟨🟥🟥🟥🟥⬛⬜⬜⬜⬜ ⬛🟨🟨🟨🟨🟨🟨🟧⬛⬜⬛🟨🟨🟥🟥🟨🟨🟨🟨⬛⬛🟨🟨⬛⬛🟨🟨🟨🟨🟥🟥🟨⬛⬜⬜⬜⬜ ⬛🟨🟨🟨🟨🟨🟨🟨🟧⬛⬛⬛🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨⬛⬜⬜⬜⬜⬜ ⬛🟨🟨🟨🟨🟨🟨🟨🟨🟧⬛⬛🟧🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟧⬛⬜⬜⬜⬜⬜ ⬜⬛🟨🟨🟨🟨🟨🟨🟨🟨⬛⬜⬛🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨⬛⬜⬜⬜⬜⬜⬜ ⬜⬜⬛🟨🟨🟨🟨🟨🟨⬛⬜⬛🟧🟨🟨🟨🟨🟨🟨🟨🟧🟧🟧🟧🟨🟨🟨🟨🟨🟨🟧⬛⬜⬜⬜⬜⬜ ⬜⬜⬜⬛🟨🟨🟨🟨⬛⬜⬜⬛⬛🟨🟨🟨🟨🟨🟨🟨🟨🟧🟧🟨🟨🟨🟨🟨🟨🟨🟨⬛⬜⬜⬜⬜⬜ ⬜⬜⬛🟨🟨🟨🟨⬛⬜⬜⬜⬛🟨🟨🟨🟨🟨🟨⬛🟨🟨🟨🟨🟨🟨⬛🟨🟨🟨🟨🟨⬛⬜⬜⬜⬜⬜ ⬜⬜⬛🟨🟨🟨🟨🟨⬛⬜⬛🟨🟨🟨⬛🟨🟨🟨⬛🟨🟨🟨🟨🟨🟨⬛🟨🟨🟨⬛🟨⬛⬜⬜⬜⬜⬜ ⬜⬜⬜⬛🟨🟨🟨🟨🟨⬛⬛🟨🟨🟨⬛🟨🟨🟨🟨⬛🟨🟨🟨🟨⬛🟨🟨🟨🟨⬛🟨🟨⬛⬜⬜⬜⬜ ⬜⬜⬜⬜⬛🟨🟨🟧🟧🟫⬛🟨🟨🟨🟧⬛🟨🟨🟨⬛🟨🟨🟨🟨⬛🟨🟨🟨⬛🟧🟨🟨⬛⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬛🟧🟧🟧⬛⬛🟨🟨🟨🟧⬛🟨🟨🟨⬛🟨🟨🟨🟨⬛🟨🟨🟨⬛🟧🟨🟨⬛⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬛🟧🟫🟫⬛🟨🟨🟨🟨🟧⬛🟨🟨⬛🟨🟨🟨🟨⬛🟨🟨⬛🟧🟨🟨🟨⬛⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬛🟫🟫🟫🟫⬛🟨🟨🟨🟨🟨🟧⬛⬛🟨🟨🟨🟨🟨🟨⬛⬛🟧🟨🟨🟨🟨⬛⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬛🟫🟫🟫⬛🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨⬛⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬛⬛🟫⬛🟧🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨⬛⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛⬛⬛🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨⬛⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛🟧🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨⬛⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛🟨🟨🟨🟨🟨🟨🟧🟧🟧🟧🟧🟨🟨🟨🟨🟨🟨⬛⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛🟧🟨🟧🟧⬛⬛⬛⬛⬛⬛⬛🟧🟧🟨🟧⬛⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛🟨🟨🟨⬛⬛⬛⬜⬜⬜⬜⬜⬜⬛⬛🟨🟨🟨⬛⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛⬛⬛⬛⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛⬛⬛⬛⬛⬜⬜⬜⬜⬜⬜

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠁⠀⠀⠀⡠⠔⠂⠁⠀⣴⣿⣯⡴⠶⠶⠶⠶⠶⠶⠶⣴⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⢀⠔⠀⢀⣠⠴⠚⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠶⣤⣤⣶⣶⣦⣤⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢀⠄⢁⡠⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠀⠀⠈⠉⠉⠙⠛⠻⠶⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠰⣡⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⣦⣄⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢶⣄⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⣄⠁⠀⠂⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠻⣿⣦⡀⠀⠀⠀⠈⠐⠂⠀⠠⢀⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠹⣿⠛⠷⣦⣄⣠⣀⣄⣤⣶⣶⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⣠⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢻⣧⠀⠈⠙⠛⠻⢿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⢀⣼⣿⣏⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠶⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⢸⣿⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙ ⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⣼⣿⣿⣿⣷⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡀⠀⣹⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣸⡏⠀⠀⠸⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣿⠽⣢⠀⠀⠈⠙⠋⠋⠁⠀⠀⠀⠀⠀⠀⠰⠷⠆⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⣸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣏⠷⣡⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠋⠁⣀⣀⢤⡤⣀⢀⠀⠀⠀⠀⠀⡀⢠⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢾⡿⡜⣥⢺⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢞⡱⣊⠶⡱⡍⣞⡹⢆⠀⠀⠀⠇⣼⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣿⣳⣌⢳⠀⠀⠀⠀⠀⠀⠀⠀⠱⢄⣀⣤⡴⣄⡀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⢀⡏⢮⡑⢮⡱⢣⡝⣤⢛⡜⡆⠀⡘⢠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⣿⡷⣽⡺⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠊⢁⡠⢞⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣏⠶⣙⢦⠹⡥⣚⢤⡓⢮⠃⠰⠀⣸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⢿⣞⠁⠀⡀⠀⠀⠀⡤⠚⢁⣠⠔⠚⠁⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⠸⣌⢳⡱⢎⡲⣭⠏⠀⠁⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠹⣶⡀⠈⠐⠠⡀⡇⠀⢸⠀⠄⢀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠚⠥⠾⠜⠃⠁⠀⠁⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⣤⡂⠈⣷⠀⠀⡄⣆⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠐⠁⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⠟⠉⠁⠀⢀⣼⡀⠀⡏⠀⠒⠤⢀⣐⠂⠠⠤⠤⠀⠀⢀⢀⡀⠀⠀⠀⠀⠀⡀⠄⠒⠀⠁⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⡾⠟⠁⠀⠀⠀⢀⣴⠿⣧⣅⡀⠃⠀⠀⠀⠀⠀⠉⠑⠒⠤⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰ ⠀⠀⠀⣠⡾⠋⠀⠈⠢⠀⠀⢰⣟⡁⠀⠀⠁⠈⠙⠶⠦⣤⣀⣀⠀⠀⠀⠀⢢⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⢠⣦⣀⠀⠀⠀⠀⢀⣿ ⠀⠀⣼⠟⠀⠀⠀⠀⠀⢡⡀⢸⡇⠈⠑⢂⠤⢄⠀⠀⠀⠀⠉⠙⠛⠳⠶⣤⡀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢽⡇⠀⠀⠀⣼⠏⠙⠻⣦⣄⠀⣼⡇ ⠀⣾⠏⠀⠀⠀⠀⠀⠀⠀⠱⣼⡇⠀⠀⠐⠠⠀⠈⠨⠐⠤⠀⡀⠀⠀⠀⠈⡇⢸⠀⠀⠀⠀⣀⣀⣀⠤⠤⠄⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠸⣷⠀⠀⢰⡏⠀⠀⠀⠀⠙⠿⡟⠀ ⣸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠩⢉⠲⢽⠜⣠⡴⠒⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢂⠀⠀⠀⠀⠀⢿⡀⢀⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡹⠑⠦⣤⣑⡠⠀⠀⠀⠀⠀⡇⠀⠀⣀⠬⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢸⣇⣼⣷⣻⠀⠀⢀⡀⠀⠀⠀⠀ ⠹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡃⢒⠀⠆⣏⠓⡶⢤⣄⡀⡇⡡⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⢻⣟⡧⣧⡄⣠⡿⠳⣦⡀⠀⠀ ⠀⠙⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⠧⣸⠟⢳⣾⣯⣗⠠⢈⣹⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢸⢯⡷⣭⣿⡟⠀⠀⠈⠛⢷⣤ ⠀⠀⠈⠛⢷⣦⣤⣀⣀⠀⠀⣠⣶⠛⡡⢿⡀⢈⠁⠒⢹⠆⠡⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⠀⠀⠀⠀⠀⠀⠘⣿⣿⡟⠀⠀⠀⠀⠀⠀⠉ ⠀⠀⠀⠀⠀⠀⣹⡏⠙⠛⠋⣿⣿⠠⢁⠜⠳⢶⣬⣦⠟⣈⠡⢙⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⢻⡏⠀⠀⠀⠀⠀⠀⠀⠀

⬛⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛⬛ ⬛⬛⬛⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛⬛⬛⬛ ⬛⬛⬛🟨⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛🟨⬛⬛⬛ ⬛⬛⬛🟨🟨⬛⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛⬛🟨🟨⬛⬛⬛ ⬜⬛⬛🟨🟨🟨🟨⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛🟨🟨🟨🟨⬛⬛⬜ ⬜⬛⬛🟨🟨🟨🟨🟨⬛⬛⬜⬜⬛⬛⬛⬛⬜⬜⬛⬛🟨🟨🟨🟨🟨⬛⬛⬜ ⬜⬜⬛🟨🟨🟨🟨🟨🟨🟨⬛⬛🟨🟨🟨🟨⬛⬛🟨🟨🟨🟨🟨🟨🟨⬛⬜⬜ ⬜⬜⬛🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨⬛⬜⬜ ⬜⬜⬜⬛🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨⬛⬜⬜⬜ ⬜⬜⬜⬜⬛🟨⬛🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨⬛🟨⬛⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬛🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨⬛⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬛🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨⬛⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬛🟨🟨🟨⬛⬛🟨🟨🟨🟨🟨🟨🟨🟨⬛⬛🟨🟨🟨⬛⬜⬜⬜⬜ ⬜⬜⬜⬜⬛🟨🟨⬛⬜⬛⬛🟨🟨🟨🟨🟨🟨⬛⬛⬜⬛🟨🟨⬛⬜⬜⬜⬜ ⬜⬜⬜⬜⬛🟨🟨⬛⬛⬛⬛🟨🟨🟨🟨🟨🟨⬛⬛⬛⬛🟨🟨⬛⬜⬜⬜⬜ ⬜⬜⬜⬜⬛🟨🟨🟨⬛⬛🟨🟨🟨⬛⬛🟨🟨🟨⬛⬛🟨🟨🟨⬛⬜⬜⬜⬜ ⬜⬜⬜⬛🟨🟨🟥🟥🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟥🟥🟨🟨⬛⬜⬜⬜ ⬜⬜⬜⬛🟨🟥🟥🟥🟥🟨🟨⬛🟨⬛⬛🟨⬛🟨🟨🟥🟥🟥🟥🟨⬛⬜⬜⬜ ⬜⬜⬜⬛🟨🟥🟥🟥🟥🟨🟨🟨⬛⬛⬛⬛🟨🟨🟨🟥🟥🟥🟥🟨⬛⬜⬜⬜ ⬜⬜⬜⬜⬛🟨🟥🟥🟨🟨🟨🟨⬛🟥🟥⬛🟨🟨🟨🟨🟥🟥🟨⬛⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬛🟨🟨🟨🟨🟨🟨⬛🟥🟥⬛🟨🟨🟨🟨🟨🟨⬛⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬛⬛🟨🟨🟨🟨🟨⬛⬛🟨🟨🟨🟨🟨⬛⬛⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬜⬛⬛⬛🟨🟨🟨🟨🟨🟨⬛⬛⬛⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛⬛⬛⬛⬛⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜

⡏⠉⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠔⠒⠓⠒⠦⢄⡀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⢀⡔⠋⢹⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⢀⣏⠦⢲⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠇⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⢸⣧⣒⢭⡗⠒⠒⠒⠒⠒⢦⣤⣀⠀⡇⢰⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⢸⡏⠀⡜⢸⣿⡇⠀⠀⡀⠸⣾⠟⡟⣷⢼⡀⠀⠀ ⡇⠀⠀⠀⠀⠀⡜⠀⣼⢁⡔⠢⡀⠠⠤⠓⠀⠀⢎⣸⢸⡇⠑⢄⠀ ⠇⠀⠀⠀⠀⢰⣷⠿⢿⠈⠣⠔⠁⠀⠀⠀⠀⠀⣠⣷⣿⠀⠀⠀⢱ ⠀⢀⡠⠴⠂⠹⠃⠀⢸⠀⠀⠀⡄⠀⠀⠀⠀⠈⠇⠈⠻⠀⠀⠀⡸ ⢏⠁⠀⠀⠀⠀⢀⠀⣜⡀⠀⠀⢸⡀⢰⠇⠀⠀⢸⠒⠒⠒⠒⠁⠀ ⠘⢆⠀⡠⠔⠊⡙⢸⡇⢡⡀⠀⠀⢃⢸⠀⠀⢠⠛⡆⠀⠀⠀⠀⠀ ⠀⠈⠉⠀⠀⠀⣇⢬⠇⠀⠑⢄⣀⡜⠸⣄⣠⠇⠀⢁⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢸⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠣⣀⠀⠀⣀⣀⣀⣀⣀⣀⣠⠊⠀⠀⠀⠀⠀ ⣇⡀⠀⠀⠀⠀⠀⢰⣯⣀⡜⠉⠀⠀⠀⠀⠈⠢⣄⣽⡆⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⠂⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⠀⠀⠀⠀⠀⠀⣠⢾⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢻⣿⣿⠏⠀⠀⠀⠀⣠⠞⠁⢸⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⢸⣿⡟⠀⠀⠀⢀⡾⠁⠀⠀⢸⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⣸⠟⠀⠀⠀⣠⠟⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⣁⣠⠤⠶⠒⠛⠶⠦⢤⣴⠃⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣯⠀⠀⠀⠀⠀⣀⡴⠚⢻⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢰⡖⣆⠀⠀⠀⠀⠀⡖⠺⣷⡀⠀⠀⠀⢸⡆⠀⣀⡴⠚⠁⠀⠈⠢⡊⢷⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠸⣿⠇⢀⠀⠀⠀⠀⠻⢿⣿⠇⠀⠀⠀⠀⡷⠞⠁⠀⠀⠀⠀⠀⠀⠈⠀⠙⢦⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡿⢆⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⡴⠉⠉⢢⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢷⡼⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠱⢤⡠⠎⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠉⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣠⡿⣤⡀⠀⢀⠀⠀⢠⡴⠚⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡷⢤⡴⢚⡉⠉⠉⠙⠳⣄⠀⣀⡚⠁⠙⣦⠉⠳⢤⡁⠢⠀⢙⡦⢤⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡧⡀⢠⢾⡁⠀⠀⠀⡀⣽⣠⠟⠛⠂⠀⣾⢀⡤⢞⡧⠀⠀⠈⠉⠙⢦⣠⢴⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⠧⣼⢿⡷⢿⣾⣿⣿⣿⣿⣿⡆⣠⡶⣷⡋⠙⠁⠀⢀⣀⡤⠶⠚⠋⠉⠿⠗⢀⢤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⢀⣠⣾⣶⠶⢿⣿⣿⣿⣿⣿⣿⢯⡇⠈⠙⢦⡀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠸⠜ ⠀⠀⠀⠀⠀⠀⢀⣠⠤⢤⣾⣻⣿⡛⠭⠝⣿⣕⠼⢿⣿⣿⣿⡟⣴⣿⠀⣠⡴⠋⠀⠀⠀⣹⣦⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⠶⠞⠛⢚⠳⠮⣄⡚⢿⣦⣤⣴⠟⢻⡆⢸⣿⣿⣿⣟⡎⢹⠛⠉⣻⣦⠴⠖⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣠⢞⣅⡀⠀⣾⣿⣷⠀⠀⠙⣦⠈⢿⠃⣉⣽⣗⡾⠿⠛⢻⣿⣷⡿⠞⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣰⠳⣿⣿⣯⠀⠙⠛⠋⣠⣶⡄⠈⣧⠘⡗⣯⣽⣟⠁⠀⠂⠀⠹⣿⣷⣦⣤⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⡏⠀⣉⣍⠉⠀⠀⠀⠘⣿⣿⡿⠀⢸⡗⣿⠏⠀⠉⠉⠛⠒⢶⠺⣯⣿⠛⠿⠿⠿⠿⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⣼⣿⣿⡃⠀⠀⠀⠀⣠⣤⣄⠀⢸⣷⠃⠀⠀⠀⠀⠀⠀⠈⠙⠓⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠹⣜⠛⠛⢃⣴⣶⣆⢸⣿⣿⣿⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠙⢦⡀⠘⢿⣿⠿⠀⠈⠉⣠⠞⠃⠀ ⠀⠀⠀⠉⠓⠦⠤⠤⠤⠶⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨 🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨 🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨 🟨⬛⬜🟨🟨🟨🟨🟨⬛⬜🟨 🟨⬛⬛🟨🟨🟨🟨🟨⬛⬛🟨 🟨⬛⬛🟨🟨⬛🟨🟨⬛⬛🟨 🟥🟨🟨🟨🟨🟨🟨🟨🟨🟨🟥 🟥🟥🟨🟨🟨⬛🟨🟨🟨🟥🟥 🟥🟥🟨🟨⬛🟨⬛🟨🟨🟥🟥 🟥🟨🟨🟨🟨🟨🟨🟨🟨🟨🟥 🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨

. ▶ ◀ \ \ / / ϞϞ(๑⚈ ․̫ ⚈๑)∩

░░░░█░▀▄░░░░░░░░░░▄▄███▀░░ ░░░░█░░░▀▄░▄▄▄▄▄░▄▀░░░█▀░░ ░░░░░▀▄░░░▀░░░░░▀░░░▄▀░░░░ ░░░░░░░▌░▄▄░░░▄▄░▐▀▀░░░░░░ ░░░░░░▐░░█▄░░░▄█░░▌▄▄▀▀▀▀█ ░░░░░░▌▄▄▀▀░▄░▀▀▄▄▐░░░░░░█ ░░░▄▀▀▐▀▀░░░░░░░▀▀▌▄▄▄░░░█ ░░░█░░░▀▄░░░░░░░▄▀░░░░█▀▀▀ ░░░░▀▄░░▀░░▀▀▀░░▀░░░▄█░░░░

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢰⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠻⣿⣿⣿⣿⣷⡖⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠻⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠘⢿⣿⣿⣿⡇⠀⠀⠉⠒⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠈⢻⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠉⠻⣿⣧⣀⠀⠀⠀⠀⠈⠑⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠛⢆⡉⠢⢄⡀⠀⠀⠀⠈⠑⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢄⡈⠒⠄⡀⠀⠀⠀⠹⠴⠒⠒⠒⠒⠒⠦⠤⢀⡀⠀⠀⠀⠀⡇⠀⠀⠀⢀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦⠌⣳⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠲⣄⠀⡇⠀⠀⠀⡜⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⡀⠀⡼⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⣠⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢼⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⢸⣿⣯⣨⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠓⢦⠀⠈⠛⠛⠛⠁⠀⠀⢀⣀⠀⠀⠀⠀⠀⣠⣤⣤⡀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡁⠀⠘⠀⠀⠀⠀⠀⡀⠀⢀⣀⡉⠁⠀⠀⠀⠀⣿⣤⣾⣿⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⣸⠀⠀⠀⠀⠀⣿⠭⣑⠻⢿⣦⢄⣀⠀⠀⠛⠛⠛⠁⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡤⠞⠁⠀⠀⠀⠀⠀⡯⠉⠀⠈⠙⢾⣿⠏⠀⠀⠀⠀⠀⣀⣀⣸⠀⢀⣀⡀⠤⠤⢤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⣠⠋⠀⠀⠀⠀⢀⠞⠁⠀⡿⠊⠉⠀⠀⠀⠀⠸⢱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⠄⠠⠿⠤⠄⣀⡀⠀⠀⠰⡀⢀⣠⠞⠁⠀⠀⠀⠀⠀⣏⠀⠀⣠⠃⠀⠀⠀⠀⠀⢀⣀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢄⡀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠧⣤⠖⠁⠀⠀⠀⠀⠀⢀⡞⠛⠓⠒⠒⠒⠒⠤⠤⠄⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡖⠢⠄⣀⠀⠀⠀⣀⡠⠔⠊⠁⠀⠀⠀⠀⢀⡠⣶⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠒⠲⠤⣀⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⣦⠤⠤⠄⣀⣀⠀⠀⠀⠀⠀⡀⢠⡾⠉⠒⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⣡⠞⡇⠀⡠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⣤ ⠀⠀⠀⠀⠀⠀⠀⠈⠓⠤⣀⣀⣀⣀⣠⡤⠤⠚⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠚⠁⣠⠞⠁⢸⠁⢰⠁⠀⠉⠒⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⣠⠔⠋⠀⠀⠀⡌⠀⡆⠀⠀⠀⠀⠀⠈⠑⠠⣀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⡀⠀⠀⢰⠃⢰⠁⠀⢠⠖⠒⠤⢄⣀⠀⠈⠑⠢⡀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡛⠭⡉⠉⠀⡈⠀⡰⠃⠀⠀⠀⠀⠀⠉⠁⠒⠦⠬⣳⣠⠞⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇⠀⠈⡓⠄⠇⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣀⣿⡷⣷⡏⠉⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣠⠉⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠉⠑⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢧⢠⠒⠂⠤⣄⣀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠠⠄⣀⡀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⡷⢄⡀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠈⠑⢤⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⣶⣿⡯⢄⠴⢋⣀⣈⡭⠟⠉⠁⠀⠀⠀⠀⠈⠉⠓⠒⠂⠤⠤⢤⣠⡤⠤⠔⠛⠶⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⠂⠤⠤⣈⣙⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛ ⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛💛 ⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛💛💛 💛⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛💛💛💛 💛💛⬛⬜⬜⬜⬛⬛⬛⬛⬛⬛⬛⬜⬜⬜⬛💛💛💛💛 💛💛💛⬛⬛⬛💛💛💛💛💛💛💛⬛⬛⬛💛💛💛💛💛 💛💛💛💛💛💛💛💛💛💛💛💛💛💛💛💛💛💛💛💛💛 💛💛💛💛💛💛💛💛💛💛💛💛💛💛💛💛💛💛💛💛⬛ 💛💛💛💛💛💛💛💛💛💛💛💛💛💛💛💛💛💛💛⬛💛 ⬛💛💛💛💛💛💛💛💛💛💛💛💛💛💛💛💛⬛⬛💛💛 💛💛💛⬛💛💛💛💛💛💛💛💛💛💛⬛💛💛⬛💛💛⬛ 💛💛⬛⬜⬛💛💛💛💛💛💛💛💛⬛⬜⬛💛⬛⬛⬛⬜ 💛💛⬛⬛⬛💛💛💛💛💛💛💛💛⬛⬛⬛💛⬛⬜⬜⬜ 💛💛⬛⬛⬛💛💛💛💛⬛💛💛💛⬛⬛⬛💛💛⬛⬜⬜ ⬛⬛💛💛💛💛💛💛💛💛💛💛💛💛💛💛⬛⬛⬛⬜⬜ 🍎🍎⬛💛💛⬛⬛⬛⬛⬛⬛⬛💛💛💛💛🍎🍎⬛⬛⬛ 🍎🍎⬛💛💛💛⬛⬛⬜⬜⬛⬛💛💛💛⬛🍎🍎⬛💛💛 🍎🍎⬛💛💛💛⬛⬜⬜⬜⬜⬛💛💛💛⬛🍎🍎⬛💛💛 ⬛⬛💛💛💛💛💛⬛⬜⬜⬜⬛💛💛💛⬛⬛⬛💛💛💛 💛💛💛💛💛💛💛💛⬛⬛⬛💛💛💛💛💛💛⬛💛💛💛

█▀▀▄░░░░░░░░░░░▄▀▀█ ░█░░░▀▄░▄▄▄▄▄░▄▀░░░█ ░░▀▄░░░▀░░░░░▀░░░▄▀ ░░░░▌░▄▄░░░▄▄░▐▀▀ ░░░▐░░█▄░░░▄█░░▌▄▄▀▀▀▀█ ░░░▌▄▄▀▀░▄░▀▀▄▄▐░░░░░░█ ▄▀▀▐▀▀░▄▄▄▄▄░▀▀▌▄▄▄░░░█ █░░░▀▄░█░░░█░▄▀░░░░█▀▀▀ ░▀▄░░▀░░▀▀▀░░▀░░░▄█▀ ░░░█░░░░░░░░░░░▄▀▄░▀▄ ░░░█░░░░░░░░░▄▀█░░█░░█ ░░░█░░░░░░░░░░░█▄█░░▄▀ ░░░█░░░░░░░░░░░████▀ ░░░▀▄▄▀▀▄▄▀▀▄▄▄█▀

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⠉⠁⠉⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡟⠉⠁⠉⠙⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡇⠀⠀⠀⠀⢽⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡏⠁⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡏⠀⠀⠀⠀⠀⠺⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠫⠁⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠙⠉⠙⠒⠒⣲⣖⣖⣒⣒⡶⠒⠚⠉⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠃⠀⠀⠀⠀⠀⠀⠈⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢯⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣜⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢾⣿⣿⡕⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⠗⣾⣿⣿⡃⠀⠀⠀⢀⣤⣴⣾⣶⣤⣀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡈⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣼⣹⣿⣿⣿⣿⡀⠀⢰⣿⣿⢿⣿⣿⣿⣿⣷⣦⣄⠀⠉⢦⣶⠀⠀⠀⠠⣸⡮⡿⡟⡻⠿⣿⣷⡆⠀⠀⠀⠀⠀⠀⠀⡀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢏⣿⣿⣿⣿⣿⡷⠀⢨⣯⣶⠿⢛⣿⣿⣿⣿⣿⣿⣧⠀⠼⠿⠦⠀⠀⠊⢁⡼⢗⣛⣻⣷⣦⡙⢿⡄⠀⠀⠀⠀⠀⠀⢁⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢰⢼⣿⣿⣿⣿⣿⣷⣄⢀⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢤⣫⣾⣿⣿⣿⣧⢹⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⡀⢧⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣼⡿⣿⣿⣿⣿⣿⣿⣿⠼⢿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀⠀⠀⠀⠀⣯⣿⣿⣿⣿⣿⣟⡤⠿⢿⣦⡀⠀⠀⠀⠀⠀⠀⠐⢸⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠋⠉⠉⠀⠀⠀⠉⠛⠩⠉⠉⠁⢀⣼⣿⡟⠀⠀⠀⠀⠀⠀⠀⠈⠉⠭⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⢻⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⣾⣫⣽⣶⣦⡀⡀⠀⠀⠀⠀⠈⠓⠀⠀⢀⠀⠀⠀⠀⠀⣤⣴⡕⠒⡀⠀⠀⠀⠀⢤⢸⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⢀⣀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⡖⣧⣾⣿⣆⠈⠒⣠⡘⠃⠀⠀⠀⠀⢿⠱⠆⠀⠹⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣢⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⠿⠀⠀⠉⠻⣷⣤⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠿⠛⢉⡀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⣼⣯⣶⣶⣦⣴⣤⣀⣀⠀⠈⠻⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⡛⠋⠉⠉⠉⠉⠛⠛⠷⢿⣿⣶⠄⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⡔⠂⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀ ⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠉⠉⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀ ⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⠀⠀⡀⠀⠀⠀⣰⣦⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀ ⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣷⣿⣿⣶⠈⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀ ⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡞⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇⠀⠀ ⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀ ⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡸⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣰⡀

⢿⣷⣶⣤⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀ ⠈⢿⣿⣿⡇⠈⠑⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡴⢶⣿⣿⣿⡿⠁⠀⠀⠀⠀ ⠀⠈⢻⣿⣇⠀⠀⠀⠀⠑⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠟⠉⠀⠀⣸⣿⣿⡟⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠹⣿⡄⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⠀⠀⠀⠀⢀⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⡠⠊⠁⠀⠀⠀⠀⠀⠀⣼⠟⠁⠀⠀⠀⠀⢀⣀⠤⢤ ⠀⠀⠀⠀⠀⠀⠈⠓⢄⡀⠀⠀⠀⠀⠘⠦⠔⠊⠉⠀⠀⠀⠀⠀⠀⠀⠉⠁⠂⠊⠀⠀⠀⠀⠀⠀⢀⠴⠊⠀⢀⣀⠤⠔⠚⠉⠁⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⢄⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠴⠊⢁⡠⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⡆ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡤⠒⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢀⣶⡿⠛⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠛⢻⣶⡄⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠈⣿⣿⣶⡿⠀⠀⠀⠀⢀⠀⠀⠀⠀⢿⣶⣿⣿⠇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠤⠄⠚⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡧⠤⢄⡈⠉⠉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠉⠉⠁⠀⣀⣀⡇⠀⠀⢠⠤⠒⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠂⠀⠀⠙⡄⠀⠀⠀⠢⠤⠴⠊⠒⠤⠠⠖⠀⠀⠀⡴⠋⠀⠀⢹⠀⠀⠀⠱⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⢠⡎⠀⠀⠀⠀⠈⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢖⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⣲⠋⠈⢒⡤⠀⠀⠀⠀⠈⢦⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠉⠲⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠊⠈⡤⠒⠉⠀⠀⣀⠤⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠉⠀⠀⠀⠀⢣⢀⡦⣶⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠈⢏⢀⣀⠵⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠈⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⡖⣏⠒⢼⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⢸⢀⠤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢻⣮⠢⠀⠑⠂⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢠⠃⠀⢀⡤⠊⢡⣮⡺⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⢄⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇⠀⠀⠀⠀⠀⡠⠃⠀⠀⠈⠀⠀⣠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠱⣄⠀⠀⠀⡄⠙⢄⠀⠀⠀⠀⠀⡃⠤⠄⡰⠀⠀⠀⠀⡰⠁⢀⠀⠀⠀⣀⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠠⠴⠓⠒⠂⠧⢤⡴⡖⠊⠀⠀⠀⠙⠀⣤⣤⡎⠒⠀⢇⣀⡤⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠐⣶⣾⣭⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡄⠀⠄⠀⠀⠀⠀⠀ ⠀⠹⣿⣿⣧⠈⠙⠳⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⢻⣿⣿⣿⢇⠀⠀⠀⠀⠀ ⠀⠀⠘⢿⣿⡄⠀⠀⠀⠙⢿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠛⠉⠀⠀⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠻⣧⠀⠀⠀⠀⠀⠙⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠉⠀⠀⠀⠀⢰⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⢷⣀⠀⠀⠀⠀⠀⠹⣦⡀⠀⢀⣀⣀⣀⣰⣶⣦⣀⣀⡀⠀⠀⣠⡶⠋⠁⠀⠀⠀⠀⠀⢀⣾⡻⠋⠀⠀⡀⣀⣄⣤⡤⣦ ⠀⠀⠀⠀⠀⠀⠀⠙⢦⣄⠀⠀⠀⠀⠈⣷⠶⠛⠉⠉⠁⠀⠀⠈⠉⠉⠛⠿⡿⠟⠁⠀⠀⠀⠀⢀⣠⣶⡿⠋⣀⣤⠼⠗⠛⠉⠁⠀⠀⡟ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠷⢦⣀⣰⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⣤⣶⣟⣣⡽⡿⠟⠋⠀⠀⠀⠀⠀⠀⢀⣾⡟ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠿⡷⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⠏⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⣯⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⣴⣿⠻⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⣴⡻⣿⣷⡀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠇⠀⣿⡿⢿⣿⠃⠀⠀⠀⣀⣀⠀⠀⠀⣿⣿⣿⣿⠇⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⣾⠟⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡤⣤⡈⠉⠉⠁⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠉⠛⠃⢀⣠⣈⣧⠀⠀⣤⣴⡶⠿⠿⠛⠉⠉⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠙⣦⠀⠀⠀⠳⠤⠴⠞⠛⠦⣤⠾⠃⠀⠀⣼⠋⠀⠈⣿⠀⠀⠈⣷⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡄⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠄⠀⣰⡟⠀⠀⠀⠀⠻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣶⣛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢒⣶⣿⢻⣷⣤⠀⠀⠀⠈⢻⣦⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⡇⠙⠳⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠶⠋⢸⡷⠞⠋⠀⣀⣠⣶⠞⠿⠙⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠁⠀⠀⠀⠉⠓⠭⣷⣦⣤⣤⡴⠦⣺⠛⠉⠀⠀⠀⠈⣷⠀⢶⣿⣟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀⣦⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠘⣷⣀⣨⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⣄⣀⣠⡟⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⢀⡇⠀⠘⣷⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢰⣿⣿⣛⣿⣁⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⢸⣱⣿⣷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⢿⣿⠻⣤⣉⠷⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⣿⠰⠠⡏⠀⠀⠀⠀⠀⠀⣰⠇⠀⢀⡴⢛⣱⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠛⢷⡀⠈⠳⣄⠀⠹⣦⠀⠀⠀⠀⠀⠀⡟⠀⠀⣷⠀⠀⠀⠀⠀⣰⠏⠀⢀⣴⠚⠉⣸⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢹⣦⡀⠈⠃⣦⠘⢷⡀⠀⠀⠀⢀⣧⣤⣤⣿⠀⠀⠀⢀⣼⠃⣀⠒⠛⢀⣤⣾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣛⣦⠴⢿⢶⣿⣿⡤⢴⣶⢿⡛⠁⠙⣿⣶⣤⣤⣾⣗⢶⣯⣤⣴⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠈⣷⣿⣿⣶⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⢰⣶⣷⣿⣿ ⠀⠹⣿⣿⣿⡄⠀⠈⠓⠦⣄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠊⠉⠀⣸⣿⣿⣽⠃ ⠀⠀⠘⣿⣿⣇⠀⠀⠀⠀⠀⠘⠶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⣿⣿⣿⠃⠀ ⠀⠀⠀⠈⢻⣿⠄⠀⠀⠀⠀⠀⠀⠈⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠙⠁⠀⠀⠀⠀⠀⠀⡸⣿⠟⠁⠀⠀ ⠀⠀⠀⠀⠀⠁⢾⡄⠀⠀⠀⠀⠀⠀⠀⠈⠱⣦⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠁⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠳⡄⠀⠀⠀⠀⠀⠀⠀⠈⠳⡆⣤⠴⠞⠛⠉⠉⠉⠉⠉⠉⠉⠳⠆⣤⣤⠞⠁⠀⠀⠀⠀⠀⠀⢀⣠⠖⠁⠀⠀⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢳⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣠⣶⠖⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠴⠶⣦⡄⠀⠀⢈⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠀⠀⢰⣾⣷⣀⣰⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣀⣠⣾⣿⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠈⠻⣍⡩⠜⠃⠀⠀⠀⠠⣤⡤⠀⠀⠀⠀⠹⠭⣉⠽⠏⠀⠀⠀⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣤⠴⠴⣤⣠⣇⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣤⣤⣼⣀⡴⢴⢦⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⢹⡁⣀⡀⠙⣱⡀⠀⠀⠀⠲⣄⣠⡴⣒⢒⣤⣤⠴⠂⠀⠀⠀⢠⡞⢁⣀⡀⢨⠃⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠉⠀⠉⠀⠈⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠈⠀⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁⠈⠈⠈⠀⠉⠀⠀⠀⠀⠀⠀

⠈⣿⣷⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠸⣿⣿⣿⣿⠈⠙⠲⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣶⣶⣶⡶⠀⠀⠀⠀⠀⠀ ⠀⠀⠘⣿⣿⣿⡄⠀⠀⠀⠉⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠚⠉⠀⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⢿⣿⡧⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠞⠉⠀⠀⠀⠀⢠⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⣿⡖⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠉⠀⠀⠀⠀⠀⠀⢠⣾⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⢢⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⢀⣠⠤⠴⠒⠒⠒⠒⠒⠒⠒⠲⠤⢤⣀⡀⢀⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⢀⣀⣠⠤⠔⠒⠉⠉⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢤⡀⠀⠀⠀⠀⠀⠈⠳⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠀⠀⠀⠀⠀⠀⠀⣀⡤⠚⠉⠀⠀⣀⡤⠔⠚⠉⠁⠀⠀⠀⠀⠀⠀⠸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢄⣀⢀⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣀⣠⠴⠚⠁⢀⣠⠴⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⣤⠔⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⢼⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⣾⣿⢉⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡏⠀⢹⣿⣦⡀⠀⢸⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠸⣿⣿⣷⣾⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⣶⣿⣿⡿⠀⠀⠐⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠤⠖⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠙⠛⠛⠋⠀⠀⠀⠀⠀⠀⠘⠓⠀⠀⠀⠀⠀⠈⠛⠛⠋⠁⠀⠀⠀⢻⡀⠀⠀⠀⣀⣀⣀⡤⠤⠒⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠿⣿⢶⣄⠀⠀⠀⠀⢀⡀⠀⠀⠀⣀⣀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⣴⣶⣶⣾⡇⠀⠀⠘⢫⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣯⢿⣝⣯⢿⣆⠀⠀⠀⠀⠙⠒⠒⠋⠉⠈⠙⠒⠒⠋⠀⠀⠀⠀⣰⣿⣻⢮⡷⢯⡗⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡿⢮⣻⣽⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣯⢷⣯⣟⣿⠃⠀⠀⠀⠀⠀⠀⠱⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠯⢷⢾⡿⠉⠓⠦⣄⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠓⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠻⡁⠀⣀⠴⠋⠁⠀⠀⠀⢀⣀⡤⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠈⠓⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠁⠀⠀⣷⠋⠁⠀⠀⣀⣠⠴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠁⠈⠲⠶⣦⡄⣀⠤⠤⠀⢐⠛⠁⠀⠀⠀⠀⠀⠀⠹⡄⢀⢦⣻⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⡀⠀⠀⠀⠀⠀⢠⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣮⣟⣽⣿⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⢀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡃⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣾⢺⠛⠢⣼⠁⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⠃⠀⠀⠀⠀⡇⢀⣠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢿⢯⡳⡀⠈⠑⢆⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣀⣀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⢀⡴⠛⢉⣼⣽⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠳⡽⠘⠓⢦⣀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣸⠂⠀⠀⠀⠀⠀⠀⠀⢠⠟⠀⠀⠀⠴⣋⡠⠔⣺⣻⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⡀⠀⠈⠳⣄⠀⢀⠹⣄⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠹⡇⠀⠀⠀⠀⠀⠀⢠⡞⠄⠀⠀⣠⠞⠁⢀⣼⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢖⡂⡀⠈⠁⢿⠀⠙⢦⡀⠀⠀⠀⠀⠀⣼⣄⣦⣴⣥⡷⠀⠀⠀⠀⠀⣠⠋⠀⣄⠑⠘⠁⢀⣠⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣖⣢⡾⠾⠴⠚⢳⣦⣠⣤⡶⠶⠛⠀⠀⠀⠘⠲⡤⣄⣀⣀⡞⠳⢤⣶⡏⣀⣠⡷⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⡏⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿ ⣿⣿⣿⣿⣿⣿⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠁⠀⣿ ⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠙⠿⠿⠿⠻⠿⠿⠟⠿⠛⠉⠀⠀⠀⠀⠀⣸⣿ ⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣴⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⢰⣹⡆⠀⠀⠀⠀⠀⠀⣭⣷⠀⠀⠀⠸⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠉⠀⠀⠤⠄⠀⠀⠀⠉⠁⠀⠀⠀⠀⢿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⢾⣿⣷⠀⠀⠀⠀⡠⠤⢄⠀⠀⠀⠠⣿⣿⣷⠀⢸⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⡀⠉⠀⠀⠀⠀⠀⢄⠀⢀⠀⠀⠀⠀⠉⠉⠁⠀⠀⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿

⡏⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿ ⣿⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠁⠀⣿ ⣿⣧⡀⠀⠀⠀⠀⠙⠿⠿⠿⠻⠿⠿⠟⠿⠛⠉⠀⠀⠀⠀⠀⣸⣿ ⣿⣿⣷⣄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿ ⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣴⣿⣿⣿⣿ ⣿⣿⣿⡟⠀⠀⢰⣹⡆⠀⠀⠀⠀⠀⠀⣭⣷⠀⠀⠀⠸⣿⣿⣿⣿ ⣿⣿⣿⠃⠀⠀⠈⠉⠀⠀⠤⠄⠀⠀⠀⠉⠁⠀⠀⠀⠀⢿⣿⣿⣿ ⣿⣿⣿⢾⣿⣷⠀⠀⠀⠀⡠⠤⢄⠀⠀⠀⠠⣿⣿⣷⠀⢸⣿⣿⣿ ⣿⣿⣿⡀⠉⠀⠀⠀⠀⠀⢄⠀⢀⠀⠀⠀⠀⠉⠉⠁⠀⠀⣿⣿⣿ ⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿ ⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿𝐏𝐈𝐂𝐊𝐀𝐂𝐇𝐔𝐏𝐈𝐂𝐊𝐀𝐂𝐇𝐔𝐏𝐈𝐂𝐊𝐀𝐂𝐇𝐔𝐏𝐈𝐂𝐊𝐀𝐂𝐇𝐔𝐏𝐈𝐂𝐊𝐀𝐂𝐇𝐔𝐏𝐈𝐂𝐊𝐀𝐂𝐇𝐔

➖⬛⬛➖➖➖➖⬛ ➖➖🟨🟧➖➖➖🟧 ➖➖➖🟨🟨🟨🟨🟧 🟧🟧➖🟨⬛🟨🟨⬛ 🟧🟧➖🟥🟨🟨🟨🟧 ➖🟧➖🟨🟧🟧🟧 ➖🟧🟨🟧🟨🟧🟨 ➖➖🟨🟧🟫🟫🟧

░░░░█░▀▄░░░░░░░░░░▄▄███▀░░ ░░░░█░░░▀▄░▄▄▄▄▄░▄▀░░░█▀░░ ░░░░░▀▄░░░▀░░░░░▀░░░▄▀░░░░ ░░░░░░░▌░▄▄░░░▄▄░▐▀▀░░░░░░ ░░░░░░▐░░█▄░░░▄█░░▌▄▄▀▀▀▀█ ░░░░░░▌▄▄▀▀░▄░▀▀▄▄▐░░░░░░█ ░░░▄▀▀▐▀▀░░░░░░░▀▀▌▄▄▄░░░█ ░░░█░░░▀▄░░░░░░░▄▀░░░░█▀▀▀

⬜⬜⬜⬜⬜⬛⬛⬜⬜⬜⬜⬜⬜⬜⬛⬛⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬛⬛⬛⬛⬜⬜⬜⬜⬛⬛⬛⬜⬜⬜⬜ ⬜⬜⬜⬜⬜🟨🟨🟨🟨⬜❤️⬜🟨🟨🟨🟨⬜⬜⬜⬜ ⬜⬜⬜⬜⬜🟨🟨🟨🟨⬜⬜⬜🟨🟨🟨🟨⬜⬜⬜⬜ ⬜⬜⬜⬜⬜🟨🟨🟨🟨⬜⬜⬜🟨🟨🟨🟨⬜⬜⬜⬜ ⬜⬜⬜⬜⬜🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜🟨🟨🟨🟨🟨🟨🟨🟨🟨⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜🟨🟨🟨⬛🟨🟨🟨⬛🟨🟨🟨⬜⬜⬜⬜ ⬜⬜⬜⬜⬜🟨🟨🟨⬛🟨🟨🟨⬛🟨🟨🟨⬜⬜⬜⬜ ⬜⬜⬜⬜⬜🟥🟥🟨⬛🟨🟨🟨⬛🟨🟥🟥⬜⬜⬜⬜ ⬜⬜⬜⬜⬜🟥🟥🟨🟨🟨🟨🟨🟨🟨🟥🟥⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜🟨🟨🟨🟨🟨🟨🟨🟨🟨⬜⬜⬜⬜⬜ ⬜⬜⬜⬜🩵🩵🩵🩵🩵🩵🩵🩵🩵🩵🩵🩵🩵⬜⬜⬜ ⬜⬜🩵🩵🩵🩵🩵🩵🩵🩵🩵🩵🩵🩵🩵🩵🩵⬜⬜⬜ ⬜🩵🩵⬜🩵🩵🩵🩵🩵🩵🩵🩵🩵🩵🩵🩵🩵⬜⬜⬜ ⬜🩵⬜⬜🩵🩵🩵🩵🩵🩵🩵🩵🩵🩵🩵🩵🩵⬜⬜⬜ ⬜🩵🩵⬜🩵🩵🩵🩵🩵🩵🩵🩵🩵🩵🩵🩵🩵⬜⬜⬜ ⬜⬜🩵🩵🩵🩵🩵🩵🩵🩵🩵🩵🩵🩵🩵🩵⬜⬜⬜⬜ ⬜⬜⬜⬜🩵🩵🩵🩵🩵🩵🩵🩵🩵🩵🩵⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜🩵🩵🩵🩵🩵🩵🩵⬜⬜⬜⬜⬜⬜

⣿⣿⣤⣌⡁⠀⠈⠀⠁⠈⠀⠈⠀⠀⠁⠀⠈⠀⠀⠁⠈⠀⠁⠀⠁⠀⠀⠁⠀⠁⠈⠀⠁⠀⠁⠀⠀⠁⠀⠈⠀⠈⠀⠁⠈⠀⠀⠁⠀⠈⠀⠈⠀⠁⠈⠀⠁⠈⠀⠈⠀ ⡇⢻⣿⣿⣿⠳⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤ ⡇⠈⢿⣿⣿⠀⠀⠈⠛⠶⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣿⣿⣿⣿⡟ ⡇⠀⠈⢿⣿⡀⠀⠀⠀⠀⠈⠉⠷⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡴⠖⠛⠉⠉⣿⣿⣿⣿⣿⠏⠀ ⡇⠀⠀⠀⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠶⠛⠉⠀⠀⠀⠀⠀⠀⣿⣿⣿⡟⠁⠀⠀ ⡇⠀⠀⠀⠀⠹⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠴⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⠋⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠤⠤⠤⠤⠶⠶⠶⠖⠒⠒⠒⠒⠒⠒⠒⠒⠒⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠟⠁⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠘⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⠶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⣴⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⢠⡶⠶⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠶⣶⣶⡄⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⣿⣄⣀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣇⣀⣼⣿⣿⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠘⠿⣿⣿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⣠⣀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⣵⢫⢞⡽⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢏⡷⢭⣛⢷⡀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⡝⣮⡝⣮⢳⣽⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⢦⡤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠸⣧⢻⡜⣧⣛⢮⡇⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⢽⣲⡝⣮⡷⠃⠀⠀⠀⠀⠀⠀⠀⣿⢏⡐⢢⢐⠡⢚⡷⠀⠀⠀⠀⠀⠀⠀⠻⣧⣛⢶⣹⡾⠁⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⢿⠈⠉⠑⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢹⡬⡑⢌⡘⠢⢌⡷⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠚⠋⠁⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠶⠼⠷⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣝⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⣀⣀⣀⢀⡀⣀⢀⡀⣀⢀⡀⣀⢀⡀⣀⢀⡀⣀⢀⡀⣀⢀⡀⣀⢀⡀⣀⢀⡀⣀⢀⡀⣀⢀⣀⣀⣀⣀⣹⡀⠀⠀⠀⠀⠀⠀⣯⢯⣿

⬜⬜⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬛⬛⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬛⬛⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬛⬛⬛⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬛⬛⬛⬛⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛⬛⬛ ⬛⬛⬛⬛⬛⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛⬛⬛⬛⬛⬛ ⬛⬛⬛⬛🟨⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛⬛⬛⬛⬛⬛⬛⬛ ⬛⬛⬛🟨🟨⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛⬛🟨🟨⬛⬛⬛⬛⬛⬜ ⬜⬛🟨🟨🟨🟨⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛🟨🟨🟨🟨🟨⬛⬛⬛⬛⬜ ⬜⬛🟨🟨🟨🟨⬛⬜⬛⬛⬛⬛⬛⬛⬜⬜⬛⬛🟨🟨🟨🟨🟨🟨⬛⬛⬛⬜⬜ ⬜⬛🟨🟨🟨🟨🟨⬛🟨🟨🟨🟨🟨🟨⬛⬛🟨🟨🟨🟨🟨🟨🟨🟨⬛⬛⬜⬜⬜ ⬜⬛🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨⬛⬛⬜⬜⬜⬜ ⬜⬜⬛🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨⬛⬜⬜⬜⬜⬜⬜ ⬜⬜⬛🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨⬛⬛⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬛🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬛🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨⬛⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬛🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨⬛⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬛🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨⬛⬜⬜⬜⬜⬜⬜⬜ ⬛🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨⬛⬜⬜⬜⬜⬜⬜⬜ ⬛🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨⬛⬜⬜⬜⬜⬜⬜⬜ ⬛🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨⬛⬜⬜⬜⬜⬜⬜⬜ ⬛⬛🟨🟨🟨🟨🟨⬛⬛⬛⬛🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨⬛⬜⬜⬜⬜⬜⬜⬜ ⬛🟥⬛⬛🟨🟨⬛⬛⬜⬜⬛⬛🟨🟨⬛⬛⬛⬛🟨⬛⬛⬛⬜⬜⬜⬜⬜⬜⬜ ⬛🟥🟥🟥⬛⬛⬛⬜⬜⬜⬜⬛⬛⬛🟥🟥🟥🟥⬛🟥🟥⬛⬜⬜⬜⬜⬜⬜⬜ ⬛🟥🟥🟥🟥🟥⬛⬜⬜⬜⬜⬛🟥🟥🟥🟥🟥🟥🟥🟥🟥⬛⬜⬜⬜⬜⬜⬜⬜ ⬛🟥🟥🟥🟥🟥⬛⬛⬜⬜⬛⬛🟥🟥🟥🟥🟥🟥🟥🟥🟥⬛⬜⬜⬜⬜⬜⬜⬜ ⬜⬛🟥🟥🟥🟥🟥⬛⬛⬛⬛🟥🟥🟥🟥🟥🟥🟥🟥🟥⬛⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬛🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥⬛⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬛🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬛🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬛🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬛⬛🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥⬛⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬛⬛🟥🟥🟥🟥🟥🟥⬛⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬜⬛⬛⬛⬛⬛⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜

⬛⬛⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛⬛⬛ ⬛🟨🟨⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛🟨🟨⬛ ⬛⬛🟨🟨⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛🟨🟨⬛⬛ ⬜⬛🟨🟨🟨⬛⬜⬜⬛⬛⬛⬛⬛⬛⬜⬜⬛🟨🟨🟨⬛⬜ ⬜⬜⬛🟨🟨🟨⬛⬛🟨🟨🟨🟨🟨🟨⬛⬛🟨🟨🟨⬛⬜⬜ ⬜⬜⬜⬛🟨⬛🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨⬛🟨⬛⬜⬜⬜ ⬜⬜⬜⬜⬛🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨⬛⬜⬜⬜⬜ ⬜⬜⬜⬜⬛🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨⬛⬜⬜⬜⬜ ⬜⬜⬜⬛🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨⬛⬜⬜⬜ ⬜⬜⬜⬛🟨🟨🟨⬜⬛🟨🟨🟨🟨⬜⬛🟨🟨🟨⬛⬜⬜⬜ ⬜⬜⬜⬛🟨🟨🟥⬛🟫🟨⬛⬛🟨⬛🟫🟥🟨🟨⬛⬜⬜⬜ ⬜⬜⬜⬛🟨🟨🟥🟥🟨🟨🟨🟨🟨🟨🟥🟥🟨🟨⬛⬜⬜⬜ ⬜⬜⬜⬛🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨⬛⬜⬜⬜ ⬜⬜⬜⬛🟨🟨🟨⬛⬛⬛⬛⬛⬛⬛⬛🟨🟨🟨⬛⬜⬜⬜ ⬜⬜⬜⬜⬛⬛⬛⬜⬜⬛⬜⬜⬛⬜⬜⬛⬛⬛⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬛⬜⬜⬜⬛⬜⬜⬛⬜⬜⬜⬛⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬛⬜⬜⬜⬜⬜⬜⬜⬜⬛⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬛⬛⬛⬛⬛⬛⬛⬛⬜⬜⬜⬜⬜⬜⬜

⢸⣷⣶⣶⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⣿⣿⣿⣿⣿⣿⣿⣷⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠘⣿⣿⣿⣿⣿⣿⡟⠀⠈⠙⠳⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠘⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠈⠙⠳⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀ ⠀⠀⠀⠘⢿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣶⣶⣿⣿⡇ ⠀⠀⠀⠀⠈⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⠶⠟⠋⠉⠁⠀⢸⣿⣿⣿⡇ ⠀⠀⠀⠀⠀⠈⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡶⠿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇ ⠀⠀⠀⠀⠀⠀⠀⠻⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⠾⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠶⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⠋⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⣀⣤⣶⠾⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠹⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡿⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠹⣷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠞⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠟⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠘⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣤⣤⣤⣤⣤⡴⠶⠶⠶⠶⠶⠖⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠳⠶⠶⢶⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠻⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡟⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡟⠁⠀⠀⠀⠄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣶⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣶⡀⠀⠀⠀⢀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠈⠻⣦⣀⣼⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⢀⣰⡾⠋⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⣸⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⢀⣠⡾⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠉⠀⣰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣾⡋⠉⠀⠀⠀⠀⠀⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡀⠀⠀⠐⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣶⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣾⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠉⠉⢚⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠋⠉⢸⢿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣯⣦⣀⣶⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣷⣂⣤⣮⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣾⣿⣿⣷⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⢀⣀⣤⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⣠⣶⣟⢯⣗⢯⡾⣹⢯⡷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡟⣯⢟⡵⣏⣿⡹⣟⣶⣄⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⢰⣟⣳⡞⣯⡞⣯⢾⡝⣧⣟⣳⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣟⡧⢿⣹⠾⣽⣹⢶⡻⣝⣮⢟⣦⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢸⡏⠀⢹⣯⣳⡽⢧⢿⣹⢾⣹⡗⣾⢭⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣠⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡞⣽⣏⡷⣻⢧⡟⡾⣽⣹⢮⡟⣽⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡇⠈⢷⣳⢯⣻⢽⣚⡷⣫⢾⣝⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⢿⣛⠛⣏⠻⡙⢏⡛⡛⠿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣽⡳⣞⡽⣳⢯⢾⣝⣧⢯⢷⣛⡿⠀⠀⠀⠀⠀⠀⠀⠀⢽⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠸⣇⠀⠀⠀⠙⠫⠷⣯⣻⣼⣯⠷⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡱⢊⠴⣉⢆⢣⡙⢦⠱⣉⢖⡩⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢷⣯⢽⡳⢯⣻⡼⣞⡽⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⠣⣍⠲⡡⢎⠦⡙⢦⡙⡜⢦⡑⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠯⠗⠛⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣢⠙⣆⠣⡜⢤⠓⣌⢣⠱⣌⠳⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⣽⣠⠓⡜⢢⡙⡤⢃⡳⢌⣳⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣮⣵⣼⣴⣭⣶⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⠈⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠈⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢸⡇⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠑⠂⠒⠔⠢⠒⠰⠂⠖⠢⠖⠂⠲⠐⠢⠒⠔⠒⠰⠂⠲⠐⠆⠲⠐⠂⠖⠰⠂⠲⠰⠂⠶⠐⠒⠰⠆⠒⠆⠖⠰⠂⠒⠢⠒⠆⠒⠰⠂⠖⠰⠆⠲⠰⠂⠶⠐⠆⠲⠐⠢⠒⠔⠂⠲⠐⠢⠒⠆⠒⠔⠂⠖⠰⠂⠲⠰⠂⠖⠒⠒⠺⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀

⡏⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿ ⣿⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠁⠀⣿ ⣿⣧⡀⠀⠀⠀⠀⠙⠿⠿⠿⠻⠿⠿⠟⠿⠛⠉⠀⠀⠀⠀⠀⣸⣿ ⣿⣿⣷⣄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿ ⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣴⣿⣿⣿⣿ ⣿⣿⣿⡟⠀⠀⢰⣹⡆⠀⠀⠀⠀⠀⠀⣭⣷⠀⠀⠀⠸⣿⣿⣿⣿ ⣿⣿⣿⠃⠀⠀⠈⠉⠀⠀⠤⠄⠀⠀⠀⠉⠁⠀⠀⠀⠀⢿⣿⣿⣿ ⣿⣿⣿⢾⣿⣷⠀⠀⠀⠀⡠⠤⢄⠀⠀⠀⠠⣿⣿⣷⠀⢸⣿⣿⣿ ⣿⣿⣿⡀⠉⠀⠀⠀⠀⠀⢄⠀⢀⠀⠀⠀⠀⠉⠉⠁⠀⠀⣿⣿⣿ ⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿ ⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿

⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛⬜⬜⬜ ⬛⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛🟨⬛⬜⬜ ⬛⬛⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛🟨🟨⬛⬜⬜ ⬛⬛⬛⬜⬜⬜⬜⬜⬜⬜⬜⬛🟨🟨🟨⬛⬜⬜ ⬛⬛🟨⬛⬜⬜⬜⬜⬜⬜⬛🟨🟨🟨🟨⬛⬜⬜ ⬛🟨🟨⬛⬛⬜⬜⬜⬜⬛🟨⬛⬛⬛⬛⬛⬛⬛ ⬛⬛🟨🟨⬛⬛⬛⬛⬛⬛⬛⬛⬛🟨🟨🟨⬛⬛ ⬜⬛🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨⬛⬛⬜ ⬜⬛🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨⬛⬛⬜⬜⬜ ⬜⬛⬛🟨🟨🟨🟨🟨🟨🟨🟨🟨⬛⬛⬜⬜⬜⬜ ⬜⬛🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨⬛⬜⬜⬜⬜ ⬜⬛🟨⬜⬛🟨🟨🟨🟨🟨⬜⬛🟨⬛⬜⬜⬜⬜ ⬛⬛🟨⬛⬛🟨🟨🟨🟨🟨⬛⬛🟨⬛⬛⬜⬜⬜ ⬛🟨🟥🟨🟨🟨🟨⬛🟨🟨🟨🟨🟥🟨⬛⬜⬜⬜ ⬛⬛🟥🟥🟨🟨🟨🟨🟨🟨🟨🟥🟥⬛⬛⬜⬜⬜ ⬜⬛⬛🟥🟨🟨🟨⬛🟨🟨🟨🟥⬛⬛⬜⬜⬜⬜ ⬜⬛🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨⬛⬜⬜⬜⬜ ⬛⬛🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨⬛⬛⬜⬜⬜ ⬛🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨⬛⬜⬜⬜ ⬛🟨🟨⬛🟨🟨🟨🟨🟨🟨🟨⬛🟨🟨⬛⬜⬜⬜ ⬛🟨⬛🟨🟨🟨🟨🟨🟨🟨🟨🟨⬛🟨⬛⬜⬜⬜ ⬜⬛🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨⬛⬛⬜⬜⬜ ⬜⬛⬛🟨🟨🟨⬛⬛⬛🟨🟨🟨⬛⬛⬜⬜⬜⬜ ⬛🟨🟨⬛⬛⬛⬛⬛⬛⬛⬛⬛🟨🟨⬛⬜⬜⬜ ⬜⬛⬛⬛⬜⬜⬜⬜⬜⬜⬜⬛⬛⬛⬜⬜⬜⬜

(๑⚈ ․̫ ⚈๑)

⢀⣠⣼⣿⢿⡿⣿⢿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢿⡿⣿⢿⡿⣿⢿⡿⣿⢿⡿⣿⢿⡿⣿⢿⡿⣿⢿⣿⣿⢯⡳⢌⠀⠀⠀⢀⠠⢀⡐⢤⢂ ⣿⣿⣻⣽⣿⣻⣟⣯⣿⣿⣿⣿⣿⣿⣿⡿⣽⣿⣻⣽⣿⣻⣽⣿⣻⣽⣿⣻⣽⣿⣻⣽⣿⣻⣯⣿⢾⣿⣯⢳⡉⠄⢁⠠⢀⠀⡂⠜⣠⠧ ⣿⡾⣟⣷⣯⣿⣽⣿⣻⣿⣿⣿⣿⣿⣿⣿⣟⣾⣟⣷⡿⣽⣷⣻⣽⣷⣻⣽⣷⣻⣽⣷⣻⣷⢿⣽⡿⣾⣯⡳⢌⡐⠀⢀⠀⠂⢡⢊⡝⡺ ⣿⣽⣿⣽⡾⣷⣿⡷⣿⣽⡿⣯⣿⢿⣻⣿⣾⣟⣾⣯⢿⣟⣾⣟⣷⢿⣽⣷⣻⣯⣷⢿⣽⡾⣟⣯⡿⣟⣿⡵⢢⠄⡈⠀⠠⢈⠆⢲⠸⡵ ⣿⣷⣻⣾⣟⣿⣿⣿⣿⣾⡝⡷⢯⣟⣿⣻⣿⡾⣟⣾⡿⣯⣿⢾⣯⣿⣻⢾⣯⣷⢿⣻⣽⢿⣻⣯⡿⣟⣿⣏⢧⢒⠠⡁⢆⡡⢎⠥⣛⠴ ⣿⡾⣟⣷⡿⣿⣿⣿⣿⠈⠙⠫⢿⣼⣳⣟⣿⣿⣻⣽⡿⣽⣾⢿⣳⣿⡽⣿⣳⣿⣻⣯⣿⣻⣯⣷⢿⡿⣽⣿⣏⣎⡳⣜⢦⡱⣎⡳⣍⡞ ⣿⣽⡿⣽⣿⠻⡝⣿⣿⠀⠀⠀⠀⠉⠓⠿⣿⣷⣿⣳⡿⣿⡽⣟⣿⢾⣟⣿⣽⡾⣯⣷⣟⣷⡿⣽⣿⣻⣯⢿⣿⣿⣿⣿⣿⣿⣽⣷⣿⣿ ⣿⣳⡿⣿⢇⡻⡜⡼⣿⣆⠀⠀⠀⠀⠀⠀⠀⠙⠿⣽⣿⣳⣿⣟⣯⣿⣻⣾⢯⣿⣻⢷⣻⣽⣟⣿⣞⣯⡿⣟⣿⣿⣿⣿⣿⡿⠟⠋⠁⠀ ⣿⣻⣽⡟⢮⡱⣝⠶⣽⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣷⣻⣟⣾⢯⣿⣻⣽⣟⣿⣻⣽⡾⣟⣾⢿⣽⢿⣿⠿⠛⠉⠀⠀⠀⠀⠀⠀ ⣿⢯⣿⣙⢧⣙⢮⣻⢷⣻⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⠯⠿⠿⠷⠛⠛⠞⠛⠛⠓⠛⠻⠿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣷⣹⢶⣹⢮⡷⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀ ⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⡀⠀⣠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢾⠍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⣀⣠⣼⣟⢧ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⣄⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡀⠀⠀⠀⠀⠀⠀⢙⣿⡷⣞⣧ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⡟⠀⠀⠀⠀⢰⣏⣉⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣏⢋⣿⣧⠀⠀⠀⠀⠀⠀⠹⣿⣽⣾ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣽⠃⠀⠀⠀⠀⠙⠿⣿⣿⠏⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠉⢿⣿⡿⠏⠀⠀⠀⠀⠀⠀⠈⢻⣿⣾ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡏⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠰⣾⣿⣤⡄⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⢀⣶⢿⡟⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡿⡿⣷⣦⡀⠀⠀⢻⣿ ⣿⣿⣿⣿⣿⣿⢿⡿⣟⣯⣟⣯⣿⠸⣿⢧⣟⣷⣿⠃⠀⠀⠀⠀⠀⠀⢀⣤⡴⢶⠶⣤⡀⠀⠀⠀⠀⠀⠀⢿⣯⣳⢟⣶⣻⡇⠀⠀⠈⣿ ⣿⢯⡷⢯⡗⣯⡻⣝⡻⣎⢷⣚⢿⡀⠈⠙⠚⠋⠁⠀⠀⠀⠀⠀⠀⢰⢿⢎⡱⣍⢚⡬⢿⡀⠀⠀⠀⠀⠀⠈⠙⠷⠿⠞⠋⠀⠀⠀⠀⣽ ⡿⣝⡞⣧⢛⠶⡹⢬⠳⣜⡲⢭⡺⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠯⣖⣬⣳⣼⠟⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸ ⣿⣽⢺⡕⡯⢞⣭⢓⡯⢼⡱⢧⣫⢟⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣞⡿⣼⣏⠿⣜⡯⣞⢧⣛⣧⢯⡿⣽⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣽⡿⣷⣯⣿⢯⣷⣻⣯⣟⣾⣯⣿⣟⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⡿⠛⠉⢸⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠟⠋⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠈⣧⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠟⠁⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣤⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠁⠀⠀⠀⠸⡆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠁⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠴⢶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⡍⠀⠀⠀⠀⠀⠀⠀⣿⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠴⠒⠋⠉⠁⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠇⠀⠀⠀⠀⠀⠀⠀⡏⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠀⠀⠀⠀⠀⠀⠀⠀⣼⠂⠀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⣀⡴⠖⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠑⠒⠦⢤⣀⣀⡠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⠿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⢀⡀⠔⠋⠁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣴⣿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣹⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⢦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠞⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡁⠰⣨⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⢀⣀⣠⡤⠖⠞⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣡⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡿⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣏⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⡁⣀⡿⡆⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠛⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢫⣿⣿⣿⣿⠃⠁⠀⠀⢸⣿⠆⠀⠀⠀⠀⠀⠀⣤⡀⠀⠐⠀⠈⠀⠀⠀⢀⣤⢖⡛⡛⢷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡞⠋⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇⡘⣿⣿⣿⠃⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⡀⣠⣴⠋⠀⠀⠀⠀⠀⠀⠀⢠⡞⣔⠪⢜⠱⣪⢵⣻⡀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠞⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣴⡃⠀⠉⠀⠀⠻⠤⠤⠤⣾⣶⣶⣶⣶⣾⢿⣟⣿⡄⠀⠀⠀⠀⠀⠀⠀⣾⣰⣎⡑⢪⣵⣭⢳⣻⡇⠀⠀⠀⠀⠀⠀⠀⠀⣻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣴⠞⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠐⣿⣆⠀⠀⠀⠀⠀⠀⠀⢹⣿⣞⣳⡽⣞⣯⣞⣿⣇⠀⠀⠀⠀⠀⠐⠈⣿⡼⢿⡷⣥⢻⡌⣟⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠞⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡧⠩⣽⣆⠀⠀⠀⠀⠀⠀⠐⢹⣾⣳⢿⣹⣞⣿⡾⣿⠆⠀⠀⠀⠀⠀⠀⠹⣯⠽⣿⣧⣳⢽⣺⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠞⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡱⣚⣿⡄⠀⠀⠀⠀⠀⠀⠐⠻⣯⣟⣿⡿⣧⡟⣿⡅⠀⠀⠀⠀⠀⠀⠀⠙⠿⣜⣻⣝⡾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣀⠀⢠⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⣠⡴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡹⣞⣿⡆⠀⠀⠀⠀⠀⠀⠀⢹⣿⡉⠵⣖⡂⣿⡐⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣀⠘⠀⠀⠀⡄⢀⠃⠀⣠⡴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢾⡟⠇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⢥⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⡀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠄⠀⠀⠁⢲⣴⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡦⣾⣿⡉⣹⣏⠙⠙⠀⠀⠀⠀⠀⠸⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣀⠄⠀⡀⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣙⣲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⡳⢿⡮⡿⣧⢹⣦⡄⠀⠀⠀⠀⠀⠀⣼⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠿⠃⠠⠀⠄⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠴⠒⠋⠉⠁⠀⠀⠹⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣦⠿⡿⡏⠊⠉⢛⠻⣻⣬⡇⠀⠀⠀⠀⠀⠀⠘⣯⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⢀⠄⡈⠄⢡⠈⠔⡙⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢰⠤⢤⣤⠖⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⣴⢶⡄⠀⣲⡟⠀⢨⣸⣧⠀⠀⠀⠀⠀⠀⠀⠈⠳⠿⣄⠀⠀⠀⠀⠀⠀⢀⣠⠞⢉⢠⠘⡀⢂⠐⡈⠄⡨⣐⡴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⡶⠞⡧⠄⣜⣷⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠉⠲⡿⣟⡤⠞⠁⠀⠀⠙⢢⠀⠀⠀⠀⠀⠀⠀⠘⣦⠀⠀⠀⣠⠴⠋⣄⠒⡈⢄⠂⡐⠄⢃⢰⣬⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⣷⠮⠁⠸⢯⣀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠤⠀⠤⠈⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠨⢧⡀⠀⠙⢦⣡⠀⠒⡐⠠⢒⣠⣬⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠸⣧⣘⢀⠀⠘⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⠀⠀⠙⢧⡂⠅⢒⡌⠹⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⠯⠬⠤⢤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⡄⠀⠀⠙⢮⡈⢷⣇⡸⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠓⠒⠒⠲⠦⠤⠤⠤⠤⣽⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣷⡄⠀⠀⡠⠛⣦⣿⠿⣽⣻⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢻⣆⣀⣴⡿⣟⢯⡟⣶⢏⣟⢿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡿⣧⢻⡞⣽⡺⣽⣺⠽⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⢿⣽⣳⡯⠗⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠁⠸⣯⣟⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢀⠂⠀⣿⣾⣱⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠘⠀⠀⠂⠀⣿⠾⠷⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠊⠀⠀⠀⡀⠁⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⡀⠀⠀⠀⠀⡿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠐⢀⠀⠐⡀⠀⠂⠀⠀⠀⠀⢰⡇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠂⠠⠐⠈⠀⠀⠀⢀⠀⠀⠀⠀⠄⢀⠄⡀⠀⠀⠀⠀⡀⠀⠂⠀⠀⠀⠀⠀⠄⠀⠄⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⡀⠉⠒⠀⠀⠀⠠⠀⠀⢂⠈⠐⠈⠀⣄⡤⠶⠒⠚⠛⠓⠒⠒⠮⢤⣀⡀⠀⠀⠐⠀⠁⠂⠄⠀⡄⢀⠁⡀⠂⠀⢀⣀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢤⣀⡀⠀⠁⠀⠀⣀⣀⣤⠶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠦⢤⣤⣀⣀⣀⣀⣀⣀⣠⣤⠶⠞⠋⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢻⡟⢻⡛⢫⠍⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠉⢹⡏⡡⣇⡘⣌⠡⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⢸⡇⢹⡇⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⢿⠀⠿⣇⠹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢯⣧⠀⢷⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣜⣇⠀⠹⣤⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⠾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⣤⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠉⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⣶⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠋⠀⠐⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠖⢉⣿⣿⣿⠟⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠀⡼ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡼⠀⠀⠈⢆⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠊⠁⠀⠀⢸⣿⡿⠃⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠁⠀⠀⠀⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠞⠁⠀⠀⠀⠀⠀⣾⠟⠡⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⡏ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠄⢼⠀⠀⢀⣀⣤⠤⠤⠤⣤⣀⣀⡤⠋⠀⠀⠀⠀⠀⠀⢀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⢀⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠟⠚⠉⠁⠀⠀⠀⠀⠀⠀⣠⠋⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠍⣀⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⡠⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠶⢷⡀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⣸⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡹⣦⠀⠀⠀⢀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠔⠚⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠚⠀⠀⠀⠀⠀⠀⠀⠈⠁⠞⡹⢾⣧⣠⣠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠔⠋⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣴⠮⡍⡏⠀⣿⣽⡄⠀⠀⠀⠀⢀⠀⣠⢶⣿⣿⣧⠀⠀⢠⠞⠀⠀⢠⡏⣳⣯⠚⠉⠯⢽⣷⢤⡀⠀⠀⠀⠀⠀⢠⠴⠚⠁⠀⠃⠀⠀⠀⠀⠀⠀⠀ ⢸⡉⢆⣀⡏⡰⣦⣇⡟⣦⠹⠿⠿⠀⠀⠀⠀⠘⠞⠹⢾⣿⣿⢟⣠⣒⣿⠿⣭⣲⣼⡿⠘⠞⠠⠀⠁⠀⢳⡄⠉⠳⢦⡀⠀⠀⠈⠳⢆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠢⠇⣴⣆⣺⡵⢹⣿⣉⢿⣇⠀⠀⠀⠦⠀⠀⠀⠀⠀⠀⠀⢇⠀⣇⠈⠿⠒⢯⠀⠻⣃⠇⠀⠀⠀⠀⠀⣜⣿⡄⠀⠀⠈⠓⢦⡀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠸⣑⢫⡵⠀⠈⠈⠳⣟⠀⠀⠙⠒⠒⠢⠤⠞⠁⠀⠀⠈⠀⠙⠣⠽⠶⠋⠀⠀⠚⠋⠀⠀⠀⠀⣼⣿⣿⣷⡀⠀⠀⢀⠜⠁⠀⠀⠀⠀⣹⠆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⢪⠳⠀⠀⠀⠀⢈⠟⠂⣢⣄⡀⠀⠀⠀⠀⠀⠀⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠁⠀⢣⢠⡴⠋⠀⠀⠀⣠⠔⠋⡄⠐⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢏⡴⠋⠁⠹⠷⣆⠀⠀⠀⢰⠏⠇⠈⠙⠲⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡏⠀⠀⣠⠖⠋⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠁⢀⠀⡹⠄⠀⠀⢸⡄⠈⠒⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣀⠀⠈⠷⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣀⠀⠀⣨⡷⢻⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⣀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡏⣉⣾⣳⣬⣺⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢩⠟⣇⠀⠁⠀⠀⠀⠀⠀⠈⠑⠢⠤⠤⠔⢊⠵⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠟⠋⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠸⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⡄⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠈⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣗⡢⠤⠄⣈⣙⣲⣤⣀⡀⠀⠀⠀⠀⠀⠹⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣲⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢯⠏⣨⠎⣳⠤⠚⠉⠀⠀⠀⠉⠙⠓⠒⠒⠒⡒⠛⠲⢤⣀⣀⣀⣀⠤⠤⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠙⠉⠀⡄⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣓⡍⠉⡒⡾⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠑⠋⠙⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⢹⠀⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡿⠛⠉⢹⣿⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠉⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣴⣿⡿⠟⢻⠉⠉⠉⠁⠀⠀⠀⠀⠀⠈⠉⠉⠛⣓⡦⣤⡀⠀⢨⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠟⠁⠀⠀⡎⠀⣴⡶⢦⡀⠀⠀⠀⠀⠀⠀⠀⣾⣩⣿⡆⢻⠳⣾⣇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⡜⠀⠀⢿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠛⠿⠟⠁⠈⡇⠈⡿⣷⣮⡆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⡼⠁⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⢈⢀⡀⠀⠀⠀⢸⠋⢻⠀⢰⢸⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⡜⡇⠀⢀⡟⠁⠉⣷⠀⠀⠀⡴⠉⠀⠀⠀⠀⠀⠀⠸⠦⣼⠀⢸⣾⣿⣿⣿⣿⡖⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠞⣄⡀⠀⠈⠷⣄⣰⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢯⣠⣾⣿⣿⣿⣿⣿⢇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡿⠛⠉⠁⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣥⣾⣿⣿⣿⣿⣿⣿⣿⣛⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⡤⠖⠊⠹⠏⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀ ⠀⣀⡤⠔⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⡟⠏⠀⠀⠀⠀⠀ ⢯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⡟⠛⠛⠛⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀ ⠈⢇⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⢾⠀⠀⣾⠃⣄⠄⠀⠀⠀⠀⠀⢡⠀⠀⢀⠀⠀⠀⠀⠀⠀⡘⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⢦⠀⠀⠀⢀⡠⠖⠋⠁⠀⡇⠀⢸⢺⠀⠘⣆⠀⠀⠀⠀⠀⠈⡇⠀⢸⠀⠀⠀⠀⠀⢰⠃⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢣⡤⠚⠁⠀⠀⠀⠀⠀⡇⠀⠘⡞⠀⠀⠈⢣⡀⠀⠀⠀⠀⢱⠀⢸⠀⠀⠀⠀⢠⠃⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⣠⠖⡇⠀⠀⠀⠀⠙⢄⠀⠀⣀⡎⠀⠈⡄⠀⠀⡰⠃⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀