Darn Emojis & Text

THESES ARE SOME ROASTS TO TELL YOUR RUDE PEOPLE ʚ🍄🌿Bruh!🌿🍄ɞ😩Did I ask?😩💅🏼I don't shut up i grow up and when i see you i throw up💅🏼🚮SAYS THE ONE WHO BELONGS IN THE TRASH🚮 😝😝😝😝😝😝😝😝😝😝

🇩🅰️Ⓜ🇳😙🤜💦😵‍💫

⋆꙳•̩̩͙❅*̩̩͙‧͙ ‧͙*̩̩͙❆ ͙͛ ˚₊⋆/ᐠ - ˕ -マ⁩▄︻デ══━一٩(ˊᗜˋ*)و⋆꙳•̩̩͙❅*̩̩͙‧͙ ‧͙*̩̩͙❆ ͙͛ ˚₊⋆

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⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣰⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠸⣿⠘⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣿⠀⠸⣷⡙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⡆⠀⠙⡽⣄⠙⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢻⡆⠀⠹⣎⠂⠀⠉⣓⣦⣤⡤⠖⠲⠶⢶⡶⠶⢤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢻⡀⠀⠘⢀⣤⣾⣿⠿⠉⣠⡤⠤⢄⣚⣷⣦⣤⠀⣈⠉⠙⠓⠶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣴⣶⡄ ⠀⠀⠀⠀⠘⣷⠄⢬⢿⡿⠏⢉⡤⠶⠾⢧⣆⠀⠹⣼⠻⣯⡾⠋⠀⠀⠑⢤⠀⠉⠳⠦⠤⠶⠶⠶⠶⠶⠶⣞⠿⣿⣻⠿⢿⣿⣿⣿⠀ ⠀⠀⠀⠀⠀⠘⣶⠋⠀⠀⠀⠁⠀⣀⠀⠈⠹⣦⡀⢹⣿⡽⠃⠀⠀⠀⠀⣠⣴⡿⡓⣀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠀⢖⠾⢿⣦⣿⡿⠀ ⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⣀⣀⣈⠱⡄⠀⣸⡿⠲⠿⠀⠀⠀⠀⠀⠀⠙⠙⠓⢻⣿⣦⣀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣶⡯⠞⠋⠀⠀ ⠀⠀⠀⠀⠀⣿⠁⠀⢀⣴⣾⣿⣟⡏⣧⠳⣄⠟⣡⡄⠀⡀⠀⣠⣤⣤⣤⣤⣤⡀⠀⠉⠓⢭⣟⠒⠲⢶⣚⣭⣭⠶⠛⠉⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢿⠀⠀⣾⢻⣿⣿⣿⣿⢹⣄⣿⢡⠇⠃⢸⠁⢨⣏⢹⠁⣿⣿⣿⣿⣆⢠⠀⠈⢻⣶⣤⠞⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣾⠀⠀⡿⠻⣿⣿⣿⢷⠿⣿⠃⠈⠀⠀⣿⠀⠸⠘⣾⡄⣿⣿⣿⣿⣿⡈⣿⡉⠉⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⣇⠀⠀⡇⠀⠀⠉⠉⠏⣿⠃⠀⠀⢠⡄⣿⣶⡀⠀⠈⠉⠙⠛⠛⠛⢋⡵⠃⡷⣄⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢿⡀⠀⢳⡄⠀⠀⠀⢳⣧⡄⢠⣴⣿⡇⢹⠻⠝⢦⣀⠀⠀⠀⠀⠚⠉⣄⣀⢻⡻⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣤⡬⣿⠖⠋⣳⣄⠀⠀⠘⠿⡗⢈⣿⢿⣷⠟⠀⠀⠀⠉⠀⡀⣄⠀⠀⠀⠀⠙⠫⣟⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠤⠖⠉⠉⠀⣀⠼⢿⣍⡽⠆⢷⢤⣀⣰⡏⣼⢳⡾⠃⠀⠀⠰⠐⠊⠉⣡⡀⠀⠀⠀⠀⠀⠀⠈⢲⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⡴⠚⠁⠀⠀⠰⢻⣦⡴⠷⠦⣨⣿⢡⣭⣘⠃⠀⠀⠀⠰⠈⠉⠉⢥⣽⢷⣍⠂⠀⠀⠀⣠⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⡼⠿⢦⡀⠀⠀⣿⣸⣾⣿⣷⡈⢣⡀⠤⠤⡼⣶⠚⠻⣄⠙⣦⡤⣲⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠻⣦⡀⠘⣟⣿⣿⣿⣷⣌⣻⡆⠀⠸⡜⣆⠀⣸⢿⣁⠟⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠰⠟⠀⠀⠀⠀⠀⠀⠈⢳⣤⡟⠉⠁⢹⢋⡼⢻⠏⠀⣀⡽⡽⡏⣠⠶⠻⡄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⢠⣞⡵⠋⢀⣞⣁⣤⣷⢿⠁⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠤⠾⠿⠯⠴⠞⠋⠁⠀⠀⠘⡎⢇⠀⠀⠀⠘⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠤⠴⠖⠒⠒⠒⠒⠢⠤⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠶⠚⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⠶⠾⢿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣾⣿⠷⠛⠋⠉⠉⠓⠲⢄⡀⠀⠀⠀⠀⣠⠋⠀⠀⠀⠀⠀⠙⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⣰⠏⡁⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠘⠋⣧⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡾⠅⠀⠀⢉⣼⣤⣠⡀⣀⣀⣀⣀⠀⠀⠀⠈⢇⠀⢸⠀⠀⠀⣀⣤⣤⣤⣾⣾⣶⣾⡆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⢻⣿⣿⣿⠿⣿⠛⠛⠛⠿⢷⣦⣀⠘⠄⠈⢀⣴⢿⣟⠉⠉⠉⢙⣻⠿⠛⠳⠤⣄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠈⠉⠙⠳⢤⣏⣀⣀⣀⣀⣀⡬⠿⠃⠀⠀⠻⠷⠼⠿⠴⠖⠚⠉⠁⠀⠀⠀⠀⠈⠹⢦⡀⠀ ⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢳⡀ ⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠟⡍⠁⠀⠉⠳⠒⠚⠉⠀⠀⠈⠙⢦⡀⠀⢶⠆⠀⠀⠀⠀⠀⠀⡇ ⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠘⠀⣁⣀⣤⡤⠤⠵⠆⠰⠶⠆⠠⠤⣤⣙⣦⡀⠀⠀⠀⠀⠀⠀⠀⡇ ⡄⠀⠀⠀⠀⣠⡽⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡵⣶⣟⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡿⠃⠀⠀⠀⠀⠀⢀⡇ ⠙⢷⡀⣰⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢔⣧⣈⠓⠒⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁⠀⠀⠀⠀⠀⢠⡾⠀ ⠀⢸⠇⣯⢀⣤⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠶⠶⠶⠟⠛⠓⠒⠒⠒⠒⠒⠚⠋⠁⠀⠀⠀⠀⠀⣀⣴⠟⠀⠀ ⣠⠟⠀⠘⣯⣥⣴⣼⣧⠀⠀⣶⣶⡆⠀⠀⠀⠀⣀⣀⡀⠀⣀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄⡤⠶⠋⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⣬⣤⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠉⢻⣯ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠻ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹ ⠀⠀⠀⠀⠀⠀⢀⠀⣠⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸ ⠀⠀⠀⠀⠀⠀⢳⣿⠁⣿⣿⠛⠿⣿⣿⣿⣿⣶⣶⣤⣤⣀⣀⣀⡀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢩⣻⣾⡿⢤⠟⠉⠉⠉⠉⠙⠛⠻⠿⣿⣿⣿⣿⣿⣷⣶⣄⢿⣧⠀⠀⠀⠀⠀⣀⣀⡰⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⡿⠁⣾⠀⠀⠀⠀⢀⣠⣤⣤⡀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⠤⠀⠀⠀⢸⣷⡿⠝⠛⣩⣷⣶⣦⣤⣠⠀⠀⠀⠀⢀ ⠀⠀⠀⠀⠀⠀⠈⢻⣇⡜⢿⣧⡀⠀⢰⣿⣿⣿⣿⣿⡀⢰⣿⣿⣿⣿⣿⣿⣿⠏⠀⠈⠀⠠⣾⣿⣧⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣾ ⠀⠀⠀⠀⠀⠀⠀⠨⢿⡆⢸⡌⢻⢶⣌⣛⣿⠿⠿⠋⣠⣾⣿⣿⣿⡿⠛⣧⡇⠀⠀⠀⠀⢐⢻⣿⣿⣿⣿⡿⠛⠋⠉⠉⠙⢿⣿⣿⡟⠋ ⠀⠀⠀⠀⠀⠀⠀⠀⢈⣙⡆⠹⡌⣄⣼⠉⠀⠀⢀⣼⣿⣿⣯⡍⠀⠀⠮⠉⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⠀⢀⣤⣶⣶⣦⠘⣷⣿⠋⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠉⠈⠉⠛⠓⠚⠚⠂⠀⠁⠀⠀⣤⣠⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⢀⣿⣿⣿⣿⡿⢀⣿⠹⠀⢰ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⠟⠋⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣾⡌⠻⠿⠏⣫⣴⣿⡿⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠹⣿⣿⣿⣏⠈⣻⠉⣿⠁⠀⠀⢸⢾ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠈⢳⠒⢦⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⢰⠿⣽⣏⣽⣷⠟⠸⠓⠀⠀⠀⡞⢹ ⡇⠀⠀⡀⠀⠀⠀⠀⣀⣊⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠰⠖⠚⢿⡀⢣⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡞⢁⠂⠁⠀⠀⠀⠀⢰⠞⠀⣷⢿ ⣿⣾⡘⠆⢱⠶⠖⠋⠙⠿⣿⣿⣷⣄⠀⠀⠠⡁⡀⠀⠉⠁⠀⠀⠘⢷⣸⡀⠀⠀⠀⠀⠀⠀⢠⣿⠉⣁⠚⠛⠂⠀⠀⠠⠾⠥⠃⣰⣧⣿ ⡉⣿⣿⣦⠉⣀⠀⠀⠀⠀⠈⠙⢿⣿⣷⣦⡀⠉⢤⠈⠣⣄⠀⠀⠀⠀⢧⠹⡀⠀⠀⠀⠀⢀⢆⣿⠏⠁⢀⣀⣀⡤⢀⡞⠁⣠⣾⣿⣿⣿ ⣧⡾⣎⣿⣷⣤⡁⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣶⣤⣠⡀⠀⠀⢀⠀⠀⠸⣷⡀⠀⠀⠀⠀⠘⢿⣯⣶⣞⣛⡏⠙⠋⠉⣠⣾⣿⣿⣿⣿⣿ ⣿⣿⣿⣷⣎⡻⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⡿⢿⣶⣶⣤⣀⣰⣆⣷⠀⠀⠀⠀⠀⢿⣏⠁⠛⠁⠀⣠⣴⣿⣿⣿⣿⣿⣿⠿⣿ ⢿⣿⣿⣿⣿⣿⣿⡏⠻⢿⣦⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠈⠛⢛⠛⠿⣿⡀⠀⠀⠀⠰⡭⡉⢁⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⣸ ⠀⢿⣿⠟⠋⠙⠻⢿⣿⣄⣁⠉⢻⣿⣷⣶⣶⣤⣤⣄⣀⣀⡀⠀⣀⠀⢈⣉⣥⣇⡀⠀⣀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣼⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣰⣤⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣶⣿⣽⣿⣿⣿⣿⣿⣿⣿⣧⣿⣷⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣛⣿⣿⣏⣿⣿⣿⣽⣿⣿⣿⣿⣿⣷⣿⣦⣄⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⣶⣾⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⡿⣿⣿⡎⣻⡆⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀ ⠀⠀⠀⠀⠻⠖⣺⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⡛⠙⠛⠛⠛⠉⠀⢻⣿⣿⣿⣶⣿⣿⡄⠀⠀⠀ ⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⠉⠉⠉⠉⠉⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⠀⠀⠀ ⠀⠀⠀⠀⠈⣿⣿⣿⣿⠇⠀⠀⡼⢲⣾⣍⠒⢦⠖⣪⣿⡖⢦⡀⠀⠀⣿⣿⣿⣿⠟⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣿⣿⣹⠀⠀⠀⢳⣜⠟⢃⣴⠀⢣⢹⣿⣃⡼⠁⠀⠀⣿⡿⣿⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⣏⣾⢻⣿⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣷⣌⠁⠀⠀⠀⠀⣿⣿⣿⡿⠛⠂⠀⠀⠀ ⠀⠀⠀⣴⡏⣿⡙⡸⠟⠀⠀⠀⠀⠘⠛⠛⢿⠿⠟⠛⠋⠀⠀⠀⠀⠀⣿⡟⠁⠐⢤⡄⠀⠀⠀ ⠀⠀⢰⠛⣷⢹⠶⡄⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⡼⢿⠀⠀⠀ ⠀⠀⢸⠀⠸⣧⡀⠀⠀⠀⠀⠀⠀⠘⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠘⡇⠀⠀ ⠀⠀⡏⠠⠀⠘⢷⣄⡀⠈⣠⣤⡴⠶⠶⠶⠶⠦⠤⠤⠤⠀⠀⢀⡀⠀⠀⢀⣾⢣⡀⠀⣇⠀⠀ ⠀⠀⡇⢰⡷⣄⠀⠻⣿⣿⣍⠙⠿⠷⢶⣶⣶⣤⣴⣶⣶⡶⣶⣏⣁⣉⣷⢿⠁⣸⢷⡄⠘⣧⠀ ⠀⢰⡇⢸⠃⠙⢦⡀⠈⠙⡟⠿⣶⣄⣀⠈⠉⠛⠉⠙⢿⣿⣿⠟⡛⠉⠀⢠⡾⠃⠀⣿⠀⣿⡀ ⠀⣾⣤⣿⣀⠀⠀⠙⠒⠲⢷⣶⣤⣍⣛⣿⣶⣦⣶⡿⠟⠉⣹⣶⣬⣤⡴⠏⠀⠀⢀⣿⣾⣿⡇ ⠀⠙⣿⡟⠘⠀⠀⢠⡆⠀⠀⠀⠀⠀⠈⢉⠉⠛⠋⠉⠉⠉⠉⠁⠀⢰⡀⠀⠀⠀⠈⢹⠃⣾⠀ ⠀⢸⣿⠀⠀⠀⠀⢸⠀⠀⠀⡆⠉⠒⠒⠚⠂⠐⠢⠀⠀⢀⠀⠀⠀⢈⡇⠀⠀⠀⠀⢸⠀⣿⠀ ⠀⣾⢿⣄⠀⠀⠀⣼⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⢸⡇⠀⠀⠀⠀⣸⠀⢻⠀ ⢠⣿⡝⣿⣧⠀⠀⡏⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠈⡇⠀⠀⠀⣼⣃⠀⢿⡆ ⠈⣿⣧⣹⣿⡇⠘⠁⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⢻⠀⠀⣸⣽⢯⣰⣾⡇

⠀⠀⠀⠀⣠⠤⠖⠒⠒⠲⠤⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣰⠋⠁⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⠃⣤⢶⣶⣶⡶⣦⡄⠠⣴⣶⣿⣿⣷⣦⠄⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡏⠀⠈⠉⠉⠉⠉⠉⠦⠽⠛⠋⠉⠉⢻⠀⠀⠀⠰⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⣰⠛⣿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⡜⢁⣼⣁⡔⠋⠉⠉⠙⠦⣄⠀⠀⠀⠀⠀ ⣀⣼⡆⢀⠀⠀⡀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⢨⠟⠉⠁⠉⠙⢦⣤⠶⣦⣀⡸⢦⣀⢴⣶⠆ ⢿⠛⠳⡎⠀⢰⣇⣀⣀⢀⡠⠖⡋⣉⢈⣭⣷⡏⠀⣠⣶⣄⠀⠀⢻⡞⠋⣿⣅⣀⣡⠞⠋⠀ ⠘⣇⠀⡇⠀⡏⠀⢀⡽⠋⢀⡴⠛⠉⠳⣿⠟⠋⠉⠉⠀⠀⠳⣖⠉⠙⢦⣇⣤⣭⠀⠀⠀⠀ ⠀⢹⠀⢧⠀⠓⠒⠉⣠⠞⠋⢀⢀⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⣤⠤⠞⠋⠀⠀⠀⠀ ⠀⠸⡇⠀⠑⠒⠒⠋⠁⠀⠀⠸⡈⢹⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠘⡆⢇⠀⠘⡄⠙⡏⠉⠻⠂⠀⣿⡉⢠⣏⡇⢠⡿⡆⢸⢀⣀⡟⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢧⠈⠒⠂⠇⠀⠧⠀⠀⠄⠀⠛⠚⠘⠁⠙⠚⠀⠁⠈⠁⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⡇⠀⠲⢤⠤⢠⣦⡀⠀⣠⡀⠀⡤⠄⢠⡄⠀⡄⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣧⠀⠀⠸⡄⢸⡷⡏⢠⡧⢷⣀⣙⣦⠀⡗⢺⡇⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢹⡄⠀⠀⠁⠀⠁⠈⠈⠁⠈⠀⠉⠀⠀⠉⠈⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢻⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠓⠒⠒⠒⠒⠒⠒⠚⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⌗ 🎧°. •♡

⠀⠀⠀⠀⠐⢠⠞⠁⠀⠀⢀⡤⢋⡿⠀⠀⠀⡄⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⠎⠀⠀⢀⣴⡿⠟⢹⠁⠀⠀⢰⠁⠀⠀⠘⡆⠀⠀⠀⠀⠀⢀⣀⡠⠄⣼⣧⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⡞⠀⠀⠀⡨⠋⠀⠀⡎⠀⠀⣇⡇⠀⠀⠀⠀⣸⣄⠀⠐⠊⠉⠁⠀⠀⣸⣩⠋⡜⠉⠉⠒⠦⣤⣄⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀ ⠀⠀⠀⠈⠙⠢⢠⠞⠁⠀⠀⠀⡇⠀⠀⣿⣁⡤⠔⠚⠉⠀⢹⡀⠀⠀⠀⠀⠀⢀⣿⢃⣎⠀⠀⠀⠀⠀⠀⢋⠉⠓⠢⢄⡀⠿⣆⠀⠀⠀ ⠀⠀⠀⠀⠀⡰⠃⠀⠀⠀⠀⠀⣇⡤⠚⡏⠁⠀⠀⠀⠀⠀⢸⠙⣄⠀⠀⠀⠀⣸⢡⠋⠸⡀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠉⢳⠘⠖⠒⠒ ⠀⠀⠀⠀⡼⠋⠉⠉⢉⠿⡉⠺⡇⠀⢰⠁⠀⠀⠀⠀⠀⠀⠈⠀⠈⠢⡀⢀⠀⣿⠃⠀⠀⢇⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠸⠀⠀⠀⠀ ⠀⠀⠀⡼⠁⠀⠀⡰⠋⠀⠇⠀⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⢣⣏⣈⣁⣀⠘⡄⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠃⠀⠀⠀ ⠀⠀⣸⠃⠀⢀⡞⠁⠀⠀⠸⡀⢡⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡹⡀⠀⠈⢉⢳⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⠇⠀⢠⡎⠀⠀⢀⣀⠀⠃⠸⡀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠙⢾⣆⠀⠘⡄⢧⠀⠀⠀⠀⠀⣜⠻⡄⠀⠀⠀⠀⠀⠀ ⠀⢸⠀⠀⠛⣳⣾⠟⠿⣷⣦⡐⢦⣇⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡇⠐⠀⠈⠓⠀⠘⠈⢆⠀⠀⠀⠀⢸⡀⠙⢆⠀⠀⠀⠀⠀ ⠀⣼⣄⣠⣾⡿⠁⠀⣠⣶⣿⣿⣦⡹⡄⢸⡆⠀⠀⠀⠀⠀⠆⠀⡇⠀⠀⠀⡇⠀⢀⣀⣀⠀⠀⠀⠈⢦⠀⠀⠀⠈⡇⠀⢎⠑⢄⠀⠀⠀ ⠀⣿⡏⢿⣿⠀⠀⢠⣿⣿⣿⣿⡿⣷⠱⡈⣿⡀⠀⠀⠀⠀⢰⠀⣧⠀⠀⠀⣇⣈⣥⣤⣤⣤⣤⣄⡀⠀⢳⡀⠀⠀⢱⠀⢸⠀⠀⠀⠀⠀ ⠀⡏⢧⠘⣿⠀⠀⢸⣿⣿⣿⣿⣦⣽⠃⠱⣽⣵⡀⠀⠀⠀⢸⡆⢿⢆⠀⠰⡟⠉⣡⣶⣿⣿⣿⣿⣿⣦⣸⠙⣄⠀⠈⡆⠘⡇⠀⠀⠀⠀ ⠀⢧⠸⡆⢻⠀⠀⢸⡿⠿⠿⣿⣿⣿⠀⠀⠀⠀⠘⢦⡀⠀⠸⡻⣿⠀⠑⠂⣽⣿⣿⣿⣿⣿⣿⣻⣯⢻⣿⡇⠈⠳⣄⢱⠀⡇⠀⠀⠀⠀ ⢣⡈⣆⢻⡌⢧⠀⠈⢷⣤⣀⣈⣿⠇⠀⠀⠀⠀⠀⠀⠈⠉⠚⠁⠀⠀⠀⠀⣿⡟⣿⣿⣿⣿⣿⣿⣿⠀⢻⣿⢄⡀⠈⠻⠆⡇⠀⠀⠀⠀ ⠀⠙⢮⡿⠓⠊⠑⠒⠚⠒⠚⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⡿⢿⣿⣿⣿⣿⡿⠀⠈⣿⡞⠉⠀⢸⠀⠀⠀⠀⠀⠀ ⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⠅⠀⠈⠙⢻⡿⠁⠀⢠⡿⣇⠀⠀⢸⠀⠀⠀⠀⠀⠀ ⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠿⣚⣉⣀⠀⠴⠋⡇⢸⠀⠀⣸⠀⠀⠀⠀⠀⠀ ⠀⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢃⠟⡆⠀⡇⠀⠀⠀⠀⠀⠀ ⠀⢸⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⢹⡼⠀⠀⠀⠀⠀⠀⠈ ⠀⠈⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣒⣉⣀⡤⠖⠀⡼⠁⠀⠀⠀⠀⣠⠀⠀ ⠀⠀⠀⣹⢦⡀⠀⠈⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⣴⣃⣀⣀ ⠀⠀⢠⣿⠈⠱⡄⠀⠀⠙⣷⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⢀⠞⠋⠁⠀⠄ ⠀⠀⠀⢸⠀⠀⠹⡄⠀⠀⠘⡄⠉⠳⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠠⠀⢠⠟⠁⠀⠀⠀⠀ ⠀⠀⠀⠸⡀⠀⠀⢻⡀⠀⠀⠘⡆⠀⢀⢀⡽⠛⠓⠲⠶⡶⠤⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁⠀⢀⠀⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀

（╯ ͡° ل͜ ͡°）╯︵ ( ͜。 ͡ʖ ͜。)

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣠⠤⠀⢀⡞⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡰⣦⣦⢳⣤⣾⡀⡀⠀⠀⠉⠉⠁⠀⠀⠀⣀⡴ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡰⡀⠀⠀⢀⣤⠞⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠛⠛⠶⣦⣉⠛⢿⣿⣿⣿⣿⣿⣷⣶⠴⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣰⠟⠁⠀⠀⠀⠀⠈⠛⠀⠀⠉⢉⣛⣛⡿⢿⣿⣇⣤⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣰⠃⠀⠀⠟⠲⡦⡀⠠⡀⠆⠀⠀⠈⠉⠉⠙⡳⣯⣻⣷⡆⠀⠀⠀ ⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠈⠙⠋⠀⠀⠀⠰⠃⢀⡀⠀⠀⢀⠈⣿⣻⣿⠀⠀⠀ ⠀⠀⠀⠀⣸⠀⠀⠀⠐⠀⠀⠀⠀⠀⢠⠎⠀⣂⢳⣤⡁⠀⠈⠂⠘⣇⣿⠀⠀⠀ ⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠑⠒⠿⠄⠠⠆⢀⢇⣿⠀⠀⠀ ⠀⡀⠀⣠⡄⠀⠀⠠⣄⠀⠉⢧⡠⢅⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⣼⡏⠀⠀⠀ ⠈⠚⡯⡛⢧⠆⠰⡀⠈⠯⡒⠤⣀⠉⠁⠀⠀⠀⠀⠀⠀⠀⣠⢊⣼⠿⠂⠀⠀⠀ ⠄⠀⠀⣴⣾⣇⠀⠑⠀⠀⠈⠀⠈⠛⠃⠀⠀⠀⠀⠀⢠⢚⣵⠟⠁⠀⠀⠀⠀⠈ ⠀⠀⡎⢸⣿⣌⣂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢎⡵⠟⠁⠀⠀⠂⠀⠀⠀⠀ ⠀⠀⠘⢄⠈⠙⡷⣯⣷⣤⣄⣀⣀⣀⠀⠀⠀⡠⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠁⠐⠒⠶⠌⠛⠛⠛⠉⠉⠁⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⡾⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⡟⠁⠀⠙⣧⡀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣴⠏⠀⠀⠀⠀⠘⢷⣀⣀⠸⣿⢷⣴⣦⡀⠀⠀⠀⠀⣀⣴⡄ ⠀⠀⠀⢀⣼⣃⣀⣀⣀⠀⠀⢶⣾⣿⣿⣿⡛⠀⠙⠙⣧⠀⢀⣤⠾⠋⢸⡇ ⠀⢀⣴⠛⠉⠁⠀⠉⠙⠛⠶⣦⣙⢷⣄⠉⠀⠀⠀⠀⠘⠟⠋⠁⠀⠀⠀⣿ ⢀⣾⠁⢀⣤⣤⡀⠀⠀⠀⠀⠀⠻⣯⣯⡶⠶⠆⠀⠀⠀⢀⠀⠀⠀⠀⠀⣿ ⢸⡇⠀⠸⣧⣈⡿⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⣠⡶⠛⠛⠉⠙⠛⠻⢦⣀⣿ ⠸⣇⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⢸⡇⣠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿ ⠀⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⢰⡏⠀⠀⠀⠀⠀⠀⢠⡶⠻⣦⠀⣿ ⠀⠀⠙⢷⣤⣀⣀⣀⣀⣠⣴⣾⠟⠀⣿⠀⠀⠀⠀⠀⠀⠀⠘⢷⣤⡿⠀⣿ ⠀⠀⠀⠀⢻⡍⠉⣉⣭⣷⠟⠁⠀⠀⠘⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠃ ⠀⠀⠀⠀⠈⣿⠛⠉⠁⣽⠆⠀⠀⠀⠀⠈⠛⠷⣤⣄⣀⣀⣀⣠⣴⠟⠁⠀ ⠀⠀⠀⠀⠀⠸⣧⡴⠟⠉⠀⣀⣤⡴⠶⠂⠀⠀⠀⣀⣽⠿⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⢷⣤⡶⠛⢉⣁⣠⣤⣴⠶⠞⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

୧ළoළ୨

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⣀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣀⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠶ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣶⣦⣤⣄⣀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣀⣠⣤⣤⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⢰⣿⣿⣿⣿⣿⠿⢛⣼⣍⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣀⣀⠀⠀⠀⠀⠀⠀ ⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⡿⠻⡆⢸⣿⣿⣿⡿⢁⣴⣿⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠄⠀⠀ ⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⡿⠷⠀⠹⢾⣿⣿⡋⠐⠟⣣⠧⢄⡈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⡼⢻⠃⠀⠀⠀⢸⣿⡿⠁⠀⠈⠁⠀⠀⢈⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⡿⠙⢿⣿⡟⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡿⢀⣿⣿⢿⣿⣿⣿⣿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⣶⣶⣿⣿⣿⣇⠙⣦⢹⡟⠘⣿⠀⠀⠀⠀⠀⣶⠀⠀⢰⡶⠀⠀⠀⠀⢰⠇⠘⣿⡖⢸⣿⣿⣿⣶⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠙⠻⣿⣿⣿⣿⡀⢸⣿⡇⠀⠹⣧⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⢀⡴⠦⠞⠀⣸⡏⠀⣿⣿⣿⣿⠿⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣷⣿⣿⣿⣷⡜⢾⣿⠀⠀⠈⣯⣭⡉⠉⠀⠀⠰⣦⡀⣠⣌⡉⠉⠁⢰⣧⠇⣸⡛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣙⡄⠀⠀⡿⣆⣙⠢⠤⠤⠴⠯⢵⣿⣿⣿⠒⡆⣞⣡⡴⣫⣽⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⢳⢿⡟⠛⠷⢶⣶⣶⣿⢠⡏⣿⢷⡿⣿⡿⠾⠛⠋⠉⠀⠉⠳⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⢿⣿⣿⣆⠘⣟⡷⠤⠤⣤⠤⣾⡟⢸⠇⡇⢸⠀⣿⠃⠀⣴⠇⠀⠀⠀⠀⠀⠹⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠸⣿⡟⢿⡛⠦⣍⠓⠒⠂⢐⡿⢁⡏⢰⠃⢸⠀⡇⢀⡾⠃⣀⣤⣤⣴⣶⣶⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⢻⡇⢸⣷⣄⠈⢙⠦⠤⡞⡇⡼⠀⣏⠀⢸⠀⣧⢜⢁⣼⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⡇⠀⣿⣿⣦⣄⠀⠀⣿⠛⠺⢦⡿⠀⠸⡄⣿⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣿⣿⣿⣿⣿⠟⠛⠉⠀⠀⠀⢹⠻⣿⣿⣿⣿⣿⡇⣾⠃⡀⢹⣿⣿⣿⣿⣶⡿⠀⠀⣸⠁⠀⠀⡇⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣼⣿⣿⣿⣯⡙⢦⣀⠀⠀⠀⠀⢸⡄⠀⠙⢿⣿⣿⡿⠃⢰⡇⠈⣿⣿⣿⣿⣿⡇⠀⠀⡇⠀⠀⠀⡇⠘⣿⣿⣿⡿⠿⠛⠋⢫⢿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⣿⣿⣿⣿⣿⣿⡆⠙⢷⡄⠀⡴⠘⡇⢸⠀⠀⠘⡟⠁⠀⣼⠃⠀⢹⣿⣿⣿⣿⣇⣀⠀⢡⠀⠀⠀⣇⠆⢹⡍⠀⠀⠀⠀⠀⠘⣾⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⢀⡞⠁⠀⡇⠘⡆⠀⠀⢹⣦⣼⣿⡀⢀⣨⣿⣿⣿⣿⣿⣿⣷⣄⠀⢀⡞⠛⢀⣾⣇⠀⠀⠀⠀⠀⠀⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠘⣿⣿⣿⣿⣿⣿⡇⠀⣀⢺⡇⠀⠀⢹⠀⣇⠀⠀⠸⡿⠛⠋⠉⠉⠉⠙⢿⣿⣿⣿⣿⣿⣿⣷⣯⣤⣶⣿⣿⣿⣿⡦⣤⣀⠀⠀⡞⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠘⢿⣿⣿⣿⣿⣷⠀⠙⠳⣧⠀⠀⠘⡆⢸⠀⠀⠀⡇⠀⣠⠞⠋⠉⠉⠉⠈⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠙⢾⡁⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣿⣿⣿⣿⣿⡄⠀⢠⡈⠂⠀⠀⢻⡘⡆⠀⢠⣧⠞⠁⠀⠀⠀⢀⣤⠞⠉⢹⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⠟⠉⢷⣄⠀⠀⠓⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⠀⠈⡇⠀⠀⠀⠀⢳⣷⡀⡞⠁⠀⠀⠀⣀⠴⠋⠀⠀⢀⣼⠟⠉⠙⣿⠛⠛⠿⠿⠛⠁⠀⠀⠀⠈⠳⡄⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣧⠀⢹⡀⠀⠀⠀⠀⠙⠿⠃⠀⠀⠐⠋⠁⠀⠀⢀⣴⠟⠁⣠⣞⠀⠈⢳⡀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠙⣿⣿⣿⣿⣿⣷⣄⣣⡄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡴⢟⣡⣴⣾⣿⣿⣷⣤⣾⠛⢦⠀⠈⢧⡀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣿⣿⣿⣿⣿⣷⡄⢶⡄ ⠀⠀⠀⠀⠀⢀⣴⣿⠿⠟⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⡇ ⠀⠀⠀⠀⢀⡾⠉⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⡇ ⠀⠀⠀⠀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣇ ⠀⠀⠀⢸⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢈⡿⠁ ⠀⠀⠀⢸⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⢠⠇⠀ ⠀⠰⠤⠼⡦⠤⠤⠤⠤⠤⠤⠤⠶⠶⠆⠀⠀⡴⠋⠀⠀ ⠀⠀⠀⠀⠈⠲⢄⡀⠀⠀⠀⠀⠀⢀⡠⠤⠊⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⠞⠒⣻⠓⠒⠒⣺⠻⠓⠒⢦⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣼⡀⢠⠇⠀⠀⢠⠇⠀⠀⠀⣸⠀⠀⠀⠀⠀ ⠀⠀⠀⠘⠒⠚⡼⠀⠀⠀⡜⠀⠀⠀⡴⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⢰⠒⠒⠓⠒⠦⣴⣡⠤⣄⠀⠉⠛⠁⠀⠀⠀⠀ ⠀⠀⣀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀ ⠰⢯⣍⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠤⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⡚⠁⠀⠀⠀⠀⠀

(╯°□°）╯︵ ( ͜。͡ʖ͜。)

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠶⣷ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢽ ⠀⠀⠀⢀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘ ⠀⠀⠀⠨⢯⣼⣫⠽⠿⠿⡷⣶⣶⣦⣦⣠⡠⣤⠀⠤⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠐⣿⢋⣏⠀⠀⣠⣴⣄⠈⣿⣿⣿⣿⣟⠆⡀⢰⣿⠗⣫⣶⣶⣤⣀⠀⢀ ⠀⠀⠀⠀⢸⣎⢮⠳⣜⣿⠿⠟⣰⣿⡿⡟⣟⠉⠀⠀⣼⣿⣿⡿⠿⠛⠛⣿⣿⡟ ⠀⠀⠀⠀⠀⢳⠂⠛⠘⠤⠤⠮⠛⠓⠀⡊⡀⠀⠀⠀⢸⡿⣿⡆⣶⣿⣷⢸⢻⢠ ⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⡺⠋⠀⠀⠀⠀⠘⡿⣿⣯⡛⣫⢵⢿⠀⣼ ⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠘⡕⠄⠀⠀⠀⠀⠸⡇⣽⡟⡷⠞⠮⢐⠠⢻ ⣦⠴⣢⣤⠔⠶⣦⣄⠀⠀⡀⠁⠤⠉⠺⣎⡀⠀⠀⠀⢀⡟⢏⠦⠄⠀⣰⡫⢠⣻ ⣽⣿⣌⡤⠀⠀⠈⠻⢿⣦⣉⠎⠒⣄⠀⠘⣕⠀⠀⠀⣤⣗⣁⡤⣄⠧⢋⣴⣿⣿ ⣿⣷⣭⣻⣦⣀⠀⠀⠀⠈⠙⠛⠶⠶⢥⣤⣯⡆⠀⠀⢸⣿⠙⢉⣠⣶⣿⣿⡿⢿ ⠹⣿⠿⠿⣧⣏⡗⢲⣦⣤⣀⣀⣀⠀⢀⢀⣝⣲⡀⣀⣩⣦⣾⣿⣿⣿⣿⣿⣷⣾

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⣿⠿⠛⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉ ⣤⣶⣶⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣶⣶⣿⣿⣿⠟⠋⠁⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠿⠻⣿⡿⠋⠁⠀⠀⠀ ⣿⣿⣿⣿⣿⡄⠀⠀⠀⣀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⢀⡤⠄⠀⠀⠈⠙⠲⣄⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⢚⡋⠀⠀⠀⠘⠛⢶⡄⠀⠀⠀⠀ ⠛⠿⠿⢿⣿⣷⣀⣄⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠣⡇⠀⢠⠏⠀⠀⠀⠀⣀⡠⠖⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢴⣿⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀ ⠀⠀⠀⠀⠈⠉⠭⣭⣽⢿⣿⠟⠛⠛⢻⡟⠉⠁⠀⠀⢧⠀⡏⠀⠀⢀⣴⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⡀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⡄⢹⡇⠀⣾⠏⠀⠀⡆⠀⠀⠘⣧⠃⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀⢸⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢹⣿⣷⢸⡇⢰⡿⠀⡄⠀⢿⡄⠀⢀⣽⠶⠋⣀⡀⠀⠀⠀⠀⣀⣰⠶⠗⠋⠉⢓⡾⠟⠉⢉⡶⠶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⠀⠀⠀⠀⠘⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⠛⠁⠘⠇⠀⠃⠀⠸⣷⣸⠋⠀⠀⠀⠀⠉⠀⢀⡶⠚⠉⠀⠀⠀⠀⣰⠟⠀⠀⣰⠋⠀⠀⠀⣠⣴⢶⣗⡤⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⢷⡄⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⣠⡾⠚⣿⣦⣤⡀⠀⠀⠀⡼⠃⠀⢀⡴⠃⠀⣤⢠⡾⠋⠀⠀⠉⠁⠶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣄⠀⠀⠀⢀⢰⣿⠁⠀⠀⣴⠟⠋⠀⣼⣿⢻⣿⣿⡄⠀⠀⠁⠀⢠⣞⣅⣠⠞⠉⣩⣴⣶⣶⣦⣤⡀⠀⠙⢺⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⢲⣿⣦⠀⢠⣼⠏⠀⢀⣤⡾⠁⠀⠀⣿⣿⣷⣾⣿⣿⠁⢀⣀⣄⡠⠾⠿⠋⢀⣴⣿⣿⣿⢛⣽⣿⣿⣿⣷⣄⣉⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⢷⡄⠀⠀⠀⣞⣷⡀⢹⡷⠠⢀⠞⠀⠀⠀⠀⠙⠿⠿⠿⠟⠁⡠⠀⠀⣀⠀⠀⠀⠀⠘⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠻⠷⠌⣿⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠘⣿⣿⡶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡦⣤⣿⣟⣷⠆⠀⠀⠀⠀⠈⠛⠛⠿⠿⠟⠛⠛⠁⠀⠀⠀⠀⠈⣳⣽⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢻⣾⣿⡿⠟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⡇⠛⣦⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣹⣿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡿⠉⠀⠀⠀⠀⠀⣠⡦⣤⡀⠀⠀⠀⠀⡀⠀⠠⣤⡀⠀⣴⠀⠀⢸⣷⠀⢸⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⣞⠉⣩⠵⠒⠻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣷⣀⠀⠀⡀⣀⣛⠓⠲⣄⡙⠳⢦⣤⣀⣘⠶⣄⡀⠙⠚⠃⢀⣀⠈⢿⡀⢚⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⠄⠋⠁⠀⠁⢀⣀⡤⢿⣟⣯⡀⠀⠀⠀⠀⠀⠀⣠⡾⠟⣻⠛⠙⢠⣄⢠⠍⣻⠻⣶⢤⣉⠛⢾⣿⣍⢿⣛⠻⣮⣿⣷⡶⣤⣀⠀⠘⣿⣯⠀⣀⣤⡁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠀⢛⣫⣴⣶⡿⢟⣯⡆⠀⠀⠀⠀⠀⠈⣻⠁⠀⠃⠀⠀⣼⣿⣧⡀⡉⢷⣼⣧⣙⢿⣳⣿⣯⠛⢯⣝⠲⢬⣝⡻⢷⣿⣛⠓⢻⣿⣿⣿⣿⣧⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⢋⡽⢟⣭⣶⠟⠍⠀⠀⠀⠀⠀⠀⢰⡿⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣷⣹⣿⣿⡻⣿⣝⣦⡀⢉⣳⡄⠙⢿⣶⣽⣿⣷⣬⡛⢿⣿⣿⣗⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣯⢆⣠⣾⠟⣿⠇⠀⠀⠶⠦⣤⣀⠀⠀⣾⢳⠇⠀⠀⣸⣿⣿⣿⣿⣿⣿⠙⠙⠉⣿⢸⣿⣨⣻⣿⣻⣾⡟⠛⠷⢦⡻⣿⣿⠙⣹⣿⣿⣿⣿⠏⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁⣠⡾⠁⠀⠀⠀⠀⠀⠀⠈⠉⠑⣿⣿⣄⡞⢀⣿⢻⠟⠻⠉⠙⠈⠀⠀⢰⢿⡆⠻⣇⢳⣻⡟⠙⢷⡀⠀⠀⡿⣎⠙⢷⣿⣿⣿⣿⣿⣷⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⣿⣧⣿⣃⡀⠀⠀⠀⠀⠀⠀⠀⠸⣾⠇⠀⢸⣼⣷⣽⣄⢨⢿⣄⠀⢸⣮⣿⣾⣿⣿⣿⣿⣿⡜⠁⠠ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠛⠉⠉⠉⠁⠉⠛⠒⠾⣿⣶⣶⣿⣶⣤⣼⣯⣿⣿⣻⣿⣷⣿⣷⣾⡿⣻⣿⣿⣿⣿⣿⣿⠧⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢁⣽⣿⣿⣿⣿⣿⢿⣿⣷⣿⣿⡿⢿⡿⠟⢿⣿⣿⣿⣿⣿⣿⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠾⣿⣿⣋⠉⠏⢫⣭⠉⢻⣿⣟⣟⢿⠸⡇⠛⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢶⣤⡄⢈⣁⣉⡉⠀⠃⠸⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⢀⢰⣄⠀⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⡍⠛⠻⢦⣄⠀⢸⣿⣿⣷⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠈⠳⣿⣧⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⡆⠄⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠛⣿⣿⣿⣿⣷⡆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⢾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⢸⡀⠀⠀⠀⠀⠀⢸⣿⡀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⢸⣷⣾⡇⠀⠀⣸⣦⡀⠀⢿⣧⠀⠀⠀⠘⣿⣿⣿⣿⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⣸⣿⢸⠇⠀⠀⠘⣷⣷⡄⠀⢽⡏⠀⠀⠀⢿⣿⣿⣿⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⡸⣰⣿⠟⠀⠀⠀⠀⠰⣿⠿⣧⡀⣸⡇⠀⠀⠀⠘⠿⣿⠟⠁⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣤⣶⠿⠟⠛⠛⠋⠉⠉⠉⠁⠀⠀⠈⠉⠙⠛⢿⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣤⡾⠿⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣆⠀⠀⠀⠀⠀⠀ ⠀⠀⣼⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣦⠀⠀⠀⠀⠀ ⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣦⠀⠀⠀⠀ ⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡆⠀⠀⠀ ⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣴⣄⡀⠀⠀⠈⣿⡄⠀⠀ ⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠿⠖⠀⠀⠀⢹⣷⠀⠀ ⠀⣿⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀ ⠀⣿⠀⠀⠀⠀⠀⠀⠘⠻⠿⠟⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀ ⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣤⣄⡀⢿⡆ ⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⣶⣶⣿⠿⠿⠛⠉⠉⠉⠉⠀⢻⣷ ⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣶⣶⣶⡿⠿⠿⠟⠛⢋⡉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿ ⢸⣿⠀⠀⠀⠀⠀⣀⣤⣴⣶⣶⣷⡿⠿⠛⠛⠛⠉⠉⠉⠁⠀⣀⣀⣠⣤⣤⣴⣶⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿ ⠎⣿⠀⠀⠀⠀⠀⠙⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠛⠛⠉⠉⠁⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿ ⠀⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿ ⠀⠈⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟ ⠀⠀⠘⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃ ⠀⠀⠀⠸⣷⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀ ⠀⠀⠀⠀⢻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠇⠀ ⠀⠀⠀⠀⠀⠛⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠻⢷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⠟⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢷⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠿⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢷⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⡾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢹⣟⠛⠿⠶⣶⣶⣶⣶⣦⣤⣤⣶⣶⡾⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠉⠢⢍⠋⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡞⠁⠈⢿⣲⡀⠀⠀⠀⠀⡀⠀⠀⠀⠉⠂⠝⠃⠀⠀⣀⣀⣀⡀⠀⠀ ⠀⠀⢠⠏⠀⠀⠀⠈⢧⠹⣄⠀⠀⠀⠘⢄⢀⠞⠀⠀⠀⣠⠖⢋⡽⠋⠁⠹⡆⠀ ⠀⢀⡏⠀⠀⠀⠀⠀⢸⠀⠘⠳⠖⠒⠚⠉⠉⠉⠙⠶⠮⣄⣠⠏⠀⠀⠀⠀⣿⠀ ⠀⢸⠃⠀⢠⡀⠀⢠⡟⠀⠀⠀⠀⠀⣠⣤⡄⠀⠀⠀⠀⣬⣿⠦⡀⠀⠀⠀⡇⠀ ⠀⢸⠀⠀⠈⠳⢶⠏⠀⠀⠀⠀⠀⣼⠷⢾⠃⠀⠀⠀⣲⠟⣾⣣⠹⣆⠀⣸⠁⠀ ⠀⠸⡆⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡿⠀⠀⡄⠀⠀⠀⠁⡀⡘⠀⠀⢹⣐⠃⠀⠀ ⠀⠀⢳⡀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⣴⣇⣿⡀⠀⢠⣴⣱⠃⠀⠀⢸⡇⠀⠀⠀ ⠀⠀⠀⢳⡄⠀⣾⠀⠀⠀⠀⠀⠀⢸⣧⢿⣸⠃⠀⣏⣾⣹⣁⠀⠀⣸⠃⠀⠀⠀ ⠀⠀⠀⠀⠙⠲⣇⠀⠀⠀⠀⠀⠀⡀⡿⠉⣩⣽⣶⡛⠸⣻⠟⠀⠀⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⠿⣆⣀⢀⣀⣈⣴⠃⠈⠻⠿⠿⠁⠀⣇⠀⢀⣼⠏⠀⠀⠀⠀ ⠀⠀⠀⣀⣠⠤⠴⠒⠊⠉⠻⢅⡠⡙⢿⡶⢶⣷⢶⡶⢫⡾⠷⢏⡁⠀⠀⠀⠀⠀ ⡴⠚⣩⡏⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠲⢝⣒⣒⣫⡴⢻⠀⠀⠀⠈⠙⠦⣄⡀⠀ ⠀⠀⣿⣠⡤⠤⠤⠴⣴⠂⠀⠀⠀⠀⠔⠀⣀⠀⠀⢀⡿⠄⣀⡀⠀⠀⠀⠈⠙⢦ ⣰⠀⠃⠀⠀⣀⡴⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢸⡇⠀⠀⠉⠛⣦⣤⠄⠀⠀

⣤⡄⠀⣬⡍⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐⢠⡄⠀⠀⢈⡄⠀⢀⠀⠀⠀⠀⣿⣿⣿⣷⣶⡀⠀⠉⠛⣇⡐⢻⣿⣌⠁⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⠀⠸⢿⡿⠀⣀⣲⣷⣤⣀⠀⠀⠀⠀⣀⠀⢀⠀⢠⣵⣤⣿⠄⠀⠀⢰⣿⣿⣿⣿⣿⣿⠀⠰⣦⣻⣷⣾⡿⠟⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢻⣿⣧⣤⣴⡾⠛⠁⢀⡜⣿⠀⡀⠀⠀⠀⠐⠋⠀⢲⣩⡶⠻⣧⣄⠀⠀⠻⠟⠙⢻⣿⡋⠀⠻⢿⡟⠛⠋⠐⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢛⣿⣽⠏⣀⠀⠀⡸⢀⣿⡇⠛⠠⠄⠀⠀⣄⠛⠿⠋⡁⢸⣿⢟⣀⣤⣾⠶⠾⠟⠛⠛⠛⠷⠾⠦⣤⣄⡀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣿⣿⣇⠀⠨⠤⠚⡁⠎⠈⣿⣞⣄⡀⠀⠀⠀⠲⠿⠘⣛⣤⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⠙⠳⢾⣀⣠⣶⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣻⣿⣿⣯⣍⡀⠀⠀⠘⣿⣍⣥⣄⣀⣰⣧⣤⠞⠋⣠⠄⠀⠀⢀⣀⠀⣀⡀⡀⣆⣀⣤⣦⣀⠀⠀⠁⠀⠀⠢⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣽⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠘⢿⣇⣈⣤⢟⣿⣷⣾⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠘⡜⠳⣄⠀⠀⠀⠀⠀⠙⠷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣟⣻⣿⣿⣷⡀⠀⠈⠛⢿⣁⠀⠉⠀⠉⠉⠛⢛⢋⠉⣁⣤⣴⢶⣿⣿⡿⠃⠀⢰⣷⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⠁⠀⠀⠉⠀⠶⣧⣀⣀⣀⣀⣠⣄⣉⠙⠉⠁⠀⠀⠋⠀⠀⠀⣼⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣋⣿⣿⣿⣶⠟⠁⠀⠀⠀⠀⠀⠀⠺⢧⣻⠿⣿⣯⡻⣷⠆⠀⠀⠀⠀⠀⢀⡼⠃⠙⣷⣝⢿⣿⣻⣦⣀⣀⠀⠀⢀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣧⣹⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠚⠛⠋⠁⠀⠀⠀⠀⣀⢸⣧⣄⠀⣹⠿⣷⣈⠿⣦⡈⠻⣷⡀⠸⣾⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⡏⢻⡿⢁⠀⠀⠀⠀⠀⠀⠄⠀⠄⠀⠀⢀⡶⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣧⡶⠶⣦⣌⠓⢮⣻⣶⣿⣿⣆⠹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣧⡞⠑⠀⠀⠀⠀⠠⠄⠀⠀⣀⡤⠴⠀⣼⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡌⠓⡾⢿⣿⣷⣦⡈⠉⠈⠙⣿⣷⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⣦⠶⠚⠉⠀⠀⠀⠀⠉⠉⠻⢿⣿⣶⣦⣄⣀⣀⠀⠀⠀⣐⣒⠀⠙⢦⡈⠉⠑⠛⠋⠙⠳⢦⣌⣼⡬⢿⣆⢀⣀⣠⠴⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣾⣿⡟⠀⠀⠀⠀⠀⠐⠛⠁⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⡙⠛⣿⣿⣿⣏⣁⣴⣄⠀⣇⠀⠀⠀⠀⠀⠀⠀⠈⠙⢧⡐⣿⡇⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⡿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⣷⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠳⠾⢿⣿⣿⣿⣿⡇⢘⣿⡀⠀⠀⠀⠀⠀⠀⠀⠈⢸⡟⣿⣧⡶⠟⠉⠙⠉⠉⠉⠉⠀⠀⠀⠀⠀ ⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣽⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠻⠏⠓⢦⣀⠄⠀⠀⠀⠀⠀⠀⠀⣾⠏⡈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣯⠻⣾⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡞⠁⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣉⠛⢿⣿⣿⣿⣿⣶⣶⣲⣶⣤⣤⣠⣤⣤⣼⡄⠀⣆⠀⠀⠀⠀⠀⠀⣖⠀⣽⠁⠀⠀⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡿⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢾⣏⡘⠙⣙⣿⣋⣛⣻⣯⣍⣛⣿⣿⣿⡷⠀⠸⡆⠀⠀⠀⠀⠀⣿⠠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡟⣻⣿⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠻⠍⠉⠉⠉⠉⠉⠙⠉⠉⠀⠀⠀⡇⠀⠀⠀⠀⡄⠳⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣏⣻⣧⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⢿⠀⣼⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⢻⣿⠘⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣰⣿⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀⡀⠀⠀⠀ ⠀⣽⢿⡄⢹⡿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⠂⠀⠀⠀⠈⠙ ⠰⣛⠛⡇⠈⠃⠙⠷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠙⢷⣌⢿⣿⣿⣿⣮⣝⣶⣦⠀⣀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⠠⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡓⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡠⠖⢁⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡇⠀⠀⠀⠀⠀⠀⠀ ⢀⣬⢶⢻⣿⣿⡿⠛⠛⠛⠛⠿⣿⣶⣶⣿⣿⣶⡀⠀⠀⡆⠃⠀⠀⠀⠀⠀⠀⠀ ⣸⢿⠈⠈⠿⣿⡁⠀⠀⠀⠀⠀⣼⠻⢸⢻⣿⣿⣷⠀⠀⡇⢠⠀⠀⠀⠀⠀⠀⠀ ⣿⠇⠀⣿⣷⣦⣝⢧⣀⠴⡒⠬⠅⡄⠀⢺⣿⣿⣿⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣶⣬⡻⠿⣞⠤⢢⡻⣻⣩⠾⣁⢤⣹⣿⣿⣿⡄⠀⡇⠸⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⡍⡹⣷⡶⣶⠼⠒⠊⣹⣿⣿⣿⣿⡿⠛⠗⠻⠅⠘⣽⢄⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⠽⠮⠯⠵⠧⣐⣿⣿⡿⣹⣿⠁⠀⠀⠈⠂⠀⠀⢸⠄⣪⣶⠋⠁ ⢸⣿⣿⣿⣿⣿⣷⠦⠖⠀⣾⣿⣿⢏⣴⣿⠈⠀⠀⠀⠀⠀⠀⠰⢹⣸⠟⠁⠀⠀ ⢠⣿⣿⣿⣿⣿⣾⣶⣤⣾⡿⢫⡳⢋⣾⣿⡄⠀⠀⠀⠀⠠⠄⡠⠞⠁⠀⠀⠀⠀ ⠸⣿⣿⣿⡇⢙⣿⣿⠿⠯⠶⠭⠄⣸⣿⣿⣇⠀⠀⠀⠀⢀⡎⢠⠀⠀⠀⠀⠀⠀ ⢐⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⢿⠀⠀⠀⢀⡰⠛⠄⠆⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄⣷⣼⣷⣤⣶⣶⣴⣄⣄⡠⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣤⣺⣷⣿⣿⠛⣿⣿⡿⠋⠿⠋⣿⡿⣿⣶⣷⣦⣀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣐⣽⣾⣿⣿⣥⣵⣾⣿⣿⣷⣤⣄⣀⣀⣠⣬⣿⡿⠿⢿⣿⣖⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣨⣽⣿⣿⣿⣿⡏⠉⠀⣼⡟⢁⣈⠉⠙⣻⣿⣿⡋⢡⣤⢤⢀⠉⢿⣿⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⣿⣿⣿⠿⠩⣿⡇⢀⣼⣿⠀⠻⢋⣤⣾⠛⠉⠹⣷⡌⠀⠀⡙⠀⠀⢹⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⣿⣿⣷⣀⣠⣴⣿⡿⠛⣿⡿⣷⣶⡿⠋⢡⣜⡯⡄⠙⢿⣶⣤⣴⡾⠟⠛⢿⣗⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⣏⢻⣿⣿⣿⠛⠉⣿⡇⣼⣿⢠⣿⠏⢿⣄⠈⠂⣠⣶⣶⣟⣿⣿⣷⣶⣶⣶⣾⣿⣜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢰⡟⠛⣼⣿⡇⢻⣧⠀⣿⣇⣿⣷⡿⠁⠐⢈⣿⣿⣿⣿⡿⠟⢻⠉⢉⣿⣿⡉⠁⠈⠉⠻⣿⣖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⡿⠛⠛⣻⣿⠿⢻⣿⣿⣿⠷⢶⣾⣿⣿⣥⣿⣿⡄⠀⢛⣦⣾⣟⠛⠛⠻⢷⣶⣤⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⢻⣿⣷⣶⣾⣿⣧⣤⣾⣿⣽⣿⣤⣶⣿⣿⣤⣭⣝⣿⡿⢿⣿⠛⠉⠻⣷⣄⣠⣴⣶⠿⠻⢿⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⢻⣷⣿⣏⣀⡀⣽⡿⠉⠉⢿⣇⠀⠀⠸⣿⡉⠉⠻⣿⡄⠹⣷⣄⢀⣨⣿⣿⣅⠀⢶⣄⠀⠙⢿⣿⣿⣂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢹⣿⣯⣙⢻⣿⣿⠶⠶⣾⣿⣶⡶⠶⣿⣧⣤⣤⣿⣿⣴⣾⣿⣿⠋⢁⡈⢿⣦⡀⠋⣤⣾⠿⠿⣿⣷⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣶⣦⡀⠻⣷⡀⠀⠘⣿⡅⢀⢸⣿⡇⠀⠈⣿⣦⠉⢁⣀⣽⣿⣾⠟⠠⣶⡄⠈⢿⣿⡅⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠀⠁⠈⠋⢻⠿⡿⠿⠿⣷⣾⣿⣧⣤⣤⣼⣿⡾⠿⠻⣿⣿⠟⠉⣉⠉⠹⣷⣄⠈⢹⡆⠈⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠗⠧⣻⠙⡿⢿⣧⣼⣿⡇⢺⣆⠀⢿⡆⠀⣍⡷⠀⠘⢿⣆⠀⣠⣶⣿⣿⠙⢿⣦⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⠀⠹⠟⢻⣿⣦⡀⠀⠈⣿⣆⠋⣁⣴⣶⣿⣿⣾⣿⣿⠿⠡⢶⠄⠙⢿⣆⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠿⠋⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠉⠀⠄⠁⠀⠀⠠⢀⠉⠻⣷⣄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡾⠛⡡⠞⠛⠀⠈⠻⠿⠿⠟⠛⠋⢁⠠⠀⠈⠋⠁⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠏ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠋⡁⠋⠀⠀⠀⠀⠀⠀⠠⠀⠀⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠟⠠⠂⠀⠀⠀⡀⡂⠀⠐⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣦⣄⢠⠂⡀⠀⠀⡀⣐⡂⠀⢀⣐⠒⠂⠂⠂⠀⢀⠀⠀⠀⠀⠀⠀⢰⠀⠠⠀⠀⠐⣰ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣦⠀⠄⠐⢐⢀⡂⢰⣦⣤⣰⣿⣷⣦⣾⣷⣀⠐⠀⠀⠀⠀⠀⠨⠀⠄⠀⠂⣼⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⡆⡧⠀⠀⠬⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠁⠀⠀⠀⠀⠈⠀⠀⠀⣽⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⡿⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⡂⠀⠀⠀⢐⠀⠀⢰⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣆⠀⠀⠀⠂⠈⠉⠉⠸⢿⣿⡿⠃⠉⠉⠀⠐⢒⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠐⠆⠀⠀⠀⠀⠀⠀⠁⠀⠀⠤⠠⠂⠀⠀⠀⠄⠀⠀⠀⠀⠨⠀⠀⠀⢸⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠀⣿⣿⣿

⠀⠀⠀⠀⠠⠀⠐⠀⠄⠀⠀⠀⠀ ⠀⢠⠊⡠⠬⣭⠵⡆⢠⢶⣓⣆⠀ ⠠⠁⠀⠙⠩⠹⠙⠁⠈⠉⠋⠸⡆ ⠀⠀⠀⠀⠀⡀⠀⣀⠠⢤⠀⠆⢠ ⢀⠀⠀⠀⠀⠁⠉⠀⠀⠁⠀⠀⡌ ⠀⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀ ⠀⠀⠁⠢⢀⠀⠠⡀⣀⠤⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⠝⠙⠉⠒⣤⡀⠀ ⠀⠀⠀⠀⢰⣧⡶⠒⡏⠉⠹⠃⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⡿⢻⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡿⠟⠛⢁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣏⠉⠉⠉⢁⣤⠴⠷⠶⠽⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣹⡶⠈⠍⢰⣾⣿⣅⠀⠙⠻⣿⣿⣿⡟⣏⣽⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⡀⠰⠋⣽⣿⣍⠁⠀⠀⠈⠛⠛⠀⡿⢿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡟⣃⠀⠀⠿⠿⠁⠐⠀⠀⠀⡄⠀⢠⣀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡏⠀⠒⣲⢤⠀⠀⠀⠀⠀⣸⠀⠀⠀⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣶⢙⣁⣀⠴⠲⡄⠀⢠⠃⠀⠀⢀⡏⢳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢮⡛⠛⠒⠃⠀⢀⡔⠁⠀⢀⡴⠋⠀⢸⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠊⡱⢤⣀⣠⠔⠋⠀⢀⡴⠋⠀⠀⠀⣼⣿⣿⣿⣿⣿⣶⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣠⠤⠒⢩⠏⠀⠀⡇⠀⠸⣍⢉⣷⠺⣥⡀⠀⠀⠀⣰⣿⡿⠛⠛⠻⣿⠉⠁⠀⠀⠈⢑⠒⢤⣄⣀⠀⠀⠀ ⠀⢠⣤⠖⠊⠁⠀⠀⢀⠎⠀⠀⠀⢇⠀⢀⡰⠃⢸⢤⠏⢣⡉⠀⡰⢻⣿⠁⠀⠀⠀⠘⣧⣀⠀⠀⠀⠀⠈⠉⣿⣿⣧⡀⠀ ⢠⢻⡇⠀⠀⠀⠀⠀⠺⢄⣀⠀⠀⠸⢴⡏⠀⢀⡏⠀⡇⠀⠙⠖⠁⣼⡇⠀⠀⠀⣠⣴⣿⣿⠇⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀ ⡞⢸⡇⠀⠀⠀⠀⠀⣠⡴⠛⠀⠀⠀⠸⠇⢠⢾⡇⠀⡇⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠙⢧⡀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⡇ ⠁⠀⡇⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⡇⢸⢱⠀⡇⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⢸⣿⣶⡶⠀⠀⢠⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠇⢸⠘⡄⢹⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⣿⠏⠁⠀⠀⠀⢸⣿⡿⠋⠉⢻⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢸⠀⢣⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠇⠀⠀⠀⠻ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⢱⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⢇⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠰⢢⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⡟⣿⣿⣟⣿⣿⢿⣍⢿⣿⣿⣿⡏⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣻⢿⣿⣿⣿⣿⣷⣿⣿⣿⣿⢺⣿⣿⣿⡇⠹⣿⣏⢿⣿⡽⠟⡾⠿⣿⣿⡷⣦⡈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢰⣿⣿⣬⣿⣿⡿⢼⢃⣿⣿⣿⣿⣿⡿⡿⠿⠞⣿⣿⣿⡜⡟⣻⣿⠇⠀⠹⣿⠿⠛⣿⡄⠀⠀⠈⣿⣿⠺⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣿⡿⠁⣠⣿⣿⣷⡰⠿⠭⣿⢿⣿⠏⠀⠀⢀⣾⣿⣿⠇⠀⢀⣿⣿⠀⠀⠀⠘⢧⡀⠈⢻⣄⠀⠀⢸⣿⡆⢠⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣾⣿⣣⣾⣯⢸⣿⣿⡇⣠⠀⠛⣾⠏⠀⠀⠀⣼⡿⣼⡟⠀⢠⣾⣿⠃⠀⠀⠀⠀⠈⢳⣄⠀⠙⣷⡀⢸⣿⡇⠘⡆⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀ ⠀⠀⠀⠀⢰⣿⣿⣿⣁⣼⣿⣿⠃⠀⠐⠀⣼⠏⠀⠀⠀⣰⣿⢁⣿⠁⢀⡞⣼⣧⡤⠴⠖⠒⠊⠉⠉⠙⢦⡀⠈⢿⣶⣿⣿⠀⡄⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠻⠿⢿⣿ ⠀⠀⠀⠀⣾⣿⣿⢠⣧⠁⣿⣿⣇⠀⠀⣼⠏⠀⠀⣠⣾⣿⢃⣿⠃⢠⡾⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢦⡀⡇⢹⣿⠀⠁⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⣿⣿⢿⣿⡟⢰⣿⣿⣿⢠⣾⠋⠀⢀⡴⣫⡾⠁⣼⣋⡼⠋⠚⢁⣤⣤⢴⣒⣾⣧⣤⣤⣤⣖⣀⡀⠀⠙⢷⣿⣿⢁⢀⢸⣿⡿⠟⠻⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣿⣿⣿⣩⠁⢨⣿⣿⣿⣟⠁⢀⣴⣿⡽⠋⣀⡾⠟⠉⠀⠀⠀⠸⠟⣳⡿⠟⠋⠿⠛⣿⣟⣻⣟⠻⣦⡀⠀⠉⣻⣾⢸⡿⠁⠀⢰⠒⢶⠹⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣸⡏⣿⠟⠉⠀⣼⣿⣿⣿⣿⣶⣿⣥⣵⡲⢶⣦⠀⠀⠀⠀⠀⠀⠀⠈⠙⠈⠀⠀⣤⣾⣿⣿⣿⣿⣄⡟⠀⠀⠀⣿⡏⢸⡇⠀⢀⣏⡀⣰⠀⢹⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⠃⣿⡄⣿⡀⢿⣿⣿⠛⢻⠟⠋⠹⠛⣿⣷⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣏⠟⠋⢹⡿⠟⠁⠀⠀⣰⡿⠁⡾⠀⣀⠻⣮⣍⠁⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⠀⣿⣿⣿⣤⣼⣿⣿⣷⡘⣇⠀⠠⣼⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⣿⣦⡴⠾⠄⠀⠀⠀⢠⣿⠃⣼⢃⣠⣬⠷⣶⠇⠀⠀⣼⣿⣿⣿⣿⣹⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⠀⣿⣿⡟⠿⣿⣿⣿⣿⣧⠙⠄⠀⢿⣇⠀⡽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⢋⣾⠃⢈⠁⣀⡾⠁⠀⣠⣾⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠀⢻⣿⣷⠖⣻⣿⣿⣿⣿⡄⠀⠀⠀⠛⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⣫⡞⠁⠀⠘⠚⠁⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⣿⡿⣿⣿⣿⡏⠻⣿⣿⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣿⣿⡿⠃⠀⠀⢀⣠⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠹⣷⠹⣿⣿⣿⠀⠈⣻⣆⠀⠀⠀⠀⠈⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢿⣫⠟⠀⠀⠀⣰⡏⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⠆⠈⢿⣿⣧⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠚⠁⠀⠀⠀⢠⠏⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢧⣀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠁⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⢻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠏⠁⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⣤⣀⠀⠀⠀⠀⠀⢀⣤⡾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⠟ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣽⣿⣿⣿⣿⣿⣷⣦⣤⣴⣾⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠒⠛⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⠗⢋⣩⣭⣭⣽⣛⢻⡟⢻⣟⣏⣉⣉⡉⠉⠛⠻⡿⣿⣼⣧⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢀⡾⠁⡏⢸⠁⠀⢀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⡇⠘⡾⣿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣠⠏⠀⠀⢷⣈⣵⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡠⣾⡇⠀⢱⡜⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢠⡞⠁⢀⡤⠞⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠻⣄⠘⣿⣃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢿⣿⣿⣿⣿⣿⣿⡿⢛⣯⣭⣭⣧⣤⣤⠖⠋⢀⡴⠋⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠙⣆⢹⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⢸⣿⣿⣿⣿⣿⣿⣷⣼⠽⠋⠀⠀⠀⠀⣀⣤⠞⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⡈⠀⣿ ⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⣾⣿⣿⣿⠿⠛⠋⢉⣀⠤⠴⠖⠒⢉⣩⡜⠁⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢡⣿⡿⠋⠀⠀⠀⠐⢁⣀⣠⣤⣶⣿⣿⠏⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠛⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠋⠁⣀⡀⠙⣦⠀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠋⢳⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠶⠛⠛⠛⠉⠉⠉⠉⠉⠉⠉⠛⠓⠚⠛⠿⠗⠒⣺⡟⠃⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⢁⡆⠀⢸⠃⠀⠀⠀⣠⡤⢶⣾⡏⢰⡶⢫⠄⣤⣦⠞⢋⣩⡵⠾⢿⠟⠀⠀⠀⠀⠀⢈⣩⣿⣷⠚⠋⠉⠉⠙⠓⠲⠤⠤⠶⢒⣶⢻⡷⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⢻⠀⠀⣼⠀⠀⣠⣾⣿⣶⣿⡿⠰⢋⡴⠃⣠⣾⠷⣊⣭⣤⠤⠤⠤⣄⡀⠀⠀⠀⠀⠉⠹⢿⠯⠅⠀⠀⠀⠀⠀⠀⠀⣀⡴⠻⣿⡾⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⣿⠀⢠⠛⣦⣰⣿⣿⣿⣫⠟⣡⣶⠞⠛⣶⠟⣡⣾⣿⠟⢀⡴⠀⣹⣷⣝⡷⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠖⢋⡁⢀⡴⠋⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⠀⣴⣿⠀⢸⠀⡿⣿⣿⡉⠉⠛⢾⣿⠃⠀⠀⢡⣾⣿⣿⣿⠀⢸⡀⠈⠛⢛⣿⣵⣣⠄⢀⡀⠀⠀⠀⠀⠈⠉⣻⡿⠀⣴⠿⢾⣿⠇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠁⣼⢁⡟⠀⣸⢢⠋⢉⣉⣩⣷⡄⠀⠙⢦⡀⢰⣿⣿⣿⣿⣿⣆⠈⠛⠶⣶⣿⡿⠋⢁⡾⠋⠀⠀⠀⠀⢀⣶⡿⠁⠀⢠⠤⢶⣿⣷⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠁⠀⣿⡾⠁⠀⣿⣼⠀⠀⠀⠀⠀⠀⠀⢀⡼⢿⠀⠈⠙⢿⣿⣿⣿⣷⠶⢞⢿⣯⣤⠶⢋⣠⣾⠃⠀⠀⢀⣿⣛⣀⣤⡀⠀⢀⣾⣿⠿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠁⠀⠀⠙⠁⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⢀⡞⠀⢸⡀⠀⠀⠈⠛⠒⢶⣤⣉⣴⣋⣉⣱⣾⣿⣟⣉⡤⠂⣠⠀⠀⠀⠈⠉⠙⠛⠉⢻⡟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠒⠒⣲⠏⠀⠀⢸⠃⠀⠀⠀⠀⠀⠈⠀⠉⠉⠙⠋⠉⠁⠀⠀⠀⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠳⢿⣀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠻⣶⡶⢶⣶⣤⡀⣠⣟⣤⡤⠤⠶⢶⣶⡾⢁⣾⡇⢀⡼⢹⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠦⠤⢤⣤⠤⣄⡀⠀⠀⠀⠉⠙⢲⣶⣤⠄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡟⠛⠉⠀⠀⠀⠀⠀⠀⠸⣤⣾⣿⣿⣿⡇⠀⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠠⣄⡋⠙⢷⡒⠀⠀⠀⠈⠩⣄⣠⣴⣶⠛⠛⠉⠁⠀ ⠀⠀⠀⠀⠀⠀⢠⠖⠓⣆⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⡿⢿⡇⠀⢹⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡑⢦⠀⠉⣷⠒⢻⡄⠀⠀⠀⠀⠠⣄⣁⣈⣹⣷⠶⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⠀⠀⠀⠈⣷⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⣼⠈⢻⡀⡄⠀⣄⠀⠀⠀⠀⠀⠀⠀⠙⠆⠀⢸⡇⠀⠀⣷⡀⠀⠀⠀⠲⢤⣉⠛⠛⠉⠓⣲⡶ ⠀⠀⠀⠀⠀⠀⡟⠀⠀⣼⠀⠀⠀⠀⣼⣷⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣇⠀⠀⠻⡝⢦⠈⢳⣤⡀⠀⢦⣄⠀⠀⠀⠀⢘⡇⠀⠀⡏⠻⣷⢦⣶⣤⣤⣈⣁⣈⠻⣍⡁⠀ ⠀⠀⠀⠀⠀⠀⡇⠀⠀⢻⠀⠀⣠⡞⢡⣿⠀⠀⢷⠀⠀⠀⠀⢲⡄⠀⠀⠀⠀⠉⠛⢷⡀⠀⠀⠀⠑⢦⣻⣿⣶⣦⠻⣷⣤⡀⠀⣸⠃⠀⠘⣧⣐⣾⢷⣝⢦⡉⣿⣿⣿⣍⡉⠉⠀ ⠀⢀⣤⣤⡤⢤⡇⠀⠀⢸⣄⣴⠋⠀⣼⡏⠀⠀⠈⠀⠀⢀⡆⠀⢧⠀⠀⠀⠀⠀⠀⠈⢷⣷⡀⠀⠀⠀⠉⣿⡽⣮⣷⣮⣽⣿⣶⡿⠀⠀⠀⣿⣿⣿⣾⣿⡛⢿⣿⠿⣏⡉⠙⠀⠀ ⠀⡾⢹⠃⠀⠸⡇⠀⠀⢸⠀⠘⡏⠻⡟⢰⣿⠀⠀⠀⠀⣼⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡄⢀⠀⠀⢻⡅⠈⣹⠏⢹⠃⠀⡇⠀⠀⢠⡇⠀⠹⡏⣿⠙⣆⠹⣿⣿⠿⢷⠦⠀ ⢠⠇⢸⠀⠀⠀⣧⠀⠀⣾⠀⠐⡇⠀⢻⣿⠇⠀⠀⠀⠰⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⣷⡀⠀⡙⢠⠏⠀⢸⠀⠀⡷⠀⠀⣾⠀⠀⠀⣿⢸⣇⠸⣿⡛⠻⢶⠀⠀⠀ ⢾⠀⢸⠀⠀⠀⠉⠀⠀⠹⠀⠀⢣⠀⢘⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⡀⢹⡟⠀⠰⠏⠀⠀⠃⠀⠐⠃⠀⠀⢰⡇⠈⣿⣿⣿⡿⣦⡀⠀⠀⠀

ヾ(@゜∇゜@)ノ

⠛⠛⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠉⠉⠉⠀⠀⠈⠙⠛⠛⠛⠛⠛ ⣖⠂⠀⠀⢐⣿⣿⣿⣿⠿⢋⠉⠛⠛⠻⣿⣿⣷⣶⣶⣶⠶⠲⠶⣶⣶⣶⣶⣆⡀ ⢿⣿⣷⣷⣿⣿⣿⡿⠑⡦⠒⠢⡀⠀⡀⠍⣻⣿⣿⣿⣦⡀⢀⣠⣼⣿⣿⣿⣿⣿ ⣾⣿⣿⣿⣿⣿⠏⠀⠀⠣⣀⡰⠇⠘⡄⠀⣸⣿⣿⡿⠛⠛⣿⣿⣿⣿⡿⠛⠛⢿ ⠉⠉⠉⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢀⠌⠉⢸⣿⡿⣍⠥⠤⢍⠉⠉⠉⠁⠀⠀⠈ ⠀⠀⢸⣿⣿⣿⣧⠀⠀⢠⡦⣤⣌⢠⠀⠀⣼⣿⠀⠀⠉⠒⢤⣱⡀⢀⣀⡀⠀⠀ ⠀⠀⠈⣻⣿⣿⣿⣷⠄⢈⢟⡩⣔⣆⣤⣾⣿⣿⠀⠀⠀⠀⠀⠈⠉⠳⠤⣈⢢⣀ ⠛⠛⠛⣿⣿⣿⡿⠿⠀⠀⠑⠖⣖⠟⠿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻ ⠁⢉⡲⠿⡟⠉⣼⠀⠀⠀⠀⠀⠸⢀⠀⠈⣗⠲⠒⠒⠒⠤⣀⠀⠀⠀⠀⠀⠀⠀ ⠚⠁⠀⠀⢇⠀⠇⡀⠀⢠⠀⠀⡆⢻⠀⠀⠃⠀⠀⠀⠀⠀⠈⢳⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⡞⠀⠣⡀⢸⢀⡴⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢇⠀⠀⠈⠙⠁⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠢⢄⣀⣀⢀⣀⡠⠕⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠘⢄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠏⠑⢄⢈⣺⠀⢠⣀⣀⣀⡴⠂⠉⠀⡏⠀⠀⠀⠀⠀

⡴⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢇⢻⡲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⡄⠹⢈⣵⢖⣒⣲⣖⠒⠠⠄⡀⠀⠀⠀⠀⠀⠀⢀⣀⡀ ⠀⠸⡔⠋⠐⡈⠳⡌⢿⠎⠀⢀⣬⢅⠈⠀⠈⠙⠻⢽⣿⠇ ⠀⢰⠁⣠⣶⣶⢢⢮⢁⢀⣠⣤⣄⠙⢶⡀⢄⡲⠖⠋⠁⠀ ⠀⠸⠀⠛⠿⣿⡟⠀⢸⠘⠶⢿⣿⣇⢖⠉⡏⠀⠀⠀⠀⠀ ⠀⢸⡀⢆⠀⢺⡤⣾⡸⠓⠄⠀⠐⠨⢼⡂⡇⠀⠀⠀⠀⠀ ⡉⠀⠻⣝⣑⣠⣓⠛⠁⠀⠬⣤⣤⠀⠀⡱⠁⠀⠀⠀⠀⠀ ⠀⢀⠔⠉⠢⡘⣾⣿⣔⡔⢪⡍⡪⡲⡋⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⡇⢈⡮⣃⠂⠿⠊⠑⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣶⣶⣶⣶⣶⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣾⣿⣿⣿⣷⣶⣯⣟⡷⣦⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⠿⠛⠉⠁⠀⠀⠀⠀⠀⠉⠛⢿⣿⣮⡻⣦⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣵⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠙⢿⣿⣞⢷⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⣴⡄⠀⠀⠹⣿⣎⢿⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠟⣿⣄⠀⠀⠹⣿⣏⣿⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢟⣽⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣧⣤⣾⠟⠃⠀⠀⢹⣿⣼⣷⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣷⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠉⠛⠀⠀⠀⠀⠀⣿⣷⣿⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣄⠀⠀⠀⠀⠀⠀⢿⣿⣿⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣿⣿⣿⣿⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣤⣴⣿⣿⣿⣶⣶⠀⠀⠀⣿⣿⢾⣏⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣶⣿⣿⣿⣿⣿⡿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣧⣻⣼⣿⠋⠀⠀⢠⣿⣿⣾⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⣾⣿⣿⣿⣿⠿⠟⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⡿⠿⣿⡧⠀⢀⣾⣿⢧⣿⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⣿⣿⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⣠⣾⣿⢯⣿⠏⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣴⣶⣿⣿⣿⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⡿⠋⠀⠀⠀ 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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣍⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣻⣿⠶⣿⣿⣿⣿⣿⠿⡛⢏⡍⠳⣌⠲⡐⠦⡑⢎⡙⢻⢿⣿⣶⣻⣷⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⡉⠛⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⢿⣿⣿⡟⣍⠳⣈⢇⡙⢢⡜⡱⢄⢣⡙⠴⣉⠦⡙⢦⡉⣿⣿⣿⣹⣷ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣆⠀⠀⠀⠀⣰⠎⠀⠂⢁⠠⠐⢀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠋⠀⠀⣿⣿⣧⢂⠳⡌⢦⡙⢆⡜⡰⣉⠖⠬⡑⢆⢣⡙⢤⣽⣿⢏⣿⣼⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣆⠀⠀⠀⠈⡀⠄⠁⠠⠀⢢⡿⠛⠀⠀⠀⠀⠀⠀⣠⣴⣾⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠁⠀⠀⠀⢸⣿⣿⡌⡱⡘⠴⣘⠢⡜⣡⠒⣌⠣⢍⠎⣆⣙⣾⣿⢋⣾⣿⣿⠏ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣦⣄⡀⠐⠀⡈⠠⠁⠈⠁⠀⠀⠀⠀⣀⣤⣶⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⢸⣿⣿⡖⣡⠙⢦⢡⢓⡸⢄⢫⠰⣉⠦⣉⣶⣿⡟⣥⣾⡿⣿⠟⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣧⣄⣤⣤⣤⣶⣶⣿⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠦⣙⠢⣑⠪⡔⢪⢅⠳⣈⢶⣽⡿⢣⣾⣿⢟⣾⠋⠀⠀ ⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣻⡟⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⣸⣿⣿⢃⠳⡄⢳⢨⠱⡌⢣⢌⢳⣼⣿⢯⣱⣿⡟⣳⡟⠁⠀⠀⠀ ⠀⠀⠀⢠⣾⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⢿⣿⠃⠀⠀⠀⠀⠀⠙⠹⠙⠫⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⢹⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣶⣦⣶⣿⣿⡟⡌⢣⠜⡡⢎⡱⢌⢣⣮⣿⠿⣱⣾⣿⣫⡾⠋⠀⠀⠀⠀⠀ ⠀⢀⣴⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⡏⠀⠂⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⡿⢋⡝⡛⠿⠿⠿⡟⢫⠔⡩⢆⡹⣐⢣⢲⣼⣿⠿⣙⣾⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀ ⠀⣼⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡟⣼⡷⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⠿⣿⣧⠀⠀⠀⠀⣀⣠⣤⣾⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣿⡿⢋⡔⢣⠜⣌⢣⡙⠦⡙⠦⣙⠰⣃⠴⣨⣶⣿⡟⣽⣾⡿⠛⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⣸⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⣼⡟⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡏⠀⠻⣿⣿⣶⣿⣿⡿⠿⠛⠉⢿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⢟⠣⡜⡡⢎⡑⠎⡔⢢⡑⢎⡡⢓⠬⡑⢦⣷⣿⠟⣧⣽⣿⣏⠀⢠⣟⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⡟⠀⠀⠀⠀⠀⠀⣠⣴⡶⢶⡤⠀⠘⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⡿⢛⠬⡌⢳⠰⡑⢎⡜⡱⡘⢥⠚⡤⠣⢍⣲⣽⣿⢟⣱⣾⣿⣿⠿⣿⣿⣫⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡟⠀⠀⠀⠀⠀⢠⣿⠋⠁⠈⠁⠀⠀⠹⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣿⣿⣿⣿⢯⡽⣫⠾⡽⢮⢧⡻⣎⢷⣣⢻⢮⡻⣵⣻⣾⣿⢿⣯⣾⣿⣿⣿⣿⡿⠟⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣧⠀⠀⠀⠀⠀⠈⣿⣆⡀⠀⠀⢀⣠⣾⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣶⣿⣿⣿⡿⢿⡻⣧⢫⡷⡽⣭⢟⡵⢯⣎⣳⢞⡷⢯⡟⣮⣿⣿⣿⢟⣯⣿⣿⣿⣿⡿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ 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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣧⡙⢆⡍⠲⢌⠣⡜⡰⡉⢖⠱⣂⠭⡘⣅⠣⠎⡜⡡⢎⡌⡓⡌⢎⡱⡘⢤⡙⠜⡢⢅⠫⠜⣢⠑⡎⡔⣢⣵⣶⣿⡿⠟⡭⣮⣽⣾⢿⣯⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣻⣿⣷⣌⠜⡱⢊⠵⣨⠑⡍⢎⠲⡡⢎⡱⢢⡙⡜⡰⡑⢎⠴⢱⡘⠦⣡⠙⡆⡜⣡⠓⣌⢣⡙⣤⣫⣴⣿⣿⠿⣛⣥⣽⣾⣿⣿⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣧⣛⣿⣿⣯⣖⡩⢒⡡⢍⡜⠬⣑⠱⣊⠔⡣⢜⡰⠱⣉⠎⡜⡡⢜⠢⣅⠳⣘⢰⣡⣯⣴⣷⣿⣿⠿⣟⣹⣦⣿⣿⠿⠋⠁⢸⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣷⣬⢛⣿⣿⣿⣷⣮⣶⣘⣦⢡⠓⡬⡘⢥⢢⡑⢣⠜⡘⠴⣑⣮⣵⣦⣷⣾⣿⣿⡿⢟⡻⣍⣶⣷⣿⣿⣿⣏⠀⠀⠀⠀⣼⢻⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣷⣦⣍⣛⠻⠿⣿⣿⣿⣿⣿⣷⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⠿⢿⠛⣏⣹⣔⣮⣷⣿⣿⣿⣿⣧⣳⣞⣿⣷⣦⣶⡾⣫⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣷⣭⣖⣦⣩⡍⢯⣙⣛⡛⣛⠻⡹⣍⣫⣕⣲⣬⣽⣶⣿⣿⣿⣿⣿⣿⠿⠛⠛⠿⣯⣽⣽⣭⣽⣿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣉⣭⡿⢻⣿⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠛⠛⠿⣿⣿⣿⡿⡾⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣾⣛⣋⣉⣁⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠳⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡴⠶⠟⠛⠛⠛⠛⠉⠉⠉⠉⠉⠉⠉⠛⠛⠶⢦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣦⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⡶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠈⢿⣄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢦⣄⠀⠀⠀⠀⠀⠀⢻⣆⠀⠀⠀ ⠀⠀⠀⠀⠀⣾⡇⠀⣀⣀⣀⣀⠀⠀⠀⢠⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣄⠀⠀⠀⠀⠀⢿⡄⠀⠀ ⠀⠀⠀⠀⠀⠘⣿⠛⠉⠉⠉⠛⠛⠛⠛⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠾⠛⠛⢷⣄⠀⠀⠀⠀⠀⠙⢷⡄⠀⠀⠀⠘⣿⠀⠀ ⠀⠀⠀⠀⠀⣤⣿⣷⣶⣦⣤⡀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢀⣀⣤⣴⠾⠛⠉⠁⠀⠀⠀⠀⠀⠉⠻⣦⡀⠀⠀⠀⠈⢿⡄⠀⠀⠀⢹⡇⠀ ⠀⠀⠀⠀⣾⣿⣿⣿⣿⡄⠈⠙⣦⡀⠀⠙⠛⠻⠛⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⠀⠀⠀⠘⣷⠀⠀⠀⠈⣿⠀ ⣀⣀⣀⣸⣏⠻⠿⠿⠟⠁⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣀⣀⡀⠀⠀⠀⠘⣷⡀⠀⠀⣿⡇⠀⠀⠀⢿⡀ ⢿⡍⠉⠉⠙⢷⣦⣤⣤⣤⣤⣴⠟⢁⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠉⠉⢩⣿⣿⣿⣷⣄⠀⠀⢸⡇⠀⠀⣸⡇⠀⠀⠀⢸⡇ ⠀⠻⣦⡀⠀⢸⡟⠀⠀⠀⠀⠀⠀⢸⣿⠛⣿⣶⣦⣤⣤⣀⣀⠀⠀⠀⠀⠀⢿⡄⠀⠸⣿⣿⣿⡿⠘⣷⡀⣾⠛⠀⢠⣻⣇⣀⣀⣀⢸⡇ ⠀⠀⠈⠛⣦⡿⠁⠀⠀⠀⠀⠀⠀⠉⢿⡀⣸⠃⢸⡏⠉⣿⡿⠿⣦⡀⠀⠀⠀⠻⢦⣄⣀⣉⣁⣀⣠⣿⣿⠏⠀⠀⣿⠉⠉⠉⠉⢉⣿⡇ ⠀⠀⠀⠀⣾⡁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣿⣤⣿⣁⣀⣿⣠⣰⣿⠇⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⣰⡟⠀⠀⢀⣿⠀⠀⠀⣠⡾⣽⠇ ⠀⠀⠀⠀⠈⠻⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⠀⢺⣧⣴⡶⠾⠋⠀⣿⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⠻⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⠀⠀⣼⣯⠀⠀⠀⠀⢸⡏⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠳⢦⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⡶⠶⣾⠟⠀⠀⠀⠀⣳⡏⠹⣧⡀⠀⢠⡿⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣴⠶⢶⣶⣤⣀⠀⠀⠉⠙⠛⢻⡷⣶⠶⠶⠶⢶⣾⠟⠛⠛⠉⢱⡿⠀⣴⠏⠀⠀⠀⢀⣴⠏⠀⠀⠘⣷⠀⣾⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⣾⠁⠀⣾⠁⡈⠙⣷⣤⣀⠀⠀⣿⠁⠹⣧⠀⣠⡾⣁⣀⠀⠀⠀⠘⣿⠀⠻⢦⣤⣤⣴⠞⠁⠀⠀⠀⠀⠘⠿⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⠀⠀⢻⡶⠏⢠⡿⠈⠙⠛⠛⣿⠀⠀⢹⣶⣿⠟⠋⠙⣷⠀⠀⠀⠙⠷⣦⠀⠀⠀⠹⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⢠⡾⠁⠀⠀⠀⢀⣿⠀⠀⣾⡏⠀⠀⠀⢠⡿⠛⠛⠷⢶⣄⣿⡇⠀⠀⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⠷⢶⣴⠾⠛⠛⠶⣦⣤⣤⣼⡏⠀⠀⢻⡇⠀⠀⢀⣿⠃⠀⠀⠀⠀⠈⠛⠁⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠈⠻⠶⠾⠿⠿⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⢶⣦⣤⣤⣤⣤⣤⣴⠶⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⡤⠊⠉⠉⠉⠑⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡘⠰⠾⠿⠶⣠⣶⠿⢿⠒⠀⢰⣆⡀⠀⠀⠀⠀⠀⠀ ⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⢇⢀⡜⡻⢃⣀⡀⠀⠀⠀⠀ ⠀⣸⢀⠀⠀⠀⠀⠀⠀⠀⠈⡪⠚⠒⢅⡠⣄⣱⣄⣠⡄ ⠘⡍⠚⢀⠃⢤⠤⢊⠭⣼⣷⠥⠴⠢⣀⠵⣉⠣⠤⠊⠀ ⠀⢱⠰⡘⢒⡡⠖⢁⣄⣈⠀⠀⠀⠀⠈⠢⢬⠝⠃⠀⠀ ⠀⠈⡄⠀⠀⠀⠀⠘⠘⠉⠀⠀⠀⠀⡀⠀⠇⠀⠀⠀⠀ ⠀⠀⢡⢇⣸⠈⡍⢹⠀⣏⢸⠄⡜⠃⠧⢼⠀⠀⠀⠀⠀ ⠀⠀⠘⡄⠀⡤⢴⡄⠠⡀⢤⠀⠀⡆⠀⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⢇⠀⠑⠘⠁⠋⠁⠒⠀⠃⠃⢰⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠉⠐⠒⠒⠒⠒⠒⠒⠊⠁⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠉⢳⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠸⠀⢀⠉⠓⠦⣀⣀⣀⣤⠤⠤⠶⠶⠾⣧⣤⠒⢳⢸⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢰⠀⢸⠉⣳⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢾⣸⠇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⣆⢸⠾⣅⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠒⢺⠿⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⢫⠈⣯⠳⣆⠀⠀⠀⠀⠀⠰⡇⢈⣦⡜⠀⠹⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠈⠳⠧⠴⠞⠀⡠⠺⣿⡟⠻⢿⡛⠋⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣾⠁⢰⣼⣴⠀⢈⡇⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠻⣄⡀⢻⣾⡤⠟⠁⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣾⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⠀⠀⠙⡆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠻⡄⠀⠀⠀ ⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁⡠⠃⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀ ⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⢀⡴⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀ ⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠉⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄ ⢰⡇⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇ ⠈⠙⠿⣿⣿⣿⣷⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣴⣶⣿⠿⠁ ⠀⠀⠀⠀⡼⣻⢋⡄⢉⣹⠿⠶⢤⣀⣀⣀⠀⣀⣀⣀⣤⣴⠾⣿⠛⠛⠿⢿⠁⢻⠋⠁⠀⠀ ⠀⠀⠀⠀⠙⠛⠚⢉⡡⠤⠤⠤⠼⠿⣟⣛⣿⣻⣽⣟⣩⣂⣴⣃⣀⣀⡴⠋⠀⢸⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠸⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⢦⣀⣀⣀⠤⠴⠒⠒⠒⠚⠒⠒⠒⠦⠤⠤⠤⠤⠤⠔⠊⠁⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠴⠒⠉⠉⢀⣠⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠖⠉⠀⠀⠀⠀⠐⠋⠉⠉⢉⣉⣉⣱⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⣴⡆⠀⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⣽⡶⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃⠀⠀⠀⠀⡎⣹⠞⢋⣹⣶⣭⣹⡦⣄⠀⠀⠀⠀⠀⠀⠈⢯⠉⢠⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⢸⠀⣡⣾⣿⣿⣿⣿⣿⣿⣦⣷⡄⠀⠀⠀⠀⠀⠈⢷⣦⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡼⠃⠀⠀⠀⠀⠈⠿⣶⣿⣿⣿⣿⣿⣿⣷⣍⢻⣿⠘⡄⠀⠀⠀⠀⠀⠀⢿⣧⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠐⣯⣤⣤⡀⠀⢀⣠⠆⠀⢿⣿⣿⣿⢽⠟⠉⢻⣿⡆⣿⣇⡇⠀⠀⠀⠀⠀⠀⠈⣿⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⣿⢿⣟⡶⠛⠁⠀⠀⠘⣿⣿⣿⣎⣷⣤⣀⣩⣴⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠻⣷⡿⠋⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⡾⠋⣠⢤⣶⠇⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀ ⠀⠀⣠⠞⠉⠀⠀⠀⠘⠁⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀ ⣠⣾⣁⣠⣤⣤⠴⢦⠶⢶⣶⣶⣶⣶⣶⣶⣦⣤⣤⣤⣄⣀⣀⣀⡀⠙⣆⠀⠀⠀⢠⡄⠀⠀⠀⢻⡇⠀⠀⠀⠀ ⠉⠉⠙⠢⣷⠙⠛⠀⠳⠋⠻⣿⣿⣿⣿⣷⣾⣿⠿⠿⠟⠛⠋⠉⠀⡴⠋⠀⠀⠀⠀⢀⡀⠀⠀⢻⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠸⠧⣾⡿⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣠⠎⠀⠀⠀⡾⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠦⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠘⠁⠀⠈⡁⠀⠀⠀⣠⠃⠀⠀⢠⡄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⣳⣶⠶⠶⣤⠾⠃⡀⠀⠀⣠⡀⠙⠲⢄⡀⡏⠀⢀⡠⠜⢻⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡋⠀⠀⠀⢠⡾⠆⢠⣿⣤⠌⠋⠳⣀⠀⠀⠙⣿⠋⠁⠀⣠⠞⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠦⢤⣀⣸⠀⠀⠛⠉⠉⠀⠀⢀⠼⠂⣀⢴⡃⠲⢮⣉⣠⣴⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⣮⣩⢽⣷⠀⠀⠀⠀⠀⠐⣇⣰⣿⣁⠀⢻⠓⢦⣤⠴⠃⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠉⣹⣧⣀⠀⠀⠀⠀⠉⠛⠟⠀⠀⢸⢷⡒⠋⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠉⠉⣿⣽⣦⣤⣤⣤⡆⠀⠀⡰⠋⠙⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⢸⡁⠈⠉⠉⠉⠡⡏⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣼⠓⢢⣭⠇⠀⠀⠀⢀⣱⡞⠓⣦⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠟⠒⠛⠁⠀⠀⠒⠛⣿⣧⠤⠞⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠒⣩⠝⠿⣕⣒⠒⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠁⠀⠀⠡⠞⠉⣍⠻⠽⠘⣷⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⣠⠤⢼⡄⠀⠀⠀⠘⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠸⡥⢼⣿⡇⠀⠀⢠⠶⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠰⡄⠀⠀⠐⠒⢉⠀⠀⠀⠘⣯⣛⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠈⠁⠀⠀⢠⠏⣀⡠⠤⣄⢹⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⢀⡾⠊⠁⠠⡤⠼⣿⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⡀⠀⠀⠈⠧⣌⠀⠀⠀⠀⠀⢀⡞⢸⢃⡤⠴⠲⡦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠻⣟⠷⣦⡲⢄⡀⠉⠀⠀⠀⠀⢸⣤⣿⠋⠀⠀⡄⡇⣨⠷⠤⣄⡀⣀⡤⢤⣀⠀⠀⢀⣀⣀⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠈⠳⡈⠹⣷⣝⡲⢄⡓⠒⠒⢫⣿⡈⢧⠀⠀⢰⡇⡇⠀⠀⠀⠙⠓⠤⣀⢈⢷⣚⢉⣀⣀⣈⠇ ⠀⠀⣴⡊⠉⢙⣦⣄⡤⠄⠺⣄⠀⠀⠀⠀⠀⠱⡀⠈⢪⡙⢶⠣⠤⢄⣁⣻⢳⠈⣆⠀⠘⣿⣿⢠⡀⠀⠀⣄⡠⢤⡤⠼⠯⠭⣉⡒⢦⡀ ⠀⢀⣤⠟⣉⠭⠲⣍⣈⠳⢆⣉⠁⠀⠐⢦⠀⠀⢱⠀⠀⠙⢦⡉⠒⠀⠀⠀⢸⠀⠀⠀⠀⠘⣿⡄⠈⢷⣦⣤⣭⣍⣉⣉⣉⣶⠦⣌⡙⠻ ⢠⠿⠒⡯⢴⡟⠛⠒⠚⠋⠓⠦⠀⠀⠀⢸⠀⠀⠀⣇⠀⠀⠀⠙⢆⡀⠀⠀⠘⠁⠀⠀⠀⠀⠘⡇⠀⠀⠚⢹⣧⠀⠀⠀⠈⠉⠉⠉⠉⠉ ⠛⠔⠚⠓⠉⠉⠉⠉⠉⢹⡗⢾⠯⣉⠁⠈⣆⠀⠀⣿⡤⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠈⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠈⡆⠀⠀⠀⠘⡆⠀⡟⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠦⢤⣿⠀⠀⠀⠀⢹⣠⡇⠀⠙⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡆⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠉⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⡊⢧⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣴⣶⣶⣾⣿⣿⣶⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⡿⠛⠻⡟⠻⠿⣿⠻⠿⠟⣿⣿⣿⣿⠿⠋⢹⠇⣉⢠⣹⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣧⣴⣶⣷⣶⣤⣤⣦⣶⡞⣿⣿⠋⣇⠀⣠⣿⡾⠋⠸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢁⣠⣼⣿⣾⡿⠋⠀⠀⠀⠈⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣴⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⠈⠉⠁⠙⢿⣿⣿⣿⣧⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⣶⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⡿⠿⠷⠀⠀⠀⠀⠀⠀⠈⠙⠏⣿⡿⠛⠁⠀⠀⢀⣀⣤⠀⠀⢹⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠛⢿⣿⣷⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠊⠉⠀⠀⠀⠀⣼⣿⣦⡴⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢻⣿⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠐⠒⢤⡀⠀⢹⣽⠋⣠⣶⡘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢻⣿⣿⣿⣿⣿⡇⠀⡀⠀⠀⠀⣀⡤⣖⡿⠋⠁⠀⠀⠀⠀⠀⢀⡤⠿⠃⣼⢀⣼⣧⢳⠻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⣿⣿⣿⣿⣿⣿⠆⠀⠉⠉⠉⠉⠁⠛⢁⠀⠀⠀⠀⠀⠀⢀⣴⠋⠀⣀⣴⠃⢸⣿⣮⡉⣧⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠘⣿⣽⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠈⢧⣄⡀⠀⠀⣠⣿⣇⣠⣴⠾⠃⠀⣸⣿⣿⡇⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣇⣽⣿⣿⣿⣿⡿⢶⣦⣄⣀⠙⣦⣰⠐⣮⣭⣴⣾⠟⠋⢉⡿⠃⠚⠀⢸⣿⡟⠋⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠸⣿⢿⣿⣿⣿⣿⣷⡒⠋⢿⣿⣿⣿⣿⡆⡎⠛⠿⢭⣛⡛⠉⠀⠀⠀⣀⡿⢹⡧⢤⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠙⢿⣾⣿⣿⣿⣟⠓⠈⠉⠉⠹⣿⣿⡇⠀⠀⠘⠾⠀⠀⠀⠀⠀⣠⡿⠁⢸⡿⢶⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣷⣦⡀⠀⠀⠙⢁⡇⠀⠀⠀⠀⢀⠀⠀⢳⣿⠛⢀⡀⣾⡇⠀⠈⠳⣶⠤⣤⣤⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⠛⢻⣿⣷⣄⠀⠀⠀⡀⢸⡇⠀⠀⢀⠀⢸⠀⠀⢾⡟⢸⢸⠀⣿⣷⡀⠀⠰⣮⡓⠘⣆⠀⠀⠀⠉⠉⠉⠙⠓⠒⠶⠤⠤⠤⠤⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣧⠀⢰⣷⠸⣿⠘⠀⠈⢁⡞⠀⠀⢀⡀⠸⣿⣼⡿⣿⣇⠀⠀⠈⣳⡀⠸⡄⠀⠀⠀⠘⠂⠀⠀⠀⠀⠀⠀⠀⠀⡌⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣧⠹⣿⣷⣾⣿⣿⣾⣇⠀⠀⣾⣀⣀⣠⠜⡇⠀⢹⣿⠀⠹⣿⡀⠀⠀⣻⠂⠀⠹⡄⠀⠀⠀⠰⡄⠀⠀⠀⠀⠀⠀⠀⢸⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⡏⣿⣧⣹⣿⣿⣿⣿⣿⠿⠓⣾⠋⢉⣠⠔⠒⠆⠀⣸⣿⠉⡄⢹⡇⠀⠀⢀⣀⡀⠀⢳⡀⠀⠀⠀⢹⣄⠀⠀⠀⠀⠀⢸⠈⡆⠀⠙⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣷⣿⣿⣿⣿⠿⠤⠤⠽⠒⠋⣁⡀⠀⠀⢀⣿⠸⣄⣿⣀⠿⠖⠚⠉⣏⣹⡦⢄⣳⠀⠀⠀⠈⣏⠓⠠⡄⠀⠀⢸⠀⢻⠀⠀⠘⢦⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⡾⠟⠁⠀⠀⢠⡾⠃⢀⡏⣀⡤⠶⠶⠒⠋⠁⠀⣹⠄⢻⣧⠀⠀⡆⠻⠀⠀⡇⠀⠀⡾⠀⢸⣇⠀⠀⠈⣷⡄⠀⠀⠀ ⢸⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣛⠋⠉⠉⠀⠀⠀⢀⣰⠟⠀⠀⢸⡇⢻⣤⣤⣥⣤⣤⣤⣾⣷⣆⠀⠻⣆⠀⠹⠀⠀⠀⣿⠀⠀⡇⠀⠀⣿⡆⠀⠀⢸⢻⡄⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣷⣶⣦⠴⠶⠖⠋⠁⠀⠀⠀⢸⣷⣀⡇⠘⣧⠀⣠⠟⠠⡓⠉⠓⠦⣌⣳⡄⠀⠀⢀⣿⠀⢸⡇⠀⠀⣿⡇⠀⠀⢸⠀⣇⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⣿⣿⣿⣿⠿⠋⠀⠀⠐⣀⣀⣀⠤⠴⠒⠛⠉⠹⣿⡇⢀⣿⡋⠁⠀⣤⣶⣶⣤⣀⠤⠈⠻⡆⢠⣾⡏⠀⡾⠀⠀⡀⢸⡇⠀⠀⡿⠀⠸⣄⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣿⠿⠿⠿⠶⠒⠒⠋⠉⠁⠀⠀⠀⠀⢀⣀⡠⠴⠟⢳⣼⣿⣷⠀⢸⡿⠩⡉⠁⠀⠀⠀⠀⣇⣾⣿⠃⢰⠃⠀⢀⡇⢸⡇⠀⣼⡇⠀⠀⢻⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠈⠛⠃⢻⣀⣀⣀⣀⣀⣀⣠⣤⣤⣶⣒⣚⣉⣉⣀⣀⣀⣀⣀⣟⣃⣁⣲⣿⣃⣀⣤⣶⣾⣿⣁⣀⣿⣿⣿⣠⣏⣀⣀⣼⣧⣼⣀⣴⣿⣇⣀⣀⣈⣄

⠉⠙⢻⣿⣿⣿⣿⣿⡋⠉⠉⣻⣿⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢻⣯⣽⣿⣿ ⠀⠀⢀⣿⣿⣿⣿⡟⠁⠀⠀⠈⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣾⣿⣿⣿⣿ ⠀⠀⢸⣿⣿⣿⠏⠀⠀⠀⠀⢰⡟⠀⠀⠀⠀⣤⠄⣀⡴⠖⣢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿ ⠀⢠⣿⣿⡟⠁⠀⠀⠀⠀⢀⣿⢳⠀⢀⣤⣶⣿⣿⣿⣿⣿⣵⣶⣶⣿⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠬⣿⣿⣿⡿⠁ ⢀⣾⣿⣿⠀⠀⠀⠀⠀⣠⣾⠏⣿⣂⣾⣿⡿⣟⠿⠟⠛⠿⠦⢾⣹⣍⠛⢿⣟⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⣤⣶⣿⣿⣿⣿⣿⣷⣬⣓⠀⠀⢻⣿⣿⡇⠀ ⣾⣿⡟⠁⠀⠀⠀⢀⣴⣿⢿⠀⠹⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠈⠋⠛⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢿⣿⡿⠿⠛⠛⠛⠛⢷⣿⣿⣿⣧⠀⠈⣿⣿⣧⠀ ⣿⠟⠀⠀⠀⠀⠀⠀⣱⣿⠀⠀⠀⢹⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣷⢠⣿⣿⣿⠀ ⠃⠀⠀⠀⠀⠀⠀⢮⣿⣿⣿⠶⢶⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⠈⣿⣿⣿⣧ ⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡅⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠏⠀⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⣾⠛⠛⠚⠻⠶⢦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣣⣿⡿⠿⣿ ⠀⠀⠀⠀⢠⡟⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠛⠃⠈⠁⠀⠀⠀⠈ ⠀⠀⠀⢰⡟⠀⠀⠈⢷⣄⣀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢦⣙⢶⠤⠀⠀⣠⡶⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠸⣷⠀⠀⢀⡴⠋⠉⠉⠙⠳⢦⣀⠀⠀⠀⠀⠀⠈⠛⢧⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⣄⠀⢀⣾⣡⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠳⢦⣾⠁⠀⠀⠀⠀⠀⠀⠈⠙⠲⢤⣙⣢⣀⡤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢾⡁⠀⠀⠀⠀⣀⣠⠴⠞⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣤⡴⠞⠋⠁⣀⣀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⠀⠀⢀⡶⢲⣿⡿⣿⣿⡻⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣷⣶⠟⣿⣿⣿⣿⡗⠆⠀⠀ ⠀⠀⠀⠀⠀⣷⡇⢰⠀⣿⡀⠘⢿⣿⣿⡿⠁⢘⣿⡄⠀⠀⠀⠀⠀⣀⡊⠀⠰⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠀⠀⠀⠀⠀⢧⠟⣻⡃⠀⢿⣿⣿⣿⡇⠀⢸⠀ ⠀⠀⠀⠀⠀⠋⣇⠘⣆⠹⡍⠓⠦⣄⣀⣤⡴⣫⣾⠃⢀⣠⡴⢖⣯⡥⠮⢤⡀⠈⠳⠯⠷⢤⣄⠀⠀⠀⠀⠀⢀⡀⠀⢀⣴⠟⢀⣀⣀⠀⠀⢦⣸⣿⣷⣽⣦⡀⠉⠉⠁⣀⡤⠜⠀ ⠀⠀⠀⠀⠀⠀⠹⣦⠙⢦⣬⣀⡉⠐⠒⠛⠋⠿⠗⠚⠉⢤⣴⠟⠉⠀⠀⣈⡟⠀⠀⢀⡀⠀⠈⢿⣄⣤⣴⠿⠋⠉⠉⠉⠀⠀⠀⣠⡴⠖⠲⣦⣌⡛⠿⠍⠙⠻⠯⠿⠝⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⡀⠀⠁⠀⠆⠀⠀⠀⠀⠀⣴⢿⡏⠀⠀⠀⢀⣸⣷⣤⣀⠀⠉⠓⠦⣄⣈⠉⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡄⠀⠀⠘⣦⠙⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠒⠲⠶⠼⢶⡶⠖⠻⣿⢸⠀⠀⠀⣴⣏⢸⣧⠙⠻⢿⣗⣒⠤⣄⣉⣉⣉⣤⣤⣤⣶⡶⠖⣿⢻⢿⡇⣄⠀⠀⠸⣧⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣌⢤⣀⠈⡧⠴⠯⣹⠀⠀⠰⣆⠉⠙⠳⢾⠿⡿⠚⠋⢉⡇⠀⢰⡏⠸⣎⠷⢹⣦⢀⣴⡿⠳⡷⠾⠗⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣌⣉⣁⣁⣴⠏⠀⠀⠀⣿⢤⣄⠀⠈⠀⢀⣀⡄⣾⠀⠀⡸⣧⠈⠘⠛⠾⠟⣫⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⠿⠛⠉⠀⠀⠀⠀⠀⡟⠀⠉⠙⠋⠉⠉⠉⠁⠁⠀⠀⠁⠙⢿⣷⣶⡶⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢸⡇⠀⠈⠉⠉⠁⣴⡿⠋⠉⠁⠀⣩⣿⣶⠀⠀⠀⢀⣀⣸⣷⣸⣧⣀⣀⣀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⢠⡄⠀⠀⢸⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢰⡏⠀⠀⠀⣀⡀⢻⣯⣻⣶⡾⠛⠛⠛⠋⠉⠉⠉⠉⠉⠙⠛⠻⢶⣶⣾⣿⣿⠟⠿⣿⣦⠈⣿⠀⢠⣿⣿⢳⡆⠀⠀⠀⠀⠀⠀⠐⠋ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠘⣷⡀⢰⣿⣿⣿⣶⡿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣷⡸⢿⡿⠀⠹⣧⣿⣿⣿⣬⡇⢹⡄⠀⠀⠀⠀⢠⡶ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠘⢷⣾⣿⠟⠉⠀⢀⣀⣠⣤⠶⠾⠿⠿⠿⠷⠶⣤⣤⣀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣾⡇⠀⠀⠻⣿⣿⣿⣿⠃⢠⡟⠀⠀⠀⠀⣾⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⢸⡇⠀⠀⠀⠀⠀⣠⣾⣿⠟⣀⣤⡾⠟⠋⠉⣀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⢷⣦⡀⢀⠀⠀⠀⠈⠻⣷⡀⠀⠀⣿⡇⣻⢸⠄⠈⡿⠒⡀⠀⠀⢿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⡇⠀⠀⠀⣠⣾⣿⣿⣿⣾⠟⠁⠀⣠⡶⠛⠋⠛⠳⢶⣄⣷⡀⠀⠀⠀⠀⠀⠀⠙⠻⣾⣷⢀⠀⠀⠀⠹⣿⣶⣶⣾⣿⣿⣾⣶⣾⣧⣴⣷⣴⣦⣼⣦ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⡇⠀⠀⣴⡟⠉⣠⣾⠋⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠙⢿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣾⣷⡄⠀⠀⠸⣿⡄⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⢸⡇⣠⣴⣿⡀⣴⡟⠁⠀⠀⠀⠀⠘⣿⡀⠀⠀⠶⠀⠀⠀⠈⢿⠿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡙⠀⠀⠀⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⢸⡇⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠘⣿⣄⠀⠀⠀⠀⠀⠀⢸⡇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡸⠀⠀⠈⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⠻⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣤⣀⣀⣀⣤⡿⠁⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⢻⣇⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⠀⠈⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠋⠉⢀⣴⡾⠛⠛⠶⣿⣦⣀⠀⠀⠀⠀⢸⣿⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⠀⣠⠀⠀⣾⠃⠀⠀⠀⠀⠀⠹⣿⡻⠀⠀⠀⢸⣿⠀⠀⣰⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣷⣶ ⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⣧⣠⣤⡾⠿⠷⣦⣄⠀⠀⣀⠀⠀⠀⠀⠀⢸⣧⣠⣿⠀⠀⣿⡀⠀⠀⠀⣀⠀⠀⠈⢿⡄⠀⠀⢸⡿⠠⢀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉ ⠀⠀⣀⣀⠠⠤⠔⠚⠻⢶⣤⡼⠟⠁⠀⠀⠀⠈⢻⣆⠀⢿⣿⣷⣄⡀⠀⠀⠙⠛⠁⠀⠀⠘⣷⡄⠀⠀⠉⠀⠀⠀⢸⣷⠀⢠⣿⠃⢀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠚⠋⠉⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀⢿⡆⠀⠙⢿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣀⠀⠀⠀⢀⣼⠇⢠⣿⡃⣠⣾⣿⣤⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠹⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠶⠶⠛⠁⣰⡿⣧⣿⠟⠉⠉⠉⠉⠉⠉⠉⠛⠛⠛⠳⠶⣶⣤⣤⣀⠀ ⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⡀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠈⠻⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⢿⣽⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛ ⠀⢱⡄⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⢿⡀⠀⠀⠀⠀⠀⢻⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣷⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⠸⣧⠀⠀⠀⠀⠀⢸⡏⠙⠷⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⠟⠋⣽⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⢿⡆⠀⠀⠀⠀⠈⣿⡀⠀⠈⠉⠙⠛⠓⠒⢶⣶⡖⠚⠛⠿⣭⣤⣤⣾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠈⣧⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⢀⣴⡟⠙⢿⣦⠀⠀⠀⠀⠀⠀⠻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢿⡄⢀⣤⡶⣶⠿⠛⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠙⣷⣄⠀⠀⠀⣠⡾⠻⣧⡀⠀⠀⠀⠀⣀⣴⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣆⠸⣿⡋⠁⠀⢸⣧⠀⠀⠀⢀⣾⠟⠁⠀⠀⠀⠀⠀⠀⠻⣦⣴⣿⡋⠀⠀⠘⢿⣄⢀⣴⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡀⠘⣧⠀⠀⠀⢿⣆⣠⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣄⡀⠀⠀⣻⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⢿⡆⠀⠀⠀⠙⢿⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡟⠁⠀⣰⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⣼⣿⣄⡀⠀⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠁⠀⠀⢰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⣄⡙⢷⣄⡀⠀⠀⠀⠉⠻⣶⣄⠀⠀⠀⠀⢀⣴⡿⠋⠀⠀⠀⣠⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠏⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣯⡛⠻⠿⣿⣦⣄⠀⠀⠀⠀⠙⠻⣦⣄⣴⠿⠋⠀⠀⠀⣠⣾⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡄⠀⠀⣉⣙⣿⣦⣤⡀⠀⠀⠈⠙⠻⢶⣦⣤⡶⣾⣿⣿⣷⣶⣶⣾⣖⡀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏⠀⠀⠀⠀⠀⠀⠀⢠ ⠀⠀⠀⠀⠙⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣶⣿⣭⣭⣥⣤⠉⠛⢷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣩⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣠⡿⠃⠀⠀⠀⠀⠀⠀⠀⡴⠋ ⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⡿⢟⣩⣽⣿⠟⠀⠀⠈⠉⢻⣶⣤⣀⠀⠀⠀⠀⣬⣭⣭⣽⣿⠿⠃⠀⠀⠀⠀⠀⣰⡟⠁⠀⠀⠀⠀⠀⠀⣴⠿⠁⠀ ⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⣿⡿⣋⣴⡾⣃⣤⡶⠾⠛⠻⣯⡛⢿⣿⡛⠛⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⣀⣠⣴⠋⣀⣀⣀⡀ ⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⡻⣿⣿⠟⠋⠀⠀⠀⠀⠀⠘⣷⡀⠈⡙⠿⢶⣤⣀⣀⠀⠀⠀⢤⠀⠀⠀⠀⢻⣀⣤⡶⠟⠋⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⣴⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣿⣿⣿⠿⢟⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⢌⡉⠴⣺⡗⠺⢿⣿⣿⡿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⢯⣄⠐⢿⣭⠂⠀⠙⠋⠟⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⠰⠠⢬⡁⠀⠀⢰⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠱⣪⣥⡐⠒⣀⠂⠀⡠⢹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⡤⢺⠤⣠⣔⢁⠠⠊⠀⢸⣿⣿⣶⣦⠤⢀⡀⠀⠀⠀⠀ ⠀⢀⡠⠄⠒⠉⡜⠀⢸⠀⢑⠚⢩⠲⠀⠠⣿⠁⠈⠹⣄⠀⠀⠐⠹⣶⣄⠀ ⠀⠎⠁⠀⠀⠀⢢⠄⠀⢲⠁⣸⠈⠀⠑⠁⡏⠀⠀⢶⡟⠃⠀⠀⢰⣿⣿⡄ ⠐⠀⠄⠀⠀⠘⡅⠀⠀⠀⠸⠜⠀⡀⠀⢸⠁⠀⠀⠀⣼⡶⠆⠀⣾⣿⣿⣧ ⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⢃⠇⠀⠈⠀⠀⠀⠀⠋⠀⠀⠀⠿⠁⠀⠻ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠱⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⢿⣩⠭⣉⡙⣻⣿⣿⠻⢶⣄⡀⠀⠀⠀⠁⠀⠀ ⠀⠀⠀⠀⢀⡀⠠⣤⣾⣿⣿⣾⣏⣧⣾⣿⣿⣿⣿⣿⣤⣹⣾⡿⣦⠀⠀⠀⠀⠀ ⠀⠀⢀⡜⠁⢀⡾⣿⣿⡟⣷⠯⠿⠏⠿⠿⣇⣿⣼⣿⣿⣿⣿⣿⣽⣷⠀⢁⠀⠀ ⠀⢠⠻⢸⠄⠸⣿⠟⠉⠀⢀⡰⠶⠊⢁⡀⠈⠳⣭⣝⠿⠿⣿⣿⣿⣿⣧⠀⠑⡄ ⠀⠌⡂⠈⣠⣾⡟⠀⠀⠀⢸⠋⣛⣿⣿⣙⣿⣦⣤⢤⣤⠀⠀⠙⢿⣿⣿⣷⣤⣀ ⠄⣠⢃⣼⣿⣿⠀⠀⠀⢻⢦⡓⠒⠊⠀⠈⠉⢏⡒⡠⠃⣀⠀⢠⠀⣿⣿⣿⣿⣏ ⠀⠸⣼⢸⣿⣿⡄⠀⠀⠀⠑⢌⣒⠶⠶⠶⠶⠦⠤⣒⠩⠊⠀⢸⠀⣿⣿⣿⣿⣿ ⡀⠀⢻⠀⢿⣿⣷⡀⠀⠀⠀⠈⡜⡏⠉⠀⢐⠟⠏⠁⠀⠀⠀⠃⢀⣿⣿⣿⣿⣿ ⠙⠳⡄⠑⣄⠩⠿⠿⠦⣀⠀⠀⠐⢜⣒⣒⣣⡊⡤⠔⠉⡽⠉⠢⣾⣿⡿⠓⠋⠀ ⠀⠀⢨⠋⠀⠀⠀⢀⡔⠁⢁⠖⠤⢄⣩⡿⠭⠜⠁⢄⠞⢀⡠⠀⠸⢄⠀⠀⠀⠀ ⠀⠀⡇⠀⠀⠀⠀⠀⠙⣄⠂⠀⡠⠊⠁⠀⠀⠀⠀⠀⠱⡭⠐⠀⠀⠀⠉⠂⢄⠀ ⢣⡀⢧⠀⠀⠀⠀⠀⠀⢸⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠐⢄⠀⠀⠀⠀⠀⢢ ⠀⠑⢌⠦⣀⠈⠁⢢⠄⠚⡷⣤⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠒⠄⡁⠀⠀⠀⠀⠀ ⠀⠀⢸⠀⠀⠀⠀⠀⠉⠐⠀⠀⠑⠢⢄⣀⣀⣀⡠⠔⠁⠀⠀⠀⠸⡄⠀⠀⠀⠠ ⠀⠀⠀⠣⣄⣠⡴⠯⢴⡶⢷⣾⣦⣀⠀⠀⠀⠀⠀⠀⠀⡠⠂⣠⣞⠑⠀⣤⠀⠀ ⠀⠀⢀⣼⡟⢷⣟⠠⠈⠱⠀⡛⠋⠏⠓⢦⢤⣤⢤⣴⣾⣷⣯⡛⢻⡟⠛⠒⠤⡀ ⠀⢠⠊⠘⣿⣸⣿⣶⠀⠴⣛⣿⣛⣂⠀⣉⣍⣽⣷⣿⠛⠭⠉⠈⢸⡇⠀⢀⡠⠆ ⣤⠇⠀⠀⠈⢻⣿⣿⣿⣶⣾⣭⡥⠭⣶⣿⣿⣿⠛⠊⠀⠀⠀⣶⣿⠁⠀⠀⠀⠀ ⡏⠐⠦⢄⡀⠀⢣⡉⠉⠛⣽⠟⠀⠀⠀⠙⠻⢿⣿⣦⣤⣤⡾⠟⠋⠀⠀⠀⠀⠀ ⠳⣄⡀⠀⠈⠉⠀⠙⠢⣴⠉⠀⠀⠀⢀⠆⠀⠀⣀⡠⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠉⠉⠉⠉⠉⠉⣯⠀⢀⡀⢠⣮⠔⡺⠉⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠉⢀⣿⠁⠉⠁⠒⢄⠈⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢀⡶⠋⠁⠀⠀⠀⠀⣼⣶⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢀⣿⡆⠀⠀⠀⠀⠾⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⣤⣿⣿⣿⠟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⡿⠋⠉⠻⣿⣿⣿⡇⠠⡤⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣇⠀⠛⠂⣼⣿⣿⣷⠤⠤⠔⠉⢹⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠻⠟⣿⣿⣿⣿⣿⣷⣖⠈⠀⣍⣋⣀⢼⠀⠀⠀⠀⢣⡸⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠉⠻⠿⣿⣿⣿⡄⠀⠎⠀⠀⠈⠀⠀⠀⠀⠀⣇⣻⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠈⠛⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡯⢿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⠀⠀⠀⠀⣀⣀⣀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡃⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⣲⠖⢲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⣈⣛⣿⣿⣿⠭⠤⠤⠤⢤⣄⡀⠀⠀⠀⠀⣀⣴⠿⠟⣛⣉⣴⠟⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⠟⠋⠁⣈⡿⠶⠟⠛⠛⠛⠚⠻⠤⣤⡈⠛⠦⠤⠖⢋⣡⠴⠛⠋⠉⠀⠀⠐⠶⣾⣟⠛⠀⣼⣻⠘⡿⣦⣤⣄⣠⣤⣸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⣤⡤⠴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⢸⡞⠋⠀⠀⠀⠀⠀⠀⠀⠀⢰⣌⠙⠀⠀⡿⠋⠰⠷⡿⢻⡿⢿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⢦⡄⢰⣆⣤⣸⣷⠀⠈⢻ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠉⠻⠿⠥⠤⠤⡤⠉⠉⠛⠒⠲⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⡏⠀⢀⣠⢴⠖⠶⢦⡀⠀⠀⠀⠀⠀⠉⠹⣼⡄⢺⠘⠟⢿⣿⡇⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠤⢤⣶⣶⠶⠶⠶⠶⠶⠶⠶⠦⠞⠀⠀⢀⣀⡤⠴⠶⠦⢤⣠⡇⠀⢿⡴⠋⣡⠴⢻⡟⢦⡹⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢸ ⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣆⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⠉⢀⣀⣀⣀⣀⣀⡀⣀⣀⡾⢁⡼⠁⠀⢸⠀⠀⢧⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣤⣼⣿⣄⣰⣶⢶⡆⠀⣼⠃⠀⢀⡶⠋⠀⠀⠀⠀⠈⢹⢹⣿⡇⣾⢧⠀⠀⣾⠀⠀⢸⠀⣿⢀⣤⣤⣤⣤⣤⣤⣤⣄⡀⠀⠀⠀⠀⢸ ⣇⣴⢦⣤⡀⠀⠀⠀⢠⡾⠋⠉⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠚⣿⠾⠁⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠘⣯⣿⣡⡏⢸⡀⢠⠇⠀⠀⢸⡇⣿⠾⣷⡝⠲⢤⣤⣤⣤⡍⣻⠀⠀⠀⠀⢸ ⣿⢡⡟⢿⣽⣆⣠⣴⣏⡀⠀⠀⣠⠖⠒⠒⠒⠒⣲⣄⠀⠀⠀⢁⣴⣴⣦⠀⢷⡀⠀⠀⠀⠀⠀⠀⠀⠹⣿⠻⣄⠀⣧⣿⠀⠀⣠⣼⡇⣿⢸⠛⠷⣤⣤⠤⠤⠴⠖⠛⠀⠀⠀⠀⢸ ⣿⣸⣶⣆⡟⢿⠀⠀⠀⣉⣳⣶⡥⠤⣴⣒⣾⣯⠿⢃⡟⢠⡗⠈⠁⠉⠘⢧⡈⠙⠒⠦⣄⡀⠀⠀⠀⠀⢺⣷⠿⣻⣧⣿⠒⠋⠁⢸⠇⡇⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠏⡿⣏⢙⡇⢸⠒⠚⠉⠉⠀⣠⡴⠚⠉⠀⠀⠀⠐⠚⠁⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠶⣤⣀⣾⣿⠐⡿⣽⠿⢦⡀⠀⢸⢰⡷⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠻⣌⣻⣥⡟⠀⠀⠀⢀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⠀⡇⢹⠀⠈⠛⢦⡼⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡆⠀⠈⠉⠁⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⡒⠒⠒⠒⠒⠻⣦⣿⣼⠀⡇⠸⡄⠀⠀⢠⠇⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠘⣇⠹⢦⣀⣀⣀⣀⣼⣿⣧⣴⠇⠀⡇⠀⢠⡞⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠉⠛⠷⠦⠤⠤⠤⠴⠿⢿⣿⠙⢦⠀⡇⢀⠞⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢤⣈⠛⠦⣄⣀⣀⠀⠀⢀⣀⡤⠤⠄⠙⣦⠈⠓⠟⠋⣠⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⢀⣀⣀⠈⠉⠙⠛⠲⢤⣉⣉⣀⣠⠤⠚⠉⠀⠘⠿⠯⠼⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⠸⣇⠀⠀⠀⠀⣿⣾⣿⣿⣳⢦⡀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⣴⢛⣧⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⢹⡆⠀⠀⠀⠈⠻⠿⣿⣧⣴⣷⡆⠀⠀⠀⠀⠘⣦⠀⣴⠋⢁⣿⡿⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠘⢷⡀⠀⠀⠀⠀⠀⠀⠚⠛⠙⢷⣄⠲⣆⠀⠀⠈⣇⠿⣦⠼⠟⠋⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠘⢧⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣛⣶⣶⣟⣤⠿⢶⡄⣠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⢸⠀⠈⠳⣤⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠟⢿⠿⠃⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⢠⠞⠀⠀⠀⠈⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⣠⣴⠶⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠶⢤⣤⣤⣤⣤⣤⠶⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠸⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⣀⣠⠤⠖⡚⡛⡋⠀⠀⠀⢐⢛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠈⠉⠉⠉⠉⠉⠙⠛⠒⠲⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸

⠀⠀⠀⣄⠀⠀⠀⠀⡇⠀⠀⠈⠛⢿⣿⣿⣿⣷⣄⠉⢻⠀⠀⠈⣿⣿⣿⣿⣿⣿ ⣀⣀⣀⣿⣆⠀⠀⠀⣷⠀⠀⠀⢠⣰⠙⢿⣄⣿⣿⣦⣀⠀⠀⠀⢸⣿⣿⣿⣿⣿ ⣿⣿⣿⣷⣿⡣⣀⣠⣿⣄⠃⢀⡀⠘⠂⠀⠙⠻⢿⣧⣼⡧⠖⠚⠿⡏⠉⠉⠉⠛ ⣿⣿⠏⣷⠞⣿⣿⣿⣿⡟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠉⠻⢾⠀⠀⠀⡇⠀⠀⠀⠀ ⣿⣿⣶⣶⣝⣌⡻⠿⠏⠀⠀⠀⠀⣀⡀⠀⣀⡀⢀⡀⠀⠀⠹⣖⠀⢸⠗⡀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠸⡸⡿⢂⠊⠐⢿⠇⡄⠀⠀⢽⠆⣼⣞⣃⢀⠀ ⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠅⣴⣯⣀⣲⣄⠈⠀⠀⠀⠘⣞⠋⠉⠋⠉⠀ ⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠘⠟⠿⡯⠿⠛⠁⠀⠀⠀⠀⠘⡅⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢠⠀⠀⠀ ⣿⣿⡿⠿⠋⠀⠀⠀⠀⠀⠀⠀⢴⣀⣉⢑⠒⠂⠀⠀⠀⠀⠀⠀⢀⡿⠈⠀⣀⡀ ⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠁⠀⠀⠈⠀⠀⠀⠀⢀⢾⡄⣰⣈⠛⣿ ⣿⣹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠂⢸⣧⣻⢺⢙⡎ ⣿⣧⠙⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⢁⡎⣾⣽⣿⡷⣼⠻ ⣿⣿⣷⣘⠳⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡰⢋⣠⠔⣼⣯⣿⣾⠻⣌⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⡼⡆⠀ ⠀⠀⠀⠀⠀⠤⠀⠤⡀⠀⢀⣆⣤⠀⠀⠀⠀⢀⡀⠤⠀⠀⠠⠤⣘⡀⠀⢃⠀ ⠀⠀⠀⢀⠎⠀⠀⠀⠀⠁⠪⠉⢷⡀⣀⠔⠈⠁⠀⠀⠀⠀⠀⠀⠀⠁⢂⠀⠆ ⠀⠀⠀⡌⠀⢀⠰⠀⠀⠀⠀⠀⠀⠈⠁⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀ ⠀⠀⠀⠁⠀⢁⠤⠮⠿⢷⣀⠠⣲⣖⠀⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁ ⠀⠀⠀⠀⢜⠀⠀⠀⠰⣶⣤⠈⠁⠀⠀⠡⡀⢘⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠉⢐⠖⣤⠤⠤⠄⢀⣀⣀⣀⣀⡺⡐⠁⡄⠀⢸⠁⠀⠀⠀⠀⠀ ⠀⢀⡀⠀⠠⠤⡇⠀⢏⣀⣀⣠⢰⠃⡘⠀⠀⠀⠣⡀⠇⠀⡈⢆⠀⠀⠀⠘⠀ ⡞⠁⡤⠀⠒⠺⣆⠀⠙⠊⠀⠊⢁⠠⠁⠀⢀⠀⢄⣊⣡⠸⠜⡕⠉⠀⡠⠃⠀ ⠑⠤⢈⠁⠒⢄⠈⠙⠶⣶⠶⠎⠒⠀⠈⠁⠀⠀⠀⠀⠘⢄⠁⡀⠈⠁⠀⠀⠀ ⠀⠀⠀⠈⠑⢆⠀⠸⣯⣭⠃⠀⢀⠤⣔⡂⠈⢉⠭⠭⠀⠉⠤⠜⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣶⣶⣶⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⣾⣿⣿⡿⠿⡿⠿⣿⠿⢿⣿⣿⣿⡿⠟⢹⠛⣩⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣀⣼⣿⣿⣿⣿⣶⣾⣷⣶⣶⣶⣶⡿⠿⢹⡅⣠⣿⠏⠙⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣠⣾⣿⣿⣿⣿⣿⡿⠟⠿⠿⢿⣿⣿⣿⣠⣶⣿⡿⠋⠀⠀⠀⣠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⠿⠇⠀⠀⠀⠀⠉⠻⢟⣿⠟⠁⠀⠀⣀⡄⠀⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠙⢿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠊⠉⠀⠀⠀⣼⣿⠔⠒⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢻⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⣠⣤⠔⠉⠀⠀⠀⠉⣲⡄⢸⠋⣴⣿⢾⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠠⣾⣿⣿⣿⣿⠁⠐⠒⠒⠒⠙⢋⠁⠀⠀⠀⠀⣠⠞⠁⣠⠏⢸⣯⡛⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢻⣿⣿⣿⣷⣄⡀⠀⠀⠀⡀⠈⢦⠄⠀⣠⣾⣧⣤⡶⠃⢀⣿⣿⠇⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠰⣷⣿⣿⣿⣿⣙⡿⣶⣤⣽⣾⢘⠷⣿⣯⡥⠴⠋⠀⠀⣼⢿⡁⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠻⣯⣿⣿⣿⠷⠀⠛⠛⣿⣿⠀⠀⠀⠿⠉⠀⠀⢀⡾⠃⣸⠾⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⢻⣿⣿⣿⠶⠀⠀⠈⢹⡄⠀⠀⠀⡄⠀⣹⡟⣁⠄⣿⠀⠈⠳⣖⢦⠤⠤⠤⠄⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢉⣽⣿⣷⡄⠀⣤⢸⡇⠄⠠⢀⡇⠀⠛⠁⣿⣠⣿⣇⠀⠈⢮⡀⢣⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠛⢆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣀⣴⣿⣿⣿⡻⣿⣦⣿⣮⣿⡀⠀⣎⣀⣀⠼⡆⠙⣿⠙⣿⡀⠀⢸⠇⠈⢆⠀⠀⠀⡀⠀⠀⠀⠀⠀⠈⡈⢦⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⣾⣿⣿⣿⣿⣿⣷⣽⣿⣿⣿⡿⠛⢾⢉⡡⠖⠒⠀⣬⣿⠱⠘⣇⢀⣀⣀⣀⠘⣆⠀⠀⠘⣦⡀⠀⠀⠀⡇⢧⠀⠱⡀⠀⠀⠀⠀ ⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣉⣉⣡⠤⠂⠀⢀⡞⠈⡖⠓⣋⣁⡠⠵⠚⡗⢾⡄⠀⠀⢳⠀⢰⠀⠀⡇⠸⡆⠀⠙⣆⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣷⢿⣿⣿⣿⣿⡛⠛⠋⠁⠀⠀⣠⠏⠀⢸⡗⣏⣀⣂⣠⣤⣴⣥⠀⢻⡄⠰⠀⠀⢸⠀⢀⠁⠀⣿⠀⠀⠸⢧⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⡾⣿⣿⣿⣿⣿⡶⠶⠖⠒⠉⠀⠀⢀⣸⣧⣽⠘⣇⡠⠋⠨⠁⠉⠒⠭⣦⠀⠀⣼⠀⢸⠀⠀⢿⡇⠀⢠⠸⡄⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣟⣁⡀⠤⠤⠒⠒⠈⠉⠁⠀⣹⣿⣠⣿⡀⢀⣾⠿⠗⠒⠀⠈⡇⣼⡇⢀⠇⠀⡄⢸⡇⢀⡏⠀⢱⡀ ⢸⣿⣿⣿⣿⣿⡿⠟⠋⠛⠛⣇⢀⣀⣀⣀⣀⣠⣤⣤⠐⣒⣈⣉⣀⣀⣟⣋⣡⣾⣃⣈⣤⣴⣖⣀⣿⣿⣇⣜⣀⣠⣷⣸⣀⣾⣇⣀⣀⣁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠤⠶⠶⠤⠤⢄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⠤⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠲⢤⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢢⡀⠀⠀⠀ ⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡄⠀⠀ ⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀ ⠀⢠⡇⠀⠀⠀⠀⠀⠀⠉⠉⠙⠓⠙⠉⣭⣭⡭⠭⢭⠭⠥⠀⠘⠀⠀⠀⠀⢳⡀ ⠀⣼⠀⠀⠀⠀⠀⠠⠶⣿⣶⣶⣷⣾⣾⡿⠆⠀⠀⠰⢷⣶⡷⠾⠶⣶⠄⠀⠀⡇ ⢠⡏⠀⠀⠀⠀⠀⠐⣶⡿⢖⠄⠀⠘⣺⡆⠀⢠⡇⠀⢸⣇⠀⠀⢤⢼⠀⠀⠀⡇ ⢸⠇⠀⠀⠀⠀⠀⠉⢹⣿⣧⣦⣶⣤⢟⠇⠀⢹⣧⠀⠘⢿⣶⣤⣶⠞⠲⠀⠀⡇ ⢸⠀⠀⠀⣀⣀⣀⠀⠉⠻⢿⣿⡿⢝⣡⣖⢠⣼⣿⣷⣤⣼⠛⠛⠛⠁⠠⣀⠀⠃ ⠈⣇⢀⠎⠁⠀⢀⣠⡤⣤⣤⣾⣶⣿⣿⣿⣛⣿⣿⣬⠝⠷⣷⣦⣤⡀⡀⢨⢸⠀ ⠀⠘⣎⠀⠀⣾⠛⠛⠉⠉⠁⠈⠙⠻⠿⣶⢶⣾⣿⣲⡦⠶⠒⠋⠉⢉⣙⡇⡏⠀ ⠀⠀⠘⢦⡀⠈⠛⠄⠀⠀⠀⠀⠀⠀⠀⢒⡩⠥⣍⠁⠀⠀⠀⠀⠀⠚⢁⠞⠀⠀ ⠀⠀⠀⠀⠙⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⠓⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠚⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠲⠤⠤⠤⠤⠤⠴⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⢹⡆⢦⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠠⠄⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡆⠀⠀⠀⠀⢀⡆⠈⠱⠟⢸⢦⣀⠀⠀⡴⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠶⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⣼⣇⠀⠀⠒⢤⣾⣿⠛⠒⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⣬⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄ ⠀⠀⠀⠀⢰⣿⣿⣷⣤⣦⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣝⢢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁ ⠀⠀⠀⠀⠘⠛⢻⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡙⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⡤⠤⣄⡀⠀⠈⢻⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⣿⠻⢷⣦⡹⣆⠀⠈⣷⡀⠀⠀⠀⠀⠀⣀⣠⣤⣴⣼⠅⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢹⣿⣧⣾⣿⡇⢹⠄⠀⠈⣿⣶⣶⣿⠿⡿⠿⠿⣟⠉⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⡏⠀⠀⠀⠀⠀⢠⡾⣿⣿⣷⣾⣭⡳⣄⠀⠀⠀⠀⠀⠀⠀⠀⢸⠹⣿⣿⣿⣿⡿⠷⠚⠀⠀⠀⣿⣿⡷⠟⠓⠛⠛⠚⠂⠛⢷⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⡟⠀⠀⠀⠀⢠⡟⣼⣿⣿⣿⣥⣿⣿⠙⣆⠀⠀⠀⠀⠀⠀⠀⢈⣓⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠈⣧⠹⣿⣿⡿⣿⣿⣿⠴⠛⠄⠀⠀⠀⠀⠀⢠⡄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⢦⣀⡀ ⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠘⠶⠼⠟⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠸⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠆⠀⠀⠀⠀⠀⢠⡟⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠷⣤⣤⣤⣤⡶⠞⠋⠁⠀⠀⠀⠀⣠⡆⣸⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠖⠀⠀⢀⡠⠆⢀⣧⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢼⣴⠾⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠙⠷⢶⣤⣤⣠⣀⣀⠀⠀⠀⣀⣀⣀⣤⡤⠴⠿⣷⠤⣥⣤⣀⠀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡇⢀⣠⣴⠟⢉⣉⣩⣼⠿⠿⣏⡧⣤⣀⣀⣀⡤⠾⣿⢷⣄⠈⠻⡟⢷⣽⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⠟⣾⡟⣭⣶⣶⣾⠿⠛⠳⣤⠀⠈⢻⡗⠶⠶⠶⠖⠋⠁⠀⠙⣦⠀⢹⡄⠈⠻⣿⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⣼⣟⣯⣽⠃⠀⠀⠀⠈⣷⠀⠀⢻⡆⠀⠀⢀⣄⣀⡀⠀⠘⣧⡀⢿⡀⠀⠘⢷⡐⠀⠀⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢿⣿⠏⣿⠇⠀⠀⠀⠀⠀⠙⣧⠀⢸⡇⡴⣞⣿⣏⣿⣿⠉⠛⠾⣧⣸⡇⠀⠀⠘⣿⡆⣄⠀⠉⠆⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⣿⡏⠀⣿⠀⠀⠀⠀⠀⠀⠀⠘⣆⣼⡧⠟⠋⠉⠻⢯⣿⡄⠀⣀⣀⣽⣿⠒⠛⠛⢿⣷⠘⠢⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⠁⠀⣿⡄⠀⠀⣀⣤⢤⡴⠶⠛⠁⠀⠀⠀⠀⠀⢘⣗⣿⠛⠉⠀⠀⠀⠀⠀⠀⢘⡇⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁⣽⡏⠀⠀⢸⣇⣰⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣀⣀⣀⠀⠀⠀⠀⠀⣀⣬⣀⣿⡇⠀⠀⠀⣿⣦⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣞⣀⣤⣄⣀⣀⠀⠀⠀⠀⢀⣰⡿⡡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⠉⣠⣶⣾⣿⣿⣿⣿⣿⣿⣇⠀⠃⠀⣿⣿⠀⠹⣦⡀⠀⠀⠀⠀⠀⣠⡾⠋⠉⠀⠀⠀⠀⠉⠉⠉⠉⠙⣿⣿⠎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣷⠀⣿⣿⣿⠿⠛⠙⠋⢹⣧⡛⢷⣤⣤⡿⢿⣤⠀⣂⠙⠓⠒⠒⠒⠛⠁⠀⠀⠀⣀⣀⣀⣤⡤⠤⠴⠒⢲⡿⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠶⠾⠛⠛⠉⠉⠉⠙⠛⠻⠷⢶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣴⡾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣦⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄⠀⠀⠀⠀⠀ ⠀⠀⢠⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣆⠀⠀⠀⠀ ⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀ ⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀ ⠀⢸⣇⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⣠⢶⠛⠋⠙⠓⢦⣄⠸⣿⠀⠀⠀ ⠀⠀⣿⠀⠀⠀⠀⣴⠾⠏⣿⣍⠉⠓⢦⡀⠀⠀⠀⢰⠏⢀⣼⠾⣲⡆⠀⠙⣶⣿⡛⢻⡆ ⠀⣤⣼⣧⡀⠀⢸⠏⠐⠺⣯⣽⡿⠀⠈⣷⠀⠀⠀⢸⡄⠀⢹⢿⣿⡷⠀⣠⡿⣿⡽⠟⠁ ⠰⣯⠡⣬⣽⠀⢾⣦⠀⠸⣯⣥⠇⠀⢠⡿⠀⠀⠀⠈⠳⣤⡈⠉⠁⣀⣴⣿⠀⠘⠻⣦⠀ ⠀⠙⠿⢾⣽⢷⣄⣙⡶⣤⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⣀⣀⣉⡙⠋⠹⠞⠁⠀⠀⠀⢹⡇ ⠀⠀⠀⢸⡇⠀⣶⠋⣿⢳⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠲⢿⣿⢀⣀⣤⢤⡾⢦⠀⠀⣼⠇ ⠀⠀⠀⢿⣧⣴⡃⠀⠁⠾⠁⣸⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠁⢸⡉⢿⠈⠷⠘⣧⣾⠟⠊ ⠀⠀⠀⣸⣏⠈⠛⢦⣄⡀⢰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⣀⣤⠾⣷⡀⠀ ⠀⠀⣰⠇⠈⠻⢦⣄⡈⠉⣿⣤⣤⣤⣄⣄⣄⣴⣄⣄⢸⣶⢶⠞⣿⡛⣋⣉⣠⠴⠾⣧⠀ ⠀⢠⣿⠀⠀⠀⠀⠈⠉⡿⢧⡤⣤⠤⠤⠤⠤⠼⠿⠿⢿⠿⣿⠛⢻⣿⠉⠁⠀⠀⠀⢹⣆ ⠀⠸⣿⠛⠲⡄⠀⠀⠀⠻⣼⡇⠙⠦⠤⠶⠶⠶⠖⠒⠚⠃⢸⠀⠀⠁⠀⠀⠀⣠⠴⢾⣿ ⠀⠀⢻⣄⠀⢿⠀⠀⠀⠀⢹⡇⠀⠓⠀⠃⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⠏⠀⣸⡏ ⠀⠀⠈⠻⣦⣾⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠸⣇⣰⡟⠀ ⠀⠀⠀⠀⠈⠙⠛⣷⠶⡄⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⣀⣠⣶⠟⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⠷⡄⠀⠀⠤⠤⠤⠖⠒⠒⠚⣛⣛⠉⠁⠀⠸⣿⣋⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣽⡷⠂⠀⠀⠀⣠⠒⠒⠒⠋⠉⠉⠉⠀⠀⠀⣛⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢿⣿⣶⡀⠀⠀⠙⠓⠒⠒⠒⠚⠉⠀⠀⠀⢠⣽⣷⠄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠠⠤⣴⡦⣦⠶⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⢀⣰⠟⠀⠘⣧⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⣤⣤⣄⣸⡏⠀⠀⠀⠿⣧⣤⣤⡄⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣸⣷⠀⠀⠀⢠⡿⠀⠀⠀⠀⠀⢻⡆⠀⠀⠀⠰⣿⣤⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠰⣿⣉⣈⣀⣀⣀⣸⡗⠀⠀⠀⠀⠀⢸⣧⣀⣀⣤⣤⣤⣼⡷⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⣀⣤⠤⠴⠶⠦⠤⠤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣴⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⡞⠁⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⣀⣈⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣾⠀⢴⡾⢿⣿⣿⣿⠿⣷⡆⢀⠴⣿⣿⣿⣿⣽⣛⡿⠶⠀⠀⠀⣰⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⡇⠀⠀⠉⠛⠛⠛⠛⠋⠁⠷⡬⠿⠛⠋⠉⠉⠉⣿⠀⠀⠀⠀⠀⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆⠀⠀⠀⠀⣿⠿⣿⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⢠⡾⠁⣠⠏⠀⣠⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣴⡋⣀⣾⣏⣴⡟⠉⠀⠀⠀⠀⠙⠳⣄⠀⠀⠀⠀⠀⠀ ⠀⣀⣽⡄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⡿⠋⠀⠀⠈⠙⢷⣀⡴⠶⣦⣄⠀⣼⢷⣀⣠⡶⣿⡆ ⢸⡿⠼⣧⣼⠃⠀⢠⡟⠀⠀⠀⠀⠀⣀⡴⠾⠛⠋⠛⢛⢶⣴⠋⠀⠀⣠⣄⡀⠀⠀⠙⣧⡤⠾⢻⣿⠁⠀⠛⣡⣾⠟⠁ ⠈⣧⠀⠀⡿⠀⠀⣾⠓⠒⠒⠶⣶⠞⠉⠀⣷⣴⣦⡜⣯⢧⣽⡤⠤⠾⠟⠛⠳⣤⢀⣠⡾⢳⡀⢸⠉⠳⠶⠞⠋⠀⠀⠀ ⠀⢹⣇⠀⣇⠀⠀⡇⠀⢀⣴⠞⠁⣀⡶⠟⠁⠀⠀⠳⣿⠛⠉⠀⠀⠀⠀⠀⠀⠉⢯⣅⠀⠀⠳⡿⠴⢖⣶⡄⠀⠀⠀⠀ ⠀⠀⣿⠀⢹⡄⠀⠛⠒⠋⠀⣠⡾⠋⠀⢀⠀⣆⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⣄⣤⣤⡴⠿⠋⠁⠀⠀⠀⠀ ⠀⠀⢻⡆⠀⠙⠦⠤⠤⠶⠛⠁⠀⠀⠀⢿⠈⢻⡾⣷⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠆⠘⠃⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢹⡆⢠⠀⠀⢠⡀⠀⠀⠀⡀⠀⠀⠀⠀⢀⣀⣀⠀⢀⣠⡀⠀⢠⣆⠀⢰⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠘⣧⠘⡇⠀⠀⣧⠈⠙⡏⠉⠉⢻⠉⠁⢺⣭⣍⢠⣾⣸⠇⢀⣾⣿⡀⣸⠀⡀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢻⡀⠻⠦⠄⢿⠀⠀⣧⠀⠀⢸⡀⠀⢸⡧⠽⠈⠟⠉⠳⠾⠇⠀⠇⠛⠊⠉⣹⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠸⣧⠀⠀⢀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢿⡄⠀⠈⠛⣖⠒⠰⡟⢲⣄⠀⣰⢷⡀⠀⣞⡓⠂⢸⡇⠀⣸⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢹⡀⠸⣟⢯⡁⠀⡷⠖⣇⢀⣌⣹⡄⠀⣗⠒⣿⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠈⠃⠀⠘⠀⠙⠀⠇⠀⠛⠀⠉⠉⠀⠀⠋⠀⠉⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠒⠒⠶⠶⠶⠦⠦⠶⠶⠶⠖⠒⠚⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⢰⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⠶⠶⠒⠒⠒⠲⠶⢶⣶⣶⣶⣶⡶⠒⠒⢒⣶⣾⣶ ⢸⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀⢀⣀⣀⣤⣤⣄⣀⡈⢻⣿⡟⠁⠀⠀⡀⢻⣿⣿ ⢸⣿⣿⣿⣿⡿⠁⠀⣀⣤⣶⣿⣿⣯⣭⣄⣀⡀⠀⠈⠹⣿⡀⠀⠠⣸⠇⠀⣿⣿ ⢸⣿⣿⣿⣏⣤⣤⣾⣿⡿⠟⠋⠉⣉⣉⣉⡉⠛⠃⠀⠀⠈⣿⠤⠾⠋⠀⠀⣿⣿ ⢸⣿⣿⣿⣿⣿⠟⠋⠁⠀⠀⡰⢫⣶⣿⣯⠺⠱⣄⠀⠀⠀⢸⡿⣄⠀⢤⣼⠋⢸ ⢸⣿⣿⣿⣟⣁⣀⣀⣀⡀⢰⠗⠃⠙⠛⠋⠔⠀⠀⠀⠀⠀⠈⡇⢸⢿⡟⠁⠀⢸ ⢸⣿⣿⣿⣿⡏⠉⠑⢌⠅⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠈⣧⡇⠎⠀⠀⠀⢸ ⢸⣿⣿⣿⠿⣷⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢠⠀⠀⠀⠀⢸ ⢸⣿⣿⡟⠀⠈⠂⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⢸⠀⠀⠀⠀⡜ ⢸⣿⣷⠃⠀⠀⠀⠀⠀⠀⠀⠙⠻⢦⡴⠏⠀⠀⠀⠀⠀⣠⠃⠇⠀⠀⠀⠀⠀⢀ ⢸⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⡾⠁⢸⠀⠀⡤⠀⠀⠀⢸ ⢸⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣿⣿⠉⠉⡏⠉⢻⠵⠋⠀⢀⣇⣼⢁⡅⠀⠀⠀⠈ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣖⣺⣿⣿⣥⡶⢄⣰⣿⠟⠛⠉⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⣠⡤⠀⠀⠀⠀⠀ ⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠓⠚⠁⠀⠀⠀⠀⠀⠀

⢰⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠤⢤⣤⣤⣤⣴⣴⣴⣴⣴⣴⣤⣤⣤⣤⣴⣤⡴⠶⠤⢶⠲⣶⣴⣶⣶⡦ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⢿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠰⣿⣿⣿⣿⣷ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣤⣤⣤⣤⣄⣀⣀⠀⠙⣿⣿⣿⡟⠁⠀⠀⠀⠀⣀⡐⠹⣿⣿⣿⣿ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⣀⣤⣴⣶⣿⣿⠿⠿⠛⠉⠁⠀⠀⠉⠉⠉⠛⠿⣿⣿⣿⠀⠀⠀⠀⢀⣸⣿⠃⠀⢻⣿⣿⣿ ⢸⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣷⣶⣶⣤⣄⡀⠀⠀⠀⠘⢿⣿⣄⡀⠀⠐⢣⣾⠏⠀⠀⠈⣿⣿⣿ ⢸⣿⣿⣿⣿⣿⣿⡟⣀⣀⣤⣴⣿⣿⣿⣿⣿⠿⠛⠉⠁⠀⠀⠀⠈⠉⡉⠉⠛⠛⠛⠀⠀⠀⠀⠀⠻⣿⣇⣤⣶⠿⠛⠀⠀⠀⠀⣿⣿⣿ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠁⠀⠀⢀⣤⠖⣛⣿⣷⣾⣟⡳⢦⣀⠀⠀⠀⠀⠀⠀⠀⢻⣯⣯⢄⡀⠀⠀⠀⢀⣼⡿⠋⣿ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠀⠀⠀⠀⠀⠀⢠⡟⢡⡞⣿⢿⣿⣿⡆⠙⠇⠻⣧⡀⠀⠀⠀⠀⠀⢸⣿⢹⣦⣄⡀⢙⣲⣾⠟⠀⠀⣿ ⢸⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣵⠟⠀⠻⢿⡿⠟⠁⡸⠂⠈⠈⠀⠀⠀⠀⠀⠀⠈⣿⡞⢏⣿⣿⣿⣿⠋⠀⠀⠀⣿ ⢸⣿⣿⣿⣿⣿⣟⣶⣶⣶⣶⣶⡶⠶⣶⣶⠂⠚⠉⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⣸⠏⣹⠟⠁⠀⠀⠀⠀⣿ ⢸⣿⣿⣿⣿⣿⣿⣿⣯⠉⠀⠀⠉⢦⣁⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣰⣿⢲⠇⠀⠀⠀⠀⠀⠀⣿ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠃⣸⠀⠀⠀⠀⠀⠀⠀⣿ ⢸⣿⣿⣿⣿⣿⡟⠛⠿⢟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⡇⠀⠀⠀⠀⠀⠀⠀⣿ ⢸⣿⣿⣿⣿⣿⠃⠀⠀⠙⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡆⠀⡆⠀⠀⠀⠀⠀⠀⢠⡿ ⢸⣿⣿⣿⣹⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣴⣆⡤⠀⢀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⣿⠇⢰⠃⠀⠀⠀⠀⠀⠀⠈⣇ ⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠶⢶⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠁⡿⠀⠚⠀⠀⠀⠀⠀⠀⠀⠀⣧ ⢸⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⣔⣤⣥⣾⠏⠀⣸⡇⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⣿ ⢸⣿⣿⣿⣿⣿⣦⣤⣄⣀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣤⣤⣤⣤⡠⣤⣶⣿⠿⠛⣿⠿⠁⠀⠀⡾⠀⣠⠤⢼⡋⠀⠀⠀⠀⠀⠀⣿ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠈⣿⠉⠉⠘⣷⣤⠞⠁⠀⠀⠀⣼⡇⣴⣿⠀⢠⡄⠀⠀⠀⠀⠀⠀⠉ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⣤⠴⣿⣶⣶⠾⠋⣀⡀⠀⠀⢀⣾⣿⣾⣿⡿⠞⠛⠁⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⣾⣿⣿⣿⣾⣿⣿⣉⣣⣴⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣀⣀⡀⢀⣀⣤⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣭⠾⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣉⣉⡉⡉⡉⠉⠁⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠶⠶⠶⠶⠶⠦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣟⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⣹⣿⣿⣏⠛⠃⠀⠀⠈⢛⣿⣿⣿⡛⠛⠃⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⢿⣿⣿⣿⠀⠀⠀⠀⠀⢺⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⢤⡀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠉⣉⣉⣀⠀⠀⠀⠀⠀⠀⠀⠙⢾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣦⡄⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡆⠀⠀⠀⠘⠋⠙⠻⠿⢿⣿⣿⣿⣿⣯⣤⠴⠋⢸⡆⢀⣤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⢁⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠸⣿⣷⣦⣤⣀⡀⠀⠀⠀⠀⠈⠛⠶⣤⣀⣀⠀⠀⠀⢀⣀⣠⡴⠞⠋⠛⢿⣿⣦⣤⣶⣶⣾⣿⣿⣿⣿⣿⣿⣷⣶⣦⣀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠿⣿⣷⣶⣶⣤⣤⣄⣀⣀⣉⣉⣉⣉⣉⣁⣀⣠⣤⣶⣾⣿⠿⢿⣿⣿⣥⣤⣄⣀⣀⣀⡀⠀⠀⠈⠻⣿⣷⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠛⠛⠻⠿⠿⠿⠟⠛⠛⠛⠛⠉⢻⡇⠀⠀⠘⢿⣿⡀⠉⠉⠉⠙⠛⢿⡷⣶⠀⠘⣿⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠈⢿⣷⡀⠀⠀⠀⠀⣾⠇⣿⠀⢠⣿⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣸⡇⣰⡇⠀⠀⠘⣿⣇⠀⠀⠀⠀⣿⠀⣿⣀⣾⡿⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣠⣶⠟⣿⣿⣯⣽⣭⣭⣹⣿⣿⣿⣷⣶⣶⣿⣿⣤⣤⣤⣴⣿⣶⣿⡿⠟⠁⠀ ⣀⣤⣤⣤⣶⣶⣶⣾⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠛⠛⠛⢻⣟⠻⠿⣿⣿⣿⣿⣿⡿⠿⢻⣿⣿⣿⣿⣿⣿⣉⡉⠉⠉⣿⢩⣿⠀⠀⠀⠀ ⠛⠛⠛⠋⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠉⠉⠛⠿⣿⣶⣤⡏⢸⡏⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⢶⣶⡶⠾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⣿⣾⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣇⠀⠀⠀⠀

⣿⣿⣿⠿⠿⡾⡟⠿⠿⠻⠛⡟⡟⢥⡉⠛⡿⠙⠏⠻⢓⣤⣀⠀⠀⠀⠀⠀⠀⠆ ⣿⣿⣿⣧⣀⠨⢛⣦⠂⠀⢸⣿⣿⣦⣽⣀⢀⣀⣈⣤⣿⣿⡿⣷⡀⠀⠀⠀⠀⠃ ⣿⣿⣿⣿⣿⣷⣾⠿⣑⡀⣠⣾⡿⠏⢠⡿⠛⠻⠿⠿⠷⠯⠉⣉⡹⢤⢠⠀⠀⠀ ⣿⣿⣿⣿⡟⡻⡏⡔⣸⡁⠠⢟⠀⢀⠈⠉⣼⢁⣾⡆⠀⠤⠄⣐⣖⠈⠉⠀⠀⠀ ⣿⣿⣿⣿⡿⣵⣿⣫⣼⣿⠟⢡⠊⠀⡀⠀⢏⠸⣿⣧⡘⠠⡠⡏⣾⣷⣦⣄⢀⣀ ⣿⣿⣿⣿⣧⣿⣾⣯⡟⡁⠀⣭⢀⢌⡒⡀⢈⡢⢬⠵⢥⣧⣴⣾⣺⣻⣫⡟⠀⠛ ⣿⣿⣿⣿⣿⣿⡿⣻⢿⣷⣠⣜⢸⣿⣸⣧⣏⣀⣯⣜⢂⣿⡟⠛⠛⠛⠓⠓⠀⠐ ⣿⣿⣿⣿⣿⡟⣵⣿⣿⣿⣤⣿⠀⠸⣿⡞⣿⢻⠉⢿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⡟⣼⡿⢹⡝⠉⢸⣷⡱⠤⠸⣯⡟⠸⣧⣰⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⡿⣽⠟⠃⠜⡄⠀⠈⠈⠓⢽⠰⠋⠀⡄⠈⣿⣦⣵⡀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⠳⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⣀⠈⠀⠀⢂⡘⣷⠀⣠⡜⢿⠿⣿⣿⣿

⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣾⣿⣿⣿⣿⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⣿⣿⣿⣿⣾⠆⠙⠳⠾⢫⡝⢛⣿⣿⣻⠿⣿⣇⢻⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⣿⣿⢳⠕⠁⠀⠀⠴⠊⣡⣴⣶⠎⠀⡿⣿⣿⣾⣿⠇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⢋⣿⣩⣥⣆⡀⠀⠤⠟⠊⠁⠀⠀⢱⠙⣿⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣼⣿⣿⡏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⢹⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⢏⢿⣿⣿⣄⠀⠀⠂⢉⠀⠀⠀⠀⢀⡏⣾⡨⡜⢄⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣷⣾⣶⡿⣿⣛⢿⣦⣄⠳⠾⠉⠀⡠⠂⠁⠏⠇⠀⠀⠙⢶⠤⣀⠀⠀⠀ ⣿⣿⣿⡿⡿⣷⠟⣿⠿⣟⣿⣄⡽⠂⠀⠊⡹⠆⠀⠀⠀⠀⠀⠀⢀⠃⠀⢈⡴⠤ ⣿⣿⣿⣿⣥⡙⠀⠈⠀⠠⠁⢹⠓⠒⠀⠀⠇⠀⠀⢀⣴⠂⠠⠄⡜⠀⣰⠛⠀⠀ ⣿⣿⣿⣿⣿⣿⠲⣂⣀⠤⠀⡞⡀⠀⠀⢰⠀⠀⠀⠈⠀⠀⣠⠎⠀⡰⠁⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣫⡽⣓⣥⢇⠈⠑⠀⢸⠀⠀⠀⠀⢀⠜⠁⢀⣰⠃⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣾⠋⠀⠀⠉⠐⠂⠤⠀⠀⠀⡠⠂⠀⠀⠀⡌⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣤⣄⣤⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⠶⠟⠛⠋⠉⠉⠉⠉⠉⠉⠉⠁⠀⠉⠉⠛⠷⢦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠲⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠖⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠁⠀⠀⠀⠈⠉⠉⠉⠙⠛⠒⠛⠛⠛⠛⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣟⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣼⣿⡿⢿⣷⢀⣠⣀⡀⠀⠀⠀⠀⠀⠀⢀⠤⠒⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⣾⡟⣿⢿⣇⣘⠁⠀⠀⠉⠓⠀⠀⠀⠀⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⣿⣿⡷⠋⠸⠁⠈⠓⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀ ⠀⠀⠀⢰⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⣠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀ ⠀⠀⢠⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣷⠀⢠⡼⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀ ⠀⢀⣾⣿⠟⠇⢠⡏⠀⠀⠀⠀⠀⠀⠀⢦⣀⡏⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀ ⢀⣿⣿⣯⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠃⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀ ⢸⣿⣻⡇⡈⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⠟⠀⠀⠈⠳⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⣿⢸⣿⡇⢸⣿⣶⣤⣤⣤⣤⣤⣀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⣤⣤⣤⣴⣶⣶⣾⠟⠛⠁⠀⠀⠀⠀⠀⠈⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆ ⠀⣿⣸⣆⠈⠀⢻⣿⡿⡇⠀⠀⠀⠈⠙⣶⣤⡷⢤⣤⠤⢤⣄⣤⣾⣿⣿⣿⣿⣿⣿⠿⠿⠿⣽⠻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁ ⠀⢿⣿⡿⣁⣀⡈⢻⣷⡳⣄⠀⠉⢁⣼⣿⣿⣧⡀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡿⠋⠁⣤⠦⣄⠈⢿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⢸⣿⣿⣿⡏⠀⠘⣿⣷⣮⣵⣶⣾⣿⣿⠁⢺⡄⠀⢠⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⣗⣻⣹⠀⣸⡽⠀⠀⣠⣴⠶⠖⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀ ⠀⠀⣿⡟⢹⣧⡀⠀⠀⠉⠿⢿⣿⣿⣿⣿⠃⠀⠙⠠⠿⠿⡟⠏⠙⡿⣿⣿⢽⢦⣀⠀⠉⢁⡠⣿⢃⡴⠟⠉⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀ ⠀⠀⢻⣇⢸⣻⣿⣶⣄⠀⠀⠀⠈⢹⣿⣿⣧⡀⠠⠄⠀⠀⡿⠶⣦⣥⡈⠙⢿⣶⣍⣽⠿⠿⣛⣵⠏⠁⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀ ⠀⠀⠘⣿⣼⢸⣿⣿⣿⣦⡀⠀⢀⣾⣿⣟⢹⠀⠀⠀⠀⣼⡆⠀⣿⣿⣿⣷⣤⣀⠀⠉⠉⠉⠁⠀⠀⣠⡤⠶⣆⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢚⠂⠀⠀ ⠀⠀⠀⠘⣿⣿⣿⣿⣯⢈⡻⠿⠿⠇⠈⠻⣾⠀⠀⠀⣼⣏⣀⣲⠏⠀⠀⠀⠈⠉⠳⣶⣤⣄⣤⣴⠟⢁⡴⠀⠹⠄⠀⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀ ⠀⠀⠀⠀⠹⣿⡿⣿⣿⣆⠹⣦⠀⠀⠀⠀⣾⠀⠀⢨⡟⡋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⢁⡴⠋⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠻⣷⣾⠈⣿⣇⡸⣷⣄⠀⠀⢻⣶⣾⡿⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡾⠋⠀⠀⠀⠀⣠⢿⣯⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⢻⣼⣹⣿⣿⡈⠛⠻⣶⣴⣿⣯⣀⣀⣬⣷⣤⣀⠀⠀⣀⣠⡤⣶⣪⡽⠋⠀⠀⠀⠀⢀⣾⣷⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣻⣹⣿⣄⠘⣦⣍⠉⠉⠙⠛⠛⠛⠛⠛⠛⢛⣫⠍⠉⠁⠀⠀⠀⠀⠀⠀⠀⣾⣿⠿⠃⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣈⢿⣆⠈⠛⠻⣷⠀⠀⠀⠀⡶⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣧⣹⣦⡀⠀⢸⠀⠀⠀⠀⠱⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⢿⣿⣝⡄⠸⣆⠀⠀⠀⠀⠘⣳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠻⠷⣾⣅⡀⠀⠀⢠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠞⠋⠁⠀⠀⠈⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⢳⣶⣦⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⠾⠋⠉⠀⠀⠀⠀⠀⠀⠀⢸⣿⢀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⣿⣿⠿⠿⠶⠿⠿⠿⠿⠿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣞⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠓⠆⠀⠀⠀⠀⠀⢀⣠⡤⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⢒⠾⠿⠧⠤⢔⠢⠤⡒⠍⠓⠊⢤⡄⢰⣤⣄⣀⣸ ⠀⠀⠀⠀⠀⠀⣀⣀⠀⢈⣉⠁⠀⠀⠀⠀⠀⡇⡄⠀⠀⠀⠀⠀⢠⣮⢨⣍⣏⢹ ⠀⠀⠀⠀⠀⠈⠢⢬⡍⠁⠤⠤⢃⡠⠤⠤⠤⠇⡧⡪⢱⢫⢆⠀⠀⠉⠀⠉⠉⢸ ⣄⡀⠀⠀⣀⠤⠀⠀⠷⠴⣶⡰⠁⠔⠉⠉⠙⣿⠱⡆⡘⠀⣼⣠⣄⠀⢠⠄⠀⢸ ⣯⣻⣦⠐⠅⣠⣂⣀⡶⡄⡈⠶⢆⠦⣀⠀⠀⢹⣣⣵⡅⠔⣿⡘⠃⠐⠚⠂⠀⢸ ⢻⣭⡸⠈⢁⠔⠉⠀⠀⠁⠁⠀⠀⠀⠀⠈⠐⢼⡇⢻⠱⢀⢸⠁⠀⠀⠀⠀⠀⢸ ⠀⠈⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢀⡰⡪⣉⣉⣺⣧⠈⠀⡘⠆⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠄⣂⣄⣉⣉⡉⢍⢫⠢⢔⡜⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠘⠄⠀⢆⠀⠰⣶⡦⠄⠁⠐⠈⠀⡠⣫⡉⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⢘⣄⠀⠈⠙⠛⢄⣄⡈⡞⣄⠋⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⡀⠀⢀⠈⠢⢄⠀⠀⠀⠛⠛⠉⠈⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⢠⠃⠀⣈⠀⠀⠀⠑⠄⣀⠀⢀⡠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⣀⠠⠴⠁⠀⡜⠁⠀⠀⠀⠀⠈⠂⠀⠃⠤⠤⠤⠄⡀⠀⠀⠀⠀⠀⠀⠀⢸

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠷⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣤⣀⣤⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡯⠟⣉⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠒⢛⣿⠽⠿⠿⠯⠯⢭⣉⠓⢤⡤⠴⣒⡭⠔⠒⠚⠉⠠⣤⡴⠂⢰⣦⢴⣤⣀⡀⣀⣸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠤⠴⠋⠁⠀⠀⠀⠀⠀⠀⠈⢗⠀⢰⠊⠁⠀⠀⠀⠀⠀⠀⠎⠁⢀⡸⠋⠸⠿⢻⡿⠿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⠴⠒⠲⠤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⡞⠀⠀⢀⣀⡀⠀⠀⠀⠀⠰⣿⣿⠆⣼⣶⣾⣿⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⣀⣩⣉⠩⠍⣀⣀⣀⣀⡽⠀⠀⢀⣀⣀⣀⣀⣸⠀⣧⡤⢚⡩⢬⣍⠳⡀⠀⠀⠀⠀⠙⠃⠁⠈⠉⠙⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄⠀⠀⠀⠀⠀⣠⠞⠉⢁⣠⣀⣀⣀⣉⣀⡟⣱⠋⠀⠈⠀⢧⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⣀⡤⠔⠒⠒⠒⠼⠷⣴⣾⣿⣄⡼⠁⢀⠞⠁⠀⠀⠀⠀⣯⣿⢇⠿⡀⢀⡇⠀⢸⣸⣇⣤⣔⠒⠒⠒⠦⢤⠀⠀⠀⢸ ⣷⢫⣿⣦⡀⢀⡼⠁⠀⢀⣠⠤⠤⢤⣀⠀⠀⠈⢋⣀⡀⢸⡀⠀⠀⠀⠀⠀⠸⣿⣾⠀⣇⡼⠀⠀⣸⣿⡏⡿⣏⠉⣁⣉⣹⣼⠀⠀⠀⢸ ⣷⣿⣮⡿⡏⠉⠈⣑⣶⠮⠤⣤⣶⠾⠟⣱⢠⡆⠉⠉⠙⢄⠙⠢⠤⣀⠀⠀⠀⢹⣾⢷⣿⣷⠒⠋⢹⢻⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠛⣿⣉⠇⡟⠋⠉⠀⢠⠔⠉⠀⠀⠀⠘⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⢤⣼⡇⢸⢿⠟⢦⡀⢸⢸⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠙⠶⠟⠁⠀⠀⢴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣠⣄⣿⡇⢸⠘⡆⠀⠙⡏⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠈⣏⠦⣀⣀⣀⣈⣿⣧⡼⠀⡇⠀⡸⢡⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠉⠛⠒⠒⠒⠚⠚⠻⣿⠳⡄⣇⡰⢁⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⡄⠀⠀⠀⠘⠒⠦⠭⢶⣤⠤⠤⠄⠖⣊⠤⠈⢦⣈⣩⣠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡆⠀⠀⢸⡇⠀⠀⠠⣾⣶⣶⣤⡀⠈⠉⠓⠒⡋⠁⠀⠀⡼⣯⠉⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⢷⠀⠀⠀⠙⠿⠿⣥⣿⡄⠀⠀⠀⠹⣄⣰⠋⣱⣿⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣧⡀⠀⠀⠀⠀⠉⠉⠻⣤⣳⣄⡀⣸⠙⣶⡋⠁⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠈⡆⠱⢄⠀⠀⠀⠀⠀⠀⠈⢿⣷⣿⡷⠋⠉⠉⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠰⠃⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⢀⠀⠀⠀⠀⠀⠙⠦⣄⠀⠀⠀⠀⠀⠀⣠⠴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⢀⡶⠋⠀⠀⠀⠀⠀⠀⠀⠀⡍⠁⠐⢲⡒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⢀⣠⠤⢖⠚⠃⠀⠀⢐⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠉⠒⠒⠒⠒⠒⠲⠤⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣍⣉⣡⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣍⡁⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⡅⠉⠉⠉⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠀⠀⠀⠀⠀⠀⢰⣶⡆⠹⣯⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⡏⠉⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣸⣿⣿⣿⡏⠉⠓⠀⠀⢀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⠴⠶⠓⠀⠀⠀⠀⠀⠘⢿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠘⠿⠟⠀⠀⠀⣀⣠⡤⠶⠞⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⡿⡿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠀⡇⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡇⠀⢀⣠⠼⠖⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢱⡰⠋⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢈⡇⠀⠀⠀⠀⠀⠀⠀⢹⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⢰⡖⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⣰⣟⣣⣼⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⣠⠞⠳⣍⣋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠖⠋⠀⠉⠉⠉⠒⢦⡀⠀⠀⠀⠀ ⠀⢠⠞⠀⠀⠀⠀⠀⠀⣰⠁⠀⠀⠀⠉⠙⠒⠒⠶⠤⠤⠤⣤⣤⣤⡤⠤⠤⠔⠒⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀ ⣠⠋⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠙⣆⠀ ⠉⠉⠁⠉⠉⠀⠀⠉⠉⠀⠈⠉⠉⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣠⠴⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡟⠁⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⡄⠈⡇⢀⣴⣋⣠⠤⠤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢷⣀⣀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠈⠉⠉⠉⠛⠒⠤⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣶⠇⢀⡵⢯⠀⠙⢦⡀⠀⠀⠈⠉⠓⠦⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢀⣀⣠⣤⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⡔⠁⠀⠀⠀⠀⠀⠳⡄⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣄⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠘⣤⣴⠾⠃⠀ ⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⢿⣦⡀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠹⡆⠀⢳⠤⣄⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀ ⠀⠀⢀⡤⠟⠛⠛⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢣⡀⠀⠀⠀⠀⠘⡆⠙⢿⣦⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⢸⣷⡌⢳⠀⠀⠀⠀⠀⣇⣀⣀⡀ ⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢳⠀⠀⠀⠀⠀⢹⠀⠈⢿⣧⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⢸⡿⢃⡞⠀⠀⠀⠀⠀⡏⠉⠀⠀ ⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢸⣤⡤⠤⠴⡶⡿⠃⠀⠈⣿⡀⣿⡄⠀⠀⠀⠀⠀⠀⢠⡟⠀⡞⠛⠋⠀⠀⠀⠀⠀⢰⣃⠀⠀⠀ ⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣾⡿⠓⠒⠲⢤⣀⢻⠁⠘⣿⣦⡀⠀⠀⠀⣴⠟⠀⡼⠁⠀⠀⠀⠀⠀⠀⣰⡞⠙⠛⠶⠀ ⢸⣿⣧⡀⠀⠀⠀⠀⠀⢰⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀⠀⠀⠀⠉⠛⠤⣀⣘⣧⡙⠒⢲⡾⠃⢀⠞⠁⠀⠀⠀⠀⢀⣠⡾⠋⠀⠀⠀⠀⠀ ⢸⣿⣯⣷⣄⠀⠀⠀⠀⠸⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠙⣟⠈⣁⡴⣃⣀⣀⣀⡤⣶⣾⡿⠋⠁⠀⠀⠀⠀⠀⠀ ⢸⠛⠋⠻⣿⢷⣄⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠾⠽⣶⣦⣤⣤⣤⠤⠤⠄⠀⣸⠛⢻⡉⠉⠉⠉⠉⠙⠻⢥⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣇⡆⠀⠈⢷⣝⢦⡀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡉⠉⠛⠛⠿⣄⡀⠀⠀⢰⡇⠀⠀⠀⣠⠞⠉⢧⠀⠹⡄⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀ ⠀⢿⣧⡆⡀⠀⠙⣮⢻⡄⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢀⡇⠀⠀⠀⠀⠀⡇⠀⠀⢈⡇⠀⠀⡼⠁⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⣀⣤⡄⠀ ⠀⠈⢿⡧⣇⠆⠀⠘⡇⢻⡄⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⡼⠀⠀⠀⠀⠀⢸⠃⠀⠀⡾⠀⠀⣸⠁⠀⠀⠀⠀⠀⣄⠀⢹⣖⠦⣄⠀⠀⠀⠀⠀⠈⣟⠉⠁⠀⠀ ⠀⠀⠀⠹⣿⡀⠀⠀⠀⠀⢷⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣭⣑⣒⣲⠶⠟⠀⢀⡞⠁⠀⠀⡇⠀⠀⠀⠀⠀⠀⠸⡆⠀⣿⣷⢺⡄⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀ ⠀⠀⠀⠀⠈⠻⣷⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣀⡴⠋⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⢠⡇⠀⡟⣫⡞⠀⠀⠀⠀⠀⠀⢸⠛⠛⠛⠀ ⠀⠀⠀⠀⠈⠳⣄⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⡀⠀⠀⠀⢿⡄⠀⠀⠀⠀⢀⣾⠃⢸⠉⠁⠀⠀⠀⠀⠀⠀⢈⡟⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠓⠤⠀⠈⠙⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠉⠁⠀⠀⠀⣠⠜⠃⠀⠀⠀⠈⢿⣄⡀⠀⣠⡿⠃⣠⠏⠀⠀⠀⠀⠀⠀⠀⣠⡾⠛⠳⠶⠀⠀ ⠀⠀⠀⠐⠦⣄⠀⠀⠀⠀⠀⠀⠀⠐⠲⢤⣄⣀⣈⣉⠉⠁⠀⠀⠀⠀⢀⣀⣀⣤⡤⠖⠋⠁⠀⠀⠀⠀⡾⢠⠈⢳⣍⢫⠟⢀⡔⠃⠀⠀⠀⠀⠀⢀⣠⣾⠟⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⠉⠙⠛⠛⠛⠛⠋⠉⠉⢁⣀⣀⠄⠀⠀⠀⠀⣤⠈⠁⣼⠀⡆⢳⠴⠾⣇⣐⡒⠤⠤⠤⣴⣾⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⠯⠍⠿⠛⠛⠋⠉⠀⠀⠀⠀⠂⠀⠀⠀⠘⠃⣼⠃⢘⡆⠀⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠈⠁⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠤⠤⠤⠤⠤⢤⣄⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣠⠖⢛⣉⣁⡀⠤⠆⠀⠀⠀⠀⠠⣄⣩⠗⠦⣀⠀⠀⠀ ⠀⠀⢠⠞⠀⠸⡿⣧⣄⣉⠆⢀⠂⡆⠀⠰⣿⢏⣉⠐⡄⠈⢦⠀⠀ ⠀⢠⢫⡤⠀⢀⣀⡀⠀⠤⠤⣾⡀⢡⡆⢀⠀⠀⠉⠉⠀⠀⠈⣷⠀ ⢀⡏⠀⠛⠓⠦⡖⣒⠤⢶⣶⡦⣈⡡⡤⣀⡀⠉⠀⠀⢂⣰⡶⢸⡆ ⢸⠀⠀⡯⢾⣦⣧⢄⣸⠉⡏⢰⠘⡗⢻⠓⡟⠻⠘⡉⡍⡋⡇⢸⡇ ⢸⡀⠀⠘⢾⣿⣬⣿⣿⡙⣛⣞⡿⣿⣻⣟⣿⣾⣭⡏⣻⡝⠀⢸⠁ ⠈⢧⠀⠀⠈⠻⢽⢿⢷⣋⣀⣈⣄⠀⢱⣹⣻⣿⢯⡵⠊⠀⠀⡸⠀ ⠀⠈⢧⠀⠀⠀⠀⠙⠾⢾⡬⣬⣤⣇⢡⡴⠜⠒⠉⠀⠀⠀⢀⠇⠀ ⠀⠀⠀⠳⣦⠀⠀⠀⠀⠀⠉⠉⢛⠋⠉⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀ ⠀⠀⠀⠀⠈⠓⢄⡀⠀⠑⠠⠤⠣⠀⠀⠀⠀⠀⢀⡠⠔⠉⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠑⠂⠤⠤⠤⠤⠄⠐⠒⠉⠁⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⡠⡒⣉⠠⠜⠒⠊⠓⠒⡄⠹⡀⠙⠛⢷⣄⣀⡀⠀⠀⠀ ⠀⠀⠀⢀⠞⣰⠉⠀⠀⠀⠀⠀⠀⠀⢹⣄⢹⣦⣤⣸⣽⡇⡼⡗⣄⠀ ⢀⣠⡴⠟⣠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠈⡸⣸⠐⠙⣿⣇⠁⣇⣿⢎⠆ ⡰⠣⢱⣼⡟⠀⠀⠀⠀⠀⠀⢀⣀⣤⡤⠄⠁⠀⠄⢹⣿⢻⣿⠁⠸⢸ ⠳⠥⢮⡏⠃⣤⣤⣤⡀⠀⠘⠛⣿⣏⠀⠀⠀⠀⠀⠸⣿⣼⣿⠀⠀⠀ ⠀⠀⠘⢧⠀⠈⠛⠑⠇⠀⠀⠈⠁⠀⠀⠀⠀⠀⡀⠀⡿⢿⣿⠀⠀⠀ ⠀⢠⠀⢨⡇⠀⠀⠀⢔⢀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⡠⠊⣹⠀⠀⡀ ⠀⢸⠀⢸⡏⠀⠀⠀⠰⠶⠢⠀⠀⠀⠀⠀⠀⠎⠀⠠⢃⡠⣿⠀⣠⠁ ⠀⠘⡆⢾⣽⡀⠀⠀⠀⢁⠁⠀⠀⠀⠀⢀⠎⢀⡠⠺⠁⠀⣿⣄⡿⠀ ⠀⠀⢡⢸⣿⠈⠂⠄⣀⠀⠀⠀⠀⣀⠔⠁⠀⢸⠀⠀⠀⠀⣿⣿⡇⠀ ⠀⠀⠈⣼⢻⠀⠀⠀⠀⠈⠉⢹⠏⡇⠀⠀⠀⣀⠦⠄⡀⢀⡇⢹⠀⠀ ⠀⠀⠀⠸⡈⠀⠀⠀⠀⠀⢀⣨⠗⢀⡀⣀⡞⠁⠀⠀⠈⢾⠀⠘⠀⠀ ⠀⠀⠀⠀⠁⠀⠀⠀⠀⡔⡱⠋⠀⠁⣀⡎⠀⠀⠀⠇⠀⠘⡀⠀⠀⠀ ⠀⠀⠀⣤⣤⣀⣀⣀⡰⣼⣀⣀⣀⣾⡿⣵⣀⣇⡀⢸⠀⠀⡇⠀⠀⠀ ⠀⠀⠀⠙⠛⠛⠓⢚⡻⠏⠺⠞⠓⠻⠿⡛⠛⠟⠛⠈⠀⠀⢠⠀⠀⠀

⠀⢸⣿⣿⣿⣶⠄⢰⠻⣿⣿⣿⣿⠀⠀⣠⣾⡿⣿⣿⣿⣿⣿⣿⡿⠋⣠⠔⣡⠖⡀⢀⣄⣀⡠⢤⡞⠁⡰⠁⢀⠀⠠⣿⡄⠰⡀⠀⠀⠀ ⠀⢠⣿⡿⣿⣿⣦⡟⠀⣿⣿⣿⣿⡇⣼⠟⣥⣼⡿⢻⣽⡷⠈⣟⣤⡾⢫⠞⣡⡞⣴⡿⢏⡁⢠⡟⢀⢤⠇⠀⠈⡇⠀⣿⣿⣧⢹⡄⠀⠀ ⠓⢾⣿⢁⣿⣿⣿⣿⡆⣿⡿⣿⣿⡟⠁⠀⠽⠛⠉⠿⠿⠏⠀⣹⣟⣵⣇⣼⣯⣾⠏⠀⣾⣽⣿⠃⡟⣼⠀⠀⠀⣧⢠⢸⣿⣿⣦⣷⣀⡀ ⠀⣾⠛⣾⣿⣿⣿⣿⣷⣿⡇⠈⣻⣧⠀⠀⠀⠀⠀⠰⢶⣄⣺⣿⣿⣿⣾⣿⡿⠁⢰⣾⣿⣿⣿⢸⣧⣿⠀⢸⡆⣿⢸⣸⣻⣿⣿⣿⣿⣷ ⡼⠃⠀⢻⣿⣿⣿⣿⣿⣿⡇⠌⠀⠙⣆⣠⣶⣦⣴⣆⣤⠆⢻⣿⣿⣿⣿⡟⠁⠀⣾⣿⣿⣿⣿⣿⣾⣿⠀⢸⣇⢸⣆⣯⣿⣿⣿⣿⣿⣿ ⡁⠀⠀⣾⣿⣿⣿⣿⣿⣿⡇⠢⣶⣾⢿⣿⢫⣾⣳⣿⠃⢠⣿⣿⣿⣿⣿⣄⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣠⢸⣿⢸⣷⣿⣿⣿⣿⣿⣿⣿ ⠛⠀⣸⣿⣿⣿⣿⣿⣿⣿⠃⣸⠟⣿⣾⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⠃⠀⠙⢦⣽⣿⣿⣿⣿⣿⣿⣿⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⢠⣿⣿⣿⣿⣿⢿⣿⡟⢰⡏⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⡏⢤⡀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠰⢿⣿⣿⣿⣿⡇⣸⣿⠁⡘⠀⢸⣿⢿⢿⣿⣿⣿⣿⣿⣿⣿⡿⢸⠰⢯⠷⣄⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⢸⣿⣿⠏⣸⠀⣿⠃⠀⠃⠀⢸⡏⢸⢸⣿⣿⣿⡿⣿⣿⣿⡇⡔⠀⢀⠀⠈⠳⣌⢿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢀⠋⣿⠏⢀⠇⢰⠃⠀⠀⠀⠀⠸⡇⠸⢸⣿⡿⠏⠀⢿⣿⣿⠀⣧⣀⡾⣄⠀⠀⠘⠞⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠧⠷⠿⣄⠀⠀⠇⠀⠀⠀⠀⠀⠀⣃⡠⠞⠋⠀⠀⠀⢸⣿⣿⠀⠘⢿⣿⣮⣧⡀⠀⠀⢻⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠈⠑⢦⡀⠀⠀⠀⠀⡔⠋⠁⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⣾⣿⣿⣿⣮⣧⠄⠘⡇⢹⣿⣿⡏⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⢸⠀⣀⣀⡀⠵⢤⡔⠒⢹⠉⣦⠀⠀⠀⣿⡇⡇⠀⠉⠻⠿⠧⢌⣻⣷⣤⣹⠸⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡖⠦⠤⠤⠄⠀⣼⠋⠀⠀⠀⠀⠘⢧⣠⠼⢀⡏⠀⠀⠀⢻⡇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣧⣿⣿⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠉⠐⠒⠠⠄⣀⡇⠀⠀⠀⠀⠀⠀⣀⡠⠔⠋⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣶⣤⡤⣀⡀⠀⠈⡝⠒⠢⢶⠊⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠉⠀⠀⠀⣹⡿⣶⣧⣄⣀⡈⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⡸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⢠⠊⣿⣷⣤⣈⣽⠽⠋⠛⠓⠤⠤⠤⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⡰⢱⣿⣯⣿⣿⣿⣿⣿⣿⢫⣿⣿⣿⣿ ⠀⠀⢸⠀⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⢠⢁⣿⢏⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⡿ ⡠⠴⢚⣿⣿⣿⣿⣿⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣼⠏⣸⣿⣿⣿⣿⣿⢟⣿⣿⣿⣿⣿⠁ ⡀⠀⣼⠛⠋⠉⠛⠻⣿⡟⠛⠒⠒⠦⠤⠤⣀⡀⠀⠀⠀⠀⠀⠛⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠃⣰⣿⣿⣿⣿⣿⠏⣼⣿⣿⣿⣿⠏⠰ ⠳⣄⠘⣷⣶⣧⣤⣼⣿⠁⠀⠀⠀⠀⠀⠀⠈⠛⢶⣤⣀⠘⢄⡀⠀⢳⠀⠀⠀⠀⠀⠀⠀⡼⠁⣰⣿⣿⣿⣿⣿⣯⣾⣷⣿⣿⣿⡟⣠⠚ ⠀⠘⢦⣻⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣍⠙⠚⠶⠾⠄⠀⠀⠀⠀⠀⠈⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠈ ⠀⣀⡠⢿⡙⢿⣿⣿⣿⡟⠉⠁⠚⠒⠢⢤⣀⠀⠀⠀⢸⠉⠑⢦⣀⢀⠀⠀⠀⠀⠀⠀⢀⢜⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠠⠀⣠

⠀⠀⣿⣿⣿⣿⣧⡆⡌⢀⡟⢿⣿⣿⣿⣿⣾⠀⠀⠀⣠⣾⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⣀⣴⠞⣡⠖⠀⠀⢀⡀⠀⢀⣠⢀⡞⠃⢀⡞⠀⠀⠀⠀⣜⣿⡄⠀⢦⠀⠀⠀⠀⢀ ⠀⠀⢸⣿⣿⢯⣿⣇⡇⣸⠁⠸⣿⣿⣿⣿⡟⡄⢈⣾⣿⠛⠑⢾⣿⡿⢋⣽⡍⢹⣿⠏⢀⣼⠟⣡⠞⢁⣴⢋⣵⣿⡷⠛⠉⣠⡿⠁⢀⣸⠀⠀⠀⡇⠀⠸⣾⣿⣴⡈⣧⣀⠀⠀⠈ ⣀⠀⣾⣿⡟⣾⣿⣿⣷⣿⠀⢨⣿⣿⣿⣿⣿⣣⡾⠋⠈⣿⣿⣿⢋⣴⣿⣿⡂⠈⣷⣾⣿⢋⡾⠃⣰⡾⣡⣿⠟⠉⣱⢤⢰⣿⠁⣰⢣⡇⠀⠀⠀⣿⠀⡀⢧⣿⣷⣷⠸⣦⠆⠀⢀ ⠙⢻⣿⣿⠀⣿⣿⣿⣿⣿⣿⠈⡟⣏⢿⣿⣿⡟⠁⠀⠠⠒⠉⠀⠰⠻⠟⠛⠁⠀⣸⡿⣵⣿⢇⣼⣿⣴⡿⠋⠀⣰⡟⣶⣿⡏⢠⡏⣸⡇⠀⠀⠀⢸⡆⡇⢸⢹⣿⡾⣇⢿⣆⣠⡀ ⠀⣸⡿⠹⣾⣿⣿⣿⣿⣿⣿⡄⣿⣿⠀⠻⣿⣧⠀⠀⠀⠀⠀⠀⠀⢲⣶⣤⠴⣺⣿⣾⣿⢫⣾⣿⣿⡟⠁⢰⣆⣿⣿⣿⣿⡇⣾⣇⣿⡇⠀⢸⡆⢸⡇⢹⠘⡟⣿⣿⣿⣼⣿⣿⣷ ⢠⡿⠁⠀⡿⣿⣿⣿⣿⣿⣿⣧⣿⣿⢀⠖⠙⢿⡇⠀⣀⣤⡤⢀⣀⡀⢈⣩⠹⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⣼⣿⣿⣿⣿⣿⣧⣿⢸⣿⡇⠀⢸⣷⢸⣿⢸⡇⡇⣿⣿⣿⣿⣿⣿⣿ ⡞⠀⠀⠈⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⠀⠀⢠⣽⣶⣿⣿⢋⣿⠛⣶⣿⠃⢀⣾⣿⣿⣿⣿⣿⡏⠀⠀⠀⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⠘⣿⢸⣧⣿⣿⣿⣿⣿⣿⣿⣿ ⣄⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠈⢻⣽⡿⠿⣿⡏⣴⣿⢃⣽⣿⠃⢀⣾⣿⣿⣿⣿⣿⡿⢶⣄⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⡇⢸⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠟⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⢀⣿⠫⣿⣾⣿⣷⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⠁⠀⠉⠳⣄⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⣰⣿⣿⣿⣿⣿⣿⢿⣿⣿⡿⠀⣾⠇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣿⣿⣿⣿⣿⢱⠇⡀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⢰⣿⣿⣿⣿⣿⣿⡟⢸⣿⣿⠃⢸⡟⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡏⣿⢀⡿⣦⡀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠈⠟⣼⣿⣿⣿⡿⢿⠇⢸⣿⡏⠀⡼⠀⠀⣿⣿⢣⡿⢸⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠇⠸⠶⡏⠻⣄⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⢠⡏⣿⣿⡿⢁⡿⠀⣼⡏⠀⠀⠇⠀⠀⣿⡇⢸⡇⣾⣿⣿⣿⣿⡿⣿⣿⣿⣿⡏⢸⠀⠀⢀⡇⠀⠈⠳⡀⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⣼⠃⣿⡿⠁⢸⠇⢠⡟⠀⠀⠀⠀⠀⠀⢹⡇⠸⡇⢿⣿⣿⣿⠟⠀⣿⣿⣿⣿⠁⢸⡀⢀⣼⡀⠀⠀⠀⠙⣇⢿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣴⢰⠀⡿⠁⠀⡎⠀⡼⠁⠀⠀⠀⠀⠀⠀⠈⡇⠀⠃⣸⡿⠛⠁⠀⠀⢸⣿⣿⣿⠀⠺⣷⣾⣧⡙⣦⠀⠀⠀⠈⠈⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠓⠛⠊⠛⢧⡀⠀⠸⠁⠀⠀⠀⠀⠀⠀⠀⢀⣥⡴⠚⠉⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠉⢿⣿⣿⣮⡳⣄⠀⠀⠀⢿⡇⢿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠉⠲⣄⡀⠀⠀⠀⠀⠀⢰⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣮⣓⢄⠀⠸⣇⢸⣿⣿⣿⣿⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠘⣆⣀⣠⠤⠖⢻⠛⢦⠀⠀⠀⠀⢻⣿⠸⡇⠀⠈⠻⣿⣟⣿⠉⠙⠿⣷⣤⡀⢿⠈⣿⣿⣿⡟⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣀⡀⠀⠀⠀⠀⠀⠀⢸⣠⠴⠒⠒⠛⠉⠉⢸⡇⠀⠀⢸⠀⣸⠀⠀⠀⠀⢸⣿⠀⣷⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠛⠿⠿⡇⢻⣿⣿⠃⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣇⡉⠓⠒⠒⠋⠁⠀⣿⠃⠀⠀⠀⠀⠀⠀⠈⠳⠶⠒⠋⣠⠟⠀⠀⠀⠀⠈⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣾⣿⣿⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠉⠙⠒⠶⢤⣄⣠⠇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠞⠁⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡇⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢤⣀⣀⡀⠀⠀⠀⠉⠉⢓⠶⢤⣄⣠⡴⠖⠊⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠁⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠿⠟⠛⠉⠙⢳⣦⣤⣀⡇⠀⠀⠀⠘⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⣠⣟⠛⠿⢿⣷⣦⣤⣄⡈⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⢀⡞⣾⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿ ⠀⠀⠀⣴⠋⣹⣾⣧⣤⣄⣠⣯⠞⠉⠉⠙⠓⠦⠤⠤⢤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⡞⢰⣿⡟⣼⣿⣿⣿⣿⣿⣿⣿⡟⣼⣿⣿⣿⣿⣿ ⠀⠀⠀⣿⠀⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠀⡼⢠⣿⡿⢹⣿⣿⣿⣿⣿⣿⣿⡿⢱⣿⣿⣿⣿⣿⡿ ⠀⠀⢀⣸⣆⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠁⣾⡿⢡⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⠃ ⠖⠛⠁⢠⣿⣿⣿⣿⣿⣿⣿⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠁⣼⣿⣿⣿⣿⣿⣿⣿⢃⣿⣿⣿⣿⣿⣿⣏⠀ ⡄⠀⢠⢾⠉⠙⠀⠉⠙⠛⣿⣿⡟⠉⠉⠙⠓⠒⠶⠦⣤⣄⣀⠀⠀⠀⠀⠀⢀⠐⠈⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠀⣰⣿⣿⣿⣿⣿⣿⡿⠃⣾⢫⣾⣿⣿⣿⡟⠀⠚ ⢻⡄⡘⢸⣗⣶⠾⢃⣃⣤⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣷⣤⣀⠀⠘⣇⡀⠀⠀⠙⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⣰⣿⣿⣿⣿⣿⣿⡿⣡⣾⢏⣾⣿⣿⣿⣿⠃⢀⠌ ⠀⠹⣧⠀⣿⣷⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⠷⠾⢭⣤⣄⣀⣼⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⣰⣿⣿⣿⣿⣿⣿⣟⣾⣿⢧⣾⣿⣿⣿⣿⡯⠖⠁⠠ ⠀⠀⠀⠳⣼⣿⣿⣿⣿⣿⣿⣿⣦⣀⣀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣙⢦⡀⠀⠉⠙⠛⠃⠠⠀⠀⠀⠀⠀⠀⠀⠀⡼⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⡟⠀⠈⠁⡀ ⠀⣀⣠⠴⠻⣏⠛⣿⣿⣿⣿⣿⡇⠀⠀⡐⠋⠙⠓⠶⣤⣀⠀⠀⠀⠀⢸⠀⠀⠙⢶⣄⣀⣀⠈⠀⠀⠀⠀⠀⠀⠀⣠⢞⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠧⠠⠄⢈⣤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣧⠀⠡⢻⣿⢦⡀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀ ⣤⣤⣤⣤⣤⣤⣤⣤⣶⡾⢿⣿⣆⣴⣾⡇⢻⡇⠀⢠⣶⣦⡿⠗⠛⣋⠅⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⡿⠿⠛⠛⠛⠒⠛⠡⠤⣷⡯⠥⢀⣀⠮⠄⣀⠑⡀⠀ ⠀⠀⠀⠀⠀⠀⢀⡤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢗⣚⣋⣭⣿⣉⣈⣀ ⠀⠀⠀⢀⣤⣶⠏⠀⠀⠀⠀⠀⠠⠀⡀⠀⠀⢀⡠⠄⣒⡂⠄⠹⡉⠉⠉⠉⠁⠀ ⠀⠀⢰⠖⠛⢻⠀⠀⠀⠀⠈⢀⠢⠬⠄⠠⠤⠐⣈⠥⠀⠀⠄⠀⣇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⣄⠤⡀⠀⠠⢄⡉⢔⠒⠒⢂⢉⠀⠀⣀⣄⡂⠠⠛⠆⠀⠀⠀⠀ ⠀⠀⠀⡤⠤⠴⡇⢒⠘⡄⢻⡷⣒⠠⢵⣄⡀⣦⣠⣮⠔⣂⣽⠃⠆⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⡄⠣⡈⠀⠑⠂⢬⣭⢭⢿⠉⠙⠫⣤⠖⢁⠌⣰⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⠈⠢⢀⠑⠢⠄⣀⣈⡁⠀⡆⠀⠀⠘⡔⣡⡾⠛⠶⠶⠒⠒⠒ ⠀⠀⠀⠀⠀⠀⠸⠂⠀⠀⠉⠐⠂⢤⠤⢤⢤⠁⠀⠀⠀⢸⡏⠁⠀⢰⣶⣶⣄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣿⡸⡄⠀⠀⢀⡞⠁⠀⠀⢘⣼⣿⡋⠀ ⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⢲⠀⠀⣤⢇⣿⣄⠈⠑⢲⠋⠀⠀⢀⡠⠚⡿⡀⠉⠙ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡘⠘⣴⠻⡇⠆⠀⢸⠀⠀⢠⠎⠀⠀⠃⠁⠀⠀ ⣤⠤⣤⡤⣤⣄⣀⣀⣀⣀⣀⣀⡇⠀⡆⠀⢠⢸⠀⢸⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⡈⢆⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡰⡋⢹⠀⢀⢤⡴⡨⡉⡥⣐⠤⠭⠈⠉⢐⣧⠀⠒⠀⠤⠄⣄⡄ ⠀⠀⠀⠀⠀⣸⠀⠀⡾⣰⣿⡻⣫⠪⣔⣵⠞⡉⣡⣢⡀⠀⠉⠀⢀⡠⢔⣈⠏⠀ ⠀⠀⠀⠀⢠⡇⣜⠀⣧⠉⠠⠈⢃⠠⣾⣿⣄⠣⣵⢟⠳⡂⠀⣠⠞⠁⢩⣯⠀⠀ ⠀⠀⠀⢀⠉⠀⠋⢠⠏⠀⢀⣀⠀⡇⠀⠛⠫⢟⣯⠷⠿⢅⠠⠉⠋⠒⣻⠂⠀⠀ ⠀⠀⠀⠘⠦⢶⣄⠼⠤⠤⡤⣢⣤⠳⡄⠀⠀⠀⠀⠀⠀⠀⢀⠤⠤⢀⠈⢑⣢⠄ ⠀⠀⠀⠆⡄⠀⢃⠀⠀⠀⠈⠛⠻⡀⡿⠀⠀⠀⠀⠀⢐⠀⡌⢂⠀⠀⡠⢭⡶⢀ ⠀⠀⠈⠀⡇⠀⣸⡂⠇⠀⢀⠀⠀⠣⣅⠉⠢⣣⣀⢦⡀⠀⡇⠈⢳⣲⢤⣥⡽⠅ ⢠⠤⢸⠀⠁⢾⣼⣄⠈⠀⠀⠃⠀⠀⠈⠦⡀⠈⡟⢽⠿⢺⠀⠸⠻⣾⡿⣿⣍⡀ ⡌⠀⠀⠀⠇⠸⠘⠃⠀⠈⠀⠀⠀⠀⠀⠀⠀⢧⢨⠎⠀⠨⠀⠇⠀⠟⣼⢯⡃⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⣿⣧⣿⣿⣱⡀⠀⠀⢹⡄⢻⣿⣯⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣿⣧⢷⠀⠈⢢⣷⠀⢿⣿⣿⣿⢿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣴⠖⠒⠀⠀⠀⢀⠤⠐⠒ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⣀⣀⣽⣿⣿⢿⣿⡌⡇⠀⠀⠀⠀⣸⣿⡏⠁⣮⣿⡇⠀⠀⠀⠀⠀⢀⣀⣀⣀⡴⣶⣾⣻⣩⣵⣶⣿⡷⢾⡟⠋⠉⠉⠀⠀⠀⠀ ⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣾⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⠹⣄⣤⣾⣿⣿⣿⠀⠀⢸⣿⣿⠀⠀⠀⠀⣰⢛⣿⣥⣥⣶⣿⡷⠿⠋⠁⠀⠉⣀⡴⠆⠀⠀⠀⠀⠀⠀⠀ ⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢻⣿⣿⡀⢾⣿⡿⣿⣷⣿⣿⣿⣿⢇⣿⠀⣠⣸⣿⠇⠀⠀⠀⢠⢇⣿⠿⣣⠝⠉⠁⠀⠀⠀⢀⡴⠞⠉⠀⠀⠰⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣼⣿⣿⡿⠿⠟⠛⠛⠛⠛⠛⠛⠛⠛⠿⠦⣤⣤⣠⣿⣾⣿⣭⣁⣤⣀⠀⠀⠀⢀⣹⣄⣀⣀⠀⠀⠀⠈⢠⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠿⠟⠉⠁⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠶⣦⣄⡉⠉⢹⡛⠿⣯⣅⣈⣉⣉⣙⣿⣶⣤⡀⢲⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠋⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠟⢿⣛⠛⠛⠛⠛⠉⠉⠉⠙⣿⡏⠉⠉⠉⠉⠈⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣷⣶⣶⣬⣭⣭⣿⣿⣤⣴⣶⠶⠶⠶⠶ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠶⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠤⠤⢤⣀⠀⠀⠻⣯⠉⠛⠉⠉⠉⠉⠀⠉⠉⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣀⣠⣴⠿⢿⡞⣻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⡒⠒⠒⠶⢤⣄⠀⠀⠀⠀⠀⠀⣠⠴⠒⠉⢁⣀⣤⣤⣀⡈⠁⠀⠀⠹⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣤⣤⣶⣾⣽⡾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠠⠖⠋⠉⠉⣉⠉⠉⠓⠲⠶⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⠉⠀⠀⠀⠀⠁⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠤⠄⠀⠒⠚⢻⣿⠉⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠉⠛⠒⠶⠶⠶⠤⠶⠶⠶⠚⠋⠁⣀⣠⠴⠞⠛⠉⠉⠉⠉⠳⠆⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠦⢤⣄⣀⣀⣀⣀⣀⣀⣠⠴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣟⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠘⣧⣀⣤⢤⣄⠀⠀⠀⠀⣀⡤⠖⠒⢒⣒⣦⣄⠉⠉⠉⠉⠉⠉⣤⠀⠀⠀⠀⠀⠀⠀⢀⣴⣒⠚⠛⠂⠀⣼⠛⠉⠻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣾⠏⡆⠀⠈⢷⡀⠒⢦⣭⣤⠶⠋⠉⠀⠀⠈⠳⣄⠀⠀⠀⠀⠹⡄⢸⠀⠀⠀⣠⠞⠋⠉⠉⢉⣓⣶⡞⠁⣀⡄⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣀⣦⣀⣠⠤⠿⣿⠀⠛⣏⠁⠈⢧⡈⠉⢹⣿⢶⣒⠒⠒⠶⠦⠤⣌⣷⣄⠀⠀⠀⡇⢸⠀⣠⣞⣡⣴⠶⠚⠉⢉⣠⣾⠇⠈⣽⠁⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠸⣆⠀⠙⣄⠀⠈⢧⡀⠀⠻⣟⠊⠙⠓⠦⠤⣀⣙⣛⣏⣛⣦⣴⣷⣯⣞⣉⣿⡻⠥⠤⠖⠛⠯⣿⠏⠀⣰⠃⢀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠘⢦⡀⠀⠛⠀⠀⠈⠓⠦⢤⣀⣀⣀⣀⣀⣀⣿⢿⡋⠀⠈⠉⠛⢦⣤⡤⠤⠤⣖⠛⠁⠀⣴⠃⠀⣼⡏⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢮⡿⣦⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠘⠯⠭⠭⠟⣻⡿⠋⢳⠀⠀⠀⠀⠀⠉⢿⡟⠯⠁⠀⣠⠞⠁⢀⣾⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠈⠳⣄⠀⠀⠉⠓⠦⣄⡀⠀⠀⠀⠀⠀⠚⠉⠁⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠙⣆⣠⠞⠁⠀⣴⣿⠿⠷⠶⠶⠶⠶⢶⠶⢶⡶⢶⣤⣶ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠈⠛⢶⣄⡀⠀⠀⠉⠙⠲⠶⠤⢤⣀⣀⣀⣀⣀⣀⡇⠀⠀⠀⠀⠀⠀⠀⠸⡆⢀⣤⣾⣿⠁⠉⠈⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡧⠄⠀⠀⠀⠀⠈⠙⠳⠤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⢀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⠁⠋⠀⠀⠀⠀⢠⡀⣴⣤⣤⣄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⢻⡖⠒⠒⣶⡖⠲⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⣥⠀⠀⠀⠀⠀⠀⣬⡿⣿⠀⣿⣿⣧⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⣿⡇⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠇⠀⠀⠀⠀⠀⠂⣿⡅⢹⡄⣿⣿⣿⠇⠀⠀ ⠀⠀⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢰⢷⡇⡠⣽⣆⠀⠀⠀⠀⠀⠀⠀⣰⡿⠃⠀⠀⠀⠀⠀⠀⠀⠈⣿⣼⣿⣿⣿⠋⠀⠀⠀ ⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣇⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⣿⠀⣸⣸⡇⠁⠀⠙⢷⣄⡀⠀⢀⣠⣾⡋⡀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⠛⠿⣧⣤⣤⣀ ⠀⠀⠀⠐⠀⠐⠒⠂⠀⠀⠋⠉⠁⠀⠈⠉⠀⠀⠀⠀⠀⠈⠽⣿⠀⠀⠀⠀⣠⣠⣿⡀⣿⣿⣷⣄⠀⠀⠀⠈⠙⠛⢻⡟⠉⠀⠀⠀⠀⠀⠀⠀⢀⣴⠿⠋⢀⡟⣿⠀⠀⠀⠀⠀⠉ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣰⢟⢻⡉⠛⣿⣇⡿⡟⢷⡀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⢸⠃⢹⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⢠⡏⠀⢸⣧⢠⠟⣿⣧⡇⠈⣇⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣠⡿⠋⠀⠀⠀⠀⠸⠄⠘⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣸⠃⠀⠀⣿⠻⠀⠘⠋⢧⠀⢹⡆⠀⠀⠀⢸⡇⠀⠀⠀⠀⣴⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⣿⠀⠀⠀⣿⠀⠀⠀⠀⢸⡄⠘⣧⠀⠀⠀⢸⡇⠀⠀⠄⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣭⣿⡟⠛⢻⣿⡿⠿⠿⢿⢿⣿⣶⣶⣶⣶⣶⣤⣤⣤⣤⣤⣤⣬⣤⣤⡇⠀⠀⠀⣿⠀⠀⠀⠀⢘⣇⠀⢻⡀⠀⠀⢸⡇⠀⠀⣼⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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