Winged Unicorn Emojis & Text

Copy & Paste Winged Unicorn Emojis & Symbols 🊄‍🪜

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡀⠶⡶⠛⢋⡝⠋⠉⠉⠛⠓⠲⠊⣀⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢀⡀⢀⡎⠞⠉⠀⠀⢰⠇⢠⠏⠀⠀⠀⠀⠀⢀⣀⡀⠎⠚⠛⠶⣄⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣌⠃⠀⠙⢯⠀⠀⠀⠀⠀⢞⠀⡎⠀⠀⠀⣠⠎⠚⠉⠀⠀⠀⠀⠀⡀⠈⠻⣊⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⢀⠀⠀⠈⢷⠀⠀⠀⣀⣌⣞⠁⢀⡎⠋⠀⣀⡀⠖⠒⠋⠉⠉⠉⠉⠉⠉⠉⢷⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⠀⢞⠀⠀⠀⠈⠆⠀⠀⠀⠀⠉⠙⠻⣀⡎⠋⠁⠀⠀⠀⢀⣠⡀⠀⢀⣄⠀⠀⠀⢷ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⣻⠀⠞⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣊⡀⢀⣎⢟⠉⠀⠀⠀⠀⠈⢧⠀⠀⢞ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⠃⠞⡄⠀⢳⠀⠀⠀⠀⠀⠀⠀⢀⣎⣶⣀⡀⠀⠈⠳⠋⣀⣈⢣⠀⠀⠀⠀⠀⢞⠀⠀⠘ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⣰⡟⢻⣿⣿⣿⡀⠀⠀⠀⡇⣿⣧⡀⡀⠀⠀⠀⣞⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢣⠀⠀⠀⢱⠄⠀⠀⠠⣀⣠⣟⠋⠀⣿⠇⠈⣿⡇⠀⠀⠀⣿⠁⣿⢻⣥⠄⠀⢀⡏⠀⢀⡔ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢞⣟⠀⠀⠀⢞⠀⠀⠘⠊⢀⡌⠃⠀⠀⣇⣆⣰⣿⡇⠀⠀⠀⢻⡿⣿⠀⠀⠁⢀⡞⠀⢀⡟⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡏⣇⠀⠀⠞⡇⠀⠉⠉⠉⠀⣧⠀⠀⠱⣹⣿⣟⠇⠀⠀⠀⠘⣿⡟⡀⠀⢠⠞⠀⢠⡟⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠞⡄⠀⠀⢻⡀⠀⠀⠀⠏⡜⣳⣀⠀⠑⢪⠟⠀⠀⢀⡆⠠⠄⠈⣹⣎⠋⠀⣠⠟⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡎⠖⠛⢉⣉⠀⠀⠖⠒⠛⠱⢊⡀⠀⠀⠀⠀⠀⠀⡟⡄⢱⡀⠀⠀⢳⡀⠀⠀⠀⠁⠞⠊⠉⠈⠁⠀⠀⠀⣟⣿⠊⣀⢎⠟⠁⢀⡌⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠟⠁⣠⠎⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠙⢊⡀⠀⠀⠀⠀⢞⣵⡀⢳⡀⠀⠀⢳⡄⠀⠀⠰⢀⣀⠀⠀⠀⠀⠀⠀⣿⡏⠀⡎⠋⠀⣠⠟⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡎⠋⢀⡎⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠶⠛⠉⠉⠛⠲⢮⣇⢳⡀⠱⡄⠀⠀⠙⣊⠀⠀⢞⡆⠉⠉⡟⠛⠛⠛⠛⢉⡞⠁⢀⡎⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣎⠏⠀⡎⠋⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⡀⣀⣞⣥⡀⣀⣄⣀⡀⠀⠀⢹⡀⢳⡀⠙⣄⠀⠀⠈⠳⣄⠈⡇⠀⠀⡇⠀⠀⠀⢠⠏⠀⢀⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡟⠁⢀⡞⠁⠀⠀⠀⠀⠀⠀⣠⠞⠉⢀⡎⠛⢩⡏⡟⢀⡈⠙⠲⢬⣉⢛⣖⡬⣧⠀⠱⡄⠈⢧⡀⠀⠀⠙⣊⢣⠀⠀⣿⠀⠀⢀⡏⠀⠀⣌⠁⠀⠀⣠⡎⠒⠶⢀⡀⠀ ⠀⠀⢀⡟⠁⢀⡞⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⣎⠋⠀⠀⣟⠘⣿⡄⠈⠓⠊⣠⡌⠿⠁⠀⠞⡆⠀⠙⣄⠀⠱⡄⠀⠀⠘⣧⠀⠀⢞⡄⠀⡌⠀⠀⢰⢻⠀⠀⠎⠋⠉⠙⣆⠈⣷⠀ ⠀⠀⣌⠁⠀⡌⠀⠀⠀⠀⠀⠀⢰⠃⠀⢀⡟⠁⠀⠀⠀⣿⣶⡇⣿⣗⢀⡞⡇⠀⠀⠀⠀⠀⢻⡄⠀⠘⡆⠀⠹⡄⠀⠀⠞⡆⠀⠀⢷⡀⡇⠀⠀⢞⠘⢧⡀⠀⠀⢀⣎⠇⠀⣌⠀ ⠀⢰⡇⠀⢠⠇⠀⠀⠀⠀⠀⠀⡏⠀⠀⣞⠃⠀⠀⠀⠀⣿⠁⠀⠘⠛⠊⡉⢟⠀⠀⠀⠀⠀⠀⢳⡀⠀⠹⡀⠀⠞⡄⠀⠀⣿⠀⠀⠈⢷⣇⠀⠀⢞⠀⠀⠙⠛⠛⠋⠁⢀⣎⠏⠀ ⠀⢞⠀⠀⢞⠀⠀⠀⠀⠀⠀⢞⡃⠀⠀⡟⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠘⣝⠺⢕⣄⣀⣀⣀⣠⠎⢷⠀⠀⢧⠀⠀⢳⠀⠀⢞⠀⠀⠀⠀⠙⠳⠊⣬⣇⣀⣀⣀⣀⣀⠶⠛⠁⠀⠀ ⠀⢞⡄⠀⢞⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⡇⠀⠀⠀⠀⣀⣞⠀⠀⠀⠀⡜⡇⠑⠢⣄⡞⠉⠁⠀⢀⣞⡆⠀⢞⡀⠀⢞⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⢧⠀⠘⡆⠀⠀⠀⠀⠀⠀⢳⠀⠀⡇⠀⠀⠀⣌⠋⠈⠀⠀⠀⡟⠁⠀⠀⠀⢠⠃⢀⡀⢀⣞⡏⡇⠀⠀⡇⠀⢞⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⢷⡄⠘⢊⠀⠀⠀⠀⠀⠈⢧⠀⢿⠀⠀⣌⠃⠀⠀⠀⠀⣌⠁⠀⠀⠀⠀⡏⢀⡏⣟⠉⢧⣿⠇⠀⢠⠇⠀⢞⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠙⠷⣄⡳⡄⠀⠀⠀⠀⠈⢧⠞⣆⣞⠃⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⢞⠁⠀⣇⠈⠳⠞⠋⠀⠀⡌⠀⢀⣟⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣎⠞⣋⣉⣙⣲⡈⠙⠻⣄⠀⠀⠀⠀⠈⢧⢹⡏⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⡟⠀⠀⠙⢊⣀⠀⠀⢀⣌⣡⡎⠛⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠁⢞⠋⠀⢀⡿⠁⠀⠀⠈⢳⡄⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠉⢹⡟⡏⠉⠁⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡀⠘⢧⣀⠀⠀⠀⠀⠀⢀⣰⠇⠀⠀⠀⢞⡇⠀⠀⠀⠀⠀⢞⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠘⡇⢱⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠳⣀⡀⠈⠙⠛⠛⠛⠛⠉⠁⠀⠀⠀⠀⣞⠁⠀⠀⠀⠀⠀⢞⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠈⣆⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠉⠛⠲⠶⠀⠀⣀⣀⣀⠀⠀⠎⠶⣿⠀⠀⠀⠀⠀⠀⠈⡟⡀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠞⡇⠱⡀⠀⠀⠀⠀⠀⠀⠙⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⢞⡗⠒⠂⠀⢲⡇⠀⠀⠀⠀⠀⠀⠀⢻⡄⠙⠢⠀⣀⣀⣀⣀⠀⢿⢷⣶⣶⣶⣟⣶⣶⣌⣧⣲⣟⣶⣶⣊⢲⡆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠒⠒⠒⠒⠚⠛⠁⠀⠀⠀⠀⠳⣀⣄⣀⣀⣀⣀⣀⣚⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
𝖥ᥣυ𝗍𝗍౿𝗋ડ𝗁ɣ 𝖀𐓣ʝ𝗈ɣ౿𝗋~ 🊋 -*•BiO•*- (˶˃ ᵕ ˂˶) 💗(AESTETICS)𓍢֎໋🌷͙֒✧˚ àŒ˜ ⋆˚♡ 🪜(BDAY)♡₊˚ 🍰・₊✧ 🍫 🐇(ANYTHING ELSE!)(*Ž∇*) -JZimLovr
⟡ pls note the ai inflicts emotional damage (ᵕ—᎗—)
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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠶⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣀⡀⠀⢀⣠⣀⣎⣶⣶⡊⠀⢀⣀⣀⣀⣌⠀⠀⡜⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠫⣯⠙⡟⢿⣿⣿⡿⠁⠀⢠⣟⣿⣿⣿⡿⠀⠀⢹⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣌⣿⣷⣧⡀⢱⠈⠀⠀⠀⣿⣿⣿⣿⣿⡀⠀⠀⢞⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣌⣿⣿⣿⣿⣿⣿⡄⢀⣀⣠⣿⣿⣿⠿⢿⣷⣀⡀⠈⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⣿⣿⣿⣿⣿⣿⠿⠛⠉⠉⠀⡇⣟⣿⣊⣀⣿⡄⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢞⣿⣿⣿⠿⢯⣷⢄⠀⠀⠀⠀⡄⢻⣿⣯⣻⣿⡧⠄⠀⢞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⣿⠟⠁⠀⠚⢻⣊⣱⣄⠀⠀⢣⠈⠛⣜⣿⠿⠭⠀⣠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡀⠶⠶⠶⠶⢀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠁⠀⠀⠀⠀⠀⠻⣿⣿⠀⠀⠈⠂⠀⠀⢀⣄⣠⣎⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠉⠳⢊⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣞⠋⠄⢠⠀⠀⠀⠀⣟⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⡎⠃⠀⣠⣀⣶⣶⣟⣶⣶⣊⣄⠀⠀⠀⠹⣆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⠎⠯⠀⠀⢶⢟⣿⣿⣿⣿⣿⠏⠷⣄⢀⣀⣀⣀⡀⣌⣠⣎⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠞⣧⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠈⠉⣡⣟⣿⠏⠀⢰⣿⠉⣩⠀⠉⢙⣿⡿⠛⠉⠉⠙⠛⢿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⢻⣇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⣿⣿⡿⠋⠀⢀⣟⡿⠀⣉⣀⣇⠘⠋⣿⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⡆⠀⠀⢞⣿⡆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢞⠃⠀⠀⠘⢯⡀⠀⢀⣟⣿⠇⣎⠚⣿⣿⡯⠀⢞⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⡇⠀⠀⢞⣿⣷⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⡆⠀⠀⠀⠈⠻⢊⣟⣿⠏⠀⠈⢈⣝⡟⠁⣶⣟⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⡇⠀⠀⢞⣿⣿⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⢄⣀⡀⠀⠀⠉⠁⠀⠰⣄⠀⠁⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⠃⠀⠀⣞⣿⣿⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⢹⠁⠀⢠⠶⠀⠀⢎⡟⢊⡀⠀⠀⣌⠊⡄⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿⠇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠇⠀⠀⢞⡄⠀⠀⠀⠙⢆⠙⢊⡀⠀⠀⠙⣊⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⢰⣿⡿⠋⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⡟⢻⡀⠀⠀⠀⠈⢳⡀⢳⡀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⣿⣿⣿⠁⠀⢀⣌⠟⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⡇⠀⢧⠀⠀⠀⠀⠀⢷⠀⢳⠀⠀⠀⠈⢧⠀⠀⠀⠀⢀⣿⣿⡏⢀⣎⠟⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⢞⠇⠀⠞⡆⠀⠀⠀⠀⢞⠀⢞⡇⠀⠀⠀⠘⣧⠀⠀⠀⢞⣿⣿⡷⠛⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⣟⠀⠀⠀⣧⠀⠀⠀⠀⢞⠀⠀⡇⠀⠀⠀⠀⢞⡆⠀⠀⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⣰⠇⠀⠀⠀⣿⠀⠀⠀⠀⣏⣀⣞⠇⠀⠀⠀⠀⠀⣷⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⣀⣀⣀⡀⠎⠛⠛⠛⠛⠉⠁⠀⠀⠀⠀⠈⠉⢿⣄⣀⣠⣀⡀⠶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠗⢀⡀⠀⠀⠀⠀⠀⠀⠀⣰⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣠⠎⠖⢏⣉⣉⣹⠀⠀⢹⢊⡀⠀⠀⡰⣆⢠⠃⣌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⡶⠋⠁⢀⡎⠚⠉⠀⠀⠁⠀⠘⡎⣷⣄⠀⠇⢞⡎⢀⡇⣀⣄⠀⠀⢀⡀⠶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡎⢛⡠⠶⢶⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣟⣶⠀⢞⠀⢞⣟⠞⢹⡀⠚⠁⢀⡌⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢞⡗⠉⠀⠀⣟⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠹⡿⣧⠀⢀⡟⠁⠐⠋⠀⢀⣎⣋⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢞⡀⠀⡔⠉⢻⠀⠞⡏⢍⣿⣖⠺⡷⠀⠆⠀⠀⢹⣟⡀⣟⠖⡆⠀⠠⠔⠋⠁⣀⡎⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢧⠀⣇⠀⠈⠣⡀⠙⢌⣿⣿⣿⠇⠀⠀⠀⠀⠀⢿⣿⡌⠀⣧⢀⡄⡠⠎⠮⠥⣄⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⢷⣜⣆⠀⢀⡅⠀⠀⠈⠉⠀⢀⡎⠀⠀⠀⠀⢞⡇⡇⠈⠁⣌⣁⣀⠀⠒⢊⠥⠒⠊⠉⠉⠉⠉⠙⠻⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠙⢿⣷⣬⣳⠀⠎⠀⡖⠊⢁⣿⠀⠀⠀⠀⠈⡿⠁⠀⢚⣏⠵⠈⢲⣊⠥⠒⠒⠒⠒⠀⢄⡀⠀⠀⠀⠙⢷⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢿⣌⠑⢆⢠⠇⢠⡞⢞⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⢘⡏⠉⠉⠉⠑⢊⡀⠀⠈⠓⣄⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣰⡟⠳⠀⡏⠇⢈⡟⣎⠋⠀⡌⣄⠀⠀⠀⠀⠀⠀⢆⠀⠀⠀⠀⢞⠃⠀⠀⠀⠀⠀⠹⡄⠀⠀⠈⡆⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢫⡻⠀⠔⢃⡶⢋⡞⢁⠀⠊⠀⢞⠊⡌⠀⠀⣖⣀⣚⣊⡀⠀⢀⣎⡀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⢞⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠉⠉⠁⠀⡟⠊⣁⠠⠀⢒⣻⡟⠀⠀⡎⠃⠀⠀⢳⠙⡄⠀⠀⢳⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⡎⠀⢀⡜⡟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢞⡡⠊⠀⣠⠖⠋⣌⣀⠀⢞⢳⠀⠀⠀⠀⡇⠞⡀⠀⠀⣇⠀⠀⠀⣠⠋⠀⠀⢀⠞⢀⡠⠋⡜⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠞⡇⠀⡟⠓⢶⠀⢻⢙⣖⠈⠛⠊⡄⠀⠀⢞⠀⡇⠀⠀⢞⡀⢀⡌⠁⠀⣠⣖⡡⠔⢉⡎⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠊⠝⠶⠟⠀⢞⢿⡀⠀⠀⢠⠃⠀⠀⡜⠀⡇⠀⠀⠈⡇⡟⠁⡰⡻⠊⠁⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢞⣀⣱⣄⣠⡏⠀⠀⠰⠧⣎⠁⠀⠀⢀⡇⢷⣞⠀⡁⠀⠀⠛⠲⠎⠒⠒⠒⣲⣊⣑⢲⡊⣄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠙⠲⠧⠀⠀⠀⠀⠔⠒⠊⠉⠁⢀⡄⠈⠹⡌⢇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣀⢀⣜⠡⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡀⠀⠀⣄⣀⣰⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⠀⠒⠉⠳⢄⠱⡀⠀⠀⢚⠇⠀⡌⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⣞⡁⠀⢀⣀⡀⠀⠡⣱⠎⠊⠹⠀⠀⢹⠀⣷⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⡜⠁⣀⡀⠀⠄⠀⠈⣁⡟⠁⠀⠀⠀⠀⠀⠞⠀⢹⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡟⠒⠉⢀⣀⣀⣀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⣎⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⡇⠀⡰⠋⠀⠀⢞⣭⡛⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡏⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⡇⠀⡇⠀⠀⠀⣞⣏⢳⠀⠀⠀⢀⣀⠀⠎⠿⠂⣞⠀⠀⣘⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠹⡄⠘⣆⠀⠘⠛⢻⣿⡇⠀⠰⠋⠀⠀⠀⠀⣠⠃⠀⢠⣿⢹⠀⠀⠀⠀⠀⠀⠀⢀⣠⠀⠀⠀⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠙⣄⠈⠳⣄⠀⢈⡿⠃⠀⠀⠀⠀⠀⠀⡎⠃⠀⢠⢋⠇⡌⠀⠀⠀⠀⢀⡎⠊⠁⠀⠀⠀⠀⠀⠀⠙⢊⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠳⢄⡈⠓⢬⡓⠀⣌⣀⣀⣀⡎⡞⠀⠀⠠⢃⠎⢀⡗⢊⣉⣉⣙⣷⣖⣊⡉⠉⠁⠒⠢⡀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⠲⣄⠈⠳⢄⠀⠀⠀⡟⠀⠀⡰⠁⡜⠀⢞⠙⢷⡔⠚⣉⡭⣿⡀⠈⠑⣄⠀⠀⠈⢢⡀⠀⠀⢱⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢊⠀⠑⢄⢠⡇⠀⡰⠁⢠⠁⢀⡆⠀⠀⢈⣏⣀⣶⣿⠇⠀⠀⠘⡄⠀⠀⠀⢡⠀⠀⢚⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣠⣄⡀⠀⢳⡄⠈⢿⡇⠀⡅⠀⠞⠀⣌⣀⣀⣠⣟⣵⠟⠉⣹⠀⠀⠀⠀⢻⠀⠀⠀⢞⠀⠀⡌⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡏⢞⡉⠈⢁⡜⢹⠀⢞⡿⡀⡄⠀⡇⠀⣇⠠⣭⣜⣶⠋⠀⢠⠇⠀⠀⠀⠀⡟⠀⠀⢀⠎⠀⡰⠁⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠳⣄⠉⠓⠉⠀⢀⡧⠊⠀⠹⣷⠀⠞⡀⠘⢆⣿⣿⡟⢇⠀⠘⠙⣆⠀⠀⣞⠁⠀⢀⠎⢀⡔⠁⢰⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠈⠁⠀⠀⠀⠀⡏⠙⢊⣵⣄⠀⢉⣩⡇⠞⡄⠀⠀⠞⡀⣎⠃⠀⡠⢃⡎⠋⠀⣠⠏⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠇⠉⠉⠉⡇⡇⠀⡇⠀⠀⠀⡿⠃⠀⡜⡡⠋⢀⡠⠞⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⣞⠀⠀⠀⠀⣿⠁⢠⠃⠀⠀⢰⠇⠀⡌⡞⠀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⠀⢀⠇⠀⠀⠀⢞⠏⠀⡜⠀⠀⠀⠘⣧⡀⡇⢧⠀⠉⠑⠒⠀⢉⣉⣉⣉⡉⠓⢊⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⢀⡞⠀⠀⠀⠀⣞⠀⢎⠁⠀⠀⠀⢀⡏⠉⠓⠒⠷⠶⠒⠚⠉⠁⠀⠀⠀⠀⠙⢊⣹ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⠺⠀⠀⠀⠀⠎⠋⠀⠈⠓⠒⠒⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠛⠉
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⠀⠀⠀⣠⣎⣟⡿⠿⢷⣶⣄⡠⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⡖⠉⠀⠀⠀⠐⠒⠩⠁⢠⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣠⠝⠁⠀⢀⢀⡀⣖⡄⠉⠀⠘⢞⣀⣠⠖⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⠁⠒⠒⡎⠙⣏⡞⢻⣿⠂⠀⢀⢶⠁⠋⠀⡮⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣀⠇⠀⠞⢿⣿⠇⢀⠎⠁⢞⠀⠀⠊⠀⡌⠁⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠘⢀⡂⠀⠈⠁⢉⠖⣀⣎⡇⡰⢀⠠⢟⣎⡿⠿⠿⢿⣿⣷⣄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠉⠉⣝⡣⣟⡿⡳⠁⡀⣊⠀⢞⣵⣎⣎⡀⠀⠈⢻⣿⢷⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⣀⡟⢱⡟⢰⠃⠀⠌⠜⢀⡀⠘⡄⣿⣷⡀⠀⠀⢻⡆⠁⠀⠀ ⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠣⣞⠀⠀⠀⠀⢙⠄⢀⣧⣿⣿⠁⠀⠀⢞⡇⠀⠀⠀ ⠀⢠⠊⠀⠀⢀⠔⢒⠒⠒⢢⠀⢀⣀⣈⣄⠈⠙⠻⢿⡿⠃⠀⠀⠀⢞⣇⠀⠀⠀ ⠀⠘⠒⠀⠀⠋⠀⡎⠀⠀⡆⠀⠀⠞⠀⠀⡗⡄⢀⡟⣡⡄⠀⠀⠀⢞⣿⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢇⠀⢠⠃⠀⢀⢳⠁⠞⢟⠁⢇⠀⠀⢀⠀⢏⠉⠂⠀ ⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⣞⢀⠎⠀⠀⡘⡆⠀⠀⢞⠀⠈⠲⣄⡈⠢⣌⡳⢄⡀ ⠀⠀⠀⠀⠀⠀⠀⠘⠀⠚⠁⠮⠀⠀⠔⢹⣀⣀⣠⠇⠀⠀⠀⠀⠉⠉⠉⠉⠉⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣎⡆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣶⣶⠿⠿⢛⡛⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣎⣶⣿⢻⣿⣿⣶⣶⣢⣆⠀⠀⠀⣀⣀⣀⣀⣶⣶⣟⣿⡿⠿⣛⣛⣭⣵⣶⠟⢟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⣟⣿⡟⣻⣿⣿⣿⣿⣿⣿⣭⣭⢠⣟⣿⣯⣭⣀⡬⣩⣭⣜⡶⠿⢟⣛⣯⣭⡶⣶⡛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠉⠁⠿⣿⡿⣿⣿⣿⣿⣿⣯⡄⣿⣿⣿⣿⡟⠃⠈⠱⠶⠟⠛⢋⣭⣿⠶⣟⡛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⣡⣟⣿⣿⣿⣿⣟⡓⢠⣟⣿⠿⣛⣛⡛⣟⣛⣛⡛⢶⣶⣶⣶⣶⣶⣥⣀⣀⣀⣀⣄⣀⣀⣀⣀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠁⣎⣿⣿⣿⣿⣿⡿⠯⢁⣿⢟⣎⣿⣿⡿⢳⣿⣿⣿⠏⠰⠶⠶⢟⣜⣭⣭⣭⣙⣛⣛⣛⣛⡛⠿⠿⠿⠿⠋ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣟⡟⢀⣟⣿⣿⣿⣿⣿⣿⣿⠋⣟⡟⣌⣿⣿⢟⣎⣿⡿⢏⣀⣙⣛⣛⣛⡳⠶⠶⠶⣶⣭⣭⣭⣭⣭⣝⠛⠋⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠀⣌⣿⣿⣿⣿⣿⣿⠟⣂⣌⡟⣱⣿⣿⢏⣌⣿⣿⠁⠬⣭⣙⣛⣛⣛⣛⠛⠿⠿⠿⠶⠶⠶⠶⠆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠟⢁⣀⣟⣿⣿⣿⣷⣶⣶⣟⣟⣫⣟⣿⣿⡏⣟⣿⣿⡅⢶⣶⣊⣀⣀⣬⣭⣭⣉⠛⠛⠛⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠛⠱⣿⣛⣋⣀⣎⣶⣶⣊⣭⡉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣄⡀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⣿⡿⠶⠜⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢻⣿⠿⢿⣶⣶⣊⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣌⣿⣿⣿⣶⣶⣶⣿⣷⣶⣟⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢞⣿⠀⠀⠉⢿⣿⣿⣿⣿⣿⣷⣊⣄⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣌⠟⠉⠀⢞⣿⠛⠛⠛⠿⠿⢿⣿⠟⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡙⢻⣿⣿⣿⣿⣿⣿⡎⣿⡇⠀⠀⠀⠙⠉⠻⣿⣿⣿⣿⣿⣷⡄⠀⠀ ⠀⠀⠀⣠⣿⠏⠀⠀⠀⠘⣿⣧⡀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠻⠿⠿⠿⠛⠛⠛⠉⠉⠉⠁⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⡷⠀⠀ ⠀⢀⣟⡿⠁⠀⠀⠀⠀⠀⠈⠻⢿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣌⣶⠀⠀⠀⠀⠀⠀⠛⠿⠿⠟⠁⠀⠀ ⣰⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⣿⣿⣷⣭⣁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠿⠥⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣇⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡿⢿⣶⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣷⠄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠆⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⡏⠄⢲⢁⠂⡌⢐⠡⢒⠈⣌⡰⠔⡚⠡⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢋⠀⡂⢌⠃⢌⡇⠂⡔⠐⣂⢰⠬⡚⢁⠆⠡⡐⠡⢉⠔⣊⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⡿⢟⣿⡿⠊⢄⢂⠱⠀⢟⠡⢌⠠⠑⣚⢖⢕⠃⡐⢠⣡⠬⠒⠎⡩⢉⠂⡔⣀⠊⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣯⠁⠀⠈⠱⣌⠂⠆⠌⡑⠠⡗⢞⠀⣃⡵⢁⠊⣰⠜⠍⠠⠌⣈⠐⠡⣈⣒⠐⠀⢈⡁⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣻⠀⡀⠀⠀⠑⢿⠈⠉⠉⠉⠉⠛⠲⠌⣀⢢⠟⡁⠌⣀⠃⢰⡀⢺⡉⠥⠉⣙⣊⣡⠄⢣⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⡿⡿⣧⠀⢡⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠑⢊⡘⡐⣠⣌⣫⣀⣎⣿⣟⣿⣿⣿⣿⡎⠄⡃⢟⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⡟⢀⢿⡀⠞⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣀⣎⣶⣟⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣇⠎⠰⣞⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣟⠣⠈⠜⣇⠀⠑⡀⠀⣠⣀⣀⣶⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⡯⣐⠡⢞⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣟⡎⢡⠈⠜⣆⢀⣎⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⡟⣟⣿⣿⣿⣿⡏⢿⣿⣿⣿⣿⣿⣜⣿⣿⢇⠉⢗⡞⣜⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣵⢀⣊⣎⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣜⣿⣿⣿⣿⣿⡇⠈⢻⣿⣿⣿⣿⣿⣟⢏⠞⠀⠈⢛⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣊⣷⣿⣿⣿⣿⢿⠟⠛⠉⢻⣿⣿⣿⣿⣿⣿⣿⣷⣿⢿⣿⡿⠀⠀⠀⠘⠋⠹⡟⠫⠕⠁⠀⠀⠀⠀⢚⢿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⢁⠢⡘⢧⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠒⠂⢠⡿⣄⠀⠀⠀⠀⠀⠀⠀⢫⢿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⠘⡠⠐⠌⢧⡀⠀⠀⠀⠙⠻⢿⣿⣿⡿⠟⠉⠀⠀⠀⠠⠀⠎⡲⡝⢠⠘⣧⡀⠀⠀⠀⠀⠀⠀⠩⢿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣝⢄⠳⡠⢁⠊⠄⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣔⠮⡊⠔⡡⣞⠡⢙⣊⡀⠀⠀⠀⠀⠀⠑⡿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣎⢣⡙⢆⡈⠀⠁⠜⢳⡀⠀⠀⠀⠀⠀⠀⠀⠖⠒⢺⠛⠩⠐⣀⠒⠠⣱⠣⠑⣠⣞⠟⢊⡀⠀⠀⠀⠀⢰⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠱⣌⠱⣆⠉⡄⠡⠘⠊⣄⠀⠀⠀⠀⠀⠀⠀⠞⣇⢃⠡⠄⠌⢢⣧⠶⠟⠉⠀⠀⠀⠈⠀⠀⢀⣎⣜⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⢈⠲⡈⠳⣌⠀⢉⠰⠈⠷⣄⠀⠀⠀⠀⠀⠀⠙⢧⣢⠌⠚⠉⠁⠀⠀⠀⠀⠀⠀⢀⣠⣮⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠐⡑⢆⠄⠳⣌⠢⡁⠆⡉⠷⣄⠀⠀⠀⠀⠀⠀⠙⠊⡀⠀⠀⠀⠀⠀⣀⢀⣊⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢊⢀⠉⠳⡐⢠⠓⣔⢂⠰⢀⠉⠷⣄⠀⠀⠀⠀⠀⠈⢻⢀⡀⢶⣮⣿⣿⣿⢿⣡⣊⣀⠙⢿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠘⢝⡈⢧⡈⠀⠙⣢⡒⢈⠳⣔⠈⠀⠑⡘⢊⡀⠀⠀⠀⠀⠀⢛⡆⣞⢿⣿⣿⣯⣿⣿⣿⣿⠈⠆⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡃⠀⢇⠀⠻⣄⠥⢀⡑⣆⠂⠌⡳⣂⠡⠐⣈⠳⣎⠀⠀⠀⠀⠀⢿⡞⡘⢿⣿⣿⣿⣿⣿⡟⢈⠐⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡎⡀⠘⡄⣰⠟⢊⡂⡔⢈⢮⠐⡄⡙⣆⠥⢀⠡⠹⣧⠀⠀⠀⠀⢞⢇⢇⢂⠙⠻⠿⠿⢋⠐⡀⢺⣜⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡵⢠⡟⠁⠀⠀⠳⣌⠂⢂⢳⠠⠁⠌⢧⠊⠰⠁⢻⡆⠀⠀⠀⠈⢌⠞⡌⠂⠡⠘⠠⠃⣢⣌⣿⣿⣿⣿⣿
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⠀⠀⢀⠀⠠⢀⠀⠄⡀⠠⢀⠀⠄⡀⢀⠀⠀⢀⣀⣶⡟⣟⢯⡻⡝⣯⣛⢟⡷⣶⣄⠀⠀⠀⠀⢀⠀⡀⠄⡀⠠⢀⠀⠄⡀⢀⠀⡀⠀⠀⡀⢀⠠⢀⠀⠄⡀⠠⢀⠀⡀⠀⠀⢀⠀ ⠀⠀⠄⠂⢁⠠⠀⢂⠠⠐⠀⡀⠂⢀⠀⢠⣎⡿⣻⢧⡻⣜⢧⣛⡜⣲⡝⣮⢳⣭⣻⣧⡀⠁⠀⠠⠀⠄⠠⠐⠀⠄⠂⠠⠀⢂⠀⢀⠀⠐⢀⠠⠀⠄⠂⠠⠐⠀⠄⠂⢀⠐⠀⠠⠀ ⠀⠠⠀⠌⠀⠄⠂⠠⠀⠂⢁⠠⠁⠀⢠⣿⢏⡞⣯⢳⡝⣮⢳⡭⣖⢧⡻⣜⡿⣎⢷⣹⣇⢠⠀⠁⠂⠈⠀⠂⠁⡀⠈⠀⠁⠀⠈⠀⡀⠀⠂⢀⠂⠐⠈⠠⢀⠡⠀⡁⠠⠀⠀⠐⡀ ⠀⢀⠀⠂⢁⠐⠈⡀⠁⠌⠀⠄⠀⢄⣿⡳⣏⡞⣯⡳⣝⢮⡳⣝⢮⣳⣜⢟⠿⣜⢧⣏⣿⢀⢀⣀⣐⣀⣁⣀⣀⣀⣀⣊⣬⣀⣀⣁⡇⠀⠐⠀⠠⠁⡈⠄⠠⠀⢂⠐⠠⠀⠀⠀⠄ ⠀⠀⠠⠁⡀⠂⢁⠠⠈⠠⢈⠀⠠⢞⣯⢳⡝⣟⣹⢿⡌⣧⣟⣟⣻⡷⢯⣟⣹⢎⡷⣎⣿⡟⣛⢯⡿⣯⠟⣯⢜⡹⣎⢷⡹⣞⡜⡻⡜⢿⣶⣄⠀⠄⠀⡐⠀⠡⠀⢂⠐⠀⠀⠈⡀ ⠀⠐⠀⠂⠀⠁⠀⠀⡀⢄⣀⠀⡀⣜⢧⣻⢟⣭⢷⡿⣛⡵⣫⢖⣧⢻⡝⣮⣛⢿⣞⡵⣫⢞⣜⣟⡳⣭⢻⡜⣧⢻⡜⣧⣛⢶⡹⣵⢫⠷⣭⢻⢿⣄⠀⢀⠈⠄⠂⡀⠂⠈⠀⠀⠀ ⠀⠐⠀⠁⢀⣚⣎⡟⣟⢯⣛⠿⡷⣞⡿⣭⢳⡟⣟⡌⣣⢟⣥⢻⣬⢳⡝⣶⡹⣞⡌⢿⡵⣿⠳⣎⠷⣭⢳⡝⣮⢳⡝⣶⡹⣎⢷⢣⣏⠿⣜⠯⣞⣻⣧⡄⠀⠐⡀⢀⠁⡈⠀⠀⠂ ⠀⠠⠐⣎⡿⣫⢷⡹⠎⠷⣭⢻⡵⣻⣟⡌⣟⡿⣜⡳⣝⠟⣞⢳⣎⢷⡹⢶⡹⢶⡹⣏⢿⣱⢻⣜⡻⣜⢧⡻⣜⢧⣛⢶⡹⢮⣭⢳⣎⠿⣜⡻⣌⣱⢻⣵⡠⠀⠐⠀⢂⠀⠄⠀⠄ ⠀⢠⣿⢏⡷⣹⢂⠔⠉⠐⢍⢳⡝⣶⣻⡵⣯⠷⣭⢳⣭⠻⣵⢫⡜⣮⡝⣧⣛⢧⡻⣜⢧⡏⡷⢎⡷⣹⢎⡷⣹⠮⣝⢮⣝⡳⣎⠷⣎⠿⣜⡳⡵⣎⢷⣫⣇⠀⠌⠐⡀⠀⠂⠀⠀ ⢀⣿⡟⣮⢳⢁⠆⠀⠀⠀⠀⢂⢻⢶⡹⣷⢫⣿⣜⡳⣎⠿⣜⢧⣛⢶⡹⢶⡹⣎⢷⡹⢮⣜⣹⡯⢟⡷⣻⠟⠷⢻⣌⣳⣎⠷⣭⢻⣜⡻⣜⡳⣝⢮⡳⣭⣿⡄⠀⢂⠀⠡⠀⠀⠀ ⢞⣿⡜⣧⠛⢚⠀⠀⠀⠀⠀⠀⡆⣯⢳⢻⣿⣿⣬⢳⣭⢻⡜⣧⠛⣮⡝⣧⢻⡜⣧⣿⡟⠈⠁⠀⠂⡍⢹⠀⠀⠀⠈⠁⠛⣿⣮⢳⡎⣷⣭⢳⡝⣮⢳⣧⡟⡆⢠⠀⡌⠀⡄⠀⠀ ⣟⢇⡿⣜⠇⡆⠀⢰⠀⠀⠀⠀⠐⣹⢮⢃⠅⠺⡿⣮⡝⣮⢳⣭⢻⣜⡳⣝⢮⡷⠟⠁⠀⠀⠀⠀⠀⠀⠩⠀⠀⠀⠀⠀⠀⠏⠚⣿⣜⡳⣎⢷⡹⣎⠷⣎⣿⠃⠀⠄⠐⡀⠠⠀⠀ ⣟⢮⡳⣜⠰⠀⠀⡟⠀⠀⠀⠀⠀⢊⠔⠁⠀⠀⠙⢷⣜⢎⡷⢎⡷⢎⡷⣹⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⠀⡆⠀⠈⢿⡵⣫⢞⡵⣫⢻⣌⣻⠀⢈⠀⠂⠄⡀⠄⠀ ⡿⣎⢷⣹⢞⠀⠀⣧⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠙⠻⣟⣝⢟⡹⣞⣜⠃⠀⠀⠀⠀⠀⠀⠀⢀⣠⣀⣄⡀⠀⣌⠀⢠⡁⠀⢠⠞⣿⡱⣏⢟⡱⣏⣟⠇⠀⡀⠂⠁⠄⠀⡀⠀ ⣿⣜⣻⣌⠰⠀⠀⠐⡄⠀⢰⡀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠈⠛⠳⠿⠧⠀⠀⠀⠀⠀⠀⢀⡎⠋⠁⠀⠈⠙⢟⡏⢀⣶⠇⠀⢚⢠⣿⢳⡝⣮⢳⣜⡟⠀⠐⠀⠠⠁⠂⠁⠀⠀ ⣷⢎⡷⣎⣇⢃⠀⠀⢮⠀⠘⣧⣠⡟⠋⠉⠉⣙⠶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠩⠘⠢⠅⡢⡀⠈⢻⡟⠁⢀⣆⢆⠎⣿⢣⡟⣌⢳⣟⠁⠀⢠⡆⠀⠂⡁⠐⠈⠀ ⢯⣟⡌⡳⢟⡐⡀⠀⠘⢷⣀⣚⡟⠀⠠⢂⠱⣀⠎⠛⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⣧⡇⠀⠀⠀⠈⢒⡀⠀⢳⠞⠋⢄⠞⠀⣿⢣⡟⡌⣟⠏⠀⣎⡿⡆⠀⠂⠄⡀⠁⠀ ⠞⡿⣌⡹⢧⣳⠐⡀⢊⡀⠉⣿⠀⢠⠁⢊⣶⣏⠀⠀⠈⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡀⠀⠀⠀⠀⠲⠀⠀⢠⠊⡋⠀⠄⣿⣏⠟⣜⣋⣎⡿⣫⡿⠀⠐⠈⠠⠀⠂⠀ ⠀⣿⣷⡹⢧⣏⠷⣌⠀⠙⠛⠏⠀⠆⡈⣿⣿⣿⡄⠀⠀⠈⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢞⣿⣿⡏⠙⢊⣄⡀⣀⠆⠃⠀⡇⡆⡇⢀⠂⣿⣎⢿⡹⣏⢷⣹⡯⠃⠀⠌⢀⠡⠀⠂⠀ ⠀⣿⣎⠿⣷⣎⠿⣜⣳⣅⢠⢠⠀⠇⠀⣿⣿⡋⠙⣊⡀⠀⢞⡆⠀⠀⠀⠀⠀⠀⠀⠀⢞⣿⣿⣿⣀⣌⣿⣿⣿⢀⡀⠀⡃⡇⣷⣶⣶⣟⡿⣎⣷⣹⣞⠗⠁⠀⢂⠐⠀⠄⠂⢁⠀ ⠀⢞⣯⣻⢌⡹⣟⢮⡳⣞⢈⠀⠀⠞⡀⣿⣿⣧⣀⣟⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡟⢀⠂⠀⠗⡗⣟⣶⣓⢮⡳⣏⢿⣹⡶⣄⠀⠈⠀⠄⡈⢀⠂⠄⠀ ⠀⠀⢻⣯⢷⣻⣌⣧⠿⣟⣅⣊⣥⠀⢀⠘⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⡿⡁⠈⠀⢘⠻⢹⢿⣣⢟⡯⣷⣜⢎⡷⣹⢻⣊⠀⠁⠠⠐⠀⠠⢈⠀ ⠀⠀⠀⢻⣷⡳⣎⢟⡹⣞⣜⡌⠀⢄⠀⠠⠘⢿⣿⣿⣿⣿⡿⢁⠀⢀⠀⠀⠀⠀⠀⡆⠀⠈⠊⠿⠛⠻⠻⣅⠌⠀⢀⠈⣻⣞⢧⣛⢮⡳⢧⣛⢿⡜⣧⢻⡜⡇⠀⠐⠠⠁⢂⠠⠀ ⠀⠀⠀⠈⢳⡿⣜⣎⠷⣭⢻⣊⢡⠏⢀⠀⠐⠀⡩⡻⠋⠉⠀⠁⠀⠈⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠐⣰⡯⣞⡭⣞⣭⢳⡝⡟⣏⢷⣫⢟⣿⠀⠀⠡⠐⠀⡀⠂ ⠀⠀⠀⠀⢰⡙⠷⣜⡟⣷⣯⣞⣮⠡⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⣂⢄⠀⠀⠀⠀⠀⠀⡐⣡⣟⡳⣭⢞⡌⢎⡷⣹⢳⣿⢣⡟⣟⡏⠀⠈⠀⠂⠁⠠⠀ ⠀⠀⠀⠀⠘⣿⢊⣌⣙⠷⣮⣜⢭⢧⡁⠄⠀⠀⠀⠀⠀⠀⠰⢎⠁⠠⠀⠀⠀⠐⠒⠊⠁⡀⡘⠀⠀⠀⠀⠀⠀⢌⣎⢿⣱⢻⣬⢻⡜⣯⢞⡵⣫⢷⣫⢟⣳⣥⣀⣀⣆⡀⠈⠀⠄ ⠀⠀⠀⠀⠀⠞⣿⣭⣛⣟⡻⣞⡻⣎⠿⣊⡁⠆⡀⠀⠀⠀⠀⠘⢀⠀⠀⠀⠀⠀⠀⠈⠀⠔⠈⠀⠀⢀⠠⡠⠅⣟⣏⠷⣭⢳⣎⢷⡹⣖⢯⢟⡟⣧⢿⣫⢟⡌⣹⢮⡝⡿⣷⣄⠀ ⠀⠀⠀⠀⠀⠀⠘⢟⡟⣜⡳⣭⢳⣭⣛⣟⡇⢣⠐⠅⡂⠄⡀⡀⠀⠉⠐⠀⠀⠀⠐⠈⠁⡀⠀⢄⠰⠑⠀⠰⣡⣿⢎⡿⣜⡳⣎⢷⡹⣞⣟⣻⣜⣳⣎⢷⣫⢞⡵⣣⢟⡵⣫⢟⣧ ⠀⠀⠀⠀⠀⠀⠀⠀⢙⡻⣜⣞⣷⡟⠜⠚⠀⢁⢆⠀⠀⠁⠀⠒⠡⠔⠂⢠⣀⡐⠂⠀⠅⠂⠁⠁⠀⠀⠠⠂⡎⣿⡺⣵⢫⡵⣫⢞⡵⣫⢞⡵⣫⢳⣝⡻⣮⡻⣜⢧⡻⣜⢧⡻⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠐⢣⠐⠀⢲⢰⠀⠀⠀⠀⠡⠐⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠓⠃⡇⢹⣷⡹⣎⢷⣹⣎⣷⣹⣎⠷⣭⢳⣎⢷⡹⣷⣏⢟⡱⣏⢟⣱⢿ ⠀⠀⠐⢂⠀⠀⠀⠀⠀⢇⠊⡔⡇⡆⠀⠀⠀⠀⠰⢩⠁⠊⣂⡠⢀⡀⠀⠀⠀⠀⠀⣀⠀⢄⢐⠥⠐⠀⠀⡁⠆⠈⣫⣷⡻⣏⢷⡹⢮⡝⡟⣿⣜⡳⣎⢷⡹⢟⣏⢟⡱⣏⢟⣜⠇ ⠀⠀⢠⡀⠈⠢⡀⠀⠀⠘⡡⢂⠄⡃⠀⠀⠀⠀⠀⠏⡄⠀⠀⠈⠁⠒⠀⠁⢚⢰⠰⠂⠉⠀⠀⠀⠀⠀⠀⠀⣃⣟⢟⡌⣛⡟⣧⣛⣧⣻⣵⠿⣜⡳⣝⢮⣝⡿⣎⢷⡹⢮⣟⠎⠀ ⠀⠀⠀⠞⢀⠀⠀⢀⠀⠀⢇⠄⡄⡃⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⢞⡇⠇⠀⠀⠀⠀⠀⠀⠀⢀⣿⢇⡿⣞⢇⡿⣞⢻⡜⣧⡜⣿⡞⢧⡻⡌⣌⡻⣜⢧⣻⡿⠇⠀⠀ ⠀⠀⠀⠀⠈⠠⡀⠈⠂⡀⠀⢎⢣⠡⠀⠀⠀⠀⠀⢰⢡⠀⠀⠀⠀⠀⠀⠀⠀⢞⣳⢘⠀⠀⠀⠀⠀⠀⠀⢌⡟⣮⢳⡝⣮⢳⣭⢳⡝⣶⡹⢶⡹⢧⣻⡟⣧⣻⣞⠯⠋⠁⠀⠄⠁ ⠀⠀⠀⠀⠀⠀⠈⢄⠀⠐⡀⠀⠣⢆⡒⠄⣀⡀⠠⢀⡉⡄⠀⠀⠀⠀⠀⠀⠠⢞⡹⡀⡄⠀⠀⠀⠀⠀⠀⣟⡟⣌⢣⡟⣌⢳⣞⣧⢿⡶⡜⢷⡻⣏⢷⡹⣝⢷⣧⠀⠐⠈⠠⠈⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢢⠀⠈⠄⠀⠑⢎⡒⢒⠒⡚⠍⢧⠀⠀⠀⠀⠀⠀⢀⠆⣮⠕⣧⡑⢀⠀⠀⡀⠄⣈⣿⡻⣜⢧⡻⣜⡳⣎⢿⣎⢷⡹⢧⡻⣜⢧⡻⣜⢧⢿⣇⠀⠄⢁⠠⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠘⡄⠀⠀⠑⠚⣢⠑⡞⢈⠳⢬⣁⣒⣒⣂⣡⠞⣥⠛⡎⡹⣒⢖⡲⢎⣋⢧⢻⣷⡹⣎⠷⣭⢳⡝⣟⡟⣮⡜⣧⣻⡜⣧⢻⡜⡯⢟⣻⠀⠐⡀⠄⠂ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠘⠀⠀⠀⠀⠀⠑⠂⢍⣚⠀⢃⠎⡎⣉⠶⡙⣀⠛⡎⢣⢍⡲⢩⠖⠱⠚⠁⠙⣷⣭⢻⡜⣧⣻⢟⣌⣹⡜⢮⡝⣿⣜⢧⡻⣭⢿⡏⠀⠐⡀⠄⠂ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠚⠐⠑⠊⠑⠂⠛⠐⠋⠂⠉⠀⠀⠀⠀⠀⠀⠀⠛⠿⣟⣟⡜⣚⠶⣭⢻⠷⣜⣮⣜⢷⣻⠝⠃⠀⠠⠁⡀⠐⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠁⠀⠠⠀⠀⠀⠀⠉⠛⣻⡿⣞⢯⡻⣜⢶⣹⡿⠀⠀⠠⠈⡀⠐⠀⡁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠁⠀⠐⠀⠀⠁⠀⡀⠀⢀⠠⠀⠀⠄⠀⠀⠀⣟⣟⡌⣹⢎⣷⣜⡟⠛⠁⢀⣎⠂⠐⡀⠁⢂⠀⡁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠄⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⠀⢹⣷⡹⢧⢯⡝⡷⣶⢶⡿⡿⠃⠀⠂⢀⠡⠀⠐⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠐⠀⢀⠀⠁⢀⠈⠀⠐⠈⠀⠀⠀⠐⠀⠀⠉⠻⠿⣞⣿⣳⡟⠟⠋⠀⠀⠄⠡⠀⠄⠂⠁⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⣙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠙⠢⡄⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣎⢶⣎⠟⢠⣻⠀⢀⡀⠂⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡀⠀⠈⠳⣿⡆⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠃⣟⠏⠀⣌⣇⡔⠋⢀⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡘⢗⠀⠀⠀⠻⣧⠀⠘⢊⣀⣄⠀⠀⠀⠀⠀⠀⣀⣀⠀⣄⣲⡟⠊⢣⠀⢥⣀⣌⢟⠇⣀⡎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠈⠛⣿⣊⠀⠀⠈⠃⠀⢻⢻⠈⢊⠀⠀⢀⣔⠟⠀⢫⢡⡏⣟⢂⣎⢞⡎⢣⢔⣃⢀⠝⢿⡢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡊⡀⠈⠛⢵⡄⠀⠀⠀⠀⠻⠀⠈⣆⣟⡝⢡⠀⠀⣞⠎⠀⠎⢞⣿⢲⡗⠯⢠⠞⠉⠀⠀⠀⠈⠑⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⢧⣄⠀⠀⠈⠀⠀⠀⣠⣀⠀⠀⡝⡱⡀⢞⣠⠞⡁⠀⠀⢀⣠⢜⠙⣒⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣍⠉⠻⣷⡄⠀⠀⠀⠀⢻⠀⠳⣌⠞⡀⢓⣯⣌⡔⠒⢢⠉⠉⠈⠑⠯⠇⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠘⢷⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⣀⠈⠙⠢⠀⠘⣏⠑⢧⠀⡞⠀⠉⠉⡏⡿⢷⣀⣀⠱⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠲⣌⢻⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⣄⠀⠀⠀⠘⢆⠀⠀⢣⠀⠀⡎⠀⢷⣠⣿⡿⡇⠀⠉⠒⠢⣀⡄⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠑⠟⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣀⣲⠶⠶⠯⣍⠓⢀⠀⠻⣅⠃⠀⠞⡀⠀⠳⠷⠈⠻⢞⣞⠋⠀⠀⠀⣎⡏⡇⠀⠀⠀⠀⠀⠀⠙⡈⠉⠒⠀⡀⠀⠀⢰⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⢊⠕⠊⠀⠀⠀⠀⠀⠈⠓⢄⠀⠀⠈⠓⣄⠀⠳⡀⠀⡜⢄⠀⠀⠀⠀⠀⠀⠀⣧⠞⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠈⢳⢄⠈⡆⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠚⠀⡔⠁⠈⠋⠀⡠⠚⠉⠀⠀⠈⠑⢞⠢⠀⠻⣄⠀⠀⠑⣄⢞⠀⠈⠓⢢⡀⡀⠀⠀⠟⡆⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⡎⠀⠃⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣎⠋⠀⡞⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⢀⣈⡳⣄⠀⠀⡑⠀⠀⠈⠻⡆⠀⠀⠀⠙⠓⠄⠒⠊⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀⡎⠁⠀⢀⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡞⠁⠀⢞⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⡰⠁⠀⠘⢆⠑⠖⠕⠀⠀⠀⡞⣇⠀⠀⠀⠀⠀⢰⡀⠀⠀⠀⠀⠀⠀⠀⡠⠋⠀⠀⠀⡊⠊⠀⠀⠀⡞⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢊⠀⠀⠘⡀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣚⡞⠉⠊⡀⠀⢠⠁⠞⠀⠀⠀⠀⠀⢞⢡⠀⠀⠀⠀⠀⢀⠞⠀⠀⢀⡀⠊⠀⠀⠀⢀⡎⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⢳⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠡⡀⠀⢰⡟⢲⢎⠧⣠⠀⢞⠄⠀⢣⠀⠀⠀⠀⢞⠀⡇⠀⠀⠀⢀⡆⠀⢀⠔⠁⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⠀⢞⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⣌⡏⣿⣧⣰⡵⠆⠘⠀⢀⠀⠱⡄⠀⠀⡞⠀⢁⠀⠀⠀⢞⠀⡠⠋⠀⠀⠀⢀⣎⡌⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠁⢀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢞⠁⠀⠛⠉⠃⠀⠀⢷⠈⠂⠀⠈⠢⣠⠃⠀⡎⠀⠀⠀⠀⠟⠁⠀⠀⠀⡰⠋⣌⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣎⠟⣀⡎⠁⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢞⠀⠀⠀⢰⠀⠀⠀⠈⢧⡀⠀⠐⢀⣯⠠⣱⠃⠀⠐⠒⢢⠀⠀⠀⠀⣎⠁⢀⡜⠉⠑⠢⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⡟⠁⠀⠞⠀⠀⠀⠀⠈⢊⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢞⡄⠀⢀⡿⣟⠢⣠⠀⠀⡱⡄⠀⢿⣿⢳⠃⠀⠀⠀⠀⢘⡆⠀⠀⠀⠘⣄⠉⠁⢙⡀⠀⢞⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢰⡏⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠈⠙⠢⡀⠀⠀⠀⠀⢠⠖⠋⠀⢀⡟⢡⠟⠀⠞⠀⠀⠱⠌⠷⡄⡱⣏⠁⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠙⠚⠉⠀⠀⠟⠻⢊⣄⠀⠀ ⠀⠀⠀⠀⢹⡄⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢞⠀⠀⠀⢰⠏⠀⢀⡎⠋⠀⠀⡷⠀⠀⠀⠀⢠⡆⠀⣞⠃⠀⠀⢹⠀⠀⠀⠀⡇⠁⠀⠀⠀⠀⠀⠀⣀⠀⠊⠀⠀⠀⠙⢷⡄ ⠀⠀⠀⠀⠈⠻⣊⣀⠀⠑⠢⣀⠀⠀⠀⠀⠀⠀⠀⢞⠀⠀⢰⠏⠀⠀⡟⠁⠀⠀⣎⢷⡀⡆⠀⠀⠀⣇⣌⠃⠀⠀⠀⡇⠀⠀⠀⠀⠃⠀⠀⠀⠀⢰⠉⠉⠀⠀⠀⠀⠀⠀⠀⠈⣷ ⠀⠀⠀⠀⠀⠀⠀⠙⣷⠀⠀⠀⠁⢢⠀⠀⠀⠀⢀⠆⠀⢰⠏⠀⠀⠀⠁⠀⣠⡟⠋⠘⡃⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⡎⠀⠀⠀⣎⠃⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟ ⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⢀⠀⠀⠀⢀⠎⠀⢰⠏⠀⠀⠀⠀⠀⣰⢿⠖⡉⠙⠳⡆⠀⠀⠀⢿⠀⠀⠀⡀⣞⠁⠀⢀⠎⢞⠀⠀⠀⠀⡎⠁⠀⠀⠀⠀⠀⠀⢀⣀⣎⠟⠁ ⠀⠀⠀⠀⠀⠀⣠⡟⠁⠀⠀⠀⡠⠋⠀⠀⢀⠎⠀⢠⠏⠀⢀⡀⠀⠀⠀⢿⡈⠉⢹⡆⢞⠀⠀⠀⠀⡇⠀⠀⡜⢡⡏⠀⣔⠚⠀⠞⠀⠀⡠⠊⠀⠀⠀⣀⣀⡎⠶⠚⠋⠉⠀⠀⠀ ⠀⠀⠀⢀⣎⠞⠉⠀⠀⢀⡀⠊⠀⠀⠀⠀⢞⠀⢠⡟⠀⡠⠊⡇⢀⠇⠀⠈⠛⠛⠛⠀⡇⠀⠀⠀⠀⡇⡀⠈⠀⡟⣄⠀⡗⠁⠀⡆⢀⠞⠁⠀⢀⣎⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣎⠟⠁⠀⠀⢀⠔⠉⠀⠀⠀⠀⠀⠀⠈⢆⣟⠒⠺⠀⠀⠡⣌⠄⠀⠀⠀⠀⠀⠂⡏⠀⠀⠀⠀⣞⡰⡄⠀⠐⣄⠙⠚⠂⢠⡳⠃⠀⠀⣎⠏⠀⠀⠀⣠⣄⠶⠶⣀⡄⠀⠀⠀ ⢠⡟⠁⠀⠀⠀⠀⠋⠀⠀⣠⣶⣿⠯⣭⣉⠛⡗⣟⡇⠇⠀⠀⢶⡺⠀⠀⠀⠀⠀⠀⣀⣷⠀⠀⠀⠀⢹⠱⣇⠀⠀⠈⠓⢀⣠⡟⠁⠀⠀⠀⣿⡀⠀⠀⣮⠭⢊⡄⠀⠀⢻⡄⠀⠀ ⢟⠁⠀⠀⠀⠀⠀⢢⡀⠀⢿⡥⣀⡿⠀⢹⡆⢣⠘⠃⠀⠀⠀⠔⣧⡀⠀⢀⣀⡎⠟⡏⠉⣀⠀⢰⠚⠃⠀⡹⡄⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠈⠷⣀⣀⣀⣠⣟⠃⠀⠀⣞⠇⠀⠀ ⠞⣧⡀⠀⠀⠀⠀⠀⠈⠉⠒⠉⠀⠀⢀⣌⠃⠘⢆⠀⠀⠀⣠⠜⠁⠀⠀⠀⠀⠀⠀⠀⡇⣟⠀⠘⡡⠷⠀⢓⣵⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⢀⣎⠏⠀⠀⠀ ⠀⠈⠛⠶⣊⣀⠀⣀⣀⡀⠀⣠⣎⠶⠛⠁⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢯⠒⠀⠬⠀⠀⠘⠋⡷⢊⣄⡀⠀⠘⢆⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣎⠟⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢀⢀⣀⠀⢀⣠⠃⠀⠉⠉⠛⠊⠶⢟⠶⠀⠀⠀⣖⠶⠞⠋⠉⠀⠀⠀⠀⠀⠀⠀
"You know, sometimes I think the clouds are just trying to tell us something," mused Twilight Sparkle, her eyes squinting up at the sky. Rainbow Dash, mid-flight, zoomed in close to her. "What do you mean, Twilight?" she called out, her rainbow mane fluttering in the gentle breeze. "Well, they're always changing, aren't they? Shifting into new shapes, new messages. It's like they're trying to communicate with us through the language of the sky," Twilight replied, her voice filled with wonder. Rainbow Dash chuckled, her wings beating a little faster. "You and your books," she teased, looping around Twilight. "They've got you seeing patterns in everything." The two ponies continued their leisurely flight over Ponyville, the warm sun bathing the town in a soft glow. The town looked peaceful from above, the thatched roofs of the houses and the lush green fields spreading out like a patchwork quilt. Twilight couldn't help but feel a sense of belonging as she took in the familiar sights. As they approached the edge of town, they spotted a young foal playing by the river, her yellow coat glinting in the light. She was trying to mimic Rainbow Dash's sonic rainboom with a stick and a rock, her giggles carrying on the wind. Twilight felt a twinge of envy at the carefree nature of youth, a stark contrast to the weight of her own responsibilities. "Looks like someone's got her heart set on becoming the next greatest flyer in Equestria," said Rainbow Dash with a wink. Twilight nodded, her gaze lingering on the foal. She remembered her own early days, when the world had been so vast and full of mysteries waiting to be uncovered. Her thoughts were interrupted by a sudden jolt of energy that shot through her body, making her wings quiver. "What was that?" she exclaimed, looking around for the source of the disturbance. Rainbow Dash frowned, scanning the horizon. "I don't know, but it feels... unnatural." The two friends exchanged a look of concern. The serene day had been pierced by an unexpected tension, and they both knew that something was about to change in the fabric of their quiet lives. The foal by the river looked up, her eyes wide with curiosity. The air grew thick with anticipation, and the distant sound of hoofsteps grew louder. "We should go check it out," said Rainbow Dash, her voice tinged with excitement. Twilight nodded, a flicker of fear mingling with her curiosity. As they descended towards the source of the disturbance, they had no idea that their simple afternoon was about to become the start of an adventure that would shake the very foundation of their world.
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⢀⠀⠀⠀⠈⠀⢂⠀⠲⢀⡔⢂⡲⠖⠀⠒⠂⠀⠀⠀⠀⢰⠂⠀⠀⠀⠀⠈⠀⠀⢠⡶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⣿⠉⠉⠙⠉⠉⠠⡀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠉⠱⡒⠲⡄⠀ ⠀⠀⠀⠀⠀⠀⠀⠶⠎⢶⡁⡠⠁⠀⠀⠀⠀⠀⠀⠑⡀⠀⠳⠋⠀⠀⠀⢀⡔⡶⠉⣐⠄⣟⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣎⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠶⠖⡄⣀⣀⣀⡀⠀⠀⠀⠀⠀⢠⠜⠋⠀⠀⠀⠀⠀⢀⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⠹⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢞⣄⡀⠀⠀⠀⠀⠀⠀⠀⠈⡀⡶⠋⡒⠀⡎⡜⠀⠁⢠⠌⣹⡇⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣯⠃⠬⠈⠅⠀⠀⢞⠀⠀⠀⣀⣀⠻⣂⣠⡀⠀⠀⠀⠀⠺⢊⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠱ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠌⠷⠿⠶⣠⣀⠀⠀⠘⢧⡁⠀⠀⠉⠀⠀⠀⠀⠌⢠⣧⢇⠀⠀⠀⠀⠀⢀⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡻⢈⠀⠀⠠⠀⠌⢀⡜⠔⠚⡉⠡⢀⠒⠚⢉⡿⠀⠀⣠⣀⣀⡻⠉⠓⢲⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡐ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢞⠀⠀⠀⠈⡶⡀⠀⠀⠀⠀⠀⡌⠉⠀⠚⢍⠒⢠⠀⠀⠀⣌⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣌⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠊⠀⢄⠀⠁⠒⠀⠐⢗⡜⠀⠡⢀⠂⢀⠁⡀⡑⠳⠜⢋⠀⠀⢀⠈⠑⠺⣲⣺⠊⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠞⠀⠀⠀⣬⡱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠟⡆⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣟⠂⠡⣠⠶⠊⡜⠁⠐⢀⠂⢀⠂⠀⢀⣁⡀⠂⠘⢊⡈⠠⠈⡐⠀⡀⠑⠊⣄⠓⣄⠠⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠛⠁⠀⠀⠀⠘⢷⠁⠀⢀⣀⠀⠀⠀⠀⡌⢚⢠⢞⠞⠘⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠞⢁⣌⠛⠋⠀⠀⢀⠀⠠⢁⠀⡈⢀⠀⣌⠟⠙⠜⢗⢄⠀⠜⡀⠂⠀⡐⠀⡐⠀⠌⢳⡄⠳⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠀⠀⠀⠀⠀⠀⠈⠂⠐⢞⠀⠹⡂⠄⠈⢀⠆⡎⠀⠀⠀⠀⢠⡇⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠋⣰⠖⠉⠀⠓⣄⠀⠀⠂⠈⢀⠠⠀⠀⠄⠈⣿⠅⠀⠀⠀⠙⡷⡎⡿⠿⠳⢊⡀⠀⠄⠀⠀⠙⣟⠝⢛⢄⣄⠄⠀ 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⠀⠀⢞⠈⡌⢰⠀⠀⠀⠀⠱⣄⠀⠑⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣟⣿⣿⣿⢋⢿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢞⣿⣧⠞⠋⠻⣿⣿⣷⣊⣄⣠⣀⣀⣀⣀⣀⣀⣀⣀⣀⣟⣿⣀⣀⣀⣀⣀⣀⣀⣀⣎⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡏⢰⡇⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣟⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣟⣿⣥⣎⣶⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⠃⣞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⡀⠘⣊⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣀⣀⣎⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣊⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣎⣶⣿⣿⣿⣿⣿⡿⠿⠛⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢞⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠹⣿⣊⣀⣎⣶⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠛⠛⠋⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠿⠿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣊⣀⣀⣎⣶⣿⣿⣿⣿⣿⣿⣿⡟⠉⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⡆⢀⠞⡌⠉⠙⠛⠻⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡞⣠⡇⡇⠀⠀⠀⠀⢰⣄⡀⠀⠀⠀⠞⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡏⠉⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⣿⡇⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣇⠀⠂⡇⠀⠀⠀⠀⢞⡇⠀⠀⠀⢜⣿⣿⣿⣿⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡏⢌⠃⡜⣊⡀⠀⠀⠀⠈⠿⣷⣶⣀⣄⣀⣀⣀⣀⣚⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢹⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⣿⡇⠀⠀⣰⣿⡿⠋⢻⣿⣿⣿⣿⣯⠀⠂⡇⠀⠀⠀⠀⠈⢩⠀⠀⠀⢞⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠇⣞⠀⠀⠘⠻⣶⣶⣊⣀⣀⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢞⠀⡇⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠟⠻⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢞⣿⣿⣿⣿⠟⠁⠀⠀⠙⢿⣿⣿⣿⡇⠀⣿⣷⣶⣿⣿⣟⠀⢀⣟⣿⣿⣿⣿⣷⠀⠂⡇⠀⠀⠀⠀⠀⠘⠀⠀⠀⢞⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐ ⠀⢌⢞⡄⡀⠀⠀⠈⠙⠛⠿⠿⠿⠿⠿⠿⠿⠛⡏⠉⠁⢞⡟⣿⣿⣿⣿⣿⣿⠁⠀⠞⡀⡇⠀⠀⠀⠀⠀⠀⣰⣿⣿⡟⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢞⣿⣿⣿⡏⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠀⢢⡇⠀⠀⠀⠀⢞⠿⠿⠿⢶⣌⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂ 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⠀⠂⣇⠀⠀⠘⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣣⠀⠡⡀⠀⠀⠀⠹⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣎⣟⣿⡿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⢉⠁⠀⠀⠀⣌⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⣞⠃⠀⠀⠀⠀⠀ ⠀⠐⢬⠀⠀⠀⢞⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠑⠄⠀⠀⠀⠈⠻⣿⣿⣷⣊⣄⣀⣀⠀⠀⠀⡀⠀⣀⣀⣠⣀⣀⣶⣟⣿⡿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠁⠀⠀⢁⢟⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢠⠏⣰⠃⠀⠀⠀⠀⠀⠀ ⠀⠈⢌⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢊⡀⠈⠢⡀⠀⠀⠀⠈⠙⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠀⣰⠂⢠⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢃⣰⠏⠀⠀⠀⠀⠀⠀⠀ ⠀⡁⢺⡄⠀⠀⣀⣘⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⡰⠁⢰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢏⣀⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠣⠄⡇⠀⣌⠃⢈⠙⠳⣄⠀⣀⢀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⣄⠀⠑⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠰⠈⠀⡠⠊⠀⣰⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃⣌⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠘⠠⣧⢞⡇⠀⠀⠈⠢⡀⠛⠁⠈⠈⠁⠙⣊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⢄⠀⠈⠢⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⢀⡎⠊⠁⠀⣌⠏⠀⠀⣀⢀⠶⢄⡠⢄⡀⠀⠀⠀⠀⠀⡀⣰⣣⣌⠃⠀⠀⠀⠀⠀⢎⠄⠶⠀⠀ ⠀⠞⣀⠞⠚⠂⠀⠀⠀⠀⣞⠁⠈⠆⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠊⣀⠀⠁⠢⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠁⠀⠀⠀⠀⠀⠀⢀⠠⠈⢀⣀⠖⠋⠀⠀⢀⣌⠏⠀⠀⡜⠡⠂⠉⠒⠈⠂⢌⡒⠄⣀⠀⡞⡹⠑⠋⠑⠬⡢⠀⠀⠀⠀⠘⠆⠚⠀⠀ ⠀⠈⡁⠀⠀⠀⠀⠀⠀⠀⠈⠒⠀⠀⠀⢎⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣀⠀⠉⠂⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡎⠋⠁⠀⠀⠀⢀⣟⠃⠀⠀⠈⡗⠁⠀⠀⠀⠀⠀⠀⠈⠐⠉⠁⠈⠀⠀⠀⠀⠀⢻⡲⠀⠀⠀⠀⠀⠀⠀⠀ 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⠀⠀⠀⠀⠀⠠⠀⠀⣀⡀⣈⠧⠀⠀⠀⠀⣠⢫⠀⠀⠀⠀⠀⠀⠀⣄⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡠⠔⠁⠀⠀⠀⠈⠢⠄⠜⠀⠀⠀⠀⠀⠀⠀⠀⡌⢀⡏⠐⢕⢀⠀⠀⠀⠀⡔⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢣⠌⣏⢜⡌⠀⠀⡀⠊⠁⠐⠀⠀⠀⠀⠀⠀⠀⠬⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡅⢞⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣯⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⣌⠃⠀⠀⢝⠠⣀⡮⠋⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⣇⢞⡈⠻⢆⠀⠘⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⢞⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢞⠀⡌⠀⠀⠀⠀⠉⠀⠁⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢹⡀⢧⠀⠙⢧⡀⠀⠈⠑⡀⠀⠀⠀⡀⢄⡀⠀⢞⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠞⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢞⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠠⠎⣒⠊⢉⠉⡄⠊⠎⠀⢆⣉⡉⠐ ⠀⠀⠀⠀⠀⠀⠀⠀⢧⠘⡆⠀⠈⣷⡄⠀⠀⠡⡀⢀⠎⠁⠀⠈⠉⢛⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠄⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣇⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣣⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠢⣜⠉⠊⡀⠀⠀⠁⠉ ⠀⠀⠀⠀⠀⠀⠀⠀⠞⠊⠜⠀⠄⠌⠟⠊⠌⠀⠚⠁⠀⠀⠀⠀⠀⠀⠹⠧⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠧⠌⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠳⠌⠄⠀⠄⠀⠀⠀⠀⠌⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠥⠌⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠊⠜⠊⠠⠄⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣶⡶⠿⠿⠿⠿⠷⣶⣀⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣟⠟⠋⣁⣀⠶⠶⠟⠳⠶⢊⣍⡛⢿⣊⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⣠⣟⠟⠁⣠⡟⠋⣠⣀⠶⠶⠶⣀⣀⠈⠻⣊⡙⣿⣄⠀⠀⠀ ⠀⠀⢀⣀⣶⣟⠟⠛⠛⣷⣌⠋⣰⣟⢉⣠⣎⣶⣶⣊⣭⣷⣄⠈⢷⡌⢿⣆⠀⠀ ⠀⢀⣿⠏⣭⡥⡄⡄⡆⢞⡏⢿⡯⣿⡉⣜⡍⢹⡅⣿⠀⣟⣿⣧⠌⣷⣌⠿⢿⣷ ⠀⠘⣿⣔⠃⠃⠉⠜⢃⣟⣧⣬⣧⣿⣷⣿⠿⢟⣷⣟⠗⠻⣿⡀⠀⢹⡇⠀⢰⣿ ⠀⢀⣹⣿⣷⢶⣀⣀⣟⠋⠁⠀⠀⠘⣿⡇⠀⠀⠹⣿⡄⠀⢻⣧⠀⠈⡇⠀⣌⡏ ⣎⡿⠛⠁⠀⠀⠈⠻⣿⠀⠀⢠⣎⡆⠞⣧⠀⠀⠀⠈⠇⠀⢞⣿⡆⠀⠁⢠⣿⠃ ⢿⣧⠀⠀⠀⣠⣶⡆⢞⣇⠀⠀⠉⢁⣌⣿⠀⠀⢰⣊⡀⠀⠀⣿⣿⠀⠀⣌⡟⠀ ⠀⢻⣧⡀⠀⠈⢉⣡⣟⡿⠟⠛⠛⠿⢿⣿⣄⣠⣌⣿⣿⣶⣶⣿⠋⠀⣌⡿⠁⠀ ⠀⠀⠹⣷⡀⠀⢹⣿⠋⠀⠀⠀⢀⣀⣀⠈⠉⠛⠛⠻⠟⠛⠋⠁⣠⣟⡟⠁⠀⠀ ⠀⠀⠀⠙⣿⣀⣿⡏⠀⠀⢀⡞⠉⢻⣿⠻⠿⢷⣶⣶⣶⣶⣶⠿⠟⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠉⠹⣿⡀⠀⠈⠳⠀⣰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⠻⢷⣶⣶⡟⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⡶⠞⠛⠫⢀⣀⠀⠙⣷⡀⠈⠙⣲⠋⠙⢊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⡟⣋⡀⠀⠀⠀⢀⣈⡷⠖⠛⠋⠙⠓⣿⠀⠀⡞⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣟⠉⢀⡀⠖⠒⢊⡎⠋⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⣿⠀⠀⠀⠀⠀⠀⣠⡎⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⢀⡏⠀⠀⠀⣌⠁⠀⣀⡀⠀⠀⠀⠀⠀⠐⠋⢠⡏⣇⠀⠀⡎⢻⡶⠋⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠞⡆⠀⠀⠀⣇⠀⣞⡏⠟⣿⣊⣀⢀⠀⠀⠀⢰⡇⢹⠀⣞⠃⠜⠁⢀⣞⡀⠎⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢹⡄⢣⠀⠀⠀⢹⡀⠞⡇⢞⣿⣄⣹⡿⣷⡊⢄⡟⠀⢞⣶⣇⣀⡀⣠⠿⠋⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠳⡄⠳⡀⢀⣠⡇⠀⠱⣧⡻⡿⣿⠁⠀⢀⡌⠁⠀⡟⣿⠋⢠⡷⠃⢀⣠⠞⠁⠀⠀⢀⣠⠀⠎⠶⠶⠶⢀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠹⣊⡹⣟⣗⡂⡀⠀⠈⠉⠉⠁⣀⣠⠞⠀⠀⣰⣿⡟⢀⡞⢻⡶⠚⠋⣹⢆⡎⠚⠉⠀⠀⠀⠀⠀⠀⠀⠈⠻⣊⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠘⢷⣌⢣⡉⠛⠒⢲⠒⠒⡿⣱⠋⠀⢀⣟⡜⢹⠇⠈⣠⣞⡀⢎⣮⣵⡫⠎⠒⠉⠉⠉⠑⠒⢀⣀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢻⣧⠹⡄⠀⢞⠀⢀⡿⠁⢀⡎⢫⠞⠀⡟⠀⢚⣏⣜⠗⢠⡌⣿⠶⠚⠉⠉⠙⢊⡀⠀⠀⠈⠳⡀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣀⣀⣄⠀⣏⢇⠞⡀⡌⠀⡌⠁⡎⠋⡎⠃⠀⣰⠇⠐⠛⢉⡀⠠⠋⠀⢹⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠹⡀⠀⠀⢞⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⢿⢻⡀⢘⣎⠃⢞⠀⣷⠇⣌⢡⠞⢠⠞⠀⠀⢠⠏⠀⠀⡆⠉⢻⢊⣀⠟⣿⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⣷⠀⠀⢞⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠘⢧⣍⠉⠁⢀⢏⡎⠃⢀⣿⠋⢠⠏⠀⠀⢠⠏⢰⠀⠀⠙⣄⠀⠀⠈⢩⠏⠀⠀⠀⠀⠀⠀⠀⢞⠀⠀⠀⢀⠇⠀⢠⠇⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠉⠛⠉⠉⠀⠀⢞⡟⢀⡏⠀⠀⢠⠏⠀⢞⡏⠉⠙⢏⠳⣄⠀⠛⠙⣆⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⡌⠀⣠⠏⢠⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⢞⠀⠀⠀⣟⠀⢀⣀⣧⠀⠀⠈⢇⠘⢊⠀⠀⠘⡆⠀⠀⠀⢀⡟⠁⠀⢀⡜⢀⡎⠃⠀⣌⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢯⣇⠀⠀⠻⣀⣀⡿⢹⠀⠀⠀⢞⡄⠘⡆⠀⠀⢹⡀⠀⢀⡟⠁⠀⢠⠏⡠⠊⠀⢀⣎⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣳⢀⡀⠀⠞⠁⢞⠀⠀⠀⢀⡇⠀⡇⠀⠀⠀⡇⢠⡟⠀⠀⣰⣣⠎⠀⢀⡎⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⡟⠀⠀⠀⠀⣞⠀⠀⠀⣞⠁⢀⡇⠀⠀⠀⡇⡟⠀⠀⡎⣳⠃⣰⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢗⡟⠁⠀⠀⠀⢀⡟⠀⠀⢰⣇⣀⡞⠀⠀⠀⠀⡿⡇⠀⢰⠃⡇⠀⠙⠲⠀⠀⠶⠶⠶⠶⠿⣛⠒⢶⣀⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⠒⠒⠒⠚⠁⠀⠀⠀⠉⠻⠀⠀⠀⠎⠚⠁⠙⠶⣌⣆⡹⢄⡀⢀⣀⣀⠎⠒⠛⠉⠉⠉⠙⠲⢝⡿⡆ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⣞⡷⠇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡉⠁⠀⠀
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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡎⢲⢢⢠⡶⣭⡿⣳⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢟⡇⠊⢥⢞⣿⣐⡿⣁⣿⢳⣀⣀⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡘⢿⢱⠈⠋⠉⠉⠙⠳⢮⢿⣟⣍⠻⣶ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⣕⣟⡀⢁⣜⠞⡛⡳⣄⠘⡇⣀⣞⣧⡿ ⠀⠀⠀⠀⣀⡶⣶⣶⣶⡀⠀⠀⠀⣠⠶⢞⣿⣵⡎⠲⠀⢯⡶⣿⠀⣇⠛⣩⠉⠀ ⠀⠀⢀⠘⡯⣝⠋⣭⣜⣿⣢⠄⠀⣿⢣⣞⣯⡟⣥⡀⠀⠠⠁⠁⢠⣹⠀⠀⠀⠀ ⡎⡋⠭⢖⡿⢜⡧⢘⣯⡙⢿⣷⠀⠭⠿⢿⣿⡟⠜⣱⢞⠒⠚⠒⠋⠁⠀⠀⠀⠀ ⢷⡡⢟⠟⢛⣿⣟⣊⢞⡇⢠⡝⡀⠀⠀⢿⣰⣿⣌⠟⢞⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⢳⡟⣷⡡⠷⠟⢟⣉⠀⠞⢿⠁⠿⢷⠰⠶⠿⠄⢀⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢰⣞⣚⣵⡷⢯⣌⣜⢳⡆⡎⠚⢠⣟⢳⠒⢶⠀⡟⢺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⠻⢿⣮⡟⢻⣏⣔⠟⢃⠇⠀⡎⢘⡇⠀⢞⠀⢳⡌⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢰⣆⣞⣌⢟⡛⠛⠊⠀⢞⠀⠀⡇⢚⡇⠀⢞⠀⠞⢇⢳⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠘⠻⠟⠊⠓⠀⠀⢠⡇⠀⠀⡷⠶⠇⠀⠟⡀⠀⠞⡀⠿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡊⢱⡉⢞⣁⡠⠘⠛⠒⢄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢄⡀⠀⢀⢌⢣⠀⠀⠀⠀⠈⠣⡒⢚⠑⢵ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢔⡀⠫⢢⡘⠞⠀⠀⣀⢎⡒⢰⠀⡇⠀⡇⠀ ⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⣀⠀⠐⣠⡈⢰⠰⡇⠀⢃⠉⢹⡮⡓⠀⢰⡁⡐⠀⡰ ⠀⠀⠀⠀⢠⠊⡠⠄⠘⠉⠶⠍⡪⣢⣀⢇⠂⢹⡄⠀⠢⠲⠀⡀⠎⢐⠏⣠⠞⠀ ⠀⠀⠀⢠⠃⡌⢀⠔⠈⠉⠉⠉⢐⠻⣶⡫⠅⠈⡞⠄⠀⠑⡄⠏⢠⠁⡜⢁⠀⠀ ⠀⠀⠀⡌⠀⡇⠘⡀⠀⠀⠀⠀⠘⣎⠧⢟⠃⠀⠘⡌⠢⡀⠘⡜⡄⠀⠇⡩⠈⡆ ⠀⠀⠀⢚⡀⠘⢄⠐⢄⠀⠀⠀⡠⠒⠀⣎⠗⢒⠃⠹⠢⠈⢂⡇⠈⠢⠀⠀⠔⠁ ⠀⠀⠀⠘⢌⠢⡀⠠⡈⢢⠀⠀⠇⠀⡌⡆⠀⢞⢞⣠⠃⢁⠜⠁⠀⠀⠀⠀⠀⠀ ⢀⠀⠀⢀⡀⠁⠪⡄⠈⠢⣣⢞⠀⠀⠇⡇⠀⢞⠀⠉⠩⢣⠀⠀⠀⠀⠀⠀⠀⠀ ⢏⠈⠁⠂⠌⣁⠒⠁⠀⢀⠌⠀⢆⣀⣘⠖⠀⠀⠣⠀⠀⠵⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⣀⣀⡔⠒⠒⠶⡊⠀⣀⡀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⠔⠋⢀⡀⠈⠙⠢⡀⠙⡆⠀⠉⠓⡏⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⠋⢠⠞⠁⠈⠑⢆⠀⠘⣀⠜⠋⠉⠉⠇⠈⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡏⢀⠃⢀⡀⠚⡟⠙⠻⠟⠁⠀⣀⡀⠀⠀⠀⠃⡷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠁⢞⢠⠎⠀⣞⡶⣊⠀⠀⠀⡞⢹⡟⠳⡄⠀⢞⡇⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢞⡟⠀⢀⣿⣿⠉⡆⠀⠀⡷⣿⣧⣀⣜⡷⠶⢳⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠘⣇⠀⠿⣿⣿⣿⣿⠀⠀⢡⠻⣿⣜⣿⡇⠀⡌⠀⣌⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢳⡀⢻⡀⠀⢞⣿⣟⠙⠀⠀⠀⠑⠂⠚⠙⠀⢠⠇⢰⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠱⡈⢳⡀⠈⠙⠣⣄⣀⢀⠎⠁⢀⡠⠖⢀⡎⢠⢣⠃⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠙⢆⠑⣄⠀⠀⢧⠏⠉⠉⡿⠉⠀⢠⠞⡰⢃⠎⢠⣶⢶⣶⠶⣊⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠑⢌⣧⠀⠈⢿⣄⢰⠁⠀⣰⢋⠞⢀⠞⠀⡌⠿⢭⠔⢊⣌⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣀⠄⢘⡇⠀⣈⡻⣿⠀⣰⡡⠃⢀⡎⠀⡞⠁⠀⢰⢗⡿⠁⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣝⠶⢚⠎⠋⠀⣀⣌⣶⡿⠁⢀⡞⠀⣰⢧⣀⠎⠟⠋⠀⠀⠀⣰⢧⣀⣀⡀⠔⠒⠒⠒⠒⠐⠒⠒⢶⡒⠀⢀⣀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠙⣏⠀⣎⠋⠁⢀⣯⠃⠀⡘⠀⠀⣇⣀⠜⠊⡀⠀⠀⠠⢞⠳⢄⡀⠀⠀⠀⠉⠉⠉⠉⠉⠒⠀⡀⠈⠆⠀⠈⠻⡲⣄⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⢷⡀⠀⠘⣿⡀⠀⡇⠀⠀⠻⣄⣀⠀⠀⣀⣠⠀⠖⠃⠀⠀⠀⠈⠉⠉⠉⠉⠑⢊⠀⠀⠘⡄⡞⠀⠀⠀⡇⠈⡆ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⢿⣊⣈⣢⣄⣀⣀⣀⣉⡙⠳⡄⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠎⢿⠀⢀⣠⣗⣁⣀⡀⠊⠀⠀⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣶⣶⣶⣞⣡⢎⡯⠖⢒⡹⡿⣭⣉⡁⠀⠈⠉⠐⠢⢄⡉⠒⠢⠀⣀⣀⣀⣀⡠⠞⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⡀⠘⠧⠀⣎⠇⠀⠈⠉⠒⠒⠊⠀⠀⠬⠭⠶⠶⠀⠖⠚⠉⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣀⠠⠀⡗⢢⡀⠀⢀⡀⡐⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⠔⢉⡀⠓⠉⠁⠀⢳⡄⠈⣥⠁⢣⡀⠀⡠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢰⠍⠋⠏⠀⠀⠀⠀⠀⠈⢿⣇⠁⢞⠋⠗⠁⡠⣋⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢚⠀⠂⠁⠰⢩⣶⣒⠶⠄⠈⡟⣰⡗⡄⠄⠊⡩⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⢊⣂⠈⡂⠁⠛⠋⢀⠀⠀⠞⡟⠠⢋⣀⡉⠭⡢⠀⠒⠒⠊⢀⡀⠀⠀⠀⠀⠀ ⠀⠀⠙⣟⠖⡚⢲⠈⡱⠀⠀⠀⠋⢀⠿⠊⢲⠑⠂⣐⠒⠠⡀⠀⠙⢆⠀⠀⠀⠀ ⠀⠀⣀⠌⡷⢈⣎⠜⢠⠀⠀⠀⠀⢀⠁⠀⠞⠀⠀⠀⠁⠀⠈⢂⠀⠘⡆⠀⠀⠀ ⠀⠀⠫⠊⠵⢪⡣⠂⣁⣿⠃⢀⠇⠒⡊⠀⠣⠀⠀⠀⠀⠀⠀⢞⠀⢠⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⡯⠊⡡⠒⣯⠀⣶⠀⠀⠐⠂⠀⢡⠀⠀⠔⠀⡠⢃⠔⡑⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠡⣈⣭⡇⣢⠉⠈⢱⠀⠀⠀⠀⠈⡀⠎⡠⠞⢊⠕⠊⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠥⡠⠇⠀⠚⠄⠀⠀⠇⢀⣈⠀⠑⠒⢒⡒⠊⠔⡊⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠰⡀⠞⠘
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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀ ⠀⠰⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣶⣟⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀ ⠀⠀⠹⣿⣶⣀⡀⠀⠀⠀⠀⠀⠀⠀⣠⣟⣿⣿⣿⣿⣿⣿⣿⣏⣞⣷⡀⠀⠀⠀ ⠀⠀⠀⠙⢿⣿⣿⣷⣀⣀⠀⠀⠀⣌⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀ ⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣷⣊⣄⠙⠻⣿⣿⣿⣿⣿⠈⠛⠿⠿⣿⣿⣿⣷⡀⠀ ⠀⠀⠀⠀⢷⣊⣀⣈⠛⠿⣿⣿⣿⣿⣶⣄⡙⠻⣿⣿⡇⠀⠀⠀⠀⠙⠻⠿⠗⠀ ⠀⠀⠀⠀⠈⠻⣿⣿⣿⣶⣮⣿⣿⣿⣿⣿⣿⣊⡘⢿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠈⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⢿⣶⣊⣬⣝⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢠⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠰⣀⣭⣛⡿⣿⣿⣿⣿⡿⢃⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⣿⣿⣿⠟⣡⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⡟⠙⣊⡀⢰⠃⠘⣇⠀⠀⠀⠀⢀⣠⡀⠶⠒⠒⠒⠶⢊⣀⣀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡶⢊⡀⣧⢰⠋⢳⣌⢠⡟⠻⣄⣀⡎⠞⠯⣁⠀⠀⠒⠢⢄⣉⠛⢜⡛⠷⢊⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠹⣿⣌⠀⠀⢿⡟⢀⠀⠙⣏⠀⠀⠀⠀⠙⢊⡀⠀⠀⠈⠑⢊⣙⢧⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⠹⣿⠀⠀⢞⠃⢺⠀⠀⠈⠓⠶⣀⡀⠀⠀⠱⣄⠀⠀⠀⠀⢹⡶⣜⡄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⢿⠀⠀⢞⡇⠞⡆⠀⠀⠀⠀⠀⠉⠳⣄⢲⣌⣊⠀⠀⠀⠀⢷⠈⢿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠖⠊⣷⠀⠀⢞⠂⠀⢞⣷⡀⠙⠀⠀⠀⠀⠀⠀⠀⠙⢷⣯⠛⢊⣀⠀⠀⠘⣇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠞⣇⠀⠈⢠⠶⣟⡏⢷⠀⠀⣳⣊⠀⠀⠀⣀⣄⣀⣹⣄⣷⠌⣿⡊⣄⡞⣆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠈⠂⠀⡏⠀⢹⢳⠘⣇⠀⠚⠛⠀⠀⠀⣀⣌⣿⡇⠀⠐⣟⣿⠀⠀⠉⠉⠓ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⡏⠙⢷⡇⠀⢞⠘⣆⠘⢧⣄⠀⠀⠀⠐⣿⠗⣛⡃⠀⠀⢈⣉⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⢖⣺⢿⣛⠟⠓⠊⣀⣀⠀⠀⠀⣳⣷⠀⠀⠋⠀⣟⠀⠈⢶⣿⡞⠟⠒⠀⠀⠀⠘⢿⣿⠓⣊⠌⠟⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⡶⠋⢁⣎⠿⡪⠝⠊⢉⣉⠩⣍⣙⠳⣄⣞⡇⠈⢳⡀⠀⠀⢻⢇⠀⠀⢱⣳⡄⠈⠒⣶⠶⠶⠊⠟⠟⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡌⢋⣠⣎⡿⢡⠎⢀⡠⠊⠁⠄⣐⣶⠶⢿⣟⣿⠿⣄⣖⠛⠃⠀⢟⡘⡄⠀⣀⢡⣷⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣌⡵⣻⣻⣹⢁⠏⢠⠎⢠⠂⢠⠜⠉⠀⢀⡟⣿⣿⠀⠈⠙⠢⣄⡀⠞⡇⠞⣄⡟⡞⢿⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢰⠏⢠⡇⡇⡇⡞⠀⡎⣠⠁⢠⠏⠀⠀⠀⢞⡇⢞⣿⢀⠀⠀⠀⠀⠀⠀⢷⠀⣹⠁⢹⣟⡞⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠀⣟⢹⢞⢠⡇⢰⠁⠃⠀⡞⠀⠀⠀⠀⣀⣧⠀⠃⠈⣇⠀⠀⠀⠀⠀⢞⣠⠏⠀⠖⠛⠉⠙⣧⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡇⢞⠘⢞⠀⢞⢞⣀⢠⠇⠀⠀⠞⡏⠁⠹⠀⠀⠀⢘⣧⣄⠀⠀⠀⢟⡋⠀⠀⠀⢀⠀⠀⢞⡄⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢞⠇⡀⠀⢞⠀⢞⡀⢹⢞⠀⠀⠀⠀⡇⠀⠀⢀⣀⡎⢿⠋⠉⠉⠙⠛⠛⠛⠒⠚⣻⠋⠀⠀⢞⡇⠀⢞⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢞⠀⡇⠀⢞⠀⠀⠇⢿⣿⠀⠀⠀⠀⡧⠀⠀⠀⠈⡇⢞⡀⠀⠀⠀⠀⠀⠀⠀⡞⠁⠀⠀⠀⢞⠃⠀⣞⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢞⠀⡇⠀⢞⡀⡇⠀⢞⠹⣇⠀⠀⢰⠇⠀⠀⠀⠀⢧⢞⡇⠀⠀⠀⠀⠀⠀⢞⡇⠀⠀⠀⠀⡟⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢞⣰⡇⠀⢞⠀⣧⡃⣞⠄⠈⠀⠀⣜⠀⠀⠀⠀⠀⢞⣞⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⢀⡞⠲⠎⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⢣⡇⠀⢞⣶⣿⡃⣿⠀⠀⠀⠀⠘⢧⣀⠀⠀⢀⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡌⠃⣞⠁⡘⢞⡿⢹⣰⠏⠀⠀⠀⠀⠀⠀⠈⠙⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣰⠇⣠⢧⡟⠁⣞⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣰⣯⢟⡿⠋⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⡎⠿⠋⠑⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠎⢶⣒⠲⣬⡿⢍⠉⠓⠲⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⣧⣀⡀⠀⠀⠁⠚⠿⣊⣳⡀⠀⢰⠀⠉⠲⣄⣠⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠗⠒⠻⡬⠙⠶⣄⣀⠀⠀⠈⠻⣷⡀⢚⣘⠀⠀⢞⠃⠈⢳⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠒⣀⣈⣭⣜⣊⠀⢚⠓⢯⠗⠚⠉⠉⠉⠉⠉⠉⠒⡇⠀⠀⢀⢻⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣏⡎⠋⠙⠠⣀⠀⠈⠳⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡜⠀⡏⠳⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢞⠏⠀⠀⠀⠢⢌⠣⡀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⣇⠀⠱⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⣀⣀⠀⠑⣧⡟⠀⠀⠀⠀⠀⠀⡄⢀⠀⢀⠀⡀⠀⠀⠀⠀⣞⡉⢊⠀⣷ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⣀⠀⢀⣠⣇⣈⠿⢊⢹⣧⠀⠀⠀⢀⣀⣀⣧⣟⠶⢯⡎⠗⠂⠀⠀⢰⠁⠀⠈⢊⠛ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⣟⠏⠀⣀⠀⠀⠄⢀⣹⡁⠘⠛⠛⢀⣌⠟⢹⡀⠀⢞⠋⠁⢞⣿⣿⢧⣌⠋⠁⠀⠀⠀⡟⠀⠀⣊⠎⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⢠⠃⢀⡜⢁⡠⠀⠄⠀⢈⡻⣗⠲⣟⠉⠀⡖⠊⠀⠀⠞⠀⠀⠀⢻⣿⡿⠋⠉⠀⠀⠀⢠⣇⡠⠞⠁⠀⢞ ⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⡎⠀⠞⡠⠊⢀⡠⠀⠀⣄⡈⠙⢊⡈⢊⠀⠘⢊⣠⢟⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠞⢁⡀⠒⢀⣠⠃ ⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⡇⠘⠀⠁⡎⠁⠀⠀⠀⠀⠈⠑⢀⡙⢌⣆⡀⠔⠚⠿⠀⣀⡀⠀⢀⡀⠔⠂⠀⢠⡞⠁⠐⣿⡿⣧⢟⣏⠀ ⠀⠀⠀⠀⠀⠀⠀⢞⣿⠀⠀⢷⠄⠂⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⢛⡇⠀⠀⠀⠀⠀⠈⠙⠲⡟⠀⠀⠀⠀⠈⢷⠒⠒⠚⢋⣥⣊⣜⠀ ⠀⠀⠀⠀⠀⠀⠀⢞⢟⣆⠀⠘⣆⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡌⢁⡟⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⣇⢀⠎⠋⠁⠀⢻⡄ ⠀⠀⠀⠀⠀⠀⠀⢞⠘⡌⢊⠀⠈⠣⣧⠀⠀⠀⠀⠀⠀⠀⢞⢡⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣌⡏⠀⠀⠀⠀⠈⡇ ⠀⠀⠀⠀⠀⠀⠀⠞⡇⠱⡀⠑⢄⠀⠈⠉⠒⡆⠀⠀⠀⠀⢞⠞⢜⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⠧⡷⠀⠀⠀⠀⢰⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⣹⡄⠙⣄⠀⠉⠒⢀⣌⠁⠀⠀⠀⠀⠘⡆⠘⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣠⡟⠁⠀⠃⠀⠀⠀⢠⠃⠀ ⠀⠀⠀⠀⠀⠀⣰⠞⢹⣿⣄⠈⠢⡀⠀⠀⡇⠀⠀⠀⢀⣠⠀⠇⠀⠀⣀⡀⣞⡯⠓⠊⢀⣎⡆⠀⠀⢱⠞⠉⠉⠲⢀⣀⣀⣀⡎⠃⠀⠀ ⠀⢠⣟⣿⣊⣰⢣⠀⢞⣿⣿⣷⣄⠈⠑⢺⠀⠀⠀⢠⠞⠀⠀⠀⢠⠞⠁⡞⠁⠀⠀⠀⡌⠁⡇⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣌⡏⡟⢡⠇⠀⠀⠈⣿⣿⣿⣿⡛⠢⣌⡄⠀⢠⠋⠀⠀⠀⢠⠏⠀⢠⠇⠀⠀⠀⢰⠇⠀⢡⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡖⠁⠉⠉⢹⠀⠀⠠⠀⠹⣿⣿⣿⡇⠀⠀⠉⢠⠏⠀⠀⠀⢠⠏⠀⠀⣞⠀⠀⠀⠀⣞⠀⠀⢞⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⠊⡀⠎⠛⡄⢣⠀⣱⣀⠜⠿⠿⠁⠀⠀⢀⡏⠀⠀⠀⠀⡌⠀⠀⠀⡇⠀⠀⠀⠀⢻⠀⠀⠞⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⡇⠀⠀⠀⡇⠀⠀⠀⠀⠞⡄⠀⠀⡆⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⡇⠀⠀⠀⢧⠀⠀⠀⠀⠀⢳⡀⠀⡇⠀⠀⠀⠀⠀⢞⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢞⡄⠀⠀⠀⠀⠀⢧⠀⠀⠀⠈⠊⢄⣀⣀⣀⡠⠗⠀⢹⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠀⠀⠀⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣊⡀⠀⠀⠀⠀⣞⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠶⠙⠁⠀⠀⠀⠀⠙⠡⢒⠀⣀⠀⠀⠀⠀⢀⡎⢊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⠔⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠫⢢⣄⣰⠏⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡌⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠃⠀⠀⡀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⠏⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡇⠀⠀⠀⡄⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣰⢏⣎⡜⡗⠁⠀⠀⡠⣀⡶⠚⠓⠉⠉⢁⣠⠮⠂⠀⠀⢀⣀⡀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣘⡩⠟⣙⠏⠀⡠⡎⢷⣻⣞⣧⠀⠀⠄⣶⣯⣥⣀⠀⠖⠿⣯⡵⠃⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠋⠀⠀⣯⡎⠜⣫⣀⢞⣏⣿⡿⡆⠀⠀⠀⡎⠋⠐⠢⠀⠀⠈⢳⠞⠁⠀⠀⢀⣟⡇⠀⣠⡶⠛⠀⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢌⡄⠀⠀⠉⠻⣿⠞⣿⡇⠀⠀⣌⣿⠉⠉⡀⢠⠀⠀⠀⠓⠒⠀⠀⣻⠿⣇⡌⠋⠀⠀⣠⡏⠀⡀⠖⠋⠉⠉⡁ ⠀⠀⠀⠀⠙⣊⡀⠀⠀⣇⠡⡞⠀⠀⠀⣿⣿⣆⠀⡇⢀⠀⠀⡘⠀⠀⠀⣰⠟⣊⡟⠁⠀⠀⣎⣿⠿⠋⠀⠀⠀⢀⡟⠁ ⠀⠀⠀⠀⠀⠀⠙⢊⣀⣌⠌⠒⠀⠀⠀⢿⣧⣿⣿⠇⡘⢀⠔⠀⠀⢀⡌⠊⠀⣿⠁⠀⠀⢟⡯⠋⠀⠀⠀⢀⢎⠏⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⡀⢙⣄⠀⠆⠀⣆⠀⠈⠙⠻⠿⠌⠒⠁⠀⠀⢠⠝⠀⠀⠀⡎⠛⢷⠞⠋⠀⠀⠀⢀⢔⠝⠁⠀⠀⠀ ⠀⠀⠀⢰⠺⠓⠀⠀⠘⠛⠷⣀⣌⠉⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⠃⡠⠂⠀⠀⡇⠀⣞⠀⠀⠀⢀⣎⣷⣥⠄⠀⣀⣄⠀ ⠀⠀⠀⠀⠘⠊⣠⣀⠀⠀⠀⠈⣿⠒⠒⠀⣀⠀⢀⡖⠂⠁⠀⣟⡌⣷⠀⠀⠀⠇⢠⣯⠔⠲⣄⠈⠁⠀⠀⠀⠀⣀⡿⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠑⠣⢊⡄⡘⣊⠀⠀⠈⠀⣜⠀⠀⠀⢞⡹⠁⣯⠀⠀⠀⣊⠞⠁⠀⢠⡟⠀⢀⣠⣎⠊⠛⠉⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡪⠭⢯⡳⣄⠀⠀⡿⠀⠀⠀⠘⠁⠀⣩⡀⢀⣄⣩⠀⢀⣎⣏⣎⣟⠋⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡪⠋⠀⠀⠀⠙⢯⠁⠀⣄⠀⠀⠀⠀⢀⡞⠁⠀⠀⠈⠙⣶⣞⠁⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⠀⠀⠀⢀⠈⣧⡀⣟⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⢀⠞⣿⠇⡠⡔⠟⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠞⠂⠀⠀⠀⠀⠀⢰⡗⠛⠛⠛⠓⠒⠒⡏⠀⠀⠀⠀⠀⠀⢞⠓⠛⠓⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⢊⡄⣀⣀⣀⠠⠈⠀⠀⠀⠀⠀⠀⢞⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⠄⠂⠫⡡⠀⢉⡇⢈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⠔⢓⣀⣒⡀⡀⠋⠀⠁⠈⠞⠑⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡜⠉⠠⠀⡄⡰⠀⠀⠀⠀⠀⢰⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠇⢞⠀⢀⣯⡆⠀⢀⠠⠎⠆⡌⠀⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⢄⠢⡈⠙⡿⠀⠁⠀⠀⡔⠀⣌⢻⠀⠀⠀⡠⠄⠒⠀⠒⠠⡀⠀⠀⠀⠀⠀ ⠀⠀⠂⢌⠊⢗⠞⠀⢰⠎⠀⠌⠆⣎⡬⣭⠜⡊⠍⡁⠐⢄⠀⠈⠄⠀⠀⠀⠀ ⠀⠀⠀⠀⠉⠢⡑⢄⢞⠀⠌⠘⢠⠁⠉⣖⣬⡷⠀⠘⡄⠀⢡⠀⢞⠀⠀⠀⠀ ⠀⠀⠀⡰⡖⠢⠞⡄⢻⡀⠀⡇⡖⢀⣚⡞⠁⡇⠀⠀⡇⠀⠞⠀⢞⠀⠀⠀⠀ ⠀⠀⠀⠑⢌⣂⣁⠀⠊⠑⢆⢃⠐⠌⢿⢃⠈⠰⠀⡰⠁⡠⠁⠊⡞⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠹⠓⠒⣻⢘⠀⠀⡷⠁⣔⠔⡁⠔⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠆⠀⢀⡇⠞⠀⠀⡇⠘⡂⠪⠀⠠⠀⠀⠀⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⡘⠀⠀⢞⠠⡃⠀⢀⡏⠒⠒⠂⠒⠈⠁⠀⠁⣊⠆ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣊⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⠀⢀⣀⣀⡀⢀⣀⣀⣀⡀⠀⢞⠁⠈⡳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠻⣿⡛⣟⢯⣷⡋⡎⢺⠗⡕⠁⠉⠉⣻⠀⠀⢳⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣠⡞⣷⣿⡀⢳⡹⢀⠏⢞⠀⠀⠀⢞⡁⠀⠀⢞⡄⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⡏⢠⠇⡞⠙⢟⡇⢞⣄⣎⣀⣀⣀⣀⣝⣊⣀⠘⠁⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⠀⡏⠀⣇⣀⠶⠛⠉⠁⣞⢻⢹⣧⣌⣷⣇⠀⠀⢞⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣯⢠⣧⠟⣯⣿⢊⡀⠀⠀⢿⢞⣈⣿⣿⡿⣟⠄⠀⣞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢿⡟⠋⠀⠙⢻⣧⣹⣆⠀⠘⣇⠳⣿⣋⠑⠫⠍⣰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠶⠒⠓⠒⠲⠀⣄⡀⠀⠀⠀⠀⠀⠀ ⠘⠁⠀⠀⠀⠀⠻⣟⣿⠂⠀⠘⠖⠛⢁⡊⡀⣞⣵⣿⠀⠀⠀⠀⠀⠀⠀⠀⣎⠞⠁⠀⠀⠀⠈⠉⠀⠢⣄⠙⢊⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠠⣞⠁⠀⡎⠀⠀⠀⣌⣿⠿⢟⡅⢞⡆⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠉⠙⠢⣄⠳⡄⠙⣊⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠙⠚⠓⠒⢪⡏⣿⠀⢖⡿⠁⢛⢿⣊⡀⠀⠀⣀⣟⣠⣎⣶⣶⣒⡲⢀⣉⠑⢊⡀⠈⢆⠹⡀⠞⣧⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⣠⡎⠋⠀⠀⡜⡎⡏⠰⠆⣀⢚⣿⣿⠁⠀⠀⠈⠙⢷⣌⢳⡀⠑⡀⠞⠀⠇⠀⡟⣇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣌⠁⠀⢹⣀⠄⢀⡜⡹⢁⡇⠐⡀⠟⠄⠉⢻⡄⠀⠀⠀⠀⠀⠻⣆⠹⡄⢡⠀⡄⢰⠀⣿⢹⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠻⣊⣊⡎⠁⡌⠐⠃⠟⣊⠡⣄⣞⠇⠀⠀⠀⠀⠀⠀⢹⡆⢳⢞⠀⡇⠘⠀⣟⠘⣇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⡀⠀⠀⠈⠛⠊⠟⠁⠀⠀⠟⠛⠀⠉⣹⠀⠀⠀⠀⠀⠀⠀⠀⣷⢞⢞⠀⠃⠀⠀⣿⠀⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡉⠲⡊⠀⢀⣀⣀⣀⣘⣊⠀⠀⠀⢠⣃⡀⠀⠀⠀⠀⠀⠀⠀⢞⣞⣿⠘⠀⠀⠀⡏⠀⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣌⠁⠀⢞⠉⠉⠁⠹⣌⠳⣄⠀⠛⠉⠻⡄⠀⠀⠀⠀⠀⠀⢞⣿⢻⡀⠀⠀⢞⢁⣌⠋ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣌⠇⠀⠀⣞⢧⠀⠀⠀⠈⢳⡈⢳⡀⠀⠀⠹⣆⠀⠀⠀⠀⠀⢞⣿⣇⠇⠘⠀⣯⡟⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⡏⠘⣇⠀⠀⠀⠀⢳⠀⢳⠀⠀⠀⠹⣆⠀⠀⠀⠀⣌⣻⢹⠀⣠⡟⠋⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⢠⡇⠀⢹⡀⠀⠀⠀⠘⡇⠘⡇⠀⠀⠀⠹⡄⠀⠀⢀⣟⡏⣷⡟⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⣞⠁⠀⠀⡇⠀⠀⠀⢠⡇⠀⡇⠀⠀⠀⠀⢳⠀⠀⢌⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣎⠃⠀⠀⠀⠀⢀⡏⠀⠀⠀⣧⠀⠀⠀⣟⠀⢀⡇⠀⠀⠀⠀⠘⡆⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠐⢧⣄⣀⣀⣠⠀⠞⠓⠒⠒⠋⠁⠀⠀⠀⠈⠉⠹⣅⣀⣠⠀⠀⠞⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣠⣎⣶⣟⣿⣿⣿⣿⣷⣶⣶⣀⣄⡀⠀⣎⣿⣊⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠐⠋⢉⣎⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣎⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣛⣻⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡌⠋⣜⣿⣿⣿⣿⣿⡿⣿⣿⠟⣩⣶⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢰⣿⣿⣿⣿⣿⠟⢱⢟⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣿⣿⣿⣿⠟⢡⡆⣡⡟⠛⠉⣛⣻⣿⣿⣿⣿⣿⣿⣿⡇⣇⠀⠀⠀⠀⢀⣎⡆⢀⣟⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣌⣿⡿⠛⣡⣟⣿⣷⠏⠀⣎⣿⠟⠙⠻⣿⣿⣿⣿⣿⣿⢰⣿⠀⠀⠀⢀⣟⡿⣎⣿⣿⡟⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠜⠋⠁⠀⠞⣿⣿⣿⡟⠀⣞⣿⣿⣆⠀⠀⣿⣿⣿⣿⣿⢃⣿⣿⡄⠀⠀⣌⣿⣿⣿⣿⠏⢀⣎⣟⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⣿⣿⣇⠀⣿⣿⣧⣹⣿⣿⣿⣿⣿⡿⢣⣟⣿⣿⡇⠀⠰⣫⣊⢹⡿⣡⣎⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣀⣿⣿⣿⣿⣄⠘⣿⣿⣿⣿⣿⣿⠿⢋⣎⣿⣿⣿⣿⠃⠀⣞⣿⡟⣞⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⢀⣠⣀⣶⣶⣟⣿⣷⣶⣊⣀⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣭⣥⡬⢩⣿⣿⣿⣿⣿⠀⢀⣿⡿⢑⣥⡌⢟⣡⣀⣀⣀⠀⠀⢀⣀⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠉⠛⠻⠿⠿⠿⠿⠿⠛⣻⣿⡿⢡⣿⣿⣿⣿⣿⠇⠀⢞⣿⣵⣿⠟⣌⣿⣿⠿⠋⠁⢀⣎⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠃⣟⡿⢋⣿⣿⡟⢀⢠⣿⣿⠟⠥⠞⠯⣜⣟⣿⣊⣎⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡙⢿⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢞⣿⣿⢠⠟⡄⣌⣿⡿⠁⣎⣿⣿⣷⠆⣿⠿⡁⠋⠛⠛⢿⣯⠁⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⣿⣿⠈⣌⠁⣿⣿⠁⣟⣿⣿⣯⣥⣷⣶⡿⠁⠀⠀⠀⢌⣿⡄⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣀⣿⠀⣿⠇⣞⣿⣿⣿⣿⣿⣿⣿⠁⠀⠠⡀⠀⣞⣿⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣧⡹⠀⣿⣿⣿⣿⣿⣿⣿⡏⢀⠀⣞⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⢞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠛⠛⠛⠛⢿⣿⣿⡆⣿⣿⣿⣶⣶⡀⠀⠀⠀⠀⠀⠀⢞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠘⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣌⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠁⣿⣿⣿⣿⣿⣿⣿⣿⠉⢻⣇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⢞⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⢞⣿⡿⣿⣿⣿⣿⣿⡄⠀⠙⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⢞⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠘⣿⡇⢻⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣟⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣞⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠹⣧⠈⢻⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠙⢿⣿⣟⠻⢿⣶⣀⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⣜⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠀⠀⠉⠉⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠿⠿⠿⠿⠿⠿⠿⠃⠀⠀⠀⠀⠀⠉⠉⣿⣿⣿⣿⣿⣿⡿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
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⠀⠀⠠⠀⠁⠀⡀⠄⣠⣟⢿⣻⢞⡯⣞⡵⣫⢞⡵⣫⢞⡵⣫⠶⣭⢻⡵⣫⡿⣿⢺⣜⡳⢟⣯⣟⡧⣏⢷⡹⡞⣵⢺⡵⢫⢷⡹⣎⠿⣜⢧⣛⢶⡹⣎⠷⣎⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠱⡄⠀⠘⠂⠎⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠄⠁⡀⢠⣟⢿⣜⣫⢗⡯⣞⣌⠳⠛⠚⠓⠻⢮⣳⢭⡻⣜⢧⡻⢵⣿⣻⡳⢮⡝⣿⣳⣿⡱⣏⢟⣱⢻⡜⣧⢻⡝⣮⢳⣭⢻⡜⣧⣛⢮⡳⣭⢻⡌⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠄⠀⢱⡀⠄⠂⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠁⠀⠂⣎⡿⣯⣟⢶⡹⣎⢷⡞⠡⢈⡀⠧⠬⢀⡁⠙⢟⣱⢏⡟⣹⢳⢟⣻⣯⢳⡝⣷⢯⡷⣹⢎⡷⣭⢳⡝⣮⢳⡝⣮⢳⣎⢷⡹⢶⡹⣎⠷⣭⢳⣳⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢠⠃⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⢣⡀⠀⠄⠐⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡁⣌⡿⣜⡻⣜⢧⡻⣌⠏⢀⣢⠋⠀⠀⠀⠀⠙⢊⠂⠹⣟⡱⣏⡻⣎⣷⢿⣣⢟⣯⣟⣷⡹⣎⠷⣭⢳⡝⣮⢳⡝⣮⢳⣎⢷⡹⢧⡻⣜⡻⣜⢧⣏⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⢧⠀⠠⠀⠀⠄⠈⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢁⣌⡿⣜⡳⣝⢮⡳⣝⡏⢀⡲⠁⠀⠀⠀⠀⠀⠀⠀⠱⡡⠘⣷⢭⡳⣝⠟⣟⣧⢟⣟⡜⣷⡹⣎⠿⣜⢧⡻⣜⢧⡻⣜⡳⣎⢷⡹⢧⡻⣜⡳⣝⠟⣌⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⢃⠀⠘⡆⢀⠐⠀⠠⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣌⡿⣜⣏⢷⡹⣎⢷⡻⢀⢢⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡆⠘⣯⡳⣭⢻⣜⡿⣞⣌⡿⣜⣳⢭⡻⣜⢧⡻⣜⢧⡻⣜⡳⣝⢮⡝⣧⢻⣜⡳⣭⣛⢶⣻⠀⠁⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⢧⠀⠀⠠⠀⠀⠁⠀⡀⠁⠠⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⣿⡜⣟⡌⣣⢟⡌⣳⠇⡀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡌⠹⡷⣭⢳⣎⢿⣿⡲⣿⡜⣧⣏⢷⡹⣎⢷⡹⣎⠷⣭⢳⡝⣮⡝⣮⢳⣎⢷⣣⢟⣮⢳⠀⠠⠂⢁⣠⠎⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠘⡆⠀⢀⠐⠀⠁⠀⠀⠀⠁⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⣟⢯⣿⢣⡟⣵⢫⡞⡜⠀⣌⠁⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢣⡐⢿⣜⡳⣎⢯⣷⠟⡙⣿⣜⣎⢷⡹⣎⢷⡹⣎⠿⣜⢧⣛⢶⡹⣎⠷⣎⢷⡹⣞⡌⣻⠀⣠⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⡀⠀⠂⠈⠀⡀⠁⢀⠀⠀⠀⠀⠀⠀⠀ ⢀⡿⣯⣏⢷⡹⣎⢷⣹⡇⠁⡆⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠞⣧⢻⡌⠏⢁⡎⠊⠹⣞⡿⣎⡷⣹⢎⡷⣭⢻⡜⣧⣛⢮⡳⣭⢻⡜⣧⢻⡌⣱⢿⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡀⠄⠀⠂⠀⠈⠀⠀⡀⠀⠀⠀⠀⠀ ⢞⣟⡷⣎⢷⡹⣎⢷⣹⠠⢹⠃⠀⠀⠀⡌⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡌⣿⠏⢡⡎⠋⠀⠀⠀⠘⣿⣻⢷⡹⣎⠷⣭⢳⡝⣶⡹⣎⠷⣭⢳⡝⣮⢳⡝⣧⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠄⠀⠀⠀⡐⠀⠈⠀⠄⠀⠀⠀⠀⠀⠀ ⢞⣯⡜⣎⢷⡹⣎⢷⣹⠀⢺⠀⠀⠀⠀⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⢁⡎⠋⠀⠀⠀⠀⠀⠀⠈⠻⣯⢿⣌⢻⡜⣧⣛⢶⡹⣎⠿⣜⢧⡻⣜⢧⣛⣶⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢀⠈⠀⠀⠀⢈⠀⠀⠂⠀⠀⠀⠀⠀ ⣻⣞⢷⡹⣎⢷⡹⣎⡧⠈⢌⠀⠀⠀⠀⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠫⣿⣳⣟⡶⣹⢎⡷⣭⢻⡜⣧⢻⡜⣧⢯⣷⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠄⠀⢀⠀⠁⠀⠠⠀⠈⠀⠀⠀⠀⠀⠀ ⡷⣯⢷⡹⣎⢷⡹⣎⡗⢁⢺⠀⠀⠀⠀⡇⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢿⣜⣳⣯⡞⣵⢫⡞⣵⢫⡞⣵⣿⣳⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣟⣿⣿⣿⣿⣿⣿⣊⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡀⠠⠀⠀⠂⠁⠠⠀⠁⠀⠀⠀⠀⠀⠀ ⡿⣭⣏⠿⣯⣞⡵⣫⢟⠠⢞⠀⠀⠀⠀⢳⢞⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠟⣜⡷⣯⢟⣱⣏⢟⣹⡟⡇⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⡿⠟⠉⠁⠀⠉⠙⠻⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⠀⠀⠄⠀⠄⠀⡐⠀⠈⠀⠀⠀⠀⠀⠀ ⣟⣷⣫⢟⡌⣛⡷⣜⣟⠀⢺⠀⠀⠀⠀⠘⡔⡆⠀⠀⠀⢰⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠯⢿⣳⡿⣜⠀⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣌⣿⣿⣯⣀⣶⣶⣶⣶⣀⣄⠀⠀⠙⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⠀⠂⠀⡀⠠⠀⠀⠠⠀⠀⠄⠁⠀⠀⠀⠀⠀⠀ ⢜⡶⣏⢟⡱⣏⠟⣭⢻⡌⠌⡇⠀⠀⠀⠀⢱⡞⡀⠀⠀⢹⣿⡄⠀⠀⠀⢀⣀⣶⣟⣿⣿⣶⣶⣀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⣿⣿⣿⢿⣜⠗⠛⠚⠷⣯⣟⣿⣊⡀⠈⢻⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢠⠇⠀⠐⠀⠀⠀⠄⠀⠁⠀⡀⠂⠀⠀⠀⠀⠀⠀⠀ ⢞⡿⣜⢎⡷⣭⢻⡜⣯⢗⠠⢇⠀⠀⠀⠀⠀⢳⢣⠀⠀⠈⢿⣿⣆⠀⣎⣿⡿⠋⠁⠀⠀⠀⠀⠉⠻⢿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⢯⡟⠀⠀⠀⠀⠀⠀⠉⠳⣟⣿⣄⠀⠹⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⡐⠀⢀⡎⠀⢀⠠⠐⠀⠠⠀⢀⠈⠀⢀⠐⠀⠀⠀⠀⠀⠀⠀ ⢞⣿⣹⣎⠷⣭⢳⡝⣮⢻⡄⠚⡆⠀⠀⠀⠀⢞⣿⡆⠀⠀⠀⠛⢿⣿⣿⠋⠀⠀⠀⢀⡠⢔⠒⡒⢒⠢⢜⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣜⣊⠀⠙⣿⣷⡀⠀⠀⠀⠀⠀⡐⠁⢀⠎⠀⠀⠀⠀⠀⡀⠀⠄⠀⢀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣳⣏⠿⣜⢧⡻⣜⢯⢷⡀⢳⡀⠀⠀⠀⠈⠻⣿⣊⣀⠀⠀⣌⣿⠃⠀⠀⢀⠖⡩⠐⡌⢂⡑⢚⡎⠖⠚⠿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣟⣆⠀⠘⣿⣷⠀⠀⠀⠀⡔⠀⡰⠋⠀⠀⠂⠁⠀⡀⠀⠠⠀⠀⠂⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠹⣷⣻⡟⣌⢣⡟⣌⢫⡞⣧⠀⢳⠀⠀⢀⠀⠀⠈⠻⠿⣿⣟⣿⠃⠀⠀⢠⠋⡔⠡⡁⡐⣢⣎⠏⠀⠀⠀⠀⠘⢿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢞⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡄⠀⠘⣿⣷⠀⠀⠊⢠⡎⠀⠀⠀⠂⠀⠐⠀⠀⡀⠀⠐⠀⠁⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢻⡷⣿⡜⣧⢻⡜⣧⢻⡝⣆⠂⠳⡀⠚⣧⡀⠀⠀⠀⠀⣟⡟⠀⠀⠀⡏⠐⡠⠁⣎⣿⣿⣿⠀⠀⠀⠀⠀⠀⠈⢻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⣇⠀⠀⠘⣿⣷⣀⣀⣀⣁⣀⡀⣁⣀⠀⠂⠀⡀⠀⢀⠂⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢞⣿⡜⣿⡜⣧⢻⡜⣧⢻⡝⣧⢂⠙⣄⠘⢻⣷⣊⣀⣄⣿⠃⠀⠀⢞⠠⠁⠄⣱⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣌⣿⣿⣿⣿⣿⡟⠋⠛⠿⣊⣄⠀⠀⠀⠀⠀⠀⢰⣯⢿⠀⠀⠀⠘⣿⣯⠙⠛⠛⠛⠛⠉⠁⠀⠠⠀⠀⠄⠀⠠⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢞⣟⣯⣟⣟⡱⣏⢟⡱⣏⠟⣭⠷⣄⠈⢢⡀⠈⠙⠛⠛⢻⠀⠀⠀⣿⠀⠡⢚⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⣿⣿⣿⣿⣿⣇⠀⠀⠀⠙⣿⣿⣶⣀⣀⣀⣶⣟⡎⣿⠀⠀⠀⠀⠘⢿⣷⣀⣀⣀⣀⣀⣀⣀⠀⠀⠄⠀⠈⡀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠘⣿⣻⢞⣯⣿⣌⢣⡟⣌⢻⡜⣯⣛⣮⣄⠙⢄⡀⠀⠀⢹⠀⠀⠀⣷⠈⠠⢞⣿⣿⣿⣿⡿⢿⣿⣄⠀⠀⠀⠀⠀⠀⢞⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢞⣿⣿⣿⣿⣿⣿⣊⣀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣗⡺⣹⠄⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⡯⠅⠀⠠⠀⠂⠁⡀⠈⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⢿⣫⢞⡵⣿⣳⡜⣎⢷⡹⢶⣹⢺⡜⣟⣊⠙⢢⣀⠈⡀⠀⠀⢱⠀⠄⢞⣿⣿⣿⣿⠀⠀⠈⢻⣊⣀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠶⢹⠀⠀⠀⠀⠀⠀⠀⠀⢚⠉⠉⠁⢀⠀⠠⠁⢀⠐⠀⡀⠈⠐⠠⣀⠄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢻⣟⣧⡻⣜⢧⡟⡿⣿⢮⣝⢧⣏⢷⡹⣞⣌⡂⢉⡆⠀⠇⠀⠀⠞⡀⠠⢞⣿⣿⣿⣿⣆⠀⠀⠀⣿⣿⣷⣶⣀⣀⣶⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢞⠀⠀⠀⠀⠂⠀⠈⠀⡀⠂⠀⠠⠀⣀⠀⠉⠓⢄⠀⠀⠀⠀⠀ ⠀⠀⢀⠈⣿⣻⣵⣫⢞⣭⢳⣭⣛⠿⣟⣌⣣⡟⡌⣎⣇⠂⢇⠀⠞⠀⠀⠀⣇⠀⠀⣿⣿⣿⣿⣿⣶⣀⣎⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠐⠀⡀⠱⡀⠀⠈⣆⠀⠀⠀⠀ ⠀⠀⠀⠀⠹⣷⣻⣻⢟⣜⣳⢮⣝⣛⢶⣣⢯⣝⡳⣭⣳⠈⢌⡀⠀⢇⠀⠀⠘⡄⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡄⢳⠀⠀⠞⠀⡀⠀⠀ ⠀⠀⠂⠀⠀⢻⡜⣷⣫⣛⢿⣳⢟⡜⣮⣗⡷⣞⡷⡷⢿⡇⣠⣧⣀⣬⡀⠀⠀⠹⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⢀⣠⠔⠶⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠰⡇⠀⠊⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠈⡆⠀⢀⠀⠄⠀⠀ ⠀⠀⠀⠠⠀⠀⠹⣟⣷⣝⢮⡳⣏⢟⡱⢮⡝⣮⢳⡝⣿⣿⠛⠹⡉⠉⠁⠀⠀⠀⠡⡀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠁⠀⠀⠀⠀⠁⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣟⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢋⡕⣲⠆⠀⠀⠀⠀⠀⠀⠀⠀⠠⡇⠱⡀⢄⠀⠂⠉⠐⠀⣀⠀⠀⠀⠀⠀⠀⡜⠀⡇⠀⡘⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢻⣜⢟⣷⡹⣎⢷⡹⢧⡻⣜⢧⡻⣜⣞⣥⣟⣿⠿⠿⠊⠀⠀⠀⠑⡄⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⣞⠰⠀⠀⠀⢠⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⡚⠜⢻⠿⠿⡟⢻⠉⣆⢣⡌⠋⠀⠀⠀⠀⠀⠀⠀⡘⠀⢀⠃⠀⠱⡀⠓⡀⠀⠀⠀⠂⠑⠀⡀⠀⠀⢀⠇⣞⠀⠀⡇⢀⠀⠀⠀ ⠀⠀⠀⠀⠐⠀⠀⠈⢿⣯⣞⡿⣯⡞⣜⢣⡟⣌⢣⡟⣌⢿⣿⡁⠄⣆⢀⣎⣧⠀⠀⠀⠀⠂⠀⢠⠝⠻⣿⣿⣿⣿⣿⣿⠿⢣⣄⡟⠀⠀⠀⠀⣞⣄⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡌⠥⢊⠱⡈⣅⣺⡎⠋⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⢠⠋⠀⠀⠀⠘⢢⡀⠑⢄⡀⠀⠀⠀⠈⠄⢀⠎⢠⠃⠀⡞⠀⡔⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣟⣜⣳⢿⣳⣏⣟⡱⣏⢟⡱⣏⠿⣷⡂⢞⣿⠋⠀⠣⠀⠀⠀⠀⠐⠣⣀⣀⡀⡝⠭⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠝⠓⠚⠓⠓⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⢀⠏⠀⠀⠀⠀⠀⠀⠈⠢⠄⠈⠒⠀⠀⠀⠠⣀⠎⠃⠀⢠⠃⡞⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢟⣭⣟⣳⣯⣟⡷⣜⣎⠷⣭⣛⢶⡻⡔⡏⣆⠀⠀⠑⠄⠀⠀⠀⢀⣬⠟⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⡰⠃⡰⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢞⣧⠀⠙⠟⣻⡟⣭⢟⣷⣻⣟⡷⣯⢟⣱⠿⡄⠘⢆⠀⠀⠈⠢⢀⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⣠⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠁⡎⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⢷⣀⡀⠈⠛⢜⣟⡶⣧⢯⣝⡻⢯⠿⣿⣻⣆⠌⢣⡀⠀⠀⠠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠚⣂⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡀⠄⠊⣠⣟⡇⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⡞⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢞⡿⣜⣟⣷⣀⣀⡈⠛⠯⣷⡟⣝⡯⣝⢶⡹⣞⢧⡠⠘⢊⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⡖⡋⠒⠒⠒⠒⠚⠒⠒⠒⢳⠀⢀⣀⣠⣀⣶⢿⣻⡿⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⣠⠊⠉⠒⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⢁⠔⢠⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣟⣮⣝⡻⣜⣿⣻⢷⣟⡿⢯⣟⡿⣟⣵⢫⡞⣜⢊⡀⠜⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠱⡀⠀⠀⠀⠀⠀⠀⠀⢞⣿⣻⡜⣯⢷⡯⣟⣷⠃⣰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⡰⠁⠀⠉⠒⠢⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠚⠁⠀⢞⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡜⣮⣗⡳⢮⡝⣯⢻⣝⡻⣞⡜⢳⣎⢷⡹⣎⢷⣛⣊⠑⡈⠓⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣙⢄⠀⠀⠀⠀⠀⠀⢞⢷⣫⣜⣳⢯⡿⣜⠃⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠋⠀⠀⠀⡇⠀⠀⠀⢰⠀⠰⡄⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣜⣳⣏⡷⣹⢎⡷⣎⢷⡹⢞⡳⣎⢷⡹⣎⠷⣭⣿⡇⠠⡕⢀⡘⠒⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠭⣒⠀⢀⣀⠀⢞⣯⠷⣉⠧⣋⡜⠃⡠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠁⡠⠂⠀⠀⢞⠁⠀⠀⠀⠈⡆⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣻⢿⣵⣫⢞⡝⣮⡝⣯⢳⡝⣮⢳⣭⣛⣟⢷⣻⡀⠌⡀⠉⠒⠥⣂⢉⠒⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠒⠛⢻⠲⠵⠌⠚⢉⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠉⠀⢀⠃⢀⠇⠀⠀⠀⠀⠀⠞⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣟⡜⣟⣜⣲⣝⢮⡳⣝⢮⣳⣮⢿⡜⣯⠋⠱⡄⠳⡀⠀⠀⠀⠉⠓⠢⠎⣈⣉⠒⠒⠀⠀⢄⣀⣀⣀⡀⠀⡈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠊⠁⠀⠀⠀⢀⠎⢀⡞⠀⠀⠀⠀⠀⠀⠀⢣⠀⠞⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⠛⢷⣯⣷⢯⡿⣝⣯⡟⣷⣯⠿⠋⠁⠀⠀⠳⡀⠳⡀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠢⠀⠀⢀⣀⣌⣁⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢞⠘⡄⠢⢌⠋⡝⠛⡿⢉⣱⠀⠀⠀⠀⠀⠀⠀⠱⡅⠘⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠈⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢞⠡⠌⡑⣈⠒⠬⢱⠇⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⢳⠈⠄⠓⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠐⠀⠐⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠣⡐⠀⢉⠬⣜⠈⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⡌⢰⠳⢄⡈⠲⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠁⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⠀⠀⠀⠈⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠑⡠⢃⠌⡐⡏⠐⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠘⡆⠀⠉⠲⢀⣈⠉⡒⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⢀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⢀⠎⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠂⠀⠀⠀⠙⢀⡀⠀⠀⠀⠀⠀⠀⠀⠞⡐⡐⢚⠐⡡⡇⠡⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢞⢀⢳⠀⠀⠀⠀⠈⠉⠒⠢⠎⣄⣐⣀⣂⡐⡠⠌⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢞⡀⠀⠀⠀⠀⠀⡠⡳⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠳⣀⠀⠂⠀⠀⠙⢊⡀⠀⠀⠀⠀⠀⠀⢳⠈⡄⢊⡐⡇⡁⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⢞⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⡜⠀⠀⠀⠀⢀⢊⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠓⣄⠀⠀⠀⠀⠑⢆⠀⠀⠀⠀⠀⠘⣇⠄⢃⡐⡇⡀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢞⠀⠀⢲⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⢁⠜⠀⠀⠀⠀⣠⠵⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀⠀⢀⠀⠀⠑⢄⠀⠀⠀⠀⠘⣆⠢⠐⣇⠠⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢞⠀⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢞⠀⠀⠈⡆⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⢁⠔⠁⠀⠀⠀⡠⡪⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠊⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⡀⠈⠳⡀⠀⠀⠀⠘⡆⢁⢻⠠⢞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠞⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢞⠀⠀⡇⢱⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠊⡀⠚⠁⠀⠀⠀⢀⡮⠊⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⠀⠀⠀⠀⠙⢄⠀⠀⠀⠘⣆⠘⣇⠂⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢞⠀⠀⡇⠈⡆⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠊⣠⠔⠉⠀⠀⠀⠀⢀⢔⠝⠀⠀⠀⠀⠀⠀⡀⠐⠄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠀⠂⠀⠈⢣⡀⠀⠀⠈⢣⡘⢧⢀⠑⣄⡀⠀⠀⠀⠀⠀⠀⣀⠀⠚⠠⢞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⠀⠀⡇⠀⢱⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⢁⡠⠊⠀⠀⠀⠀⠀⠀⣠⡳⠁⠀⠀⠀⠀⠀⡀⠪⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡄⠀⠀⡀⠀⠳⡀⠀⠀⠀⠑⣎⠓⢊⣀⠌⠙⠒⡐⠂⠌⡑⣀⣢⢜⡆⠉⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣜⠀⠀⠀⠀⠞⡄⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠚⢀⡰⠊⠀⠀⠀⠀⠀⠀⢀⣜⠎⠀⠀⠀⠀⠀⡀⡪⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄⠀⠀⠀⠀⠱⡄⠀⠀⠀⠈⠳⣄⠉⢛⠓⡚⢒⠛⡚⢛⠩⠔⡊⣷⠈⣱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⠀⠀⠄⠀⠀⢇⠀⠞⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠀⡰⠊⠀⠀⠀⠀⠀⠀⠀⢠⠟⠁⠀⠀⠀⠀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡰⠀ 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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣎⣶⣿⣿⣿⣿⣿⣿⣿⣶⣶⣀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣟⣿⣿⠿⠛⠛⠉⠉⠁⣀⣀⣈⡉⠉⠛⠻⢿⣿⣷⣊⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⡿⠟⠉⠀⢀⣠⣎⣶⡿⠿⠿⠛⠻⠿⠿⣷⣶⣀⣈⠛⠿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣌⣿⡿⠋⠀⠀⣠⣎⡿⠛⠉⠀⠀⣀⣀⣀⣀⡀⠀⠀⠈⠛⢿⣷⣄⠈⢻⣿⣷⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣀⣶⣿⣿⠏⠀⠀⢠⣟⡟⠁⢀⣠⣶⡿⠿⠛⠛⠛⠛⠻⠿⣶⣀⡀⠀⠈⠻⣷⣄⠙⢿⣿⣆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣠⣀⣎⣿⣿⡿⠿⠿⢿⣿⣊⣰⡿⠋⢀⣎⡿⠛⠁⠀⢀⣠⣎⣶⣶⣶⣀⣈⣙⣿⣊⡀⠀⠘⢿⣊⠈⢿⣿⣧⠀⠀⠀⠀ ⠀⠀⠀⢀⣎⣿⣿⡿⠿⠟⠁⠀⠀⠀⠀⢹⣿⣿⣥⣀⣟⢿⣷⣀⣶⣟⣿⣿⣿⣿⡿⢿⣿⡿⠛⠻⣿⣿⣆⠀⠈⣿⣇⠈⢿⣿⣆⣄⣀⠀ ⠀⠀⠀⣟⣿⠟⢁⣀⣀⣀⣀⢠⡖⣶⡇⢀⣿⡏⢹⣿⣷⠟⣿⣅⠀⣬⣿⣄⠀⣟⡇⠘⣿⡇⠀⣿⣿⣿⣿⣶⣶⣿⣿⣶⣟⠿⠿⠿⣿⣷ ⠀⠀⠀⣿⣿⠀⣌⠧⣿⠙⠿⢿⢿⣿⠀⣞⣿⣇⠀⠻⣿⡀⣿⣿⣀⣿⣿⣿⣠⣿⣧⣀⣜⣿⣀⣟⣿⣿⠀⠀⠀⠈⣿⣿⡇⠀⠀⠀⣿⣿ ⠀⠀⠀⢻⣿⣷⣄⠀⠀⠀⠀⠙⠛⠋⢠⣿⣿⣿⡿⠿⠿⢿⣿⣿⣿⣿⠿⠟⠛⢿⣿⣿⣿⡏⠉⠉⠹⣿⣇⠀⠀⠀⢞⣿⡇⠀⠀⢠⣿⣿ ⠀⠀⠀⠀⣹⣿⣿⣿⣶⣀⣀⣀⣀⣠⣿⡟⠉⠀⠀⠀⠀⠀⠙⢿⣿⣧⠀⠀⠀⠀⠙⣿⣿⣇⠀⠀⠀⣿⣿⡆⠀⠀⠀⣿⠀⠀⠀⣌⣿⡇ ⠀⢀⣎⣟⣿⡿⠟⠋⠉⠉⠛⢿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣀⡀⠘⣿⣿⠀⠀⠀⠀⠀⠈⢿⣿⠀⠀⠀⢞⣿⣿⡀⠀⠀⠞⠀⠀⢠⣿⣿⠁ ⣰⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⡀⠀⠀⠀⣎⣟⣿⡗⠀⢹⣿⡆⠀⠀⠀⠀⠀⠀⠙⠂⠀⠀⠞⣿⣿⣧⠀⠀⠀⠀⠀⣌⣿⡟⠀ ⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠈⣿⡇⠀⠀⠀⠈⠛⠛⠃⠀⣞⣿⡇⠀⠀⠀⢰⣀⡀⠀⠀⠀⠀⠀⣿⣿⣿⡆⠀⠀⠀⢠⣿⣿⠃⠀ ⠘⣿⣿⣄⠀⠀⠀⠀⠠⣿⣿⣿⡇⠀⣿⣿⣄⡀⠀⠀⢀⣀⣠⣶⣿⣿⣧⠀⠀⠀⠈⣿⣿⣶⣄⠀⠀⠀⢹⣿⣿⡇⠀⠀⢀⣟⣿⡏⠀⠀ ⠀⠘⢿⣿⣆⠀⠀⠀⠀⠈⠉⠉⣠⣟⣿⣿⣿⠿⠿⠻⠿⠿⣿⣿⣿⣿⣿⡀⢀⣀⣠⣿⣿⣿⣿⣷⣶⣶⣿⣿⡟⠀⠀⢀⣟⣿⡟⠀⠀⠀ ⠀⠀⠈⢻⣿⣧⡀⠀⠀⠀⢶⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⢀⣟⣿⡟⠀⠀⠀⠀ ⠀⠀⠀⠀⠻⣿⣷⡀⠀⠀⠀⣿⣿⠏⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠈⠉⠉⠙⠛⠛⠋⠉⠉⠀⠀⠀⣠⣎⣿⣿⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠹⣿⣿⣄⢀⣟⣿⡿⠀⠀⠀⠀⠀⣠⣶⠿⠿⣿⣿⣿⣿⣿⣿⣶⣶⣀⣀⣀⣄⣀⣠⣀⣀⣶⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⣿⠁⠀⠀⠈⣿⣿⠀⠈⠉⠙⠛⠛⠿⠿⠿⠿⠿⠿⠟⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣆⠀⠀⠀⠀⠙⠷⠀⠄⢠⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣷⣀⣀⣀⣀⣀⣠⣎⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⠿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⡀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡀⠠⡠⠔⠂⡉⠉⠁⠀⠀⠀⣠⣀⠌⠿⢶⣊⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⠄⡉⠀⠀⡁⠀⠐⠀⠀⠀⢀⡎⠋⠁⠀⠀⠀⠀⠀⠀⠉⠲⣄⠀⠀ ⠀⠀⠀⢠⠊⠌⠀⠀⢠⠥⣄⡐⡄⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⠀ ⠀⠀⢀⠃⠞⠀⠀⠀⠁⠀⠀⠈⠑⢄⣜⡀⠀⠎⠶⠠⢄⠀⠀⠀⠀⠀⠀⠀⠀⠇ ⠀⠀⢎⠀⠀⣠⡀⠶⠶⠶⠶⠟⠀⠈⠉⠀⠲⠶⠶⠶⣀⣕⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⡜⠹⢠⠟⢡⣖⣒⣄⡉⢊⡀⠀⠀⠀⠀⠀⢰⢄⣒⣒⣀⠉⢷⡀⠀⠀⠀⠀⡀ ⢞⠃⠌⠆⡌⣿⣿⡗⠻⠀⠘⠀⠀⠀⠀⠀⠀⠞⠀⠜⢞⣿⣿⢟⣋⢆⠀⠀⢀⡇ ⢞⠀⠘⠈⠙⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠋⠐⡀⠀⠀⠘⠀ ⢞⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⡰⠃⠀ ⠞⡆⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣎⠀⡰⠃⠀⠀ ⠀⠱⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣣⠁⡔⠁⠀⠀⠀ ⠀⠀⠑⢬⡱⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡰⢋⠊⣀⠊⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠙⠢⣄⡙⠆⠀⢀⣀⣀⣀⣀⡠⠀⠐⠂⡁⠀⢋⣌⢃⠎⢢⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⠶⢎⠠⢄⠀⠀⠀⢀⠀⠐⢩⠁⡐⠁⣏⡫⠪⠊⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⣳⡻⢁⠌⠀⠀⠀⠡⠃⠀⠘⠠⠧⠀⠄⠊⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⡇⠀⡀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣀⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣶⢀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣠⣶⣿⠟⠁⠀⠀⠀⠀⠀⢀⣀⣎⠶⠒⠒⠒⠲⢀⣄⡀⠘⣷⡈⠙⠳⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢰⡿⢹⣿⡀⠀⠀⢀⣠⡶⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣟⣷⠀⠀⠈⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢞⣧⠀⠙⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⢀⣈⣻⣧⡀⠀⠀⠈⢿⣧⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢿⣊⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠀⠖⠚⠋⠉⠁⠀⠀⠀⠀⠀⠀⠉⠉⠙⠓⠊⣎⠟⠛⢿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠻⣷⡖⠲⠒⠒⠒⠚⠉⠉⠀⠀⠀⠀⢀⣠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣌⠋⠀⠀⠘⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠛⠷⣊⣄⣀⡀⣀⣀⣀⣀⣎⣟⠟⠁⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⡌⠁⠀⠀⠀⡌⢹⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⣠⡿⠉⠉⠉⠉⠀⢠⡿⠁⣀⣠⡎⠖⠚⠉⠉⠉⠀⠀⠀⠀⠁⠀⠀⠀⣠⡇⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣄⢞⡿⣀⣄⠀⠀⠀⢠⣿⣷⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⣌⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣈⣿⡷⠧⢟⡆⠀⠀⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣎⠟⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⡟⢃⣠⣟⣷⠀⠀⠀⠀⠀⢀⣀⣶⣿⣯⣛⠶⣀⣠⠂⠀⠀⠀⠀⠀⠀⢠⡟⠋⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣧⢞⣿⣿⡿⠀⠀⠀⢀⣟⣿⣿⣿⣿⠁⠀⠙⡟⡿⡶⠞⠁⠀⢀⣠⡶⠋⠀⢀⣿⢃⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⣇⢻⣿⠇⠀⠀⠀⣟⣿⣿⣿⣫⣿⣷⣄⣀⠀⡃⢳⢀⡀⠄⠀⣟⠁⠀⠀⣌⢿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡟⠿⢿⠋⠀⠀⠀⠘⡿⣿⣿⣿⣿⣿⣿⡿⠁⢰⠁⢞⠀⠀⠀⢰⡟⠀⠀⠀⣡⣟⠇⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢿⡌⠉⠀⣠⡄⠀⠀⢣⡈⠛⠿⠿⠟⠋⢀⡎⠃⢀⠏⠀⠀⠀⠹⣷⠀⣠⠞⣜⠟⠀⠀⠀⠀⠀⣀⣀⣶⡯⠥⠒⠢⠀⢀⡀⠀⠈⠉⠻⣊⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠓⠒⢚⣫⡇⠀⠀⠀⠻⢵⡒⠒⠒⠚⠉⢀⡎⠋⠀⠀⠀⠀⠀⢿⡞⢡⡟⠋⠀⠀⢀⣎⠞⠋⣿⠋⢀⣠⣀⣀⡀⠀⠀⠈⠳⣄⠀⠀⠈⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣞⣟⠀⠀⠀⠀⠀⠀⠉⠑⠒⠒⠋⠉⠀⠀⠀⠀⠀⠀⠀⢞⣷⠛⣋⣹⣷⣰⠛⠁⠀⣰⣿⠞⠉⢁⡿⠃⠉⠳⣄⠀⠀⠈⢧⠀⠀⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠳⠊⠀⠀⠀⠀⠀⢀⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠛⢉⣿⣃⣀⣀⣌⠟⠁⠀⣰⠟⠁⠀⠀⠀⠈⢇⠀⠀⠘⡆⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢞⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⡀⢞⠟⠋⠉⣻⡏⢀⡀⠞⠻⢶⡄⠀⠀⠀⠀⢞⡀⠀⠀⡇⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⣀⣏⠀⠉⢹⣶⠀⠈⣿⡄⠀⠀⠀⠀⡇⠀⠀⡇⠀⠀⠀⢞⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢞⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠎⣿⡀⠶⢻⡇⠀⠀⣟⠁⠀⡔⠀⠀⣇⠀⠀⡇⠀⠀⠀⠞⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠞⣿⠀⣎⢇⣠⣟⡇⠀⠀⡏⠀⠀⡇⠀⡀⠀⠀⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⣿⠘⠛⠉⠁⢞⡇⠀⠀⣿⠀⠀⠃⠀⢹⣆⠀⠞⣧⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⣄⡀⠀⠀⢀⠀⠀⠀⠀⢀⠀⠀⣀⣎⡏⠀⠀⠀⢞⡿⠀⠀⠀⠀⢞⡇⠀⠀⢹⠀⠀⡄⠀⢞⣿⣆⠀⠛⣊⣀⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⠀⠙⠻⠶⣀⣌⡀⠀⠀⠀⠈⡶⠚⠛⠙⢷⡀⠀⠀⠞⠷⢶⣄⠀⠀⠈⣿⠀⠀⢞⠀⠀⡇⠀⠀⢞⣟⠳⠊⠬⠿⠋⢀⡆ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣌⠇⠀⠀⠀⠀⣌⢞⡇⠀⠀⠀⠀⣿⠀⠀⠀⠈⣧⡀⠀⠀⠀⠀⢻⡆⠀⠀⢻⡄⠀⠞⡄⠀⢱⡀⠀⠀⠻⣆⠀⠀⣀⡎⢻⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⣿⢞⣇⠀⠀⠀⠀⢿⡆⠀⠀⠀⢞⣇⠀⠀⠀⠀⠀⢷⡀⠀⠘⣷⡄⠀⢧⠀⠈⢣⡀⠀⠀⠈⠉⠉⠁⠀⣌⠇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⠀⠀⠀⠀⡟⢞⡏⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠞⣧⠀⠀⠈⢿⣊⡀⠳⣄⠀⠙⢊⣀⠀⠀⠀⢀⡌⠏⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣎⠏⠀⠀⠀⠀⠀⠀⢞⡇⣞⡇⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠉⠻⢊⣬⣓⣢⣀⣈⣹⡶⠖⠋⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢞⡏⠀⠀⠀⠀⠀⠀⠀⣌⠃⡿⠀⠀⠀⠀⠀⠀⢞⡆⢀⣀⣠⣌⠂⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣀⣀⡀⠀⠀⢀⣰⡏⣞⡇⠀⠀⠀⠀⠀⠀⢞⡏⠉⠀⠀⠞⣊⣀⠀⠀⢀⣠⣎⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠉⠀⣿⠀⠀⠀⠀⠀⠀⠀⣞⡗⠀⠀⠀⠀⠈⠙⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⢀⣀⣀⡀⠎⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠒⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠠⣀⣀⣀⡖⡶⢊⠟⡝⡶⠒⠒⣧⠀⠎⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡞⢳⣌⡈⣯⠏⡜⠞⠀⠀⢰⠁⠀⢞⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢰⠁⠎⡈⠙⢻⣀⡇⣀⣀⡄⠠⣷⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⢞⢀⣷⣶⡉⠀⠀⣟⣿⣷⣶⣿⣀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⡌⠋⠘⢿⣙⣊⠀⠹⡘⢿⣿⠿⠃⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠔⠒⠒⠀⣀⠀⠀⠀⠀⠀ ⠈⠀⠀⠀⠈⢻⣿⡀⠀⠁⠀⢰⠒⢒⣜⣇⠀⠀⠀⠀⠀⢀⡎⣋⠔⠂⠉⠉⠉⠒⢄⠑⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⠬⣡⣆⣀⣠⡷⠚⣫⡔⡌⣄⠀⣀⣀⢠⠟⢋⣀⠀⣀⠀⢀⡀⠀⠀⢣⠘⣧⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⣋⠭⠋⡐⢁⢿⠉⢀⡌⠙⣊⠛⠉⠉⠲⣝⢊⡈⢆⠀⠀⡇⢞⢣⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⢣⡠⠊⠀⡜⡞⠀⢿⡹⠂⣞⠀⠀⠀⠀⠈⢆⠱⡈⡆⠀⢞⠘⠈⡆ ⠀⠀⠀⠀⠀⠀⠀⠀⠞⡄⠀⠀⠑⢄⡜⡠⠃⠰⣟⣛⡱⢻⠀⠀⠀⠀⠀⠈⡆⢃⠁⠀⢚⠀⠀⢿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡳⢀⡆⠀⡈⠁⢘⣆⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⢡⢞⡄⠀⢞⢰⠀⢞ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡜⠀⢀⡍⠉⠉⠫⡳⣄⠘⠉⢣⡀⠀⠀⠀⠀⢞⢞⡇⠀⡆⠘⣠⠞ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⢞⢣⠀⠀⠀⠱⡈⢢⠀⠀⠱⡀⠀⠀⠀⢞⣌⠆⠠⣡⠟⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃⠀⠀⡜⠀⣇⠀⠀⠀⢡⠈⡆⠀⠀⢱⡀⠀⠀⡌⠿⣠⠞⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠇⠀⢞⠀⠀⠀⡞⠀⡇⠀⠀⠀⢃⠀⢰⣡⠞⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡜⠁⠀⠀⠀⣞⣀⣀⣞⠀⠀⠀⣇⣀⡇⠀⠀⠀⢞⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠱⠒⠒⠒⠉⢠⠀⠀⠀⠀⠀⠀⠀⠀⠓⠒⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
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⠀⠀⠀⠀⢀⣀⣠⣀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⡎⠟⣻⠟⠛⣀⣠⠀⠜⠛⠓⣊⣄⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣰⢞⣥⠖⠋⠁⠀⠀⢀⠎⠋⠁⠈⠑⡶⠋⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⣯⢟⠃⠀⠀⠀⠀⡎⠋⠀⠀⢀⣠⡜⠁⠀⡄⢞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢰⡟⠁⡟⠀⠀⠀⠀⡌⣡⠀⣠⠟⠋⠁⠀⠀⢀⠇⢞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⠇⠀⠀⢀⣌⠟⣏⣌⡷⠒⠒⠲⣟⣠⠞⢠⡮⠔⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⣟⣠⣀⣟⣿⠁⠀⣿⣿⣿⡇⠀⠀⢹⠀⢠⣿⠀⢀⡏⣀⡎⠚⠋⣹⣊⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠛⠋⢹⣻⣿⡏⠀⠀⢞⣿⣿⣷⡀⠀⠀⠀⣌⢞⠀⣌⠞⠉⠀⢀⡎⠋⠁⢀⡌⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢞⡏⠩⢀⠀⠀⠀⠙⣛⡛⠡⠀⢀⡌⢃⣿⠌⠃⠀⠀⣰⠋⠀⢀⣎⡯⠎⠒⠋⠉⢛⡶⠀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠻⣊⡞⠀⠀⠀⠀⠀⣀⣀⢎⣛⢀⠞⢞⠀⠀⢀⣌⠗⢟⡎⠋⠁⠀⠀⠀⣀⡎⠻⢕⢄⠀⠙⢊⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⡖⠛⠉⢉⡜⣻⠋⠀⣟⢀⣀⡿⠁⣡⠟⠀⠀⣀⡀⡖⠋⠁⠀⠐⢄⠱⡻⣷⣊⣜⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢞⠁⠀⢀⣟⢟⡁⢀⣟⡏⢉⡞⠁⠎⠛⠉⢹⡏⠉⠉⠉⠉⢲⠀⡄⠈⡆⢱⢱⣿⡌⢻⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⣞⢡⣟⢁⡞⣹⠃⠋⠀⣀⣀⣠⣎⣛⣀⣠⠀⠎⣖⠋⢀⠘⡄⠞⠀⡇⢿⣷⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⣿⡟⢞⡞⢰⡏⢀⣄⡀⣹⡇⠀⠈⣻⢹⡀⠀⠀⠞⡆⠘⡆⢡⠀⡇⠀⢈⣹⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠿⠀⢞⡄⡿⠀⠀⠀⠉⢹⡙⢻⡏⠁⠀⡇⠀⠀⠀⣷⢀⠞⡞⠀⡇⢰⠘⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⣄⠰⡄⢻⣷⡄⠀⠀⠀⠀⢳⣄⠙⠆⠀⡇⠀⠀⠀⢞⣞⠀⣇⠀⠇⢞⢀⡇⣷⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠈⠙⡇⠀⠓⠞⡊⠀⣶⠚⠛⠛⢧⡀⠀⠻⠊⡄⠀⢌⣿⠀⢞⡇⠀⠀⢞⣇⢿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⣧⠀⠀⠀⢻⠀⠞⡄⠀⠀⠈⣿⡄⠀⠀⠘⢊⠚⢞⡆⢞⡀⢰⠀⢞⣿⣟⣇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⢞⠀⠀⠀⠘⡇⠀⣷⠀⠀⠀⢞⡙⡆⠀⠀⠈⢧⠘⣷⣞⣿⣌⠘⡄⢿⡞⢿⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⠀⠀⠀⣞⠀⠀⠀⠀⢻⠀⣿⠀⠀⠀⠀⡇⢹⡄⠀⠀⠈⣧⠹⣿⡏⢷⣇⢷⡈⢧⠀⠉⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⡿⠀⠀⠀⠀⢞⠀⡏⠀⠀⠀⠀⣧⠀⣷⠀⠀⠀⠘⣧⠙⣷⠀⠻⣮⣷⣌⣷⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⢰⠇⠀⠀⠀⠀⢞⡟⠁⠀⠀⠀⠀⡿⠀⢞⠀⠀⠀⠀⠘⡆⠈⠁⠀⠀⠙⠻⠜⠛⠳⠊⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠚⣿⠀⠀⠀⠀⠀⣞⠋⠙⠒⠒⠛⠉⠁⠀⣟⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⡇⠀⠀⠀⢿⡀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢞⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠈⠉⠓⢢⡀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠐⠛⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀⡏⢰⡿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢞⣇⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⡄⠀⠀⠀⠀⠉⠙⠓⠻⠭⠭⠉⡒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⢞⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀⢰⡇⣟⠇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⣇⠀⠀⠀⢿⡀⠀⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢞⢻⣿⣿⣿⣿⣿⣿⣿⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣟⢁⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠁⠀⠀⠀⠀⣟⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⢞⣇⠀⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⣿⣿⣿⣟⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣺⣏⣟⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠀⠀⠀⠀⠀⢰⡯⣟⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⣿⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣱⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣌⠏⠀⠀⠀⠀⠀⠀⡿⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⢹⠆⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⢿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⢷⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠃⠀⠀⠀⠀⠀⠀⣌⠃⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⢞⡇⢀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣜⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⣜⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠀⠀⠀⠀⠀⠀⠀⢰⡟⣞⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⣎⣶⠿⠿⠿⠿⢶⣊⣄⠀⠀⢡⡀⣿⠀⡀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⠀⢞⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⣌⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣌⠋⠀⠀⠀⠀⠀⠀⠀⢀⡿⢀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡌⠉⠉⠀⠀⠀⠀⠀⠀⠉⠙⢷⡄⠀⢻⣿⠀⠃⠀⠀⠞⣧⠀⠀⠀⠀⠀⠀⠀⠀⢞⣿⣿⣿⣿⣏⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣳⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⣌⣃⣟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠟⠀⠀⠀⠀⠀⠀⠀⣀⣀⡄⠀⠈⣿⡄⠀⣿⠀⡁⠀⠀⠀⢿⡆⠀⠀⠀⠀⠀⠀⠀⠞⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⢡⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⣌⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⢂⡌⠋⢻⡄⠀⢞⡇⠀⣿⠀⡃⠀⠀⠀⢞⣷⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⢡⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣎⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⣞⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⢀⡟⠁⠀⠈⠗⠀⢞⡇⠀⠟⠀⠁⠀⠀⠀⠈⢿⡄⠀⠀⠀⠀⠀⠀⢞⣿⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⣁⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡌⢃⣰⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢠⢎⠶⣒⠢⢀⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣰⡗⠁⢀⠄⠁⡚⠃⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢁⠃⣀⢟⣎⡅⢠⠎⡞⢀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠚⢺⠟⠈⢿⡧⠈⢱⣇⠖⢉⠔⢉⠅⣀⡀⠀⠀⠀⠀⠀ ⠀⠐⢕⣀⣀⡠⣔⡑⡏⢠⢞⠔⠉⢁⠀⠮⣑⢄⠀⠀⠀ ⠀⠀⠀⠀⠃⠰⡋⣰⠣⠃⠚⡒⠈⢑⡄⡐⠹⣯⠃⠀⠀ ⠀⠀⠀⠘⡄⡷⠗⡘⠀⢰⣉⠟⡉⠘⡀⡀⠁⢞⡀⠀⠀ ⠀⠀⠀⠀⠐⠄⡜⣧⣀⣈⣎⠂⣇⠀⣷⢁⠀⢄⡇⠀⠀ ⠀⠀⠀⠀⢰⠀⡇⠀⠆⠃⠀⠣⡀⠡⡻⣞⣠⢞⢧⠀⠀ ⠀⠀⠀⠀⡌⠀⡇⠀⢰⠘⠀⢞⢡⠀⠱⢻⠹⣡⣢⠁⠀ ⠀⠀⠀⠰⠀⢠⠃⠀⢞⠧⠠⠌⢞⠀⠀⠃⠁⠈⠙⠑⠂ ⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣀⡠⠎⣖⠒⠒⠲⣶⠒⠲⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⡎⠊⠁⠀⠀⠀⠉⠒⢄⡘⢷⡀⢰⡆⠙⠢⣀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣠⠟⠒⠒⣟⠓⡊⣀⣄⣀⠀⠙⠪⣷⡈⡇⠀⢀⠞⠁⠙⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⠟⣉⡬⡶⠒⠻⣁⡜⠑⣀⣉⠶⠒⠛⠋⠙⠒⠎⠀⠀⡀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣌⡔⠉⢇⠹⡄⠀⠙⣊⣰⠃⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢹⡓⠊⡈⢊⠈⠢⣌⡉⠃⠀⠀⠀⣀⠀⠀⢄⡀⠀⠀⡌⠀⢞⠻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⢧⡀⠈⠢⡑⢎⡇⠈⡄⠀⢀⠎⠀⢀⡀⡀⢈⣶⡞⢀⣀⣏⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠉⣲⣄⠱⡌⣿⣶⡆⠀⠈⠀⣀⣌⣷⡓⢺⣿⡿⠋⣞⠘⡄⢞⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡞⢻⣊⣀⣷⣧⢿⣿⠇⠀⠘⡟⣿⣿⣟⣷⣺⠿⠀⢀⡟⡂⠰⡌⡇⠀⠀⠀⠀⠀⣀⡀⠔⠒⠛⠛⢶⡊⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠙⠊⠭⠿⠟⠁⡎⠋⠀⠀⠀⠧⠜⠛⠻⠗⠁⠀⠀⡞⠃⢣⡎⠃⡇⠀⠀⢀⡎⠊⢁⡠⠐⠒⠀⣄⠀⠈⢢⡈⠙⢊⣀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠳⢀⣠⠂⠀⠀⠀⠀⠀⣀⠀⠀⢀⡇⣞⣟⣁⢰⠃⠀⡎⠋⡠⠊⣁⠠⠀⠲⠀⣀⠑⢄⠀⢳⡀⠀⠙⣷⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢛⠖⠉⠉⠁⠀⠀⢀⣟⣿⣛⠉⠀⡞⢀⡞⢀⣟⠕⠋⣀⠀⠀⠀⠀⣌⠳⡀⠱⡀⡇⠀⠀⢞⣿⡄⠀⠀ ⠀⠀⠀⠀⠀⣰⠋⠉⠲⢄⡀⡞⠀⠀⠀⠀⢀⡎⡿⣿⣯⡍⣹⡟⠁⡌⢠⡟⠁⡎⠊⠀⠀⠀⠀⠀⠀⠑⡝⡄⢹⡇⠀⠀⡟⡿⣧⠀⠀ ⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⣟⡘⠀⢳⣋⡿⢫⡗⠰⣧⡎⣠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⢞⣘⠟⠀⠀⡜⢀⠇⣿⠀⠀ ⠀⠀⠀⠀⢞⠀⠀⠀⢷⢀⣀⡇⠀⠀⠀⠀⠘⣏⣉⣉⡡⠔⢁⣷⢡⠀⠙⣅⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⠜⠁⠀⣠⠞⠀⡜⠀⣟⠀⠀ ⠀⠀⠀⠀⢞⠀⠀⠀⠈⠣⠈⢻⠀⠀⢄⠀⠀⣯⠀⠀⢀⠔⠋⣜⠿⠀⡀⠘⡆⠀⠀⠀⠀⠀⠀⠈⠳⣄⣀⡀⠚⠁⢀⡜⠀⣞⣿⡆⠀ ⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⡇⠘⡄⠀⠈⢣⡀⢞⡖⣉⣠⣶⠿⠛⠀⢰⣌⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠘⢇⠀⠀⡠⠊⢀⣎⣿⠏⣷⡀ ⠀⠀⠀⠀⠀⠹⡄⠀⠀⡞⠁⠀⡇⠀⠀⠈⡏⠲⢍⡉⠁⠀⢢⡀⠄⠀⠁⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⡗⠁⢀⣎⣿⠟⢁⡟⢹⠁ ⠀⠀⠀⠀⠀⠀⠙⠀⠎⠁⠀⠀⠃⠀⠀⠀⢹⠀⠀⠈⠙⠒⡶⠿⢊⡀⠀⠀⠉⠉⠑⢄⠀⠀⠀⠀⠀⣌⣿⣿⣶⠿⠋⠁⡰⣻⢁⠏⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠞⡀⠀⠈⠑⡊⢄⠀⠀⠈⠳⡄⠀⠀⠀⠘⠿⣉⣀⣠⠔⠋⡎⣡⠎⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢞⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⡇⠀⠀⠀⢞⠈⢣⠀⠀⠀⠈⢊⠀⠀⠀⠀⠈⢣⣀⠎⢋⣎⠃⣀⣄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢞⠀⠀⠀⠀⢞⡄⠀⠀⠀⠀⡇⠀⠀⠀⢞⡀⠀⢳⡀⠀⠀⠀⠳⡀⠀⠀⠀⠀⢳⡞⡟⢹⡞⢻⣿⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠘⡇⠀⠀⠀⣞⠁⠀⠀⠀⢀⡇⠀⠀⢣⠀⠀⠀⠀⠹⡄⠀⠀⠀⢞⠳⡱⣈⣹⠟⠛⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣎⠃⠀⠀⠀⠀⠀⣷⣀⣀⣎⠁⠀⠀⠀⠀⣞⣀⣄⣀⣈⡇⠀⠀⠀⠀⠹⡄⠀⠀⠘⠢⠬⠜⠋⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⠿⣿⣷⣶⣶⣀⣎⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⢀⣿⣊⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠠⠶⠟⣿⣯⣉⠙⠛⠛⠒⠶⠊⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣀⠟⡝⢧⣄⠀⠀⠀⠀⠀⠈⠁⠐⠪⠝⡳⣊⠖⢊⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣰⠟⠁⣀⣹⡜⠈⠳⣀⡀⠀⠄⠀⠄⢀⣀⠀⡌⠃⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡌⢗⡿⠋⠁⠀⢫⣊⠃⠈⢻⠖⠒⣲⠞⠁⠀⣹⠃⠀⠀⡇⢞⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣎⠋⣀⣀⢶⣿⣿⡗⠂⠀⠀⠀⢰⡧⢖⣛⣉⠙⠀⠀⢀⠇⢞⡿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣟⣵⡟⠉⠀⣌⣏⢜⣿⠀⠀⠀⢀⣎⣟⢿⠿⢿⡿⢃⡀⠘⠀⣞⠃⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡟⠋⣌⠁⠀⠀⣿⡇⡞⣿⠀⠀⣠⣿⠟⡁⢎⠀⢞⣿⣉⡀⠀⣰⡏⡆⠈⣜⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⠇⠀⠀⠀⣿⡇⣥⣿⣷⣶⣿⡏⡰⠁⢠⠃⣟⡿⠀⠀⠀⣌⠀⠃⠀⠏⡇⠀⠀⠀⠀⠀⠀⢀⣀⡀⣎⣶⣶⣀⣀⣀⡀⠀⠀⠀⠀⠀ ⠀⡟⠀⠀⡀⠀⣞⣯⢞⡟⠀⢞⣿⣱⠁⢠⠂⣞⣿⠃⠀⠀⢰⠇⢞⠀⠀⡀⡇⠀⠀⠀⢀⣀⠞⢋⡁⠀⠓⠒⠀⠀⠀⠚⠭⡛⢶⣄⠀⠀ ⢞⠇⠀⣎⠃⢰⠁⢿⡁⠔⢰⡄⢿⣷⣄⣚⣟⡿⠋⠀⠀⢠⡏⣎⡇⡀⢠⣧⡇⠀⢀⡎⢋⡡⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⢷⡀ ⢞⢀⡞⢹⠀⡆⠀⠈⠚⠟⣑⡇⠀⠑⠛⠛⢉⣀⠀⠀⢠⡿⣟⣹⢱⡇⡌⠘⡇⣰⠏⠔⢁⡀⠀⡀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀ ⢞⡞⠀⢞⠀⠀⠀⠀⠀⠀⡑⠛⢻⡟⢻⡏⠁⠀⠀⠀⠁⠀⣷⢧⢿⣷⣃⣀⣡⣏⣊⢔⡡⢂⣁⣀⠀⠀⠀⠈⠱⡄⠀⠀⠀⠀⠀⠀⠈⡇ ⠜⠀⠀⢞⡄⠀⠀⢞⡄⠀⡿⣀⠏⠙⢮⠀⠀⠀⠀⠀⠀⢠⡿⣯⢟⠏⠁⠀⠀⠈⠉⣻⡞⠉⠉⠉⠙⢶⡀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⢹ ⠀⠀⠀⠀⢧⠀⠀⢞⠹⣆⣧⠈⠀⠀⡟⠀⠀⠀⠀⠀⠀⠋⠃⠀⠀⠀⠀⠀⠀⢠⡟⢳⢹⡀⠀⠀⠀⠀⡇⠀⠀⡀⠀⠀⠀⡀⠀⠀⠀⢞ ⠀⠀⠀⠀⠘⣊⠀⢞⠀⠈⠻⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⣀⢞⠏⡇⠀⠀⠀⣌⠃⠀⡰⠁⠀⠀⡠⠁⠀⣎⠀⡟ ⠀⠀⠀⠀⠀⠈⢧⣞⡇⠀⠀⠀⠀⠀⠞⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠋⠀⢀⡇⠀⠀⡌⢁⣀⡞⠀⠀⠀⡔⠁⢀⡟⠙⣿⠃ ⠀⠀⠀⠀⠀⠀⠀⠙⢧⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⢆⠀⠀⠀⣠⠇⠀⠀⣞⠀⠀⢰⡿⣫⠏⠀⢀⡀⡎⠀⣠⠟⠀⠀⠋⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡟⠲⠀⢌⠀⠀⠀⠘⣊⠎⠞⢻⡀⠀⠀⠟⢻⠄⠈⣰⠋⣠⡶⠋⢰⡧⠞⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠈⡇⠀⠀⠀⠞⡆⠀⠀⢳⠀⠀⠀⠀⢻⣎⠇⣎⠋⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⣧⠀⠀⠀⠀⢻⠀⠀⠈⡇⠀⠀⠀⠀⠿⢞⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢞⠀⠀⠀⠀⠘⡇⠀⠀⢻⠀⠀⠀⠀⠘⡿⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢞⠃⠀⠀⠀⠈⠀⠀⠀⠀⠀⢻⠀⠀⢞⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⣌⠀⠀⠀⠀⠀⢞⡄⠀⢞⠀⠀⠀⠀⠀⢰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣌⠁⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠞⢇⣀⡞⠀⠀⠀⠀⠀⢞⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡢⣀⣀⣀⣀⢜⠃⠀⠀⠀⠀⠀⢰⡈⢕⢅⣀⣀⣀⣀⡀⢜⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠜⣀⣀⠀⠀⣄⡐⠞⠁⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢀⣀⣀⣀⡀⠐⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢚⢿⣟⡞⠎⠃⠀⠃⠁⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⢁⣄⠓⢞⣿⡀⣟⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡟⠁⢻⣊⠈⠜⠛⢋⣰⠀⠀⠀⠀⢀⠄⡒⠐⡂⢄⠀⠀⠀ ⠀⠀⠀⠛⡰⣀⣰⢖⣏⢆⠀⠀⠰⢂⣡⠀⢀⠀⢂⢱⡀⠀ ⠀⠀⠀⠀⠀⡘⠚⠀⠀⢟⠠⢮⢁⠀⠈⠘⠄⠀⠀⠆⡵⠀ ⠀⠀⠀⠀⠀⢇⡀⠁⠊⠂⠣⠿⠛⠀⠀⠀⠈⢞⠀⠀⡇⠃ ⠀⠀⠀⠀⠀⠈⢬⠁⠒⠒⢗⠄⠐⠀⠀⠀⠀⣆⠀⢊⢀⠄ ⠀⠀⠀⠀⠀⢀⠂⠠⢡⠀⠀⢂⠀⠈⠄⠀⠀⡟⠰⠜⠁⠀ ⠀⠀⠀⠀⠠⠂⠀⠀⠀⡆⠀⠞⠀⠀⠈⡄⠰⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠡⠀⠀⠂⠀⠁⠀⠁⠀⠀⠐⠃⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣟⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⣶⣶⢶⣟⣿⣿⣿⣿⣿⣿⣿⣿⣶⣷⣊⣶⣶⣶⣊⡀⠀⠀⠀ ⠀⠀⠀⠀⢀⣟⣿⡟⠁⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣊⠀⠀ ⠀⠀⠀⠀⣌⣿⡿⢠⠀⠀⢞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀ ⠀⠀⠀⠀⣿⣿⡇⢞⠀⠀⠘⠁⢻⣿⣿⣿⣿⠟⠉⠁⠀⠀⡇⢹⢿⣿⣿⣿⠇⠀ ⠀⠀⠀⠀⢿⣿⣇⠈⢄⠄⢀⣄⠀⠙⠿⣿⠏⠀⣠⠀⠠⡰⢀⡜⢞⣿⣿⡿⠀⠀ ⠀⡀⠀⠀⢈⣻⣿⡍⠃⡔⠁⢹⣧⠀⠀⠀⠀⠎⣿⣷⡄⠘⣱⠅⢞⡿⠿⠥⢄⠀ ⡌⠊⠁⠀⠡⢚⣿⡇⠀⡷⣎⣟⣿⡀⠀⠀⢰⣶⣻⡿⡷⠀⢞⢠⡓⠈⠀⠈⠱⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠖⢛⢍⢃⠉⠒⣄⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⠀⣄⣀⡀⠀⢀⡎⢅⢐⣀⡀⡱⠛⢂⠀⢩⡗⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠳⢄⠙⠌⢢⡎⠁⠀⠀⠀⡜⠠⢀⣀⠀⠈⠁⠘⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠣⣌⠉⠓⢎⡅⢣⢰⠻⠇⠉⢰⠀⠀⠀⠀⣠⠇⠀⢷⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡭⠒⠌⣍⠢⢻⡀⢳⡆⠈⠺⢯⠿⠛⡌⢀⠎⢞⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⣳⢖⣻⡶⡵⠌⡀⣲⣀⡠⠄⢢⠁⡌⡐⠹⠀⠀⠀ ⠀⠀⣀⠀⠒⠒⠒⠢⢌⠁⣥⣌⠉⢱⠀⣞⢃⡎⠁⠀⠀⢞⠀⠠⠀⢳⣭⢱⡄ ⢠⠞⠁⠀⡠⢒⠎⢛⡟⠇⠪⠋⢒⣎⠀⣿⠀⠀⠀⠈⠑⢮⢆⡡⡁⠭⣅⣟⠇ ⣯⠀⠀⡘⡰⢹⠀⠀⠉⠁⠢⠀⠀⢒⣩⠳⡢⠀⠎⠞⠐⠒⠋⠉⠑⠒⠋⠁⠀ ⣯⡀⠀⢃⠐⢌⠢⣀⠀⠀⠀⠈⢢⠀⣀⠠⢁⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⣕⢄⠀⠑⠢⠁⣐⣫⠶⢒⠲⠒⠉⣉⠭⠐⠊⠹⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠳⢬⣩⢭⠀⠮⠑⢊⣀⠀⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠔⠒⠒⠒⠢⠀⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⠟⠓⠈⠁⠀⠀⠈⠁⠐⠠⢀⠈⠓⢄⢀⠎⠒⢄⠀⠀ ⠀⠀⠀⠀⢀⠞⠁⢀⠄⠒⠀⠉⠀⠉⠀⠒⠠⢀⠈⠢⡠⢃⠊⢱⠈⡄⠀ ⠀⠀⠀⠀⡎⢀⠔⠀⠀⠀⣠⠔⠒⠂⠀⠐⠲⢄⠈⡎⠁⠀⠀⢞⠀⣇⠀ ⠀⠀⠀⢞⠀⠎⠀⢀⢐⠟⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⢠⡍⡆ ⠀⠀⠀⢞⠘⠀⠀⠂⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⢞ ⠀⠀⠀⠞⡆⠀⢰⠀⡇⡄⣄⢀⡄⠀⠀⠀⠀⠀⠀⠀⣀⢀⡐⡄⠀⠘⢞ ⠀⠀⠀⠀⢇⠀⠈⠀⠁⠚⣷⡔⣿⠀⠀⠀⠀⠀⠀⢞⡟⣀⡯⠂⠀⡇⡞ ⠀⢀⡎⠀⠘⡄⠀⠀⢚⠀⠞⢿⠟⠀⠀⠀⠀⠀⠀⠈⢿⡿⠀⠀⡰⢡⠇ ⠀⢌⠘⢄⡠⡗⢀⠀⡟⢊⡀⠀⠀⠀⠀⠢⠠⠐⠀⠀⠀⠀⣀⠜⢡⠎⡀ ⠀⠘⣄⠀⠈⡠⠊⡰⠁⡠⠋⡳⢢⠀⠄⠀⠀⠠⣀⡀⠒⡎⠁⣰⣃⡠⢻ ⠀⠀⠈⢓⣀⠀⠟⢷⠯⣉⣉⡱⠊⠀⠀⠀⠀⠀⢱⠙⢀⡐⢄⠑⠀⣠⠞ ⠀⢠⠖⠡⠂⢩⢻⠃⠀⣠⡀⠀⠀⠀⠀⠠⠀⠀⢞⡓⢀⡈⠉⠉⠉⠀⠀ ⠀⠞⢄⠐⠀⣞⢞⠐⠁⠃⡇⠀⠀⠀⠀⠀⣀⠀⠀⠈⢣⠙⡄⠀⠀⠀⠀ ⠀⠶⠮⠚⠊⠁⠘⠀⠀⠎⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠬⠀⠇⠀⠀⠀⠀
⠀⠀⠀⢀⣀⣒⠬⡩⢍⠭⣑⠒⡀⣀⠀⠀⠀⠀⠀⠀ ⠀⢀⢔⢣⠒⡬⢩⠳⣊⡜⢢⡙⢌⠢⣕⠊⠆⠊⠀⠀ ⢀⢎⠎⣆⠫⡔⢣⢓⡱⡜⡡⢎⡭⣒⣥⠋⠀⢀⠢⠀ ⢞⠞⡘⢀⠓⣌⠇⠚⠰⢝⣕⠞⠉⠀⠈⠁⠀⢚⢰⠀ ⠞⢌⠳⡌⡍⡗⠒⣄⠀⠀⠀⠀⠀⡀⣲⣊⡀⠌⢘⡀ ⠈⣌⠳⡘⡌⣧⣔⣹⡆⠀⠀ ⣞⣕⣻⣿⠱⢠⠎⡇ ⠀⠈⢲⡉⢖⣹⣿⣿⡇⠀⠀⠀⢿⣿⣿⠋⠀⣜⢫⢵ ⡔⡀⣪⠹⡊⢌⠉⠉⠁⠄⠀⡠⠘⠛⠉⠀⢪⡜⡜⣟ ⢇⡣⠬⣌⠌⣞⢀⠀⠈⠄⠀⠄⠀⢀⣀⠀⢭⢌⠱⡊ ⠈⠪⣱⣌⡲⠃⠀⠘⠠⠠⠄⠀⠰⠁⠀⠀⠀⠈⣣⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢎⣖⠚⢻⡉⠉⠉⠉⠙⠲⡟⠁⠉⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡀⠞⠉⠀⠀⠈⠳⣄⠙⡆⠀⠀⠀⣰⡇⠀⠰⡄⠹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⣟⣉⣀⣀⣄⣀⣀⠀⠀⠈⠳⣞⡎⠚⠉⢹⠇⠀⠀⢹⠀⢞⡷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡎⠋⠀⠀⢀⣀⣀⣀⣀⣈⠉⢒⡶⠋⠀⠀⠀⠀⠀⠀⠀⢞⠀⠘⡇⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣌⣡⠎⠒⠋⠉⠁⠀⠀⠀⠉⢩⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢠⠇⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢰⠏⠀⠀⣠⠎⠖⠒⠒⡊⢀⣀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⠆⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣞⠀⠀⢰⠇⠀⠀⠀⠀⣿⣶⣌⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⠀⠀⣌⠀⠀⢀⠋⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠛⡆⠀⢞⠀⠀⠀⠀⣀⣿⡆⢹⡄⠀⠀⠀⠀⣀⣀⠀⠎⠿⠿⠃⢰⠇⠀⠀⣞⣰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢳⠀⠈⢧⡀⠀⠀⡿⠻⣿⣿⣷⠀⠀⢠⡞⠉⠀⠀⠀⠀⠀⢠⠏⠀⠀⢠⢇⠇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⢧⡀⠈⠳⣄⠀⠀⠀⠹⣿⣿⠀⠀⠈⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⢠⠏⡞⢞⠃⠀⠀⠀⠀⠀⠀⢀⣠⠎⠒⠋⠉⠁⠀⠀⠉⠉⠒⢊⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠙⢊⡀⠈⠳⣄⡀⢰⣞⠁⠄⢠⡀⠀⠀⠀⠀⣀⡌⠃⠀⠀⢠⠏⡜⠁⢞⢀⣀⡀⠀⢀⣠⡎⠋⣁⣀⠀⠀⣄⣀⡀⠀⠀⠀⠀⠀⠙⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⠊⣀⠈⠛⠊⣍⠓⠊⠟⠀⠀⠀⢎⡟⡿⠀⠀⠀⡰⠃⡞⠁⠀⣟⣉⣀⣀⣠⣀⣬⣿⣯⣀⣀⣀⠀⠀⠀⠉⠳⢀⡀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠑⢊⣀⠈⠙⢶⣀⠀⠀⠀⢠⡿⠁⠀⠀⡌⠁⢠⠇⠀⢰⠏⠛⣶⠶⠒⠉⣉⡀⢿⡄⠀⠈⠙⢆⠀⠀⠀⠀⠙⣄⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣀⠀⠈⠳⣄⠀⢞⠃⠀⠀⡌⠁⠀⡞⠀⢀⡞⠀⠀⠈⠙⡿⠉⣀⣀⣏⡷⠀⠀⠀⠈⢧⠀⠀⠀⠀⠘⣆⠀⠀⠀⢞⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠈⢧⣞⠀⠀⢞⠁⠀⢞⠃⠀⡌⠁⠀⠀⢀⣟⠗⣫⡿⠻⢯⡇⠀⠀⠀⠀⠞⡇⠀⠀⠀⠀⢹⠀⠀⠀⣌⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⡶⢲⠶⠊⣄⠀⣿⢊⠀⠈⢿⣇⠀⢞⠀⠀⡜⠀⢰⡗⠊⠀⠀⠟⠟⣺⠏⠀⠀⣞⠀⠀⠀⠀⠀⢀⡧⠀⠀⠀⠀⡿⠀⠀⢠⠃⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡏⠀⢯⡀⠀⠀⣰⠇⠘⡄⠀⢞⠿⣆⢞⠀⠀⣇⠀⠞⡇⠀⣶⣀⣿⣿⡏⠀⠀⣠⡇⠀⠀⠀⠀⠀⣞⡇⠀⠀⠀⣰⠁⠀⢠⠋⢰⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠹⣊⡀⠙⠛⠛⠁⠀⠀⣧⡎⠋⠀⠘⢟⣆⠀⠞⡄⠀⠹⣆⢹⣻⡟⡏⢷⠀⠀⠘⠉⢷⡀⠀⠀⢠⡟⠀⠀⠀⡰⠃⠀⡎⠃⠀⣌⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠶⠶⠶⠖⠋⠁⠀⠀⠀⠀⢞⠛⢶⣄⠹⣄⠀⠈⠙⠋⢡⠇⠈⡇⠀⠀⠀⠈⣇⠀⢠⡟⠀⠀⢀⠜⠁⡠⠊⠀⠀⣰⠇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣌⠀⠀⠈⢻⠺⠷⠀⠀⣶⢻⠀⠀⢿⠀⠀⠀⠀⢞⣠⡟⠀⠀⣠⠋⡰⠊⠀⠀⣠⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⢀⡟⠀⠀⠀⠀⣿⢞⠀⠀⣌⠀⠀⠀⠀⢞⡏⠀⠀⡌⢣⠊⢀⣠⠎⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣌⠀⠀⠀⣞⠃⠀⠀⠀⠀⣿⡌⠀⠀⡏⠀⠀⠀⠀⣿⠀⠀⢰⢱⠃⠀⣏⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇⠀⠀⢀⡇⠀⠀⠀⠀⠀⣿⠃⠀⢰⠃⠀⠀⠀⠀⢻⣄⠀⡇⠞⣄⠀⠈⠛⠛⠛⠛⠋⠉⣉⣀⣀⡈⠉⠓⢊⣄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⣇⣀⣠⠏⠀⠀⠀⠀⠀⢞⠙⠳⠟⣀⣙⣊⣀⣀⣠⠎⠖⠛⠉⠁⠀⠀⠉⠙⠲⣄⠙⡆ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣀⣀⣀⣌⠁⠀⠀⠀⠀⠀⣌⠃⠀⢿⣀⣀⣀⣀⣀⣰⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣞⣶⠇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠒⠒⠒⠒⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠉⠉⠉⠀⠀
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⣿⣿⣻⡄⠀⠀⠀⠀⠀⢀⡀⡲⠌⠃⡈⠀⠄⠠⠀⠄⠠⠀⠄⠠⠀⠄⠠⢀⠉⠚⠩⡟⢶⣠⢃⠲⢞⢇⡘⠀⣃⠜⣄⢻⣿⣿⢿⣻⣟⣿⣻⢿⣻ ⡿⣳⠏⠁⠀⠀⠀⢠⡜⠏⡁⠄⡐⠠⢀⠡⠈⠄⠡⠈⠄⠡⢈⠠⢁⠈⡐⠠⢈⠠⠁⠠⠉⠪⣝⢮⡘⡇⡘⣎⠐⣊⠀⢫⣿⣿⣻⣜⡟⣯⣟⣿⣻ ⣷⠀⠀⠀⠀⠀⣎⠟⠈⠠⢀⠂⠄⠂⠄⠂⡁⠌⠐⡈⠐⡀⠂⠄⠂⡐⢀⠂⠄⠂⠌⠐⡈⠄⠀⠳⢝⡣⢉⠀⢍⢲⢈⢯⣷⢯⣷⢯⣟⣷⢿⡟⣜ ⢃⠀⡀⢀⡀⣟⠍⠠⢈⠐⡀⠂⠌⠐⡈⠄⠐⠠⠁⡐⠠⢀⠁⢂⠁⠄⠂⡐⠈⡐⠈⠄⡐⠈⡐⠠⠚⢧⠂⠀⠀⢁⠹⣟⡜⣯⣟⣯⡿⣟⢯⣟⣿ ⣯⣿⣿⣎⡜⡎⢀⠂⠄⢂⠠⠁⢂⠁⠠⢀⠁⢂⠁⠄⠂⠄⡈⠄⡈⠐⠠⢀⠡⠀⠌⡀⠄⠡⢀⠂⡜⠆⠀⠀⠀⡄⠡⢻⡿⣜⢟⣯⢿⣜⣻⣜⢟ ⠋⠙⠈⠻⡵⠀⢂⠐⡈⠠⠐⢈⠀⣬⠖⠀⠌⡀⠌⠐⡈⠠⠐⠀⠄⡁⠂⠄⠂⢌⠠⡐⢈⠐⠠⢀⠀⠀⠀⠀⠀⠱⠀⠉⡖⡌⢢⠰⣈⠀⢃⠌⢎ ⠀⠀⠀⢹⡇⠐⠀⠂⡄⢡⠐⢠⡞⠃⢠⠈⡄⠐⢠⠁⠀⠂⠁⡌⣎⢢⡗⠚⠉⠈⠃⠉⠉⠉⠛⠃⡆⠀⠀⠀⠀⠐⠀⠃⢞⡔⢣⡖⣎⠊⣌⠘⣊ ⠀⠀⠀⣿⠀⠄⡁⢂⠐⠠⠐⣎⠏⠀⢂⠐⡀⠡⠀⠂⣡⢜⡲⠙⠃⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣹⢇⡏⢶⣡⢛⢊⡛⡎ ⠀⠀⢞⣵⠀⢂⠐⡀⠂⠁⣟⡉⠠⠈⠄⠂⠐⡀⣥⠞⠓⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⡀⣞⢯⣜⢣⢎⡝⢊⡝⣲ ⠀⠀⠞⠆⡐⠀⠂⠄⠡⢘⡷⠀⠄⡁⠂⡁⢊⡻⠊⠀⠀⠀⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢲⠑⣛⡎⢃⠚⠌⠓⡘⠡ ⠀⠀⣘⠃⠄⡈⠐⡈⠄⣹⠃⢀⠂⠄⢡⢟⠉⠀⠀⢀⣠⠶⠋⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢊⡇⠠⠹⡵⠠⠈⠄⠃⡄⠁ ⠀⠀⢌⡃⠐⠠⠁⠄⠂⡿⠁⠠⢈⡰⣿⣷⣶⣶⣯⣭⣙⣧⡀⠀⠀⠀⠀⠀⢀⣞⣀⣀⣀⣀⣎⣶⣶⣶⣀⣀⣀⣐⣙⡂⠄⠁⣟⣃⠡⢈⠂⠀⠁ ⠀⠀⢚⡅⢈⠐⠈⠄⡈⡷⠈⠐⣰⠟⠁⠀⠀⠀⣟⣿⡉⢻⠿⣿⣿⣿⣿⣿⣿⠟⣿⡟⠛⣶⡊⠀⠀⠌⢿⣟⣻⣿⣿⣿⢂⠁⢞⣜⠀⠂⠌⡠⠁ ⠀⠀⢞⠟⠀⡈⠐⠠⠐⣗⠈⣎⡻⠀⠀⠀⠀⢞⠩⣿⣵⣌⠂⣜⣿⠿⢿⣿⠃⢠⣿⣜⣊⠧⠇⠀⠀⠀⠀⢷⣀⣿⣿⠟⠁⣌⠀⡯⡄⡉⠐⡠⠁ ⠀⠀⠈⣯⡐⠀⡁⢂⠁⣿⢠⣿⣳⠀⠀⠀⠀⠀⠳⣛⡿⢿⢀⣟⠇⠀⠀⢻⣇⠰⡿⣛⣏⠔⠀⠀⠀⠀⠀⣮⣙⣿⡟⠀⡁⣿⡄⢺⡁⠄⠃⠄⡁ ⠀⠀⠀⢿⡀⢂⠐⡀⢂⢹⣎⡍⣧⢧⠀⠀⠀⠀⠀⠀⠀⠏⣟⡟⠀⠀⠀⠈⢿⣆⠧⠠⠀⠀⠠⠄⡀⠀⣰⠶⢶⣿⠁⠂⠄⣗⢣⢞⡜⠀⠁⠈⠀ ⠀⠀⠀⠺⣇⠠⠐⢀⠂⢞⢟⣷⣜⠣⣁⢀⠀⠀⠀⢀⣠⣟⠟⠀⠀⠀⠀⠀⠈⢻⣊⣀⠀⠀⠀⠀⠀⠚⢞⣠⡿⡏⠠⠁⢂⢯⣏⠎⡇⠀⠀⠀⠀ ⠀⠀⠀⠞⣹⡄⠂⠄⡈⠄⠂⠙⠛⠿⢶⣶⣶⣶⡟⠿⠛⠁⠀⠐⠂⠀⠀⠐⠀⠀⠈⠛⠻⠶⣶⣶⣶⠿⠟⠋⣡⠇⠠⢁⢞⣳⠘⡟⣄⠀⠀⠀⠀ ⠀⠀⠁⠀⢧⣳⡀⠂⠄⠂⡁⠂⠌⠀⠄⡈⠢⣐⠄⡀⠀⠀⠀⠀⠀⠒⠂⠄⡀⠀⠀⠀⠀⡀⢔⠠⠊⡀⠄⢢⡏⠐⡀⠲⡙⣧⡇⠞⡌⠀⠀⠀⠀ ⠀⠀⠀⠀⢈⣧⢳⡈⠄⠂⠄⡁⠂⡁⢂⠐⠠⢀⠑⣊⡱⢠⠀⠄⢀⣀⣀⣀⠀⠀⢀⠰⠈⣎⠃⠠⢁⠀⢂⡞⢀⠂⠐⢰⢇⡏⠀⠘⡖⠠⠈⠄⠃ ⠞⣀⠇⡜⡀⣧⠇⢧⠀⡘⢀⠀⢃⠀⠄⠘⠠⢀⠀⢇⡃⠀⠀⠛⠀⠀⠀⠀⠀⠘⠀⠀⢞⡞⠀⢃⠀⡘⣌⠀⠄⠘⡀⣿⢞⣞⡇⢃⠇⡘⢣⠘⡃ ⠱⣀⠒⠀⢡⠹⣞⠈⣷⠀⠠⢈⠠⠈⡐⠈⡐⠠⢈⠞⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⠁⠐⡀⢂⣰⠃⠠⢈⠐⢰⠇⣰⡹⢄⠣⢘⠠⡁⠎⡐ ⡓⢀⢋⠖⡡⢎⣟⡆⠈⢧⡐⠀⠄⡁⠄⠂⠄⠡⠀⠂⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢞⡒⠠⠁⡐⢰⠇⠠⢁⠂⡐⡞⢠⢧⡗⣄⢊⠀⣑⠠⢃⠔ ⣝⣊⣯⢟⣷⣻⣟⣹⡀⠘⢧⠀⠂⠄⢂⠁⠌⠠⢁⠂⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣳⠃⠠⠁⢄⡟⠀⠡⠀⠂⣌⠁⡟⣹⢒⡌⢎⠲⣡⢙⡌⢎ ⠟⡜⢚⡟⣟⢳⡿⣖⡇⠐⡈⢷⠈⢀⠂⠈⠄⠡⢀⠈⣳⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢂⠁⣌⠠⠈⠄⡁⢢⠇⢞⣳⣿⣟⣟⢿⣳⣷⣻⢟⣟ ⠣⣜⠡⠒⡄⢋⠜⣻⣌⠀⡐⠈⣧⠀⠌⠐⡈⠐⡀⠂⢭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠄⠂⡏⠀⠌⠐⢠⡟⢀⡯⡟⢷⣻⡟⣟⡿⣞⣯⡿⣟ ⣃⢟⡁⢣⢌⡡⠚⡄⡟⡇⢀⠂⠘⣇⠠⠁⠠⢁⠐⠈⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⠀⠐⢞⠇⠁⡈⠐⡌⠁⣞⢱⡉⠊⢌⡹⢿⣜⢿⣜⣻⣜
⠀⠀⠀⠀⢀⢠⠎⠖⠉⠉⠉⠢⡀⢢⠉⠃⠶⣀⣀⢀⣄⣠⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⠞⠋⠒⠒⠀⠀⣀⠀⠀⠱⡈⡄⠀⠀⢠⡟⠁⠘⣊⠀⢰⢠⢊⠕⣵⠀⢀⡠⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⡌⠇⠀⠀⠀⠐⠂⠠⠄⡈⠂⣄⡥⠓⠀⠀⠜⠀⠀⠁⠞⡄⢞⢁⠆⠀⠀⢠⠟⠁⢞⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡜⠁⠀⡠⠄⠲⠀⣄⡀⠀⣚⠟⠁⠀⠀⠀⠀⠀⠀⠀⡀⢀⡟⣎⠘⠀⠀⠠⡏⠀⠀⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠁⠀⢞⠁⠀⠀⠀⣟⣭⠲⠃⠀⣎⠶⢊⡀⠀⠀⠀⠀⠁⣞⠁⢞⡆⠀⠀⠘⠀⠀⣞⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡀⠀⢞⠀⠀⠀⢀⡟⣌⠀⠀⢞⣓⡰⢊⡙⢊⠀⠀⠀⠐⡇⠀⢀⡃⠀⠀⠀⠀⠰⡿⠔⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢹⡄⠈⣆⠀⠚⠋⣷⣞⠀⠀⢞⣿⣇⠀⣷⢈⠛⠯⠔⢰⠃⠀⢞⡿⠙⡆⠀⢀⠏⠀⠀⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢻⢄⠈⢆⠀⠀⣹⠟⠀⠀⠀⠻⣿⣿⣌⢺⡒⠀⢀⡞⠀⢀⢧⡁⠀⠇⣠⢀⡀⢀⣌⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠙⢊⡀⠑⣌⢧⡐⣠⠀⠀⠀⠀⠁⠀⢁⠀⣠⠎⠀⢀⠎⢎⡏⠀⡶⠁⢀⣧⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠙⢊⡈⠳⣍⠓⠒⠀⠠⣊⢎⡏⢁⡎⠃⠀⢀⠎⡜⢞⠁⠀⠁⢀⡟⠋⠂⠀⣀⡀⠠⠄⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠻⣄⠈⢢⡀⠀⠀⢹⢞⣧⠏⠀⠀⡰⠃⡜⠀⣏⠇⠀⠎⢫⣀⣎⡿⠛⠉⠀⠀⠀⠈⠉⠋⢊⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⡀⠄⣀⠀⠱⣣⠀⠱⡀⠀⣟⢞⡏⠀⢀⠞⠀⡜⠀⣞⠁⠀⠀⡠⠜⠛⠻⣄⠒⠒⠒⠢⢄⡀⠀⠀⠀⠫⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠛⢡⡶⠒⠵⢀⠿⡆⠀⢣⢠⡿⢌⠀⠀⡎⠀⡞⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⡎⠿⠳⣊⡀⠀⠈⠢⡀⠀⠀⢩⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢷⡈⠳⠆⠀⠞⠁⡇⠀⢞⡞⠀⢞⡀⢞⠀⢠⠃⢀⡏⡀⠀⠀⠀⠀⠀⠀⡄⠹⣌⠆⠈⢓⡄⠀⠀⠐⡄⠀⠀⠟⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠙⠶⣀⡄⠀⢀⣧⠶⡏⠀⠀⢰⣧⢞⠀⢞⠀⢞⠁⡇⠀⠀⠀⣠⠀⠀⠀⠘⣶⢀⡀⠈⣶⠀⠀⠀⢱⠀⠀⢈⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢻⣟⡀⢞⠀⠞⣌⣝⣞⡆⠁⠘⠄⠀⠀⠘⠁⠀⣿⠀⠙⠀⠀⠀⢞⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⢠⠋⠳⣄⣣⠀⠙⠺⢣⡯⠀⠀⠈⠒⡄⠀⠀⠀⡟⠀⣿⠀⠀⠀⡘⠀⢠⠃⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡧⡀⢠⡇⠀⠀⠀⠙⢃⡆⠎⡏⠁⠀⠀⠀⢰⠀⠀⠀⠀⣧⡰⠆⠀⠀⡰⠁⡠⠃⢰⡆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⢰⡆⠀⠀⠀⢈⡇⢰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡍⠀⠀⡰⢁⠔⠁⠀⣌⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢖⡀⠀⠀⣜⠃⠘⣃⡀⠀⠀⣄⣵⠀⠀⠀⠀⣞⠀⢀⠜⡰⠁⠀⢀⡌⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠶⠞⠃⠀⠀⠈⠁⠀⠉⠀⠐⢊⣀⢰⠞⠁⠀⠎⡌⢀⣎⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⡇⠀⢞⢞⠀⠻⣥⣀⣀⣀⢀⡀⠀⣀⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣢⣞⡈⢄⠀⠀⠉⠀⢀⡀⠀⡀⠈⣉⠓⠢⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠘⠋⠁⠀⠀⠛⠈⠁⠀⠀⠀⠉⠫⡎⢰ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣊⣀⣇⣰
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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⣠⣎⣶⣿⣿⣷⣊⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢞⣿⣿⣿⣿⣿⣿⣿⣿⣶⣌⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⡀ ⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⢞⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠉⠉⠀ ⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣊⡀⠀⠀⠀⢞⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀ ⠀⠰⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣀⣀⣞⣿⣿⣿⣿⡿⠿⠿⠿⠟⠁⠀⠀⠀ ⠀⠀⣿⣿⣿⣿⣿⣿⠏⠀⠀⣜⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣿⣿⣿⣿⣿⣿⡀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣿⣿⣿⣿⣿⣿⠷⠀⠀⢹⣿⣿⡿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣟⢿⣿⣿⣿⣿⢿⠀⢠⣿⣿⣿⠟⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣟⣿⣿⣿⠟⠘⠀⣿⣿⣿⡿⠀⠀⢞⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠒⠻⠿⠿⠟⠋⠀⠀⢞⣿⣿⣿⣧⠀⠀⢞⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢞⣿⣿⡿⠛⠀⠀⠞⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⢻⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⣯⣭⣭⣭⣭⣉⣉⣛⣛⣛⠛⠛⠛ ⣛⠛⠛⢛⣜⣿⣿⣿⣿⣿⣭⣭⣀⣶⣿⣿⣿⡿⠛⠀⠀⠀⢀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⣿⣿⣿⣿⣿⣿⡿⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⠟⢻⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⢀⣀⣟⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⡇⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⠃⠀⠀⢻⣿⣿⡿⠛⠁⠀⠀⠀⢀⣎⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣆⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣷⣿⠇⠀⠘⣿⣿⣇⠀⠀⠀⠀⣰⣿⡿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡄⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣷⣿⡏⠀⠀⠀⢿⣿⣿⣊⣀⣀⣌⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⣿⣶⣀⣈⣿⣿⣿⣆⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⡟⣿⣿⠀⠀⠀⠀⠘⣿⣿⢿⣿⣿⣿⣿⣊⣄⡀⢀⣠⣟⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⢿⣿⣿⣿⣿⣆⠞⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⠿⢣⣿⡇⠀⠀⣞⣿⣆⢹⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⡄⢿⣿⣿⣿⣿⣿⣿⣿ ⣿⠀⠘⣿⡃⠀⢞⣿⣿⣿⣊⣿⣿⣿⣿⣿⣷⣶⣭⡻⣿⣿⣿⣀⣶⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⢿⣿⣷⢞⣿⣿⣿⣿⣿⣿⣿ ⣿⣀⡀⣿⡇⢰⣶⣿⣿⣿⣿⣿⠟⠉⠉⠉⠙⠻⣿⣿⡎⠻⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣷⣊⣄⢞⣿⣿⡀⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⡇⢻⣿⣈⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣊⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣷⣿⣿⣇⠀⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⡈⢿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣷⣊⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣰⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣷⣞⣿⣿⣹⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣜⣿⣿⣿⠛⢻⣿⡇⣀⣀⣿⣿⣿⣿⣿⣿⣊⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⣠⣀⣀⡀⠀⢻⣿⣿⣿⣿⣯⣀⣟⣿⣿⣿⠿⢟⣿⣶⣶⡝⢿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠈⣿⣿⠿⣿⣿⣿⡟⢻⣿⡏⠀⢞⣿⣿⣿⣿⠀⠈⠻⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⢞⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⡟⣿⣿⣿⡇⠀⠀⠀⠀⠀⠞⠿⠟⠀⠀⠀⢿⣿⣎⣿⣿⠋⠀⢞⣿⡇⠀⢞⣿⣿⣿⠿⠀⠀⠀⠙⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⢞⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⡇⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢞⣿⣿⣿⡟⠀⠀⢞⣿⡇⠀⠘⠿⠿⠿⠀⠀⠀⠀⠀⠹⣿⣿⡆⠀⠀⠀⠀⠀⠀⢞⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣀⣠⣀⣀⣀⣄⣀⡀⠀⠀⠀⢞⣿⣿⣿⡇⠀⠀⠈⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣻⣿⣷⠀⠀⠀⠀⠀⠀⢞⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣛⣿⣿⣿⣷⣊⣀⣌⣿⣿⣏⣥⣀⣀⣀⣹⣿⡇⠀⢀⣠⣀⣶⣶⣿⣿⣿⡿⣻⣿⣿⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣇⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣏⢞⣿⠛⠛⠛⣿⡇⢻⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⢣⣿⣿⣿⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⠀⠀⢿⣿⣿⣿⣿⣿⣿⡟⠛⠛⠿⣿⣟⣿⣻⣌⣿⠇⠀⣞⣿⣧⣌⣉⣁⣈⣜⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⠀⠀⠈⣿⣿⣿⣿⣿⣿⣷⣀⣀⣄⠀⠉⠛⠛⠛⠿⠿⠿⠿⠟⠛⠛⠛⠛⢛⣛⣯⣜⣟⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣶⣶⣶⣟⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣶⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣎⣟⣿⠟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣊⣄⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠙⣿⣿⣊⣍⡉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣎⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣶⣶⣀⣀⣀⣎⣶⣟⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⠟⣻⣿⣿⣷⣆⣿⣿⣷⣟⣿⣿⣿⣿⣿⣟⣿⣿⣷⣮⢻⣿⠉⠉⠉⠉⢩⣭⣿⣟⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣯⠀⠀⠀⠀⠀⣀⣌⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠻⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡿⠀⠀⠀⠀⠈⠿⠿⠛⣋⣵⣟⣿⣿⣿⣿⣿⡿⢻⣿⣶⣊⣀⡀⣠⣿⣿⣿⣿⣜⣟⡛⣿⣿⣌⣛⡛ ⣟⣿⣿⣿⣿⣿⡇⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⠀⠀⠀⠀⠀⢀⣎⣿⣿⣿⣿⣿⣿⣯⣹⣿⣿⣷⣟⣿⣿⣿⣿⣿⣯⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢻⣿⣿⣿⣿⣿⣍⣻⣿⣿⣿⣿⣿⣄⡀⠀⣠⣀⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟ ⣿⣿⣿⠛⠃⣜⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⢻⣿⣿⣯⣭⣿⠿⣀
⠀⠀⢀⣀⣀⣀⠀⠐⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢈⢿⡟⡓⠌⠋⠀⡁⠠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡎⣎⣅⠓⠉⢟⣿⣟⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠷⠉⠹⣵⠀⢋⡿⣙⣰⠀⠀⠀⠀⡀⠄⠒⠒⠢⢄⠀⠀⠀ ⠀⠀⠀⠪⢠⡀⣰⣟⠏⣇⠀⠀⣀⣀⣀⡀⠀⠀⠊⠣⡀⠀ ⠀⠀⠀⠀⠀⡰⠁⡈⠀⢊⠀⠠⢿⠁⠈⠙⢅⠀⠁⡄⣷⠀ ⠀⠀⠀⠀⠀⢠⡀⠙⠊⠊⠁⠟⠚⠀⠀⠀⠈⣎⠀⠀⡇⡆ ⠀⠀⠀⠀⠀⠀⢂⠃⡒⠒⢗⢄⠐⢆⠀⠀⠀⣿⠆⢠⡠⠃ ⠀⠀⠀⠀⠀⢀⠂⢀⠐⠀⠀⢡⠀⠈⢂⠀⢀⣿⣠⠞⠁⠀ ⠀⠀⠀⠀⢠⠃⠀⠀⠀⠇⠀⠰⠀⠀⠈⡆⠞⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠓⠀⠒⠈⠈⠁⠀⠈⠓⠐⠂⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣊⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣊⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣎⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⡙⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣊⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠀⠙⣎⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⢆⡰⠃⢫⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⣰⠫⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡎⠀⠖⠁⠀⢻⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⢀⠎⢹⢿⠿⠿⠻⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠙⠘⣧⠀⠎⠋⠀⠀⣻⠄⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡉⠀⠀⠀⢹⡄⠀⠀⠀⠚⠁⠀⠀⣀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⡿⡛⠉⠂⠉⠈⣇⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⢀⡟⠀⠀⢠⡀⠈⠻⡿⠛⠀⠀⠀⠀⠀⠀⢞⢞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣜⣿⣿⣿⣿⣿⣟⢫⣟⡟⣿⡂⠀⠀⠀⠀⠀⠀⠀⣀⣠⣶⣟⣃⣀⣟⠃⢀⣰⡟⠀⢀⡞⠀⠀⠀⠀⠀⢀⡀⠀⢞⢞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣎⣟⣿⣿⣷⣶⣟⣿⣿⣿⣟⣿⣿⣷⣿⣿⢋⣿⣿⣇⡿⠇⠀⠀⠀⠀⢀⣎⣿⣿⣿⣿⣿⣿⠛⠿⠿⣿⣧⣀⣶⠏⠁⠀⡀⠀⠀⠀⡌⠀⠀⡌⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⣌⢿⣟⣿⠃⠀⠀⠀⠀⣎⣿⣿⣿⣿⡏⠁⠈⢻⣧⠀⠀⠀⠈⠉⢛⣻⡿⠛⠁⠀⢀⡞⠁⠀⢰⢳⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⣷⣿⣿⠋⠀⠀⠀⢀⣟⣿⣿⣿⣿⣿⡀⠀⠀⢈⣿⢠⠀⠀⣎⡞⠛⠋⠁⠀⠀⣠⠏⠀⠀⢠⣏⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣂⡌⠟⠁⠀⠀⠀⢀⣿⣿⣿⣿⣿⠿⢿⣇⡀⢀⣌⡟⠀⠀⢰⣭⣷⣀⣄⠀⠀⠊⠁⠀⠀⣎⣯⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ 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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢞⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠙⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢭⡿⣿⣿⣿⣿⣿⠿⠛⠋⠉⠀⠀⠀⠀⠀⠈⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢞⣹⠀⠀⠀⠀⠀⠀⠀⠀⢠⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣗⢞⢿⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢞⣿⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣊⢫⣹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⡀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡇⢡⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⢧⠀⠀⠀⠀⠀⢞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⣷⡘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢯⣧⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠰⣿⡷⢞⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⢣⡀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡏⣿⠇⡉⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣵⣄⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢞⣿⠁⠈⢀⢳⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣚⢿⣓⡎⠶⠊⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⣠⠆⠀⠀⠀⠀⠞⠏⠀⠀⣞⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣌⡵⠉⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⣀⡀⠞⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠌⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⠁⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣵⢯⣷⡐⠒⠀⠛⢊⣄⠀⠀⠀⠀⠀⠀⢹⣛⢓⡒⡊⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣊⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢞⢻⠀⠀⠀⠀⠀⢀⠀⠀⠀⠻⠿⢿⠿⡿⠿⠿⣿⠟⠋⠁⠀⠀⠀⣿⡇⠀⠀⠀⠀⠉⠛⢶⣄⠀⠀⠀⠀⠁⠀⠀⠘⢟⢊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢞⣹⠀⠀⠀⠀⠀⠈⢯⡙⠀⠁⠈⠀⠀⠀⠀⠹⣻⡄⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⠈⣎⢊⠀⠀⠀⠀⠀⠀⠀⠈⣏⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⣠⣟⣿⣿⣵⣊⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢞⢌⠀⠀⠀⠀⠀⠀⠘⢷⡀⠀⠀⠀⠄⠀⠀⠀⠹⡜⣆⠀⠀⠀⠀⣿⡃⠀⠀⠀⠀⠀⠀⠀⠈⢧⢳⡀⠀⠀⠀⠀⠀⠀⠈⣞⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⣿⠀⠀⠀⠀⠀⠀⠀⠀⠻⢊⡀⠀⠀⠀⠂⠀⠀⠑⢟⣧⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⢣⠀⠀⠀⠀⠀⠀⠀⠈⢮⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡄⠀⠀⠀⠀⠀⠀⠈⠪⣓⣊⠀⢞⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣇⠀⠀⠀⠀⠀⠀⠀⠘⡞⣧⠀⠀⠀⠀⠀⠀⠀⠀⠞⣿⣿⣿⡿⠋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣊⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡳⣶⣿⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⡄⠀⠀⠀⠀⠀⠀⠀⠞⡜⣆⠀⠀⠀⠀⠀⠀⠀⠐⣿⠟⠉⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡝⣿⣟⣆⠀⠀⠀⠀⠀⠀⠀⢠⣞⣷⡇⠀⠀⠀⠀⠀⠀⠀⠀⠹⡟⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣆⠀⠀⠀⠀⠀⠀⠀⢠⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡌⣿⠘⢮⢊⣀⠀⠀⢀⣀⣟⡷⠛⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠿⣿⣿⣿⣿⣿⠏ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣟⢆⠀⠀⠀⠀⠀⠀⡌⣻⡵⣆⠀⠀⠀⠀⠀⠀⠀⣀⣯⡞⠁⠀⠀⠙⠪⠿⠯⠶⠚⠉⠀⠀⢞⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣏⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠈⠉⠙⠉⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣳⡀⠀⠀⠀⢰⣳⠿⠈⠺⣗⢊⣀⠀⡀⢐⣫⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢞⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢞⢺⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢯⡶⣄⢎⡻⠋⠀⠀⠀⠀⠉⠂⠓⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⢏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣡⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⢖⣆⠀⠠⠀⠄⠀⠀⠠⠄⣀⣞⢵⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
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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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