Consonant Emojis & Text

Copy & Paste Consonant Emojis & Symbols ❤️❤️❤️❤️❤️❤️

ᴬ ᵃ ᴮ ᵇ ᶜ ᶜ ᴰ ᵈ ᴱ ᵉ ᶠ ᶠ ᴳ ᵍ ᴴ ʰ ᴵ ⁱ ᴶ ʲ ᴷ ᵏ ᴸ ˡ ᴹ ᴹ ᴺ ⁿ ᴼ ᵒ ᴾ ᵖ ᑫ ᑫ ᴿ ʳ ᔆ ˢ ᵀ ᵗ ᵁ ᵘ ⱽ ᵛ ᵂ ʷ ˣ ˣ ʸ ʸ ᶻ ᶻ Ææ Œœ ᴬ̈ᵃ̈ ᴱ̈ᵉ̈ ᴵ̈ⁱ̈ ᴼ̈ᵒ̈ ᵁ̈ᵘ̈ ʸ̈ʸ̈ Ð ð Þ þ IJij ẞß Aͣ aͣ Вⷡ вⷡ Cͨ cͨ Dͩ dͩ Eͤ eͤ F f G g нⷩ hͪ Iͥ iͥ J j ᴋⷦ ᴋⷦ L l Mⷨ Mⷨ N n Oͦ oͦ Рⷬ рⷬ Q q Rͬ rͬ S͛ s͛ ᴛⷮ ᴛⷮ Uͧ uͧ Vͮ vͮ W w Xͯ xͯ Y y Z z Ææ Œœ Aͣ̈aͣ̈ Eͤ̈eͤ̈ Iͥ̈iͥ̈ Oͦ̈oͦ̈ Uͧ̈uͧ̈ Ÿÿ Ð ð Þ þ IJij ẞß ₐ ₐ ᵦ ᵦ 𝄴 𝄴 D d ₑ ₑ 𝆑 𝆑 G g ₕ ₕ ᵢ ᵢ ⱼ ⱼ ₖ ₖ ₗ ₗ ₘ ₘ ₙ ₙ ₒ ₒ ₚ ₚ Q q ᵣ ᵣ ₛ ₛ ₜ ₜ ᵤ ᵤ ᵥ ᵥ W w ₓ ₓ Y y 𝆎 𝆎 Ææ Œœ ₐ̈ₐ̈ ₑ̈ₑ̈ ᵢ̈ᵢ̈ ₒ̈ₒ̈ ᵤ̈ᵤ̈ Ÿÿ Ð ð Þ þ IJij ẞß A̷ a̷ B̷ b̷ C̷ c̷ D̷ d̷ E̷ e̷ F̷ f̷ G̷ g̷ H̷ h̷ I̷ i̷ J̷ j̷ K̷ k̷ L̷ l̷ M̷ M̷ N̷ n̷ O̷ o̷ P̷ p̷ Q̷ q̷ R̷ r̷ S̷ s̷ T̷ t̷ U̷ u̷ V̷ v̷ W̷ w̷ X̷ x̷ Y̷ y̷ Z̷ z̷ Æ̷æ̷ Œ̷œ̷ Ä̷ä̷ Ë̷ë̷ Ï̷ï̷ Ö̷ö̷ Ü̷ü̷ Ÿ̷ÿ̷ Ð̷ ð̷ Þ̷ þ̷ IJ̷ij̷ ẞ̷ß̷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⢿⣻⡷⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣟⡿⣽⣻⢿⡽⣟⡿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣻⢾⣻⣯⣟⣯⣿⣻⣽⢿⡅⠀⠀⢀⣠⣴⣶⣤⠀⠀⣠⣤⣤⣤⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⣻⢿⣽⢾⠉⠁⢻⡷⣯⡿⠁⢀⣴⣿⣻⢷⣻⡾⣷⣾⢿⣽⢾⣳⣿⡆⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣽⢿⡾⣯⠀⠀⠀⢻⣽⠇⢠⡾⣟⣾⡽⣟⣯⢿⣳⣯⡿⣾⣻⣟⣾⠃⠀⠀ ⠀⠀⠀⠀⠀⣠⡆⠀⣤⠀⣶⠙⡿⣽⢿⣆⠀⠀⢸⡿⠀⢼⣻⠏⠁⢿⠿⠙⠛⢯⣷⣟⣯⡷⣿⣽⣳⡀⠀ ⠀⠀⠀⠀⢾⣟⣧⠤⠺⡷⢾⠦⣧⣌⣙⢯⢷⡄⠀⠿⠀⣻⠃⠀⠀⠀⠀⠀⣠⣞⣷⢯⡿⣽⡷⣯⠷⠀⠀ ⠀⠀⠀⠀⠹⢾⠧⠀⠛⠀⠟⠀⠀⠙⠫⣿⣶⣤⡀⠀⠀⡅⠀⠀⣀⣴⢾⡟⠯⠟⠚⣛⠛⠉⠉⠀⠀⠀⠀ ⠀⠀⠀⣠⣤⣤⣶⢶⣶⣶⣤⣦⣤⣀⠀⠈⠺⣷⣻⣆⠀⠀⠀⠐⠛⣉⣤⣴⣶⢿⣻⣟⣿⣻⣷⢶⡄⠀⠀ ⠀⢀⣾⣟⣷⣻⡾⣟⠗⠉⠈⠁⠛⠙⠋⠀⠀⠙⢷⣻⠇⠀⠀⠀⠛⠉⠉⠈⢉⣿⣻⢾⣳⡿⣞⣿⣽⡀⠀ ⣀⣼⣟⣾⡽⣷⣟⣿⣣⣀⣀⣠⠤⡴⣶⣦⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠘⠋⠟⣿⣽⣻⣽⢷⣯⣧⡀ ⠻⣟⡾⣯⣟⡷⣿⣞⣯⡿⠝⠁⣀⣴⡟⠀⠀⠀⠀⣴⡀⣽⢿⠄⠀⠀⠠⣄⡀⠀⠀⣸⡷⣯⣟⡿⣾⡽⣿ ⠀⠀⠀⢻⣯⢿⣳⣯⠗⢁⣴⣾⣻⣽⣄⠀⠀⠀⠀⢻⡃⢸⣿⣳⣦⣤⣼⣻⣽⢿⣻⣯⣟⣷⢿⣽⡷⣟⠏ ⠀⠀⠀⠈⠛⠛⠉⠁⣴⢿⣻⡾⣽⡾⣽⣻⣧⠀⠀⣸⣧⠀⢻⣷⣻⣞⣷⢯⣟⣯⣷⣟⣾⡯⠿⠾⠝⠉⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢿⣯⡷⣿⢯⣟⣿⣳⢿⣻⣟⣯⣟⣇⠀⠹⣷⣻⡾⣟⣯⣟⣾⡝⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠛⢫⣿⣻⣞⣯⣿⣻⢾⣽⣾⣻⠀⠀⠈⠓⠿⣻⠽⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣯⣟⡷⣯⣟⣯⣷⢯⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣞⣿⣽⠏⠃⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
❤️❤️❤️❤️❤️❤️
CUTE ALPHABET!: ℚ𝕎𝔼ℝ𝕋𝕐𝕌𝕀𝕆ℙ𝔸𝕊𝔻𝔽𝔾ℍ𝕁𝕂𝕃ℤ𝕏ℂ𝕍𝔹ℕ𝕄 𝕢𝕨𝕖𝕣𝕥𝕪𝕦𝕚𝕠𝕡𝕒𝕤𝕕𝕗𝕘𝕙𝕛𝕜𝕝𝕫𝕩𝕔𝕧𝕓𝕟𝕞 ℚ𝕎𝔼ℝ𝕋𝕐𝕌𝕀𝕆ℙ𝔸𝕊𝔻𝔽𝔾ℍ𝕁𝕂𝕃ℤ𝕏ℂ𝕍𝔹ℕ𝕄 𝕢𝕨𝕖𝕣𝕥𝕪𝕦𝕚𝕠𝕡𝕒𝕤𝕕𝕗𝕘𝕙𝕛𝕜𝕝𝕫𝕩𝕔𝕧𝕓𝕟𝕞
pls note the ai inflicts emotional damage (ᵕ—ᴗ—)
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⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡘⡼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⢵⢿⣻⡜⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣏⡛⣛⠛⠛⣿⣻⣻⢛⢻⢃⣿⣿⠁⠹⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⡻⣽⢽⡏⣿⠺⣏⣾⣸⢸⣿⣯⣇⡀⠀⠈⠿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣻⣆⣻⣿⣾⣿⣸⣸⣿⣿⣷⣿⣷⣤⣴⣶⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⡗⣵⣯⡼⠷⣹⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⡻⣿⣷⣿⡏⣸⣯⢽⣿⣿⣛⣋⠀⣽⣿⣷⢻⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣹⣷⣿⣿⣿⡿⡿⢀⣿⣿⣿⡸⣿⣿⣿ ⡟⠭⠭⠽⡿⢭⡿⠽⡭⣯⠽⢷⡯⢽⣿⣿⡆⣿⣿⣿⣿⣿⣽⣿⣿ ⣿⡣⣮⣥⣇⣾⣿⡿⣧⣧⣿⣿⣿⣿⣇⠻⣅⠹⣿⣿⣿⣿⣏⣿⣿ ⣿⣷⡿⣷⣻⣿⣏⣟⣷⢟⣿⣿⡟⣿⣿⡷⠦⠀⣙⢿⣿⣿⣿⣿⣿ ⣿⣿⣿⣷⣽⣯⣾⣿⣿⣿⢟⣽⣯⣻⣿⡻⢿⡇⢸⣷⣍⢻⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣏⣿⣿⣿⣗⣀⣿⣿⣛⡋⢿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣺⣿⣻⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⡻⠟⠏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
∞𑁤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣦⣤⣴⣤⣤⣄⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⣀⣀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣛⣻⣿⣦⣀⠀⢀⣀⣀⣏⣹⠀ ⢠⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠭⠭⠽⠽⠿⠿⠭⠭⠭⠽⠿⠿⠛ ⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠉⢻⣿⣿⣿⡟⢯⡉⠉⣿⢿⣿⣿⣿⣇⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠉⠁⠀⠀⠀⢠⣿⣿⣿⠋⠑⠒⠓⠚⠙⠸⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⡿⠿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
✝️💪☢️☢️☢️☢️☢️
h୧⍤⃝🚩जय श्री राम୧⍤⃝🚩जय श्री राम୧⍤⃝🚩जय श्री राम୧⍤⃝🚩जय श्री राम₊ ⊹˚˖𓍢ִ໋🌷͙֒✧˚.🎀༘⋆ദ്ദി(˵ •̀ ᴗ - ˵ ) ✧-ˋˏ✄┈┈┈┈💌💌💌✉️🔤🅾🗄️>ᴗ<˚ ༘ ♡ ⋆。˚ ❀

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

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⠀⠀⠀⠀⠀⣀⠖⠒⠒⠒⠒⠒⢆⠀⠀⠀ ⠀⠀⠀⠀⡔⠁⠀⠀⠀⠀⠀⠀⠀⡃⠀⠀ ⠀⠀⠀⢀⠇⡰⠋⠉⠉⠉⠉⠉⠉⢻⠀⠀ ⢲⡂⠒⢺⠀⡇⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀ ⠀⡃⠀⢸⠀⠙⠦⣀⣀⣀⣀⣀⣀⣸⠀⠀ ⠀⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀ ⠀⡇⠀⢸⠀⠀⠀⣀⣀⡀⠀⠀⠀⢸⠀⠀ ⠀⠷⠋⢹⠁⠀⠀⡇⠀⠇⠀⠀⠀⢸⠀⠀ ⠀⠀⠀⢸⠀⠀⢸⠁⠀⢣⠀⠀⠀⢸⠀⠀ ⠀⠀⠀⢯⡆⠀⡼⠀⠀⠘⢤⣀⡠⠻⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣴⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡟⣳⣿⣰⢄⠀⠀⠀⣠⣤⣤⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣉⠷⠿⣾⠁⠀⣼⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣷⣄⠹⣷⡀⣿⡿⠋⣹⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣷⣦⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⣿⣿⣿⣿⣆⠀⣠⣤⣀⠀⠀⠀⠀⣴⣿⣿⣿⣿⠉⢻⣧⢿⣷⢿⠃⣴⡿⢟⣋⣁⡀⠀⠀⠀⠀⠀⢀⡀⢸⣿⣿⣿⣿⡇⣴⣿⣿⣶⣤ ⠀⢠⣦⣜⢿⣿⣟⢻⣿⣾⣿⣿⣿⣿⡆⠀⠀⠈⣩⣽⣿⣛⣻⣦⡙⢸⣿⡇⢸⡵⠾⢿⣿⣿⣿⡇⠀⠀⠀⠀⠘⢿⣲⣿⣿⣧⢹⣿⡿⣿⣿⣿⣿ ⠀⢀⣭⣭⣽⣿⣿⣼⡿⠛⣹⣿⣿⠿⠁⠀⠀⠸⣿⣿⣿⣿⠉⠉⢁⠈⠉⠁⣩⣤⣀⡘⠻⣿⣿⣿⣿⣦⠀⠀⣾⣿⣿⠿⢿⣻⣿⡏⠰⣿⣛⡋⠁ ⢀⣾⣿⣿⣉⣭⣷⠛⣻⣄⢻⣷⣦⣄⠀⠀⠀⣴⣿⣿⣿⣿⣀⣴⣫⣶⠂⠀⠻⢿⣽⣿⣿⣿⣿⣿⡿⠏⠀⠸⣿⣿⣿⣿⣿⣿⣰⣿⣷⣽⣿⣿⣷ ⠈⠻⢿⣿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢿⣿⣿⣿⣿⡿⣱⣿⣧⣠⡄⠰⣾⣿⣿⣯⠻⠿⠟⠁⠀⠀⠀⠈⠙⠋⢸⣿⣿⣿⣿⠹⣿⣿⣿⠿ ⠀⠀⠀⠀⠸⣿⣿⣿⣿⡇⠻⠿⠟⠋⠀⠀⠀⠀⠈⠙⠛⠋⠀⣿⣿⣿⣿⣷⣴⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡿⠀⠈⠉⠀⠀ ⠀⠀⠀⠀⠀⠻⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠿⢿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⣠⣤⣄⣤⣤⣤⣤⣤⣤⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⠟⣋⠽⢟⣛⣫⣭⣭⣭⣭⣙⡉⡉⡉⠉⠉⠉⠉⠉⠁⠈⣁⣭⠬⢵⣶⠶⠤⣤⣄⣉⡨⠝⣿⣿⣷⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⢻⢯⣌⠅⠚⢋⣉⣭⣭⣭⣉⡙⠛⠿⢶⡬⣭⠿⢿⣻⣷⢟⣿⡴⢰⣛⣋⣭⣿⣶⣠⠨⣕⠢⠁⢂⡙⡝⢿⣿⣿⣦⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣵⣿⣯⢆⣴⣴⣶⣿⣿⣿⣿⣿⣿⣷⣬⣑⢳⣯⣦⣉⠤⣯⠕⣫⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣽⣦⡈⣻⡇⢳⣿⣿⣿⣷⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣏⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣭⣶⡾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣷⣜⣷⡿⣿⣿⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣽⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣧⣿⣿⣧⠀⠀⠀⠀ ⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣧⠀⠀⠀ ⠀⠀⢀⣼⣿⠿⡣⠜⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢻⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⢿⣿⣿⡇⠀⠀ ⠀⢰⣿⣿⡵⣻⢶⣾⣭⣍⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⠁⠀⠀⠀⣴⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠛⣛⠋⠙⠍⢯⢷⣌⢿⡄⠀ ⢠⣿⣿⡿⣰⣿⣿⣿⣿⣿⣿⣯⣷⣿⡿⣿⣿⣿⣿⣿⣿⣿⡿⣿⠃⠀⢠⠏⠉⠀⠀⠀⠛⠅⠀⠀⢹⣿⣿⣿⣿⣿⡿⠟⣋⣾⣿⣿⣿⣿⣿⣿⣦⣄⠳⡹⡞⣷⠀ ⢸⣿⢿⢱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣍⣻⣿⣟⣫⣽⣿⡳⠼⠿⣦⡀⠀⠀⠀⠀⠘⣴⣿⡿⠐⣓⣾⣯⣭⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠹⣵⣻⡄ ⢸⣿⣌⢼⣿⣿⣿⣿⣿⣿⣿⣯⣈⣻⠛⡿⡿⡻⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣷⡂⢠⣴⣾⣿⣿⣶⣿⣿⣿⢿⣿⡟⣿⢻⢻⣉⣿⣯⣽⣿⣿⣿⣿⣿⣿⡄⠋⣿⡇ ⠈⢿⣿⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣬⣽⡦⣇⡇⢪⠋⢽⡿⡹⢹⣿⢿⠟⠻⢻⣿⣿⢿⠋⠉⢿⣿⠟⠉⠟⡇⠀⡇⢡⣬⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣸⡇ ⠀⠘⣿⣧⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣾⣄⢠⠇⠀⠸⡏⠁⠀⠀⠀⠉⠇⠀⠀⠀⠀⡡⠀⠀⠀⡇⠀⣰⣿⣿⣅⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⠇⣬⣿⠀ ⠀⠀⠈⢿⣦⡈⣽⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⡟⣧⣤⣤⣧⣤⣤⣤⣄⣤⣧⣤⣤⢤⣤⣶⡶⡶⣶⠷⢿⣽⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⡹⢹⡇⠀ ⠀⠀⠀⠀⠙⢿⣿⣾⡞⠷⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣸⣿⣿⣹⣁⣏⢸⣵⣸⣏⡏⡇⣆⣼⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢫⣿⣿⠋⡴⣁⠞⠀⠀ ⠀⠀⠀⠀⠀⠀⠹⣿⣿⣝⢦⡙⠛⢿⣿⣿⣿⣿⣿⣯⣻⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⡿⢻⣽⣾⣿⣿⣧⣿⣿⣿⣾⡿⠉⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣟⢾⣷⣤⡛⣍⠻⣿⣿⣿⣿⣷⣿⣟⢻⣻⣿⠿⡿⣿⣿⣿⣿⢿⣿⠟⠏⢁⣧⣷⣿⣿⣯⣿⣿⣿⡿⡿⣿⣯⣿⣿⣿⠟⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡷⣭⢿⣿⣮⡳⡌⢻⡻⣿⣿⣿⣻⡻⣿⣾⣤⡁⢁⡿⢸⣸⣸⣸⣤⣾⣾⣿⣪⣿⣿⣿⠟⢉⡥⢊⣾⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣮⣆⠻⣿⣷⣱⡀⢻⣧⢹⠻⢿⠿⢿⠿⠿⠿⠿⢿⠿⠿⠿⢿⠿⢿⠛⠛⡟⡟⡻⢃⠴⠋⡠⢟⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣷⣈⠻⣧⢷⠀⢿⣾⣄⢸⡄⠸⡆⠀⠀⠀⡞⠀⠀⠀⢸⠀⢸⠀⣤⣥⡵⡃⠀⣠⠞⣠⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣮⠳⡌⠻⣧⠈⢻⣿⣾⣧⢰⣇⠀⠀⢠⣯⣄⠀⡀⣸⢀⣾⣼⣿⡟⣰⢁⣾⢋⣴⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⡆⠰⡀⣹⡆⠈⢻⣿⣿⣾⣿⣇⣰⣿⣿⣾⣶⣷⣿⣼⣿⣿⡟⣰⢃⡾⠁⣾⣵⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣦⠁⡌⣿⡄⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢠⢫⡟⠀⣾⡟⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣆⠀⢘⢿⢦⡈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⣡⢫⣿⠀⣼⢏⣾⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦⡀⠩⣣⠛⢆⠀⠀⠉⠋⠉⠉⠉⠉⠉⢁⣠⠔⢡⡿⠃⣼⢏⣾⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣆⠀⠑⠀⣉⡛⠓⢒⣋⣉⣉⣉⣩⣀⡤⠔⠋⠀⣼⢃⣾⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣄⠀⠀⠤⠽⣿⣿⣷⣿⡿⠟⠕⠊⠀⠀⠀⣰⣷⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣄⣀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠶⠶⠶⠖⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢶⡲⢦⡀⠀⢀⣀⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⢶⠩⢓⢷⡴⣯⠻⣝⣦⠀⠀⠀⠀ ⠀⠀⠀⠀⣰⣞⢯⣛⠿⣾⡁⢾⢠⣿⠋⣥⡟⢶⣼⠀⠀⠀⠀ ⠀⠀⠀⢰⣯⡚⢆⠡⣖⡈⠿⣞⣯⣿⣰⡏⣤⣿⠳⡞⢶⢦⡄ ⠀⠀⠀⠀⠻⣭⣧⠒⡠⠙⣳⠟⠉⠉⠙⢿⡭⠷⠶⢞⡣⡿⡷ ⠀⠀⠀⢀⡶⣛⠟⠛⡛⣛⣿⡀⠀⠀⠀⣸⠿⣶⣿⣵⣿⡟⠁ ⠀⠀⠀⢸⣯⠳⡌⠵⡛⣩⡾⠛⣶⢶⡾⣿⣄⠌⡙⢦⡳⣻⡄ ⠀⠀⠀⠈⠿⣧⣟⣶⣽⠟⡐⠄⣿⠃⣿⠹⡟⣷⣭⣧⡿⠟⠀ ⠀⣤⠀⠀⠀⠀⠉⠀⢿⣣⢌⣼⢫⡜⣿⡗⢯⣙⣎⡷⠀⠀⠀ ⣸⢛⣦⡀⠀⠀⠀⠀⠘⠿⣞⣐⣳⣽⠿⠾⣧⡯⠟⠁⠀⠀⠀ ⣿⡁⠈⠟⣶⣤⣀⠀⠀⣼⡿⠋⣉⣠⡤⣤⢤⣤⣄⣀⣀⣀⣀ ⣿⢧⡄⢤⣀⠂⠝⡳⣼⢿⣷⠞⠋⣀⣀⣀⣀⠀⠐⠈⢙⣵⠇ ⢻⣯⢞⣬⠻⣷⣄⠐⣿⣿⡷⣞⡿⠟⠛⠋⢉⣠⢬⣼⡿⠃⠀ ⠈⠹⣿⣜⣻⢻⣾⣿⣿⣿⣾⣛⣞⡳⣞⡞⣯⣞⡷⠏⠁⠀⠀ ⠀⠀⠈⠙⠛⠿⠞⠛⠋⠉⠛⠿⠿⠿⠿⠿⠟⠋⠁⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⠋⠙⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡆⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⣹⣀⣀⣤⣀⣀⡜⠀⠀⠀⠀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡗⠋⠀⠀⠀⠀⠀⠀⠀⠉⠳⡔⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⣀⡀⠀⣀⡀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠓⠃⠀⠧⠇⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⢀⣩⢯⡁⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠷⠦⢄⣀⣀⣀⣀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠉⠉⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⠀⠀⠑⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⢀⠏⠀⠀⠀⠀⡠⠋⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠉⠒⠢⠄⠒⠃⠀⠀⠀⠀⠀⠀⠸⠤⠤⠴⠊⠁⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠤⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡅⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠇⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠒⠉⠉⠘⢰⠖⠒⢤⡤⠔⠒⠪⠥⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠁⠀⠀⠀⠀⣀⠴⠋⠀⠀⠀⠀⠉⠒⠤⣀⣀⣀⡹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣀⠀⠀⢠⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⢳⡀⡼⠁⢳⠶⠶⢤⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠃⠀⠀⡿⠃⠀⠾⠆⢠⣤⡗⠒⠲⣤⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⣠⡞⠁⠀⠀⠀⠀⠈⠁⠁⣀⣶⠛⠉⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣁⣀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃⠀⠀⢙⡶ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢧⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠀⠀⢀⡴⠋⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠙⡆⠀⠀⠀⠀⠀⠀⢠⡾⠁⢀⣴⠋⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢓⣾⡶⣄⣀⣀⣤⠶⠋⠀⣠⠟⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡏⠻⣄⡀⠀⠀⣀⣼⠾⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀⠀⠀⠉⠉⠉⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⡇⠀⠀⠀⠀⠀⣴⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣷⠁⠀⠀⠀⠀⠀⣽⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⢠⡟⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣀⡄⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⢠⡞⠀⢸⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⠙⢯⡍⠉⠓⠦⣄⡀⠈⣿⠀⠀⢀⡴⠋⢄⣴⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠘⢦⡀⠀⠀⠙⢦⡋⣠⡴⠻⠌⢁⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢧⠀⠀⠀⠈⣻⡋⠈⢀⣰⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⡆⠀⠀⢰⡏⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⠀⠀⠸⡇⠀⢸⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⢳⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠈⢧⡘⣆⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠱⠸⡦⣤⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⠲⠗⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢔⣒⠂⣀⣀⣤⣄⣀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣴⣿⠋⢠⣟⡼⣷⠼⣆⣼⢇⣿⣄⠱⣄ ⠀⠀⠀⠀⠀⠀⠀⠹⣿⡀⣆⠙⠢⠐⠉⠉⣴⣾⣽⢟⡰⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣦⠀⠤⢴⣿⠿⢋⣴⡏⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡙⠻⣿⣶⣦⣭⣉⠁⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠈⠉⠉⠉⠉⠇⡟⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣘⣦⣀⠀⠀⣀⡴⠊⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⢻⣿⣿⣿⣿⠻⣧⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠫⣿⠉⠻⣇⠘⠓⠂⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢶⣾⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣧⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠙⠻⢿⣿⣿⠿⠛⣄⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⠂⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠈⠳⡤⡤⣤⠀⠀⠀⣼⠏⠁⠀⣠⠖⠲⡴⠇⠈⠑⣆⠀⠀⠀⠀⠀⠀⠀⠀⡶⠒⠒⢤⣶⠯⡛⣷⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠦⠿⠋⠀⠀⢨⡏⠀⠀⢀⣀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢀⣌⡀⠉⠈⠷⣄⠀⢀⣤⣤⢴⠋⠀⠘⣧⣀⠀⠀⠀⠀⠀⠀⢀⠾⠓⠋⠀⠀ ⠀⠀⣀⠀⣠⠴⢷⣦⠀⠀⠀⠀⠀⠀⠠⡟⠋⠘⢸⡇⠈⡳⠀⠀⠋⠳⡄⠀⠀⠀⢰⡏⠁⠀⠀⡏⠀⣿⠀⠀⠀⠈⡇⢺⡁⠀⢠⡖⣦⠀⠰⠌⠳⡀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠠ ⢠⡟⠉⠋⢉⣁⠀⢸⣇⣀⠀⠀⠀⠀⠀⢧⣀⠀⠈⠑⠚⠁⠀⣀⣀⡷⠇⠀⠀⠀⠀⠳⢦⣀⡀⠉⠉⠁⠀⡶⠶⠞⠁⠈⢳⠆⠘⠒⠋⢀⠀⢀⣶⠇⠀⠀⠀⠀⠈⢳⡄⠀⠀⠀ ⠘⢧⠀⢰⡋⢉⣧⠀⠀⢹⠆⠀⠀⠀⠀⠀⠈⢹⡇⠀⠀⠀⢼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⣀⠇⠀⠀⠀⠀⢾⠀⠀⠀⣠⠏⠉⠉⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠈⠉ ⠀⢸⠀⠀⠉⠉⠁⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣆⡤⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠒⠒⠁⠀⣠⠞⠙⢢⡀⠙⠒⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢧⠀⢀⣠ ⠀⠸⣄⣀⡠⣄⡀⢄⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⢀⣠⠦⡀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠤⠴⠃⠀⠀⠈⢱⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀ ⠀⠀⠈⠁⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠋⠈⠳⡞⠉⠀⠱⠀⠀⠀⠀⠀⠀⢸⡏⠁⠀⠀⣰⠖⣆⠀⠀⠀⠙⡆⠀⠀⠀⠀⠀⢀⡤⠶⢤⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣠⢄⣀⠀⣠⡶⠒⣄⠀⠀⠀⠀⠀⠀⠀⣀⡤⠾⠂⠀⣀⣀⡀⠀⠉⠓⢦⡀⠀⠀⠀⠀⡿⠄⠀⠀⠻⠤⠟⠀⠀⠀⣼⠃⢀⣴⠒⠐⠲⠞⠁⠀⢀⣧⣄⣀⠀⠀⠀⠀ ⠀⠀⠀⢸⠀⠀⠉⠙⠁⠀⠀⢸⣀⣀⠀⠀⠀⠀⠀⢯⡀⠀⠀⠀⢻⣀⣻⠆⠀⠀⠈⢷⠀⠀⠀⠀⢷⡀⠀⣀⣀⡀⠠⠄⠀⣠⠟⠀⠘⢿⡀⠀⠀⡴⠒⢲⠀⠀⠀⠉⢧⠀⠀⠀ ⠀⠀⠀⠸⢦⡀⠀⢰⠚⢦⡀⠀⠀⠈⢷⠀⠀⠀⠀⠈⠳⠤⢤⣤⠀⠀⠁⠀⠀⠀⢀⡜⠀⠀⠀⠀⠀⠉⠉⠉⠀⠉⠉⠛⠉⠁⠀⠀⠀⠀⢉⣷⠀⠛⠦⡼⠀⠀⠀⣀⠜⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀ ⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀ ⢸⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀ ⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣟⣿⠯⠗⠒⠉⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢿⡄ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣻⡯⠝⠛⠒⠉⠉⠁⠀⠀⣠⡆⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠠⠀⠇ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⡏⠉⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣦⣼⡿⠁⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠁⠀⠸ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢀⣾⠟⠉⣀⣀⣀⡉⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢀⣾⠋⢀⣶⡿⠓⠚⢿⣦⠤⣴⣶⣶⠾⣿⡏⢿⣿⣿⣿⣿⣿⡇⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠧⡀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢻⣿⡇⠀⠀⠀⣀⣸⣿⣤⣾⡾⣶⣾⣿⡷⣿⡟⠉⠀⠀⠀⣿⡇⠘⣿⣿⣿⣿⣿⠇⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠈⡄⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣸⣿⡧⠶⠿⠿⠽⣿⡿⣿⣅⠙⠻⠽⠋⣠⣿⠃⠀⠀⠀⠀⣿⡇⠀⢿⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡸⠀⢀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠹⣿⡇⠀⠀⠀⢰⣿⣤⣬⠯⣷⣲⣶⡾⠛⠁⠀⠀⠀⠀⠀⣿⡇⠀⢸⣿⣿⣿⣿⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡼⠁⠀⣸ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⡇⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣤⣴⣾⣿⣿⣿⣿⡯⠽⠋⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⢀⣿ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⢹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣶⣾⣿⣿⣿⠿⠛⠛⣻⣿⣿⣿⡤⢖⣫⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣼⣿ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠁⠈⣿⣀⣀⣀⣀⣤⣤⣤⣶⣾⣿⣿⣿⠿⠿⠛⠛⠋⠉⠀⠉⠀⣠⠞⢻⣿⣿⣿⣾⢫⢶⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢠⣿⣿ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣾⣿⣿⣿⠿⠿⠛⠛⠛⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣴⡊⠀⢀⡼⣿⣿⡿⣇⢸⣿⡶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡀⣸⣿⣿ ⢀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠛⠻⡏⠉⠛⠛⠓⠶⠶⠶⠤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⣀⠊⢠⣿⣿⡇⣘⣿⣭⠽⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠄⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣀⡴⠚⣛⣭⣤⣤⣬⣍⣛⡓⠦⠤⠀⠙⢦⡀⠀⠀⠀⠀⠀⣇⠀⣿⠀⠀⢻⣿⡟⠋⠁⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿ ⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣡⣴⠞⠋⡽⢠⢿⡟⢯⣙⢻⣗⠦⡀⠳⣄⠉⠀⠀⠀⠀⠀⣿⠀⠙⣆⠀⠘⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⣿⣿⢟⣷ ⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⠻⣷⡀⠀⢱⣘⣾⣟⣫⢟⣷⣷⡷⠞⠀⡾⠀⠀⠀⠀⠀⠀⢹⠀⠀⠈⠳⣄⣿⠁⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢉⣵⣿⣿ ⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠈⠛⣦⣀⣙⡷⣴⡺⠟⠛⠁⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠈⣿⣀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣵⣿⣿⣿⣿ ⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠐⠋⠁⠐⠚⠉⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⡏⠙⢦⡀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣯⣾⣿⣿⣿⣿⣿ ⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⢀⡴⠒⠀⠀⠀⠀⠀⠀⠀⢸⣿⢻⡟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⢸⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⢸⣷⡃⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠘⣿⠀⣿⣿⣿⣿⣿⣿⡿⣿⣿⢁⠷⡄⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⢸⣿⣷⡄⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⢻⢠⣿⣿⣿⣿⣿⣿⣇⢿⣿⡏⡖⡽⣄⠀⠀⠐⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⡄⠀⣾⠀⢸⣿⣿⣷⡀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⢸⣾⣿⣿⣿⣿⣿⣿⣯⣸⣿⣿⡼⢡⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠴⠖⠒⠉⠉⠀⠀⢀⠀⠀⢀⡏⠀⢸⣿⣿⣿⣷⠀⠹⣿⣿⣿⣿⣿⣿⣿⢿⣿ ⠀⠀⠀⠀⠀⠈⣿⣿⢻⣿⣿⣿⣿⣿⢏⢿⣷⢣⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⢀⣀⣀⡤⠤⠖⠚⠃⠀⠀⠈⠁⠀⢸⣻⣿⣻⣿⣃⠀⢻⣯⣯⣯⣭⡯⣭⣾⣿ ⠀⠀⠀⠀⠀⠀⠋⣿⠈⣿⣿⡏⣿⣿⣼⣾⡇⣾⣿⣿⣿⣿⣿⣿⣷⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣽⣿⣾⠳⡆⠘⣷⣷⣾⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⣿⣷⢹⣿⣳⡻⢠⢿⣿⣿⣿⣿⣿⣿⣿⠀⠉⢲⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⡵⣿⡀⠸⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⣿⣿⠸⢿⡟⡇⡼⣼⣿⣿⣿⣿⣿⣿⣿⡇⠀⠈⡇⠻⡷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣖⠭⣾⣿⣿⣿⠋⣾⠗⣧⠀⢿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⡇⡇⢻⢹⣿⠀⢸⣿⠀⠇⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠸⣆⡿⣚⡩⣙⠶⣤⣄⡀⠀⠀⠀⠀⢀⣠⡤⢞⣫⣵⣫⠽⣿⣿⡿⢚⡥⣺⠜⡆⠈⣿⣿⣿⣿⣿⣿
ᥲ δ ᥴ ɗ ᥱ f g ɦ i j κ ᥣ ⲙ ᥒ ᧐ ρ q r s ᴛ ᥙ ᥎ ᥕ ᥊ y ᤁ (search clxdellia for more , ill upload in future alphabets and probs combos)
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⡢⢫⠰⣉⢞⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣻⣽⡾⣯⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢍⠌⡲⣡⣉⡜⠊⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣸⣿⣳⣟⣷⣟⡿⣾⣽⣄⠀⠀⠀⠀⠀⠀⠀⠀⢯⢋⡶⢡⡲⠀⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⢿⣻⣟⡿⣽⡷⣿⢾⡽⣟⣷⣯⢿⣄⠀⠀⠀⠀⠀⠀⠰⣡⠃⠸⠖⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⢯⣿⣻⢾⣟⣯⣿⣽⣻⣟⡯⣷⡿⣯⣿⡄⠀⠀⠀⡠⣊⠕⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣳⡿⣯⢿⣞⣷⡯⣷⣿⣳⡈⣿⡷⣯⣷⠀⢀⠔⣐⠊⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣽⢿⣽⡾⣷⡌⠳⣿⡇⢸⣿⣳⡇⠠⢢⠭⠁⢀⣠⣴⣾⡿⣿⣻⣟⣿⣻⣿⣦ ⠀⠀⠀⠀⣴⣿⡿⣿⢿⣷⣶⣦⣄⣙⠿⣾⣽⢯⣷⡀⠘⠇⠘⣿⠝⡐⡡⡓⢀⣴⣿⣟⣯⣷⢿⣯⢷⣟⡷⣟⣾⡽ ⠀⠀⠀⠀⣿⡷⣿⣻⣟⣾⢷⣯⢿⣽⢿⣞⣯⡿⣯⣇⠀⠀⠀⢉⠎⡴⡑⠰⠿⠿⠷⠯⠷⢿⣻⡾⣿⣽⣻⢿⣽⠃ ⠀⠀⣀⣴⡿⣽⣷⣻⣽⡾⡿⠾⠿⠽⠿⠾⢯⣟⣷⣿⠀⠀⢀⠢⡍⡔⠀⠀⠀⣀⣤⣶⣿⣻⢯⣟⣷⣯⣟⣯⡇⠀ ⢀⣾⡿⣯⣟⡿⣾⡽⣷⣷⣶⣦⣤⣤⣄⡀⠀⠈⠙⠾⠄⠀⡎⢱⠨⠁⢀⣤⣾⣿⣻⢷⣯⣟⣿⣻⣞⣷⣻⣽⣷⠀ ⢸⣿⡽⣿⣽⣻⢷⣿⣻⣞⣷⡯⠟⠋⣀⣀⣀⣀⠀⠀⠀⢸⠘⠤⠃⠀⠈⠉⠉⠁⢉⣉⠈⠉⠑⠻⢽⣾⣟⣷⣻⡆ ⠈⢻⣽⡷⣯⣟⣿⣞⣷⡿⣫⣤⣶⣿⣟⣿⣻⣟⣿⠀⠀⠀⠀⠀⠀⠀⠀⠚⠿⣿⣟⣯⣿⢿⡷⣦⣄⠈⠙⠺⠿⠃ ⠀⠀⠈⠙⢿⣾⡽⣾⢯⣿⡽⣯⡿⠓⢁⣴⣿⠞⠁⠀⠀⠀⣄⠀⠀⠀⠀⢠⣤⣤⣬⣙⠺⣿⣽⢿⡽⣿⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⠑⠻⣟⣿⣞⠟⢋⣠⣴⣿⣟⠎⢀⣂⠀⠀⢰⣿⡆⠙⣿⣦⡀⢻⣯⣟⡿⣿⢿⡽⣯⣿⢯⣿⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡿⣟⡿⣾⡝⢀⣾⣿⣧⠀⢸⣿⢿⠀⠘⣿⢿⣦⣻⡾⣿⣽⣻⢿⣽⡾⣟⣷⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⣯⣟⡿⣽⡻⢡⣾⣟⡾⣿⠀⣾⣟⡿⡇⠀⢻⣯⣟⣷⢿⣽⣾⣻⣯⡷⣿⣻⣽⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⣿⣽⣷⣻⣟⡿⣷⢿⣳⣿⣻⣿⣰⡿⣯⢿⣿⠀⠈⢷⡿⣾⣻⢷⣯⡷⣿⣽⢷⣟⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣾⢷⣻⣽⣟⣯⡿⣞⣷⣟⣯⣿⣻⢯⡟⠀⠀⠘⣿⢯⣟⡿⣾⣽⢷⣯⣿⢾⠇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣯⣷⣻⣽⣻⢯⣷⢿⣽⣞⣯⡿⠁⠀⠀⠀⠹⣿⢯⣿⡷⠋⠉⠈⠉⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠷⠿⢽⣳⣿⣻⣽⢿⡾⡽⠋⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠚⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠦⣀⣰⠒⠠⡤⠤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢖⠒⠡⡂⡗⢬⡚⠖⠊⢉⣁⠌⣝⣁⣀⠀⠤⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⡔⠈⠒⠈⠼⡒⠢⢄⠠⠀⢠⠃⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠰⡀⠀⠀⠀⠈⠀⠀⠑⠄⠈⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⢠⣠⢎⠃⣤⠤⣀⠄⡄⡀⠀⠱⠀⠀⠀⠀⠀⠀⢰⡼⡄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣰⢒⠛⠋⠒⠺⣫⢊⠏⠃⢰⠁⠀⣧⢡⠀⠀⡇⠀⠀⠀⠀⠀⠀⡻⡇⠃⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡀⠠⢤⠬⠱⡈⣡⠔⡩⠃⠁⠀⡀⠈⢆⠀⡟⡆⡜⠠⠁⠀⠀⠀⠀⠀⠀⡼⠇⢠⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⢢⠀⠑⡀⡐⠁⠀⠁⠀⠀⠀⠇⠀⠌⡄⢇⢠⠁⠀⠀⠀⠀⠀⠀⠀⠈⠼⡀⢹⢨⣤⠒⠤⣀⣀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢡⠀⠁⢻⡄⠀⠀⠀⠀⠀⡀⠀⢊⠴⠈⢽⠀⠀⠀⠀⠀⠀⠀⠀⡰⡱⠁⣆⢓⢌⣇⠉⢉⠭⡻⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡏⢂⣷⡁⠀⠀⠈⠉⠛⠵⣬⣢⢚⡇⠈⠢⣤⡤⣤⡤⠄⢴⡊⢔⡁⠴⠁⠀⠉⠪⠑⢢⡜⠉⠝⠉⡹⠃ ⠀⠀⠀⠀⠀⢰⠎⡜⡫⡀⠀⠀⠀⠀⠀⠀⠁⢫⡵⢊⣙⠥⢷⣽⡞⢹⢤⣻⡰⠅⠀⡆⠀⠀⠀⠀⠀⣵⠘⠀⡜⠀⠀ ⠀⠀⠀⠀⠀⠀⢞⡅⢜⢔⠀⠀⠀⠀⠀⠀⠀⡰⠀⠀⢀⡴⠯⠁⠀⠸⠈⢫⣝⢆⠀⡄⠀⠀⠀⠀⠈⣫⢀⢲⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠺⡄⠑⢅⠂⡴⠂⡐⢏⢝⡰⣶⡪⠋⠀⠀⢸⠀⡇⠀⢸⣌⠎⠈⠀⠀⠀⠀⠀⢀⡿⡄⠾⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠡⡹⣦⢣⠀⡇⡟⡀⠀⠀⠀⠐⠤⣼⣀⠁⠀⠘⡍⠀⠀⠀⠀⠀⠀⠀⢽⡃⠻⠆⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⢃⠸⡀⠀⠀⠀⠀⠀⠀⠈⢻⢦⢀⡀⢑⣤⡤⣀⢀⣀⡠⢔⠝⢠⠝⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⢡⠀⠀⠀⠀⠀⠀⡆⡈⠀⠁⠃⠈⢱⡞⡏⢲⡨⡖⡱⠒⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⡀⠀⠀⠀⠀⠈⣆⣦⠖⠒⡇⠀⠀⡇⡇⠀⠀⠀⠀⠘⢣⠁⡌⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣰⠖⠈⠉⠈⠈⠉⠉⠋⠓⢤⣀⠀⠸⡇⠀⠀⠨⢇⠀⠁⠃⠀⠀⠀⠀⠀⡌⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣀⣀⣔⠀⠐⠂⠄⡉⠒⠤⣈⠑⢄⠐⢌⠱⡈⣫⡑⢄⡠⠃⢿⣴⠀⠀⠀⠀⠀⢠⢡⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠙⠯⣍⠀⠤⠓⣒⠶⠓⠀⠵⢄⡢⡘⡝⢥⢠⡠⠊⣘⣺⠀⠀⠀⠀⠀⡌⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠁⠒⠶⠤⢤⣄⣖⠨⠭⠬⠵⢵⡀⢹⠔⡪⢐⠂⠀⠀⠀⠀⢰⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡹⣾⡭⡔⡏⡆⠀⠀⠀⠀⠆⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠮⠕⣲⠱⢱⡸⠅⡇⠀⠀⠀⠸⣘⣀⣀⣤⠤⠤⡤⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢛⣂⡝⢸⠀⣧⡟⠀⠝⠀⠀⣴⢇⡏⡙⡱⡠⠐⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⣉⢥⠎⡇⠘⣴⠋⠁⠀⠀⠀⠀⡟⣸⡰⢑⣉⠉⠉⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠅⡲⡁⢰⢃⡔⠃⠀⠀⠀⠀⠀⢧⠣⣯⡑⠒⣀⠴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠔⠀⣃⣼⠋⠀⠀⠀⢠⠀⠀⠀⡆⡈⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⢊⣠⠞⠋⠀⠀⠀⠀⠀⢸⠀⠀⢰⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⡇⡼⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢓⡔⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠘⡇⡧⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠃⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⡄⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
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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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⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠒⣻⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡏⠦⣄⡀⠀⠀⠀⠀⢀⣴⠞⠁⡀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⡇⠀⠈⠙⠲⣄⠀⢠⡾⠁⠀⡜⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠸⡇⠀⢢⡀⠀⠈⢷⣾⡇⠀⢀⡇⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢿⡀⠀⠉⢳⡄⠀⢿⡇⢀⠾⠁⢀⣾⣷⠶⠒⠲⠶⣤⣀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⢷⣤⡀⠀⢻⠀⣸⠑⠠⠤⢴⠟⠉⠀⠀⠀⢀⣀⠀⠈⠛⢦⡀ ⠀⠀⠀⠀⣀⡤⠶⠒⠛⠛⠷⣦⠊⠁⠀⠀⠀⢸⡑⠲⠶⠖⠋⠁⠀⠀⣠⠶⠒⠛ ⢤⡠⠴⠚⠁⠀⠀⠀⣀⣤⣤⡈⠃⠀⠀⠀⠀⡠⠛⢶⣤⣤⠤⠴⠖⠋⠁⠀⠀⠀ ⠈⠓⢤⣀⠀⠐⠒⠉⠁⠀⢀⣤⡷⠒⠒⠄⣾⠀⡇⠀⠈⠙⢷⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠙⠲⠶⠤⠶⠾⣿⠋⠀⣠⠖⠁⣿⡀⠻⣄⠀⠀⠈⢷⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⢸⠃⠀⠀⣿⢷⡄⠈⠑⢆⠀⠸⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⠀⠀⣼⠏⠀⠙⠶⣄⡀⠀⠀⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢁⣠⠞⠁⠀⠀⠀⠀⠀⠉⠳⣴⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠤⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣦⣶⣾⣿⣷⣶⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣟⠯⠓⣉⣩⣭⣝⣻⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⠗⢡⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠏⣰⣿⣿⣿⣿⣿⣿⣿⠋⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⢠⣿⣿⣿⣿⣿⠿⢿⣿⣀⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣸⣿⣿⣿⠋⠀⠀⠀⣨⣩⠉⠀⢹⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⣿⣿⣿⡏⣀⣀⣀⣀⢧⣿⠂⣀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣶⣿⣿⠗⡤⢤⣀⡉⠊⡱⢋⣉⣉⣷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡝⣿⣿⠀⠈⠙⠿⠃⠀⡇⠽⠛⢻⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⡀⠀⣀⠤⠾⣄⡹⣄⠀⢸⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣋⢹⣿⣿⣷⡾⢄⠀⠀⠀⠀⢈⣶⣿⠿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣇⣸⣿⣿⣿⣿⣿⡏⢻⣿⣿⣇⠈⠡⢄⣀⠐⢉⣿⣿⣴⣿⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⡿⠟⢻⣿⣿⣿⠀⠀⠻⣿⣿⣷⣤⣄⣠⣴⣿⣿⣿⣿⣿⣿⣇⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⠔⠒⠒⠉⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠉⠛⢿⣿⡿⠛⠋⠘⣿⣿⠿⢯⠛⠂⠤⢄⡀⠀⠀⠀⠀ ⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⢻⠁⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⡇⠀ ⣰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇⠀⠀⢣⠒⠲⠤⣀⡀⠀⡀⣀⠤⠒⠂⠸⡀⠀⢱⠀⠀⠀⠀⠀⠀⠙⣄ ⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⡀⠀⢣⡀⠀⠈⠀⠈⠀⠃⠀⠀⠀⠰⠧⠀⠚⠀⠀⠀⠀⠀⠀⠀⠙ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠲⠻⠷⠒⠞⠂⠸⠣⠲⠖⠖⠀⠀⠻⠻⠿⠼⠟⠿⠧⠿⠃⠀ 🚩🚩 Jai Shree Ram 🚩🚩⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣟⠻⡿⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣸⣻⠿⢮⡿⣾⡖⠚⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣄⠒⢦⠸⣿⣄⠙⣧⠀⠰⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣛⣷⣞⠳⣄⠘⡆⠙⢇⠀⠀⠰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣸⣯⡝⠻⣿⣏⠉⠻⣮⣷⣝⣶⣼⡀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣇⠈⠙⢤⠈⢳⡀⠀⠹⣌⢻⠀⠙⣧⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣼⠋⠳⢤⣄⡑⠀⠹⡄⠀⣌⠀⢳⡀⠸⡆⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⣠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢹⣄⠀⠂⢻⡉⠑⣦⠹⡄⠸⡄⠀⢷⡄⡇⠀⠀⡇⠀⠀⠀⠀⣀⠤⠒⠋⠁⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⠿⣶⣤⣝⠀⠀⠀⢿⡶⢧⠀⠸⡇⡗⠀⢀⠃⠀⢀⡴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣤⣤⣀⣀⡀⠀⠀ ⠀⠀⠀⠀⢀⣀⣀⣀⡀⠙⢻⣷⣦⡀⠈⠋⠈⢧⠀⠀⡇⠀⠈⠀⠔⠋⠀⠀⢀⣀⣤⣤⣤⡶⢶⣿⠿⠭⢥⢽⣁⣤⠀⠒⠿⠿⣿⣷⣆ ⠀⢀⡠⠚⠉⠉⠀⠀⠀⠀⠀⠙⢿⣿⣶⣤⣤⡘⣆⣼⣃⣴⣦⠀⠀⣀⡴⠞⣛⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠘⣿⣛⣖⠲⠦⣄⣸⡿ ⢠⠾⠒⠶⠀⠀⠀⠀⠀⡀⠀⡙⢺⣏⠛⢿⣿⣿⣿⣿⣿⣿⣿⣶⠞⡩⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠒⠤⣍⣙⣓⠶⣴⣶⠟⠁ ⡾⠀⠂⠀⠀⠀⠀⠀⠈⠑⠉⢡⣿⣿⠛⠲⣤⣯⣿⣿⣿⣿⣿⣥⡞⠒⠒⠚⠛⠓⠠⣀⠀⠀⠀⠠⠄⠀⠠⣤⣷⣌⢙⣿⣦⡾⠋⠀⠀ ⡗⠺⠤⠛⠉⠉⠁⠐⠉⠉⣹⣿⢿⢃⣠⣾⢋⣾⣿⣿⣿⣟⠻⠏⡿⣗⣦⡀⠀⠀⠀⠈⠙⠲⣄⡀⠀⠀⠀⠈⠙⠿⣿⣿⠟⠀⠀⠀⠀ ⣇⣠⠤⠀⠀⠀⠀⢀⣴⡾⢛⡽⢋⣽⣟⣵⢫⣿⣿⣯⡏⢣⠀⠄⠀⠈⠉⢙⣻⠖⢦⣄⡀⠀⠤⢙⠶⣤⡀⠈⢳⣰⡟⠁⠀⠀⠀⠀⠀ ⢿⠀⠀⠀⢀⡴⢪⠟⢩⠖⠋⢠⡾⢻⡟⢁⣿⣿⣿⡟⡀⠘⠀⣴⠀⣤⡐⠂⠈⠉⢗⣟⠿⣶⣤⡀⠲⣤⣹⣿⠞⠉⠀⠀⠀⠀⠀⠀⠀ ⠘⣧⠀⠀⠈⠀⠀⠀⠀⡀⣠⠏⣴⠏⠀⢸⣿⠟⠻⢀⠆⠀⢀⠈⢳⡸⡗⢤⡀⠉⠪⠙⢧⡀⠉⠙⠓⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠘⢧⡀⠀⠀⢀⡴⢂⣜⡥⠚⠁⠀⠀⠀⠁⢠⡆⢸⣰⠀⠈⣧⠀⠑⢿⠀⠙⢦⠀⠀⡀⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠳⣤⣖⣋⡴⠟⠉⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⢹⠆⠀⢸⡄⠀⠈⢷⡀⠀⠑⢦⡜⢦⣹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⣼⣾⠀⠈⢀⢳⡀⢠⡈⢻⣦⡀⠀⠙⢮⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⡿⡼⠀⠄⠈⠈⣇⠀⠹⣌⠹⣿⣄⠳⢰⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡁⢻⠀⠀⠀⠀⠙⠂⠀⠹⡁⡈⡻⣦⠾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⣸⡄⠀⠀⠀⠀⠀⢰⣄⣃⡴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⠒⠒⠒⠒⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢔⣒⠂⣀⣀⣤⣄⣀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣴⣿⠋⢠⣟⡼⣷⠼⣆⣼⢇⣿⣄⠱⣄ ⠀⠀⠀⠀⠀⠀⠀⠹⣿⡀⣆⠙⠢⠐⠉⠉⣴⣾⣽⢟⡰⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣦⠀⠤⢴⣿⠿⢋⣴⡏⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡙⠻⣿⣶⣦⣭⣉⠁⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠈⠉⠉⠉⠉⠇⡟⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣘⣦⣀⠀⠀⣀⡴⠊⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⢻⣿⣿⣿⣿⠻⣧⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠫⣿⠉⠻⣇⠘⠓⠂⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢶⣾⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣧⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠙⠻⢿⣿⣿⠿⠛⣄⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⠂⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀ 🌹
˚˖𓍢ִ໋🌷͙֒✧˚.🎀༘⋆ ₊˚ʚ ᗢ₊˚✧ ゚.
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⢤⣶⣶⣶⣦⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⣤⣤⣤⣄⡀⠀⠀⠈⠛⣿⣿⣿⣿⣿⣦⣀⠀⠀⠀⠀ ⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀ ⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣆⠀ ⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡄ ⢠⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⠇ ⢸⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⡟⠀ ⠘⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠿⠟⠋⠀⠀ ⠀⢿⣿⣿⠀⠀⠀⢀⣴⣾⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠀ ⠀⠈⢿⣧⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣴⣶⣿⡿⠁⠀ ⠀⠀⠀⠹⣆⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠻⠿⠿⠿⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣄⣀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣖⣤⣿⣿⣟⣹⠻⢿⣿⣳⡀⠄⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⡏⣿⠏⠉⢣⡇⠀⠀⠻⡁⢻⡄⠀⠈⣴⣳⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣧⢸⡀⠀⠈⠀⠀⠐⡄⢡⡆⣿⠀⠀⠀⠻⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⣼⡄⠀⢠⠀⠀⠀⠈⣸⢠⡿⠀⠀⠀⠀⠀⠀⠾⣽⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣠⠿⢄⡀⠀⠀⠻⣿⣿⣶⣄⡄⠀⡀⣠⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠉⣶⠉⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⡿⡟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣴⡀⠀⠀⠀⠀⠀⠈⣇⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⣷⠋⠀⠀⠀⠀⠀⠀⢸⡀⡇⠀⠀⠀⠀⠀⠀⢀⠔⡿⣳⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⠀⠀⠀⠀⣠⠂⡡⢞⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠻⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⢹⢸⠀⠀⣠⣾⡕⣩⡵⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠙⠻⢷⣦⡀⠠⢄⡀⠀⠘⣏⣆⣾⣿⣺⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⣤⣻⣷⣆⣟⣿⣿⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢾⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⡀⣀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀
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