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⠀⠀⠀⠀⠀⠀⢀⣤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⢤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡼⠋⠀⣀⠄⡂⠍⣀⣒⣒⠂⠀⠬⠤⠤⠬⠍⠉⠝⠲⣄⡀⠀⠀ ⠀⠀⠀⢀⡾⠁⠀⠊⢔⠕⠈⣀⣀⡀⠈⠆⠀⠀⠀⡍⠁⠀⠁⢂⠀⠈⣷⠀⠀ ⠀⠀⣠⣾⠥⠀⠀⣠⢠⣞⣿⣿⣿⣉⠳⣄⠀⠀⣀⣤⣶⣶⣶⡄⠀⠀⣘⢦⡀ ⢀⡞⡍⣠⠞⢋⡛⠶⠤⣤⠴⠚⠀⠈⠙⠁⠀⠀⢹⡏⠁⠀⣀⣠⠤⢤⡕⠱⣷ ⠘⡇⠇⣯⠤⢾⡙⠲⢤⣀⡀⠤⠀⢲⡖⣂⣀⠀⠀⢙⣶⣄⠈⠉⣸⡄⠠⣠⡿ ⠀⠹⣜⡪⠀⠈⢷⣦⣬⣏⠉⠛⠲⣮⣧⣁⣀⣀⠶⠞⢁⣀⣨⢶⢿⣧⠉⡼⠁ ⠀⠀⠈⢷⡀⠀⠀⠳⣌⡟⠻⠷⣶⣧⣀⣀⣹⣉⣉⣿⣉⣉⣇⣼⣾⣿⠀⡇⠀ ⠀⠀⠀⠈⢳⡄⠀⠀⠘⠳⣄⡀⡼⠈⠉⠛⡿⠿⠿⡿⠿⣿⢿⣿⣿⡇⠀⡇⠀ ⠀⠀⠀⠀⠀⠙⢦⣕⠠⣒⠌⡙⠓⠶⠤⣤⣧⣀⣸⣇⣴⣧⠾⠾⠋⠀⠀⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⣭⣒⠩⠖⢠⣤⠄⠀⠀⠀⠀⠀⠠⠔⠁⡰⠀⣧⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⢤⣀⣀⠉⠉⠀⠀⠀⠀⠀⠁⠀⣠⠏⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠒⠲⠶⠤⠴⠒⠚⠁⠀⠀

﹫♥︎mini symbols pack﹟prt3 𖥵⑅𖥵 ‣ ᭟ ˙˖ ˓𖤣𖥧ᝢ 𖡋 ៹° ゐ 𓆰 ╱ ໑ ﹫⚝៸៸ ᦾ ╱ ꜜ ░ ʚ 𖤐 ⤸ 𖧧 ࣪ ͎ 𖤬 ⃕ ᭥ 𖤣 ⵓ ◞ ꒦꒷ ꜜ 𖧒 ៶ ៸ あ 𖤣𖥧˚. 𖥨 ꉂ ៹ 𖧧 ָ࣪ᬡ ᵎ 𓄹𓈒 ‹ › (\ /) ˶ᵔ ᵕ ᵔ˶ ‣ ┈─ ⊹ ִֶָ໑ .*⸝ ｡༴ ๑ ໑﹆ ꒰⇉ᦾ ₆⁶₆ ꞋꞌꞋ ⊹ ↶↷ ⃕ ҂ ⚙﹫⌗ 𖥸 𖤍 𓇇 𖥕 𖥻 𖥾 𖦆𖦝 𖦞 𖨌 𖧾 𖧧 𖧡 𖧣 𖤩 \ ꜜ © ฅ^•ﻌ•^ฅ ‣ 𖦆 ꜜ｡ᝰミ˖ ᵕ̈ ҂ ꜜ 𖠌 ˖͢ 𖥨⊹ ִֶָ ꜜ ⤸ ⌕ ≡ ➭ ⁽ ⁾ ꜜ ᩠ ᘞ 𐀔 ҩ ៹ ⌂ ७. ٪ 〃 ◠◠ ⊹ ⌁ ⃕˖ ₎ キ﹫ꪶ Ꮺ ᕱ⑅ᕱ ‣ 𖤐✰★☆✦✧✶ ❥ 𑁍 ✿ ❃ ✱ ∗ ❁ ꕤ ⌘ ♡⃕ᝢ ♡̷͎ ☽ で 女 あ の 女 𓆸 ダ リヾ ২ う 𖧷 絶 ପ(⑅ˊᵕˋ⑅)ଓ ‣ ʚĭɞ ୨୧ ꒰ ꒱ ᨳ᭬ ʚɞ ╲ ╱ ৎ ໒ ୭̥ ꒲ ⌇ ༊࿐ ꒰╱ ؏ ୭ ꪶ ⌗ 〻 ᜴ ꉂ 𖠣 ଽ ❨ ন ◟͠╸Ձ ੭ ど ╳ ᥀ ᘛ ᖚ ʕ•ᴥ•ʔ ‣ 𖨂 ⋮ ⇣ 𖥲 જ ⌁𖠱 ᶻᶻᶻ ‣ ꗃ ଡ଼ ঌ 𖤣 𖡡 ◜◞𖧧 ָ࣪𓄼 © ˚ 𖥨┉┈ ﹫╰ ꜜﾐ 𖡋 三 𓂅 ᭟ ⪧ ៹°. ҉ ⨟ ⃟ ྀུ ᥀﹟ ៚ 🏁⛓💭 ♡🕷՞๑​ 🗯﹆ ⋮ 𖤐₊˚ ⚝ ʚ ♡ ₊˚ ៹ ₊ ﾉ ⨾ ◟ 𑂻𑂴 ꈍᴗꈍ Add my dc cuz im lonely af: @iluv_chips search iluv_chips for more ig

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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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⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⢠⡾⢳⣿⣿⠿⠦⣤⣼⠿⠿⠆⣰⣿⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣰⢉⣠⣿⠶⠋⠁⠀⠀⠀⠀⠀⠀⠠⠤⠤⠬⠙⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⡗⣰⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣉⣒⡚⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠒⠊⠉⢁⡀⠀⠉⠙⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡴⡾⠀⠀⠀⠀⠀⣀⡠⠄⠒⠉⠁⣠⡇⠀⠀⠀⠀⣼⣾⣿⣿⡿⠦⣄⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢰⢻⡇⠀⠀⠀⡠⠊⠁⠀⢀⣠⣴⣿⠟⡀⠀⠀⠀⢠⣿⣿⣿⢿⡀⠀⠈⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⣾⠃⠀⣠⠎⠀⣠⣴⣾⠿⣿⡿⠃⠀⢣⠀⠀⠀⢸⣿⣿⠿⠻⣿⣆⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢰⣫⣾⠀⠀⢁⣴⣾⣿⠿⠾⠻⠻⠅⠀⠀⠘⡆⠀⠀⣿⣿⣿⣀⣀⣨⣿⡄⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⢺⡿⠀⣠⣿⡷⢟⡥⢶⣾⣿⡝⢺⡄⠀⠀⢧⠀⠀⣿⣿⣿⣿⣿⡏⠙⣷⠀⡘⣷⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⠀⡇⢰⡯⠋⡀⠙⠤⣘⠿⠿⢃⡿⠁⠀⠀⣽⠀⠀⣿⣿⣿⡟⠿⠥⠴⠋⢰⡏⢻⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠸⠸⡇⠀⠀⡀⠈⠓⠒⠲⠒⠚⠉⠀⢰⡿⢤⢹⠀⠀⣿⣿⣿⠁⠠⠤⠤⠞⠋⢀⣼⣿⣷⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢰⡇⠀⠀⠈⠓⠦⠤⠴⠂⠀⠀⡴⢹⠁⠀⢹⠀⠀⣿⣿⣿⠀⠀⠀⠀⣀⠴⠚⢻⣿⣿⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣼⠁⢀⠀⠀⠀⠀⣠⣀⣶⡴⠋⠁⠸⠶⣤⣄⣀⣀⣿⣿⣿⠀⣄⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀ ⣧⠀⠀⣸⢻⠀⠸⡄⠀⠰⢿⡟⠛⠙⠦⣀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⡀⠈⣻⣷⣦⠀⠀⢸⢿⣿⡿⠀⠀⠀⠀⠀ ⠘⠦⣄⣧⡏⠀⠀⣇⠀⠀⠸⠀⠀⠀⠀⠀⠉⠑⠒⠤⠤⠤⠤⠭⠽⠿⠗⠒⠻⠧⡛⠀⠀⢸⢸⣿⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⣹⠉⠀⠀⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⢸⠸⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⡇⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⢿⡆⠀⠀⠀⠀⠀ ⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⢸⡇⠀⠀⠀⠀⠀ ⠀⠀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣆⠀⠀⠀⠀ ⠀⠀⠀⠘⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢰⠇⠿⡄⠀⠀⠀ ⠀⠀⠀⠀⠈⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⠈⣴⠏⠹⣆⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⠶⣴⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⣿⣧⣾⣿⡇⠀⠘⢦⡀

⠀⠀⠀⠀⠀⡰⢂⣾⠿⠛⠒⠚⠛⠃⠺⢶⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⡣⠋⠁⠀⠀⠀⠀⠀⢀⡐⠒⢙⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⢄⠉⠀⠐⠀⠀⠙⢦⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣾⠁⠀⠀⠄⠂⢈⣠⠎⠀⠀⣸⣿⡿⠓⢬⡇⠀⠀⠀⠀⠀ ⠀⠀⢸⡟⠀⠔⣁⣤⣶⣿⠋⢰⠀⠀⣿⡟⠻⣦⠀⢳⠀⠀⠀⠀⠀ ⠀⠀⣷⡇⢠⣾⢟⢭⣭⡭⡄⠀⡆⠀⣿⣷⣶⠺⡆⢸⡄⠀⠀⠀⠀ ⠀⠀⠇⡇⠛⠡⣑⣈⣛⠝⢁⡀⠇⠀⣿⡿⠛⠒⣡⠇⣧⣀⠀⠀⠀ ⠀⠀⢠⠁⠈⠐⠤⠄⠀⣠⢸⠈⠢⠀⣿⡇⠀⠀⠠⠚⣿⣿⠀⠀⠀ ⡄⠀⢾⠀⡆⠠⣴⠞⠯⡀⠈⠙⠲⣶⣿⡇⠑⣦⡄⠀⣿⣿⠀⠀⠀ ⠈⠺⡮⠀⢡⠀⠀⠀⠀⠀⠁⠐⠒⠒⠛⠃⠈⠛⠇⠀⡏⡏⠀⠀⠀ ⠀⢰⠁⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⢷⠀⠀⠀ ⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⢸⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀ ⠀⠀⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠸⡳⡀⠀ ⠀⠀⠀⠑⢄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣯⣼⡇⠑⣄

⠀⠀⢀⣤⣶⣶⣦⣄⠀⠀⠀⠀⠀⢀⣤⣶⣶⣤⣄⠀⠀ ⠀⣴⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣷⡄ ⢰⣿⣿⣿⣿⣿⣿⣿⣧⣤⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣷ ⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡍⣿⣿⣿⣿⣿⣿⣿⣿⠏ ⠀⠀⠉⠙⢩⣿⣿⣿⣿⣿⠸⠇⢿⣿⣿⣿⣯⠛⠉⠁⠀ ⠀⠀⠀⠀⢸⣿⣿⣿⡏⠹⠀⠁⠈⣿⣿⣿⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠸⣿⣿⠻⠃⠀⠀⠀⠀⠙⠻⣿⡿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠹⣿⠀⠀⠀⠀⠀⠀⠀⠐⡿⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⡿⠟⠋⡩⠝⠛⢿⣿⣿⣿⣷⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⠟⠋⠐⠒⠥⢄⣀⠀⠀⡃⢹⣿⡿⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠤⢼⣿⣿⣿⡁⠀⠀⠹⣛⣽⣶⠀⠁⣠⣧⡾⠞⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣴⣇⠈⠙⡻⡇⡇⠀⠀⠀⠀⠉⠈⢀⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⠜⠛⠛⢴⡶⠃⡇⠱⠀⠀⣀⠀⠰⡀⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠠⠁⠀⠀⠀⠀⢻⡀⢰⠀⢡⡀⠸⣿⣶⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡠⠘⢰⠀⠣⡀⢿⠛⠉⢱⠈⢏⣤⡶⣢⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡰⠁⢰⡇⡀⠠⠑⢄⠙⠢⢼⢞⣽⡟⠀⠀⠀⠡⣀⠀⠀⠀⠀⠀ ⠀⠀⢀⠄⠀⠀⡇⢀⡖⠇⡇⠀⠀⠀⡱⡞⡁⢸⢁⣴⣤⣀⡴⢠⠇⠀⢄⠀⠀⠀ ⠀⢀⠎⡰⠁⡐⣠⠊⢸⠀⡑⠒⢂⠔⢠⡏⢠⣿⡿⣻⣿⣟⢖⡙⠀⠀⠀⠑⢖⠂ ⢠⠊⡐⠁⣰⡵⠡⠤⢜⠬⠤⡤⡮⢴⢕⣴⠽⡇⡷⣿⢯⠙⣿⢧⠤⣀⠉⠁⠀⠀

⠀⠀⣀⣤⣤⣤⣾⣿⣿⣿⣿⣿⣿⣶⣾⣿⣷⣶⣶⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀ ⣿⣿⣿⣿⡘⣿⣿⣿⡟⢄⣀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀ ⢻⣿⣿⣿⢿⣿⠻⣿⡳⢀⠀⠉⠑⠢⡙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⡀ ⠈⣿⣿⡟⠘⠿⡀⡎⠑⠘⣻⢶⢶⣄⠈⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢀⣿⡟⠀⠀⠀⡹⠁⠀⠀⠻⢿⡀⠘⡄⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠚⠁⢠⠀⢤⠸⡀⣀⡄⠀⠀⠀⠀⠁⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⣣⠀⢛⠦⢄⣀⣀⣀⡀⠀⠀⣴⠟⢋⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⣿⣷⡀⠈⠐⠒⠂⠉⠁⠀⡜⢀⠔⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠻⠿⣿ ⠀⠀⢸⣿⣿⣧⡀⠀⠀⠀⣀⠠⠔⠛⠠⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀ ⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀ ⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢀⡊⠁⠀⠀⠠⢄⠩⡒⡌⡑⢄⣀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⠮⠃⠀⣤⣆⣀⣦⣿⣶⣶⣶⣶⣾⣦⣶⣬⣿⣮⡢⡈⠀⠀ ⠀⠀⠐⠒⠒⠒⢢⡇⡄⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢫⡢⠀ ⠀⠀⠀⠀⠀⢠⢡⣧⣷⣿⣿⣿⡿⠛⠋⠁⠀⠀⠀⠉⢹⠿⣿⣿⣿⣿⣿⡿⣿⠀ ⠀⠀⠀⠀⠀⣆⢸⣿⣿⣿⣿⠋⠀⠀⣀⠀⠀⣤⣤⣴⡶⠦⣬⡻⣿⣿⣿⣷⣿⣗ ⠀⠀⠀⠀⠀⠿⣾⣿⣿⡿⢁⣴⡾⠿⠟⠀⠀⠈⢉⡴⠋⠉⡉⡉⠻⣿⣿⠿⠿⢿ ⠀⠀⠀⠀⢠⣧⠸⣿⣿⡷⠋⠉⣉⣳⣦⠀⠀⢠⣿⠒⣽⣯⠉⢻⡄⢹⣿⡄⠀⠀ ⠀⠀⠀⢠⣾⣿⣷⣿⠿⡇⢰⠋⠀⣾⣿⡷⠚⠛⣿⠢⢙⡋⢤⡾⠁⣼⠛⠃⠀⠀ ⠀⠀⢠⣿⣿⣿⣿⢸⡆⡇⠈⠓⠒⠖⢋⡟⠀⠀⠘⢷⣦⣀⣀⣤⠜⠃⠀⢀⡀⣴ ⠀⢠⢻⣿⣿⣿⣿⡄⠙⠧⣄⣀⣀⡤⠿⡀⠀⠀⠀⣀⠏⠀⠀⠀⠀⠀⢀⣾⣷⣿ ⠀⢿⣿⣿⣿⣿⣿⣿⣦⣲⡈⠀⠀⠀⠀⠈⠑⠒⠋⡀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿ ⣨⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⢀⣅⣠⠬⠤⠀⠀⠀⣠⣾⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⣀⠀⠉⠀⠀⢀⡠⠔⠊⠹⣿⣿⣿⣿⣿ ⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⣸⣿⠙⠻⢿ ⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⣰⣿⠇⠀⠀⠀

⠀⠀⠀⠀⠀⠀⣀⣠⢔⡂⡉⣭⣯⣉⢑⠢⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣴⣊⢬⣥⣯⣵⣿⣿⣿⣿⠗⠻⣽⡟⡄⠀⠀⠀⠀⠀ ⠀⠀⢀⢿⣿⠟⣉⡉⠁⠁⠁⠉⢙⠛⠾⡿⢿⣿⣿⠀⠀⠀⠀⠀ ⠀⢠⣲⡟⠑⠉⠀⠀⠀⠀⠀⠀⠀⠈⠑⢌⢯⣢⣧⣢⠀⠀⠀⠀ ⠀⢀⢽⢀⢔⣭⣴⡄⠀⠀⠀⢀⣤⣒⠠⡀⠸⣾⣿⡟⠀⠀⠀⠀ ⠀⣸⡞⠄⢧⣿⣿⠇⠀⠀⠀⣼⣿⣿⢱⢰⠀⣿⣿⡇⠀⠀⠀⠀ ⠀⣽⡇⠈⠊⠙⠋⢀⡀⠀⡀⠙⢞⣇⡊⠎⢀⣿⣿⡃⠀⠀⠀⠀ ⡘⠀⢣⠀⠀⠀⠀⠈⠁⠈⠁⠀⠀⠀⠀⠀⣸⣿⢿⣇⠀⠀⠀⠀ ⠣⡈⠠⠢⠀⠀⠀⠀⣀⣤⣄⠀⠀⠀⠀⣠⢿⡀⠜⠀⠀⠀⠀⠀ ⠀⠐⠁⠀⠈⢢⣄⡀⠛⠛⠋⢀⣀⣤⣾⣧⢀⠬⠂⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⡡⡂⠀⠀⠀⠀⠈⠙⠙⢄⠀⠈⠀⠀⢀⠀⣀⣠⠤⠀ ⠀⠀⢀⡴⠁⣸⢄⠀⠀⠀⠀⣎⢆⠈⢢⣀⠀⠀⠀⠉⠛⠻⢿⣶ ⠀⠰⢀⡇⢸⠇⢻⣄⣀⣀⣾⣿⣿⡷⡀⢱⠈⠑⠢⢀⠀⠀⠀⣿ ⠀⠀⢀⠇⣸⠀⢸⣿⣿⣿⣿⣿⣿⠿⠁⠈⣧⣴⣶⣴⣇⠀⡴⠟ ⠀⠁⠸⠀⠇⡀⢹⣿⣿⣿⣿⣿⣿⡧⠀⠀⠟⡛⠛⡛⣋⡡⠖⠁

⣿⣿⠀⢸⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣻⢿⣿⢼⣿⠀⠀⠀⠀ ⣿⣿⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢀⡔⠾⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀ ⣿⣿⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⢀⠤⢊⠁⠀⠀⠀⢙⣿⣿⣿⣿⣿⢿⠀⡇⠀⠀ ⢿⣿⠀⢸⣿⣿⣿⣿⡇⢀⠔⢊⠔⠒⣊⠈⠂⠄⣀⠼⣉⢿⣿⣿⣺⣸⠀⡇⠀⠀ ⣀⣀⠀⠀⠀⠈⠉⠉⣧⠂⡠⠁⠐⠉⠀⠀⠀⠀⠀⠠⠀⠊⣿⣿⡏⡿⡆⡇⠀⠀ ⣿⣿⠀⢸⣿⣿⣿⣿⡇⢰⢅⣀⣔⡂⠲⠀⠀⠀⠀⣀⣉⢠⣿⣿⡇⡇⠃⡇⠀⠀ ⣿⣿⠀⢸⣿⣿⣿⠟⠃⠢⡄⠘⠏⠀⠙⠃⢠⢂⡴⢶⣪⡾⣿⣿⣧⡇⠀⠇⠀⠀ ⣿⣿⠀⢸⣿⣿⡇⠆⠀⠀⠘⡀⠀⠀⠀⠘⢢⣴⠇⠀⠀⢸⠀⠈⣿⡿⠀⢠⣴⣶ ⣿⣿⠀⢸⣿⣿⣧⣣⣀⣀⠰⠤⡀⠀⠀⠀⠀⠙⡠⠤⠔⡁⢀⣴⢿⡇⠀⣿⣿⣿ ⣿⣿⠀⢸⣿⡿⠋⠀⠀⡹⠛⡇⢨⣀⡠⠔⠀⠟⠀⠀⠀⠈⢿⣿⣸⢃⣠⣿⣿⣿ ⠿⣿⠀⠸⣿⣇⠀⠀⣰⠁⠀⠑⣈⢷⡸⠓⡝⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⢱⠦⢼⠀⠀⠀⠀⠀⠀⠀⢣⣠⠴⠶⢏⣴⣿⣿⣿⣿⣿⣿⣿⣿ ⠠⠔⠂⠉⠉⠁⠐⠢⢄⣇⠀⠀⠀⠀⠀⠀⠀⡝⠀⢀⠼⠿⠿⠿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⢀⣠⣽⢷⠒⢦⣠⢤⣖⡻⠉⠉⠁⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿ ⠀⠀⣀⠠⣤⣶⡿⠛⢉⡠⢚⠦⠤⡏⠓⢄⠉⠒⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛

⣷⣤⣀⠀⣢⣍⣶⣦⣿⣿⣞⣿⣆⠡⢶⢆⢀⣴⡡⠎⣀⣤⣗⣿⣒⣴⣦⡇⠀⠀ ⠀⠈⠙⢿⣾⣿⣿⣿⣿⣿⣿⠿⠟⠳⠴⠯⠿⡷⢕⢉⣿⡍⠙⣿⣿⣿⠘⡇⠀⠀ ⣤⠀⠀⠀⠙⣿⣿⡿⠛⠋⡀⢀⣄⣀⣴⣦⣀⡀⣀⢁⡀⠉⠻⢿⣿⠿⡄⠃⠘⣆ ⠘⠳⣦⡀⢠⢮⠏⣀⣶⣾⠛⢙⠉⠉⣉⣩⣽⠿⠿⣿⣧⣦⠀⣀⠈⠣⡁⠀⠀⢉ ⣀⣀⡈⠛⣾⣫⣾⣿⣾⣷⣾⣧⣶⣞⣯⣵⣶⣶⣾⣿⣿⣿⢿⣿⣤⣤⢣⠐⣶⣿ ⢉⣙⢿⣀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣿⠿⣿⣝⣷⡌⠻⣷⣶⣆⠘⠟ ⣿⣧⡏⣿⣾⣿⣿⣿⣿⡿⡿⠿⠛⣩⠽⠟⠛⠉⠀⠀⠘⢿⣿⣿⣦⣼⣿⣿⣆⠀ ⠘⣋⢸⣿⣿⣿⣏⢩⣍⠻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⡿⢐ ⠀⠀⣿⣿⣿⠛⢺⠟⠛⠓⢺⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣼⣿⠈ ⠀⢾⢸⣿⠏⠀⠀⠀⠄⠀⣿⣿⠻⠷⠀⣀⣄⣀⣀⣠⣤⣤⣄⠈⣿⣿⣿⣿⡟⠀ ⠢⣀⠀⣀⠀⠀⠀⠀⠀⠀⠉⠛⠀⠀⠀⠈⢻⣿⣿⠗⠢⢤⣬⠃⣿⣿⣿⣿⡇⠀ ⠦⡀⣝⠈⠑⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠹⠟⠋⣿⣿⢏⣿⠀⠀ ⠀⠘⢆⡙⢢⠊⠀⣼⣶⣠⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡏⢼⣷⠀⠀ ⠀⠠⠀⡽⠁⢀⠌⠑⠢⠝⢉⡲⡾⠭⢴⣒⣠⣤⣄⣀⣀⣀⣀⣈⠿⠴⠍⠍⠀⠀ ⠀⠀⠈⠀⢠⣏⡉⠦⠒⠈⢀⡠⠂⠀⠜⠩⠭⠿⠿⠤⠀⠀⠠⠞⠂⠠⠄⠀⠀⠀

⠀⠀⠀⢀⣤⣴⠶⠶⢤⣄⠀⠀⠀⠀⠀⢠⣤⢂⣤⠷⡄⠀⠀⠀⠀⡠⠁⠀⠀ ⢦⣠⣸⡿⠟⠁⠒⢂⠄⠛⢿⣶⡤⣀⠀⠀⠹⣋⠀⠀⡃⠀⠀⡈⠘⠀⠀⠀⠀ ⢴⡟⠏⢠⠃⠀⠀⡇⢀⠕⡨⠉⠻⣀⢳⣆⠀⠘⢢⠚⢁⠀⡀⡅⠀⠀⠀⠀⠀ ⢸⣶⡀⡣⠈⠀⡑⢉⠵⠉⠀⠀⠀⠘⣿⣿⠀⠀⠚⠐⡁⠀⠀⠈⠢⠤⠂⠀⠀ ⠘⣿⣷⣅⣀⡊⠜⠀⢠⣾⣿⣷⣄⠀⣸⡿⠀⢸⡟⡙⢈⠀⠉⠒⠂⠀⠀⠀⠀ ⠚⠹⣿⠷⡀⠀⠀⠀⠈⣿⡟⠉⠀⡰⠋⠀⠀⠸⢰⠡⢈⣂⡀⠒⢈⠍⠀⠀⠀ ⠀⠀⢻⣄⠈⢢⡀⠀⠀⠈⠀⣀⠔⢱⠒⣤⣶⢤⣋⠀⠃⢙⠙⠀⠘⠠⠀⠀⠀ ⠀⠀⠘⣿⣻⣿⣿⠗⡦⣿⠿⣭⡢⣼⠀⢹⡏⡟⢉⡧⠛⠁⡈⠖⣤⠤⣤⠀⠀ ⠀⠀⠀⠸⠿⡿⢯⠀⠉⠉⠙⢻⣷⡈⣆⣜⡿⠀⣫⠂⠀⠀⠈⠁⡟⢀⣿⠀⠀ ⠀⠀⢀⢠⠠⠂⠈⡆⠀⠀⠀⠘⠻⣟⣿⢼⠗⢎⠁⠀⠀⠀⡠⠚⠀⠀⠁⠀⠀ ⠀⢴⠁⡀⠀⠀⠀⠇⠀⠀⠀⠀⠰⢡⡏⠀⠱⣌⠦⣀⠠⠊⠀⠀⠀⢀⡀⠀⠐ ⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⢀⡇⠀⠘⠤⠀⠀⠀⠈⠁⠀⠀⠀