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.|ɒƚiqɒɔ ꙅ'ɘƚɒƚꙅ ɘʜƚ ꙅi ɘɘꙅꙅɒʜɒ||ɒT .ɒɘɿɒ ᴎɒdɿu ꙅuo|uqoq ƚꙅom ꙅ'ɒbiɿo|ꟻ ꙅi ɒɘɿɒ ᴎɒƚi|oqoɿƚɘm imɒiM ɘʜT .(ʏƚᴎuoƆ |ɒvuᗡ ʜƚiw ɘ||ivᴎoꙅʞɔɒႱ Ꮈo ᴎoiƚɒbi|oꙅᴎoɔ ɘʜƚ oƚ ɘub) ꙅɘƚɒƚꙄ bɘƚiᴎU ꙅuouǫiƚᴎoɔ ɘʜƚ ᴎi ɒɘɿɒ ʏd ʏƚiɔ ƚꙅɘǫɿɒ| ɘʜƚ bᴎɒ ɘƚɒƚꙅ ɘʜƚ ᴎi ʏƚi|ɒqiɔiᴎum ꙅuo|uqoq ƚꙅom ɘʜƚ ꙅi ɘ||ivᴎoꙅʞɔɒႱ .ꙅɘƚɒƚꙅ .Ꙅ.U ɘʜƚ Ꮈo bɘƚɒ|uqoq ʏ|ɘꙅᴎɘb ƚꙅom-ʜƚ8 ɘʜƚ bᴎɒ [9],ꙅuo|uqoq ƚꙅom-bɿ ɘʜƚ ,ɘviꙅᴎɘƚxɘ ƚꙅom-bᴎ ɘʜƚ ꙅi ɒbiɿo|ꟻ .ɒbiɿo|ꟻ Ꮈo ꙅƚiɒɿƚꙄ ɘʜƚ ʏd ʜƚuoꙅ ɘʜƚ oƚ bᴎɒ ,ᴎɒɘɔO ɔiƚᴎɒ|ƚA ɘʜƚ ʏd ƚꙅɒɘ ɘʜƚ oƚ ,ɒiǫɿoɘᎮ bᴎɒ ɒmɒdɒ|A ʏd ʜƚɿoᴎ ɘʜƚ oƚ ,ɒmɒdɒ|A bᴎɒ oɔixɘM Ꮈo Ꮈ|uᎮ ɘʜƚ ʏd ƚꙅɘw ɘʜƚ oƚ bɘɿɘbɿod ꙅi ɘƚɒƚꙅ ɘʜT .ꙅɘƚɒƚꙄ bɘƚiᴎU ɘʜƚ Ꮈo ᴎoiǫɘɿ ᴎɿɘƚꙅɒɘʜƚuoꙅ ɘʜƚ ᴎi ɘƚɒƚꙅ ƚꙅomᴎɿɘʜƚuoꙅ ɘʜƚ ꙅi ("ꙅɿɘwo|Ꮈ Ꮈo bᴎɒ|" ɿoᎸ ʜꙅiᴎɒqꙄ) (ᴎɘƚꙅi| bᴎuoꙅ ꙅiʜƚ ƚuodA) /əbɪɿa|Ꮈˈ/ ɒbiɿo|ꟻ .ɘƚɒmi|ɔ |ɒɔiqoɿƚ ɒ ʜƚiw ɘƚɒƚꙄ .Ꙅ.U |ɒƚᴎɘᴎiƚᴎoɔ ʏ|ᴎo ɘʜƚ ꙅi bᴎɒ iiɒwɒH ꙅi ɘᴎo ɿɘʜƚo ɘʜƚ ,ɘƚɒmi|ɔ |ɒɔiqoɿƚ ɒ ꙅɒʜ ƚɒʜƚ ꙅɘƚɒƚꙅ owƚ ʏ|ᴎo Ꮈo ɘᴎo ꙅi ɒbiɿo|ꟻ .ɘƚɒƚꙅ ɘʜƚ Ꮈo ƚɿɒq ᴎɿɘʜƚuoꙅ ɘʜƚ ᴎi ʞɿɒꟼ |ɒᴎoiƚɒͶ ꙅɘbɒ|ǫɿɘvƎ ᴎi bᴎuoᎸ ɘd ᴎɒɔ ɘɘƚɒᴎɒm bᴎɒ ,ɿɘʜƚᴎɒq ɒbiɿo|ꟻ ,ɘ|iboɔoɿɔ ᴎɒɔiɿɘmA ,ɿoƚɒǫi||ɒ ᴎɒɔiɿɘmA ɘʜT [0].ʜƚuoꙅ ɘʜƚ ᴎi |ɒɔiqoɿƚ oƚ ʜƚɿoᴎ ɘʜƚ ᴎi |ɒɔiqoɿƚduꙅ moɿᎸ ꙅɘiɿɒv ɘƚɒmi|ɔ ɘʜT .ɘƚɒƚꙅ .Ꙅ.U ʏᴎɒ Ꮈo ƚᴎioq ʜǫiʜ ƚꙅɘwo| ɘʜƚ ꙅɒʜ ɒbiɿo|ꟻ .|ioꙅ ʏɿɒƚᴎɘmibɘꙅ ʏd bɘƹiɿɘƚɔɒɿɒʜɔ ꙅi bᴎɒ |ɘvɘ| ɒɘꙅ ɿɒɘᴎ ɿo ƚɒ ꙅi ɘƚɒƚꙅ ɘʜƚ Ꮈo ʜɔuM .ᴎɒɘɔO ɔiƚᴎɒ|ƚA ɘʜƚ bᴎɒ oɔixɘM Ꮈo Ꮈ|uᎮ ɘʜƚ ʜƚod ꙅɿɘbɿod ƚɒʜƚ ɘƚɒƚꙅ ʏ|ᴎo ɘʜƚ ꙅi ƚI .ꙅbᴎɒ|ꙅi ɿɘiɿɿɒd ʏᴎɒm ɘʜƚ Ꮈo ᴎoiƚudiɿƚᴎoɔ ɘʜƚ ǫᴎibu|ɔᴎi ƚoᴎ ,(mʞ 0,) ꙅɘ|im 0, ʏ|ɘƚɒmixoɿqqɒ ,ꙅɘƚɒƚꙄ bɘƚiᴎU ꙅuouǫiƚᴎoɔ ɘʜƚ ᴎi ɘᴎi|ƚꙅɒoɔ ƚꙅɘǫᴎo| ɘʜƚ ꙅɒʜ ɒbiɿo|ꟻ .ᴎɒɘɔO ɔiƚᴎɒ|ƚA ɘʜƚ bᴎɒ oɔixɘM Ꮈo Ꮈ|uᎮ ɘʜƚ ᴎɘɘwƚɘd ɒ|uꙅᴎiᴎɘq ɒ ꙅɘiquɔɔo ɒbiɿo|ꟻ Ꮈo ꙅbɿiʜƚ-owƚ ƚuodA .ɿɒW |iviƆ ᴎɒɔiɿɘmA ɘʜƚ ɿɘƚᎸɒ ᴎoiƚɒǫɘɿǫɘꙅ |ɒiɔɒɿ bᴎɒ ,ꙅᴎɒɔiɿɘmA ɘviƚɒͶ ɘʜƚ ƚꙅᴎiɒǫɒ ꙅɿɒW ɘ|oᴎimɘꙄ ɘʜƚ Ꮈo ᴎoiƚɒɔo| |ɒqiɔᴎiɿq ɒ ꙅɒw ƚI .8 ᴎi ꙅɘƚɒƚꙄ bɘƚiᴎU ɘʜƚ ᴎi booʜɘƚɒƚꙅ bɘᴎiɒǫ ƚi ɘɿoᎸɘd ꙅɿɘwoq |ɒiᴎo|oɔ ᴎɒɘqoɿuƎ ɘʜƚ ɿoᎸ ɘǫᴎɘ||ɒʜɔ ɒ ꙅɒw ɒbiɿo|ꟻ – []ɒbiɿo|ꟻ ɒuɔꙅɒꟼ ,ᴎoꙅɒɘꙅ ɿɘƚꙅɒƎ ɘʜƚ ᴎi ɘɿɘʜƚ ǫᴎibᴎɒ| ᴎoqu ("ꙅɿɘwo|Ꮈ Ꮈo bᴎɒ|" [ɒðiɾˈo|Ꮈ ɒ|]) ɒbiɿo|ꟻ ɒ⅃ ƚi bɘmɒᴎ oʜw – ᴎòɘ⅃ ɘb ɘɔᴎoꟼ ᴎɒuႱ ɿɘɿo|qxɘ ʜꙅiᴎɒqꙄ ʏd ᴎi ɘbɒm ꙅɒw ƚɔɒƚᴎoɔ ᴎɒɘqoɿuƎ ƚꙅɿiᎸ ɘʜƚ ɘɔᴎiꙄ .ꙅɘɘɿiƚɘɿ ɿoᎸ ᴎoiƚɒᴎiƚꙅɘb ɿɒ|uqoq ɒ ꙅɒ bᴎɒ ,ɿɘƚᴎɘƆ ɘɔɒqꙄ ʏbɘᴎᴎɘ⋊ ɘʜƚ ,ꙅqoɿɔ ɘǫᴎɒɿo ,ꙅʞɿɒq ƚᴎɘmɘꙅumɒ ɿoᎸ bɘᴎwoᴎɘɿ oꙅ|ɒ ꙅi ɒbiɿo|ꟻ .ʏɿuƚᴎɘɔ ʜƚ9 ɘƚɒ| ɘʜƚ ᴎi bɘqo|ɘvɘb ʜɔiʜw ,ᴎoiƚɒƚɿoqꙅᴎɒɿƚ bᴎɒ ,ɘɿuƚ|uɔiɿǫɒ ,mꙅiɿuoƚ ᴎo ʏ|ᴎiɒm ꙅɘi|ɘɿ ʏmoᴎoɔɘ ꙅ'ɘƚɒƚꙅ ɘʜT .ꙅɘuꙅꙅi |ɒƚᴎɘmᴎoɿivᴎɘ ǫᴎiꙅɒɘɿɔᴎi ꙅƚi ɿoᎸ ꙅɒ ||ɘw ꙅɒ ,ʜƚwoɿǫ ᴎoiƚɒ|uqoq ʜǫiʜ bᴎɒ ʏƚiᴎummoɔ ɘƚɒiɿƚɒqxɘ ᴎɒduƆ ɘǫɿɒ| ꙅƚi ɿoᎸ ɘviƚɔᴎiƚꙅib ꙅi ɒbiɿo|ꟻ ,ʏɒboT .ꙅƚɿoqꙅ ɿɘƚɒw bᴎɒ ǫᴎiɔɒɿ oƚuɒ ,ꙅiᴎᴎɘƚ ,Ꮈ|oǫ ɿoᎸ ᴎwoᴎʞ ʏ||ɒᴎoiƚɒᴎɿɘƚᴎi ꙅi ƚI .ꙅɘƚɘ|ʜƚɒ bᴎɒ ꙅɘiƚiɿdɘ|ɘɔ ƚɔɒɿƚƚɒ oƚ ꙅɘuᴎiƚᴎoɔ bᴎɒ ,ꙅmɒi||iW ɘɘꙅꙅɘᴎᴎɘT bᴎɒ ʏɒwǫᴎimɘH ƚꙅɘᴎɿƎ ,ꙅǫᴎi|wɒЯ ᴎɒᴎᴎi⋊ ɘiɿoꞁɿɒM ꙅɒ ʜɔuꙅ ꙅɿɘƚiɿw ʏᴎɒm bɘƚɔɒɿƚƚɒ ꙅɒʜ ɒbiɿo|ꟻ .ɘᴎiꙅiuɔ bᴎɒ ɘɿuƚɔɘƚiʜɔɿɒ ɘʜƚ ᴎi bᴎuoᎸ ɘd ᴎɒɔ ꙅɘǫɒƚiɿɘʜ oᴎiƚɒ⅃ bᴎɒ ,ꙅuoᴎɘǫibᴎi ,ᴎɒɘqoɿuƎ ,ᴎɒɔiɿᎸA ɘɔᴎɒƚiɿɘʜᴎi ɘ|qiƚ|um bᴎɒ ꙅɘɔᴎɘu|Ꮈᴎi Ꮈo ᴎoiƚɔɘ|Ꮈɘɿ ɒ ꙅi ɘɿuƚ|uɔ ɒbiɿo|ꟻ
⣻⣻⣻⡏⠘⠃⠐⣻⠇⠟⠉⠉⠙⠁⣻⣻⣻⣻⢿⣻⡿⠀⠀⣻⣻⣻⡇⢸⣻⣻ ⣻⣻⣻⠁⠀⣀⣀⣉⣀⡀⠀⠀⠀⠀⠙⠛⠻⡿⢺⡟⠁⠤⢶⣻⣻⣻⣇⡿⠀⣻ ⣻⣻⡿⢴⠞⠋⠉⠉⢿⣻⣻⣦⡀⠀⠀⠀⠀⠀⠋⠀⠀⠀⡼⠛⠻⠿⠚⠀⠀⣻ ⣻⣻⡇⠸⣄⠀⠀⠀⠘⠿⡿⠟⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⣻ ⣻⡿⡇⠀⠈⠛⠛⠛⠓⠦⠤⡀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢲⣻⣻⡿⠛⠻⣶⣴⠏ ⣻⠃⠩⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡸⠀⠀⢈⣉⣉⡀⠀⠀⣸⡿⠛ ⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠈⠉⠚⠋⠀⢨ ⡿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣻ ⡇⠀⠙⠳⠤⠄⠀⠀⠘⣦⣤⣤⢒⣺⣭⣙⣒⠒⢄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣻ ⣧⠀⠀⠀⠀⠀⠀⠀⠀⢹⣻⣻⣻⣻⣻⣻⣻⣻⣆⣷⡴⠂⠀⠀⠀⠀⠊⠁⣼⣻ ⣻⣧⠀⠀⠀⠀⠀⠀⠀⠀⣻⠋⠀⠉⠻⣻⠋⠉⣻⡿⠁⠀⠀⠀⠀⠀⠀⣼⣻⣻ ⣻⣻⣷⣄⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⣻⠀⠀⢿⠁⠀⠀⠀⠀⠤⣤⣾⣻⣻⣻ ⣻⣻⣻⣻⣷⣤⡀⠀⠀⠀⣾⣡⡀⠀⠀⢻⡀⠀⢸⠇⠀⠀⣀⣤⣾⣻⣻⣻⣻⣻ ⣻⣻⣻⣻⣻⣻⣻⣶⣄⠀⠀⠁⠙⢦⣄⠈⠁⠀⣼⣀⣴⣾⣻⣻⣻⣻⣻⡿⠟⠋ ⠀⠀⠀⠉⠉⠑⠚⠭⣍⡑⠢⢀⠀⠀⢹⠀⢀⣼⣻⣻⣻⣻⣻⣻⣻⠟⠋⠀⠀⠀
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˗ˏˋ ♡ ˎˊ˗ ➫ noel *ੈ♡⸝⸝🪐༘⋆zepeto🐬🌺🌊🦩⚡️🌴🐚🦜🌺🥥☀️𓆉︎𓆉︎
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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⢀⣴⠟⠉⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣀⢀⣾⠿⠻⢶⣄⠀⠀⣠⣶⡿⠶⣄⣠⣾⣿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢻⣿⣿⡿⣿⠿⣿⡿⢼⣿⣿⡿⣿⣎⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠉⠛⢛⣛⡉⠀⠀⠙⠛⠻⠛⠑⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣧⣤⣴⠿⠿⣷⣤⡤⠴⠖⠳⣄⣀⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣀⣟⠻⢦⣀⡀⠀⠀⠀⠀⣀⡈⠻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠉⡇⠀⠀⠛⠛⠛⠋⠉⠉⠀⠀⠀⠹⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⠀⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠈⠑⠪⠷⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣦⣼⠛⢦⣤⣄⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠢⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠲⠖⠛⠻⣿⡿⠛⠉⠉⠻⠷⣦⣽⠿⠿⠒⠚⠋⠉⠁⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣾⠛⠁⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⠀⠀⠀ ⠀⠀⠀⠀⣰⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀ ⠀⠀⠀⣰⣿⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣧⣄⠀⠀⠀⠀⠀⠀⢳⡀⠀ ⠀⠀⠀⣿⡾⢿⣀⢀⣀⣦⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⣫⣿⡿⠟⠻⠶⠀⠀⠀⠀⠀⢳⠀ ⠀⠀⢀⣿⣧⡾⣿⣿⣿⣿⣿⡷⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢿⣿⣧⠀⡀⠀⢀⣀⣀⢒⣤⣶⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⠀⡾⠁⠙⣿⡈⠉⠙⣿⣿⣷⣬⡛⢿⣶⣶⣴⣶⣶⣶⣤⣤⠤⠾⣿⣿⣿⡿⠿⣿⠿⢿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⣸⠃⠀⠀⢸⠃⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⠟⡉⠀⠀⠀⠈⠙⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⣿⠀⠀⢀⡏⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠛⠉⠁⠀⠀⠀⠀⠀⠉⠠⠿⠟⠻⠟⠋⠉⢿⣿⣦⡀⢰⡀⠀⠀⠀⠀⠀⠀⠁ ⢀⣿⡆⢀⡾⠀⠀⠀⠀⣾⠏⢿⣿⣿⣿⣯⣙⢷⡄⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣻⢿⣷⣀⣷⣄⠀⠀⠀⠀⢸⠀ ⢸⠃⠠⣼⠃⠀⠀⣠⣾⡟⠀⠈⢿⣿⡿⠿⣿⣿⡿⠿⠿⠿⠷⣄⠈⠿⠛⠻⠶⢶⣄⣀⣀⡠⠈⢛⡿⠃⠈⢿⣿⣿⡿⠀⠀⠀⠀⠀⡀ ⠟⠀⠀⢻⣶⣶⣾⣿⡟⠁⠀⠀⢸⣿⢅⠀⠈⣿⡇⠀⠀⠀⠀⠀⣷⠂⠀⠀⠀⠀⠐⠋⠉⠉⠀⢸⠁⠀⠀⠀⢻⣿⠛⠀⠀⠀⠀⢀⠇ ⠀⠀⠀⠀⠹⣿⣿⠋⠀⠀⠀⠀⢸⣧⠀⠰⡀⢸⣷⣤⣤⡄⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⢼⡇ ⠀⠀⠀⠀⠀⠙⢻⠄⠀⠀⠀⠀⣿⠉⠀⠀⠈⠓⢯⡉⠉⠉⢱⣶⠏⠙⠛⠚⠁⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⠀⠀⠀⠀⠀⠻⠄⠀⠀⠀⢀⣿⠀⢠⡄⠀⠀⠀⣁⠁⡀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⢀⣐⡟⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢠⡇
⠀⢀⠀⢀⣀⣠⣤⣤⣤⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣠⣤⣤⣤⣤⣀⠲⢦⣄⡀⠀⠀ ⡶⢟⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠰⣷⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣬⡛⢷⣔ ⣾⡿⠟⠋⠉⠁⠀⡀⠀⠀⠀⠀⠈⠉⠉⠙⠛⢻⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠈⠙⢛⣛⣛⣛⣛⣉⢉⣉⡀⠀⠀⠀⠀⠀⠈⠉⠛⢿⣷⣝ ⠃⠀⠀⠀⠀⠀⠀⣛⣛⣛⣛⣛⣛⢛⡛⠛⠛⠛⣰⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣌⠛⠛⢛⣛⣛⣛⣛⣛⣛⣛⣓⣀⠀⠀⠀⠀⠀⠈⢻ ⠀⠀⠀⢀⣤⡾⠛⢻⣿⣿⣿⡿⣿⡟⢻⣿⠳⠆⠘⣿⣦⠀⠀⠀⠀⠀⠀⠀⣰⣿⠁⠐⠛⣿⡟⢻⣿⣿⣿⣿⢿⣟⠛⠻⣦⣀⠀⠀⠀⠀ ⠀⠀⢴⠿⣧⣄⣀⣘⣿⣿⣿⣿⣿⡿⣀⡙⢷⠀⢀⡿⠁⠀⠀⠀⠀⠀⠀⠀⠈⢻⡖⠀⣾⣋⣀⣺⣿⣿⣿⣿⣿⣏⣀⣤⣴⠿⢷⠀⠀⠀ ⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠙⠉⠉⠉⠉⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠉⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠆⠀⠀⢀⣿⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⠟⠁⠀⠀⠀⣾⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣤⣤⣴⣶⣾⠿⠛⠋⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀
⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣧⣤⣄⣀⣀⣀⣤⠶⢺⠟⢛⠷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠰⠾⣷⠒⠒⣻⠿⠋⢡⠞⠁⡰⠋⣰⠛⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢻⡖⠋⠀⣠⠞⠁⢀⠞⠁⡴⠁⢰⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢻⣤⠞⠁⠀⡰⠋⢀⡜⠁⣰⠃⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠻⣦⣀⠞⠁⢀⡞⠀⣰⠃⢀⢿⡇⠀⠀⣀⣀⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠙⠲⠦⣯⣤⣴⣧⡤⠾⢾⡟⢛⡿⠋⣡⠋⢀⠞⢉⡿⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡷⠋⢀⡴⠁⣰⠋⢀⡞⠁⣤⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣠⠎⠀⡴⠁⣠⠏⢀⡞⠁⢀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⢠⠞⠀⡴⠁⡴⠋⣠⠞⣁⣹⣤⢤⡤⠤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣤⣎⣠⣞⣤⠾⠟⠛⠛⢻⠀⣸⠁⢠⠇⠀⣹⠻⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠇⢠⠏⢀⡴⠁⢀⡼⢻⣆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⢀⠏⢀⠞⢀⡴⠋⢀⣠⢿⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠎⡰⢋⡴⢋⣠⣶⣯⣿⣿⣿⠲⡶⢤⣄⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢾⣵⣯⠾⠿⠛⠉⠉⠫⣽⣿⢸⠁⢀⡞⠛⢶ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡌⢀⡞⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⢇⠞⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣛⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⣤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⢤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡼⠋⠀⣀⠄⡂⠍⣀⣒⣒⠂⠀⠬⠤⠤⠬⠍⠉⠝⠲⣄⡀⠀⠀ ⠀⠀⠀⢀⡾⠁⠀⠊⢔⠕⠈⣀⣀⡀⠈⠆⠀⠀⠀⡍⠁⠀⠁⢂⠀⠈⣷⠀⠀ ⠀⠀⣠⣾⠥⠀⠀⣠⢠⣞⣿⣿⣿⣉⠳⣄⠀⠀⣀⣤⣶⣶⣶⡄⠀⠀⣘⢦⡀ ⢀⡞⡍⣠⠞⢋⡛⠶⠤⣤⠴⠚⠀⠈⠙⠁⠀⠀⢹⡏⠁⠀⣀⣠⠤⢤⡕⠱⣷ ⠘⡇⠇⣯⠤⢾⡙⠲⢤⣀⡀⠤⠀⢲⡖⣂⣀⠀⠀⢙⣶⣄⠈⠉⣸⡄⠠⣠⡿ ⠀⠹⣜⡪⠀⠈⢷⣦⣬⣏⠉⠛⠲⣮⣧⣁⣀⣀⠶⠞⢁⣀⣨⢶⢿⣧⠉⡼⠁ ⠀⠀⠈⢷⡀⠀⠀⠳⣌⡟⠻⠷⣶⣧⣀⣀⣹⣉⣉⣿⣉⣉⣇⣼⣾⣿⠀⡇⠀ ⠀⠀⠀⠈⢳⡄⠀⠀⠘⠳⣄⡀⡼⠈⠉⠛⡿⠿⠿⡿⠿⣿⢿⣿⣿⡇⠀⡇⠀ ⠀⠀⠀⠀⠀⠙⢦⣕⠠⣒⠌⡙⠓⠶⠤⣤⣧⣀⣸⣇⣴⣧⠾⠾⠋⠀⠀⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⣭⣒⠩⠖⢠⣤⠄⠀⠀⠀⠀⠀⠠⠔⠁⡰⠀⣧⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⢤⣀⣀⠉⠉⠀⠀⠀⠀⠀⠁⠀⣠⠏⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠒⠲⠶⠤⠴⠒⠚⠁⠀⠀
⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣴⣿⣿⠿⣟⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣏⡏⠀⠀⠀⢣⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣟⠧⠤⠤⠔⠋⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⣿⡀⢀⣶⠤⠒⠀⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢹⣧⠀⠀⠀⠀⠀⠈⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠈⢿⣆⣠⣤⣤⣤⣤⣴⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣾⢿⢿⠀⠀⠀⢀⣀⣀⠘⣿⠋⠁⠀⠙⢇⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣾⢇⡞⠘⣧⠀⢖⡭⠞⢛⡄⠘⣆⠀⠀⠀⠈⢧⠀⠀⠀⠙⢿⣄⠀⠀⠀⠀ ⠀⠀⣠⣿⣛⣥⠤⠤⢿⡄⠀⠀⠈⠉⠀⠀⠹⡄⠀⠀⠀⠈⢧⠀⠀⠀⠈⠻⣦⠀⠀⠀ ⠀⣼⡟⡱⠛⠙⠀⠀⠘⢷⡀⠀⠀⠀⠀⠀⠀⠹⡀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠹⣧⡀⠀ ⢸⡏⢠⠃⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠸⣷⡀ ⠸⣧⠘⡇⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⣿⠇ ⠀⣿⡄⢳⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠈⠆⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀ ⠀⢹⡇⠘⣇⠀⠀⠀⠀⠀⠀⠰⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⣼⡟⠀⠀ ⠀⢸⡇⠀⢹⡆⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢳⣼⠟⠀⠀⠀ ⠀⠸⣧⣀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⢃⠀⢀⣴⡿⠁⠀⠀⠀⠀ ⠀⠀⠈⠙⢷⣄⢳⡀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⣠⡿⠟⠛⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠻⢿⣷⣦⣄⣀⣀⣠⣤⠾⠷⣦⣤⣤⡶⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠴⠶⠶⠶⠶⠶⢤⣤⡖⠻⢯⣛⣲⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⢁⡠⠤⠒⠒⠒⠊⠉⢹⠲⡜⠦⣄⡀⠻⡶⣶⠷⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⠴⠶⣶⣿⠛⠁⣠⠞⠁⠀⢀⡞⠙⣆⠠⣄⡾⠀⠈⢎⠳⡈⠉⠓⠊⠘⢦⣨⡳⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣏⠙⠦⠞⣁⠟⢠⠞⢹⡏⠳⣴⠊⠑⣄⠘⢆⠀⠉⠲⡀⠈⢦⠹⡄⠀⠀⠀⠀⠻⡵⡀⠫⣲⠒⢶⡄⠀⠀ ⠀⠀⠀⢀⣼⠒⠒⠋⠁⡴⠁⠀⣠⠟⢆⠘⢆⠀⠈⢦⠈⢣⠀⠀⠙⡄⠀⢳⣹⡀⠀⠀⠀⠀⢹⡘⡄⠙⣦⠀⠹⡄⠀ ⠀⠀⠀⣸⡥⠤⣀⢠⠎⠀⢠⠎⠁⠀⠈⢧⠀⢣⠀⠈⢇⠈⢇⠀⠀⢱⠀⠀⠱⡗⠀⠀⠀⠀⠀⢣⠘⡄⠹⣳⡤⠇⠀ ⠀⠀⣰⣿⠀⠀⠈⠙⣦⠀⠹⡄⠀⠀⠀⠈⢧⠈⡇⠀⠘⢆⢸⡆⠀⠈⡆⠀⢀⠧⠤⠤⠔⠶⣄⠈⡆⢱⠀⣧⢱⡀⠀ ⠀⢰⡿⢯⠀⠀⠀⠀⠘⡆⠀⠹⡄⠀⠀⠀⠈⠧⠷⠀⠀⠀⠉⠀⠀⠀⡇⢠⣯⠚⠉⠉⠉⠑⣾⡄⢇⠈⠧⢿⠀⢣⠀ ⠀⡼⣿⠀⠉⠲⣄⠀⠀⢻⠀⠀⣧⠀⢀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⣻⠏⠓⠒⠒⠒⠚⠒⠛⣧⣼⠒⠲⢿⠀⠘⡆ ⠀⡇⠘⡄⠀⠀⠘⡄⠀⠘⡆⢀⠼⠚⢉⡽⢦⡈⠉⠉⠉⠉⠉⠛⠛⠉⠉⢹⡏⠉⠉⠉⣉⣉⣉⣙⣯⣉⡁⢸⣴⠆⡇ ⢸⡇⠀⢹⡀⠀⢀⡇⠀⠀⣷⠁⠀⡴⠋⠀⠐⠛⠛⠛⠛⠛⠛⠛⢯⠹⢍⣉⣉⣉⣉⣉⣉⣈⣿⣿⠛⠊⡝⢸⡏⠛⡇ ⢸⡇⠀⠀⢳⠀⢠⠇⠀⠀⠙⠢⣜⢧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⣧⣼⣿⠀⡇ ⠈⠿⣄⠀⠀⢣⡘⠦⠤⠤⣀⠀⠈⠓⠬⣙⠲⣖⠒⡤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⣸⠀⡇ ⠀⠀⠈⠙⠒⠤⣇⡘⠓⣤⢸⡀⠀⠀⠀⠈⠙⠪⣗⣮⣛⢷⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏⣠⠇⣰⠃ ⠀⠀⠀⠀⠀⢀⣠⢿⠁⣸⡻⢽⡒⠦⣄⠀⠀⠀⠀⠉⠺⣷⢽⣯⡢⡀⠀⠀⠀⠀⣀⣀⣀⠀⣠⣔⡵⢁⠞⠁⣰⡇⠀ ⠀⠀⠀⠀⢰⠏⢻⣀⠑⠦⣝⡳⣄⠸⣄⠳⣄⠀⢠⣶⢤⡌⢣⡳⡽⣽⣟⠯⠭⢉⣉⣉⡬⣽⣿⠏⡰⠋⢀⠜⠉⡇⠀ ⠀⠀⠀⠀⣾⠀⢠⠏⡳⣄⡀⠙⢮⣦⢙⢿⣯⣳⡘⠫⠞⣃⡀⠱⡜⢮⢿⡉⠒⠒⠚⠒⢺⣿⠃⡜⠁⡴⠁⠀⠀⡇⠀ ⠀⠀⠀⠀⠸⢦⣸⣸⢡⠏⡟⣦⠀⠹⣷⢾⢿⣞⢿⣦⣾⣉⣹⠂⠘⡎⢿⣇⠀⠀⠀⠀⣿⠃⡸⠁⡞⠀⣰⣏⢸⠁⠀ ⠀⠀⠀⠀⠀⠀⠙⢻⣯⡸⣡⠋⣧⡀⠹⡖⠛⡵⣳⠀⢻⡈⠁⢀⡴⠃⢨⡿⠦⠤⠤⠴⢿⣠⠃⡸⠀⡄⢸⠃⡜⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣇⣞⡟⠱⡄⠹⡼⡆⢧⡇⠘⡷⠊⠁⠀⣴⠉⠀⠀⠀⠀⠀⢀⡿⠀⠧⣈⢢⠇⣸⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣀⡀⠈⢦⢙⣧⡼⠧⢤⣧⠀⠀⠀⠈⠉⠑⠒⠒⣒⠒⠉⠀⠀⠀⡞⡎⡰⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢯⣷⡦⠞⠉⠀⠀⠀⠀⠙⠲⣤⣠⠊⠉⠉⠉⢉⣷⠶⠊⠉⠉⠓⠚⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⢿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠈⠉⠛⢿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠘⢿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠀⠀⠀⠀ ⠀⠀⠀⠀⣀⣤⣶⣾⣿⡿⠿⠿⠿⠛⠛⠛⠛⠛⢿⣿⡿⠷⠶⢶⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣶⣶⣾⣿⣿⣿⡇⠀⠀⠀ ⠀⢀⣴⣿⣿⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠁⠀⠀⠀⢻⣿⣿⣿⣿⣿⠿⠋⠉⠀⠀⠀⠀⠈⠉⠉⠙⠛⠻⣿⣿⣷⠀⠀⠀ ⢠⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠃⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣇⠀⠀ ⣾⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠃⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⡆⠀ ⢿⣿⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⠋⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠂ ⠈⠻⣿⣿⣿⣆⣀⣀⡀⢀⣀⣠⣴⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠙⠛⠛⠛⠛⠛⠛⠋⠉⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⠿⠟⠛⠛⠉⠉⠉⠉⢹⣿⣿⣿⣿⣿⠷⢶⣤⣤⣤⣤⣶⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠈⠉⠙⠛⠿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣧⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣶⣶⣄⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⣿⣿⣿⣿⡟⠋⠀⠉⠈⠙⠿⣿⣿⣿⠁⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣾⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠹⣿⡿⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣟⠁⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⣿⠥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢻⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢻⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⣦⣄⣀⣀⣀⣀⣀⣤⣴⣶⣿⣿⡟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠛⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣶⣶⣿⣷⣆⠀⠀⠀⠀ ⠀⠀⠀⢀⣤⣤⣶⣶⣾⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⡆⠀⠀⠀ ⠀⢀⣴⣿⣿⣿⣿⣿⣿⡿⠛⠉⠉⠀⠀⠀⣿⣿⣿⣿⣷⠀⠀⠀ ⣠⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⢤⣶⣾⠿⢿⣿⣿⣿⣿⣇⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠈⠉⠀⠀⠀⣿⣿⣿⣿⣿⡆⠀ ⢸⣿⣿⣿⣏⣿⣿⣿⣿⣿⣷⠀⠀⢠⣤⣶⣿⣿⣿⣿⣿⣿⣿⡀ ⠀⢿⣿⣿⣿⡸⣿⣿⣿⣿⣿⣇⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣧ ⠀⠸⣿⣿⣿⣷⢹⣿⣿⣿⣿⣿⣄⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⢻⣿⣿⣿⡇⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠘⣿⣿⣿⣿⠘⠻⠿⢛⣛⣭⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⢹⣿⣿⠏⠀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋ ⠀⠀⠀⠈⣿⠏⠀⣰⣿⣿⣿⣿⣿⣿⠿⠟⠛⠋⠉⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⡿⠿⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠛⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣠⣤⣴⡶⠶⠤⠤⢼⣿⢤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣴⣧⠀⠀ ⠀⣠⣾⡟⠋⠁⠀⠀⠀⠀⠀⣼⠏⠀⠀⢻⣿⣿⣟⠉⠁⠀⠀⠉⠉⠉⠻⣿⡄⠀ ⢰⣿⣿⠀⠀⠀⠀⠀⠀⠀⣴⠏⠀⠀⠀⢸⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡀ ⠈⢿⣷⣄⠀⠀⠀⢀⡠⠞⠁⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁ ⠀⠀⠉⠛⠛⠛⠉⠉⠀⠀⣀⣤⣤⠤⠤⣼⣿⣿⣇⡀⠀⠀⢀⣴⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⡶⠋⠁⠀⠀⠀⠀⢸⣿⣿⡏⠉⠙⠛⠻⢿⣿⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠉⠷⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣤⣶⣶⣶⣤⡀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣴⣿⡿⠟⠛⠿⣿⣿⡆⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⣿⠟⠀⠀⠀⠀⠈⣿⠇⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⣾⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠻⣄⡀⠀⠀⠀⠀⠀⢀⣰⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠙⠒⠒⠶⠶⠾⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⣿⠛⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣰⣟⣿⣿⣳⠈⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣠⡶⠛⠋⠁⠀⠀⠀⠀⠀⠈⠙⠛⠶⣄⣀⣤⢴⢤⣤⡀⠀⠀⠀ ⠀⠀⠀⢀⣴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣦⣅⢹⡇⠀⠀⠀ ⠀⠀⣠⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣼⠇⠀⠀⠀ ⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀ ⠀⣸⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠶⣤⡀ ⢠⡇⠀⢰⣾⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣶⡀⠀⠀⠀⠀⠀⢸⡆⣼⡏ ⢸⡇⢀⠾⢿⣿⠿⠃⠀⣤⣀⣀⣀⣤⡄⠀⠘⢿⣿⡿⠓⣆⠀⠀⠀⠀⢸⡟⠋⠀ ⠈⢳⠈⠓⠚⠃⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠙⠒⠚⠋⠀⠀⠀⠀⣼⠀⠀⠀ ⠀⠸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠟⣷⡀⠀ ⠀⠀⠘⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⡧⠶⠟⠀⠀ ⠀⠀⠀⠀⠉⠳⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡴⠞⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣹⠉⠛⡖⠶⠶⠶⢶⡶⠚⠉⣿⡿⠀⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⡿⢤⣀⣹⡆⠀⠠⣿⣁⣠⡆⠛⣷⡦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣸⣱⢶⣼⣍⠀⠀⠀⣩⣿⡵⣧⡀⣿⣷⣤⣤⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢿⡉⣨⣤⢸⠆⠀⠀⣏⠠⣄⡉⣿⣿⠀⢈⣹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠳⣼⣥⣿⣀⣀⣀⣹⣄⣫⡿⠿⠓⠚⠛⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⡇ ⠀⠀⠀⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠉⠉⠉⠉⠉⠉⠉⠛⠿⣿⣿⣿⣿⡇ ⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣧ ⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿ ⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠋ ⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣤⣤⣤⣤⣴⣶⣿⣿⣿⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠛⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢀⣠⣴⡖⠒⠒⢶⡒⠒⢤⡴⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣾⣋⠀⠄⢀⣉⡦⠴⠓⠒⠲⠇⠀⡿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡾⢁⡤⠒⠒⣶⠋⠀⠀⠀⠀⠀⠀⣴⠁⣇⠀⠀⢀⡀⣠⠖⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⢸⠀⠀⢠⠇⢀⡴⣤⣄⠀⠀⠀⠀⢸⠸⡀⢠⢋⡟⠁⡼⣁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢱⠘⡄⠀⠈⡇⠘⣟⢸⣏⢳⣶⣦⠀⡞⠀⣧⣏⣈⢀⡼⠋⢁⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠳⡘⢄⣀⡼⠀⠹⢿⣿⡿⠀⢀⡜⠀⢸⣿⠃⣼⡊⢀⣔⡁⠀⢀⡤⠔⠒⠒⠒⠶⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠹⣎⠻⡳⠴⠀⣀⠀⣤⢶⠎⠀⣠⡿⡏⠐⢁⠟⣁⣤⣿⣚⡁⠤⠤⠄⣀⠀⠀⠀⠙⢦⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⢷⡜⢄⠀⡹⠀⡶⠃⣠⢞⠟⢰⠃⢰⣟⡿⢨⣽⡯⠔⠒⠒⢤⡀⠀⠙⢢⡀⠀⠈⣇⠀⠀⠀⠀⠀⠀ ⠀⣴⡶⢦⢈⢿⠈⣄⡇⡼⢁⠞⡱⠃⠀⡎⠀⢉⣥⡀⠋⣀⡇⠀⠀⠀⠀⠱⡀⠀⠀⢱⠀⠀⢸⡀⠀⠀⠀⠀⠀ ⠀⢿⡳⠤⠊⢸⢀⡝⢠⡷⢃⠜⠀⠀⡜⡀⠀⢧⠈⠛⠲⢽⠇⠀⠀⠀⠀⠀⡇⠀⠀⢠⠇⠀⡞⡇⠀⠀⠀⠀⠀ ⠀⠀⠉⠒⠒⠛⠉⠀⢸⠃⡌⠀⠀⡜⠀⣷⠒⠺⡷⢄⠀⠚⢢⠀⠀⠀⠀⢠⠇⠀⠀⡞⢀⡜⢸⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⡇⠀⢸⡇⠤⣼⠀⠀⠘⡌⢣⠀⠀⢧⠀⠀⢀⡞⠀⢀⠌⡠⠊⠀⡞⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡀⣓⡾⠛⡆⠀⠀⢣⠀⡇⠀⠘⡄⢠⠎⠀⣠⣣⠊⠀⣠⠞⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢃⠏⠀⠀⢀⠇⠀⠀⡇⢀⠇⠀⠀⣧⡏⠀⣰⡟⢡⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡏⠀⠀⠀⣼⠀⠀⢸⣤⠞⠀⠀⢀⡿⡄⢠⠻⡅⠈⠓⠒⠒⠒⣒⣺⣯⣑⢲⣄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠈⠓⠳⠽⠦⠤⠒⠊⠁⠀⠀⠀⠀⠙⣿⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⠉⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠋⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⡼⠇⠀⠀⠀⠘⡆⠀⠀⠐⠀⠀⠀⢀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠓⠢⢼⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⣠⠎⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠈⣇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⢀⡼⡇⠀⠀⠀⠀⠀⠀⢸⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⢠⠞⠀⢹⡄⠀⠀⠀⠀⠀⠘⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⣰⠁⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⢹⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⡴⠃⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⡇ ⠀⠀⠀⠀⠀⠀⠀⢰⠋⠀⠀⠀⠀⠀⠀⢀⡾⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⢸⡁⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⡇ ⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⡿⣯⡷⡴⢦⣤⡠⣶⡶⠀⢷⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⡾⠀ ⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⣼⣥⣤⣤⣤⣤⣤⣤⣤⣀⣀⣀⣀⠀⠈⢧⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢀⡇⠀ ⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠉⠙⠻⢿⣿⣿⣿⣿⣿⣿⠛⢦⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⡇⠀ ⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⠳⠀⢳⡀⢹⡇⠀⠀⠀⠀⠀⡾⡇⠀ ⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡿⠘⠀⠀⠹⣼⡇⠀⠀⠀⠀⢠⠇⠀⠀ ⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡿⠁⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⡾⠀⠀⠀ ⠀⠀⢠⡏⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠁⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⢸⠁⠀⠀⠀ ⠀⠀⡾⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⡟⠀⠀⠀⠀ ⠀⣴⠓⣾⣳⣀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠃⠀⠀⠀⠀⠀⠀⢸⡇⢀⠇⠀⠀⠀⠀ ⣾⠃⠀⠀⠀⠑⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠈⡇⢸⠀⠀⠀⠀⠀ ⠹⡀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣾⠀⠀⠀⠀⠀ ⠀⢳⡄⠀⠀⠀⠀⠘⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⣿⠀⠀⠀⠀⠀ ⠀⠀⣷⡄⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⡏⠀⠀⠀⠀⠀ ⠀⢀⡇⢹⣄⠀⠀⠀⠀⣀⠉⠓⠶⢄⡀⠀⠀⠀⠀⠀⢀⣠⠴⠋⠣⣄⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⣸⣧⠀⠀⠀⠀⠀ ⠀⣴⣿⠋⠘⣆⠀⢰⠶⠤⢍⣛⣶⠤⠿⣷⣦⡀⠒⠚⡟⠀⠀⠀⠀⠈⠛⠢⠤⡄⠀⠀⢀⡴⢯⠴⣳⠇⠀⠀⠀⠀⠀ ⠀⠀⠉⠀⠀⠘⢦⡈⠻⣖⠤⣤⣉⣉⣹⣯⣭⠉⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠛⣫⣼⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠑⣄⠉⢦⡀⠀⠀⠈⠉⠁⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢿⣷⢚⡝⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢶⣷⠇⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠷⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⠏⢠⣶⣿⠿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⣤⣴⠾⠟⢩⣿⣯⣾⠟⠁⠀⠀⠀⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠟⠁⠀⠀⠀⠀⢀⣼⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⣿⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⢋⣠⣀⣀⣀⣠⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⣿⡿⠙⠟⠛⠻⢿⣿⣿⡅⠀⢀⣀⣄⣀⣀⣠⡀⠀⠀⢠⡆⠀⠀⢀⡄⠀⠀⣾⡏⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣀⣠⣤⣾⣿⣅⣀⠀⠀⠀⠀⠈⢿⣽⡄⠹⣿⡟⠛⣿⡿⠁⠀⣼⡟⠁⠀⢠⣿⠇⠀⢀⣿⣶⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀ ⢀⣴⡾⠛⢋⣿⡟⠛⠛⠿⣿⣶⣄⠀⠀⠈⣿⣿⣠⡿⠃⣰⡿⠁⠀⣼⡿⠀⠀⢠⣿⠏⠀⠀⣼⣿⣿⠿⠛⣿⣧⡀⠀⠀⠀⠀⠀ ⣾⡟⠀⠀⠸⠟⠀⠀⠀⠀⠈⠻⣿⣷⡀⠀⣿⡿⠋⠀⢰⣿⠃⢀⣴⣿⣷⣤⣴⣿⣿⣀⣤⣾⣿⡿⠁⠀⠀⠸⣿⣿⣦⣄⣀⣀⡄ ⣿⣷⡀⠀⣀⣤⣤⣤⣤⣤⣤⣄⣸⣿⣿⣿⡟⠀⠀⠀⠸⣿⣿⠟⠋⠈⠛⠛⠋⠹⠿⠿⠿⠛⠿⠃⠀⢀⣀⣠⣬⣿⣿⣿⠿⠋⠀ ⠘⢿⣿⣿⣿⣯⣵⣶⣶⡾⠿⠟⠛⠻⠿⣯⣀⡀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠾⠛⠋⠉⠉⠀⠀⠉⢻⣆⠀ ⠀⢸⡏⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠀ ⠀⠈⢳⣄⠀⠀⠀⠀⣠⣴⡾⠿⠟⠛⠷⠦⣤⣄⡀⠀⠉⠙⠛⠿⢷⣶⣤⣄⣠⣴⡟⠋⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⡾⠟⠋⠀⠀ ⠀⠀⠀⠉⠳⢶⣴⣿⣏⣥⡤⠀⠀⠀⠀⠀⠀⠀⠙⠳⢦⣄⡀⠀⠀⢀⣽⡿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣼⡿⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣶⣾⡟⠁⠀⠀⠀⠀⠀⣠⢴⠿⠟⠛⠛⠶⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⢿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣴⠾⠛⠉⠙⠻⢷⣦⣄⣀⣴⡯⠋⠁⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠲⠶⠶⠶⠶⠿⠟⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⠛⠳⠶⠶⠶⠶⠶⠶⠿⠟⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠿⠛⠛⠛⠲⠦⣄⡀⠀⠀⠀⢀⣴⡿⠋⠀⢀⣠⣤⣶⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠁⠀⠀⠀⠀⠀⠀⠀⠙⢲⣤⣶⠟⠋⠀⣠⣶⠿⠋⠁⠀⣠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⢤⣤⣤⣤⣤⣴⠶⠿⠛⠉⠉⢓⡶⣾⣯⣥⣤⣤⣴⡾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⢿⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⡿⣽⣻⡽⢯⡿⣽⣫⡟⣽⣫⢟⣽⢫⡟⣽⢫⡟⣭⡻⣭⢻⡭⢯⡽⣭⢯⡽⣭⠻⣜⡣⢟⣜⡣⢟⡜⣣⢛⡜⣣⢛⡜⣣⢏⡼⣡⢏⡼⣡⢏⡼⣡⢏⡼⡱ ⣿⣷⣻⣟⣾⣳⢿⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⡷⣯⣟⡷⣯⡽⣯⢷⣏⡷⣽⣣⢯⣟⢮⣯⢽⣚⡷⣹⢧⣻⡜⣧⣛⢧⡻⣜⢮⡳⣭⢻⡔⣏⡳⢎⡝⢮⠼⣱⢫⠼⣱⢫⡜⡱⢎⠶⡱⢎⠶⡱⢎⠶⡱⢎⠶⣙ ⣿⢿⣽⡾⣷⣟⣯⢿⡾⣽⣻⢾⣽⣻⢾⣽⣻⢾⣽⣻⣞⣯⣟⣾⣳⣟⣾⣳⣟⣾⣳⣟⣾⣳⣟⣾⣳⣟⣾⣽⣻⢾⣽⣻⢾⣽⢾⣯⢷⣟⣾⣳⣟⣾⣳⣟⣾⣳⣟⣾⣳⢯⣟⡷⢯⣟⡷⣻⣵⡻⣾⣱⢷⣫⠷⣞⢯⡞⣧⢟⡼⣏⢷⣣⢟⡵⣫⢞⡽⣎⢷⡹⣞⢣⡞⣱⢭⡛⡼⣙⡞⣥⣋⢗⣣⠳⣜⡹⢎⡳⣙⢎⡳⣙⢎⡳⣙⢮⡹⣒ ⣿⣯⣷⢿⣳⣯⣟⣯⡿⣽⢯⣿⢾⣽⣻⢾⣽⣻⣞⡷⣯⢷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⢯⣷⣟⡿⣞⡿⣞⣯⡿⣞⣷⣻⣞⣷⣻⣞⣷⣻⣾⣽⣿⣾⣿⣿⣾⣿⣷⣿⣷⣯⣟⣾⣭⢿⡹⣾⣹⢮⣏⢷⣫⢞⡵⣫⢷⡹⣎⢷⡹⣎⠷⡭⢮⡕⣏⠶⣹⢱⢣⠞⡴⣩⠞⡴⣋⠶⣙⢮⡱⣍⢮⡱⣍⢮⡱⡍⢶⣑⢣ ⣿⡾⣽⡿⣽⡾⣽⣳⡿⣯⣟⣾⣻⢾⣽⣻⣞⡷⣯⢿⡽⣯⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⢾⡽⣟⣾⣽⣻⡽⣟⣯⣷⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣧⣛⡾⣼⢣⡟⣮⢳⡝⣮⢳⡝⣮⠳⣭⢛⡼⢣⢞⡬⡳⣍⢎⢧⡛⡴⢣⡛⡴⣍⢞⡱⢎⡵⣊⠶⡱⢎⡖⣱⡙⢦⡍⡖ ⣿⣻⣽⣟⡷⣟⣯⡷⣟⡷⣯⢷⣻⣟⣾⣳⢯⡿⣽⢯⣟⡷⣯⢷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⢾⡽⣯⣟⣯⡷⣯⣷⣟⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣵⣫⢞⡵⣏⢾⡱⢯⡞⡵⣛⢦⣛⡼⣍⠾⣰⠳⡜⣎⠶⡹⣜⢣⡝⡲⣍⢮⡱⢫⠴⣩⠞⣡⠳⡜⡥⣚⢥⡚⡜ ⣿⣽⣳⣯⣟⣯⡷⣟⣯⢿⡽⣯⢷⣻⢾⡽⣯⢿⣽⣻⢾⣽⣻⢯⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⢾⡽⣯⢿⡽⣞⣯⢿⣳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣞⡽⢮⡝⣧⡛⣵⡩⢖⣣⠞⣬⠳⣥⢛⡼⣌⢳⡱⢎⢧⡚⡵⣊⠶⣉⢧⢛⡤⣛⠴⣋⠼⡱⡜⣆⢧⡙ ⣿⢾⣽⡾⣽⣳⣟⣯⣟⣯⢿⡽⣯⣟⣯⢿⣽⣻⢾⣽⣻⢾⣽⣻⡞⣷⣻⣞⣷⣻⣞⣷⣻⢾⡽⣯⢿⡽⣯⣟⣯⣟⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣣⢟⠶⣙⢦⡛⡵⢪⡝⢦⡛⡴⣋⠶⣩⢖⡹⢎⠶⡹⠴⣩⠞⡱⢎⡣⠞⡴⢋⡼⣡⠣⡵⣈⠦⣙ ⣿⢯⣷⣟⣯⡷⣯⣷⣻⣞⣯⣟⣷⣻⣞⡿⣾⣽⣻⢾⡽⣻⡞⣷⡻⢷⣛⣾⣳⣟⣾⣳⣯⡿⣽⢯⡿⣽⣳⣟⡾⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣟⣿⢻⡽⢺⡝⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣎⢯⡹⣆⠻⣜⢣⠞⣥⢛⡴⣩⢞⡱⢎⡵⢋⡞⣱⢋⠶⣉⠷⡩⢞⡱⣘⠣⢖⡡⢓⡴⣉⠖⣡ ⣿⣻⢷⣻⡾⣽⢷⣯⢷⣻⢾⡽⣞⡷⣯⣟⣷⣳⢯⣟⢾⣳⢟⣳⣟⣯⣟⣾⣳⡽⣞⡷⣯⢿⡽⣯⣟⣷⣻⣞⣿⣿⣿⡟⢥⠲⡝⣾⣟⣿⣿⣻⣿⣟⣿⣯⢿⣞⣷⣻⣽⣚⠷⣘⢧⡚⡕⢦⢫⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣲⢣⡭⢳⢬⢣⡛⡴⣋⠶⡱⢎⡵⢋⡜⣣⠞⡥⢫⡜⡱⢎⡱⢎⠴⢣⡙⢦⡙⢦⠱⣌⠚⡤ ⣿⣽⣻⢷⣻⢯⣟⡾⣯⣟⣯⢿⣽⣻⢷⣻⢮⣽⣳⢯⣻⣭⡟⣷⣞⣳⣞⡷⣯⢿⡽⣽⣏⣯⣟⣷⣻⣞⣷⣻⣿⣿⠫⠄⣉⣳⣽⣼⣿⣿⣿⢿⣟⣿⢯⣟⡿⣞⣷⡳⢞⡜⢢⠏⡖⡩⢞⡥⣛⣞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢣⢞⡱⢎⢧⡙⢶⡩⢞⡱⣋⠶⣩⠞⣡⠞⣱⠣⡜⡱⢊⠖⡩⢎⡱⡘⠦⡑⢎⡱⢌⡓⡔ ⣿⢾⣽⣻⣯⢿⣽⣻⢷⣻⣞⣯⢷⡯⣟⣞⡿⣼⢏⣯⢷⣳⣻⣳⣞⢷⣫⣟⡷⣯⣟⢷⣻⢮⡽⣞⣷⡻⣞⣿⣿⠁⠳⢾⣧⣽⣞⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⡿⣿⡝⣮⢞⡳⣎⠳⡵⢊⡴⢻⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢮⠳⣍⠶⣙⢦⡙⣎⠵⣊⠗⡱⢎⡱⣊⠥⡓⣬⢱⡉⢎⡱⢊⠴⣡⠣⣙⠢⡑⠦⡱⢌ ⣿⢯⣟⡷⣯⣟⣾⡽⣯⢷⣻⣞⣯⣽⣻⣼⣛⣾⣛⡾⣏⡷⣏⡷⣞⣯⢷⢯⡽⣶⢯⣛⣧⢿⡽⣳⢾⣽⣻⣿⠃⢉⡷⣿⣹⢯⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣯⡿⣯⢟⡞⣞⡳⣜⣫⡑⠳⠾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢌⡳⢬⢳⡩⢖⡹⡸⡜⡡⢏⡕⢎⡱⣉⠖⡱⢢⠱⡘⠦⡑⣍⠲⢄⠳⣄⢣⡙⢆⡱⢊ ⣿⣯⢿⡽⣷⣻⣞⡿⣽⢯⣷⣻⢮⢷⣳⣳⠿⣜⣯⢷⣏⡿⣽⣹⢯⣞⣯⢯⣟⡾⣽⣛⣾⣫⡽⢯⣷⣫⣿⡟⢠⣯⣄⢿⣿⣿⣿⡧⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡱⢦⡝⢳⡒⠦⡄⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣎⡱⣋⠶⣙⢎⡵⢱⠱⣙⠲⡘⢎⡱⢌⢎⡑⢣⠱⣡⢣⡑⠦⡙⣌⢃⢆⠣⡜⠢⣅⠣ ⣿⣞⣿⡽⣷⢯⡿⣽⣻⣟⡶⣯⢟⣯⣗⡯⣿⠽⣞⣯⢾⣝⡧⣟⡧⢿⣜⡯⢾⡽⣞⡽⣶⢏⣿⣛⡶⣯⣿⠇⠿⢱⣿⢸⣿⣿⣡⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣎⠧⡝⢲⠱⣌⡠⢘⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠳⣍⢞⡱⢎⠴⣋⢜⣢⡙⡱⢣⠜⡌⠦⣙⢂⠳⡐⠦⣑⢣⠱⡌⠎⡜⢢⡑⢣⠆⢣ ⣿⡾⣽⣻⡽⣯⣟⣷⣻⠾⣝⣳⣟⣞⡾⣽⢞⡿⣽⣺⣝⣮⡽⣞⡽⣏⡾⣝⣯⠾⣽⣹⢞⣟⣮⢿⣱⢯⣿⠀⣐⡊⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣜⢣⠷⢤⡡⠉⠆⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡎⡵⣊⢮⡱⢍⡲⢩⡒⢤⢣⡑⢣⠚⢬⡑⢢⢍⠲⣉⠖⡡⢎⠱⡘⡜⣠⠣⣘⢂⢎⡡ ⣿⡽⣷⢯⣟⣷⣻⢾⣽⣻⡽⣳⢾⣝⡾⣭⢿⣹⢧⢷⢾⣱⡟⡾⣵⢏⣷⢻⡼⣻⡵⢯⣾⣹⢮⣯⣻⣿⣧⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣶⣭⡞⢣⢏⣬⡱⡌⢒⡠⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡜⢲⠍⣦⠱⡎⡜⣡⠚⡔⢢⡙⢢⡙⢦⡘⢥⢊⠵⡨⠜⡐⢎⠱⡐⢆⡡⢒⡡⢊⠴⡐ ⣿⣳⣟⡾⣽⢯⣟⡾⣽⣫⢷⣻⣞⣽⣳⣛⣞⢯⣞⠾⣼⢏⣷⡳⡽⣞⡽⣞⢧⡿⣱⠾⣭⡟⡾⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠾⢞⡩⣇⠣⠌⡑⢺⣿⣿⣿⣿⣿⣿⣿⣿⢟⣿⣿⣿⡑⢎⡴⢩⡒⢥⠣⣍⠲⣑⠪⡑⢎⡱⢨⠱⡌⢚⠤⢃⠲⡑⡌⢆⠓⡌⢃⠎⡱⠘⡄⢣ ⣿⡽⣞⡿⣽⣻⢾⣽⣳⢯⣟⡵⣞⣧⢷⡻⣼⢏⣾⢻⡽⣺⢧⢿⣹⢾⣹⡞⣯⠾⣝⡯⣗⢿⡿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣖⣿⢯⢀⢒⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡶⡷⣎⠷⣤⢓⡒⣩⢒⣿⣿⣿⣿⡟⡹⠋⢴⣆⡘⣿⣷⣏⢲⡘⢥⡙⢆⠳⣨⠱⠌⡥⣙⠢⣅⠣⢃⠍⡆⠣⠍⠦⡑⠌⡌⠱⡈⠆⡜⢠⠃⡜⢠ ⣿⡽⣯⣟⡷⣯⣟⡾⣵⣻⠾⣽⣻⡼⣳⢏⣷⢻⢮⣏⡷⣏⢿⡺⣽⣚⣧⢟⣧⢿⣹⢾⣹⢾⣹⢟⡿⢥⣼⣿⣿⣿⣿⣿⣿⣿⣿⢳⠚⡼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣭⡛⠿⡵⣉⠞⣩⠳⢦⡀⢎⣽⣿⣿⣿⣇⢠⣅⠮⠿⢿⠿⣿⣗⠦⣙⢢⡙⣌⠳⣄⠫⡜⡰⢡⠣⡔⢩⢊⠜⡰⢩⠘⡰⢁⠞⡄⢣⠑⡌⠔⡡⢊⠔⡡ ⣿⣽⣳⣯⣟⡷⣯⣟⣳⣽⢻⣳⣭⠷⣏⣟⡮⣟⡽⢮⣗⢯⡯⢷⡳⣏⣾⢫⣞⣳⢯⢾⣹⡞⣽⡞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡭⣇⡋⡔⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⢮⡓⢦⡙⣷⡳⣬⣦⢥⡛⣤⡙⣦⣿⣿⣿⣿⣏⣿⢸⣿⣿⣿⣿⣾⣿⡜⣌⠣⣜⠰⢣⢌⡱⢢⢙⣂⠳⢌⡡⠎⢆⡑⢢⠡⡑⢊⠴⡈⢆⠱⣈⠒⡡⠎⡰⢁ ⣿⣞⣷⣻⢾⣽⣳⢯⣷⢫⣯⢷⣚⣯⡽⣞⡵⣯⢽⡻⣼⣛⠾⣯⢽⡳⣽⢻⡼⣽⡺⣏⡷⣽⢣⣟⡞⣿⣾⣥⣿⣿⣿⣯⣿⡳⢷⡈⡑⠌⢠⡸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡽⣶⣍⢏⡞⣴⣙⣦⡹⢆⣿⣴⣽⣾⣿⣿⣿⣿⠐⡻⢷⢩⣿⣿⣿⣿⣿⡗⣨⠱⣌⠹⣂⠎⡔⢣⢌⠢⢃⠆⢢⠍⢢⠘⡄⢣⠘⣐⠢⡑⢌⠢⡁⢎⠰⡁⢆⠡ ⣿⢾⣳⣯⢿⡾⣽⣻⣼⣻⢞⣽⣹⢶⣻⢼⣻⢼⣳⡻⣵⣫⢟⡮⣗⣻⡼⣳⡽⣖⣻⡝⣾⡱⣟⢮⣽⡟⢻⣿⣿⣿⣟⣿⣯⢳⣦⣷⣶⣿⣿⢿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣼⣆⢳⣎⠿⣖⣾⣿⣾⣿⣿⣿⣿⣿⡀⣟⢈⣦⣹⣿⣿⢿⣿⠓⡤⢓⣌⢣⠱⡊⢜⡂⢎⡱⢊⡜⢄⠚⡄⢣⠘⡄⢃⠆⡱⢈⠆⡱⢈⠆⡱⢈⠄⡃ ⣿⢯⣟⡾⣯⣟⡷⣯⢶⣏⣟⡮⣗⣻⡼⣏⡾⡽⢶⡻⣵⢫⣾⡹⣞⡵⣫⢷⣹⢞⡵⣻⢖⣻⡝⣾⣿⠁⠰⠟⣿⣯⢸⣿⣯⡧⣴⣠⣴⣶⣦⣄⣳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⢿⣿⣿⣮⣷⣾⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣟⠃⢿⣿⠟⣽⣿⣿⠣⡙⡔⢣⠜⣢⠣⢍⠢⡙⢄⢢⠡⡘⢄⠣⡘⢄⠣⡘⢄⠊⡄⠣⡐⢄⠃⡔⢠⠃⡌⡐ ⣿⢯⡿⣽⣻⢾⡽⢯⡷⣞⢧⣟⣭⠷⣝⡾⣱⠿⣭⢗⣯⢳⡞⣵⡻⣼⣛⢮⡗⣯⡝⣧⡟⣧⢻⡞⣿⠀⠀⣦⣿⣿⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣹⢯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣠⣛⣷⠿⣫⣾⢃⠧⡱⡘⢥⠚⣄⠳⣈⠱⡈⢆⠢⡑⢌⠢⡑⢌⠢⡑⠰⡈⢆⠡⢃⠌⡂⠜⡠⢂⠅⢢⠁ ⣿⢯⣿⣳⣟⣯⣟⣯⠷⣏⡿⡼⣞⢯⣻⠼⣏⣟⢮⣻⡜⣯⢞⣳⡽⣣⢯⣳⢻⡼⣽⢲⡟⣼⡳⣏⢿⣆⠀⢿⣿⣿⣿⣯⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠶⢟⣿⢅⠺⡰⢡⡙⠤⢋⠤⠓⡄⢣⠘⡄⢣⠘⡄⢣⠘⠤⡑⢨⠑⠌⡄⢃⠢⡘⠄⡃⠔⣁⠊⡄⢃ ⣿⣻⣞⡷⣿⢮⡽⣞⣿⡹⣞⡽⣞⢯⣳⢻⡝⣮⢟⡶⣻⡝⣞⣧⢻⡵⣫⣗⢯⣳⡭⢷⣫⢷⡹⣎⡯⢿⣆⠘⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⢀⢻⡯⢌⢣⡑⢧⠘⡥⢋⠌⡓⢌⠢⡑⢌⠢⡑⢌⠢⢉⠆⢡⠂⡜⡐⢌⠂⡅⠢⡑⠌⢒⡀⠣⠌⡄ ⣿⣳⢯⡿⣽⣏⡿⣽⣲⢟⡽⣞⣭⢷⣫⢟⡼⣏⡾⣳⢧⣛⢷⡺⣝⡾⡵⣞⢯⡖⣯⡳⣝⡮⢷⡹⣞⣻⣿⡄⣿⣿⣿⡟⢛⣫⣿⣿⣿⣿⣿⣿⠟⣿⠛⢿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠸⣹⡟⣌⠲⣡⠊⡕⢢⠡⢚⠰⡈⠖⡡⢊⠔⠡⢂⠱⡈⢌⠂⡅⢒⡈⢄⠣⡐⢡⠂⢍⠂⡌⢡⠒⠠ ⣿⡽⣯⣟⡷⣯⢷⣳⡽⢾⣹⡞⡽⣎⡷⣫⡽⣞⡵⣛⣮⢟⣮⢽⣣⢟⣵⢫⡾⣹⢖⣯⢳⡝⣧⢻⡜⣷⣿⣿⣿⣿⣿⣴⣿⡿⡏⢻⣿⣟⣤⣽⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠠⢚⡯⣐⠣⢆⠹⣠⢃⠣⢌⠢⡑⠌⠴⢁⢊⠱⡈⢆⠘⡠⢃⡘⢄⡘⢄⠢⢑⢂⠩⢄⠊⡔⠡⠌⡡ ⣿⣽⣳⣯⣟⣷⣛⣶⢻⡝⣧⡻⣝⢾⣱⣏⢷⣹⢞⡽⣎⢿⡜⣧⣛⠾⣜⢯⣳⣛⠾⣜⢧⡻⣜⢧⡻⣜⣿⣿⣿⣿⣿⣿⡟⠳⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠌⡐⢫⢄⠫⡜⢠⢃⠌⡒⢌⠢⢑⠊⡄⠣⢌⠰⡐⡈⢆⠡⢂⠔⡂⠔⡈⢆⠡⢊⠰⡈⠒⢄⠣⡘⠠ ⣿⣞⣷⣻⣞⡾⣝⡾⢯⣽⢺⡵⣏⡟⣶⡹⣞⡽⣚⡷⣹⢮⡻⣵⢫⡟⡽⣎⠷⣭⣛⢮⡳⣝⢮⡳⣝⡞⡶⣿⣿⣿⣿⡿⠈⢀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠬⣙⠆⢳⠘⠤⣉⠆⡱⢈⢆⠡⢊⠰⡁⢆⠡⢂⠱⣀⠣⠌⢒⡈⢆⠡⢂⠱⡈⠤⢡⠉⡂⢆⠡⡁ ⣿⢾⣽⣳⢯⣟⡽⣞⡿⣜⣳⡽⣺⡝⣶⢫⢷⡹⣝⠾⣭⣳⢻⣜⡳⣽⢳⣭⣛⢶⣭⢳⡝⣮⢳⡝⣮⣝⡳⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⡈⠴⣈⢏⠰⣉⠒⡡⢊⠔⡡⢈⠆⡡⢒⠈⡔⡈⢆⠡⡐⢂⡑⠢⡐⢂⠅⡊⠔⡠⢃⠢⡑⠨⠄⡃⠔ ⣿⣻⢾⣽⣳⢾⣹⣳⢽⡺⣵⢫⢷⡹⣞⡽⢮⣽⣚⢯⣳⢭⣳⢭⣳⢭⣳⢮⡝⡾⣜⢧⡻⣜⢧⡻⢶⣭⢳⢧⣿⣿⣿⣿⣿⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⡐⢈⠲⢡⢎⡱⢄⡩⢐⠡⢊⠄⣃⠰⢁⠢⡑⠰⡈⢄⠃⡔⣁⠢⡑⢄⠃⡌⠰⣁⠒⡄⢃⠌⡑⢌⠰⢁ ⣿⣽⣻⢾⡽⣞⣧⢟⣞⣳⡭⣟⢮⢷⡹⣞⣳⢮⡝⣾⣱⢻⡜⣧⣛⢮⡳⣏⢾⣱⢏⡾⣱⢏⡾⣹⢳⣎⡟⡾⣴⢛⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠭⡀⢡⠌⡡⢂⡅⢺⡔⡨⢔⡡⢊⡅⢒⠠⡑⣈⠒⡈⢅⠒⣈⠒⡐⢄⠒⡨⠐⡌⠰⣁⢂⠒⡈⢆⡘⠰⢈⠢⢁ ⣿⢾⡽⣯⢷⣻⢮⣛⣮⢳⣝⣮⣛⢮⢷⡹⣎⢷⣹⠶⣭⣳⣛⠶⣭⡳⣝⡞⣧⣛⢮⣳⡝⣮⢳⣝⡳⢮⣝⡳⣯⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢻⡁⠞⡌⠐⡤⠂⠤⢡⠘⣐⠣⣏⡐⠆⡔⣡⠈⡆⡑⠰⣀⠃⡜⢠⢊⡐⢌⠰⣈⠂⡅⢃⠌⡡⢐⢂⠱⢈⠆⢌⠡⢊⠄⠡ ⡿⣯⣟⡷⢯⢷⣫⠷⣭⢷⣚⢶⡹⢮⡳⣝⢮⣳⢭⣛⢶⣣⢏⡟⡶⣝⢮⣝⠶⣭⡳⢧⣻⣜⡳⢮⣝⡳⢮⣽⣟⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣍⡳⢍⢦⣹⡰⢬⠑⡠⠨⠰⢀⣋⠄⠳⣼⡄⣙⠰⢠⡘⠤⣁⠣⡐⢌⡐⢢⠐⡰⢈⠢⠄⡃⠔⣈⠢⠑⡂⢌⠢⡁⢎⠠⠃⡄⢊⠐ ⣿⢷⣯⣟⢯⢷⣫⣟⢮⣳⡝⣮⣛⢧⣛⢮⡳⣝⡮⣝⣮⢳⣏⣞⡳⣝⠾⣜⡻⢶⣹⢳⡳⢮⣝⡳⢮⣝⡳⣞⢿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣭⢻⣌⠳⣭⢖⣦⠳⣌⢌⠡⢁⠒⢡⠈⢎⠡⠜⣷⡈⠜⣠⠘⡰⢀⢣⠘⡄⠒⡄⢣⠐⡡⢂⠱⢈⠒⡠⢁⠣⢘⠠⢂⠅⢊⠐⠡⠐⠂⠌ ⣿⣻⢶⢯⣛⡾⡵⣞⢯⢶⡹⣖⢯⡞⣭⣳⢻⣜⡳⣝⢮⡳⣞⡼⣳⢭⣛⣮⡝⣧⢏⡷⣹⢳⢮⣝⡳⣎⠷⣭⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢯⣽⣳⢮⡳⣎⡳⡼⡞⡴⢫⡜⠌⢦⠉⠈⠄⡐⠂⡜⢨⢽⣿⡔⢂⠱⣀⠃⢆⠱⣈⠱⡈⢆⠱⣀⠣⡘⢄⠣⡐⢡⠊⡄⠣⢌⠘⡀⢊⠡⠌⠡⢈ ⣟⡷⢯⣟⡽⣺⣝⢾⡹⣎⢷⡹⢮⣝⠶⣭⡳⢮⣝⢮⡳⣝⢮⡳⣝⢮⣳⢮⣝⢮⡻⡼⣭⣛⠾⣜⡳⣭⣛⠶⣭⢿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣏⣟⡳⢞⡥⢯⡽⣭⢳⢧⡹⢜⣣⡙⢾⡀⠎⠡⠀⢄⠡⡀⠣⢎⢿⣿⣧⣖⡠⢉⠆⡒⠤⡑⡈⢆⠱⣀⠣⡘⢄⠣⡘⢄⠣⡘⠰⡈⠆⡁⠢⠐⡈⢂⠁ ⣯⣟⣟⣮⡽⣳⢞⣯⢳⡝⣮⢽⡳⣎⡟⡶⣝⢯⡞⣧⣛⢮⢷⡹⣞⢧⣛⠾⣜⢧⡻⣵⢣⣏⠿⣜⡳⢧⣏⠿⣜⡧⣏⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣟⢾⡸⣹⡍⣞⣱⠞⣥⢻⢦⡙⣦⠧⡙⢦⡑⢎⠡⡀⠆⠰⢀⢣⠘⡼⣷⣏⡿⣿⣶⣾⣤⣵⣠⡑⣈⠒⠤⢑⠰⡈⢆⠱⡈⢆⠡⢃⠜⡠⠑⣂⠑⡠⠁⠌ ⣷⣻⡼⢶⣻⢵⣫⢞⣧⢻⡜⣧⢻⡼⣹⢳⡝⣮⡝⡶⣭⣛⢮⣳⡝⣮⣝⡻⣜⢧⡻⣜⡳⣞⡽⢮⣝⡳⣎⠿⣜⡳⣝⠾⣭⣛⠿⡿⢿⠿⣿⢿⣿⠋⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣞⡧⢷⡩⡜⠶⣥⢯⡙⣧⣾⠵⣣⠝⣌⠣⡜⢢⠡⡁⠂⠅⣂⠢⠘⢤⢫⡝⣻⣷⣻⢞⣽⣻⣟⣿⡿⣿⣶⣮⣴⣡⣈⠆⡑⠌⢢⠁⢎⡐⠡⡀⠎⢠⢁⠂ ⣷⣳⢻⣏⣞⢧⣛⡾⣜⢧⡻⣜⣧⢻⡵⣫⢾⡱⣏⢷⣣⢟⣮⢳⡝⡶⣭⢳⡝⣮⢳⣭⢳⡝⣞⡳⢮⡝⣾⡹⢧⡻⣜⡻⢶⡍⡷⣍⣛⠮⡵⢎⣽⠀⠀⠀⠀⢮⣿⣿⣿⣿⣿⣿⡿⡞⣥⢳⡉⢳⡜⣦⢿⡻⣌⠷⣢⠝⣠⠒⡌⢠⠃⡔⢁⠂⠴⢈⡑⢎⡳⢼⢯⡷⣯⣟⣮⢷⣻⣾⣟⡿⣽⣿⣻⣿⣿⣿⣷⣾⣤⣉⡤⠘⢠⠁⡌⠂⡄⢂ ⡷⢯⣛⣞⢮⡻⣜⡳⣝⢮⢷⡹⣎⢷⡹⢧⣏⢷⡹⣎⢷⣫⢞⣧⢻⡵⣫⢷⡹⣎⢷⡺⣝⠾⣱⢏⡳⣝⢶⣹⢳⡝⣧⣛⢧⠞⡵⢎⢧⡛⣜⢣⢾⡃⠀⠀⠀⠠⣼⣿⣿⣿⣿⣟⣷⡻⣬⢓⣌⠶⣹⣯⣗⣳⣭⠳⡆⣍⠲⠠⠄⠃⡜⠐⡌⡀⢂⠬⠑⡎⡵⢋⡞⣹⢳⣻⣾⣿⢿⣟⣾⣟⣷⣿⣿⣽⣷⡿⣯⣿⣿⣿⣿⣿⣦⣴⣀⠡⠐⠂ ⣟⢯⡽⣎⣯⢳⡭⣗⢯⡞⣧⢻⡜⣯⣝⡳⢮⣏⢷⡹⣎⢷⣫⢞⣧⢻⡵⣫⢷⡹⣎⠷⣭⢻⡥⣏⢷⡹⣎⢷⣫⢞⡵⣭⠺⡭⣝⢮⢣⡝⣬⠓⡾⡇⠀⠀⠀⠐⢼⣽⣿⣿⣿⣿⣷⣿⠶⣏⢬⣛⣷⣻⣞⡷⣊⠷⣉⠦⣁⠣⣘⠐⡈⠱⣀⠖⠡⠀⡝⡘⡔⠫⡔⢣⡞⣿⣿⣿⣿⣿⣿⣾⣿⣿⣾⣿⣾⢿⣟⣷⡿⣯⣿⣿⢿⣿⣿⣿⣾⣤ ⣯⣛⢾⡱⣏⢷⡹⣎⢷⡹⣎⢷⣛⠶⣭⣛⠷⣎⢯⡳⡽⣎⢷⣫⢞⣧⢻⡵⣫⠷⣭⢻⡜⣧⢳⡝⣎⢷⡹⣎⢷⣋⠾⣜⢫⡵⣚⡬⢳⡜⢦⡛⡴⣧⠀⠀⠀⠀⠀⢙⣿⣿⣿⣿⣿⣯⡿⣜⡶⣹⣾⢯⣟⣳⡽⢎⡕⢢⠰⣁⠣⡜⢀⠡⡘⢠⠁⢆⠐⡤⢩⠓⣬⢓⡞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣯⣿⣻⣿⣿ ⡷⣭⡗⣯⠽⣎⢷⣫⢞⡵⣫⡞⣭⣛⠶⣭⢻⡼⣣⢟⡵⣫⢞⡵⣫⢞⣧⢻⡵⣻⡜⣧⢻⣜⡳⢞⡭⡞⣵⢫⡞⣭⢻⢬⡳⣜⡱⢺⡱⢎⢧⡙⡖⣿⠀⠐⠄⢀⠀⠀⠉⣿⣿⣿⣿⣿⣟⡷⣏⣷⣿⣿⢿⣻⡝⢮⡜⣡⠓⠬⣑⠜⣨⠂⡁⢃⡚⢤⡈⢠⢃⡝⢦⣛⡾⣽⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣽⣿⣽⣿ ⣟⡵⣻⣜⡻⣜⢧⣛⢮⡳⢧⡻⣵⢫⡟⡼⢧⡻⣵⢫⡞⣵⢫⡞⣵⢫⡞⣧⣛⢶⡹⣎⢷⣪⠽⣹⢼⣙⢮⣳⢹⡜⣣⢳⣙⠦⣝⢣⡝⢎⢶⣭⡿⠛⠀⠀⠀⢹⠆⣄⣀⠿⣿⣿⣿⣿⣯⣿⡽⣾⣿⣯⡿⣧⣛⢧⡚⡥⢊⠶⣩⢎⡡⢚⠄⢃⠜⡢⣄⠣⡘⣬⢣⠿⣽⣳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣯⢞⡵⣎⡷⣹⢎⣯⢳⡽⣳⡝⣮⢳⡽⣹⢧⡻⣜⢧⡻⣜⢧⣻⡜⣧⣛⢶⡹⣎⢷⡹⢶⣩⢏⠷⡮⣝⡞⣬⡓⣞⣱⢫⡜⣹⢬⣳⡾⠟⠋⠁⠀⢀⠀⠀⠀⢸⡅⣦⢉⡉⢿⣿⣿⣿⣿⣽⣿⣿⣿⣿⡿⣖⡻⢦⡛⣌⢏⡾⡵⢪⡕⢯⣌⢣⣌⡱⢎⡧⣙⣤⢏⡿⣵⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢷⣫⢞⡵⣫⢗⡯⣞⢧⡻⣵⢻⡜⣧⢻⡵⣫⢷⡹⣎⢷⡹⣎⢷⡹⢶⡹⣎⢷⡹⢎⡗⣯⣜⢫⢷⡹⡖⣽⠲⣝⡼⢲⣍⣾⠟⠋⡁⢀⠀⠀⠀⢰⣿⠀⠀⠀⠈⡇⠸⣧⣌⣻⣟⣿⣿⣿⣿⣿⣿⣿⣿⡿⣥⣋⢷⡙⣞⣮⡽⣽⢳⣚⠷⣜⡲⣬⡳⢯⣶⢻⣼⣻⣞⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣟⡼⣫⢞⡵⣫⢞⡽⣎⠷⣭⢳⡝⣮⢷⡹⢧⣏⢷⡹⣎⢷⡹⢮⡝⣧⢳⡝⡮⡝⣏⡞⢶⢎⡿⢬⡳⣝⠮⣝⣲⣽⠟⠋⠀⠠⠀⢀⡀⢀⡈⢷⣾⣿⠀⠀⢠⠀⢻⡄⢽⣷⣎⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢧⡍⣎⢿⣼⣳⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣾⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡾⣱⣏⣞⡳⣝⢮⣳⢭⡟⣼⢫⡞⣵⢫⣝⡳⣎⢷⡹⣞⢧⣛⢧⢻⡜⣳⠞⡵⣋⢶⡹⣚⢮⡜⢧⣛⡼⣹⣶⠟⢡⣀⠈⢒⠠⣇⢢⣽⣦⣿⣿⣿⣿⠃⠀⠈⢣⠀⢳⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣟⡼⣣⢟⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢿⣻⢯⣟⡳⡽⣎⢷⣛⣾⣳⣿⣿⣿⣿⣿⣿⣿ ⣳⢯⡽⣹⢧⡻⣜⢯⡞⣵⢫⡞⣵⢫⡞⣽⢣⡟⡼⢧⡻⣜⡻⣜⢮⣓⢏⡖⢧⠻⣜⡣⢟⣬⢓⡮⢫⣵⡿⠋⠀⠈⢻⣤⣚⡤⢿⡞⣿⣻⣿⣿⣿⠏⠀⠀⠀⠈⡆⠸⡄⠘⣿⣿⣿⣿⣿⣿⣿⣿⡵⣿⣿⣿⣧⣻⣾⣿⣿⣿⣿⣿⣿⣿⢿⡿⣿⣿⡿⣟⣿⣯⣿⣟⡿⣿⣻⣿⣽⣟⣷⣿⢾⣟⡾⣽⣳⢧⣻⣼⣻⣽⣿⣿⣿⣿⣿⣿⣿⣿ ⢯⡞⣵⢏⡾⣱⢯⡞⡽⣎⢷⡹⣎⢷⡹⣎⢷⡹⣝⢧⡟⣼⡱⢏⡶⢭⡺⣜⢫⣝⡲⢭⣓⢮⡹⣼⡟⠃⠀⠀⠀⣐⡠⠞⣿⡽⢎⡽⣶⢿⣾⢏⡆⠀⠀⠀⠀⠀⠑⠀⣧⠀⢺⣿⣿⣿⣿⣿⣿⡿⠀⣿⣿⣿⣿⣿⣿⣿⡿⣿⣻⣝⡮⣝⡾⣿⣳⣿⣟⣿⣿⣽⣷⣿⣿⣿⣿⣷⣿⣿⣿⣯⣿⣾⣟⣷⣿⣻⣷⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣟⡼⣣⡟⣼⢣⡟⣼⢳⡝⣮⢳⡝⣮⢳⡝⣾⡱⣏⠾⣜⢧⡝⡞⣜⡣⢗⣎⠳⣎⣵⣫⣼⣶⠟⣉⣠⠀⠀⠀⢀⡿⣷⢍⣙⣧⣿⣾⣿⣫⣝⣾⣤⣄⣲⣤⣹⣦⠲⠤⣄⠀⠈⢿⣿⣿⣿⣿⣿⠃⢤⣿⣿⡿⢫⣙⢮⣳⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣻⣷⣿⡿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡷⢯ ⣞⡳⣝⢾⡱⣏⣞⢧⡻⣜⢧⡻⣜⢧⡟⣼⢣⡝⣮⣛⡼⢎⣞⡹⡲⣍⣷⡾⠟⢋⢉⣥⣶⣾⣿⣿⣿⣿⠿⡩⢞⣷⠟⠉⡐⢎⠛⡍⢯⡽⣻⣿⡻⢿⣿⣿⣿⣿⣷⣦⣜⣦⡀⠹⣿⣿⣿⣿⠏⢀⣿⡿⠉⢁⠣⣞⣯⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⣟⣿⣟⣿⡾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⠾⣝⢯ ⣯⣝⢾⣣⢟⡼⣎⡷⣹⢎⣯⢳⡝⣮⡝⣮⢳⡝⢶⡹⣜⣫⣖⣽⠿⢋⡡⢴⠶⣞⡾⣞⣷⣿⣾⣿⣿⣟⡶⣡⣿⠋⠀⠀⢁⠢⠕⡚⢡⢎⡱⠭⣽⠿⣟⢿⡻⣝⣮⣿⣿⣿⣷⡧⣿⣿⣿⡋⢥⣿⡏⣠⣄⣠⣔⣫⢿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⢿⣿⣟⡿⣿⣾⣿⣿⡿⣟⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⢿⣻⣽⣯⢿⡽⣞ ⡷⢮⣳⡝⣮⢳⡝⣾⡱⣏⡞⣧⣛⢶⣽⣮⡷⠿⢛⠛⡫⢍⠋⡅⣎⢱⡙⣎⠿⣜⣻⡽⣿⣾⣿⣿⣿⣿⣿⣿⠏⢀⢠⡐⣠⠉⠒⠬⡁⢎⡰⢿⣬⡻⣜⣯⢷⣻⣿⣿⣿⣿⣿⣷⣉⡟⢦⡑⣮⢯⣴⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢷⣻⡾⣿⣟⣯⡿⣿⣿⣯⣟⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⡷⣯⡿⣽⢯ ⣽⢳⢧⡻⣜⢧⡻⢶⣹⢮⣽⡶⠿⠛⠉⠀⠐⠤⠣⡘⠐⢊⠒⡌⢂⠧⣜⡎⣷⣹⡾⣽⣷⡿⣿⣿⣿⣿⠿⣡⠲⣌⢶⡹⢿⣆⣙⣲⠱⣮⢙⠶⣣⢿⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡦⠥⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣻⢷⣯⣟⣷⣿⣳⣯⢿⡽⣷⣿⣾⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣳⣿⣿⡷⣟⣯⣿ ⣳⢯⡞⣵⣫⢞⣽⣳⠟⠋⠁⠀⠀⠀⠀⠐⠠⠂⢀⠈⠄⢡⠘⡰⣍⡞⣴⢯⡷⣯⣟⣿⡾⣟⡿⡹⣍⢆⡳⢣⡽⣘⣮⡟⣽⣿⣿⢣⠷⣌⣯⣛⣷⣻⢾⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⣶⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣟⣯⢷⡿⣜⢯⢾⣭⢿⡿⣿⡿⣿⣾⢿⣿⡿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣾⣿⣻⣿⣾ ⣟⢮⣽⢺⣵⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣀⠢⡜⢢⡝⢲⣟⡾⣽⣯⣿⣿⣻⡽⣛⢥⢳⡱⢎⢎⣝⢣⡻⣵⣳⡿⣟⣿⣞⣯⢿⣝⡶⣛⡾⣽⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⢳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢯⣟⡾⣞⡯⣝⢿⣫⡗⣾⣯⣿⡽⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣟⣿⣷⣿ ⣻⢞⣼⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣂⠔⣠⠒⣭⠳⡜⣧⣿⣟⣷⣯⢷⣫⢇⡧⣙⢎⢣⠳⡞⡼⣌⢷⣻⢽⣯⢿⡽⣯⣟⡞⡿⣮⣽⢳⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠘⢦⡈⢿⣞⣿⣿⣿⣿⣷⡿⣿⣟⡾⣽⣟⡾⣽⢣⡟⣽⣺⢷⣻⢽⣳⣯⣿⢿⣻⣿⣻⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿ ⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢬⡸⣔⢫⢖⣻⣾⣿⠿⣝⡾⣡⠧⣍⠞⣰⠙⢎⡲⢥⣛⣼⣻⡼⢯⡟⣞⢯⣿⣱⢿⡜⣷⡝⣾⢻⣶⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢳⣄⡆⣹⣜⣿⣿⣿⣿⣿⣿⣿⢿⣟⣿⣳⢏⡷⣭⢗⣯⣛⣷⢻⣾⢯⣿⣻⣽⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢆⡞⠶⣱⣮⣾⣿⣿⢿⡽⣛⡮⢱⡡⣚⡜⡸⢣⢛⣤⡝⣫⣼⠶⡽⢾⡹⡞⡭⢞⠶⢭⢞⡹⣞⡽⣮⢿⣟⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡦⠀⣻⣽⢻⡼⣾⢿⣿⣿⢿⣻⣿⣿⣾⣳⢯⡻⣼⢛⡾⢧⣻⣼⣻⣾⢿⣽⣿⣻⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡒⡌⣞⣬⣿⣿⣿⣿⣿⣯⣿⡟⢧⠘⡅⣶⢩⠞⣱⢛⣼⢲⡝⣣⢟⡽⢞⡹⢻⡱⣛⢮⣙⣧⢫⡷⣭⢷⣯⣟⣾⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣰⣿⣿⣻⣿⣯⣿⣿⣿⣿⣿⣟⣮⢷⡏⣯⢳⣭⢻⡼⣟⣧⣿⣹⣽⣻⣯⣿⢿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠄⠈⠀⠀⠀⡜⣰⣿⣿⣿⣻⣽⣯⢿⣿⣯⠳⡜⢠⢛⡘⢤⡃⣞⡥⢏⡞⡶⣙⢮⣟⡼⡳⣍⣳⣫⡝⣮⣝⣮⣻⡽⢯⣿⣾⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⡷⢧⣿⣿⣿⣿⢯⣟⡾⣽⢻⡯⣟⣳⡛⢾⣳⣽⡽⣞⡿⣿⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠠⡘⡼⣼⣿⣻⣷⢿⣽⣿⣽⣿⣿⣦⠃⡄⠙⠦⠸⠀⡗⡌⢲⡛⣜⠶⣙⡞⣼⣱⢯⣝⣣⢿⣝⣯⣟⣾⣳⣿⣿⢯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡿⣼⣿⣋⢿⡟⣞⣻⣞⡷⣹⢏⡷⣫⢷⣹⣛⣷⣻⣽⣿⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⢠⡉⣥⢻⣽⣷⢿⣷⣯⣿⣿⣿⣿⣿⣿⠂⠄⠡⠒⠐⠈⠳⢐⡚⡡⢜⡭⢻⡴⣛⢶⣭⡞⣧⣟⣯⢿⣭⣟⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡛⢿⠙⣇⣿⢫⡝⣭⣓⣮⠷⣳⢾⣱⢟⣯⣟⣯⣷⣻⣾⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣻⣷⣟⡷⣯⣿⣿ ⠀⠀⣀⣄⣠⠌⢦⡱⣯⣿⣻⣾⡿⣯⣿⣿⣿⣿⣿⣿⡏⠙⠀⠀⠀⡰⣃⡤⢋⣜⣍⣫⣜⣣⣷⣻⣟⣶⡿⣟⣾⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⡉⠁⡫⢜⠣⢯⣜⣦⠳⣬⠷⣽⣚⣷⣞⣳⣾⣷⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢯⣿⣹⣿⣽⣯⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢰⠀⠀⠀⠀⣄⠀⠀⠀⠀⡆⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠘⣆⠀⠀⠀⠸⡄⠀⠀⠀⣿⠀⠀⠀⢠⠇⠀⠀⠀⣰⠃⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄⠀⠀⠀⠹⡄⠀⠀⠠⡇⠀⠀⣰⣿⣧⠀⠀⢸⠀⠀⠀⢠⠏⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢦⠀⠀⠀⠀⠹⡄⠀⠀⠀⢳⠀⠀⠀⢹⠀⣼⣿⣿⣿⣷⡀⡏⠀⠀⠀⡜⠀⠀⠀⣠⠏⠀⠀⠀⠀⡴⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠀⠀⠀⠸⣆⠀⠀⠈⣧⠀⠀⢸⣿⣿⣿⠟⣿⣿⣿⡇⠀⠀⣼⠃⠀⠀⣰⠃⠀⠀⠀⣠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠈⢳⡀⠀⠀⠘⣧⠀⠀⠸⡆⢀⣾⣿⣿⠏⠀⠈⢿⣿⣿⡄⢰⠏⠀⠀⣼⠃⠀⠀⢀⡼⠁⠀⠀⠀⣀⡴⠂⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⠢⣄⠀⠀⠀⠙⢦⡀⠀⠘⣷⡀⠀⢻⣾⣿⣿⠃⠀⠀⠀⠈⢿⣿⣿⣿⠀⢀⣼⠃⠀⢀⡴⠋⠀⠀⠀⣠⠜⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠢⣄⡀⠀⠀⠀⠈⠳⣤⡀⠀⠈⠳⣆⠀⠈⢷⣠⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⢻⣿⣿⣦⣾⠁⠀⣠⠞⠁⠀⢀⣴⠞⠁⠀⠀⠀⢀⣠⠔⠀⠀ ⠀⠀⠀⠀⠙⠲⢤⡀⠀⠀⠈⠙⢦⣄⠀⠙⢷⣄⣸⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣧⣠⡾⠋⠀⣠⡶⠋⠀⠀⠀⢀⡤⠒⠉⠀⠀⠀⠀ ⢀⣀⠀⠀⠀⠀⠀⠉⠳⢦⣄⡀⠀⠙⢷⣦⡀⣻⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣁⣴⡾⠋⠀⢀⣠⡴⠚⠁⠀⠀⠀⠀⢀⣀⠀ ⠀⠈⠙⠒⠶⢤⣀⡀⠀⠀⠈⠙⠷⣦⣀⠙⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡋⣀⣴⠾⠋⠁⠀⠀⣀⣠⠤⠖⠛⠉⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⠛⠶⢤⣤⣀⡈⢙⣿⣿⣿⠏⠀⠀⢀⣀⣠⣤⣤⣶⣶⣤⣤⣤⣀⡀⠀⠘⣿⣿⣿⣋⣁⣠⣤⠶⠞⠛⠉⠀⠀⠀⠀⠀⠀⠀ ⠐⠒⠒⠦⠤⣤⣄⣀⣀⠀⠀⠈⠉⢻⣿⣿⣿⠋⣀⣤⡶⠟⠛⢉⣉⣉⣉⣉⣉⣉⠙⠛⠿⣶⣤⡈⢿⣿⣿⡟⠉⠀⣀⣀⣀⣤⣤⠤⠴⠒⠒⠂⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⢻⣾⣿⣿⣣⢶⣫⣷⣶⡿⠛⠛⣿⢿⣿⣿⣿⡟⠛⠻⣷⣦⣭⡻⢮⣿⣿⣿⣟⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠠⠤⠤⠤⠤⠤⠤⠴⠶⣶⣾⣿⣿⣿⠗⠋⠁⠀⣿⡇⠀⢸⣿⣶⣿⣿⣿⣿⠀⠀⢹⡇⠀⠉⠳⠿⣿⣿⣿⣷⠶⠶⠶⠶⠶⠶⠶⠶⠖⠂⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣿⣿⡟⢫⡀⠀⠀⠀⠀⢿⣇⠀⠸⣿⣿⣿⣿⣿⡟⠀⠀⣾⠇⠀⠀⠀⠀⢨⠿⣿⣿⣧⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣀⣠⠤⠤⠴⠒⠚⠛⣻⣿⣿⡟⠀⠀⠓⢤⣀⠀⠀⠘⢿⣆⠀⠈⠙⠛⠛⠉⠀⢀⣼⠟⠀⠀⢀⣠⡴⠃⠀⠹⣿⣿⣯⡉⠙⠛⠓⠒⠦⠤⠤⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠏⠀⠀⠀⠀⠀⠙⠻⢶⣤⣤⣛⣿⣦⣤⣤⣤⣤⣾⣟⣡⣤⣴⠶⠛⠁⠀⠀⠀⠀⠘⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣀⣤⠴⠖⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠻⠿⠿⠿⠿⠟⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⡍⠓⠶⢤⣄⡀⠀ ⠀⠀⠉⠁⠀⢀⣾⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⡄⠀⠀⠀⠈⠁ ⠀⠀⠀⠀⢠⣾⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣆⠀⠀⠀⠀ ⠀⠀⠠⢴⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣟⠂⠀⠀ ⠀⠀⠰⠿⠿⠛⠻⣿⠿⠻⠿⠿⠿⡿⠿⠿⠻⣿⠿⠿⢿⡿⠿⢿⡿⠿⢿⡟⠿⣿⡿⠿⢿⠿⠿⠿⡿⠿⠿⠿⣿⠻⠿⠟⠻⠿⣿⠟⠿⠿⠷⠀⠀ ⠀⠀⠀⠀⠀⡠⠞⠁⠀⠀⠀⣠⠞⠀⠀⠀⣼⠃⠀⠀⡿⠁⠀⢸⠁⠀⢸⠀⠀⢸⡇⠀⠘⣧⠀⠀⠹⣆⠀⠀⠈⠳⣄⠀⠀⠀⠈⠑⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁⠀⠀⠀⡼⠁⠀⠀⣼⠁⠀⠀⡟⠀⠀⢸⠀⠀⠘⣇⠀⠀⠹⡆⠀⠀⠙⢆⠀⠀⠀⠈⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⢀⡜⠁⠀⠀⢰⠃⠀⠀⢸⡇⠀⠀⢸⠀⠀⠀⢹⠀⠀⠀⢹⡀⠀⠀⠈⢧⠀⠀⠀⠀⠙⠄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⡏⠀⠀⠀⣸⠀⠀⠀⢸⠀⠀⠀⠘⡆⠀⠀⠀⢧⠀⠀⠀⠀⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⡾⠀⠀⠀⠀⡏⠀⠀⠀⢸⠀⠀⠀⠀⣇⠀⠀⠀⠈⡇⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠰⠃⠀⠀⠀⠈⠀⠀⠀⠀⢸⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉⠉⠈⠈⠈⠉⠉⠉⠉⠉⠉⠉⠉⠙⠻⣄⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⣄⠀⠀⢀⠀⢀⣀⣤⠄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣉⣩⣤⠴⠶⠶⠒⠛⠛⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠤⠶⠒⠚⠋⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣾⡍⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣫⣭⣷⠶⢶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠶⠶⠖⠚⠛⠛⣹⠏⠀⠀⠀⠀⠀⠀⠀⠀⠴⠛⠛⠉⡁⠀⠀⠙⠻⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡷⠷⢿⣦⣤⣈⡙⢿⣿⢆⣴⣤⡄⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⣤⡀⣸⡄⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣿⣟⣩⣤⣴⣤⣌⣿⣿⣿⣦⣹⣿⢁⣿⣿⣄⣀⡀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⣿⠋⠻⢿⡁⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠿⠛⢦⣽⣿⣿⢻⣿⣿⣿⣿⠋⠁⠘⣿⣿⣿⣿⣿⣿⣼⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⠁⠀⠀⠙⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠿⣿⣯⣼⣿⡿⠟⠃⠀⠀⠀⣿⣿⣿⣿⣿⡛⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣧⣴⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⠟⠃⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⢁⣀⣀⣀⣀⣀⣠⣀⣀⢀⢀⢀ ⠀⠀⢿⠿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠙⠛⠛⠙⢻⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⡇⠀⠘⠃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡟⢿⣿⣆⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡼⠁⢀⣀⡀⠀⠀⠀⣦⣄⠀⣠⡄⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣷⣬⢻⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⣰⣿⡿⠿⠦⢤⣴⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠒⣿⣿⣿⡿⠟⠹⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⠸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡖⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡿⣾⣿⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣆⣀⣀⣤⣴⣶⣶⣾⣿⣷⣦⣴⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡇⣿⣿⡛⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢾⡟⠛⠛⠻⠛⠛⠛⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠓⢁⣬⣿⠇⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⢰⡿⣻⠇⠀⠀⠀⠀⠀⣠⣶⣶⣶⣶⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢐⣯⠞⠁⠀⠀⠀⠀⠀⠀⣄⠱⣄⠀⠀⠀⠀⠸⡧⠟⠆⠀⠀⠀⠀⠘⠿⢿⠿⠿⣿⡿⣿⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡈⠂⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⡄⠀⠀⠑⠄⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣦⣦⣼⡏⠳⣜⢿⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢠⣷⣦⣤⣀⣀⣀⣴⣿⣿⣿⣿⣿⡿⠻⠆⠸⣎⣧⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⣠⡄⠀⣿⢹⡇⢸⡀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠴⠶⠒⠚⠉⠉⠙⠒⠒⠲⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠛⠁⠀⡸⠀⠀⠀⠀⠀⠀⠈⢦⣠⡀⠀⠈⠙⡲⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠉⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠈⣇⢳⠀⠀⠀⠉⢆⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⣠⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡘⣇⠀⠀⠀⠈⢷⡀⠙⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢏⡄⢰⠇⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠸⡀⠀⠀⠀⠀⢳⡀⠈⢳⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⡞⠀⡏⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⣷⠀⠀⠀⠀⠀⢳⢀⡼⠋⠉⠉⠉⠳⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⢸⠁⢸⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣸⡇⣸⡆⠀⠀⠀⠀⠈⣿⠁⠀⠀⠀⠀⠀⠀⠙⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡇⡟⠀⣸⠀⠀⠀⠀⠀⠀⠀⢣⣀⣀⠤⠤⠴⢚⣿⢟⣿⣿⡻⢷⣞⣧⠀⠀⠀⠀⠀⢻⣇⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⡇⠀⣷⢀⣤⣤⣤⣴⡒⠛⠉⠁⠀⠀⠀⠀⢼⢁⣿⣿⣿⣿⣮⠹⣾⠀⠀⠀⠀⠀⢸⣿⣄⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠆⡇⢰⣾⣿⢯⣿⣿⣯⡙⠆⠀⠀⠀⠀⠀⠀⠀⢹⣿⣇⠈⣿⣿⠀⢹⡇⠀⠀⠀⠀⠀⣿⣿⣇⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠿⢻⣿⡟⢻⣿⡟⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⡟⠀⠀⣷⠀⠀⠀⠀⠀⣟⣾⢟⣧⡀⠀⠀⠹⡄⠀⢸⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠈⣯⡇⠸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⢹⠀⠀⠀⠀⢠⡏⢸⣿⣿⣷⣄⠀⠀⢻⡄⢸⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⢸⡄⠀⠙⠛⠛⠋⠀⠀⠀⠀⣀⣤⡤⠤⠤⢤⣄⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠘⣿⠞⢻⡇⠙⠿⣷⣄⠈⣿⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⣴⡏⠁⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡟⠀⠀⡇⠀⠀⠈⠛⠢⣽⠅⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⣠⠟⠀⠀⠀⠀⠀⣠⡿⠀⠀⠀⠠⡏⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠻⣄⡀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⠤⠴⠚⠁⠀⠀⢀⣀⢴⡞⣿⣿⠀⠀⠀⠀⡧⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠉⠓⣦⠤⢤⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⣾⣿⡇⢸⠀⡟⢹⠀⠀⠀⠀⡇⠀⢸⠀⠀⠀⠀⢀⣴⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⢸⡆⠀⠀⢻⣏⣿⣽⣿⣇⠀⠀⠀⢀⣿⣿⠇⢸⠀⣷⢸⠀⠀⠀⠀⡇⠀⣼⠀⠀⠀⣰⠏⠾⠤⠤⠴⠂⠤⠤⡄ ⠀⢀⣀⣤⣤⣿⡙⠦⣄⠀⠀⠀⠀⠀⢱⡀⠀⠀⠀⠀⣿⡤⠴⠾⣿⣿⡟⠉⠉⠉⠉⣹⡘⣯⢿⣆⣼⡦⠟⢿⠀⠀⠀⢰⡇⠀⡇⠀⢀⣴⠁⢰⠀⠀⠀⠀⠀⣠⠜⠁ ⣾⡏⠀⠀⣠⠆⠱⡄⢘⡷⢄⡀⠀⠀⢨⣷⠀⠀⠀⠀⠹⡀⠀⠀⠀⠀⠱⣄⠀⠀⣰⠃⢧⡇⠀⢻⣆⠀⠀⢸⠀⠀⠀⣹⠁⢸⣇⡴⠋⡏⠀⠀⠀⠀⣃⡴⠚⠁⠀⠀ ⠙⠳⢦⣀⠁⠀⠀⢠⡞⠁⠀⠙⢆⠀⢸⠃⢳⡀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠈⠳⣤⣇⡀⢸⡇⢀⡠⠏⠀⠀⡏⠀⠀⠀⡏⠀⢸⣿⠁⠀⠧⠤⣤⡴⠚⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠉⠉⠉⢹⠋⠀⠀⠀⠀⣸⡇⡟⠀⠀⢱⣄⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠈⠛⠯⠝⠉⠛⠋⠀⠀⠀⡇⠀⠀⣾⠁⠀⣾⣏⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⣦⠀⠀⢀⡾⠉⣿⠃⠀⠀⢸⣏⢢⡀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⣴⡧⠀⢠⡟⠉⠓⠒⠒⣶⠟⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⣧⡴⠋⠀⠀⠹⡀⠀⢀⡎⠙⢦⠙⠦⣄⣳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣀⢼⣹⣯⠀⡼⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⢧⠀⡼⠁⠀⠈⢦⠀⢈⣷⠿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡇⢸⠃⢸⡼⠃⠀⠀⠀⢀⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠘⣷⠃⠀⠀⠀⠀⢧⣾⠃⠀⠈⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⢹⣸⡀⣼⠃⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⡄⠀⠀⠀⠘⣷⡄⠀⠀⢀⣾⣿⡀⠀⠀⢨⡷⠦⠤⠤⠤⠤⣤⣤⣤⣸⠀⠀⣠⣿⡟⠁⠀⠀⠀⠠⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⢳⡀⠀⠀⠀⠙⡇⠀⠀⣾⠁⠀⠙⠲⢶⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⠚⠉⠉⡇⠀⠀⠀⠀⢦⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣰⣏⣀⣀⣷⣀⣀⣀⣀⣀⣴⣸⣇⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣇⣀⣀⣀⣐⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣤⣶⣦⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠛⠉⠙⠛⠛⠛⠛⠻⢿⣿⣷⣤⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠋⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠈⢻⣿⣿⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣸⣿⡏⠀⠀⠀⣠⣶⣾⣿⣿⣿⠿⠿⠿⢿⣿⣿⣿⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⠁⠀⠀⢰⣿⣿⣯⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣷⡄⠀ ⠀⠀⣀⣤⣴⣶⣶⣿⡟⠀⠀⠀⢸⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⠀ ⠀⢰⣿⡟⠋⠉⣹⣿⡇⠀⠀⠀⠘⣿⣿⣿⣿⣷⣦⣤⣤⣤⣶⣶⣶⣶⣿⣿⣿⠀ ⠀⢸⣿⡇⠀⠀⣿⣿⡇⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀ ⠀⣸⣿⡇⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠉⠻⠿⣿⣿⣿⣿⡿⠿⠿⠛⢻⣿⡇⠀⠀ ⠀⣿⣿⠁⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⠀⠀ ⠀⣿⣿⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀ ⠀⣿⣿⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀ ⠀⢿⣿⡆⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀ ⠀⠸⣿⣧⡀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠃⠀⠀ ⠀⠀⠛⢿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⣰⣿⣿⣷⣶⣶⣶⣶⠶⠀⢠⣿⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⣿⣿⡇⠀⣽⣿⡏⠁⠀⠀⢸⣿⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⣿⣿⡇⠀⢹⣿⡆⠀⠀⠀⣸⣿⠇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢿⣿⣦⣄⣀⣠⣴⣿⣿⠁⠀⠈⠻⣿⣿⣿⣿⡿⠏⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠿⠿⠿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠿⣿⣧⡀⠀⠀⠀⢸⣿⡏⠀⠻⣿⣿⣄⣠⠀⠘⠛⠒⠔⠆⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⣿⣿⡏⠀⢻⣿⡟⠳⣄⢦⣿⣿⠁⠀⠀⠹⣿⣿⣇⠀⠀⠘⣂⠘⢦⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣸⣿⡿⠀⠀⠈⣿⣿⣶⣧⣸⣿⡿⠀⠀⠀⠀⠹⣿⣿⣆⠀⠘⡿⠟⢣⠀⠀⠀ ⠀⢀⡤⠀⠀⠐⠛⠀⠀⠀⢠⣿⣿⠃⠀⠀⠀⢹⣿⣿⠀⣿⣿⡇⠀⠀⠀⠀⠀⢹⣿⣿⣆⣐⣛⣓⣻⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⠖⠀⢠⠀⣿⢿⠟⠀⢀⠀⠀⢀⣹⣿⣦⣿⣿⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣯⣉⣁⣸⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣇⠀⢸⣸⣧⡆⠀⠀⣨⠄⡾⠿⠛⣿⣿⣿⣿⣶⣦⣤⣤⣀⣀⠀⠈⢿⣿⣿⣿⣉⣹⠀⠀⠀ ⠀⠀⠀⠇⠀⠀⣹⠀⢸⣿⠒⠷⣤⠖⠁⠈⠁⢀⣼⣿⣿⣻⣿⣷⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⡛⠛⠀⠀⠀ ⠀⠀⠠⡀⠀⢸⠁⢀⣿⣿⣆⡀⠁⠀⢀⡴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀ ⠀⠀⠀⡇⠀⠀⣹⣿⣿⣿⣿⣿⡇⠀⠟⣵⣿⣿⣿⣿⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀ ⠀⠀⠀⠀⢰⣾⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⠿⠿⠟⠀⠈⠛⠉⠉⠉⠉⠯⣉⠉⠉⠉⠙⣿⣿⣿⣿⣧⠀⠀ ⠀⠀⠀⢠⣿⣿⣿⣿⣿⠏⣿⡿⠿⠛⠉⠁⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⣿⡟⠛⠻⢿⡀⠀ ⠀⠀⢀⣿⣿⣿⣿⣿⠏⠤⠁⠀⢄⠀⠀⠀⠀⠀⠀⢀⠏⠀⢀⣀⡤⠤⠔⠒⠒⠚⣧⠀⠀⣿⡇⠀⠀⠀⢳⡀ ⠀⠀⣼⣿⣿⣿⡟⠜⠁⠀⠀⠀⠀⠑⣄⠀⠀⠀⠀⢼⢶⣿⣿⣿⣦⡀⠀⠀⠀⣰⡇⠀⣾⣿⣷⣤⣄⣀⠈⡇ ⠀⢰⡿⣿⣿⡿⢠⠀⢀⣠⣤⣤⣴⠒⢿⠀⠀⠀⠀⣸⠿⠿⠿⠟⠛⠛⠒⠚⠉⠀⠉⠉⣽⣿⣿⣿⣿⣿⣿⡇ ⠀⠀⠠⡿⣿⡇⠘⣏⠁⢰⣿⣿⣿⡷⠟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠀⠀⠈⠙⠻⣧ ⠀⠀⠀⠀⣿⡇⢠⣸⠓⠛⠛⠉⠁⠀⠀⣠⠞⠉⠓⢦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠇⠀⠀⠀⠀⠀⢸ ⠤⠤⠄⣠⣿⣷⠈⠁⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣶⣶⣤⣄⡀⠀⠀ ⠀⠀⢸⣿⠛⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⢻⣿⣿⣿⣿⣦⡄ ⠀⠀⠘⠁⠀⢘⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⡿⠃ ⠀⠀⠀⠀⢠⣾⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣶⣿⣿⣿⣿⣿⣿⡿⠉⠀⠀ ⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣤⣀⣀⣀⣤⡄⠀⠀⠀⠐⣿⣿⣿⡿⠿⣿⣿⣏⠉⠀⢸⡇⠀⠀⠀ ⠀⠀⠀⠀⠙⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠻⢿⡿⠃⠀⠀⠀⠀⠉⠀⠀⠀⠀⠛⢿⣿⣷⣦⣀⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣈⠁⠀⠀⠀⢀⣸⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣦⠀⠀⠀ ⠀⠀⠀⢀⣴⣿⣿⣷⣄⣴⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⠿⠀⠀⠀ ⠀⠀⢠⣾⣿⣿⡿⣋⡁⠀⠀⠀⠀⢀⣀⣠⣤⣶⣾⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡃⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⣿⣿⣿⣿⣿⣿⣦⡀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣸⣿⣿⣿⣿⣿⣿⣧⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣾⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⣾⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⡿⢻⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣼⣿⣿⣿⡍⣿⢷⣿⠟⠉⢀⣾⣿⡿⠛⢻⣿⣿⣿⣿⣿⣿⣇⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⡏⠉⣜⠙⠐⠁⡾⠟⠛⠻⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠢⢄⡀⠈⠙⢷⣼⠀⠀⠀⠀⠀⠀⠀⢢⣙⣿⢿⣿⢿⢿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠟⠁⠀⢀⣤⠜⠉⠉⠺⡿⠀⣦⠀⠀⣀⠀⠀⢸⠁⠀⠚⢱⡀⢙⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⢾⣿⠁⠀⠀⠐⠁⠀⠀⠀⢀⣼⡑⠒⣃⠀⠀⠏⣀⣀⠇⠀⠀⢀⣾⢧⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦ ⠀⠀⠀⠀⣀⠔⠊⠉⠀⠀⢸⡇⠀⠀⠀⠀⠀⢠⠀⢀⣾⡇⢣⡀⢳⣀⣀⠀⠀⠈⠁⢀⡼⠟⠻⣿⣿⣿⣷⣄⠈⢉⠉⠉⠉⠙⠛⠛⠛⠛ ⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⢸⠃⢀⠀⠀⠀⠀⡎⠀⣾⠁⠉⠢⣱⡀⠓⠚⠀⠀⣀⡤⠊⠀⠀⠀⢻⣿⣟⢯⡙⠛⠦⠉⠒⠄⠀⠀⠀⠀⠀ ⢀⡔⠁⠀⠀⠀⠀⢀⡠⠖⠛⡀⠀⠀⠀⠀⢰⡇⢠⣿⠀⠀⠀⠈⢻⣶⠒⠊⡉⢁⡆⠀⠀⠀⠀⠀⠂⠹⣷⡈⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡇⠀⠀⠀⠀⢰⠋⠀⠀⠀⠣⠀⠀⠀⠀⠈⠁⢸⣿⣧⡀⠀⠀⠀⡧⠔⠚⠒⠚⠓⠤⣄⡀⠀⠀⠀⢀⣿⠇⠀⢠⠗⠢⠤⣀⠀⠀⠀⠀ ⠀⢰⠀⠀⠀⠀⠈⠒⠤⠤⢤⡴⢻⡀⠀⢠⠀⠀⢸⣿⣿⣿⣦⣰⠞⠁⠀⠀⠀⠀⠀⠀⠀⠈⠑⣶⣤⣾⠏⠀⠀⠀⠀⠀⠀⠀⠉⠲⢄⠀ ⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⡃⠀⠘⡄⠀⠸⣿⣿⣿⣿⣿⣷⣦⣤⣤⣤⣄⣠⣤⣴⣾⣿⣿⣿⠋⠀⠀⢠⠊⠀⠀⠀⣀⣤⣶⣿⡇ ⠀⠀⢱⡀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡇⠀⠀⢃⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⡠⠃⠀⣠⣶⣿⣿⣿⣿⣿⡇ ⠀⠀⠀⠱⣄⠀⠀⠀⠳⡀⠀⠀⠈⣷⠀⠀⠘⡄⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠀⣠⠔⠀⡔⢁⣴⣿⣿⣿⣿⡿⢿⠟⠛⡗ ⠀⠀⠀⠀⠀⠑⢄⠀⠀⠑⣦⣶⣶⣿⠀⠀⠀⢡⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠀⣀⠴⠊⠀⣀⠸⢀⣼⣿⡿⠟⠋⠁⠠⠊⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠑⢄⣴⣿⣿⣿⣿⠀⠀⠀⠈⡆⠀⠀⠻⣿⣿⣿⠿⠛⠉⣀⠠⠔⠊⠀⠀⠀⠀⢹⠸⢸⣿⠁⠠⠤⢄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣦⡀⠀⠘⠦⣀⠀⠉⠁⠠⠒⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠘⣶⣾⡟⠀⠀⠀⠀⠙⠆⠀⠀⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⡿⠋⠉⠽⣿⣶⣄⣀⣀⣠⣤⡀⠀⠠⠤⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⢈⣹⢿⠀⠀⠀⠀⠀⠸⡀⠀⠰⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠃⡰⠁⢠⠿⢿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣠⠄⠀⠀⠀⠀⠀⣠⠖⠉⠀⠀⠳⡀⠀⠀⠀⠀⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢁⡜⠀⢠⠃⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣤⠴⢾⠋⠁⠀⠀⢀⡤⠞⠢⡀⠀⢀⡆⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⣱⡞⠀⢠⠃⠀⠀⠀⠀⠃⠈⠝⠛⠻⠿⠿⠟⠛⠛⠛⠛⠉⠀⠀⢀⣧⣀⣤⡶⠋⠀⠀⠀⠈⠑⠉⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣴⡿⠿⠛⠛⠳⣦⣤⣴⠶⠾⠛⠛⠛⠛⠷⠶⣴⠾⠛⣛⡛⠿⣶⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⣿⠏⠀⣾⣿⣷⣦⠀⠉⢠⣄⣀⡀⠀⠀⢀⣀⣴⡆⠀⢸⣿⣿⣷⡌⢻⡆⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⠀⠀⠛⠻⠟⠋⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠀⠀⠀⠈⠙⠛⠋⠀⠀⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⡏⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀ ⠀⠀⠀⢠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀ ⠀⠀⠀⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⠀⠀ ⠀⠀⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⠀⠀ ⠀⢀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡆⠀ ⠀⣸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠊⠁⠀⠀⠀⠈⠉⠒⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⠀ ⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⣠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣄⠀⠀⠀⠀⠀⠀⠀⠸⣿⡆ ⢰⣿⡇⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⠀⠀⠀⠀⠀⠀⠀⣿⡇ ⠈⣿⣇⠀⠀⠀⠀⠀⣰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⣰⣿⠇ ⠀⠹⣿⣄⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⢠⣿⠏⠀ ⠀⠀⠙⣿⣦⡀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣴⣿⠋⠀⠀ ⠀⠀⠀⠈⣿⢿⣦⣀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣡⣴⣿⠏⠀⠀⠀⠀ ⠀⠀⠀⠀⢿⣤⣈⠙⠻⢷⣶⣤⣤⣤⣀⣀⠀⠀⠀⢀⣀⣀⣀⣀⣤⣶⠾⠟⠋⠁⢸⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠉⠹⣦⡶⠶⣬⣯⠉⠉⠙⠛⠛⠛⠛⠛⠛⠉⠉⠉⣿⣤⣶⣄⣀⣾⡟⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀
⢰⣷⢶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠶⢶⣆ ⢺⣿⣶⡎⠙⠿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠁⠀⠀⠠⡟ ⠈⣿⣿⣷⣄⠄⠈⢻⣷⣦⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⣼⠁ ⠀⢸⣿⣿⣿⣠⣤⣤⣿⡟⠉⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⠷⣶⣶⣄⠀⠀⣰⠇⠀ ⠀⠀⢻⣿⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣃⢰⠏⠀⠀ ⠀⠀⣼⣿⠇⠀⢠⡀⠀⠀⠀⣀⣴⡇⠀⠀⢀⣴⣤⠀⠀⠀⠀⠀⠈⣿⡿⠀⠀⠀ ⠀⠀⠉⠀⣀⣠⣾⣿⣷⣴⣿⣿⣿⡿⠀⠀⢿⣿⣿⣷⣶⣤⡀⠀⠀⠈⠃⠀⠀⠀ ⠀⠀⠀⠀⢿⣿⣏⠉⢹⠛⢿⣿⣿⠁⠀⠀⢸⣿⡿⢿⠿⢿⣷⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⢿⣿⣦⣤⣤⣿⣿⠇⠀⠀⠀⠸⣿⣄⣘⣀⣸⣿⠂⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠛⠻⡿⠿⣿⠟⠀⠀⠀⠀⠀⠹⣿⣿⣿⡿⠿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠓⠦⣀⠔⠊⠀⠘⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⠾⠤⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠠⢤⣤⣄⠀⠠⢤⡤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡟⢿⣧⡀⠀⡇⠀⢀⣤⠴⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠻⣿⣦⡇⠀⣿⣿⠀⠈⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣴⠧⠀⠀⠘⢿⡇⠀⠙⢿⣀⣸⠟⠁⠰⣿⠆⠀⠀⠀⠀⠀⠀
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⡇⠀ ⠻⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀ ⠀⠀⠀⠀⠀⠀⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠋⠉⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⣤⣤⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⡠⠤⠒⠒⠒⠙⠒⠒⠤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⡦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡼⠅⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣌⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⢣⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⡄⢹⡄⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣀⣀⣀⣀⠿⠀⠀⠀⠈⠷⠤⣄⣀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⡇⠐⡇⠀⠀⠀⣠⠊⢠⡀⠉⠲⡄⠀⠀⠀⠀⠀⠀ ⠘⢯⡉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣉⣒⣦⣄⠀⠈⢦⡀⠀⠀⠀⠀⣇⢰⠇⠀⠀⡜⠁⣴⣿⣿⣶⡄⠘⢦⠀⠀⠀⠀⠀ ⠀⠀⠉⠲⢄⣀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣟⠛⣿⣿⣿⣿⣦⡀⠳⡀⠀⠀⠀⣿⡟⠀⠀⠀⠸⡀⠙⢻⣿⡿⠀⠀⣸⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⣿⡷⠖⠀⠀⠀⠀⠀⢚⠻⣿⣿⡿⣿⠏⠘⢷⣶⣷⡄⠀⢸⡟⠁⠀⠀⠀⠀⠱⡀⠈⠛⠀⠀⡠⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠾⣏⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠂⠀⠀⠀⠈⠙⣏⢀⣤⣾⡴⢻⠂⠀⠀⠀⠈⠉⠒⠤⠤⠊⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⣻⡉⠉⣽⠃⠀⠀⠀⠲⠀⣀⣠⡄⠀⠤⠤⠄⠈⣡⣾⠟⠁⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⣿⠹⣤⡧⠤⠶⢾⣍⣉⠍⠀⣰⠧⣤⣤⡤⣶⠿⢋⣡⣄⡞⢁⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠣⣌⠑⢢⣤⡤⠤⣖⣠⡜⠁⠀⢻⣧⣍⣉⣉⣭⣶⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⡟⠁⠀⠀⠀⠀⠉⠉⠁⠺⢿⣿⣁⣴⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣷⣼⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⠟⠉⠉⠁⠒⣒⠤⢄⣀⠀⠀⠀⠀⠀⣠⣴⡶⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢯⡀⠀⠀⠀⠀⠀⠀⢠⡀⠈⠑⠢⢄⠀⠀⠋⣹⣆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢹⣆⠀⠙⣿⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⡞⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠙⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢿⣧⡀⠉⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡒⠤⣷⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠈⠶⠼⢿⣷⡆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡄⠐⡇⠀⠀⠐⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⠃⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⢹⠀⠀⠀⠀⠀⠀⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⡏⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡈⢣⡀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠑⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⢀⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠙⠲⣤⣀⣀⣀⣀⣀⣀⣤⣾⣿⠛⣧⡉⠓⢶⣤⣤⢤⡴⣶⡎⠁⠀⢴⠟⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠘⢦⡈⠙⠛⢻⠉⠀⣼⠟⠀⡇⠈⠓⠤⣀⠀⠀⢣⣼⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠀⠉⠉⢁⣧⠀⠀⠀⠀⠀⠙⢦⡀⠸⠀⣸⣇⠈⠀⡇⠀⠀⠀⠈⠑⠦⣈⡏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡴⠊⠁⠀⠀⠀⢀⠞⠁⠘⡆⠀⠀⠀⠀⠀⠀⠈⠓⠚⠁⠈⢳⠀⡇⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣀⠔⠁⠀⠀⠀⠀⠀⠰⠁⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⢀⣀⣀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⣶⠒⠹⠄⠀⢻⠛⠀⠀⠀⠀⠀⠀⢀⠔⠉⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀ ⠸⢏⣀⣀⣀⠜⠘⠀⠀⠀⠀⠀⢀⡠⠊⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⢱⠀⠀⠀⡇⠀⠀⡠⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⣄⠀⠀ ⠀⠀⠀⢸⠀⠀⠀⠘⠒⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⣆⠀ ⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣿⠀ ⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⢀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⡸⢹⡄ ⠀⠀⠀⠀⠀⠈⠒⠠⠤⠄⠠⣇⠀⠀⡼⠤⠀⠀⠀⢀⠤⢴⠁⠀⢰⠁⠸⣸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢸⠀⢀⠇⠀⠀⠀⠀⠈⡄⠀⡣⠀⠈⢆⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠸⡇⠘⡄⠀⠀⠀⠀⠀⡇⡰⠁⡄⠀⡸⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣴⡱⢸⠁⠀⠀⠀⠀⢠⢱⠁⠀⠀⢰⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡱⠹⡆⡇⠀⠀⢀⡠⠂⡇⠀⠀⡆⠇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠭⠤⠧⠀⠀⠈⠉⠉⠀⠴⣒⣁⠇⠀⠀⠀
⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢰⣿⡿⠗⠀⠠⠄⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⡜⠁⠀⠀⠀⠀⠀⠈⠑⢶⣶⡄ ⢀⣶⣦⣸⠀⢼⣟⡇⠀⠀⢀⣀⠀⠘⡿⠃ ⠀⢿⣿⣿⣄⠒⠀⠠⢶⡂⢫⣿⢇⢀⠃⠀ ⠀⠈⠻⣿⣿⣿⣶⣤⣀⣀⣀⣂⡠⠊⠀⠀ ⠀⠀⠀⠃⠀⠀⠉⠙⠛⠿⣿⣿⣧⠀⠀⠀ ⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡇⠀⠀ ⠀⠀⠀⣷⣄⡀⠀⠀⠀⢀⣴⡟⠿⠃⠀⠀ ⠀⠀⠀⢻⣿⣿⠉⠉⢹⣿⣿⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠉⠁⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⢸⣆⠀⠀⠈⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣶⣄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡎⠀⠀⠀⣀⡤⣖⣒⣋⣉⣉⡉⠛⠒⠲⣄⡀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣆⣀⣘⣆⣀⣀⣀⡞⠀⠀⣠⠶⢤⣀⣼⡗⠲⠚⠉⠉⠃⠈⠳⣾⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⣠⠿⠛⣋⠁⠀⠀⠀⠀⠉⠳⢦⣄⠀⠙⢦⡀⠀⠀⠀⠀⢹⣄⠀⠀⠀⠀⠀⠀⣰⣿⡿⠛⠉⠁⠀⢀⡼⠋⠉⠉⠻⣇⠀⠀⠈⢿⣇⠀⠀⣀⠀⠀⠀⠀⢹⣇⠀ ⠀⠀⠀⠀⠀⣷⠎⠁⣠⠞⠁⣠⠀⠀⠀⠀⠀⠀⠀⡘⢦⡀⠀⠙⢦⣀⠀⣀⡈⠻⠷⣦⡀⠀⢀⣼⠟⠁⠀⠀⠀⠀⠀⢻⣤⠀⠀⠀⠀⠙⠂⠀⠀⠀⠉⠉⢿⠉⢣⡀⠀⠀⠘⢿⡀ ⠀⠀⠀⢀⣾⠃⠀⠐⣁⣤⠞⠁⠀⠀⠀⠀⠀⠀⣠⠇⠀⠈⣳⣦⣤⣬⣭⣭⡽⢶⣤⣦⣳⣤⠞⠁⠀⠀⠀⣀⡤⠶⠾⠀⠙⣳⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⣄⠃⠀⠄⢀⡀⠇ ⠀⠀⢀⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⢀⣠⠞⠋⢁⣠⠖⠀⠀⠀⠀⠀⠀⠈⠙⠶⣶⣶⠞⠛⠁⠀⠀⠀⠀⠀⠀⠀⠙⡶⢤⣀⡀⠀⠀⠀⠀⢠⡇⠙⢦⠀⢠⣿⣇⠀ ⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⣋⣤⣶⠟⠁⠀⣠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠉⠀⠀⠉⠓⠦⣄⠀⠈⣧⠀⠀⠀⠸⠿⣿⡆ ⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⡿⠛⠋⠁⣸⠃⠀⠀⣸⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⡳⣄⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠈⠱⣤⡟⠀⠀⠀⠀⠀⡼⠀ ⠀⠀⡇⠙⠶⠤⠤⠤⢖⣪⡽⠿⠛⠋⢲⡀⢠⠇⠀⠀⠰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡜⢦⠀⠀⢠⠞⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡛⠒⠾⣆⠀⢀⠇⠀ ⠀⠀⡇⠀⠀⣀⡤⠞⠋⢡⠴⠂⠀⠀⢸⡇⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠊⢧⠐⠋⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⢀⣀⣈⣙⣋⠀⠀ ⠀⢀⣻⡴⠚⠉⠀⠀⠀⠀⠀⠀⣀⡄⣸⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠙⠶⢤⡄⠀⠀⣴⠟⠁⣀⡴⠛⠉⠀⠀⠀⠉⠛⣗ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠚⠉⣰⡏⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⣀⣀⣀⣤⣴⣯⣥⡴⠛⠉⠁⠀⠒⠒⠶⣶⡚⠋⠉ ⠀⠀⠀⠀⠀⠀⢀⡤⠖⠉⢀⣠⣾⠉⣇⠠⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠞⠛⠛⠉⠁⢀⡠⠀⠈⠉⠓⢦⣘⡶⢤⡀⠀⠙⢷⠀⠀ ⠀⠀⢀⣤⠴⠚⣉⣤⠴⠛⠋⠁⠸⠛⡿⢧⣼⣆⠀⠀⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠄⠚⠋⢁⣀⣀⣀⣤⣬⣿⣷⡄⠙⠦⣄⠈⡆⠀ ⠀⠀⣀⣤⡶⠟⠉⠀⠀⠀⠀⠀⠀⣼⠁⠀⠈⢻⡄⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⢀⣠⡴⠟⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠃⠀ ⠤⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠈⢷⡀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣼⣿⣿⣿⣷⡀⠀⠀⢀⣴⠞⠁⠀⠀⠀⠀⠀⠈⢧⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣿⣿⣿⣿⣿⣷⡶⠚⠋⠀⠀⠀⠀⠰⠛⠁⠀⠀⠘⣆⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣾⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⢀⡾⠋⠀⠐⠀⠀⢠⡔⠉⡠⢚⡿⠉⠀⢀⢀⣴⡾⠉⠀⣠⣤⣴⢞⡿⠋⠀⣠⢄⡞⠁⠀⠀⢰⠇⠀⢸⡀⠘⢆⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⢠⠏⣠⣾⢶⣟⣀⣀⣈⡴⠋⡾⠁⣠⡾⠋⡴⣳⠋⠀⣠⠜⠀⡜⠀⠀⠀⣠⡏⠀⠀⡀⠘⡄⠈⡆⠀⠀ ⠀⠀⠀⠀⠀⣸⠁⠀⠀⣸⡜⠀⠎⣴⠟⢡⠎⣠⠎⡠⠋⠉⣹⠓⢲⠿⢄⣼⣟⠁⠀⡴⠋⠀⣰⠃⠀⠀⣰⡟⠀⠀⢠⡇⠀⠸⡆⠸⡀⠀ ⠀⠀⠀⠀⢀⣷⡀⢀⢀⡟⠀⢠⠞⠁⢀⣎⣼⢃⠞⠀⠀⢠⠇⠀⠁⠀⣼⡟⠉⣩⠟⠉⠉⣍⡇⠀⠀⣰⡟⢀⠀⢠⣿⠀⠀⠀⣿⠀⡇⠀ ⠀⠀⠀⠀⢸⠉⣧⣀⣿⣳⣦⣾⣶⣶⣾⣿⣷⣿⣤⣀⡀⣼⣦⠂⢀⠎⡜⢀⣾⠃⠀⠀⠈⡾⠀⠀⢸⡿⢀⡞⢀⣾⡟⠀⠀⠀⣿⡆⡇⠀ ⠀⠀⠀⠀⠈⠀⢹⣆⣿⠛⠻⢿⣯⣙⣿⡿⠋⠛⠻⣿⣿⣿⣯⡀⠀⡜⣠⢿⠃⠀⠀⠀⣰⡇⠀⠀⣾⡿⣿⠀⣰⣿⠃⠀⠀⢀⡿⡇⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠈⠹⠟⠒⠦⠤⣀⡹⣌⣿⢻⣿⣴⣽⣧⡏⠀⠀⠀⡜⣿⠀⠀⣸⠋⢸⠋⣷⣿⠇⠀⠀⢀⡿⢱⠁⠃⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⣧⠀⠀⠀⣀⢅⠀⠀⠀⠀⠈⠙⠻⠍⠈⡿⠁⣿⠁⠀⠀⡜⠀⡏⠀⢠⣿⣶⣧⣞⣀⡟⠀⠀⠀⡼⠁⡜⢠⠀⠀ ⣆⠀⠠⠀⣆⠀⠰⣿⠈⣯⠀⡄⡨⠗⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣃⡄⣸⠀⠀⡜⣀⣼⡧⠶⣿⣻⡿⢯⠛⣻⣧⡄⠀⡰⠃⣰⠃⡜⠀⢀ ⠛⣆⠀⠀⢸⡀⠀⠘⡆⠈⢇⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠉⢹⡶⢾⠟⠁⠘⡇⢠⡟⠯⣀⡼⠐⢋⣽⣿⠞⠁⣰⡟⣰⠃⠀⠎ ⠀⢟⣦⠀⠀⣷⣀⠀⠹⡄⠀⠻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆⣼⠀⠀⠀⡇⡌⠙⠒⢤⡀⠀⠉⢼⡟⢦⠞⣹⣵⠏⡴⠃⠀ ⢀⣘⠀⢓⣤⣍⠉⠳⢤⣘⢆⠀⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠤⠀⠀⠸⣇⢳⡤⠊⠉⠒⢲⠿⡟⠁⣰⣿⡿⠋⠀⠀⠀ ⣾⠿⣧⢸⡏⢹⡇⢆⠀⠈⢉⡓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠞⠀⠀⠀⠀⠀⢠⣧⢞⣽⡟⠀⠀⠀⢀⣀ ⣿⠀⣿⣸⡇⣼⠇⠈⠇⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠁⠋⢸⠀⠀⠀⠀⠀⠙ ⣿⠀⣿⣿⠁⣿⠀⠀⠀⠀⠀⠈⣧⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠸⡀⠀⠀⠀⠀⠀ ⡿⠀⠈⣿⢠⡿⠀⠀⠰⠤⠀⢀⡞⢏⣉⡩⣍⡉⠒⠢⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⢇⠉⠒⠤⢤⣤⠄ ⠀⢀⡾⣿⠿⠃⠀⠀⡀⠀⠀⠘⡿⠋⢹⡇⠀⢯⠉⠉⠙⡟⠛⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡰⢻⡄⠀⠀⢸⠑⠒⠈⢉⡀⠀ ⣠⣾⠇⢸⡄⠀⣤⠀⢱⠀⠀⠀⠙⠒⠺⡇⠀⢸⠀⢠⠀⡇⠀⠀⢤⡈⠑⠒⠦⠶⣶⡀⠀⠀⠀⠀⢠⣿⠁⠈⡇⠀⠀⡜⠀⠀⠐⠁⠀⢀ ⠋⠉⡆⠀⢷⠀⠘⣄⠀⢇⠀⠀⠀⠀⢀⡇⠀⢸⠀⢸⠀⣇⡀⠀⠀⠈⠒⠶⢄⡀⠀⠙⠲⢄⣀⡰⠟⠼⠀⣰⢁⣠⠞⠁⣀⡠⠤⠒⠒⠛ ⠀⠀⡇⠀⠸⡆⠀⠈⢦⡈⡄⠀⢀⠀⢸⠀⠀⠰⠀⣾⠀⠀⢿⠀⠀⠐⣄⠀⠀⠉⠒⢤⣀⠀⠉⠳⢄⡀⠈⠉⠉⠀⠀⢸⡁⠀⠀⠀⠀⠀ ⡇⠀⡇⠀⠀⣧⠀⠀⠀⠙⢿⡴⣜⡆⢠⠀⠀⠀⢇⡟⠀⠀⢸⡄⠀⠀⠈⢆⠀⠀⠀⠈⢳⣍⡒⢤⣀⠈⠑⠢⢄⣀⠀⢠⣧⠀⠀⠀⠀⠀ ⠘⢀⣡⣤⣄⢼⠀⠀⠀⠀⠸⣿⣿⣼⣾⠀⡆⠀⢸⡇⠀⠀⢼⢷⡀⠀⠀⠈⢷⡀⠀⠀⠀⢹⡝⠦⣍⡛⠶⣤⣀⠈⠙⠺⣿⣷⣤⣶⠒⠒ ⣴⡟⢋⣾⠏⢸⠀⠀⠀⠀⡀⢻⣿⣿⣧⠀⠇⢠⢸⡇⡀⠀⠈⠀⠳⡄⠀⠀⠈⢻⣄⠀⠀⠀⣿⢦⡀⠙⠲⣄⣀⠉⠒⢤⣈⠈⠉⠙⢷⠤ ⠋⣠⡟⠁⠀⢸⠀⠀⠀⠀⢣⠈⣟⣿⣿⡆⠀⢈⣿⠀⡇⠀⠀⠀⠀⠙⢄⠀⠀⠀⠉⢃⣀⣀⣿⣤⣽⠾⠤⠬⠭⠷⠤⢀⡈⠙⠒⢤⣈⠀ ⣼⠟⠠⢤⣤⣼⣄⣀⠀⠀⠀⠻⣿⣟⣿⣿⡀⠘⣿⠀⡟⠀⣀⡠⠤⠀⠀⠁⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣀⣀⣀⣠⣽⣿

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⠀⢀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠹ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣤⣤⣄⡀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢈ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠀⠀⠐ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀⢈ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠀⠀⠈ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
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⠀⠀⠀⠀⠀⠉⢷⣄⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⢻⡶⠂⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⢻⣦⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠃⠊⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⢯⡸⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣵⠇⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⢮⣻⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠛⠉⣆⣀⢀⣀⠀⠀⠀⢀⡀⣴⣶⠀⠀⠀⠀⠀ ⡀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠒⠂⠋⠉⠉⠛⠉⠛⠛⠉⠉⠉⠉⠉⠉⠁⠀⠀⠉⢉⠙⢿⣯⠑⠒⢾⣷⣿⢺⠀⠀⠀⠀⠀ ⠇⠀⠀⠀⠀⠀⢠⣴⡋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠀⠙⢷⣄⡈⠈⣿⢸⠀⠀⠀⠀⠀ ⠀⠐⠀⠀⠀⠀⠐⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣧⠐⣿⠸⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠻⣶⣿⣢⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣆⡀⣀⢀⠤⣤⢤⡴⠦⠀⠀⠀⢠⠀⠙⠒⣶⣤⣤⣄⡀⠈⢻⣿⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣷⣿⣾⣧⣝⠿⡿⢿⣽⡆⠀⠀⣔⡒⡀⠀⠀⠀⠂⣠⣿⣿⣿⣿⣿⣿⡇⠉⢹⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣼⢻⣯⣽⣿⣿⣿⣿⣿⣿⣷⡄⠚⢹⠀⠀⠘⣧⣷⡄⡇⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠸⢿⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠻⣿⣧⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠈⣷⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⣿⣿⣿⣿⣿⣿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠹⣾⡟⠻⠿⣿⣿⣿⠿⠟⠛⠁⠀⠃⠹⣇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠋⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠘⣷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣧⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⢀⣀⠀⠀⠀⠉⠉⢉⣙⣷⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣇ ⠀⠀⠀⠀⠀⠀⢉⡁⣤⠋⠁⠀⠀⠀⠀⢀⣀⣄⣤⡉⡛⠛⠿⣿⣿⣿⣖⠀⢿⣿⠿⠋⠁⣀⠤⠤⢼⡀⠀⠀⠀⢰⠀⢸⣿ ⠀⠀⠀⠀⠀⢸⣥⡴⠃⠀⢀⠤⠤⢚⣩⣽⠟⠛⣛⣿⣶⣖⠒⠀⠉⠙⢿⡿⠸⣇⢠⡀⣰⣶⠲⠤⣜⠛⠂⠀⠀⠸⡄⢸⡿ ⡄⠀⠀⠀⠀⠀⣾⠇⠀⠀⠀⣤⣾⠛⣏⠈⠀⠐⠋⣀⣿⣿⣷⣞⣂⣰⣈⣿⣤⣿⣾⣿⡿⢻⣶⠀⠘⣧⠀⠀⠀⠈⠄⣼⠃ ⡇⠀⠀⡀⠠⠀⠇⠀⠀⠰⠊⠋⣽⠁⠇⣶⡄⠀⠚⠋⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⠼⣿⡇⠀⠈⠀⠀⠀⢠⢟⡿⠀ ⣷⠄⠀⣿⠀⠘⢦⣀⠀⠀⠰⡀⢻⣀⡀⣿⠀⠀⠀⠀⠟⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⢀⣖⣻⡟⠁⠀ ⠿⣷⠀⠸⣇⢾⠀⠙⣆⠀⠀⠀⠀⠈⠙⢿⡀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠋⠉⠃⠀⠀ ⠐⣿⣷⡀⠈⠆⢿⠀⠈⠂⠀⠆⠀⠀⠀⠈⢧⡀⠀⠸⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠉⠀⠀⠀⠀⠀ ⡶⣿⣿⣿⡄⠈⠈⠳⣄⡀⠀⠀⠀⠀⡐⠀⠀⠙⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀ ⡀⠨⢹⣿⣿⠀⠀⠀⠐⠿⢶⡀⠀⢰⡁⢲⠒⠀⠠⢤⡤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠁⠀⢸⣿⣿⡀⠀⠀⠀⠀⠀⠁⠀⠈⢀⠘⠀⠀⠀⠘⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠋⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
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⠉⠉⠉⠉⢄⡀⠈⠁⠈⠉⡄⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⠉⠁⠀ ⠀⠀⠀⠰⡄⠑⣄⠀⠀⠀⣿⡄⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⢳⠀⡈⢦⠀⠀⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⣇⢻⣦⡁⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⢀⣤⣶⠟ ⠀⠀⠀⠀⠀⢹⡜⣿⣿⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢩⡿⠛⠉⠴⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣴⣾⣿⣿⠏⠀ ⠀⠀⠀⠀⠀⠀⢧⢹⣿⣿⣿⣿⣿⣿⣿⡿⢫⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⠸⡆⣿⣿⣿⣿⣿⣿⠟⠀⠉⠀⠀⠀⠀⢀⡤⠦⢤⣀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠂⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢷⣿⣿⣉⠓⠈⠁⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠁⠂⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣶⡟⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⡠⠖⣿⣷⣶⣄⠀⠀⠀⠐⢦⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢙⣀⣀⠀⠀⠀⠀⠀⠀⠠⠃⠀⣾⠁⠐⠉⣿⣿⣿⣆⠀⠀⠀⠀⠙⢿⣿⠟⢉⠤⢌⠹⣿⣿⣿⣿⣿⣋⣠⡴⠂⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⢉⣒⡀⠀⠀⠀⠀⠀⠀⠧⠀⠀⣿⢿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠉⢰⠛⠲⡀⠁⢿⣿⣿⣿⣿⣿⡯⠂⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠹⡀⢀⡏⢠⣿⡄⠀⠀⠀⠀⠀⠐⠄⠀⠹⣏⠉⣹⠃⠀⠀⠀⠀⠀⠀⠀⠈⡦⠀⣷⡀⣸⣿⣿⣿⠟⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣼⡅⢠⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⣠⠟⢀⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡧⠀⢿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⢁⣴⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠘⣟⠁⠀⠀⠀⠀⠀⢀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠲⢀⡠⠤⣒⣨⣥⣤⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⢿⠋⠀⢀⣀⡀⣀⠤⠚⣁⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⠀⠀⠀⠈⠳⣿⣿⡿⠋⠀⠸⡇⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⣀⡼⠗⠛⣩⠜⠋⢀⣴⠟⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠙⢿⠁⠀⠀⢰⠃⠀⠀⠀⠀⢀⡴⣋⣠⠖⢋⣡⣴⠶⠋⢁⣠⡴⢿⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⣄⡀⠀⠑⠦⠴⠋⠀⠀⠀⢀⣴⣿⠟⣉⣴⣿⠿⠋⠀⣠⣴⣿⣿⣃⣨⣷⠀⠀⠀⢀⣀⣤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢤⣀⠀⠀⠀⣰⣾⡿⠋⣠⣾⠿⠋⢁⣠⢴⣿⡿⢿⣿⣿⣿⣿⣋⣉⡤⠟⠛⠉⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⡿⣹⠟⠒⠛⠉⠉⠉⠉⠉⠙⠛⠛⠿⣿⣿⣯⣴⡾⠛⠁⠀⠀⠀⢀⡰ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠁⠀⠀⣠⠔⠚⠉⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠋⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⣠⠞⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠞⠁⢀⣴⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡁⠀⠀⠀⢀⣠⠞ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⢉⣠⣦⣶⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣀⣤⡶⠟⠁⠀
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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⣤⣴⠶⠦⠤⠤⠤⠤⢄⣀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠿⠿⠿⠿⠿⠿⠿⠿⠿⠶⠤⠤⣀⣀⡀⠀⠀⢈⣻⣦⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⡖⠋⠀⠀⠙⢷⣄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⢀⡠⠞⠛⣇ ⠀⠀⠀⠀⠀⠀⢶⣶⠒⠦⣄⣠⣶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⢀⠔⠉⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠉⢛⣷⠞⠛⢿⣦⣄⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠘⠒⠒⡞⠋⢙⣷⣶⠞⢟⢻ ⠀⠀⠀⠀⠀⢀⣠⡾⠋⠁⠀⣠⠀⠀⠉⠉⠉⠉⠉⠛⠛⠛⠛⠛⠓⠒⠒⠒⠒⠂⠈⠉⣩⠀⠀⠀⠀⠀⠈⠉⠉⠉⡟⢰⣼⠚ ⠀⠀⠀⢀⣴⠟⠉⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⣾⣿⠀ ⠀⢀⣴⠟⠁⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⠀⠀⠀⢀⡴⠃⠀⢠⣴⠟⢻⠂⠄⠀⠀⠀⡎⠀⢹⠏⠀ ⢀⣿⣧⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⠀⢠⡾⠁⠀⢠⡟⠁⠀⡈⡇⠀⠀⢀⡼⠥⠔⠋⠀⠀ ⢸⡀⠈⠻⢦⣴⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⠀⠀⠀⠀⢀⣤⢿⡅⠀⠀⣾⠁⠀⣸⡏⣣⡀⣠⠞⠀⠀⠀⠀⠀⠀ ⢸⠳⢦⣀⠀⣿⠷⠦⠤⠤⠤⠤⣀⣀⣀⣀⣀⣤⣾⡿⠗⠒⠒⠒⠊⠹⠁⡼⠁⠀⢰⡇⠀⠀⣿⡇⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀ ⣈⠣⣀⠀⠉⠁⠀⠘⢦⠉⢉⡽⠗⠊⠉⠙⠻⢿⣏⡀⠀⠀⣀⣀⣀⠴⠚⠁⠀⣰⣿⠁⠀⠀⠻⣵⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠸⣄⠀⠉⠑⠢⠤⣤⣀⣛⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣿⣿⡿⠀⠀⣀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠉⠻⢦⣤⣀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠀⠀⣼⡿⠁⠈⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠉⠛⠻⠶⠶⣤⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⠶⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠓⠂⠂⠓⠲⠂⠂⠒⠒⠀⠐⠓⠚⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⣀⣠⣤⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⢤⣀⣠⠴⠚⠋⠉⠉⠉⠩⠽⠛⠳⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠁⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠲⢾⡷⢦⡀⣀⡀⠈⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣠⠞⣋⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣤⣄⣠⠤⠤⠛⠉⠉⠉⠉⠙⢦⣻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠉⢉⡽⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠙⡟⣧⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠚⠉⢉⠁⠀⠀⠀⠀⠀⠀⠁⠸⠈⠉⠛⠶⣤⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡇⠀⢀⠀⠀⠀⢀⡴⣿⣿⣷⣀⠀⠀⠀⠰⡄⢀⡔⢁⣠⣴⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣦⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⢧⢀⡇⠀⠀⠀⣼⡅⠊⢀⣸⣿⠀⠀⢀⡀⢿⣾⣴⣿⡞⠁⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⠀⠀⠀ ⠀⠀⠀⠀⢸⣾⠀⠀⠀⠀⠘⣿⠄⣻⣿⣷⢃⣧⢸⣧⢸⡿⠟⢻⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀ ⠀⠀⠀⠀⠈⢸⠀⠀⠀⠀⠀⠈⢻⠍⠀⣾⡞⠘⢾⡏⠳⢧⡀⡌⣦⠀⡿⢷⡀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀ ⠀⠀⠀⠀⠀⢸⢀⡆⠀⠀⢀⠀⣼⠀⠀⢿⠁⠀⠈⠛⠀⠀⠹⢹⠛⣷⢿⣸⡇⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠀⠀⠀⢸⣾⠃⣠⡎⣸⣠⡏⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⠼⠟⠁⢤⣍⠹⡄⣿⡇⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀ ⣀⣀⣠⣴⠶⣯⣿⠚⠁⣧⠏⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠈⠉⠛⢿⣷⠀⢦⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀ ⠉⠈⠉⠛⠲⢤⣉⡓⠾⣇⠀⡇⠁⠀⠘⣄⠀⠀⠀⠀⠀⣸⠄⠀⠀⠀⠀⠀⠀⠀⡼⢹⣇⠈⠳⣄⠈⠒⠤⢤⣀⣀⠀⠀⠀⣼⠁⠀⠀⠀ ⢄⡀⠀⠀⠀⢀⣀⣉⣓⣮⣝⡷⣀⢀⠖⠚⢷⣄⢀⡴⠋⠹⡀⠀⠀⠀⠀⠀⠀⣼⢃⣿⠛⢧⣀⠀⠉⠉⠉⠉⠉⠉⠈⠉⠳⢾⡄⠀⠀⠀ ⠤⠒⠓⠉⠉⠉⠀⠀⠀⠉⠉⠛⠻⠿⢤⣀⣀⠈⠉⠀⠀⠀⢧⣀⠀⠀⠀⠀⣼⢃⣾⠃⠀⠉⢻⡛⠒⢶⠒⠒⠶⣆⡒⠂⠀⠀⠙⠢⢄⡀ ⠀⠀⠀⠀⠀⠐⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⣉⣛⠶⣆⠀⠀⠀⠀⣉⠽⠋⣹⢧⠋⣿⣄⠀⠀⠈⢧⡀⠘⣧⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠚⠉⠀⠀⠀⢄⠸⡆⣠⡶⢋⡠⠔⢚⡏⡎⠸⡄⠙⠻⠶⠶⠚⢷⡄⠈⢳⣄⠀⠀⠀⠈⠓⠤⠄⢀⡤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡏⡴⠁⠀⠀⢸⡇⡇⠀⠳⢄⣀⡤⠤⠖⠒⠛⢶⣄⠈⠳⠦⣤⣠⣤⡴⠮⠗⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣷⡇⠀⠀⠀⠈⢧⡀⠐⠤⣀⣀⣤⠤⠖⠒⠉⠉⠛⣿⡗⠒⠶⠶⠶⠒⠒⠂⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⣀⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⣾⣧⣀⣀⣀⣀⣀⣀⣠⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⡿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣼⢿⣯⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⡝⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣯⠈⣿⣿⣮⣛⢿⣿⡿⠿⠿⢿⣿⣿⣿⢿⣿⣿⣿⢧⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣹⣧⣽⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠘⠛⢿⣿⡟⣾⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣏⣿⣿⡟⠁⠀⠀⠀⣤⣴⣶⣶⢸⣶⣶⣄⣘⣿⢳⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣹⡿⠇⠀⣠⣶⡾⢿⣿⣿⣿⠀⢺⣿⣿⡿⣿⣼⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⡿⠙⠁⠀⠘⣿⣿⣦⣈⣼⣿⡿⠀⠀⠹⣤⣥⣿⡇⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠉⣿⣿⣿⡿⠟⠁⠈⣲⠃⠘⢻⣿⠷⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⢰⣦⡈⠋⠁⠀⠀⠐⠊⠀⠈⠂⢀⠁⠀⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠈⠁⠒⠓⠀⠀⠀⠀⠀⠀⠀⠶⠋⢰⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿ ⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿ ⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿ ⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿ ⣿⣿⣯⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣽⡿⠿⢿⡿⠿⣷⣿⡿⡾⠻⠿⠿⠿⠷⠚⠴⠠⠄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⡇⠀⠀⣧⣼⠁⢸⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⠙⠢⠤⠒⠒⠊⠉⢓⠏⠀⠀⣷⡀⠀⣹⣿⣠⡿⠂⢸⡷⠤⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠋⠉⢉⣉⢀⡘⡇⢀⣬⣿⡀⠀⠐⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⣴⣿⣟⣿⣷⣽⠸⡇⠈⢧⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⢀⠔⣿⠀⠀⠀⠀⢸⠟⠛⠻⠿⣙⢻⡀⠙⢦⡀⢳⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⢀⣮⣾⡇⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠉⠁⠀⠈⣿⣿⡇⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠤⢼⣄⠎⠁⢀⡇⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⣿⢻⡀⣀⣠⡞⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠐⠢⡤⠝⠀⣰⠋⠀⠀⣆⠀⠀⠀⠈⠳⢤⣀⣀⣀⠀⢀⣼⣿⠀⡇⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⣼⣁⡀⠀⠀⠙⣦⡤⠤⠤⠒⠋⠁⠀⠈⠑⠻⢿⣈⠀⠙⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠓⠉⣉⡉⠉⠉⠓⠞⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⣩⡴⢊⣩⠜⠛⠛⠳⣶⣄⡈⠢⡄⠀⠀⠀⠀⢠⣀⠀⠀⠀⠀⠀⠈⠻⣦⣧⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⣮⡞⢁⣼⠟⠁⠀⠀⠀⣠⡇⠈⠻⣦⠈⢢⡀⠀⠀⠀⢿⣷⣤⡀⠀⠀⠀⠀⠀⡇⠈⢆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⡿⣿⢋⠓⠤⠤⠒⠚⣿⡷⠄⠀⠈⢷⡄⠱⠀⠀⠀⠈⠙⠳⢌⡁⠒⢦⡴⠊⠀⠀⠈⡆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢰⠉⡿⢿⢡⠇⢸⢀⣠⠴⠒⠋⠁⠀⣀⣤⣤⣼⣿⡄⠀⠀⠀⠀⠀⠀⠀⠙⠲⢼⡁⠀⠀⠀⠀⢁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣮⣼⣁⡼⠉⢀⣾⠏⠀⠀⠀⣠⠶⣋⡽⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠤⡀⠀⡎⠀⠀⠀⠀ ⠀⠀⠀⣠⡴⢻⣿⣿⣿⢁⡴⠋⢸⠀⠀⣠⠞⢑⡶⠋⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡄⠀⠀⠀⠀ ⠀⢠⡞⠋⠀⢸⢉⡟⢻⠟⠁⠀⠸⡄⢠⠋⢰⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⠀⠀⠀ ⣰⣏⣀⡀⠀⢸⣞⣠⠏⠀⠀⠀⠀⢷⡏⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀ ⣿⣿⣿⣿⣷⣾⣿⠏⠀⠀⠀⠀⠀⠈⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀ ⠙⠿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆ ⠀⠀⠈⠙⠛⠻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢄⡀⠀⠀⠀⠀⠀⣸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹ ⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⠒⢒⣿⣿⡟⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞ ⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⠿⣿⣮⣷⣄⣀⠀⠀⠀⠀⠀⢀⣀⡠⠄⠀⠀⠀⢀⠜⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⠢⣄⣀⣤⠶⠶⠶⠿⠿⠿⠿⠭⠭⠽⠋⠙⠓⠦⣧⣤⣽⣿⠿⠿⠟⠛⠛⠉⠉⠉⠁⠈⠐⠦⠖⠁⠀⠀

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⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⡤⠚⠁⢀⠛⣦⡴⠿⠛⠓⢦⡤⠛⡄⠈⠑⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⡀⠀⠀⡼⠐⣿⢆⡄⠀⠀⠀⠀⢸⡀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠣⣀⣼⣥⡤⠘⠋⠀⢤⣤⣀⠀⠀⢣⣄⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡧⣴⣶⡄⠀⠀⢠⣶⣦⠀⠀⠀⢸⡇⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⡤⢴⠃⠙⢻⣷⡆⡀⠀⠙⠋⣠⠤⡀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀ ⠸⣇⡀⠙⢙⡏⠻⡖⠉⢃⡖⠚⠃⢀⣷⣶⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⣛⠋⠛⠊⠓⡾⢆⠀⠀⠀⠀ ⠀⠘⠧⠴⠻⢿⣯⣉⣲⡋⠉⠲⢤⣿⡾⠛⢇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⠀⠀⠁⣸⣇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⢠⣿⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠒⠒⠢⠤⠤⣀⡀⠀⣠⠏⠀⠀⠀⠈⣸⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⠀⢀⣺⠏⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣾⡿⠇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⣧⡀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢈⡿⣆⡀⠀⡇⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣀⡀⠤⠔⠊⠀⠈⠛⠦⣧⡀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⡎⠙⠢⡀⠀⠀⠀⠠⡟⢻⠳⠶⠤⣠⣄⣀⣳⡄⠀⠀⠀⠀⠀⠳⠤⣄⠀⠀⠀ ⠀⢀⡜⠀⠀⢀⡔⠒⠒⠒⠒⠒⠚⠁⠀⠀⢳⠀⠀⠀⠀⢷⠈⣆⠀⠀⠀⠈⠈⣏⠉⠢⡀⠀⠀⠀⠀⠀⢹⡇⠀⠀ ⠀⡞⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⢸⠀⠈⠒⠤⡀⠀⠀⠈⢲⡄⠑⠢⢄⡀⠀⠀⠀⢇⠀⠀ ⠀⠻⣆⠤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⢸⠀⠀⠀⠀⢸⠆⠀⠀⢸⠏⠀⠀⠀⠈⢢⠀⠀⠘⡄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⠀⠀⠀⣠⠎⠀⠀⢀⠇⠀⠀⠀⠀⠀⠈⣇⠀⠀⠹⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣷⡦⠄⠸⠀⢀⣾⠃⠀⠀⢀⡎⠀⠀⠀⠀⠀⠀⢠⡾⢲⠖⠀⣷ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⣀⠤⠞⠀⠀⠙⠒⠒⠒⠉⠀⠀⠀⠀⠀⠀⠀⠸⠷⠼⠤⠔⠋ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣖⣒⣒⣒⠒⠀
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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣶⣶⣮⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⣴⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⣠⢚⠟⠻⡿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢒⣿⣿⣿⠿⢿⣿⣶⣲⣤⣬⣥⣬⣭⣿⣿⠗⠀⠿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⣿⣿⡋⠱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⢽⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠹⣿⠅⠸⣿⣿⠿⢿⡿⣻⣻⣿⡬⣝⣿⣿⣠⡼⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢿⣤⣤⢿⣿⣙⣹⣿⣿⣿⡏⣯⣵⣿⣏⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠙⣞⡏⣿⠁⢸⣻⣿⣅⣸⠏⣾⡿⣼⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣷⣽⣴⡇⠀⠀⢀⣽⣶⣿⡷⠇⢿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣸⠈⠻⣟⡛⠚⣻⠿⠟⠛⠋⠀⢠⣾⣿⣿⣯⡳⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡐⣿⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⣽⣿⣿⣿⣹⡇⣿⣆⠀⠀⠀⠀⠀ ⠀⠀⠀⠠⢹⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⡇⣿⣿⣷⣄⠀⠀⠀ ⠀⠀⠀⠀⣿⣿⣿⣦⣠⠀⠀⢀⣴⣶⡄⣴⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣷⣄⠀ ⠀⠀⠀⠀⣿⣿⣿⣿⣿⠂⣠⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⡆ ⠀⠀⠀⠠⢹⣿⣿⣿⣿⡘⣿⣿⣿⡟⣼⣿⣿⣿⣿⣿⡿⣷⢿⣻⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⢚⣿⣿⣿⣿⣧⣻⣿⣿⣷⣿⣿⣿⣿⣿⡿⣱⣷⣁⣵⣿⣿⣿⣿⣿⡟ ⠀⠀⠀⠀⠈⣟⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⡿⠃⠙⣿⣿⣿⣿⣿⣿⣿⣿⠁ ⠀⠀⠀⠀⠀⠘⡿⣿⣿⣿⣿⢁⣿⣿⣿⣿⢟⠅⠁⠀⢸⣟⣿⣻⣿⣿⣿⡿⠃⠀ ⠀⠀⠀⠀⠀⠀⠈⠎⠛⣽⣿⢮⣿⣿⡟⡇⠂⠀⠀⠀⠀⠑⠛⠛⠛⠛⠉⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀⢿⣾⣿⣿⢨⣋⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣾⢻⡾⣜⣾⡓⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠙⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠤⠤⠤⠤⢤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡤⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢦⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄⠀⠀⠀⠀ ⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀ ⠀⡾⠁⠀⠀⠀⣠⡴⠶⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠲⠦⣄⠀⠀⠀⠀⢳⡀⠀ ⣸⠃⠀⠀⠀⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠈⣧⠀ ⡟⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸⠲⢤⣄⡀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢸⡄ ⡇⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸⠀⠀⠈⣙⡷⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢸⡇ ⣧⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸⡤⠖⠋⠁⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢸⠃ ⢹⡄⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠀⠀⠀⢀⡟⠀ ⠀⢷⡀⠀⠀⠀⠙⠲⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠖⠋⠀⠀⠀⠀⡼⠁⠀ ⠀⠈⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀ ⠀⠀⠀⠙⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠉⠳⢦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠞⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠒⠲⠶⠶⠖⠒⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣿⣿⣿⡿⠿⠿⠿⢿⣿⣿⣿⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⡿⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⢿⣿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⣾⣿⠿⠋⠀⠀⠀⠀⢀⣠⣴⣶⣶⣶⣶⣶⣦⣄⡀⠀⠀⠀⠈⠙⠿⣿⣷⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⣾⣿⣿⡇⠀⠀⠀⠀⢀⣴⣿⡿⠛⠉⠉⠉⠉⠙⢿⣿⣿⣦⡀⠀⠀⠀⠀⠈⣿⣿⣷⣄⠀⠀⠀⠀ ⠀⠀⢀⣼⣿⣿⣿⣿⡆⠀⠀⠀⢰⣿⡿⠃⠀⠀⠀⢰⣶⡆⠀⠀⣿⣿⣿⣿⣆⠀⠀⠀⠀⣿⣿⣿⣿⣦⡀⠀⠀ ⠀⢀⣾⣿⠟⢿⣿⣿⡇⠀⠀⠀⣿⡿⠀⠀⠀⠀⠀⠘⠛⠁⠀⢀⣿⣿⣿⣿⣿⡄⠀⠀⢀⣿⣿⣿⢻⣿⣧⠀⠀ ⠀⣾⣿⡏⠀⠈⣿⣿⣧⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⣀⣠⣤⣴⣿⣿⣿⣿⣿⣿⡇⠀⠀⢸⣿⣿⠃⠀⢹⣿⣧⠀ ⢰⣿⣿⣷⡄⠀⢹⣿⣿⠀⠀⠘⣿⣧⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⣿⣿⡟⠀⠀⣼⣿⣿⡆ ⣼⣿⠛⢿⣧⠀⠈⢿⣿⣇⠀⠀⢻⣿⣦⠀⢰⣿⣿⡏⠀⣹⣿⣿⣿⣿⣿⣿⡟⠀⠀⣸⣿⣿⠃⠀⣸⣿⢻⣿⣇ ⣿⣿⠀⢸⣿⣆⠀⠈⣿⣿⣧⡀⠀⠙⣿⣷⣄⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⣴⣿⣿⠃⠀⢠⣿⡇⠀⣿⣿ ⣿⣿⠀⢸⣿⣿⡄⠀⠈⢻⣿⣿⣦⣀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠁⣀⣴⣿⣿⡿⠁⠀⢀⣾⣿⡇⠀⣿⣿ ⣿⣿⠀⢸⣿⣿⣿⣦⡀⠀⠉⠻⢿⣿⣿⣶⣦⣄⠈⠉⠉⠉⠉⣠⣤⣶⣿⣿⡿⠟⠋⠀⢀⣴⣿⣿⣿⡇⠀⣿⣿ ⣿⣿⠀⢸⣿⣿⣿⣿⣿⣶⣦⣄⣀⡈⠉⠛⢿⣿⣷⡆⠀⢠⣾⣿⡿⠛⠉⠁⣀⣠⣤⣶⣿⣿⣿⣿⣿⡇⠀⣿⣿ ⣿⣿⠀⢸⣿⣿⣿⣿⣿⡿⠿⠿⢿⣿⣷⣦⣄⡙⢿⣿⠀⣸⣿⠋⣠⣴⣾⣿⡿⠿⠿⢿⣿⣿⣿⣿⣿⡇⠀⣿⣿ ⣿⣿⠀⠸⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠈⠙⢿⣿⣿⡟⠀⢸⣧⣾⡿⠋⠉⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⡇⢰⣿⡿ ⢻⣿⡆⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣾⣿⡿⠁⠀⠈⢻⣿⣷⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⠟⠀⢸⣿⡇ ⢸⣿⡇⠀⠀⠈⠙⠛⠛⠛⠛⠛⠋⠉⠙⢿⣿⠟⠀⠀⠀⠀⠀⠙⢿⣿⠋⠉⠉⠛⠛⠛⠛⠛⠛⠁⠀⠀⢸⣿⡇ ⢸⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⣤⣤⡀⠀⠀⣤⣤⡀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡇ ⠈⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠟⠀⠀⠀⠹⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠀ ⠀⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡿⠋⠀⠀⠀⠀⠀⠘⢿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠀ ⠀⠘⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⣿⣧⣄⣀⣤⣿⣦⣀⣠⣼⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠁⠀ ⠀⠀⢻⣿⣇⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⣼⣿⡟⠀⠀ ⠀⠀⠈⣿⣿⡄⠀⠀⠀⣾⣿⣿⣿⣿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⢿⣿⣿⣿⣿⠀⠀⠀⣰⣿⡿⠁⠀⠀ ⠀⠀⠀⠘⣿⣿⡄⠀⠀⣿⣿⣿⠏⠁⠀⠈⠛⠻⠟⠋⠉⠙⠻⠟⠛⠁⠀⠀⠹⣿⣿⣿⠀⠀⢠⣿⡿⠃⠀⠀⠀ ⠀⠀⠀⠀⠘⣿⣿⣆⠀⢹⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡟⠀⣰⣿⡿⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⢻⣿⣶⡌⢿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡿⢡⣾⣿⡟⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣶⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣾⣿⡿⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣷⣤⣤⣀⣀⣀⣀⣀⣀⣀⣤⣤⣾⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⠿⠿⠿⢿⣿⡿⠿⠿⠿⠿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣰⣄⡀⣠⣀⣀⣀⣀⣀⣀⣀⣀⣀⡄⠀⢀⣀⣀⣀⣀⠀⠀⠀⡄⡤⣤⡄⢠⢠⠤⠠⡄⢤⢠⡠⠤⠀⠀ ⠀⠀⠘⢛⠛⠓⠛⠃⠚⠒⠁⠘⠛⠚⠛⠓⠛⠒⠛⠚⠚⠃⠓⠉⠀⠀⠓⠘⡁⠚⠓⠛⠒⠓⠛⠒⠓⠓⠁⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢴⡶⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⢠⠟⠀⠀⠀⠀⠐⢶⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⢀⣟⠤⢒⡿⠁⠀⠀⠀⠻⣶⣍⠙⣳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢤⣀⠈⠀⣠⠾⣅⣀⡀⠀⠀⠀⠘⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣀⠀⠀⠀⠀⢀⡠⠖⠚⢉⡀⠀⠀⠀⠀⠀⠀⠈⣍⠒⠦⣀⠘⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣎⠉⠉⣹⠟⠉⠀⠀⠀⣼⠁⠀⠀⠀⡀⠀⠀⠀⠈⢳⡄⠈⠓⢼⡿⣿⣿⣷⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣳⠞⠁⢀⠄⠀⠀⢸⠃⠀⠀⠀⠀⠹⡄⠀⠀⢸⣧⡹⡆⠀⠀⡿⢻⣿⣿⣦⣽⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⢠⠏⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⣿⣟⠿⠶⣾⣧⣄⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⢀⡟⠀⠀⢠⢾⡇⠀⠀⠀⠀⠀⠀⢸⡄⠀⢤⣽⣿⣿⣶⣿⢿⣿⣿⣿⣿⣿⣿⣿⣶⡆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⡾⢠⡏⠀⢸⠇⠀⣴⠋⢸⠁⠀⠀⠀⠀⠀⠀⢸⣷⡀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⢿⣿⣿⣿⠇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⠾⠃⣼⠀⠀⣿⣠⣾⠇⠀⣸⡀⡀⠀⠀⠀⠀⠀⢸⡏⢳⡄⠦⣤⣀⣤⠬⠞⢿⣿⣿⣿⣷⣽⣿⢿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣼⣫⡤⠤⠧⠤⠖⠛⢉⠀⠠⣴⠿⡷⣇⠀⠀⠀⠀⠀⢸⡗⠒⠻⡆⠀⣤⡄⠀⡀⠈⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⡿⢦⣀⡀⣀⡴⠃⢀⡴⠋⠀⢻⣼⡀⠀⠀⠀⠀⣸⠃⣀⠀⠹⡆⣿⡇⢰⡇⠀⡟⣿⣿⣿⣿⡋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣈⡧⠟⢉⣠⡴⠊⣠⣤⢺⣷⡿⣷⡀⠀⢲⡀⣿⣿⡿⠻⢿⣿⡿⣿⣼⠀⢰⢷⢿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠛⢳⡞⠉⠙⣧⢾⠟⠉⠀⠈⠻⠙⢷⡀⠀⢳⡏⠉⠀⠀⠀⠉⠀⣿⠃⢠⣿⡟⡾⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⢳⣄⠀⣜⣦⡀⠀⠀⠀⠀⠀⠀⠘⠓⠲⠷⡄⠀⠀⠀⢀⡼⠃⣀⣿⠋⢸⡃⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⣽⡼⢳⣬⣿⡓⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢉⣿⣿⡁⢸⢾⡷⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣏⠁⠀⠀⠀⠀⠐⠦⢄⠤⠔⠂⠀⠀⠀⠀⠀⢸⣿⠉⠳⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣟⣹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⣠⢴⣯⣼⢁⣉⣀⣀⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣿⣿⣿⣿⣚⣓⣾⣿⣷⠦⣤⣤⡴⠞⠋⣀⣼⣰⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠄⠂⣠⣾⣿⣿⣿⣿⣿⣿⣿⣯⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⣿⣿⣿⣿⣿⣿⠙⢆⣤⣾⣿⣿⡿⣿⣽⡾⠿⠯⣿⣿⣿⣷⣤⣤⣤⣄⣀⣀⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣤⠖⠋⠉⠹⣿⣿⣿⣿⣿⣴⣿⣿⣿⣿⣿⡿⠟⠉⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣇⣀⠀⠀⠀ ⠀⢀⣠⡤⠴⠖⠚⣻⢟⣹⣼⡙⢦⡀⠀⠀⢻⣿⣛⢻⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⠃⣿⣿⠏⠉⠉⠉⢳ ⠀⢹⡇⠀⢀⣴⣾⣵⣿⣿⣿⣿⣷⡿⠲⣄⢸⣿⣿⣿⣿⡿⠟⠋⣀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⢠⣿⣿⠀⢀⠄⠀⠀ ⠀⣸⠳⡆⢿⡀⣹⣿⣿⣿⣿⣿⣿⢧⣀⡽⠈⣿⣿⠟⠋⠁⠀⢀⡏⡳⢤⣀⠀⠀⢀⣠⣿⣿⣿⣿⣿⣿⣿⡏⢸⣿⡿⠀⠈⠀⠀⠀ ⠀⣿⠀⠹⡌⠛⣿⣝⢿⣿⣿⠟⣡⣾⣧⣠⠶⠋⠁⠀⠀⠀⠀⣸⢇⣿⣷⣮⣽⠶⢋⣼⣿⣿⣿⣿⣿⣿⣿⡇⣾⣿⡇⣴⣰⠀⠀⠀ ⠀⡟⠀⠀⣿⠀⢹⣿⣷⣄⣠⣾⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠻⣼⡿⣿⣿⣿⠞⠉⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⡇⣿⠏⠀⠀⠀ ⢸⡇⠀⠀⢸⡆⠀⢻⣿⠉⠉⣿⣿⣿⣿⣿⣿⣶⣄⣠⣤⠴⡖⣋⣥⠟⠻⣞⣧⠀⣰⣿⣿⣿⣿⣿⣿⣿⡿⣺⣿⣿⠀⡿⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⠿⠷⠶⣦⣄⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣴⠟⠋⠉⠀⠀⠉⢙⣷⣄⢀⣤⣴⡶⠶⠒⠛⠛⠛⠛⠛⠛⠛⠲⢶⣦⣴⡛⠓⢤⡀⠀⠀⠀⠉⠻⣶⡄⠀⠀⠀ ⠀⠀⠀⣰⡟⠁⠀⠀⠀⠀⢀⠔⢉⣴⠿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣦⡀⠙⢦⡀⠀⠀⠀⠈⢿⣄⠀⠀ ⠀⠀⣰⡟⠀⠀⠀⠀⢀⡴⢁⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⠀⠱⡄⠀⠀⠀⠈⣿⡀⠀ ⠀⠀⣿⡇⠀⠀⠀⣠⠎⢀⡾⠃⠀⠀⠀⡴⠀⠀⠀⢠⡄⠀⠀⠀⠀⠐⡄⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⡀⠹⡄⠀⠀⠀⣿⠃⠀ ⠀⣀⢹⡇⠀⠀⢠⠋⢠⣿⠁⠀⠀⠀⢸⠇⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⢱⡄⠀⣼⠟⠀⠀ ⢸⡟⠛⢻⣆⢠⡏⠀⣼⠃⠀⠀⠀⠀⡾⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⢹⣧⣀⣷⡾⠿⣦⣤⡀ ⣨⣿⣵⣶⠿⢾⣄⣠⡟⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢠⣿⣿⡄⠀⠀⠀⠈⢻⡍⠙⠻⣶⣴⠏⠁ ⣿⡀⠀⠀⢀⣴⡿⢹⡇⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⣿⠘⣷⠀⠀⠀⠀⠘⡇⠀⠀⣠⣿⠇⠀ ⠘⣧⣀⣴⢟⡟⠁⣿⡇⠀⣠⣠⣤⣤⣧⣠⣤⣤⣤⣸⣧⣤⣄⣀⣀⣀⣸⣆⣀⣀⣀⣿⠀⣿⠀⠀⠀⠀⠀⣿⠾⢿⡏⢙⣧⠀ ⠀⠈⣿⡇⠸⣧⣤⣿⡇⠀⣏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠛⠉⠀⠹⠷⠶⣶⡀⠀⣿⡆⠀⣿⡟⠉⠀ ⠀⠀⠛⠷⢶⠾⠉⢹⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⣿⡟⠛⠛⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⢿⡀⠀⢀⡷⠊⠉⠑⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠚⠉⠙⠦⡇⠀⠀⣿⠇⠀⣿⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⣧⢀⣈⠀⠀⠀⠀⠀⠛⠂⠀⣠⠶⢦⣀⠀⠘⠁⠀⠀⠀⠀⠙⣀⣀⣿⠀⢰⡏⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⣿⡏⠉⠛⢦⠀⠀⠀⠀⠀⠀⠛⠁⠈⠋⠀⠀⡀⠀⠀⢀⡴⠋⠁⢸⡟⢠⡿⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣧⡈⣷⡀⠀⠈⣷⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⡼⠃⠀⠀⢸⠁⠀⢀⣾⢀⡾⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣼⣿⣶⣖⠉⠀⠀⠀⠀⠙⠶⠦⠴⠶⠊⠁⠀⠀⠀⠘⣦⣤⣾⣳⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⡽⠟⠷⠶⣶⣤⣤⣄⣀⣀⣀⣀⣠⣤⣶⠶⠟⠛⠿⣿⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠋⠀⠀⠀⠀⠀⢻⠸⣄⠀⠀⠀⢀⡟⣼⠀⠀⠀⠀⠀⠈⠻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠈⠳⢬⣙⣒⣒⣋⡴⠃⠀⠀⠀⠀⠀⠀⠀⠈⢻⣆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁⠀⠀⣄⠀⠀⠀⠀⠀⠐⢤⣤⣟⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⣤⡄⠀⠈⢿⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠹⢷⣄⣀⣀⣀⣀⡼⠷⠿⢦⣀⠀⠀⣀⣀⣀⣀⣠⡾⠟⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⢹⠛⣿⠶⣿⠹⡏⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⣿⡀⣿⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣦⣤⣤⣤⣤⣤⣤⣤⣤⣼⣧⣿⣦⣿⣤⣷⣤⣤⣤⣤⣤⣤⣤⣤⣤⡶⠟⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠙⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠘⠃⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⢀⡄⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⢠⣿⣿⡄⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⣠⣿⣿⣿⣿⣆⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣆⠀⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠂⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣤⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀ ⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀ ⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀ ⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀ ⠴⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠠⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠧ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣴⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⡾⠿⠛⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣻⣷⢶⣒⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣶⣤⣀⣀⠀⠀⠀ ⠀⠀⠀⣼⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣌⡉⠙⠯⡁⠀⠀ ⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⢄⠈⠢⡀ ⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⠟⠛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠘⢷⡓⣄⠀ ⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⡖⢍⠁⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⠁⠀⠀ ⠰⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣇⠉⠉⠀⠀⠀⠐⠚⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣌⠉⢒⣦⠀ ⠀⡏⣿⣿⣿⣿⣿⣿⣿⣿⢻⡿⣆⣀⣀⠀⠀⠀⠀⠸⣿⣧⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠉⠀⠀ ⠀⠱⢿⣿⣿⣿⣿⣿⣿⣿⣎⢷⡈⢆⠀⠈⠉⠁⠐⠂⢻⣿⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡦⣇⠀⠁⠀⠀ ⠀⠀⠀⠘⢿⣿⣿⣿⡟⣿⣿⣶⣷⣤⠤⣤⣤⣤⣤⣤⣼⣯⣭⣽⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠰⢿⣿⠻⡗⠾⠿⠟⢳⡇⠀⠀⠀⠘⢿⡈⠿⣿⣿⣽⠟⠁⢸⡿⣿⣧⣸⣿⣿⣿⣿⣿⣿⣇⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⢿⡇⠙⠄⠀⠀⠛⠁⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠸⠁⣿⣿⣿⣿⣽⣿⣿⣟⢻⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⢻⠀⠀⠀⠀⡸⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⢿⣿⡿⠻⢟⢺⣿⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠑⣄⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣯⡄⢀⠏⠸⣿⡇⠀⠀⢸⣟⢣⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⠀⠤⢤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⢀⠜⢀⣼⣿⠃⠀⢀⣾⣿⣆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⠀⠐⠤⡀⠉⠉⠉⠀⠀⠀⣠⣶⡿⣿⣿⣗⣁⣠⣾⠟⠋⠀⢀⡾⠛⢯⠈⣧⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡌⢦⠀⠀⠀⠀⠀⢀⣠⠔⠻⣿⣿⣿⣿⣿⡿⠟⠋⠀⠀⠀⠀⡼⠁⠀⠀⠁⠈⢧⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠦⠤⣤⡊⢁⣿⣿⣶⣿⣿⣿⣿⣯⡀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⢣⡀⠻⣄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⢿⣟⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣴⠁⠀⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⠏⣩⣿⠿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣭⣷⣶⢿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⣾ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⣡⡞⣉⠤⣴⣿⣥⠟⣿⡏⠉⣻⣿⣿⣿⣿⣿⣶⣿⣿⡿⣦⡐⠀⠀⠀⠀⠀⠀⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣛⣥⠾⡫⢋⣠⣼⣿⣿⡵⠊⠉⢓⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⠈⣿⣦⡀⠀⠀⠀⠀⣟ ⠀⠀⠀⠀⠀⠀⠀⣀⣶⡿⠋⣩⣾⠷⠋⢉⣡⣼⡿⠋⠁⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣷⣼⡌⡿⣶⡄⠀⢸⣿ ⠀⠀⠀⠀⠀⣠⣾⡟⢁⣠⣾⠛⠁⢀⣴⣿⠛⠀⠀⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣦⣽⣦⣸⣿
⠀⠀⣠⣾⡿⢋⣴⢟⣴⣿⣿⣯⣿⣿⣿⣿⣿⡿⠁⠉⠉⠉⠻⡿⠉⠉⠉⠉⠀⠉⢿⣷⢹⣟⣿⡏⣿⣿⣻⣿⣧⠈⢻⣿⡏⣿⣿⡝⣿⣿ ⣠⣾⠿⢫⣶⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⡇⠀⠀⠀⠀⣭⣿⡇⠀⠀⠀⠀⠀⠘⣿⣿⢻⣽⣷⢹⡿⣷⣿⢿⣧⠀⢿⣿⣸⣿⣿⣾⣿ ⠛⣡⣴⡿⠟⣹⣿⣿⣿⣿⣿⣿⣿⣿⢹⢸⣿⠃⠀⠀⠀⠀⠘⡏⠁⠀⠀⠀⠀⠀⠀⢹⣿⠀⢿⣿⡀⡇⢻⣿⣾⣿⣧⠈⢿⡇⣿⣿⣿⣿ ⣾⠋⠁⠀⢠⣟⣿⣿⣿⣿⣿⣿⡿⡿⢸⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣦⠼⣿⡇⢱⠈⣿⣿⢿⣿⣷⡌⣿⢹⣇⣿⣿ ⣿⣷⣄⣠⣿⣿⣿⣿⣿⣿⣿⣿⣇⣧⡤⣿⣿⣻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠟⠋⠉⣿⡀⠀⢹⡇⢸⠀⢹⣿⣾⣿⢸⣿⣾⣏⣿⡿⠁ ⣿⣿⣿⣿⣁⣿⣿⡟⣿⣿⢿⡿⠿⢿⣿⣿⣿⡿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠋⠀⠀⡠⢖⣿⣷⣾⣿⣿⣺⣦⡼⣿⣧⣿⣿⠹⣿⣿⣿⡇⠀ ⣿⣿⣿⣿⣿⡿⣽⢇⣿⠇⢼⣇⠀⠘⣿⣿⣿⣿⣎⠻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠈⣰⡿⢻⣿⣿⣿⣿⣿⠉⢻⣿⣿⣿⣿⠀⣿⣿⣿⡇⠀ ⣿⣿⣿⣿⣿⣩⣿⣾⣿⡄⠀⠹⣄⡀⠙⠻⠿⠛⠙⢧⣼⣧⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠘⠻⣿⣿⣿⠋⠀⣰⠇⢿⣿⡿⠀⢸⣿⣿⠀⠀ ⣿⣿⣿⣿⡿⣿⢯⣿⣿⡇⠀⠀⠈⠛⠓⠒⠚⠁⠀⠀⣾⣿⠀⠀⠀⠀⠀⠀⠀⠈⠉⠐⠷⢶⣤⣤⣤⡴⠟⠃⠀⢸⣿⡇⠀⢸⣿⣿⡀⠀ ⡞⣿⢿⣻⣹⠏⢞⣿⢿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡿⠀⠀⢸⣿⣟⡇⠀ ⢹⣦⣀⡹⣧⠀⢸⠃⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣽⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⣸⣿⣿⡀⠀ ⠈⢧⠀⠀⠈⢷⠇⠰⡸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠛⠿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢣⠯⢵⠀ ⠦⡄⠣⡀⠀⠀⠀⠀⠙⣿⣧⠀⠀⠀⠀⠀⠀⠈⣦⣾⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡃⢺⠀ ⣀⠉⠲⣟⣄⠀⠀⠀⠀⢿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠻⠿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣍⣹⣇ ⠯⣿⣶⣄⡙⢻⢷⣄⠀⠈⠛⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⢛⣿⣙⣿⣿ ⠀⠰⣌⠉⠙⠲⢧⡉⠓⠤⡀⠀⠙⢄⠀⠀⠀⠀⢀⣀⢀⠠⠤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⠿⠛⢹⣿⠿⠿⢿ ⡀⠀⠈⠑⢄⠀⠀⠙⠦⡀⠈⠀⠀⠈⣧⡀⠀⠀⠈⠉⠉⠛⢿⣦⣤⣤⣤⣄⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⡾⠃⣼⡟⠀⠐⠀ ⢀⠐⠠⢄⣀⠉⠢⣀⠀⠈⠢⣀⠀⠀⣿⢯⠢⡀⠀⠀⠀⠳⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣟⣿⠟⠋⠀⢀⣿⡇⠀⠀⠠ ⠀⠈⠒⠤⣀⠉⠒⠀⠑⠄⡀⠈⠑⠂⣿⠀⣧⢘⣦⡀⠀⠀⠈⠙⠒⠒⠒⠒⠊⠁⠀⠀⠀⠀⠀⣠⣾⣿⣿⡿⠏⠀⠀⠀⢸⠇⡇⠀⠀⠰ ⠀⠀⠤⣀⡀⠉⠲⢄⡀⠀⠈⠳⢄⠀⡎⠀⢹⠀⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠻⢹⡯⣽⠿⠒⠀⠀⠀⢀⣿⠀⠇⠀⣒⣿ ⠀⠀⠀⠀⠈⠉⠒⠀⠌⣒⠤⡀⠀⠁⡇⠀⠀⡇⠘⣿⣿⣿⣦⣄⣀⣀⣀⣀⣀⣤⣴⣺⠟⠁⠀⠞⠋⠀⠀⠀⠀⠀⠀⢸⢿⢸⣶⣾⣿⣿ ⠀⠀⠀⠀⠀⠠⣀⠀⠀⠀⠀⠈⠓⠀⡇⠀⠀⢸⠀⠹⣿⣻⣿⣿⣿⣿⣟⠉⡩⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿ ⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣃⠀⠀⠈⡄⠀⢻⡝⠿⠿⠟⡿⠛⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⣾⢏⠹⣿⣿⣿⣿⣿⣿
⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⡤⠤⠤⠤⣤⣤⣤⣀⣀⠀⠀⠀⣀⣴⠶⠚⠛⠶⢦⣄⠀⠀⠀⠀ ⠀⠀⣀⣤⠶⠶⠶⣦⡀⠀⠀⣀⣤⡶⠟⠋⠉⠁⠀⠀⠀⠀⠀⢠⠤⣀⡀⠈⠉⠙⠛⠾⣯⣀⠀⠀⠀⠀⠀⠙⢷⡄⠀⠀ ⢀⡼⠋⠀⠀⠀⠀⠈⢿⣶⠾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠁⠀⠀⠉⠉⢒⠆⠤⠤⢈⣙⣷⣦⡀⠀⠀⠀⠈⢿⡄⠀ ⡾⠁⠀⠀⠀⠀⠀⠀⠈⣿⡀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠚⠙⢆⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⢀⣼⣧⡀ ⠁⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⢀⣠⠔⠉⠀⠀⠀⠈⢣⠀⠀⠀⠠⣧⠴⠒⣶⣶⣶⣶⡶⠒⠺⢿⣴⣿⡾⣿⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⢀⣠⣴⣖⣭⣤⣴⣶⣶⠂⠀⠀⠺⡇⠀⠀⠀⢣⠀⠀⢸⣿⣿⣿⣿⣄⠀⠈⣿⠿⠖⣿⠋ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠟⠋⠙⣿⣿⣿⣿⣿⣿⣦⣀⢀⣰⡏⠀⠀⠀⠈⢆⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⡄⢠⣿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠈⠣⣀⠀⣈⣿⡿⢿⣿⣿⣿⡇⢸⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢠⠀⠀⠀⠻⢿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠲⡀⠀⡄⢀⠜⠋⠁⠀⠀⠀⠀⠈⠙⢦⣿⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠳⢄⡀⠀⠀⠉⠉⠉⢉⡥⠋⠀⠀⠀⠀⢱⣴⡿⠁⠀⠀⠀⠀⠀⠀⢠⠉⡆⠀⠙⡄⠀ ⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠤⣄⣀⣉⣑⣒⣠⠤⠒⠁⠀⠀⠀⠀⠀⠀⢸⢻⠁⠀⠀⠀⠀⠀⠀⠀⠸⠀⡇⠀⠀⢹⠀ ⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠛⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⢸⠀ ⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀ ⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⣸⠀⠈⠛⠳⠶⢤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⠶⠷⢄⡀⠀⠀⠀⠀⠀⠀⣀⡴⠋⠀⠀ ⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣠⡞⠛⠿⣍⡿⠉⠉⢹⣯⣅⡀⠀⠀⠀⠀⠈⣿⠒⠒⠒⠊⢹⡏⠀⠀⠀⠀ ⠀⠀⠘⣇⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⢰⡏⠀⠀⡀⢸⠙⠂⠤⠼⢷⡈⣷⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀ ⠀⠀⠀⢹⡄⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⣾⠁⠀⢀⡇⡞⠀⢠⡤⣤⢤⠳⣿⡀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡇⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⡟⠀⠀⠈⣿⠀⠀⠈⢧⣤⠟⢀⣼⠇⠀⠀⠀⠀⠈⣇⠀⠀⠀⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡟⠀⠀⠀⣸⠃⠀⠀⠀⠀⢸⡇⠀⠀⠠⣿⠀⠀⠀⠀⠀⣰⠟⡇⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⣿⠀⠀⠀⠀⠀ ⣦⣠⠤⠞⠁⠀⢀⡼⠃⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢻⡋⠑⠒⠒⠒⣿⠀⡇⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠘⣧⡀⠀⡀⠀ ⠙⠓⠲⠤⠴⠖⠋⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠸⣇⠀⠀⠀⢠⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣄⣀⣩⡿⠋⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢿⡀⠀⠀⠘⢧⣠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠸⣧⠀⠛⠀⠀⠻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣠⣴⠎⠉⠒⠢⢄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡾⠿⢤⠀⠀⠈⢿⣶⣑⢄⠀⠀⠀ ⠀⠀⠀⣠⣿⣿⣓⣧⡿⠶⣶⣾⠛⠉⠉⠀⠀⠀ ⠀⠀⣜⣽⡿⠿⠛⠛⠷⣀⠲⣿⣷⡀⠀⠀⠀⠀ ⢶⣶⠾⠁⠀⣄⠀⠀⠀⣤⠉⠙⡻⣓⠆⠀⠀⠀ ⢻⡫⢦⠀⠀⠁⢀⣄⡀⠉⠀⢀⠯⣳⡗⠀⠀⠀ ⠀⠀⠀⠓⢤⢀⠀⠁⢠⡤⡴⠊⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⠃⠀⠀⠀⢀⠄⠈⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢇⡤⠎⠀⠀⢇⡠⠂⠘⣄⣀⢀⣀⠤⡀ ⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⠆⠀⡈⠓⠒⡒⣤⠃ ⠀⠀⠀⠀⠀⠀⠀⠑⡖⢀⣜⣤⣃⣤⣶⠗⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠈⠉⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠠⠠⠤⠀⠠⠤⠠⠤⠄⠀⠀⠤⠦⠔⠶⠄⠠
⠀⠀⠀⠀⠀⠀⢸⣦⡻⣶⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠞⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⡈⣹⠗⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣯⡀⠀⢀⡀⣀⣠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢁⡴⠋⠀⢠⣾⣿⡿⣽⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢰⡞⠉⠀⢀⣠⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⠏⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠙⢶⣾⣿⡏⣰⡟⢸⣿⣿⣿⣿⣿⠟⠟⣁⣴⡾⠿⠷⢾⣿⡿⠿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣯⣙⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢰⠟⣹⢳⣿⣧⣾⣿⡿⣿⡿⠁⠀⠰⣿⠉⠀⣀⣀⠀⠹⡇⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⣃⣼⣿⣿⣿⠃⢀⣤⣤⡀⠀⠀⢹⠀⠀⣿⣿⡃⢠⡟⠀⢿⣿⣿⣿⣿⣿⣟⢿⣿⣿⡉⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠷⣶⣶⣾⣿⣿⣿⣴⡟⠁⠀⣽⡄⠀⠈⠛⠢⠾⠟⠛⠙⠀⠀⠙⠛⠻⠋⣿⣿⠛⣸⣿⣿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠐⠻⢿⣿⣿⣿⣿⡇⠀⠸⣿⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣿⣯⣾⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢰⡿⠋⠙⣿⣷⠔⡒⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣦⣴⣿⣿⣿⣿⡆⠈⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⣃⡤⠴⠿⠛⡇⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣧⡀⠹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠸⣄⠀⠀⠈⠛⠉⠀⠀⢀⣀⡤⠴⠲⣿⡉⠉⠻⣿⣿⣿⣿⣿⣿⣦⠀⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⡀⠀⣀⡴⠚⠉⠙⢷⡀⣀⣼⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣷⢼⣿⢦⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⠉⢒⡒⠒⢦⡜⠋⠉⢳⣀⣠⣴⣾⣿⣿⣿⣿⣿⡿⢟⣿⣿⠗⠾⢿⣿⣿⣿⡘⢯⣷⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢻⡟⠀⠸⣇⢀⣠⣶⣿⣟⣽⣾⣿⣿⣿⣟⣩⣾⣿⡿⠛⠀⠀⠀⢻⣿⣿⣷⠈⢻⠟⢦⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠸⠿⠀⣀⣽⣿⠟⠉⠀⣿⣿⣿⣿⠿⡿⣾⣿⠋⠁⠀⠀⢰⠀⠁⢸⣿⣿⣿⣇⠈⢷⡀⠳⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠇⠀⢀⣴⠞⡟⠀⠻⣦⠀⠀⣿⡿⠛⠁⣸⣺⣿⡿⠛⡀⢣⡜⠀⠀⠀⠀⣿⣿⣿⣿⠀⠸⣷⡄⢳⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⣰⡿⠋⠺⠿⠂⠀⢹⣷⣾⡟⠀⠀⢠⢣⣿⣟⠣⠄⠀⢁⣀⠀⠀⠻⠆⢿⣿⣿⣿⡇⠀⣿⠹⡄⢣⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⡀⠀⠀⠿⠇⣴⣿⡟⠀⠀⠀⡎⢸⣏⡻⠀⠀⠀⣀⡀⠤⢤⣤⡨⣽⣿⣿⣿⣇⠀⢹⣆⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣾⣿⣿⠁⠀⢀⣾⠇⣿⣿⡅⡔⣰⠆⢀⣀⣀⣬⣥⣬⣿⣿⣿⣿⣿⣤⣀⣿⣄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣶⣿⣷⠀⣀⠼⠛⠀⣿⣿⣷⣸⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⢻⡏⠟⢋⣡⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⠟⠋⠉⠀⠀⠀⠀⠀⠉⢿⠇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⡙⣽⣷⣾⣿⣿⣿⣟⣻⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠛⡎⡇⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠀⠁⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⣉⣀⣤⣤⣤⣶⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀ ⠖⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⣴⣷⠿⠛⠛⠉⠉⡉⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠟⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢀⣤⠾⠛⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣧⡀⠀⠀⠻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣦⣀⣤⡶⠾⠿⠛⠛⠛⠛⢉⠀⠈⠙⢿⡄⠀⠀⠙⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⡀⢠⣾⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⢨⠍⠛⠷⣦⡹⣄⠀⠀⠈⢿⣆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠛⠛⠉⢀⣿⣿⠟⢀⣠⠄⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠈⢻⣞⣷⡀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⠀⣀⢸⣿⠏⢠⣿⠃⠒⠲⢶⣤⡀⠀⠀⠀⣿⢀⣤⣄⠀⠈⣿⡌⠻⣦⡀⠀⠀⠻⣧⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀⢰⡇⢸⣿⠀⣿⡇⠀⠀⠀⠀⠈⠻⣦⡀⠀⢻⣿⣀⣿⣧⠀⢹⣧⣤⣿⣿⣶⣦⣤⣈⡻⣄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁⠀⠀⠀⢸⡇⠸⡇⠀⣿⡄⠀⡴⠿⣷⣄⠀⠘⣷⡀⠀⢻⣿⠿⣣⣴⠿⠿⣿⣿⣿⣿⣿⡏⠛⢿⣦⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⢸⣧⠀⠀⠀⢿⣇⠀⣧⣀⣿⣿⡇⠀⢸⡇⠀⣀⣽⡿⠋⠀⠀⢀⣿⣿⣿⣿⡿⠀⠀⠈⣿⣷⢠ ⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⠀⠀⢿⡆⠀⠀⠈⢿⣆⠈⠻⠿⠟⠀⠀⣼⣡⡾⠛⣿⣧⣄⣤⣴⣿⣿⣿⣿⡿⠁⠀⠀⢀⣿⡏⣼ ⠀⠀⠀⠀⠀⠀⠀⣰⠁⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⢀⣴⣿⡷⠶⠶⠦⠤⢠⡿⠋⠀⠀⠻⠿⠿⠟⠛⢿⣿⣿⠟⠀⠀⠀⢀⣾⠟⠀⣿ ⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠈⠀⠀⠀⠀⠀⠀⠠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠁⠀⠀⢀⣴⠟⠁⠀⢀⣿ ⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⣀⣀⣠⣤⣀⡀⠀⠀⠀⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⣸⡿ ⠀⠀⠀⠀⠀⠀⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣠⠾⠛⢿⣯⡉⠉⠁⠀⠀⠀⠀⠀⠀⠘⠿⠗⠀⠀⠀⣀⠴⣻⡏⠀⠀⠀⠀⢠⣿⠃ ⠀⠀⠀⠀⠀⠀⢸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⠀⠀⠀⠀⠙⠿⣶⣤⣄⣀⡀⠀⠀⠀⠀⣀⣀⣤⡶⠛⢁⣴⠏⠀⠀⠀⠀⢀⣾⡏⠀ ⠀⠀⠀⠀⠀⠀⠀⢿⣷⡀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣶⣤⣄⡀⠀⠀⠀⠉⠉⠙⠛⠛⠛⠛⠛⠉⠉⠀⣀⣴⡾⢳⣇⠀⠀⠀⢀⣾⡟⠀⠀ ⠀⣠⡀⠀⠀⠀⠀⠈⢿⣷⡀⠀⠀⠀⠀⠀⢀⣿⡇⠀⠉⠛⠻⠿⢶⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣿⣟⠁⠀⠈⣿⣆⣀⣠⣾⠟⠀⠀⠀ ⢰⣿⣇⠀⠀⠀⠀⠀⠈⢿⣷⣄⠀⠀⠀⠀⢸⣿⠃⠀⠀⠀⠀⠀⠀⣾⣿⣍⠉⠉⠉⠉⠉⠉⠉⣿⣼⣿⠀⠀⠀⠈⠻⠿⠟⠁⠀⠀⠀⠀ ⣿⠁⢿⠀⣄⠀⠀⠀⠀⠈⠻⣿⣦⡀⠀⢀⣿⡿⠀⠀⠀⠀⢀⣤⡾⢿⣹⡿⢿⣷⣶⣶⣶⣾⣿⢿⣏⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⠀⠸⣾⡿⣦⠀⠀⠀⠀⠀⠈⠻⢿⣷⣾⡿⠁⠀⠀⢀⣴⡿⠋⠀⠀⠙⠿⢾⣿⣤⣿⣧⣿⣿⣾⣟⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⡆⠀⠹⡇⢹⣇⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⢠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣽⠏⠁⠉⠹⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠸⣷⡀⠀⠁⠀⢻⡆⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⢀⡇⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠻⣧⡀⠀⠀⠀⢳⣿⢻⣆⠀⠀⠀⢀⣤⡶⢿⡟⠀⠀⠀⠀⣴⠇⠀⠀⠀⠀⢀⡾⠁⠀⠈⠛⠶⢶⡏⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠹⣷⡀⠀⠀⠀⠛⠀⢻⣆⢀⣴⠟⠉⠀⠚⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⡿⣦⡿⢀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⢿⣦⡀⠀⠀⠀⠈⣿⡿⠁⠀⠀⠀⠀⠙⠶⣦⡀⢸⡇⠀⠀⠀⠀⠀⣿⡇⠀⠀⡀⢰⡇⠘⢡⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢿⣦⣀⠀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣼⣇⠀⠀⠀⠀⠀⣿⣇⠀⠀⣷⠟⢀⣴⠟⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡄⠀⠀⠀⠀⢉⣻⣷⣤⣀⣴⡿⠁⠀⠙⣿⠷⠶⠶⠶⣶⣤⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⢀⣤⠴⠶⠶⠶⢶⣿⣸⡗⠀⠀⠔⠚⠋⠉⠉⢉⠙⠻⣧⡀⠀⠀⠀⠠⣄⡀⠘⢦⡉⢻⡆⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣆⠀⠀⢠⠎⠀⠀⢦⡀⠀⠰⣌⠻⣷⣿⠀⠀⠀⢤⡀⠀⠈⢷⡄⣹⡇⠀⠀⠀⠀⠀⢹⡆⠀⣿⣼⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣤⣿⠀⠀⠀⠀⢻⡆⠀⢻⡆⢹⣿⡀⠀⠀⠈⢿⡄⠀⢈⣷⣿⣷⣤⣤⣤⣤⣤⣾⣷⣾⠿⠋⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣷⣤⣤⣤⣾⣧⣤⣼⣷⡿⠛⢷⣤⣤⣤⣾⣷⣶⡾⠟⠁⠈⠉⠉⠙⡉⡉⢉⣁⠀⠀⠀⠀⠀⠀
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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠶⢤⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢰⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢁⣤⣤⡀⢳⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠸⣽⣮⣕⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢋⣴⣿⣿⣿⡇⢸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢳⢿⣿⣷⣷⠤⠤⠖⠚⠋⠉⠉⠉⠛⠲⠴⠋⢠⣾⣿⣿⣿⣿⠇⡼⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢫⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠿⣿⡿⢰⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣇⣀⣀⠀⠀⡄⠀⡇⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⠘⠃⡞⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣿⠟⡟⢿⣿⡇⠀⣷⣶⣿⠟⢩⠉⢻⣿⡏⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡞⠹⣦⣧⣾⡿⣁⡀⢸⣿⣿⣦⣼⣵⣾⠟⠁⢀⠄⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠲⢼⢽⣳⣤⡼⠙⢢⡼⠃⠀⠙⢯⡉⠉⣉⣠⠤⠚⠁⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣐⣾⣒⣺⠋⢀⡴⠊⠉⠳⣄⠀⠈⢙⣏⠶⠤⢄⣀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀ ⠀⠀⠈⢩⣿⡿⠟⠓⢦⠀⠀⠀⠀⠈⢃⠽⣟⢿⡯⡑⠢⣄⠉⠓⢄⡀⠀⠀⠀⣧⠀⠀⠀⠀⠀ ⠀⠀⠀⠘⢹⡀⠀⠀⠀⠳⠤⠤⠤⠖⠋⠀⠋⡆⠙⢎⠆⠈⠳⡄⠀⠙⠀⠀⠀⢹⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⢳⠀⠀⠹⠆⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀ ⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣇⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀ ⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀ ⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀ ⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀ ⠸⠤⠤⠤⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠤⠤⠼⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠶⠚⠋⠉⠉⠓⠶⢦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣶⡀⠀⠀⠀⢀⣴⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⡀⠀⠀⠀⢠⣶⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⣯⡇⠀⠀⠀⢸⡇⠀⢰⠆⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⢸⡇⠀⠀⠀⢸⣹⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣿⣿⠀⠀⠀⢸⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠈⡇⠀⠀⠀⣿⢻⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⠟⠁⢿⠀⠀⠀⣾⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣷⠀⠀⠀⣿⠀⠻⣆⠀⠀⠀⠀ ⠀⠀⣠⠞⠁⠀⠀⠘⡇⠀⢀⡏⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢹⡀⠀⢸⠋⠀⠀⠈⠳⣄⠀⠀ ⢠⡾⠁⠀⠀⠀⠀⢀⣿⣄⣼⠃⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠘⣧⠀⣾⡀⠀⠀⠀⠀⠈⢷⡄ ⢸⡇⠀⠀⢀⡴⠛⠉⠀⣸⠇⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠸⣇⠀⠉⠛⢦⡀⠀⠀⢸⡇ ⢸⡇⠀⠀⣿⠀⠀⠀⢠⡟⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢻⡄⠀⠀⠀⣿⠀⠀⢸⠇ ⠀⢿⠀⠀⣿⠀⠀⠀⣿⢠⣤⣶⣶⣶⣿⣤⣀⡀⠀⠀⠀⢀⣤⣤⣿⣷⣶⣶⣤⣄⣿⠀⠀⠀⣿⠀⠀⣿⠀ ⠀⢸⡄⠀⢿⡀⠀⠀⣿⢸⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⡏⣿⠀⠀⢀⡿⠀⢠⡇⠀ ⠀⠸⣇⠀⠈⢷⡀⠀⢿⠈⢿⣿⣿⠿⣋⡷⠂⠀⠀⠀⠀⠀⠘⢮⣙⠿⣿⣿⡿⠁⣿⠀⢀⡾⠁⠀⣸⡇⠀ ⠀⠀⠻⣇⠀⠀⠻⣆⠸⣆⣀⣉⡼⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢦⣀⡀⢰⡇⣠⠟⠁⠀⣠⠟⠀⠀ ⠀⠀⠀⠹⣆⠀⠀⠈⠳⢿⣯⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣽⡿⠞⠁⠀⠀⣴⠟⠀⠀⠀ ⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⢹⡍⠳⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠞⢩⡏⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠻⣀⠀⠀⠸⡇⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⡇⠀⠀⣀⡞⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⠀⢷⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⣾⠀⠀⣠⠟⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⢸⡆⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢰⡇⠀⣠⠟⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠸⡇⠀⢸⣀⡤⣷⣶⢦⣶⣾⣤⡀⡇⠀⢸⠇⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⣷⠀⢸⣿⡇⣿⣿⢸⣿⣿⣿⣷⡇⠀⣿⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣻⣴⡟⢸⡇⣿⣿⣿⣿⣿⣿⡇⢻⣤⡇⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⢸⡇⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢡⡇⢸⡇⠻⣿⣿⣟⠛⢻⡇⢸⡏⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⣿⠛⠁⠀⠈⠛⢾⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⢼⡇⠀⠀⠀⠀⠀⢸⣧⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⡄⠀⠀⠀⠀⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
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⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢉⡭⠏⠉⠉⠉⠉⠉⠉⡉⠉⠉⠉⠉⠛⠻⢭⣍⠉⠉⠙⣧⡈⠉⠉⠀⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠤⠀⠀⠀⠀⠠⠀⠀⠀⢀⣤⡶⠄⠀⠀⠀⠀⠀⠀⠈⠙⠲⢤⣀⠙⠢⣄⠈⣛⢦⣄⠈⠙⢦⣄⡀⣴⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⡚⠉⠀⠀⠀⠀⠀⠀⠀⢤⣀⡀⢠⣾⠟⣁⣀⣀⣀⡀⠀⣠⣤⣄⠲⣦⡀⢩⣀⠀⠀⢽⢮⣳⣌⠳⣄⠀⠈⠀⢧⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣩⡶⠋⠁⠀⠀⣠⢴⣚⣭⣄⣄⣀⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣾⣿⣿⣿⣮⢿⣷⣟⣷⣜⢷⣄⠀⢾⠀⠀⠀⠀ ⢀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢠⡾⠋⢀⠀⠀⢀⢄⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣮⣷⣝⡇⢽⡳⣼⠀⠀⠀⠀ ⠉⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⣡⣿⠔⢀⣾⠀⠀⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⡌⢻⣮⡳⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⣱⡇⢸⡿⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋⠉⠉⠛⠿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢠⣿⣷⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⢠⣿⠃⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠈⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣿⣿⡅⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⢀⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠋⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⡆⠠ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣀⡈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣧⣸ ⠖⠀⠀⠀⠀⠀⠀⠀⠀⠒⠞⣿⡆⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⠀⠀⠀⠀⠀⠀⣀⣤⡄⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡿⠿⠟⠛⣛⣿⣶⣄⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇⣈⢻⣿⣿⣿⣿⣿⣿⣷⠟⠁⢀⣠⣴⣶⣾⣿⣿⣿⡟⠀⠀⠀⠀⠈⠙⠋⠉⠉⣁⣴⡾⠿⠛⠋⠛⠛⠻⢷⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠛⢹⣷⣽⣿⣿⣿⣿⣿⠋⢀⣴⣿⡿⠿⠿⠿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠟⠋⠀⠀⠀⢀⠀⠀⡀⠀⠈⠻⣿⣿⣿⣿⣿⠿⠛⠛⠻⠿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⢙⣻⣿⣿⣿⣿⣇⣴⣿⠿⠿⠿⠿⢿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠋⣠⣤⢶⣟⠛⠛⠛⠿⣿⣷⡀⠀⠝⣿⡿⣿⡇⠀⠀⠀⠀⠀⠙ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣄⠐⢮⣿⣿⣿⣿⣿⣿⠿⠃⠀⠀⠀⢀⡀⢉⣙⣿⣶⡀⠀⠀⠀⠀⠀⢸⣿⣿⠟⠉⣼⣼⣿⣿⣆⠀⠀⠈⣿⣧⠀⠀⢸⣷⢿⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⠀⠀⢐⣴⣶⠟⠛⢉⢹⣯⣽⣿⣄⠀⣀⣠⣴⣿⣿⣿⡀⠀⢿⣿⣿⣿⡟⠀⠀⣠⣿⡟⠀⠀⢸⣿⢸⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣗⠀⢰⣿⠏⠁⠀⠀⣾⣿⣿⣿⣿⣿⢿⠛⠋⠉⠹⣿⣿⠳⣦⣀⣉⢉⣉⣀⣤⡾⣿⡿⠀⠀⣴⣸⡿⠀⢿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⡟⣿⡏⠀⢹⡟⠀⢸⣿⡄⠀⠀⠀⠈⠻⠿⣿⣿⣿⣤⠀⠀⠀⠀⠻⣿⣧⡀⠈⠛⠛⠛⠉⠀⠚⠋⠀⢀⣀⣽⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⠀⢸⡇⠀⠀⠹⣿⠶⠤⠤⢤⣴⠾⠋⢰⡿⠋⠀⠀⠀⠀⠀⠸⣟⡻⣶⣄⡀⠀⠀⠀⠀⠀⣀⣭⣿⠟⠁⠀⠀⠀⠀⠀⣶⠀⢀⣾ ⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠷⢿⣧⢸⡇⠀⠀⠀⠀⠐⠒⠀⠀⠀⠀⣠⡿⡁⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣻⠷⣶⣶⠶⢿⡛⠋⠁⠀⠀⠀⠀⠀⣿⣶⣿⠆⣿⣿ ⠀⠈⠀⢀⣶⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠋⠻⣿⣟⡀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣾⣿⣿ ⠀⠀⢀⣼⢉⣘⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠈⠝⠿⢷⣶⣦⣤⣴⣶⠿⠟⠉⠈⣧⡀⠀⠀⠀⠀⠀⠀⢀⣠⣴⢿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢿⣿⣿⣿⣿⣿⣿ ⠀⠠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠂⣶⡀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⠶⠤⣤⣤⡶⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿ ⠀⠸⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⢂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⡴⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠒⠂⠀⠈⠛⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣁⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣂⣀⣀⣤⣴⣶⡶⠶⠶⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣩⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠞⠋⠁⠐⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣄⣀⣀⡀⠀⠀⠀⠀⠐⠒⠛⠉⠀⠀⠀⠀⠀⠈⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡏⠛⠻⢿⣿⣿⣿ ⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⠃⠀⠀⠀⠀⠉⠛ ⠀⠀⠨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢹⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢀⣿⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡞⡇⣠⡠⣴⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⠞⠀⡿⣿⠛⢿⣏⠉⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠤⠤⠤⠀⠀⠀ ⠀⣴⠏⢀⡴⠁⣿⡄⠀⠉⢣⡤⢬⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⠒⠛⠀⠀⠀⠀⠀⠀ ⣼⣿⠀⠀⣠⠞⢛⣷⡀⠀⠀⡃⠀⠈⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⠏⠉⢹⣧⢞⢿⡻⣿⣷⣴⠃⠀⠀⠀⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠴⠯⠤⠄⣀⣀⠀⠀⠀⠀⠀⠀ ⢳⠊⣉⣿⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠚⠂⠀⠀⠀⠀⠀⠉⠉⠓⢤⡀⠀⠀⠀⠀⠀⠉⠒⢦⡀⠀⠀ ⡏⠀⣟⢹⡼⠋⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠓⠢⣄⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠀⠀⠀⠀⠀⠀⠀⠈⠒⠠ ⠀⠀⢘⣿⣏⡁⠀⠹⣤⠖⠊⠉⠒⢄⠀⠀⠀⠀⠀⠐⢬⣆⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠓⠦⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⠀⠄⢀⡩⠟⠁⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠈⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢁⠴⣶⣤⣌⣿⡒⢤⣀⡀⠀⠀ ⠀⠀⣸⠴⠊⠁⠀⠀⠀⠀⠀⠀⢰⡾⠃⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣡⣿⠊⠀⠀⠀⠀⠈⠉⢛⠛⠋⠓ ⠒⠉⠀⠀⠀⠀⠀⠀⢀⡠⡄⠀⠀⠉⡇⠀⠀⠀⠀⠀⡆⠀⠀⡠⠔⠒⠒⠒⠒⠒⠢⠤⣀⡀⠀⠀⡂⣿⠁⠀⠀⠀⠀⠀⠀⠰⠁⠀⠀⠀ ⠀⠀⠀⠀⣀⡠⠔⠊⠁⢳⡸⡄⠀⠀⠹⡀⠀⢀⡤⢲⠃⡠⠋⡠⠒⠀⠀⠀⠀⠈⠑⠒⠤⣈⠑⠦⣏⢿⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀ ⠒⠒⠯⣉⠏⠀⠀⠀⠀⠀⠳⡘⢦⠀⠀⠘⢤⠁⠀⢸⡸⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠙⡜⡷⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠉⠐⠛⢼⡄⠀⠀⠀⠀⠀⠀⢨⠳⣕⠦⢄⣀⡀⠀⣸⡇⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⢹⡇⠈⣮⡟⢒⠦⠤⣦⣀⣀⡀⠀ ⠀⠀⠀⠼⠽⠦⢄⣀⠀⠀⠀⣀⣱⢦⣉⠒⠂⠄⠨⠹⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡷⠴⠿⢞⡁⠀⠀⠀⠀⢸⠉⠉ ⠀⠀⠀⠀⠀⠀⠀⠀⢉⣉⠭⠕⠓⠉⠉⠉⠙⠒⠒⠒⢿⡇⠀⠀⠀⠀⢀⠆⠀⠀⠀⠀⠀⠀⡇⠀⠀⢿⡇⠀⠀⠀⠉⠓⠦⢄⣀⣸⡄⠀ ⠀⠀⠀⠀⠀⠀⠔⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⠘⣧⠀⠀⠀⣠⠞⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⣸⠁⠀⠀⠀⣀⠀⠀⣠⠚⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢻⣧⣀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣤⣟⡡⠔⠊⢉⡠⠄⣴⠋⠀⠀⠀⠀

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⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠠⠤⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⢀⠀⠀⠀⠀⡂ ⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⣀⣤⢶⣶⣿⣟⣛⣿⠷⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠦⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⠀ ⣶⣄⡀⠀⠀⠀⢠⣀⣀⣀⣠⣿⢟⣵⡿⠿⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣀⠹⣆⠀⠀⠀⠀⠀⠀⢈⠀ ⠛⠉⠉⠁⠀⠀⠀⠳⣄⠉⠉⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡌⠙⠛⠛⠛⠛⠛⠛⢀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⡦⢄⡘⠫⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣄⠀⠀⠀⠀⠀⠸ ⠀⠀⠀⣀⣀⣀⡠⠤⠞⠉⠀⠀⢈⡝⠁⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣄⡑⢦⡀⠀⠀⠀ ⠀⠀⠛⢏⡁⠀⠀⠀⠀⠀⠀⢀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢄⡀⢣⠀⠀⠀⡀⠀⠀⢠⣾⣿⣿⡿⢩⣿⣦⣈⠓⠦⡀ ⠀⠀⠀⠀⠉⠓⠦⣄⠀⠀⣀⡜⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠺⡆⠀⠀⠈⠢⣠⣿⣿⣿⣿⠃⣿⣿⣿⣿⢷⡀⠀ ⠀⠀⠀⠀⠀⣠⠼⠷⠒⠉⢰⠃⡜⠐⠻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠘⢧⡀⠀⢸⡀⣏⠈⠉⠛⢦⣹⡄ ⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡼⢀⣇⣀⠀⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠆⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠻⡄⠀⢧⠸⣄⠀⠀⠀⢀⡟ ⠀⠀⠀⠀⠀⠀⠀⠀⢧⣀⣷⣾⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢸⠀⠀⠀⠀⠀⠀⠙⣄⠈⢆⠙⣦⠀⣰⠿⠄ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣿⠁⣠⣙⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠂⢀⣀⠀⠀⠀⢠⡇⠀⠘⡄⠀⠀⠀⠀⠀⠀⠘⣷⣤⣷⣼⠟⠁⠀⠀ ⠂⠀⠀⠀⠀⠀⠀⡴⠃⠀⣿⠀⣣⠾⣿⣿⠀⠀⠀⠀⠀⠀⠀⣤⣶⣽⠿⠿⣶⣾⣏⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠘⡿⠛⠁⠀⠀⡀⠀ ⠀⠀⠀⠀⠀⢀⠎⠀⡃⢀⢿⣟⣿⣄⣼⠿⡆⠀⠀⠀⠀⠀⡴⠛⣡⣞⠛⠲⡄⠙⢿⣷⡀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠈⠀ ⠀⠀⠀⠀⠀⡎⠀⠰⠀⢸⠀⠻⢮⣛⣋⡼⠀⠀⠀⠀⠀⠀⠀⠀⡇⡏⠛⢹⢿⠀⠈⢻⣿⣦⣼⣤⡤⠖⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⠁⠀⠀⠀⣼⠀⠀⢀⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡳⠖⢋⡜⠀⣠⣾⠟⠉⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀ ⠀⠀⢀⠀⠈⣇⠀⠘⡞⢻⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠭⣥⡤⠞⠛⠁⠀⡴⢉⠆⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀ ⠀⠀⠀⠙⠢⣌⡢⣀⡆⠘⡆⠀⠠⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠀⠀⠀⣀⠴⠋⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢹⠚⠧⣀⠸⡄⠀⠘⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢯⡙⠉⠉⠀⠀⠀⢀⡊⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣄⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡠⠃⠀⠀⠀⠀⠘⢦⢠⠏⠳⢭⣉⣙⠒⠒⢤⣤⠄⠀⠀⠀⠈⠒⠤⠤⠤⢴⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠈⠲⣄⠀⠀ ⠈⠳⣍⠉⠉⠀⠀⠀⠀⢀⡄⠀⠀⢻⠀⠀⠰⠀⠈⠉⠛⡹⠃⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣶⣶⣦⣄⡙⠂ ⠀⠀⠀⠙⠒⢤⡤⠴⠚⠁⠀⠀⠀⠈⢇⠀⠀⠀⣠⠴⠊⠀⠀⠀⠀⠀⢀⣀⠤⠖⠛⣿⠃⠀⠀⠀⠀⠀⠀⢀⣤⣶⡿⠿⠓⠒⠒⠚⠛⠒ ⠀⠀⠀⢀⡴⠋⢀⣴⠀⠀⣀⣀⣀⡠⠜⢠⣴⠋⠀⠀⠀⣀⣀⣤⣴⣾⡯⢄⠀⢀⣼⠇⠀⠀⠀⠀⢀⡠⠖⢡⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠀⡰⠁⢸⠘⠛⠛⠋⠀⠀⠀⣹⠉⠓⠒⠋⢩⣿⣿⣿⣿⣿⣧⣀⠝⣻⡟⠀⠀⠀⡠⠒⠉⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣀⠀⠀⠀⡀⠀⠀⠘⡆⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⢸⡋⠻⢿⣿⣿⣟⣵⣿⡿⠀⠀⠴⠋⠀⠀⠀⠀⢸⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠋⠉⠁⠀⠀⠀⠀⢅⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⡀⠀⠀⢀⡄⢿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⢀⡤⠀⣤⢠⡄⣷⣴⡆⢸⠹⡆⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⣸⣇⠀⡏⢿⡇⢹⠹⠷⣼⠀⠙⠘⣯⢻⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⡏⠙⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠇⢿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠋⠆⠀⠀⠀⠀⢀⣀⣀⣠⣤⣤⡤⠴⢴⣤⣤⣼⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣀⣤⠴⠒⠊⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣇⣀⣤⠴⢦⣤⣀⣀⣤⣤⣴⣶⣶⣶⣶⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠋⠀⠀⣾⣿⣯⣿⣿⣿⣿⣿⠟⠛⠛⠻⢾⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⣶⣿⣿⣿⣿⣿⠿⠿⡏⠀⠀⠀⠀⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢒⡶⠊⠀⠀⠀⣰⠯⢞⣾⣿⡄⠀⠀⢀⠇⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡵⠋⠀⠀⠀⢀⣼⠋⠀⠀⢻⣿⣧⣀⣠⣼⠤⣄⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⡶⢦⣠⠞⠁⠀⠀⠀⢀⡾⠁⠀⠀⢀⣈⢿⡿⠟⣿⣿⣧⠈⢧⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣯⠀⢰⠃⠀⠀⠀⠀⢠⡾⠁⢀⣴⣿⣾⡿⠀⠀⠀⠛⠛⠋⡇⢸⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⢄⣿⠀⠀⠀⠀⠀⣿⡇⠀⠋⠛⠙⠛⢁⡤⣤⠀⠀⠀⠀⡿⢸⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⢈⣧⠀⠀⠀⠀⠀⢸⣴⢸⡄⠀⣠⡾⠁⣾⣧⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⣠⣾⣿⣆⠀⠀⠀⠀⠀⠉⠓⠛⠉⠁⢀⣼⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⣠⣾⠟⠀⣻⣿⣮⣤⣀⡀⠀⠀⠀⠀⣀⡴⢿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⡿⣿⣿⣿⣿⣿⣿⡷⣶⣯⣥⣀⣼⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⡇⠛⠻⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡇⡆⠂⠀⠀⠈⠃⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣶⣀⠀⠀⠀⠀⠀⠀⠀⢹⣻⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠫⠉⠉⠉⠛⠛⠲⠶⢦⣤⣤⣄⣈⢙⣛⢿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠻⠿⠿⠟⢻⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣴⠻⣏⠱⡄⠀⠀⠀⣀⣠⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣀⣀⠀⠀⠀⢀⡴⣻⠷⣦⠀ ⢰⠃⠀⢹⠀⣧⡴⠒⠋⠉⠁⠀⠉⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠉⠉⠉⠙⠲⢤⣸⠈⡏⠀⢸⣇ ⢸⠀⠀⢸⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⢻⠀⡇⠀⠀⢸ ⠈⢿⣠⠎⠀⠀⢀⣀⣀⣀⣀⣀⡀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠁⣷⠀⢀⡞ ⠀⠈⠛⠚⠓⠛⠉⠉⠉⠉⠉⠉⠉⠙⢿⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠚⠓⠒⠚⠛⠙⠛⠛⠛⠒⠒⠤⠧⣶⠿⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠶⠤⣄⣀⣀⣠⡤⠴⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠂⠀⠀⢀⣠⠤⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⣀⣼⣧⣤⣶⣾⡿⣶⡶⠾⠿⠥⢄⣀⡀⣀⣀⣀⣀⣠⣾⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀ ⠀⠐⣿⡟⢿⣄⣹⠗⠲⠖⠒⢚⣿⣿⣿⣿⣿⣿⣏⣴⣶⣶⣤⣭⣤⣴⠟⠋⠉⠁⠈⣿⣿⠏⠀⣿⡿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢹⡇⠘⣿⠇⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⡿⠿⢶⣤⣶⣬⣿⣶⡒⠂⠀⠀⠒⣻⣧⠀⢰⣿⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠘⣿⡟⠁⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣹⡟⣷⣦⣠⣀⠈⠻⣄⠉⠙⣦⡀⠀⡔⠃⠀⣰⣯⡾⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠹⣿⣶⡆⢲⡿⢃⣾⣿⣿⣿⣿⣧⢻⠀⣿⢿⡿⢯⠳⣄⡸⣷⣍⠻⣿⢶⣵⢾⠉⠠⢞⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠸⠿⣿⣿⠟⡜⢸⢃⣿⣿⢩⢿⢸⡆⢹⣆⠙⠦⡑⢌⠑⢌⢻⡃⠈⠳⣿⡟⠺⣏⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡠⠒⣿⣿⣾⠀⠁⣾⢀⣿⢿⢠⠀⠧⠀⣿⢦⣄⠘⢿⣷⣤⣡⣷⡄⠀⣿⣿⣶⣧⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣸⣿⠁⢠⠀⣾⣟⡎⢹⣼⡄⠳⡀⠀⣿⡄⠙⣷⣆⠹⣿⣿⣿⣟⡄⠈⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠔⣹⡇⠀⢸⠀⢿⣿⣤⣤⣟⣱⡀⠈⠢⢸⣻⡀⣽⣞⣻⣿⡿⢿⡇⢀⠀⠘⣿⣿⠿⣷⣤⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣿⠳⡀⠘⣆⢸⣉⠙⣿⣿⣿⣿⠦⣀⠈⣇⠹⣿⣿⢿⡿⢀⡞⣧⡼⠀⢠⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⢆⠱⡀⠘⢯⡏⠳⠤⣉⣉⠉⠀⠈⠑⣾⣄⠈⢓⠒⠋⠉⢀⣿⠇⢠⣾⣿⠿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠂⡟⠢⡈⣳⣆⣀⣤⣀⠀⢝⣷⣦⣼⠁⠊⡠⠔⠀⢰⢾⣿⣴⣿⣿⣿⠀⠈⠙⠂⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣾⣿⡁⠀⠀⠉⠺⣥⣤⡼⠀⠈⠀⠀⣀⡀⢀⣿⣿⠟⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠸⣿⣿⣷⣶⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢀⣽⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣷⣤⡀⠉⠉⠉⠉⠁⢀⡤⢾⢁⣿⣯⠟⢿⣿⡏⢻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣠⡴⠋⣸⡇⢈⣿⣿⡇⢹⠻⡗⠦⠤⠖⠚⠁⠀⡏⠘⢹⢸⠀⠈⠻⣷⣸⠏⢧⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣠⣴⣶⣾⢿⡉⢧⠀⢿⣧⠀⠉⣿⣿⢸⡄⠹⡄⠀⠀⠀⠀⠐⠁⢀⣸⢸⡀⠀⠀⢨⡟⠀⢸⣷⣄⠀⠀⠀⠀⠀⠀ ⢰⣿⡿⢋⣿⣿⣤⣳⣼⣧⡈⠻⣧⡀⠀⢿⣿⣇⠀⠁⠀⠀⢀⣠⠔⠊⢡⠇⡼⠀⣠⠖⠋⢀⣴⡿⠃⢹⡆⠀⠀⠀⠀⠀ ⢸⣿⣧⣼⣿⣿⡀⠈⠙⠻⢷⣄⠈⠙⠷⣬⡻⣿⡄⠉⠒⠈⠉⠀⠀⣠⣧⡾⠶⢋⣡⣴⠾⢋⣁⡴⠶⠛⣷⣄⡀⠀⠀⠀ ⠀⠿⣿⣿⣿⣿⣇⠠⠀⠀⠀⠙⠳⢶⣦⣮⣻⣿⣿⡄⠀⣀⣴⠿⠟⠋⣁⣤⣾⣿⡯⠷⢾⡿⠉⠀⠀⢰⡟⣻⣿⣷⣄⠀ ⠀⠀⠈⠙⠻⢿⣿⣷⢶⣤⣀⡀⠀⠀⠈⢛⠋⢛⢿⣿⣿⣿⣾⣶⣾⣿⡿⠟⠋⠀⠀⣰⠏⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⡇ ⠀⠀⠀⠀⠀⠀⠈⠙⠛⠶⣭⣝⡓⠶⠤⠈⠀⠀⠉⠠⠌⠉⠉⠉⠉⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⢠⣾⣿⣿⣿⣿⡿⠃⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⡶⠦⣤⣀⣀⡀⠁⠐⠀⠀⠀⠀⠀⢀⣀⣀⣀⡤⠀⠤⠶⠛⠛⠛⠛⠛⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠒⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣾⣿⣿⣿⣷⣶⣤⣤⣶⣶⣶⣦⣤⣴⣶⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡿⠟⠋⠉⠉⠛⠻⠿⣿⣿⣿⡏⢉⠀⠈⢙⣿⣿⠿⠿⠿⠿⠿⢷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⠁⣠⣴⣾⣿⣿⣷⣦⡀⠈⣿⣏⠉⢉⣿⡟⠋⠉⣿⡄⠀⣀⣤⣤⣄⣀⠙⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⣿⠃⢠⣾⣿⣿⣿⣿⣿⣿⣿⣷⣾⢧⣏⡟⠋⣻⠙⠦⣞⣹⣿⣾⣿⣿⣿⣿⣿⣷⣄⠹⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣿⠃⢠⣿⣿⣿⠿⡿⢻⣿⣿⣿⣿⣿⣄⡉⠓⠲⣿⡖⠒⠛⣏⣹⣿⣿⡿⡿⠻⠿⣿⣿⣆⢹⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣼⡏⢀⣾⣿⢋⣴⣶⣦⠈⣿⣿⠿⠿⢿⣿⢙⠻⣏⣁⡹⠶⣶⣿⡏⠟⣁⣴⣶⡆⠀⠈⠻⣿⡌⣷⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⠃⢠⡟⢁⣿⣿⣈⡁⠀⢹⣿⠦⠤⣄⠘⣿⣶⣿⣿⡇⢠⠇⣹⡇⢼⣿⠿⣋⡀⠀⠀⠀⠸⣇⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⠀⠀⠀⣾⣿⣿⣿⣿⣦⣼⣿⣤⣀⠈⠛⠲⢾⣸⢿⡦⠞⠋⣹⡇⣨⣶⣿⣿⣿⣷⣄⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⡄⠀⢰⣿⣿⣿⣿⣿⣿⣿⣇⠀⠈⠓⠦⣀⣘⣿⣆⣻⠖⠋⢻⣷⣿⣿⣿⣿⣿⣿⣿⣧⣸⣿⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣇⠀⢸⣿⡿⠟⠛⠿⣿⣿⣿⣷⣦⣤⣀⣀⣀⣏⣋⢻⣤⣶⣿⣿⣿⠟⠛⣛⡛⠿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⢿⡀⠸⠋⢴⣾⣷⡄⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⡿⣿⣿⠁⠀⢸⣿⣿⡆⠘⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⢿⡄⠀⠘⠛⣿⣤⡈⠛⣿⠋⠛⠿⣿⣿⣿⡿⠟⠛⠉⠀⢸⡟⣠⣶⣾⣿⠋⠀⢠⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦⠀⣾⣿⣿⣿⣶⣿⣀⣀⣠⣤⣤⣬⣴⣶⣶⣶⣶⣾⣷⣿⣿⣿⡿⢃⣴⡿⢋⣤⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢁⣾⠃⠀⠀⢀⣴⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⣾⣿⣿⡇⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⡿⠋⠉⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⠟⢀⣾⡏⠀⠀⣠⡞⠁⠀⠀⠀⠀ ⠀⠀⠀⣰⣿⠋⢠⡿⠃⠀⠀⣴⡞⠻⣿⣿⣿⣿⣏⠀⣀⡴⠖⠚⠉⠉⠉⠙⠲⢿⣿⣿⣿⠏⠀⣾⡿⠁⣠⣾⠏⠀⠀⠀⠀⣀⠀ ⠀⠀⣸⣿⠏⠀⠟⣁⣤⡄⣸⡿⠀⢀⠀⣹⠻⣿⣿⣿⡏⠀⠀⣀⡤⠤⠤⠤⠤⠤⣿⣿⡏⢀⣼⣿⢣⣾⡿⠁⠀⠀⠀⠀⣺⡿⠃ ⠀⣰⣿⣿⠀⢠⣾⠋⣹⣧⡿⣿⢇⣼⠟⣽⣶⣶⠛⢿⣷⣴⠟⠁⠀⠀⣀⣤⣤⣤⣬⣿⡇⣼⣿⣿⣿⡟⢠⡾⢻⣿⠃⣼⡟⠁⠀ ⠀⣿⣿⣿⡿⠿⡿⠞⢡⣿⣵⠟⣼⢋⣾⣷⣾⡿⠞⠀⠙⢿⣦⣀⡴⠋⠁⠀⣀⣤⠴⠿⢧⣿⠛⣿⡟⢠⣿⣧⣾⣧⣾⣿⣶⠟⠀ ⠀⠻⠛⠁⠀⠀⠀⠀⠘⣉⣁⣈⣥⣄⣿⣴⣅⣀⣀⣀⣀⣀⣹⣿⡃⣠⡶⠋⠁⠀⠀⠀⠀⠙⢦⣻⣷⡂⠀⠀⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣯⣭⣭⣿⣻⣛⣿⠿⢿⣿⣿⡋⠀⢀⣠⠤⠶⠚⠛⠳⢾⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀ ⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣭⣷⡖⠋⠁⣀⣠⣤⣤⣤⣼⢛⣿⠟⣿⣿⣿⣿⡆⠀⠀⠀⠀ ⣾⣿⣿⣿⣿⣿⣿⣿⣧⣙⣦⣿⣻⣈⠇⢹⡟⢻⠿⣿⢻⡿⣿⢿⠿⣿⣷⠞⠉⠁⠀⠀⠀⠀⢘⣾⣿⣿⣿⣿⣿⣻⡇⠀⠀⠀⠀ ⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣲⡾⠧⠼⠤⣿⣼⣇⣯⣸⣠⣣⡟⠛⠒⠶⠤⠤⠴⠒⢻⣿⡏⣿⣼⡵⠟⠋⠀⠀⠀⠀⠀ ⠈⠷⣟⡟⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣶⣶⣶⣿⣿⣿⣿⠉⠉⠒⠶⠤⣤⣤⣤⣴⠟⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠙⠻⢾⣇⣿⡙⣟⢿⡿⣿⡿⣿⡿⢿⣿⡿⣿⣿⠿⠿⣅⠈⠓⠦⣄⣀⠀⣀⣴⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⢷⣼⣧⣀⣙⣦⡘⠷⣄⠙⠳⣄⣈⠛⠦⢄⣀⣀⣽⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠿⠿⠶⠶⠿⠿⠿⠿⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠖⠋⠉⠉⠁⠀⠀⠀⠈⠉⠉⠉⠓⠶⢦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠞⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠉⠀⠀⠀⠀⢀⣀⡤⠤⠤⠤⠤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣴⠟⠁⠀⠀⠀⢀⡴⠚⠉⠁⠀⠀⠀⠀⠀⠀⠈⠙⢦⡀⠀⠀⠀⠀⠀⣀⣤⠶⠒⠒⠲⠦⣽⣦⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⢀⣰⠟⠒⠉⠉⠉⠉⢩⣿⣿⣉⠉⠉⠉⠉⢹⡄⠀⠀⠀⡾⠿⠷⠶⠶⠤⢤⣤⣀⣈⣛⣦⠀⠀⠀⠀ ⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠈⢻⡶⠶⠤⠶⠶⠦⠾⠿⠿⠿⠶⠒⠒⢲⡟⠀⠀⠀⠘⢷⠶⠶⠤⣤⣠⣾⣿⣶⡄⠈⠙⢧⡀⠀⠀ ⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⣀⠀⠀⠀⠀⠀⣀⣀⡤⠞⠉⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠉⠉⠉⠙⠛⢻⣧⠀⠀ ⠀⢰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠑⠒⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠦⢤⣄⣀⣤⠤⠖⠉⠘⣇⠀ ⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⡄⠀⠀⠀⠀⢀⣀⣤⣤⣤⣀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀ ⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠃⠀⠉⠀⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣦⣶⣿⣿⣿⣿⣿⣶⣄⡀⠀⠀⢠⣶⣶⣦⡀⠀⢨⡇ ⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⠀⠀⠀⣿⣿⡀⠀⡇ ⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⠃⠀⡇ ⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠻⠿⢿⣿⡿⠿⠿⠛⠛⠉⠀⠀⠀⠀⠙⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠃⠀⠀⡇ ⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⢸⠃ ⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀ ⠀⠀⠻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀ ⠀⠀⠀⠻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀ ⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣄⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠲⠤⢤⣀⣀⠀⠀⠀⠀⠀⠹⣆⣀⣀⣠⡤⠶⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⣩⡿⠻⣟⠛⠒⠶⢤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠉⠀⠀⢹⡆⠀⠀⠀⠀⠈⠉⠙⠶⢦⣀⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⢷⡀⠀⠀⠀⠀⠀⠀⠀⣀⣌⣻⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠁⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⣀⣀⣤⣴⣶⡿⠿⢿⠻⣿⢿⡆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⣀⣀⣀⣀⣤⣤⣤⣴⣶⠾⢿⠛⠛⠉⠉⠉⠀⠀⠀⢸⡗⢹⠀⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣇⣴⣿⣽⡿⠗⠚⠋⠉⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡋⡏⠈⢻⡄⠀⠀⠀⠀⠀⠀⢈⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣀⠀⠀⠀⠀⠀⠀⣠⢶⡄⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢻⣍⠻⣦⣀⠀⠀⢰⠏⢸⢿⡶⠋⠉⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⢸⡙⢆⠀⠙⣦⣠⡏⠀⣼⠘⣷⠀⢠⣇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣿⠾⣇⠈⡆⠀⠈⣿⡇⠀⢿⢦⣿⠁⠙⢛⡧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠠⣾⡯⠀⠀⠙⠛⠁⠀⠀⡸⠒⠀⠀⠀⠀⠀⠀⢠⣙⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⠶⣟⠉⠐⠂⠐⠃⠀⠀⠀⢚⠃⠀⠀⠀⠀⠈⠳⠤⠄⢿⣹⡷⠺⡛⡶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⢿⡀⠀⠀⡀⠀⠀⠀⠀⠀⢘⣤⠄⠤⣄⡀⠀⠀⡀⠀⠠⣟⡷⠂⠉⠉⠙⠳⣤⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣨⠿⠶⠭⠅⠒⠒⠲⠤⡈⠉⠀⠀⠀⠀⠉⠓⠦⢙⣂⠤⠚⢁⡠⠤⠚⠂⠀⠈⠻⣄⣀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡼⠉⠀⡠⠖⠒⠒⢦⡀⠀⢹⡆⢀⡔⠁⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⠀⠀⠀⣸⠀⠀⠀⠹⢿⡃⠀⠀ ⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⢣⠀⠠⣷⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣀⣠⠔⠁⠀⠀⠀⠀⠀⠻⣆⠀ ⠀⢀⣠⡞⠃⠀⢀⠀⠀⣀⡠⠤⠤⠖⠒⠊⠁⠀⠀⠀⠀⠀⡤⠀⠀⣀⡠⢤⡷⠖⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆ ⠀⣽⠋⠁⠀⠀⠘⢄⢘⡅⠀⠀⠀⠀⠀⠀⣀⣠⣤⡴⠶⠿⢷⠞⡍⠀⣠⡮⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣦⣧ ⢸⠃⠀⠀⠀⠀⠀⠈⢻⣷⠤⠴⠶⠶⠛⠋⠉⠁⠀⠀⠀⠀⠸⠷⠧⣤⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉ ⢹⣼⠀⠀⠀⠀⠀⠀⠀⠹⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀ ⠈⢿⡄⠀⠀⠀⠀⠀⠀⠀⠙⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣤⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⢀⡞⠀⠀ ⠀⠘⣧⣠⠀⠀⠀⠀⠀⠀⢀⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⣿⠀⠀⠀⡀⠀⡀⠀⠀⠀⣠⣾⣵⠟⠀⠀⠀ ⠀⠀⠈⢿⣷⡀⠀⠀⠀⠀⠈⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⡸⢁⣾⠁⣀⣴⠟⠉⠉⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠻⣦⡀⠀⢀⣠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣀⣷⠟⣿⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⢻⡆⢸⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⠏⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢻⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⡿⠁⠀⠀⠀⣀⣐⣲⡾⢻⣷⠟⠉⠀⣴⣿⣿⣿⣿⠃⠀⠀⢰⣿⣿⣿⣿⣿⡟⠀⠸⣿⣿⣿⣿⡀⠹⣿⣿⣿⣿⡇⠙⣦⡴⠀⠀⢀ ⣿⣿⠁⠀⣠⣶⣛⣹⡿⠋⣴⣿⠏⠀⠀⢸⣿⣿⣿⣿⠇⠀⠀⠀⢸⣿⣿⣿⣿⣿⠇⠀⠀⣿⣿⣿⣿⣇⠀⠘⣿⣿⣿⠀⢀⡼⢁⡠⠐⢿ ⣿⡏⢠⣾⣿⣾⣿⠟⠀⣼⣿⡟⠀⡀⠀⣼⣿⣿⣿⣿⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⠸⣿⣷⡴⠾⣿⣿⡆⠀⠀ ⣿⠁⣾⣿⣿⣿⡏⠀⢸⣿⣿⠃⠜⠁⠀⣿⣿⣿⣿⣧⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⡄⠀⠀⣿⣿⣧⣼⣿⣿⣿⡀⠀ ⡏⢸⣿⣿⣿⣿⠁⠀⣿⣿⣿⠀⠀⢀⣠⣿⣿⣿⣿⡇⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⢻⣿⣿⣿⣿⣿⣿⡇⠀ ⠁⣿⣿⣿⣿⣿⠀⠰⣿⣿⡏⠀⠀⠀⠸⣿⣿⣿⣿⡇⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡀⠀⠀⢸⣿⣿⣿⣿⣷⠀⠀⢸⣿⣿⣿⣿⡿⢸⣿⠀ ⢀⣿⣿⣿⣿⣿⠀⢠⣿⣿⣷⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⢸⣿⣿⣿⣿⠃⣿⣿⠀ ⣿⣿⣿⣿⣿⣿⠀⠸⣿⣿⣿⡀⠀⠀⠀⢻⣿⣿⣿⣿⡀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣧⣴⠶⠾⠿⣿⣿⠿⣿⣤⣤⣼⣿⣿⣿⠃⣼⣿⣿⠀ ⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣇⣀⣀⣠⣸⣿⣿⣿⣿⣧⣤⠶⠞⠛⠉⢿⣷⣤⣴⣶⣶⣶⣾⡿⢿⡿⢿⣷⣦⣤⡏⠈⣹⠃⣠⣿⣿⣿⠀ ⣿⣿⣿⣿⣿⣿⣿⣶⣿⢻⣿⣿⣿⣿⣿⣿⣿⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀⠉⠀⠉⣩⣵⣶⣾⣿⣿⣷⣿⣥⣾⣟⣹⣿⢿⣶⣿⣿⣿⡏⠀ ⣿⣿⣿⣿⣿⣇⠸⣿⣿⣿⡈⢳⣜⣷⣽⣦⣶⣶⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⡿⠃⢸⣿⣿⣿⣿⠁⠀ ⣿⣿⣿⣿⣿⣿⢀⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⣼⡿⠋⠀⠀⣿⢃⣀⣿⣿⣿⣿⣭⣤⣀⣾⣿⣿⣿⡏⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠁⠀⢸⡏⢀⣹⣿⣿⡆⠀⠀⠀⠀⠀⢠⣿⠁⠀⠀⠀⢻⡞⠹⠿⣿⣿⣿⠷⠦⢬⣿⠟⠁⣿⠁⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠘⢧⠛⢿⣿⣿⣧⠀⠀⠀⠀⠀⢸⡏⡀⠀⠀⠀⠀⢈⣓⣶⣾⡿⣟⠓⠲⠚⢁⡴⠒⣿⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⡶⣻⣿⣿⣧⣀⣀⣀⣙⣲⡶⠟⠛⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠛⠋⠉⠉⠟⢋⣩⣴⡇⠀⢠⣿⠀⢸⡇⠀⠀⢠ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠘⣧⠙⠛⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⣿⠃⣤⣸⣉⢠⡟⠀⠀⣠⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⡏⠀⢉⣿⠀⢀⣴⣿⣿ ⡙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⠂⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠖⠚⠁⢠⣾⣿⣿⣯ ⣷⣄⠻⣿⣿⣿⣿⣿⣿⣿⣿⣦⣼⣧⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣒⣒⣚⣥⣤⣍⣳⣤⠀⠀⠀⠀⠀⠀⠀⣰⣿⠋⢄⣀⣴⣿⡿⣫⣾⣿ ⣿⣿⣧⡘⢿⣿⣿⣿⣿⣿⣿⣿⣬⢻⣦⠀⠀⠀⠀⠀⠀⠀⣾⣿⣯⣿⣵⣶⣿⣟⣻⠏⠀⠀⠀⠀⠀⢀⣴⡟⠭⢲⣴⣿⡿⢫⣾⣿⣿⣿ ⣿⣿⣿⣿⣌⢻⣿⣿⣿⣿⣿⡽⣿⣦⣛⣷⣄⠀⠀⠀⠀⠀⠈⢷⡉⠉⠉⠉⣀⣼⠏⠀⠀⠀⠀⢀⣴⣿⣿⣷⣼⣿⣿⠟⣴⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣆⢻⣿⣿⣿⣿⣿⡙⣿⣷⡈⢛⢿⣦⣄⠀⠀⠀⠀⠙⠓⠒⠛⠉⠁⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⣿⠃⣼⣿⣿⣿⣿⣿⣿ ⠘⣿⣿⣿⣿⣿⡌⣿⣿⣿⣿⣿⣷⠿⣿⣷⡌⠆⠋⢻⣿⣶⣤⣀⡀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣸⣿⣿⣿⣿⣿⣿⡟ ⡀⠹⣿⣿⣿⣿⣿⡼⣿⣿⣿⣿⣿⣷⣿⣿⣿⣄⣀⢸⣿⣿⣿⣿⣿⣷⣶⣶⣾⣿⣿⣿⡿⢉⣿⣿⣿⣿⣿⣿⣿⢱⣿⣿⣿⣿⣿⣿⡟⢠ ⢳⡀⢻⣿⣿⣿⣿⣷⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⠙⢿⣿⣿⣿⡿⠁⢸⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⣿⣿⡿⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣏⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢹⡄⠀⡀⠀⢀⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⣴⣶⠀⠀⠀⣿⠈⣧⢸⣿⠂⢿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣹⡇⠀⠈⣿⣦⣀⣸⡏⠀⢸⣿⣿⣦⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣿⡷⣶⣿⣿⡿⠟⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⢀⣀⣤⣤⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣷⠸⣿⡀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡁⣀⣤⠶⠟⠛⠉⠁⠸⣧⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣆⢻⣧⠀⠀⠀⠀⠈⣿⣿⣿⣿⠛⠋⠁⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀ ⠀⣀⣀⣀⣀⣠⣤⣀⣀⣀⣴⡾⠟⠻⣿⡼⣿⡆⠀⠀⠀⠀⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀⠀ ⣿⠉⠉⠉⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠛⠿⣿⣿⣀⠀⠀⣀⣿⡿⠋⠀⠀⠀⠀⠀⠀⣀⡀⠀⣼⠇⠀⠀⠀⠀ ⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⣼⠇⠙⣾⠋⠀⠀⠀⠀⠀ ⠘⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣏⠀⠀⠘⣧⣀⣀⣤⣤⣀ ⠀⠘⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⠀⠀⠀⣿⠉⠁⠀⠉⠁ ⠀⠀⠈⠻⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣷⣶⣶⠄⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⣿⣀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⣾⠏⠙⠛⠷⣦⡀ ⠀⠀⠀⠀⠀⠀⢿⣄⠀⠀⠀⣀⣠⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⣠⡿⠀⠀⠀⠀⠈⠀ ⠀⠀⠀⠀⠀⠀⠈⢻⣦⣶⠟⠉⠀⠀⣠⠄⠀⠀⢰⡇⠀⠀⠀⠀⢀⣰⡟⠛⢻⣷⣶⣿⡟⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢰⡿⠋⠙⠷⣦⣤⣾⡁⠀⠀⠀⠈⠿⣶⣤⣶⣶⣿⣯⡶⠞⠋⠁⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠉⠛⠛⠛⠛⠛⠛⠛⠻⣾⠏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡆⠀⠀⢀⣶⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇⣀⣀⣼⣿⠆⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⡟⡝⣿⣿⣿⠿⢯⠀⠀⠀ ⣀⠀⢀⣆⠀⠀⣰⣿⣷⣶⣿⣿⣿⣭⣼⣇⠀⠀ ⢹⣷⣼⡿⡄⢰⣿⠟⣁⠀⣀⠈⠙⣿⣿⣿⣀⠀ ⢸⣦⣿⣷⣷⠈⡏⠈⠉⠈⠉⠈⠓⢿⣿⣿⣿⡇ ⢸⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠟⠀ ⠀⠉⠉⠉⠀⠀⠀⠈⠁⠀⠀⠀⠀⠈⠁⠀⠀⠀
⣴⡟⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠻⠿⣿⣿⣿⣿⣿⢦⠤⠀⠀⠀ ⣿⣧⣤⣴⣿⣿⠛⠛⣿⣧⣼⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣷⡆⠈⠀⣀⣿⣷⡾⢿⣿⣿⣿⢿⣿⣿⣿⠁⠀⠀⣠⣿⣿⣿⣿⡏⠀⠀⠀⠀ ⣿⣿⡿⣿⣿⣿⣶⣾⣿⣿⣿⣿⢿⣧⠈⠙⠻⠿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣆⡹⠿⣿⣿⣿⣿⣿⣷⣦⠴⣿⣿⣿⣿⠋⣻⣴⣤⣄⠀ ⣿⣿⠇⠻⣿⣿⣿⡿⡋⠙⣻⣿⠿⣟⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣇⠀⢹⡟⢹⣿⣿⣿⣿⣶⣿⣿⣿⣿⠟⢋⡿⢿⣿⣷ ⣿⣿⡆⣴⣿⣿⣿⣿⢗⣒⣾⣉⣳⡬⠶⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠘⠀⣾⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⣾⣿⣾⣿⣟ ⣿⣿⣿⠿⣿⣾⣿⣍⡉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠉⠙⠛⠋⠁⠀⠀⠀⣼⣿⣿⣷⣻⣿ ⣿⣿⣿⣾⣿⣿⣏⣱⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⢯⣿⣿⣇⣿ ⣿⣿⣿⣿⠿⠋⠉⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⣿⢏⣾⣿⣿⢸ ⣽⣿⣋⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠞⢇⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⠌⢻⣿⣿⢸ ⣿⣿⡙⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⢋⡱⢏⣴⠾⢆⠀⠀⣦⣾⣆⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡎⠚⢿⡟⢸ ⣿⣿⣿⣷⣤⣀⡀⠀⠀⠀⠀⠀⣠⣤⣾⣿⠯⠐⠒⠉⡀⠀⢈⣦⠰⣼⠛⠿⣍⣓⣤⣄⣸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡀⠐⢁⡿ ⣿⣿⣿⣿⣿⡿⠛⠛⠿⣥⣴⣾⣿⣷⣿⣿⣶⣾⣉⣲⣙⠀⡼⠀⠙⢿⣧⠄⢼⣯⣽⣿⣟⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⡘⣷ ⣿⣿⣷⣿⣿⠟⠒⠒⠤⢽⣿⣿⣟⠉⠹⣿⡟⠛⠻⡟⠊⢣⠃⠀⠀⠀⣻⣶⣿⣿⣾⣿⣿⣿⣿⣿⣦⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿ ⣿⡿⢋⠟⠁⠀⠀⠀⢀⡞⠁⡟⣿⣦⣀⣘⣦⠴⠺⢿⣭⣽⣷⡀⠀⠀⠀⣏⡀⠀⣡⠏⠀⢀⣿⣿⠿⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣧⣎⡴⠂⠀⠀⢀⡿⠀⠀⡇⠹⠿⠟⠋⠀⠀⠀⠀⣿⠀⠀⠉⠒⠤⣀⡀⠙⢻⣧⣤⣤⣾⡍⠀⠀⢀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢲⣶⣶ ⣿⣿⣿⣁⠀⠀⣠⣾⣥⡀⠈⡇⠀⠀⠀⠀⠀⠀⠀⡠⠿⠦⣀⠀⠀⠀⠀⠉⠳⠦⢌⣛⠛⠛⠀⠀⠀⠘⠀⣿⣦⣀⡀⠀⠀⠀⠀⠈⢿⣿ ⣿⣿⣿⣿⣲⠟⠉⠉⠀⣀⣀⡇⠀⠀⠀⠠⣤⠔⣫⣤⣤⣤⣄⡑⢦⡀⠀⠀⡀⠁⠀⠉⠙⠲⣦⣀⠀⡀⢠⣿⡏⠉⠛⠷⣶⣄⡀⠀⠀⣷ ⣿⣿⣿⢳⠃⣠⠴⠒⠾⠛⠉⢹⢦⡀⠀⠀⠈⣷⣿⣿⣿⣿⣿⣿⢀⣞⣑⡞⠁⠀⠀⠀⠀⣸⡇⠀⢹⠇⣾⠛⢷⣄⠀⢀⡼⠉⠛⢷⣼⣿ ⣿⣏⣹⣿⣼⡏⠀⠀⠀⠀⠀⠈⢦⡇⠀⠀⠀⢸⣿⡿⢿⠷⠿⣿⣿⣿⠏⠀⠀⠀⠀⠀⢠⣿⠓⠦⠼⠞⠁⢧⡀⠙⣷⡌⠀⠀⠀⢸⡟⠙ ⣟⠛⠟⢻⣿⣗⠀⠀⠀⠀⠀⠀⠘⢦⠀⠀⠀⠀⣿⣧⣀⣴⡶⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⢿⣷⠀⠀⠀⠀⠈⢷⡀⠈⢻⡆⠀⣠⣿⡁⢀ ⠘⢿⣼⣿⠁⠈⠒⠤⣀⢀⠀⠀⢀⡾⠓⣄⠀⠀⢈⠒⠒⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡿⠗⣶⣤⡤⠀⠀⢓⣀⣀⣁⡴⠿⣿⣷⣾ ⠀⢀⠘⣿⣦⣤⣄⠀⠈⢹⣷⡞⢡⣀⡀⠈⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠾⢻⠋⢀⠔⢹⣿⣄⣤⢞⣉⠀⠀⠀⠀⠀⠈⡏⠃ ⣾⡃⢀⡼⣿⣿⣿⣶⣶⣿⣿⡿⣄⡻⣿⣿⠋⠛⢷⣦⣀⣀⣀⣀⣤⣤⣶⠾⠛⣩⠔⣤⠋⠀⠀⠀⠘⣿⣿⠇⢫⡞⠀⠀⠀⠀⠀⠀⡁⠸ ⣿⣿⣿⣿⣿⣿⣿⡛⠋⠉⠉⠉⠉⠙⠛⢿⣧⢠⣾⣿⣿⣿⡿⠟⠋⠉⠀⡠⠞⣡⡞⠁⠀⠀⠀⠀⠀⠙⠛⠚⣹⠁⠀⠀⠀⠀⠀⠀⠄⠀ ⣿⢿⢟⠟⣽⠟⠉⣉⢉⣉⣙⡳⠦⣤⣤⠘⠒⠛⠻⣿⡍⠀⠀⢀⡀⠖⠉⢠⣾⠋⠀⠀⠀⠀⠀⠀⠀⢀⠀⣠⣋⠀⠀⠀⠀⠀⠀⠀⠀⠀

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