Editorial for LCC '24 Contest 2 S3 - Partners - MCPT: Mackenzie Competitive Programming Team

Editorial for LCC '24 Contest 2 S3 - Partners

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Author: JojoTheWarrior

For every $a_i$ ~a_i~, there's another $a_j$ ~a_j~ such that $a_i$ ~a_i~ + $a_j$ ~a_j~ = $X$ ~X~, where $X$ ~X~ is the sum of each pair.

If you add every $a_i$ ~a_i~ together, you'll end up adding $N$ ~N~ pairs of $X$ ~X~, so the sum is $NX$ ~NX~. Since we know $N$ ~N~, we can just divide this sum by $N$ ~N~ to find $X$ ~X~. Then, it remains to subtract $a_i$ ~a_i~ from $X$ ~X~ to find your partner.

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