CF1272F Two Bracket Sequences

You are given two bracket sequences (not necessarily regular) $ s $ and $ t $ consisting only of characters '(' and ')'. You want to construct the shortest regular bracket sequence that contains both given bracket sequences as subsequences (not necessarily contiguous). Recall what is the regular bracket sequence: - () is the regular bracket sequence; - if $ S $ is the regular bracket sequence, then ( $ S $ ) is a regular bracket sequence; - if $ S $ and $ T $ regular bracket sequences, then $ ST $ (concatenation of $ S $ and $ T $ ) is a regular bracket sequence. Recall that the subsequence of the string $ s $ is such string $ t $ that can be obtained from $ s $ by removing some (possibly, zero) amount of characters. For example, "coder", "force", "cf" and "cores" are subsequences of "codeforces", but "fed" and "z" are not.

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