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.

给你两个括号序列（不一定是合法的）$s$ 和 $t$，它们仅由字符 '(' 和 ')' 组成。你需要构造一个最短的合法括号序列，使得给定的两个括号序列 $s$ 和 $t$ 均为其子序列（不一定是连续子序列）。

回顾什么是合法括号序列（regular bracket sequence）：

• () 是一个合法括号序列；
• 若 $S$ 是合法括号序列，则 (S) 也是一个合法括号序列；
• 若 $S$ 和 $T$ 均为合法括号序列，则 $ST$（即 $S$ 与 $T$ 的拼接）也是一个合法括号序列。

回顾：字符串 $s$ 的子序列是指从 $s$ 中删除若干（可能为零）个字符后得到的字符串 $t$。例如，“coder”、“force”、“cf” 和 “cores” 都是 “codeforces” 的子序列，但 “fed” 和 “z” 不是。

The first line of the input contains one bracket sequence $s$ consisting of no more than $200$ characters '(' and ')'.

The second line of the input contains one bracket sequence $t$ consisting of no more than $200$ characters '(' and ')'.

输入的第一行包含一个括号序列 $s$，由不超过 $200$ 个字符 '(' 和 ')' 组成。

输入的第二行包含一个括号序列 $t$，由不超过 $200$ 个字符 '(' 和 ')' 组成。

Print one line — the shortest regular bracket sequence that contains both given bracket sequences as subsequences (not necessarily contiguous). If there are several answers, you can print any.

输出一行——包含给定的两个括号序列作为子序列（不一定是连续的）的最短正则括号序列。如果存在多个答案，输出任意一个即可。