Codeforces Round 605 (Div. 3) |
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Finished |

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dp

strings

two pointers

*2200

No tag edit access

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F. Two Bracket Sequences

time limit per test

2 secondsmemory limit per test

512 megabytesinput

standard inputoutput

standard outputYou 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.

Input

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 ')'.

Output

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.

Examples

Input

(())(() ()))()

Output

(())()()

Input

) ((

Output

(())

Input

) )))

Output

((()))

Input

()) (()(()(()(

Output

(()()()(()()))

Codeforces (c) Copyright 2010-2023 Mike Mirzayanov

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