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Problem Statement

You are given $n$ strings $\\mathit{str}\_1, \\mathit{str}\_2, \\ldots, \\mathit{str}\_n$, each consisting of ( and ). The objective is to determine whether it is possible to permute the $n$ strings so that the concatenation of the strings represents a valid string.

Validity of strings are defined as follows:

• The empty string is valid.

• If $A$ and $B$ are valid, then the concatenation of $A$ and $B$ is valid.

• If $A$ is valid, then the string obtained by putting $A$ in a pair of matching parentheses is valid.

• Any other string is not valid.

For example, "()()" and "(())" are valid, while "())" and "((()" are not valid.

Input

The first line of the input contains an integer $n$ ($1 \\leq n \\leq 100$), representing the number of strings. Then $n$ lines follow, each of which contains $\\mathit{str}\_i$ ($1 \\leq \\lvert \\mathit{str}\_i \\rvert \\leq 100$). All characters in $\\mathit{str}\_i$ are ( or ).

Output

Output a line with "Yes" (without quotes) if you can make a valid string, or "No" otherwise.

Sample Input 1

3
()(()((
))()()(()
)())(())```

### Output for the Sample Input 1

```plain
Yes```

* * *

### Sample Input 2

```plain
2
))()((
))((())(```

### Output for the Sample Input 2

```plain
No```

* * *

### Source Name

[Japan Alumni Group Spring Contest 2014](http://acm-icpc.aitea.net/index.php?2013%2FPractice%2F%BD%D5%A5%B3%A5%F3%A5%C6%A5%B9%A5%C8%2F%B0%C6%C6%E2)

* * *