Concatenating Parenthesis Strings

You are given $n$ strings $str_1, str_2, \ldots, str_n$, each consisting of ( and ) only. Decide whether the $n$ strings can be arranged in some order so that their concatenation is a valid parenthesis string. You may reorder the strings, but the contents of each string stay as they are.

A valid parenthesis string is 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 $A$ inside a pair of matching parentheses is valid.
• No other string is valid.

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

The first line contains the number of strings $n$ ($1 \le n \le 100$). Each of the next $n$ lines contains one string $str_i$ ($1 \le |str_i| \le 100$). Every character of $str_i$ is ( or ).

Print Yes on the first line if a valid parenthesis string can be built, and No otherwise. Do not print the quotes.