Bracket Sequencing

A bracket sequence is a string that is one of the following:

1. An empty string;
2. The concatenation of (, A, and ) in this order, for some bracket sequence A ;
3. The concatenation of A and B in this order, for some non-empty bracket sequences A and B /

Given are N strings S_i. Can a bracket sequence be formed by concatenating all the N strings in some order?

Constraints

• 1 \leq N \leq 10^6
• The total length of the strings S_i is at most 10^6.
• S_i is a non-empty string consisting of ( and ).

Input

Input is given from Standard Input in the following format:

N S_1 : S_N

Output

If a bracket sequence can be formed by concatenating all the N strings in some order, print Yes; otherwise, print No.

Examples

Input

2 ) (()

Output

Yes

Input

2 )( ()

Output

No

Input

4 ((())) (((((( )))))) ()()()

Output

Yes

Input

3 ((( ) )

Output

No

inputFormat

Input

Input is given from Standard Input in the following format:

N S_1 : S_N

outputFormat

Output

If a bracket sequence can be formed by concatenating all the N strings in some order, print Yes; otherwise, print No.

Examples

Input

2 ) (()

Output

Yes

Input

2 )( ()

Output

No

Input

4 ((())) (((((( )))))) ()()()

Output

Yes

Input

3 ((( ) )

Output

No

样例

3
(((
)
)

No