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

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