human
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
Solve the task in PYTHON3.

=====
Give me a Python code to print `Yes`?
assistant
#Here is Python code to print `Yes`.

def main():
    import sys
    def input(): return sys.stdin.readline().rstrip()
    n = int(input())
    lx = []
    rx = []
    for i in range(n):
        a = 0
        cnt = 0
        for j in input():
            if j == '(':
                cnt += 1
            else:
                cnt -= 1
            a = min(a, cnt)
        
        if cnt >= 0:
            lx.append((a, cnt))
        else:
            rx.append((a, cnt))
    lx.sort(key= lambda x: -x[0]) # -aの昇順
    rx.sort(key= lambda x: x[0]-x[1]) # -bの昇順(bの降順)
    total = 0
    check = True
    for x,cnt in (lx+rx):
        if total + x < 0:
            check = False
            break
        total += cnt
    if total == 0 and check:
        print('Yes')
    else:
        print("No")
    



if __name__ == '__main__':
    main()