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
import sys
# input = sys.stdin.readline


def parse(s):
    bottom = 0
    delta = 0
    for c in s:
        delta += (1 if c == "(" else -1)
        bottom = min(bottom, delta)
    return bottom, delta


def compute(pars):
    pars.sort(reverse=True)
    h = 0
    for bottom, delta in pars:
        if h + bottom < 0:
            print("No")
            sys.exit()
        h += delta
    return h


def main():
    N = int(input())

    incs = []
    decs = []
    for _ in range(N):
        bottom, delta = parse(input())
        if delta > 0:
            incs.append((bottom, delta))
        else:
            decs.append((bottom-delta, -delta))

    inc_tot = compute(incs)
    dec_tot = compute(decs)
    if inc_tot == dec_tot:
        print("Yes")
    else:
        print("No")


if __name__ == '__main__':
    main()
