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
from operator import itemgetter
N = int(input())
S = sys.stdin.read().split()
HT_high = []
HT_low = []
for s in S:
    t = 0
    h = 0
    for c in s:
        if c == "(":
            h += 1
        else:
            h -= 1
            if h < t:
                t = h
    if h >= 0:
        HT_high.append((h, t))
    else:
        HT_low.append((h, t))
HT_high.sort(key=itemgetter(1), reverse=True)
HT_low.sort(key=lambda x: x[0]-x[1], reverse=True)
h0 = 0
for h, t in HT_high + HT_low:
    if h0 + t < 0:
        print("No")
        exit()
    h0 += h
if h0 != 0:
    print("No")
else:
    print("Yes")
