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

n = int(input())

plus = []
minus = []
for _ in range(n):
    min_s = 0
    ts = 0
    s = input().strip()
    for c in s:
        ts += 1 if c == '(' else -1
        min_s = min(ts, min_s)
    if ts >= 0:
        plus.append((-min_s, ts))
    else:
        minus.append((-(min_s - ts), -ts))

plus.sort()
minus.sort()

s1 = 0
for m, t in plus:
    if s1 - m < 0:
        print('No')
        exit()
    s1 += t

s2 = 0
for m, t in minus:
    if s2 - m < 0:
        print('No')
        exit()
    s2 += t

if s1 == s2:
    print('Yes')
else:
    print('No')
