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
from collections import deque,defaultdict
import bisect
N = int(input())
S = [input() for i in range(N)]

def bend(s):
    res = 0
    k = 0
    for th in s:
        if th == '(':
            k += 1
        else:
            k -= 1
        res = min(k,res)
    return res

species = [(bend(s),s.count('(')-s.count(')')) for s in S]

ups = [(b,u) for b,u in species if u > 0]
flats = [(b,u) for b,u in species if u == 0]
downs = [(b,u) for b,u in species if u < 0]


ups.sort()
high = 0
for b,u in ups[::-1] + flats:
    if high + b < 0:
        print('No')
        exit()
    high += u

rdowns = [(b-u,-u) for b,u in downs]
rdowns.sort()
high2 = 0
for b,u in rdowns[::-1]:
    if high2 + b < 0:
        print('No')
        exit()
    high2 += u

if high == high2:
    print('Yes')
else:
    print('No')
