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 collections import deque
def input():
    return sys.stdin.readline().strip()

tozan = []
gezan = []

def check():
    s = input()
    m = 0
    res = 0
    for i in s:
        if i == "(":
            m += 1 
        else:
            m -= 1
            res = min(res,m)
    if m >= 0:
        tozan.append([res,m])
    else:
        gezan.append([res-m,-m])

N = int(input())
for _ in range(N):
    check()

tozan.sort(reverse=True)
gezan.sort(reverse=True)

t = 0
g = 0

for res,m in tozan:
    if t + res < 0:
        print("No")
        exit()
    t += m

for res,m in gezan:
    if g + res < 0:
        print("No")
        exit()
    g += m

if t == g:
    print("Yes")
else:
    print("No")