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
def input(): return sys.stdin.readline().rstrip()

n = int(input())
ls, rs = [], []
total = 0
for i in range(n):
    s = input()
    h, b = 0, 0
    for c in s:
        if c=='(':  h += 1
        else:       h -= 1
        b = min(b, h)
    if h > 0:   ls.append((b, h))       # 増減+ はb:最下点, h:増減を取る
    else:       rs.append((b-h, -h))    # 増減- は、上下左右逆さに考え、b:右から見た最下点、h:増減のマイナスを取る
    total += h
ls.sort(reverse=True)
rs.sort(reverse=True)   # 増減-は右から見るので、大きい順にsort

def chk(s):
    h = 0
    for sb, sh in s:
        b = h + sb
        if b < 0: return False
        h += sh
    return True

if (chk(ls) and chk(rs) and total==0):
    print("Yes")
else:
    print("No")