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()[:-1]
n = int(input())
plus, minus = [], []
for _ in range(n):
	s = input()
	mi, cur = 0, 0
	for i in range(len(s)):
		if s[i] == "(":
			cur += 1
		else:
			cur -= 1
		mi = min(mi, cur)
	if cur >= 0:
		plus.append((mi, cur))
	else:
		minus.append((mi, cur))

plus.sort(key=lambda x: -x[0])
minus.sort(key=lambda x: x[0] - x[1])
res = plus + minus

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

if cur != 0:
	print("No")
	exit()
print("Yes")