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
N = int(input())

S_list = []
for _ in range(N):
	S_list.append(input().strip())

data = []
for s in S_list:
	bottom = 0
	height = 0
	for c in s:
		if c == ")":
			height -= 1
			if bottom > height:
				bottom = height
		else:
			height += 1
	if height == 0:
		k1 = 1
		k2 = 0
	elif height > 0:
		k1 = 0
		k2 = -bottom
	else:
		k1 = 2
		k2 = bottom - height
	data.append((k1, k2, bottom, height, s))

data.sort()

def check():
	height = 0
	for k1, k2, b, h, s in data:
#		print(height, b, h, s)
		if height + b < 0:
			return False
		height += h
	return height == 0

if check():
	print("Yes")
else:
	print("No")

