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
n=int(input())
jsum=0
gjlist=[]
ejlist=[]
esum=0

def jouka(t):
	global jsum
	global gjlist
	global ejlist
	global esum
	
	tmpj=0
	tmpe=0
	
	for i in range(len(t)):
		if t[i] == "(":
			tmpj += 1
		else:
			if tmpj == 0:
				tmpe +=1
			else:
				tmpj -=1
		
	if tmpe == 0:
		jsum += tmpj
	elif tmpj == 0:
		esum += tmpe
	elif tmpj > tmpe:
		gjlist.append([tmpe,tmpj])
	else:
		ejlist.append([tmpe,tmpj])

for j in range(n):
	jouka(input())

gjlist.sort(key=lambda x:x[0])
ejlist.sort(reverse = True,key=lambda x:x[0])

streak=jsum
for gj in gjlist:
	if gj[0] > streak:
		print("No")
		sys.exit()
	else:
		streak += gj[1]-gj[0]

for ej in ejlist:
	if ej[0] > streak:
		print("No")
		sys.exit()
	else:
		streak += ej[1]-ej[0]

if streak == esum:
	print("Yes")
else:
	print("No")



