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
# coding: utf-8
# Your code here!
import sys
read = sys.stdin.read
readline = sys.stdin.readline 

n = int(input())
s = read().split()

dp = []
dn = []
for i in s:
    a = 0
    d = 0
    for j in i:
        if j == "(": d+= 1
        else: d -= 1
        if d < a: a = d
    
    #print(a,d,i)    
    if d >= 0:    
        dp.append((a,d))
    else:
        dn.append((a-d,-d))
    
dp.sort()
dn.sort()

def check(dp):
    D = 0
    while dp:
        a,d = dp.pop()
        if D+a < 0: return False
        D += d
    return [D]

#print(dp)
#print(dn)
a = check(dp)
b = check(dn)
#print(a,b)

if a==False or b==False:
    print("No")
else:
    if a[0] != b[0]:
        print("No")
    else:
        print("Yes")
        





    
    
    
    
    