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())
if N==0:
    print("Yes")
    exit()

P=[]
M=[]
for i in range(N):
    s=input()
    f=0
    m=0
    cnt=0
    for j in range(len(s)):
        if s[j]=="(":
            cnt+=1
        else:
            cnt-=1
            if cnt<m:
                m=cnt
    if cnt>=0:
        P.append([m,cnt])
    else:
        M.append([m-cnt,-cnt])
P.sort(reverse=True)
M.sort(reverse=True)
#print(P)
#print(M)
SUM=0
for i,j in P:
    SUM+=j
for i,j in M:
    SUM-=j
if SUM!=0:
    print("No")
    exit()

SUMP=0
for i,j in P:
    if SUMP>=(-i):
        SUMP+=j
    else:
        print("No")
        exit()
        
SUMM=0
for i,j in M:
    if SUMM>=(-i):
        SUMM+=j
    else:
        print("No")
        exit()
print("Yes")