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
input = sys.stdin.readline

n=int(input())
s=[input().strip("\n") for _ in range(n)]
p=[];m=[]
for si in s:
    cnt=0;a=0;b=0
    for i in range(len(si)):
        if si[i]==")":
            cnt+=1
        else:
            cnt-=1
        a=max(a,cnt)
    cnt=0
    for i in range(len(si)-1,-1,-1):
        if si[i]=="(":
            cnt+=1
        else:
            cnt-=1
        b=max(b,cnt)
    if b-a>=0:
        p.append((a,si))
    else:
        m.append((-b,si))
p.sort();m.sort()
ss=""

for _,si in p:
    ss+=si
for _,si in m:
    ss+=si
cnt=0
for i in range(len(ss)):
    if ss[i]=="(":
        cnt+=1
    else:
        cnt-=1
    if cnt<0:
        print("No")
        exit()
if cnt:
    print("No")
else:
    print("Yes")

