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(input()) for i in range(n)]
r = []
l = []
ans = 0
for i in s:
    now = 0
    c = 0
    for j in i:
        if j =="(":
            now += 1
        else:
            now -= 1
        c = min(c,now)
    if c == 0:
        ans += now
    elif now >= 0:
        l.append([c,now])
    else:
        r.append([c-now,now])

l.sort(reverse =True)
r.sort()
for i,j in l:
    if ans + i < 0:
        print("No")
        exit()
    else:
        ans += j

for i,j in r:
    if ans +i+j < 0:
        print("No")
        exit()
    else:
        ans += j
if ans == 0:
    print("Yes")
else:
    print("No")
