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())
D, E = [], []
t,l = 0, 0
res = 0
for _ in range(N):
    S = input().rstrip()
    x,y = 0,0
    for s in S:
        if s=="(": x+=1
        else: x=max(x-1,0)
    for s in reversed(S):
        if s==")": y+=1
        else: y=max(y-1,0)
    D.append((x,y))
D.sort(key=lambda x:x[1])
t = 0
for x,y in D:
    if x-y>=0:
        if t>=y: t+=x-y
        else: print("No"); exit()
D.sort(key=lambda x:x[0])
s = 0
for x,y in D:
    if y-x>=0:
        if s>=x: s+=y-x
        else: print("No"); exit()
if t!=s: print("No")
else: print("Yes")
