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()))
C_p = []
C_m = []
for i in range(N):
    kakko = input()
    temp = 0
    temp_min = 0
    for s in kakko:
        if s == "(":
            temp += 1
        else:
            temp -= 1
            temp_min = min(temp, temp_min)
    if temp >= 0:
        C_p.append((temp_min, temp))
    else:
        C_m.append((temp_min - temp, temp_min, temp))
C_p.sort(reverse=True)

flag = 0
final = 0
for l, f in C_p:
    if final + l < 0:
        flag = 1
    final += f

C_m.sort()

for _, l, f in C_m:
    if final + l < 0:
        flag = 1
    final += f
    
if final != 0:
    flag = 1

print("Yes" if flag == 0 else "No")