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())
flag = 0
ML = []
MM = []
MR = []
L = 0
R = 0
for _ in range(n):
    s = input()
    saisho = 0
    cur = 0
    for w in s:
        if w == "(":
            cur += 1
        else:
            cur -= 1
            saisho = min(saisho, cur)
    if cur > 0:
        ML.append((saisho, cur))
    elif cur < 0:
        MR.append((-cur + saisho, -cur))
    else:
        MM.append((saisho, cur))
ML.sort(reverse=True)
MR.sort(reverse=True)
leftnow = 0
for saisho, delta in ML:
    if leftnow + saisho < 0:
        flag = 1
    leftnow += delta
for saisho, delta in MM:
    if leftnow + saisho < 0:
        flag = 1
    leftnow += delta
rightnow = 0
for saisho, delta in MR:
    if rightnow + saisho < 0:
        flag = 1
    rightnow += delta

if rightnow != leftnow:
    flag = 1
if flag:
    print("No")
else:
    print("Yes")
