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
# F - Bracket Sequencing

N = int(input())
L = []
R = []
for _ in range(N):
    S = list(str(input()))
    len_S = len(S)
    L_d = 0
    L_min_d = 0
    R_d = 0
    R_min_d = 0
    for i in range(len_S):
        if S[i] == '(':
            L_d += 1
        else:
            L_d -= 1
            L_min_d = min(L_min_d, L_d)
        if S[len_S-i-1] == ')':
            R_d += 1
        else:
            R_d -= 1
            R_min_d = min(R_min_d, R_d)
    if L_d >= 0:
        L.append((L_d, L_min_d))
    else:
        R.append((R_d, R_min_d))

L.sort(key=lambda x: x[1], reverse=True)
R.sort(key=lambda x: x[1], reverse=True)

ans = 'Yes'
l_now = 0
for d, min_d in L:
    if l_now + min_d < 0:
        ans = 'No'
        break
    else:
        l_now += d

r_now = 0
for d, min_d in R:
    if r_now + min_d < 0:
        ans = 'No'
        break
    else:
        r_now += d

if l_now != r_now:
    ans = 'No'

print(ans)