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 heapq
import sys
input = sys.stdin.readline
n = int(input())
sss = [input()[:-1] for _ in range(n)]

a = []
b = []
ss = 0
ii = 0
for i in sss:
    mi = 0
    ma = 0
    s = 0
    for j in i:
        if j == "(":
            s += 1
        else:
            s -= 1
        mi = min(mi, s)
        ma = max(ma, s)
    ss += s
    if s >= 0:
        a.append([s, mi, ma, ii])
    else:
        mi = 0
        ma = 0
        s = 0
        for j in reversed(i):
            if j == ")":
                s += 1
            else:
                s -= 1
            mi = min(mi, s)
            ma = max(ma, s)
        b.append([s, mi, ma, ii])
    ii += 1


if ss != 0:
    print("No")
    exit()
a.sort(reverse=1, key=lambda x: x[1])
b.sort(reverse=1, key=lambda x: x[1])


def ok(a):
    s = 0
    for i, j, _, _ in a:
        if s + j < 0:
            print("No")
            exit()
        s += i

ok(a)
ok(b)
print("Yes")
