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
read = sys.stdin.buffer.read
readline = sys.stdin.buffer.readline
readlines = sys.stdin.buffer.readlines
sys.setrecursionlimit(10 ** 7)

n = int(readline())
inc = []
dec = []
for _ in range(n):
    s = readline().rstrip().decode()
    d, r = 0, 0
    for m in s:
        d += (1 if m == '(' else -1)
        r = max(r, -d)
    (dec if d < 0 else inc).append((d, r))
inc.sort(key=lambda x: x[1])
dec.sort(key=lambda x: x[0] + x[1])
p1 = 0
p2 = 0
flag = True
for i in inc:
    flag &= i[1] <= p1
    p1 += i[0]
for d in dec:
    flag &= p2 >= d[0] + d[1]
    p2 -= d[0]
flag &= p1 == p2
print('Yes' if flag else 'No')
