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
import heapq
input = sys.stdin.readline

N = int(input())

forward = []
backward = []

for _ in range(N):
    pos = 0
    Min = 0
    for c in input()[:-1]:
        if c == '(':
            pos += 1
        else:
            pos -= 1
            Min = min(Min, pos)
    if pos >= 0:
        heapq.heappush(forward, (-Min, pos))
    else:
        heapq.heappush(backward, (pos-Min, -pos))

ansflg = True
pos1 = 0
while forward:
    down, pos = heapq.heappop(forward)
    if pos1 >= down:
        pos1 += pos
    else:
        ansflg = False
        break

pos2 = 0
if ansflg:
    while backward:
        down, pos = heapq.heappop(backward)
        if pos2 >= down:
            pos2 += pos
        else:
            ansflg = False
            break

if pos1 != pos2:
    ansflg = False

if ansflg:
    print("Yes")
else:
    print("No")


