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())
scop = [] #高低差,min値
scom = []
ssum = 0

for i in range(n):
    s = input()
    sa = 0
    ms = 0
    for i in range(len(s)):
        if s[i] == "(":
            sa += 1
        else:
            sa -= 1
        if ms > sa:
            ms = sa
    if sa > 0:
        scop.append([ms,sa])
    elif not sa == ms:
        scom.append([ms,sa])
    ssum += sa

if not ssum == 0:
    print("No")
    exit()

scop.sort(reverse = True)
scom.sort()

now = 0
for i in scop:
    if now + i[0] < 0:
        print("No")
        exit()
    now += i[1]
for i in scom:
    if now + i[0] < 0:
        print("No")
        exit()
    now += i[1]

print("Yes")
