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
#!/usr/bin/python3


def countpars(s):
    lc = 0
    rc = 0
    for ch in s:
        if ch == '(':
            lc += 1
        else:
            if lc > 0:
                lc -= 1
            else:
                rc += 1
    return (lc, rc)


n = int(input())

ssl = []
ssr = []
for i in range(n):
    (clc, crc) = countpars(input())
    if clc >= crc:
        ssl.append((clc, crc))
    else:
        ssr.append((clc, crc))

ssl.sort(key=lambda x: x[1])
ssr.sort(reverse=True)

lc = 0
rc = 0

for (clc, crc) in ssl:
    lc -= crc
    if lc < 0:
        print('No')
        exit()

    lc += clc

for (clc, crc) in ssr:
    lc -= crc
    if lc < 0:
        print('No')
        exit()
    lc += clc
        

if lc == 0:
    print('Yes')
else:
    print('No')    
    




