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
input=lambda: sys.stdin.readline().strip()


n=int(input())
A=[]
#
PM=[[0,0] for i in range(n)]
for i in range(n):
    now=0
    mini=0
    for j in input():
        if j=="(": now+=1 
        else:
            now-=1 ; mini=min(mini,now)
    PM[i]=[mini,now]

if sum( [PM[i][1] for i in range(n)]  )!=0 : 
    print("No")
    exit()

MINI=0
NOW=0
PMf=[PM[i] for i in range(n) if PM[i][1]>=0]
PMf.sort()
for i in range(len(PMf)):
    MINI=min(MINI , NOW+PMf[-i-1][0] )
    NOW+=PMf[-i-1][1]
    if MINI<0 : print("No") ; exit()

PMs=[PM[i] for i in range(n) if PM[i][1]<0]
PMs=sorted(PMs , key=lambda x : x[1]-x[0])
for i in range(len(PMs)):
    MINI=min(MINI , NOW+PMs[-i-1][0] )
    NOW+=PMs[-i-1][1]
    if MINI<0 : print("No") ; exit()

print("Yes")
