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())
S=[]
L=0
R=0
for i in range(N):
    s=input()
    n=len(s)
    data=[s[j] for j in range(n)]
    l=0
    r=0
    yabai=float("inf")
    for j in range(n):
        l+=(s[j]=="(")
        r+=(s[j]==")")
        yabai=min(l-r,yabai)
    S.append([yabai,l-r])
    L+=l
    R+=r

if L!=R:
    print("No")
else:
    first=[]
    last=[]
    for i in range(N):
        yabai,gap=S[i]
        if gap>0:
            first.append(S[i])
        else:
            last.append([gap-yabai,yabai])
    first.sort(reverse=True)
    last.sort(reverse=True)
    G=0
    for i in range(len(first)):
        yabai,gap=first[i]
        if 0>G+yabai:
            print("No")
            exit()
        else:
            G+=gap
    for j in range(len(last)):
        gapminus,yabai=last[j]
        if 0>G+yabai:
            print("No")
            break
        else:
            G+=gapminus+yabai
    else:
        print("Yes")
