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().rstrip()

N = int(input())

S_p = []
S_n = []

for i in range(N):
  end = 0
  mim = 0
  for c in input():
    if c == "(":
      end += 1
    else :
      end -= 1
    mim = min(mim,end)
  
  if end >= 0:
    S_p.append([mim, end])
  else:
    S_n.append([end-mim, end])
  
S_p.sort(reverse=True)
S_n.sort(reverse=True)
#print(S_p)
#print(S_n)

check = 0
flag = True
for i in range(len(S_p)):
  if check + S_p[i][0] >= 0:
    check += S_p[i][1]
  else:
    flag = False
    break
  #print(check)
  
for i in range(len(S_n)):
  if check + S_n[i][1] - S_n[i][0] >= 0:
    check += S_n[i][1]
  else:
    flag = False
    break
  #print(check)
  
if check == 0 and flag:
  flag = True
else:
  flag = False

print("Yes" if flag else "No")