Problem:
Score : 600 points

Problem Statement

A bracket sequence is a string that is one of the following:

An empty string;

The concatenation of (, A, and ) in this order, for some bracket sequence A ;

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.

Sample Input 1

2
)
(()

Sample Output 1

Yes

Concatenating (() and ) in this order forms a bracket sequence.

Sample Input 2

2
)(
()

Sample Output 2

No

Sample Input 3

4
((()))
((((((
))))))
()()()

Sample Output 3

Yes

Sample Input 4

3
(((
)
)

Sample Output 4

No

Solution in Julia (1.4.0) (judge verdict: Wrong Answer)

const double = Float64
const int = Int64
const vint = Vector{int}
const vdouble = Vector{double}

int(x) = parse(int,x)
parseint(x) = parse(int, x)
readint() = map(parseint, split(readline()))

function main()
  N = readint()[1]

  HT = Array{int,2}(undef,N,2)
  
  # input とまえしょり
  for i in 1:N
    s = readline()
    
    h = 0
    t = 0
    for c in s
      if c=='('
        t += 1
      else
        t -= 1
        h = min(h,t)
      end
    end
    HT[i,:] .= h,t 
  end

  HT = HT[sortperm(HT[:,1],rev=true),:]
  
  h = 0
  flag = true
  for i in 1:N
    if h+HT[i,1] < 0
      flag = false
      break
    end
    h += HT[i,2]
  end

  if flag && h==0
    println("Yes")
  else
    println("No")
  end

end

main()