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 Ruby (2.7.1) (judge verdict: Wrong Answer)

N = gets.to_i
A = N.times.map do
  w = gets.chomp
  r = 0
  l = 0
  w.size.times do |i|
    c = w[i]
    if c == '('
      l += 1
    elsif l > 0
      l -= 1
    else
      r += 1
    end
  end
  [r, l]
end
A.sort_by!{|(r,l)| [r, r - l] }

sum = 0
success = true

until A.empty?
  r,l = A.shift
  if sum >= r
    sum = sum - r + l
  else
    success = false
    break
  end
end
puts (success && sum.zero?) ? 'Yes' : 'No'