Problem:
Score : 600 points

Problem Statement

We have N strings of lowercase English letters: S_1, S_2, \cdots, S_N.

Takahashi wants to make a string that is a palindrome by choosing one or more of these strings - the same string can be chosen more than once - and concatenating them in some order of his choice.

The cost of using the string S_i once is C_i, and the cost of using it multiple times is C_i multiplied by that number of times.

Find the minimum total cost needed to choose strings so that Takahashi can make a palindrome.

If there is no choice of strings in which he can make a palindrome, print -1.

Constraints

1 \leq N \leq 50

1 \leq |S_i| \leq 20

S_i consists of lowercase English letters.

1 \leq C_i \leq 10^9

Input

Input is given from Standard Input in the following format:

N
S_1 C_1
S_2 C_2
:
S_N C_N

Output

Print the minimum total cost needed to choose strings so that Takahashi can make a palindrome, or -1 if there is no such choice.

Sample Input 1

3
ba 3
abc 4
cbaa 5

Sample Output 1

7

We have ba, abc, and cbaa.

For example, we can use ba once and abc once for a cost of 7, then concatenate them in the order abc, ba to make a palindrome.
Also, we can use abc once and cbaa once for a cost of 9, then concatenate them in the order cbaa, abc to make a palindrome.

We cannot make a palindrome for a cost less than 7, so we should print 7.

Sample Input 2

2
abcab 5
cba 3

Sample Output 2

11

We can choose abcab once and cba twice, then concatenate them in the order abcab, cba, cba to make a palindrome for a cost of 11.

Sample Input 3

4
ab 5
cba 3
a 12
ab 10

Sample Output 3

8

We can choose a once, which is already a palindrome, but it is cheaper to concatenate ab and cba.

Sample Input 4

2
abc 1
ab 2

Sample Output 4

-1

We cannot make a palindrome, so we should print -1.

Solution in Ruby (2.7.1) (judge verdict: Runtime Error)

class String
  def mirror?
    (1 .. size / 2).all?{|i| self[i - 1] == self[size - i]}
  end
end
N = gets.to_i
S = (1 .. N).map do
  s,c = gets.split
  [s.chomp, c.to_i]
end

q = []
S.each do |s,c|
  q << [s, "", c]
  q << ["", s, c]
end
100.times do
  status = q.min_by(&:last)
  q.delete(status)
  l,r,t = *status
  lr = l + r
  if lr.size > 0 && lr.mirror?
    puts t
    break
  end
  
  if l.size > r.size
    suffix = l[r.size, l.size - r.size].reverse
    S.select{|s,c| s.size >= suffix.size ? s.end_with?(suffix) : suffix.end_with?(s) }
      .each{|s,c| q.push([l, s + r, t + c]) }
  elsif l.size < r.size
    prefix = r[0, r.size - l.size].reverse
    S.select{|s,c| s.size >= prefix.size ? s.start_with?(prefix) : prefix.start_with?(s) }
      .each{|s,c| q.push([l + s, r, t + c]) }
  else
    raise "unreachable"
  end
end