Problem:
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Matrix-chain Multiplication

The goal of the matrix-chain multiplication problem is to find the most efficient way to multiply given $n$ matrices $M_1, M_2, M_3,...,M_n$.

Write a program which reads dimensions of $M_i$, and finds the minimum number of scalar multiplications to compute the maxrix-chain multiplication $M_1M_2...M_n$.

Input

In the first line, an integer $n$ is given. In the following $n$ lines, the dimension of matrix $M_i$ ($i = 1...n$) is given by two integers $r$ and $c$ which respectively represents the number of rows and columns of $M_i$.

Output

Print the minimum number of scalar multiplication in a line.

Constraints

$1 \leq n \leq 100$

$1 \leq r, c \leq 100$

Sample Input 1

6
30 35
35 15
15 5
5 10
10 20
20 25

Sample Output 1

15125

Solution in Ruby (judge verdict: Wrong Answer)

def matrix_chain_order(input_array)
  n = input_array.length-1
  array = Array.new(n+1).map{Array.new(n+1,0)}
  2.upto n do |l|
    1.upto n-l+1 do |i|
      j = i+l-1
      array[i][j] = Float::INFINITY
      i.upto j-1 do |k|
        q = array[i][k] + array[k+1][j] + input_array[i-1]*input_array[k]*input_array[j]
        array[i][j] = (array[i][j] > q) ? q : array[i][j]
      end
    end
  end
  # puts array[1].last
  array.each do |x|
    p x
  end
end

array = []

n = gets.to_i
n.times do |i|
  input = gets.split(" ")
  array << input[0].to_i if i == 0
  array << input[1].to_i
end

matrix_chain_order(array)