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 input
  size = []
  n = gets.chomp.to_i
  (1..n).each do |i|
    sz = gets.chomp.split(/\s/).collect{ |x| x.to_i}
    size << { :row => sz[0], :col => sz[1]}
  end
  [n, size]
end

def solve(n, size)
  dp = { }
  0.upto(n - 1).each do |i|
    i.upto(n - 1).each do |j|
      dp[[i, j]] = 0x3fffffff
    end
  end

  0.upto(n - 1) { |i| dp[[i, i]] = 0}

  1.upto(n - 1).each do |k|
    0.upto(n - k - 1).each do |i|
      i.upto(i + k - 1).each do |j|
        sz = size[i][:row] * size[j + 1][:col] * size[i + k][:col]
        dp[[i, i + k]] = [dp[[i, i + k]], dp[[i, j]] + dp[[j + 1, i + k]] + sz].min
      end
    end
  end
  dp
end

def main
  n, size = input
#  p size                                                                                                                                                                        
  dp = solve(n, size)
  puts dp[[0, n - 1]]
end

main