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: Accepted)

INF = (1 << 31) - 1

n = gets.to_i
ms = n.times.map {gets.split.map(&:to_i)}

dp = Array.new(n + 1) {Array.new(n + 1, 0)}
dim = [ms[0][0]] + ms.map(&:last)

2.upto(n) do |l|
  1.upto(n - l + 1) do |i|
    j = i + l - 1
    dp[i][j] = INF
    i.upto(j - 1) do |k|
      tmp = dp[i][k] + dp[j][k] + dp[k + 1][j] + dim[i - 1] * dim[k] * dim[j]
      dp[i][j] = [dp[i][j], tmp].min
    end
  end
end

puts dp[1][n]