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 JavaScript (judge verdict: Accepted)

function range(begin, end) {
  return Array.from(Array(end - begin), (e, i) => begin + i);
}

(function main() {
  const lines = require('fs').readFileSync('/dev/stdin', 'utf8').trim().split('\n');
  const n = Number(lines.shift ());
  const p = lines.map(l => l.split(' ')[0]).concat([lines[n-1].split(' ')[1]]).map(Number);

  const m = Array.from(Array(n + 1), () => (Array(n + 1)));
  for (let i = 0; i < n + 1; i++) m[i][i] = 0;

  let i = 0, d = 1;
  for (d = 1; d <= n - 1; d++) {
    for (i = 1; i <= n - d; i++) {
      m[i][i+d] = range(i, i + d).map(
        k => m[i][k] + m[k + 1][i + d] + p[i - 1] * p[k] * p[i + d]
      ).sort((a, b) => a - b)[0];
    }
  }
  console.log(m[1][n]);
})();