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 C# (judge verdict: Accepted)

using System;

namespace B
{
    class Calc
    {
        public int matricChainOrder(int[] p)
        {
            int n = p.Length-1, i;
            int[,] m = new int[n+1, n+1];
            for (i = 1; i <= n; i++)
            {
                m[i, i] = 0;
            }
            int l, j=0, k, q;
            for (l = 2; l <= n; l++)
            {
                for (i = 1; i <= n - l + 1; i++)
                {
                    j = i + l - 1;
                    m[i, j] = int.MaxValue;
                    for (k = i; k < j; k++)
                    {
                        q = m[i, k] + m[k + 1, j] + p[i - 1] * p[k] * p[j];
                        m[i, j] = min(m[i, j], q);
                    }
                }
            }
            return m[1, n];
        }

        public int min(int m, int q)
        {
            if (m<q)
            {
                return m;
            }
            else
            {
                return q;
            }
        }
    }

    class B
    {
        static void Main(string[] args)
        {
            string input = Console.ReadLine();
            int n = int.Parse(input), i;
            string[] input2 = new string[2];
            int[] p = new int[n+1];
            Calc calc = new Calc();
            for (i = 0; i < n; i++)
            {
                input2 = Console.ReadLine().Split(' ');
                p[i] = int.Parse(input2[0]);
                p[i+1] = int.Parse(input2[1]);
            }
            Console.WriteLine(calc.matricChainOrder(p));
        }
    }
}