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 Program
    {
        static void Main(string[] args)
        {
            var n = int.Parse(Console.ReadLine());
            int[] dims = new int[n + 1];
            for (int i = 0; i < n; i++)
            {
                var strs = Console.ReadLine().Split(' ');
                dims[i] = int.Parse(strs[0]);
                dims[i + 1] = int.Parse(strs[1]);
            }
            int[,] cost = new int[n + 1, n + 1];
            for (int len = 2; len <= n; len++)
            {
                for (int i = 0; i < n - len + 1; i++)
                {
                    int j = i + len - 1;
                    cost[i, j] = int.MaxValue;
                    for (int k = i; k < j; k++)
                    {
                        var tmp = cost[i, k] + cost[k + 1, j] + dims[i] * dims[k + 1] * dims[j + 1];
                        if (tmp < cost[i, j]) cost[i, j] = tmp;
                    }
                }
            }
            Console.WriteLine(cost[0, n - 1]);
        }
    }
}