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;
using System.Collections.Generic;
using System.Linq;

namespace Dynamic_Programming
{
    class Matrix_Chain_Multiplication
    {
        static void Main(string[] args)
        {
            var n = int.Parse(Console.ReadLine());
            Console.WriteLine(Solve(n));
        }

        static int Solve(int n)
        {
            var dim = new int[n + 1];
            for (int i = 0; i < n; i++)
            {
                var rc = Console.ReadLine().Split(' ').Select(s => int.Parse(s)).ToArray();
                dim[i] = rc[0];
                if (i == n - 1) dim[i + 1] = rc[1];
            }

            var cost = new int[n, n];
            for (int i = 0; i < n; i++)
                cost[i, i] = 0;

            for (int l = 1; l < n; l++)
            {
                for (int i = 0; i < n - l; i++)
                {
                    cost[i, i + l] = int.MaxValue;
                    for (int k = i; k < i + l; k++)
                    {
                        var tmp = cost[i, k] + cost[k + 1, i + l] + dim[i] * dim[k + 1] * dim[i + l + 1];
                        if (tmp < cost[i, i + l]) cost[i, i + l] = tmp;
                    }
                }
            }

            return cost[0, n - 1];
        }

        static int Argmin(List<int> list)
        {
            var min = list[1];
            var index = 1;
            for (int i = 0; i < list.Count; i++)
            {
                if (min > list[i]) { min = list[i]; index = i; }
            }
            return index;
        }
    }
}