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 AOJ_ALDS1_10_B
{
    class Program
    {
        static void Main(string[] args)
        {
            var n = int.Parse(Console.ReadLine());

            int[] r = new int[n + 2];   // c.lastを追加
            for (int i = 0; i < n; i++)
            {
                var input = ReadInt();
                r[i + 1] = input[0];
                if (i == n - 1) r[n + 1] = input[1];//最後を修正
            }

            int[,] dp = new int[n + 1, n + 1];
            for (int i = 1; i < n; i++)
            {
                dp[i, i + 1] = r[i] * r[i + 1] * r[i + 2];
            }

            for (int i = n - 2; i >= 1; i--)
            {
                for (int j = i + 2; j <= n; j++)
                {
                    int min = int.MaxValue;

                    for (int k = i; k <= j - 1; k++)
                    {
                        int cand = dp[i, k] + dp[k + 1, j] + r[i] * r[k + 1] * r[j + 1];
                        min = Math.Min(min, cand);
                    }

                    dp[i, j] = min;
                }
            }

            Console.WriteLine(dp[1, n]);
            Console.ReadKey();
        }

        static int[] ReadInt()
        {
            int[] ret = Console.ReadLine().Split().Select(int.Parse).ToArray();
            return ret;
        }
        static long[] ReadLong()
        {
            long[] ret = Console.ReadLine().Split().Select(long.Parse).ToArray();
            return ret;
        }
    }
}