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: Time Limit Exceeded)

using System;
using System.Collections.Generic;

class Program{
    class Pair{
        public int r;
        public int c;
    }

    static long CountChainMul(Pair[] matrixes){
        if (matrixes.Length<=1) {
            return 0;
        }
        var subMatrixes=new Pair[matrixes.Length-1];
        var result=long.MaxValue;
        for (var i=0; i<matrixes.Length-1; i++) {
            var j=0;
            for (; j<i; j++) {
                subMatrixes[j]=matrixes[j];
            }
            subMatrixes[i]=new Pair();
            subMatrixes[i].r=matrixes[i].r;
            subMatrixes[i].c=matrixes[i+1].c;
            for (j=i+2; j<matrixes.Length; j++) {
                subMatrixes[j-1]=matrixes[j];
            }
            var tmp=CountChainMul(subMatrixes)+
                matrixes[i].r*matrixes[i].c*matrixes[i+1].c;
            if (tmp<result) {
                result=tmp;
            }
        }
        return result;
    }

    public static void Main(){
        var n=int.Parse(Console.ReadLine());
        var matrixes=new Pair[n];
        for (var i=0; i<n; i++) {
            var s=Console.ReadLine().Split(' ');
            matrixes[i]=new Pair();
            matrixes[i].r=int.Parse(s[0]);
            matrixes[i].c=int.Parse(s[1]);
        }

        Console.WriteLine(CountChainMul(matrixes));
    }
}