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;

					
public class Program
{
	static int[,] DP;
	static int[] p;
	
	public static void Main()
	{		
		int n = int.Parse(Console.ReadLine());
		DP = new int[n+1,n+1];
		p = new int[n + 1];
		
		string[] buf = Console.ReadLine().Split(" ".ToCharArray());
		p[0] = int.Parse(buf[0]);
		p[1] = int.Parse(buf[1]);
		for(int i = 1; i < n; i++) {
			buf = Console.ReadLine().Split(" ".ToCharArray());
			p[i+1] = int.Parse(buf[1]);
		}
		
		for(int i = 0; i < n; i++) {
			DP[i,i] = 0;
			if(i >= 1) {
				DP[i, i +1] = p[i-1]*p[i]*p[i+1];
			}
		}
		
		for(int j = 0; j<= n-3; j++) {
			for(int i = 3+j; i <= n; i++) {
				DP[i - 2 - j, i] = Rec(i - 2 - j, i);
			}
		}
		
		Console.WriteLine(DP[1,n]);
	}
	
	public static int Rec(int r, int c)
	{
		int min = int.MaxValue;
		
		for(int i = 0; i < (c-r); i++) {
			min = Math.Min(min, DP[r,r+i] + DP[r+i+1,c] + p[r-1] * p[r+i] * p[c]);
		}
		
		return min;
	}
}