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 JAVA (judge verdict: Accepted)

import java.util.Scanner;


public class Main {
	
	private static int[][] cache;
	private static int[] r;
	private static int[] c;
	

	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in); 

		int n = sc.nextInt();
		cache = new int[n][n];
		r = new int[n];
		c = new int[n];

		for (int i = 0; i < n; i++) {
			r[i] = sc.nextInt();
			c[i] = sc.nextInt();
		}
		for (int j = 0; j < n; j++) {
			for (int i = 1; i <= n && i + j <= n; i++) {
				cache[i-1][i+j-1] = mcm(i, i + j);
//				System.out.println(i + " " + (i + j));
			}
		}

		System.out.println(cache[1 - 1][n - 1]);
		
		sc.close();
	}
	
	private static int mcm(int i, int j) {
		if (i == j) {
			return 0;
		} else {
			int min = Integer.MAX_VALUE;
			for (int k = 0; k < j - i; k++) {
				assert c[i+k-1] == r[i+k+1-1] : i + k + ":" + c[i+k-1] + "," + r[i+k+1-1];
				int result = cache[i-1][i+k-1] + r[i-1] * r[i+k+1-1] * c[j-1] + cache[i+k+1-1][j-1];
				if (result < min) {
					min = result;
				}
			}
			
			return min;
		}
	}
}