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)

#include<stdio.h>
#define MAX 100

int main(){

  int n,A[MAX+1],B[MAX+1][MAX+1];
  int i,j,k,u;
  scanf("%d",&n);


  for(i=1;i<=n;i++){
    scanf("%d%d",&A[i-1],&A[i]);
  }

  for(i=1;i<=n;i++){
    B[i][i]=0;
    for(u=2;u<=n;u++){
      for(i=1;i<=n-u+1;i++){
	j = i+u-1;
	B[i][j] =(1<<21);
	for(k=i;k<=j-1;k++){
	  if(B[i][j] < B[i][k] + B[k+1][j] + A[i-1] * A[k] * A[j]){
	    
	    B[i][j] = B[i][j];

	  } else if(B[i][j] > B[i][k] + B[k+1][j] + A[i-1] * A[k] * A[j]){

	    B[i][j] = B[i][k] + B[k+1][j] + A[i-1] * A[k] * A[j];

	  }
	}
      }
    }
  }

  printf("%d\n",B[1][n]);

  return 0;

}