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 Python (judge verdict: Accepted)

def matrix(X):
    x = [[0 for i in range(len(X))] for j in range(len(X))]
    for l in range(2, len(X)+1):
        for i in range(0, len(X)-l+1):
            j = i + l - 1
            x[i][j] = min(x[i][k] + x[k+1][j] + X[i][0]*X[k][1]*X[j][1] for k in range(i, j))

    print x[0][len(X)-1]

n = input()
X = []

for i in range(n):
    X.append(map(int, raw_input().split()))

matrix(X)