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 Python3 (judge verdict: Accepted)

def multi_chain_multiplication(n, P):
    M = [[0]*(n+1) for _ in range(n+1)]

    if n > 1:
        for l in range(2, n+1):
            for i in range(1, n-l+2):
                j = i + l - 1
                M[i][j] = float('inf')
                for k in range(i, j):
                    M[i][j] = min(M[i][j], M[i][k] + M[k+1][j] + P[i-1] * P[k] * P[j])
        return M[i][j]
    else:
        return 0

def read_and_print_min_multiplication(n):
    P = [0] * (n+1)
    for i in range(n):
        A = [int(i) for i in input().split()]
        if i == 0:
            P[i] = A[0]
            P[i+1] = A[1]
        else:
            P[i+1] = A[1]
    print(multi_chain_multiplication(n, P))

n = int(input())
read_and_print_min_multiplication(n)