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)

import sys

def mcm(sizes, memo, l, r):
    if l == r:
#        print('a:', l, r)
        return 0
    if memo[l][r] >= 0:
#        print('b:', l, r)
        return memo[l][r]
#    print('c:', l, r)
    m = sys.maxsize
    for k in range(l, r):
        m = min (m, mcm(sizes, memo, l, k) + mcm(sizes, memo, k+1, r) + sizes[l][0] * sizes[k][1] * sizes[r][1])
    memo[l][r] = m
    return memo[l][r]

if __name__ == '__main__':
    # Load input
    n = int(input())
    x = []
    for _ in range(n):
        y = tuple(map(int, input().split(' ')))
        x.append(y)
    
    # Create memo:
    memo = []
    for _ in range(n):
        memo.append([-1]*n)
#    print(x)
    print( mcm(sizes = x, memo=memo, l = 0, r = n-1) )