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: Wrong Answer)

#!/usr/bin/env python
from __future__ import division, print_function
from sys import stdin


def main():
    num_mat = int(stdin.readline())
    data = [int(s) for s in stdin.readline().split()]
    for _ in range(num_mat-1):
        _, row = (int(s) for s in stdin.readline().split())
        data.append(row)
    num_dat = len(data)

    bin_op = tuple(data[i]*data[i+1]*data[i+2] for i in range(num_dat-2))
    parts = [(data[0]*data[1], data[-2]*data[-1]), bin_op]

    for j in range(3, num_mat):
        part = parts[-1]
        new_part = []
        for i in range(num_dat-j):
            a = data[i]
            b = data[i+1]
            c = data[i+j-1]
            d = data[i+j]
            new_part.append(min(part[i] + a*c*d, part[i+1] + a*b*d))
        parts.append(new_part)

    L = data
    if num_mat < 2:
        print(0)
    elif num_mat < 3:
        print(data[0]*data[1]*data[2])
    else:
        print(min(parts[i][0] + parts[-(i+1)][-1] +
                  L[0]*L[i+1]*L[-1] for i in range(len(parts))))


main()