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)

n = int(input())
r = [0] * (n+1) # M1=r0*r1, M2=r1*r2, ... , Mn=rn-1*rn
m = [[100**4] * (n+1) for _ in range(n+1)] # m[i][j] = Mi...Mj の最小コスト
for i in range(n):
    r[i], r[i+1] = list(map(int, input().split()))

for i in range(1, n+1): # 1個の行列のコスト
    m[i][i] = 0
for i in range(1, n): # 2個の行列のコスト
    m[i][i+1] = r[i-1] * r[i] * r[i+1]
for j in range(2, n): # j+1 個の行列のコスト
    for i in range(1, n-j+1): # Mi...Mi+j
        for k in range(j): # Mi...Mi+k と Mi+k+1...Mi+j に分割
            # print('i=',i,' i+k=',i+k,' i+j=', i+j)
            cost = m[i][i+k] + r[i-1]*r[i+k]*r[i+j] + m[i+k+1][i+j]
            if cost < m[i][i+j]:
                m[i][i+j] = cost
print(m[1][n])