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: Runtime Error)

def cost( i,k,j ):
  return m[i][k] + m[k+1][j] + p[i][0] * p[k][1] * p[j][1]
 
n = input()
M = []
m = [[ 0 for i in xrange(n) ] for j in xrange(n) ]
for i in xrange(n):
  M.append( map (int, raw_input().split() ) )
 
M_long = len(M)
for l in xrange( 2,M_long+1 ):
  for i in xrange( 0,M_long-l+1 ):
    j = i+l-1
    m[i][j] = min( cost( i,k,j ) for k in xrange( i,j ) )
 
print m[0][M_long-1]