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 Ruby (judge verdict: Accepted)

m = []
N = gets.to_i
(N-1).times{|i|
  m[i] = gets.split[0].to_i
}
m.concat gets.split.map &:to_i
cost = Array.new(N){Array.new(N, 0x7fffffff)}
N.times{|i| cost[i][i] = 0}
(1...N).each{|d|
  (0...N-d).each{|first|
    last = first + d
    a = []
    (first...last).each{|s|
      a << cost[first][s] + cost[s+1][last] + m[first] * m[s+1] * m[last+1]
    }
    cost[first][last] = a.min
  }
}
puts cost[0][N-1]