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)

n = gets.chomp.to_i

# rows, cols = [], []
# n.times { |i| rows[i], cols[i] = gets.chomp.split.map(&:to_i) }

pAry = Array.new(n + 1)
mAry = Array.new(n + 1) { Array.new(n + 1) }

1.upto(n) do |i|
    pAry[i - 1], pAry[i] = gets.chomp.split.map(&:to_i)
end

1.upto(n) do |i|
    mAry[i][i] = 0
end

2.upto(n) do |l|
    1.upto(n - l + 1) do |i|
        j = i + l - 1
        mAry[i][j] = Float::INFINITY
        i.upto(j - 1) do |k|
            mAry[i][j] = [mAry[i][j], mAry[i][k] + mAry[k + 1][j] + pAry[i - 1] * pAry[k] * pAry[j]].min
        end
    end
end

puts mAry[1][n]