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.to_i

@ms = {}
@dp = {}

class Matrix
    attr_reader :row, :col

    def initialize(row, col)
        @row = row
        @col = col
    end
end

[*1..n].each do |i|
    r, c  = gets.split.map(&:to_i)
    @ms[i] = Matrix.new(r, c)
end


def set_value(x, y)
    if x == y
        @dp[[x, y]] = 0
     elsif y - x == 1
        @dp[[x, y]] = @ms[x].row * @ms[x].col * @ms[y].col
    else
        candidate = []
        [*1..(y - x)].each do |k|
            candidate << @ms[x].row * @ms[x + k].row * @ms[y].col + @dp[[x, x + (k - 1)]] + @dp[[x + k, y]]
        end
        @dp[[x, y]] = candidate.min
    end
end


1.upto(n) do |y|
    n.downto(1) do |x|
        unless x > y
            set_value(x, y)
        end
    end
end

p @dp[[1, n]]