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
h = Array.new(n + 1)
m = Array.new(n + 1){Array.new(n + 1){0}}
1.upto n do |i|
	h[i - 1], h[i] = gets.split.map(&:to_i)
end

2.upto n do |l|
	1.upto n - l + 1 do |i|
		j = i + l - 1
		m[i][j] = Float::INFINITY
		i.upto j - 1 do |k|
			m[i][j] = [m[i][j], m[i][k] + m[j][k] + m[k + 1][j] + h[i - 1] * h[k] * h[j]].min
		end
	end
end

puts m[1][n]