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 Scala (judge verdict: Accepted)

import scala.io.StdIn

object Main extends App {

  private val n = StdIn.readLine().toInt
  val memo = Array.fill(n+1, n+1)(0)
  val p = Array.fill(n+1)(0)
  
  (0 until n).foreach{ i =>
    val Array(r, c) = StdIn.readLine().split(' ').map(_.toInt)
    p(i) = r 
    p(i+1) = c
  }
  //println(p.toList)
  
  def matrixChainMultiplication() = {
    (2 to n).foreach{ l =>
      (1 to (n - l + 1)).foreach{ i =>
        val j = i + l - 1
        memo(i)(j) = Int.MaxValue
        (i until j).foreach{ k =>
          memo(i)(j) = scala.math.min(memo(i)(j), memo(i)(k) + memo(k+1)(j) + p(i-1) * p(k) * p(j))
        }
      }
    }
  }
  
  matrixChainMultiplication()

  println(memo(1)(n))
  
}