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 Kotlin (judge verdict: Accepted)

fun main(args: Array<String>) {
    val n = readLine()?.toInt() ?: return
    val inputMatrix = List(n) {
        val input = readLine()?.split(" ".toRegex())?.map(String::toInt) ?: return
        return@List input[0] to input[1]
    }
    val matrixChain = inputMatrix.map { it.first }.plus(inputMatrix.last().second)
    val multiplicater = MatrixChainMultiplicater(matrixChain)
    println(multiplicater.getMatrixChainOrder())
}

class MatrixChainMultiplicater(private val matrixData: List<Int>) {
    private val memo = Array(matrixData.size - 1){IntArray(matrixData.size - 1)}
    init {
        for (i in memo.indices) {
            memo[i][i] = 0
        }
    }

    fun getMatrixChainOrder(): Int {
        for (i in 1..memo.lastIndex) {
            for (j in 0..memo.lastIndex - i) {
                val row = j
                val column = j + i
                val costs = arrayListOf<Int>()
                for (k in row until column) {
                    costs.add(memo[row][k] + memo[k + 1][column] + matrixData[row] * matrixData[k + 1] * matrixData[column + 1])
                }
                memo[row][column] = costs.min() ?: 0
            }
        }
        return memo.first().last()
    }
}