Problem:
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Minimum Cost Sort

You are given $n$ integers $w_i (i = 0, 1, ..., n-1)$ to be sorted in ascending order. You can swap two integers $w_i$ and $w_j$. Each swap operation has a cost, which is the sum of the two integers $w_i + w_j$. You can perform the operations any number of times.

Write a program which reports the minimal total cost to sort the given integers.

Input

In the first line, an integer $n$ is given. In the second line, $n$ integers $w_i (i = 0, 1, 2, ... n-1)$ separated by space characters are given.

Output

Print the minimal cost in a line.

Constraints

$1 \leq n \leq 1,000$

$0 \leq w_i\leq 10^4$

$w_i$ are all different

Sample Input 1

5
1 5 3 4 2

Sample Output 1

7

Sample Input 2

4
4 3 2 1

Sample Output 2

10

Solution in Kotlin (judge verdict: Accepted)

fun main(args: Array<String>) {
    readLine()
    val xs = readLine()!!.split(' ').map { it.toInt() }
    println(minimumCostSort(xs))
}

private const val MAX = 10000

private fun minimumCostSort(xs: List<Int>): Int {

    val sorted = xs.sorted()
    val table = IntArray(MAX + 1)
    val visited = BooleanArray(xs.size) { false }

    var min = MAX

    for (i in 0 until xs.size) {
        min = minOf(min, xs[i])
        table[sorted[i]] = i
    }

    var ans = 0

    for (i in 0 until xs.size) {
        if (visited[i]) continue

        var cur = i
        var s = 0
        var m = MAX
        var n = 0
        while (true) {
            visited[cur] = true
            n++
            val v = xs[cur]
            m = minOf(m, v)
            s += v
            cur = table[v]
            if (visited[cur]) break
        }

        ans += minOf(s + (n - 2) * m, s + m + (n + 1) * min)
    }

    return ans
}