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 JavaScript (judge verdict: Accepted)

function solve(arr, len) {
    let ans = 0;
    const V = [];
    const sorted = [];
    const mapTable = [];
    const min = Math.min(...arr);

    for (let i = 0; i < len; i++) {
        sorted[i] = arr[i];
        V[i] = false;
    }

    sorted.sort((a, b) => a - b);

    for (let i = 0; i < len; i++) {
        mapTable[sorted[i]] = i;
    }
    for (let i = 0; i < len; i++) {
        if (V[i]) continue;
        let cur = i;
        let s = 0;
        let m = 10000;
        let an = 0;
        while (1) {
            V[cur] = true;
            an++;
            let v = arr[cur];
            m = Math.min(m, v);
            s += v;
            cur = mapTable[v];
            if (V[cur]) break;
        }
        ans += Math.min(s + (an - 2) * m, m + s + (an + 1) * min);
    }

    return ans;
}


function main(_stdin) {
    const stdin = _stdin.split('\n');
    const len = parseInt(stdin.shift(), 10);
    const seq = stdin.shift().split(' ').map(e => parseInt(e, 10));

    const ans = solve(seq, len);
    console.log(ans);
}


main(require('fs').readFileSync('/dev/stdin', 'utf8'));