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.

Constraints

* $1 \leq n \leq 1,000$
* $0 \leq w_i\leq 10^4$
* $w_i$ are all different

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.

Examples

Input

5
1 5 3 4 2


Output

7


Input

4
4 3 2 1


Output

10
#include<stdio.h>
#include<algorithm>

#define MAX 1000
#define WMAX 10000

int main() {
    int n;
    int A[MAX], B[MAX], V[MAX], T[WMAX+1];

    scanf("%d", &n);
    int min = WMAX;
    for (int i = 0; i < n; ++i) {
        scanf("%d", &A[i]);
        B[i] = A[i];
        V[i] = false;
        min = std::min(min, A[i]);
    }
    std::sort(B, B+n);
    for (int i = 0; i < n; ++i) T[B[i]] = i;

    int ans = 0;
    for (int i = 0; i < n; ++i) {
        if (V[i]) continue;

        int cur = i;
        int num = 0;
        int sum = 0;
        int m = WMAX;
        while (true) {
            V[cur] = true;
            num++;
            sum += A[cur];
            m = std::min(m, A[cur]);
            cur = T[A[cur]];
            if (V[cur]) break;
        }
        ans += std::min(sum + (num - 2) * m, sum + (num - 2) * m + (m + min) * 2 - (m - min) * (num - 1));
    }
    printf("%d\n", ans);

    return 0;
}