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 <iostream>
#include <algorithm>
#include <cstring>
using namespace std;

const int Max = 1005;
const int M = 10005;
int w[Max], s;
int b[Max];
int t[M];
int visit[Max];

int solve(int w[], int b[], int n)
{
    memset(visit, 0, sizeof(visit));
    for(int i=0; i<n; i++)
        t[b[i]] = i;
    int result = 0;
    for(int i=0; i<n; i++)
    {
        if(visit[i]) continue;
        int cur = i, sum = 0, num = 0, m = M;
        while(!visit[cur])
        {
            visit[cur] = 1;
            m = min(m, w[cur]);
            sum += w[cur];
            num++;
            cur = t[w[cur]];
        }
        if(num)
        {
            result += min(sum+(num-2)*m, sum+m+(num+1)*s);
        }
    }
    return result;
}
int main()
{
    int n;
    s = M;
    cin >> n;
    for(int i=0; i<n; i++)
    {
        cin >> w[i];
        b[i] = w[i];
        s = min(s, w[i]);
    }
    sort(b, b+n);
    cout << solve(w, b, n) << endl;
}

