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 <bits/stdc++.h>
using namespace std;
long long ans;
void solve(int a[], int n) {
  int b[1000], t[1000], vmin, vmax = 1000;
  bool vis[1000];
  for (int i = 0; i < n; i++) {
    b[i] = a[i];
    vis[i] = false;
  }
  sort(b, b + n);
  vmin = b[0];
  for (int i = 0; i < n; i++) {
    t[b[i]] = i;
  }
  for (int i = 0; i < n; i++) {
    int cur = i, m = vmax, sum = 0, num = 0;
    while (1) {
      vis[cur] = true;
      num++;
      sum += a[cur];
      m = min(a[cur], m);
      cur = t[a[cur]];
      if (vis[cur]) break;
    }
    ans += min(sum + (num - 2) * m, sum + m + (num + 1) * vmin);
  }
}
int main() {
  int n, a[1000];
  cin >> n;
  for (int i = 0; i < n; i++) {
    scanf("%d", &a[i]);
  }
  solve(a, n);
  cout << ans << endl;
  return 0;
}
