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;
int n, a[1005], s;
int b[1005], c[1005];
int main() {
  int ans = 0, pos = 0, mi = 10005, sum = 0;
  cin >> n;
  s = 10005;
  for (int i = 0; i < n; ++i) {
    cin >> a[i];
    b[i] = a[i];
    s = min(a[i], s);
  }
  sort(b, b + n);
  for (int i = 0; i < n; ++i) {
    if (a[i] != b[i]) {
      c[pos++] = a[i];
      mi = min(mi, a[i]);
    }
  }
  for (int i = 0; i < pos; ++i) {
    sum += c[i];
  }
  ans = min(sum + (pos - 2) * mi, sum + mi + (pos + 1) * s);
  cout << ans << endl;
  return 0;
}
