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[1000], b[1000], V[1000], T[10000 + 1], ans = 0, mi = 10000;
void solve() {
  int i;
  for (i = 0; i < n; i++) {
    b[i] = a[i];
  }
  sort(b, b + n);
  for (i = 0; i < n; i++) {
    T[b[i]] = i;
  }
  for (i = 0; i < n; i++) {
    if (V[i]) continue;
    int S = 0;
    int an = 0;
    int cur = i;
    int m = 1000;
    while (1) {
      V[cur] = 1;
      an++;
      m = min(m, a[cur]);
      S += a[cur];
      cur = T[a[cur]];
      if (V[cur]) break;
    }
    ans += min(S + (an - 2) * m, S + m + (an + 1) * mi);
  }
}
int main() {
  memset(V, 0, sizeof(V));
  cin >> n;
  int i;
  for (i = 0; i < n; i++) {
    cin >> a[i];
    mi = min(mi, a[i]);
  }
  solve();
  cout << ans << endl;
  return 0;
}
