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>
const int dx[] = {1, 0, -1, 0};
const int dy[] = {0, 1, 0, -1};
using namespace std;
const int MAXN = 1010;
pair<int, int> P[MAXN];
int main() {
  cin.tie(0);
  ios::sync_with_stdio(false);
  int n;
  cin >> n;
  for (int i = 0; i < n; i++) {
    cin >> P[i].first;
    P[i].second = i;
  }
  sort(P, P + n);
  int ans = 0;
  for (int i = n - 1; i >= 0; i--) {
    if (P[i].second == i) continue;
    int j;
    for (j = 0; j < n; j++) {
      if (P[j].second == i) break;
    }
    ans += P[i].first + P[j].first;
    swap(P[j].second, P[i].second);
  }
  cout << ans << endl;
  return 0;
}
