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;
const int INF = 0x3f3f3f3f;
const int MAXN = 200005;
int w[1005], B[1005], L[1005], flag[1005];
int main() {
  int n, ans = 0, Min = INF;
  cin >> n;
  for (int i = 0; i < n; i++) {
    cin >> w[i];
    B[i] = w[i];
    Min = min(Min, w[i]);
  }
  sort(B, B + n);
  for (int i = 0; i < n; i++) L[B[i]] = i;
  for (int i = 0; i < n; i++) {
    if (flag[i]) continue;
    int temp = i, S = INF, m = 0, cnt = 0;
    while (!flag[temp]) {
      cnt++;
      flag[temp] = 1;
      S = min(S, w[temp]);
      m += w[temp];
      temp = L[w[temp]];
    }
    ans += min(m + (cnt - 2) * S, m + (cnt + 1) * Min + S);
  }
  cout << ans << endl;
  return 0;
}
