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 <iostream>
#include <algorithm>
using namespace std;

const int VMAX = 10000 + 1;
const int MAX = 1000;
int s;
int W[MAX];
int B[MAX], T[VMAX];

int solve(int n) {
  int ans {0};
  bool V[MAX];

  for (int i = 0; i < n; i++) {
    B[i] = W[i];
    V[i] = false;
  }

  sort(B, B+n);
  for (int i = 0; i < n; i++) T[B[i]] = i;

  for (int i = 0; i < n; i++) {
    int currrent_index = i;
    int S = 0;
    int m = VMAX;
    int an = 0;
    if ( V[i] ) continue;
    while (true) {
      V[currrent_index] = true;
      an++;
      int v = W[currrent_index];
      m = min(m, v);
      S += v;
      currrent_index = T[v];
      if (V[currrent_index]) break;
    }
    ans += min(S + (an - 2) * m, m + S + (an + 1) * s);
  }
  return ans;
}

int main() {
  int n {0};
  cin >> n;
  s = VMAX;
  for (int i = 0; i < n; i++) {
    cin >> W[i];
    s = min(s, W[i]);
  }
  int ans = solve(n);
  cout << ans << endl;
  return 0;
}

