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;
using ll = long long;
#define INF (2e9)

int main() {
  int n; cin >> n;
  int A[1000];
  int s = 10000;

  for(int i = 0; i < n; ++i){
    cin >> A[i];
    s = min(s, A[i]);
  }

  int B[1000];
  bool V[1000];
  for(int i = 0; i < n; ++i){
    B[i] = A[i];
    V[i] = false;
  }

  sort(B, B+n);

  int T[10001];
  for(int i = 0; i < n; ++i){
    T[B[i]] = i;
  }

  int ans = 0;
  for(int i = 0; i < n; ++i){
    if(V[i]) continue;
    int an = 0;
    int m = 10000;
    int S = 0;
    int cur = i;

    while(1){
      V[cur] = true;
      an++;
      int v = A[cur];
      m = min(m, v);
      S += v;
      cur = T[v];
      if(V[cur]) break;
    }
    ans += min(S+(an-2)*m, m+S+(an+1)*s);
  }

  cout << ans << endl;

  return 0;
}
