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 main() {
  long long int n;
  cin >> n;
  vector<long long int> v, vs;
  for (long long int i = 0; i < n; i++) {
    long long int in;
    cin >> in;
    v.push_back(in);
    vs.push_back(in);
  }
  sort(vs.begin(), vs.end());
  vector<long long int> t;
  for (long long int i = 0; i < n; i++) {
    for (long long int j = 0; j < n; j++) {
      if (vs[i] == v[j]) {
        t.push_back(j);
        break;
      }
    }
  }
  long long int ans = 0;
  long long int c = -1;
  long long int m = 0;
  for (long long int i = 0; i < n; i++) {
    for (long long int j = 0; j < n; j++) {
      if (vs[j] != v[j]) {
        long long int k = v[j];
        if (c == -1 || m > k) {
          c = j;
          m = k;
        }
      }
    }
    if (c == -1) break;
    ans += v[c] + v[t[c]];
    swap(v[c], v[t[c]]);
    for (long long int j = 0; j < n; j++) {
      if (t[j] == c) {
        t[j] = t[c];
      }
    }
    c = -1;
  }
  cout << ans << endl;
}
