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 = 1e9 - 1;
vector<int> a, b;
vector<char> c;
int main() {
  int N;
  cin >> N;
  int aa;
  for (int(i) = (0); (i) < (N); (i)++) {
    cin >> aa;
    a.push_back(aa);
  }
  b = a;
  sort(b.begin(), b.end());
  for (int(i) = (0); (i) < (N); (i)++) {
    c.push_back(a[i] == b[i] ? 'o' : 'x');
  }
  unsigned long long cost = 0;
  int i, x, y, key;
  for (i = 0; i < N; i++) {
    if (a[i] == b[i]) continue;
    key = b[i];
    x = find(a.begin(), a.end(), key) - a.begin();
    do {
      key = b[x];
      y = find(a.begin(), a.end(), key) - a.begin();
      int tmp = a[x];
      a[x] = a[y];
      a[y] = tmp;
      cost += a[x] + a[y];
      x = y;
    } while (a[x] != b[x]);
  }
  cout << cost << endl;
  return 0;
}
