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 long long N = 1e5;
long long a[N], b[N], check[N];
signed main() {
  long long n;
  cin >> n;
  long long m = 114514, m2 = 1919810;
  for (long long i = 0; i < n; i++) {
    cin >> a[i];
    b[i] = a[i];
    m = min(m, a[i]);
  }
  sort(b, b + n);
  long long cost = 0, cost2 = 0, cnt = 0;
  for (long long i = 0; i < n; i++) {
    if (b[i] == a[i]) check[i] = 1;
    if (b[a[i] - 1] == a[i] && a[a[i] - 1] == b[i] && !check[i]) {
      check[i] = check[a[i] - 1] = 1;
      cost += b[i] + b[a[i] - 1];
    }
    if (!check[i]) {
      cost2 += b[i];
      cnt++;
      m2 = min(m2, b[i]);
    }
  }
  if (cnt == 0)
    cout << cost << endl;
  else
    cout << cost + min(cost2 + (cnt - 2) * m2, cost2 + m2 + (cnt + 1) * m)
         << endl;
  return 0;
}
