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 num[1005], n, a[1005];
int main() {
  scanf("%d", &n);
  for (int i = 1; i <= n; i++) {
    scanf("%d", &num[i]);
    a[i] = num[i];
  }
  sort(a + 1, a + n + 1);
  int res = 0;
  while (1) {
    bool ok = false;
    for (int i = n; i >= 1; i--) {
      if (num[i] == a[i]) continue;
      ok = true;
      int id;
      for (int j = 1; j <= n; j++)
        if (num[j] == a[i]) id = j;
      swap(num[id], num[i]);
      res += (num[id] + num[i]);
    }
    if (!ok) break;
  }
  printf("%d\n", res);
}
