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 MAX_N = 1000;
const int MAX_W = 10001;
int a[MAX_N];
int b[MAX_N];
int c[MAX_W];
int main() {
  int n, res = 0;
  cin >> n;
  for (int i = 0; i < n; i++) {
    scanf("%d", &a[i]);
    b[i] = a[i];
    c[b[i]] = i;
  }
  sort(a, a + n);
  for (int i = n - 1; i >= 0; i--) {
    if (a[i] != b[i]) {
      res += a[i] + b[i];
      b[c[a[i]]] = b[i];
    }
  }
  cout << res << "\n";
}
