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>
#pragma warning(disable : 4996)
using namespace std;
int n, a[1009], c[1009];
bool vis[1009];
int main() {
  scanf("%d", &n);
  for (int i = 0; i < n; i++) scanf("%d", &a[i]);
  for (int i = 0; i < n; i++) {
    for (int j = 0; j < n; j++) {
      if (a[i] > a[j]) c[i]++;
    }
  }
  int ret = 0;
  for (int i = 0; i < n; i++) {
    if (vis[i]) continue;
    int pos = i, m = 0;
    while (!vis[pos]) {
      vis[pos] = true;
      ret += a[pos] * 2;
      m = max(m, a[pos] + a[c[pos]]);
      pos = c[pos];
    }
    ret -= m;
  }
  printf("%d\n", ret);
  return 0;
}
