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 n;
int w[1000];
int k[1000];
int u[1000];
int main() {
  scanf("%d", &n);
  for (int i = 0; i < (n); ++i) {
    scanf("%d", &w[i]);
  }
  vector<int> v(w, w + n);
  sort(v.begin(), v.end());
  for (int i = 0; i < (n); ++i) {
    k[i] = lower_bound(v.begin(), v.end(), w[i]) - v.begin();
  }
  int x = *min_element(w, w + n);
  int ans = 0;
  for (int i = 0; i < (n); ++i) {
    if (u[i]) {
      continue;
    }
    int c = 1;
    int s = w[i];
    int m = w[i];
    u[i] = true;
    int j = k[i];
    while (!u[j]) {
      ++c;
      s += w[j];
      m = min(m, w[j]);
      u[j] = true;
      j = k[j];
    }
    ans += min(s + m * (c - 2), s + x * (c - 2) + (m + x));
  }
  printf("%d\n", ans);
  return 0;
}
