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 MAXN = 1000 + 2;
int ans, n;
int w[MAXN], a[MAXN];
int check() {
  for (int i = 0; i < n; ++i)
    if (w[i] != a[i]) return 0;
  return 1;
}
int main() {
  cin >> n;
  for (int i = 0; i < n; ++i) {
    cin >> w[i];
    a[i] = w[i];
  }
  sort(a, a + n);
  while (1) {
    if (check()) break;
    int now = 10001, m1, m2;
    for (int i = 0; i < n; ++i) {
      int j = 0;
      for (; j < n; ++j)
        if (a[j] == w[i]) break;
      if (i != j && w[i] + w[j] < now) now = w[i] + w[j], m1 = i, m2 = j;
    }
    ans += now;
    swap(w[m1], w[m2]);
  }
  cout << ans << endl;
  return 0;
}
