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;
signed main() {
  long long n;
  cin >> n;
  vector<long long> w(n);
  for (long long i = 0; i < n; i++) cin >> w[i];
  vector<long long> sorted_w = w;
  sort(sorted_w.begin(), sorted_w.end());
  long long ans = 0;
  for (long long i = 0; i < n; i++) {
    long long x = sorted_w[i];
    long long y = w[i];
    long long j;
    for (j = i + 1; j < n; j++) {
      if (w[j] == x) break;
    }
    if (j == n) continue;
    for (; j >= 1 && y < w[j - 1]; j--) {
      swap(w[j - 1], w[j]);
      ans += w[j - 1] + w[j];
    }
    for (; j < n - 1 && y > w[j + 1]; j++) {
      swap(w[j + 1], w[j]);
      ans += w[j + 1] + w[j];
    }
    if (w[j] < w[i]) {
      swap(w[i], w[j]);
      ans += w[i] + w[j];
    }
  }
  cout << ans << endl;
  return 0;
}
