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 cou = 0;
int main(void) {
  int n, x, sum = 0;
  int w[1000] = {0}, _w[1000] = {0};
  scanf("%d", &n);
  for (int i = 0; i < n; ++i) {
    scanf("%d", &x);
    w[i] = x;
  }
  for (int i = 0; i < n; ++i) {
    for (int j = 0; j < n; ++j) {
      if (w[i] > w[j]) {
        ++_w[i];
      }
    }
    _w[i] = i - _w[i];
  }
  int min, max;
  for (int i = 0; i < n; ++i) {
    for (int j = 0; j < n; ++j) {
      if (_w[j] == 0) {
        ++cou;
      } else {
        if (cou == j) {
          min = max = j;
        }
        if (_w[min] > _w[j]) {
          min = j;
        }
        if (_w[max] < _w[j]) {
          max = j;
        }
      }
    }
    if (cou == n) break;
    cou = 0;
    sum += w[max] + w[min];
    x = w[min];
    w[min] = w[max];
    w[max] = x;
    _w[max] -= max - min;
    _w[min] += max - min;
  }
  printf("%d\n", sum);
}
