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>
int p[10001];
int partition(int *a, int p, int r) {
  int x = a[r];
  int i = p - 1;
  int tmp1;
  for (int j = p; j < r; j++) {
    if (a[j] <= x) {
      i++;
      tmp1 = a[j];
      a[j] = a[i];
      a[i] = tmp1;
    }
  }
  a[r] = a[i + 1];
  a[i + 1] = x;
  return i + 1;
}
void quickSort(int *a, int p, int r) {
  if (p >= r) return;
  int q = partition(a, p, r);
  quickSort(a, p, q - 1);
  quickSort(a, q + 1, r);
}
int calc(int *w, int *a, int n) {
  int c = 0;
  int p0, p1, w0, w1;
  for (int i = 0; i < n; i++) {
    while (a[i] != w[i]) {
      w0 = a[i];
      p0 = p[w0];
      w1 = a[p0];
      p1 = p[w1];
      w[p0] = w1;
      w[p1] = w0;
      p[w0] = p1;
      p[w1] = p0;
      c += w0 + w1;
    }
  }
  return c;
}
int main() {
  int i, n;
  scanf("%d", &n);
  int w[n];
  int a[n];
  for (i = 0; i < n; i++) {
    scanf("%d", w + i);
    a[i] = w[i];
    p[w[i]] = i;
  }
  quickSort(a, 0, n - 1);
  printf("%d\n", calc(w, a, n));
  return 0;
}
