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>
typedef struct {
  int num;
  int index;
} W;
int main() {
  int n, i, j, jMin, min, cost = 0, iTmp, tmp, max;
  W w[1000], c;
  scanf("%d", &n);
  for (i = 0; i < n; i++) {
    scanf("%d", &w[i].num);
    if (i == 0)
      max = w[i].num;
    else if (max < w[i].num)
      max = w[i].num;
  }
  for (j = n - 1; max >= 0; max--) {
    for (i = 0; i < n; i++) {
      if (max == w[i].num) {
        w[i].index = j;
        j--;
      }
    }
  }
  for (i = 0; i < n - 1; i++) {
    min = w[i].index;
    jMin = i;
    for (j = i; j < n; j++) {
      if (min > w[j].index) {
        min = w[j].index;
        jMin = j;
      }
    }
    if (i != jMin) {
      for (j = 0; j < n; j++)
        if (jMin == w[j].index) iTmp = j;
      c = w[iTmp];
      w[iTmp] = w[jMin];
      w[jMin] = c;
      cost += w[iTmp].num + w[jMin].num;
    }
  }
  printf("%d\n", cost);
  return 0;
}
