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 = 1010;
int a[maxn], id[maxn];
inline bool cmp(int x, int y) { return a[x] < a[y]; }
int main() {
  int n;
  long long ans = 0;
  scanf("%d", &n);
  for (int i = 1; i <= n; i++) {
    scanf("%d", a + i);
    id[i] = i;
  }
  sort(id + 1, id + 1 + n, cmp);
  id[n + 1] = n + 1;
  for (int i = n; i; i--) {
    if (id[i] != i) ans = ans + a[id[i]] + a[i];
    id[id[i]] = id[i];
    id[i] = i;
  }
  printf("%lld\n", ans);
  return 0;
}
