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 = 1000 + 2;
int n, ans;
int a[MAXN];
struct fbg {
  int val, sit;
} w[MAXN];
int check() {
  for (int i = 1; i < n; ++i)
    if (w[i].val < w[i - 1].val) return 0;
  return 1;
}
int main() {
  w[1000].val = 0x7f7f7f;
  cin >> n;
  for (int i = 0; i < n; i++) {
    cin >> w[i].val;
    a[i] = w[i].val;
  }
  sort(a, a + n);
  while (1) {
    if (check()) break;
    int now = 1000;
    for (int i = 0; i < n; ++i) {
      for (int j = 0; j < n; ++j) {
        if (a[j] == w[i].val) {
          w[i].sit = j;
          if (i != j && w[i].val < w[now].val) now = i;
        }
      }
    }
    int x = now;
    while (1) {
      x = w[x].sit;
      if (w[x].sit == x || w[x].sit == now) break;
    }
    swap(w[x].val, w[now].val);
    ans += w[x].val + w[now].val;
  }
  cout << ans << endl;
  return 0;
}
