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 do_cycle(vector<int> &v, int x) {
  int s = 0, m = 1 << 30;
  for (auto &e : v) s += e, m = min(m, e);
  return min(s + (v.size() - 2) * m, s + m + (v.size() + 1) * x);
}
int main() {
  int N, x = 1 << 30, r;
  scanf("%d", &N);
  vector<int> v(N + 1), b(N + 1);
  vector<vector<int> > cycles;
  for (int i = 1; i <= N; i++) scanf("%d", &v[i]), x = min(x, v[i]);
  for (int i = 1; i <= N; i++)
    if (!b[i]) {
      vector<int> cycle;
      int k = i;
      do {
        cycle.push_back(k);
        b[k] = 1;
        k = v[k];
      } while (k != cycle[0]);
      r += do_cycle(cycle, x);
    }
  printf("%d\n", r);
}
