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 n;
int w[10001];
int f[10001];
int edge[10001];
bool used[10001];
vector<int> vs;
void dfs(int v) {
  used[v] = true;
  vs.push_back(w[v]);
  if (!used[edge[v]]) dfs(edge[v]);
}
int main(void) {
  scanf("%d", &n);
  for (int i = 0; i < n; i++) {
    scanf("%d", &w[i]);
    f[i] = w[i];
  }
  sort(f, f + n);
  long long res = 0;
  for (int i = 0; i < n; i++) {
    if (f[i] == w[i])
      edge[i] = i;
    else
      edge[i] = lower_bound(f, f + n, w[i]) - f;
  }
  for (int i = 0; i < n; i++) {
    if (edge[i] != i) {
      vs.clear();
      dfs(i);
      int all = vs[0];
      int minx = vs[0];
      for (int j = 1; j < vs.size(); j++) {
        minx = min(minx, vs[j]);
        all += vs[j];
      }
      res += min(all + (vs.size() - 2) * minx, all + (vs.size()) * f[0] + minx);
    }
  }
  printf("%d\n", res);
  return 0;
}
