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;

typedef long long ll;

const int INF = 1e9;

int main()
{
  int n = 0;
  fscanf(stdin, "%d", &n);
  vector<int> w(n);
  int smallest = INF;
  for (int i = 0; i < n; ++i) {
    fscanf(stdin, "%d", &w[i]);
    smallest = min(smallest, w[i]);
  }
  vector<int> seen(n, 0);
  vector<int> v(w);
  sort(v.begin(), v.end());
  vector<int> pos(10005, -1);
  int ans = 0;
  for (int i = 0; i < n; ++i) { pos[v[i]] = i; }
  for (int i = 0; i < n; ++i) {
    if (seen[i]) { continue; }
    int next_pos = i;
    int cur = w[i];
    int least = w[i], sum = 0, len = 0;
    while (!seen[next_pos]) {
      // fprintf(stderr, "DEBUG: cur=%d\n", cur);
      seen[next_pos] = 1;
      ++len;
      sum += cur;
      least = min(least, cur);
      next_pos = pos[cur];
      cur = w[next_pos];
    }
    int cost = sum - least + (len - 1) * least;
    cost = min(cost, sum + least + (len + 1) * smallest);
    ans += cost;
  }
  fprintf(stdout, "%d\n", ans);
  return 0;
}