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 N = 1e3 + 10;
bitset<N> went;
int bot, tot, a[N], t;
pair<int, int> b[N];
void dfs(int n) {
  if (went[n]) return;
  went[n] = true;
  t++;
  tot += b[a[n]].first;
  bot = min(bot, b[a[n]].first);
  dfs(a[n]);
  return;
}
int main() {
  int n, low = 1e5 + 10;
  ;
  long long int ans = 0;
  scanf("%d", &n);
  for (int i = 0; i < n; i++) {
    scanf("%d", &b[i].first);
    low = min(low, b[i].first);
    b[i].second = i;
  }
  sort(b, b + n);
  for (int i = 0; i < n; i++) a[b[i].second] = i;
  went.reset();
  for (int i = 0; i < n; i++)
    if (!went[i] && a[i] != i) {
      tot = 0;
      bot = 1e5 + 10;
      t = 0;
      dfs(i);
      ans += min(tot + t * low, tot + (t - 2) * bot);
    }
  printf("%lld\n", ans);
}
