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, W[1005], C[1005], c = 0, t, p;
map<int, int> H;
map<int, int> rH;
int main() {
  scanf("%d", &N);
  for (int i = 0; i < N; i++) scanf("%d", C + i);
  memcpy(W, C, sizeof(C));
  sort(C, C + N);
  for (int i = 0; i < N; i++) {
    H[C[i]] = i;
    rH[i] = C[i];
  }
  for (int i = 0; i < N; i++) W[i] = H[W[i]];
  for (;;) {
    int mc = 10000000, cp = -1;
    for (int i = 0; i < N; i++) {
      if (W[i] != i && rH[W[i]] + rH[W[W[i]]] < mc) {
        cp = i;
        mc = rH[W[i]] + rH[W[W[i]]];
      }
    }
    if (cp == -1) break;
    c += rH[W[cp]] + rH[W[W[cp]]];
    t = W[cp];
    p = W[cp];
    W[cp] = W[p];
    W[p] = t;
  }
  printf("%d\n", c);
  return 0;
}
