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 A[200005], B[200005];
int n;
int mina = 1 << 24;
int main() {
  scanf("%d", &n);
  for (int i = 1; i <= n; i++) {
    scanf("%d", &A[i]);
    mina = min(mina, A[i]);
    B[i] = -100000;
  }
  long ans = 0;
  for (int i = 1; i <= n; i++) {
    int ming = 1 << 24;
    int sum = 0;
    int n = 0;
    int j = i;
    if (B[i] == 0) continue;
    while (B[j] != 0) {
      B[j] = 0;
      ming = min(ming, A[j]);
      sum += A[j];
      n++;
      j = A[j];
    }
    ans += min(ming * (n - 2) + sum, mina * (n + 1) + ming + sum);
  }
  printf("%ld\n", ans);
  return 0;
}
