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>
typedef struct {
  int sum;
  int flag;
} CC;
CC C[10001];
int A[1000], B[1000];
int main() {
  int i, n, min = 0, m, k, now, sum = 0;
  scanf("%d", &n);
  for (i = 1; i < n + 1; i++) {
    scanf("%d", &A[i]);
  }
  for (i = 0; i < 10001; i++) {
    C[i].sum = 0;
    C[i].flag = 0;
  }
  for (i = 1; i < n + 1; i++) {
    C[A[i]].sum += 1;
    C[A[i]].flag += 1;
  }
  for (i = 0; i < 10001; i++) {
    C[i].sum += C[i - 1].sum;
  }
  for (i = 0; i < n; i++) {
    if (C[A[i]].flag == 1) {
      k = i;
      now = k;
      m = 0;
      B[C[A[k]].sum] = A[k];
      C[A[i]].flag = 0;
      min = A[k];
      k = C[A[k]].sum;
      while (A[now] != A[k]) {
        if (m == 0) sum += A[now];
        B[C[A[k]].sum] = A[k];
        C[A[k]].flag = 0;
        sum += A[k];
        if (min > A[k]) min = A[k];
        k = C[A[k]].sum;
        m += 1;
      }
    }
    if (m > 1) sum += min;
    m = 0;
    min = 0;
  }
  printf("%d\n", sum);
  return 0;
}
