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>
int A[1000];
int B[1000];
int N;
int ans;
void swap(int *x, int *y) {
  int tmp = *x;
  *x = *y;
  *y = tmp;
  return;
}
int partition(int *A, int p, int r) {
  int j;
  int x = A[r];
  int i = p - 1;
  for (j = p; j < r; j++) {
    if (A[j] <= x) {
      i++;
      swap(&A[i], &A[j]);
    }
  }
  swap(&A[i + 1], &A[r]);
  return i + 1;
}
void quickSort(int *A, int p, int r) {
  int q;
  if (p < r) {
    q = partition(A, p, r);
    quickSort(A, p, q - 1);
    quickSort(A, q + 1, r);
  }
}
void solve(int *A, int *B, int n) {
  int i;
  quickSort(B, 0, n - 1);
  for (i = 0; i < n; i++) {
    if (B[i] != A[i]) {
      ;
      ans += A[i];
    }
  }
}
int main(void) {
  int i;
  scanf("%d", &N);
  for (i = 0; i < N; i++) {
    scanf("%d", &A[i]);
    B[i] = A[i];
  }
  solve(A, B, N);
  printf("%d\n", ans);
  return 0;
}
