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[1000];
int dupA[1000];
int pos[10001];
int dupPos[10001];
int main() {
  int N;
  scanf("%d", &N);
  for (int i = 0; i < N; i++) {
    cin >> A[i];
    dupA[i] = A[i];
    pos[A[i]] = i;
    dupPos[A[i]] = pos[A[i]];
  }
  sort(A, A + N);
  int temp1 = -1, temp2 = -1;
  for (int i = 0; i < N; i++) {
    if (pos[A[i]] == i) {
      if (temp1 == -1) {
        temp1 = A[i];
      } else if (temp1 > A[i]) {
        temp1 = A[i];
      }
    }
  }
  for (int i = 0; i < N; i++) {
    if (pos[A[i]] != i) {
      if (temp2 == -1) {
        temp2 = A[i];
      } else if (temp2 > A[i]) {
        temp2 = pos[A[i]];
      }
    }
  }
  if (temp1 != -1 && temp2 != -1 && temp1 < temp2) {
    int temp = dupPos[temp1];
    dupPos[temp1] = dupPos[temp2];
    dupPos[temp2] = temp;
  }
  int cost1 = 0, cost2 = 0;
  {
    int i = 0;
    while (i < N) {
      if (pos[A[i]] != i) {
        cost1 += (A[i] + A[pos[A[i]]]);
        int temp = pos[A[i]];
        pos[A[i]] = pos[A[temp]];
        pos[A[temp]] = temp;
      } else {
        i++;
      }
    }
  }
  {
    int i = 0;
    while (i < N) {
      if (dupPos[A[i]] != i) {
        cost2 += (A[i] + A[dupPos[A[i]]]);
        int temp = dupPos[A[i]];
        dupPos[A[i]] = dupPos[A[temp]];
        dupPos[A[temp]] = temp;
      } else {
        i++;
      }
    }
  }
  cout << ((cost1) > (cost2) ? (cost2) : (cost1)) << endl;
  return 0;
}
