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 minimumCostSort(int *W, int n) {
  int X[1000], R[1000];
  for (int i = 0; i < n; i++) {
    X[i] = W[i];
  }
  sort(X, X + n);
  for (int i = 0; i < n; i++) R[X[i]] = i;
  int m = X[0];
  int sum = 0;
  for (int i = 0; i < n; i++) {
    int cur = i;
    if (X[cur] == -1) break;
    int s = 0;
    int mm = 10000;
    int nn = 0;
    int v;
    while (true) {
      nn++;
      X[cur] = -1;
      v = W[cur];
      mm = min(v, mm);
      s += v;
      cur = R[v];
      if (X[cur] == -1) break;
    }
    sum += min(s + (nn - 2) * mm, s + mm + (nn + 1) * m);
  }
  return sum;
}
int main() {
  cin.tie(0);
  ios::sync_with_stdio(false);
  int n;
  int W[1000];
  cin >> n;
  for (int i = 0; i < n; i++) {
    cin >> W[i];
  }
  int c = minimumCostSort(W, n);
  cout << c << endl;
  return 0;
}
