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 ll = long long;
using namespace std;
int n, A[1010], cost = 0;
pair<int, int> P[1010], Q[1010];
int main() {
  cin >> n;
  for (int i = 0; i < n; ++i) scanf("%d", &A[i]);
  for (int i = 0; i < n; ++i) {
    P[i].first = A[i];
    P[i].second = i;
  }
  sort(P, P + n);
  for (int i = 0; i < n; ++i) {
    Q[i].first = A[i];
    Q[P[i].second].second = i;
  }
  int s = P[1].first;
  for (int i = 0; i < n; ++i) {
    int j = Q[i].second;
    if (j >= 0 && j != 1) {
      int m = 1, amin, sum;
      amin = sum = Q[i].first;
      while (j != i) {
        int next = Q[j].second;
        if (next < amin) amin = Q[j].first;
        sum += Q[j].first;
        m++;
        Q[j].second = -1;
        j = next;
      }
      cost += min(sum + (m - 2) * amin, sum + amin + (n + 1) * s);
    }
  }
  cout << cost << "\n";
}
