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 main(void) {
  std::ios_base::sync_with_stdio(false);
  int n, input;
  std::cin >> n;
  std::map<int, int> w;
  std::vector<int> vector(n + 1, 0);
  for (int i = 1; i <= n; ++i) {
    std::cin >> input;
    vector[i] = input;
  }
  std::vector<int> vector_min = vector;
  std::sort(vector_min.begin(), vector_min.end());
  for (int i = 1; i <= n; ++i) {
    w[vector[i]] = vector_min[i];
  }
  std::map<int, int> w_1(w);
  int cnt = 0;
  for (int i = 1; i <= n; ++i) {
    int temp = 0;
    while (vector_min[i] != w[vector_min[i]]) {
      temp += vector_min[i] + w[vector_min[i]];
      std::swap(w[vector_min[i]], w[w[vector_min[i]]]);
    }
    int temp_1 = static_cast<int>(1e5);
    if (i > 1 && vector_min[i] != w_1[vector_min[i]]) {
      temp_1 = vector_min[i] + vector_min[1];
      std::swap(w_1[vector_min[i]], w_1[vector_min[1]]);
      while (vector_min[1] != w_1[vector_min[1]]) {
        temp_1 += vector_min[1] + w_1[vector_min[1]];
        std::swap(w_1[vector_min[1]], w_1[w_1[vector_min[1]]]);
      }
    }
    cnt += std::min(temp, temp_1);
  }
  std::cout << cnt << std::endl;
  return 0;
}
