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 <algorithm>
#include <iostream>
#include <map>
#include <vector>
using namespace std;

const int INF = 100000;

int main() {
  cin.tie(0);
  std::ios_base::sync_with_stdio(false);

  int n;
  cin >> n;
  vector<int> w;
  for (auto i = 0; i < n; ++i) {
    int t;
    cin >> t;
    w.push_back(t);
  }

  vector<int> v = w;
  sort(v.begin(), v.end());

  map<int, int> m;
  for (auto i = 0; i < n; ++i) {
    m[v[i]] = i;
  }

  vector<int> u;
  for (auto i = 0; i < n; ++i) {
    u.push_back(false);
  }

  int p = 0;
  int s = 0;
  while (p < n) {
    if (u[p]) {
      ++p;
      continue;
    }
    u[p] = true;
    int t = w[p];
    int r = INF;
    int c = 1;
    int q = m[w[p]];
    if (p == q) {
      continue;
    }
    while (p != q) {
      u[q] = true;
      t += w[q];
      if (w[q] < r) {
        r = w[q];
      }
      q = m[w[q]];
      ++c;
    }
    s += min(t + (c - 2) * r, t + r + (c + 1) * v[0]);
  }

  cout << s << endl;

  return 0;
}

