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;
constexpr int MAX_N = 1000;
constexpr int MAX_VAL = 10001;
int minCostSort(int* w, int* ref, int n, int minval) {
  bool isfixed[MAX_N] = {0};
  int cost = 0;
  for (int i = 0; i < n; i++) {
    if (isfixed[i]) {
      continue;
    }
    int fromindex = i;
    int n_chain = 0;
    int minelm_in_chain = MAX_VAL;
    int sum = 0;
    while (true) {
      sum += w[fromindex];
      isfixed[fromindex] = true;
      ++n_chain;
      if (minelm_in_chain > w[fromindex]) {
        minelm_in_chain = w[fromindex];
      }
      int destindex = distance(ref, lower_bound(ref, ref + n, w[fromindex]));
      if (destindex == i) {
        break;
      }
      fromindex = destindex;
    }
    if (n_chain < 2) {
      continue;
    }
    cost += min(sum + (n_chain - 2) * minelm_in_chain,
                sum + n_chain * minval + 2 * minelm_in_chain);
  }
  return cost;
}
int main() {
  cin.tie(0);
  ios::sync_with_stdio(false);
  int n;
  cin >> n;
  int w[MAX_N];
  int ref[MAX_N];
  int minval = MAX_VAL;
  for (int i = 0; i < n; i++) {
    cin >> w[i];
    ref[i] = w[i];
    if (minval > w[i]) {
      minval = w[i];
    }
  }
  sort(ref, ref + n);
  int cost = minCostSort(w, ref, n, minval);
  cout << cost << endl;
  return 0;
}
