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 N, W[1005], C[1005], c = 0, t, p;
long long res = 0;
map<int, int> H;
map<int, int> rH;
vector<int> S;
int main() {
  scanf("%d", &N);
  for (int i = 0; i < N; i++) scanf("%d", C + i);
  memcpy(W, C, sizeof(C));
  sort(C, C + N);
  for (int i = 0; i < N; i++) {
    H[C[i]] = i;
    rH[i] = C[i];
  }
  for (int i = 0; i < N; i++) S.push_back(W[i]);
  for (int i = 0; i < N; i++) {
    int nn = rH[i];
    int np = find(S.begin(), S.end(), nn) - S.begin();
    for (; np != H[nn];) {
      int dn = rH[np];
      int dp = find(S.begin(), S.end(), dn) - S.begin();
      swap(S[np], S[dp]);
      res += nn + dn;
      np = dp;
    }
  }
  printf("%lld\n", res);
  return 0;
}
