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[1000], s;
int a[1000], d[1001];
long solve() {
  long ret = 0;
  bool v[1000];
  for (int i = 0; i < n; ++i) {
    a[i] = w[i];
    v[i] = false;
  }
  sort(a, a + n);
  for (int i = 0; i < n; ++i) d[a[i]] = i;
  for (int i = 0; i < n; ++i) {
    if (v[i]) continue;
    int cur = i;
    int sum = 0;
    int m = 10000;
    int an = 0;
    while (1) {
      v[cur] = true;
      an++;
      int z = w[cur];
      sum += z;
      m = min(m, z);
      cur = d[z];
      if (v[cur]) break;
    }
    ret += min(sum + (an - 2) * m, m + sum + (an + 1) * s);
  }
  return ret;
}
int main() {
  scanf(" %d", &n);
  s = 10000;
  for (int i = 0; i < n; ++i) {
    scanf(" %d", &w[i]);
    s = min(s, w[i]);
  }
  printf("%ld\n", solve());
}
