#include <bits/stdc++.h>
using namespace std;
namespace cyl {
const long long inf = 1e18;
int n;
long long a[100005], dp[63][100005];
template <class T>
bool chkmin(T &x, T y) {
  return x > y ? x = y, 1 : 0;
}
int main() {
  scanf("%d", &n);
  for (int i = 1; i <= n; ++i) scanf("%lld", &a[i]);
  sort(a + 1, a + n + 1);
  for (int i = 1; i <= n; ++i) a[i] = a[n] - a[i];
  for (int i = 0; i <= 62; ++i)
    for (int j = 0; j <= n; ++j) dp[i][j] = inf;
  dp[0][0] = 0;
  for (int i = 0; i < 62; ++i) {
    sort(a + 1, a + n + 1, [&](long long x, long long y) {
      return (x & (1ll << i) - 1) > (y & (1ll << i) - 1);
    });
    int cnt = 0, tot = 0;
    for (int j = 1; j <= n; ++j) tot += a[j] >> i & 1;
    for (int j = 0; j <= n; ++j) {
      cnt += a[j] >> i & 1;
      chkmin(dp[i + 1][cnt], dp[i][j] + j - cnt + tot - cnt);
      chkmin(dp[i + 1][tot - cnt + j], dp[i][j] + n - j - (tot - cnt) + cnt);
    }
  }
  cout << dp[62][0] << endl;
  return 0;
}
}  // namespace cyl
int main() { return cyl::main(); }

### Prompt

Please formulate a CPP solution to the following problem:

You are given n numbers a_1, a_2, ..., a_n. In one operation we can add to any one of those numbers a nonnegative integer power of 2.

What is the smallest number of operations we need to perform to make all n numbers equal? It can be proved that under given constraints it doesn't exceed 10^{18}.

Input

The first line contains a single integer n (1 ≤ n ≤ 10^5).

The second line contains n integers a_1, a_2, …, a_n (0 ≤ a_i ≤ 10^{17}).

Output

Output exactly one integer — the smallest number of operations we need to perform to make all n numbers equal.

Examples

Input


4
228 228 228 228


Output


0

Input


3
2 2 8


Output


3

Note

In the first example, all numbers are already equal. So the needed number of operation is 0.

In the second example, we can apply the operation 3 times: add 8 to first 2, add 8 to second 2, add 2 to 8, making all numbers equal to 10. It can be proved that we can't make all numbers equal in less than 3 operations.

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
namespace cyl {
const long long inf = 1e18;
int n;
long long a[100005], dp[63][100005];
template <class T>
bool chkmin(T &x, T y) {
  return x > y ? x = y, 1 : 0;
}
int main() {
  scanf("%d", &n);
  for (int i = 1; i <= n; ++i) scanf("%lld", &a[i]);
  sort(a + 1, a + n + 1);
  for (int i = 1; i <= n; ++i) a[i] = a[n] - a[i];
  for (int i = 0; i <= 62; ++i)
    for (int j = 0; j <= n; ++j) dp[i][j] = inf;
  dp[0][0] = 0;
  for (int i = 0; i < 62; ++i) {
    sort(a + 1, a + n + 1, [&](long long x, long long y) {
      return (x & (1ll << i) - 1) > (y & (1ll << i) - 1);
    });
    int cnt = 0, tot = 0;
    for (int j = 1; j <= n; ++j) tot += a[j] >> i & 1;
    for (int j = 0; j <= n; ++j) {
      cnt += a[j] >> i & 1;
      chkmin(dp[i + 1][cnt], dp[i][j] + j - cnt + tot - cnt);
      chkmin(dp[i + 1][tot - cnt + j], dp[i][j] + n - j - (tot - cnt) + cnt);
    }
  }
  cout << dp[62][0] << endl;
  return 0;
}
}  // namespace cyl
int main() { return cyl::main(); }

```