#include <bits/stdc++.h>
using namespace std;
const int N = 100005;
int n, id[N], f[N][62], s[N][2];
long long a[N];
inline void ckMin(register int& p, const int q) { p = (p < q ? p : q); }
int main() {
  scanf("%d", &n);
  register int i, j, k, x;
  for (i = 1; i <= n; ++i) scanf("%lld", &a[i]);
  std::sort(a + 1, a + 1 + n);
  for (i = 1; i <= n; ++i) a[i] = a[n] - a[i], id[i] = i;
  memset(f, 127, sizeof(f)), f[0][0] = 0;
  for (k = 0; k <= 60; ++k) {
    std::sort(id + 1, id + 1 + n, [&](const int p, const int q) {
      return (a[p] & ((1ll << k) - 1)) < (a[q] & ((1ll << k) - 1));
    });
    for (i = 1; i <= n; ++i)
      s[i][0] = s[i - 1][0], s[i][1] = s[i - 1][1], ++s[i][(a[id[i]] >> k) & 1];
    for (i = 0; i <= n; ++i)
      j = s[n][1] - s[n - i][1],
      ckMin(f[j][k + 1], f[i][k] + s[n - i][1] + s[n][0] - s[n - i][0]),
      j = n - s[n - i][0],
      ckMin(f[j][k + 1], f[i][k] + s[n - i][0] + s[n][1] - s[n - i][1]);
  }
  printf("%d", f[0][61]);
  return 0;
}

### Prompt

Generate 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;
const int N = 100005;
int n, id[N], f[N][62], s[N][2];
long long a[N];
inline void ckMin(register int& p, const int q) { p = (p < q ? p : q); }
int main() {
  scanf("%d", &n);
  register int i, j, k, x;
  for (i = 1; i <= n; ++i) scanf("%lld", &a[i]);
  std::sort(a + 1, a + 1 + n);
  for (i = 1; i <= n; ++i) a[i] = a[n] - a[i], id[i] = i;
  memset(f, 127, sizeof(f)), f[0][0] = 0;
  for (k = 0; k <= 60; ++k) {
    std::sort(id + 1, id + 1 + n, [&](const int p, const int q) {
      return (a[p] & ((1ll << k) - 1)) < (a[q] & ((1ll << k) - 1));
    });
    for (i = 1; i <= n; ++i)
      s[i][0] = s[i - 1][0], s[i][1] = s[i - 1][1], ++s[i][(a[id[i]] >> k) & 1];
    for (i = 0; i <= n; ++i)
      j = s[n][1] - s[n - i][1],
      ckMin(f[j][k + 1], f[i][k] + s[n - i][1] + s[n][0] - s[n - i][0]),
      j = n - s[n - i][0],
      ckMin(f[j][k + 1], f[i][k] + s[n - i][0] + s[n][1] - s[n - i][1]);
  }
  printf("%d", f[0][61]);
  return 0;
}

```