D. Make Equal
time limit per test
4 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

You are given $n$ numbers $a_1, a_2, \dots, a_n$. 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 $n$ ($1 \le n \le 10^5$).

The second line contains $n$ integers $a_1, a_2, \ldots, a_n$ ($0 \le a_i \le 10^{17}$).

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.