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D. Make Equal

time limit per test

4 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputYou 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.

Codeforces (c) Copyright 2010-2021 Mike Mirzayanov

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