You have an array $a$ of length $N$. In one operation, you can choose a number in the array and flip one of its bits, as long as the resultant number is non-negative and strictly less than $2^{30}$. What is the minimum number of operations required to turn the array into a non-decreasing sequence?

Constraints

For all subtasks:

$2\le N\le 100$

$0\le a_i<2^{30}$

Input Specification

The first line contains a single integer $N$.

The second line contains $N$ integers $a_i$.

Output Specification

Output the minimum number of operations required to turn the array into a non-decreasing sequence.

Sample Input

5
10 7 8 3 4

Sample Output

3

Explanation for Sample Output

A possible final array could be $[2,7,8,11,12]$, which takes $3$ moves to transition to.