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.