# Swaps

As a programmer you are familiar that for every integer there is a binary representation of the number. For example, 4 is 100 in binary, 5 is 101, 15 is 1111... Every number can be represented with leading zeros, so 5 can be represented also as 0101, 000000101, ...

In this task, you are given a non-sorted list of N integers, each between 1 and 4095, inclusive. You should make changes in the list, so the result will be a new list of integers that are sorted in non-decreasing order.

The only operation permitted for making changes is swapping two bits in the binary representation of a specific number.

Output the minimum number of swaps necessary to reach the goal – a new sorted list. It will always be possible to reach the goal.

Note: all the numbers are considered to have exactly 12 bits for swap purposes. So, 1 would be represented as 000000000001 and with one swap we could get 512 = 001000000000, or even 2048 = 100000000000; but not 3 = 000000000011 (because you're only allowed to swap two bits in the specific number), or 4096 (because 4096 can't be represented with 12 bits).

### Input

The input is in the following format: line 1 contains N, the size of the list (1 <= N <= 2000). In the next N lines, you have the numbers Ai, the i-th number in the list for 0 <= i < N.

### Output

The output consists of a single integer - the count of minimum swaps.

### Constraints

Time limit: 1 second
Memory limit: 64 megabytes

### Examples

 ```input 5 2 9 8 12 11``` ```output 2``` ```input 3 3 2 7``` ```output 1```

Explanation for the first test case: We can swap the 2nd and 4th bit of the binary representation of 9 (000000001001) to get 3 (000000000011). Similarly with one swap in the number 11 (000000001011) we can get 14 (000000001110). In total, we need 2 swaps to get the sorted list: 2,3,8,12,14. In this example 2 is the minimal number of swaps that have to be done to reach the goal.

Explanation for the second test case: 2 = 000000000010, and we can swap the 2-nd with the 3-rd bit to get 4=000000000100.

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Note: You are now solving the task on the MENDO grading system. During the actual JBOI 2016 contest, for this task, there were a number of subtasks earning different amount of points. They were as follows:

- For 13 points, N <= 10, and each of the numbers in the list, when represented as a binary number, will have at most 4 bits equal to 1.
- For 11 points, N <= 100, and each of the numbers in the list, when represented as a binary number, will have at most 8 bits equal to 1. The minimal swaps can be accomplished by making at most 1 swap in each number in the list.
- For 25 points, N <= 100, and each of the numbers in the list, when represented as a binary number, will have at most 8 bits equal to 1.
- For 12 points, N <= 2000, and the minimal swaps can be accomplished by making at most 1 swap in each number in the list.
- For 39 points, N <= 2000.