#### Hackonacci Matrix Rotations

We define a *Hackonacci *series as follows:

*hackonacci (n) = 1. hackonacci (n-1) + 2. hackonacci (n-2) + 3. hackonacci(n-3)*

*hackonacci(1)= 1*

*hackonacci(2)=2*

*hackonacci(3)=3*

We define a *Hackonacci Matrix* to be an *n X n* matrix where the rows and columns are indexed from 1 to n , and the top-left cell is (1,1) . Each cell (i,j) must contains either the character `X`

or the character `Y`

. If *hackonacci ((i.j)^2) * is *even*, it’s `X`

; otherwise, it’s `Y`

.

Next, we want to perform* q *queries where each query* i *consists of an integer, *angle-i*. Each* angle-i* is a multiple of* 90 *degrees and describes the angle by which you must rotate the matrix in the *clockwise* direction. For each *angle-i* , we want to count the number of cells that are different after the rotation. For example, the diagram below depicts the *270* rotation of a Hackonacci Matrix when *n=2*:

As you can see, there are two cells whose values change after the rotation. Note that we filled each initial cell using the Hackonacci formula given above:

Given the value of and queries, construct a Hackonacci Matrix and answer the queries. For each query , print an integer on a new line denoting the number of cells whose values differ from the initial Hackonacci Matrix when it’s rotated by degrees in the clockwise direction.

**Input Format**

The first line contains two space-separated integers describing the respective values of and .

Each line of the subsequent lines contains an integer denoting .

**Constraints**

- It is guaranteed that each is multiple of degrees.

**Output Format**

For each , print a single integer on a new line denoting the number of different cells that differ between the initial matrix and the matrix rotated by degrees.

**Sample Input 0**

```
4 3
90
180
270
```

**Sample Output 0**

```
10
6
10
```

**Explanation 0**

Because , we must build a Hackonacci matrix and then perform queries, shown below. The following diagrams depict each query rotation, and cells whose values changed after performing a rotation are highlighted in orange:

- When we perform a rotation on the matrix, there are cells whose values change:

Thus, we print on a new line. - When we perform a rotation on the matrix, there are cells whose values change:

Thus, we print on a new line. - When we perform a rotation on the matrix, there are cells whose values change:

Thus, we print on a new line.

**Source : Hackerrank**

**Solution**

`Working on the solution`