_{This problem is a programming version of Problem 173 from projecteuler.net}

We shall define a square lamina to be a square outline with a square "hole" so that the shape possesses vertical and horizontal symmetry. For example, using exactly thirty-two square tiles we can form two different square laminae:

With one-hundred tiles, and not necessarily using all of the tiles at one time, it is possible to form forty-one different square laminae.

Using up to tiles how many different square laminae can be formed?

**Input Format**

The only integer is given on the first line.

**Constraints**

**Output Format**

Print the only integer which is the number of such square laminae.

**Sample Input 0**

```
100
```

**Sample Output 0**

```
41
```

**Explanation 0**

As written in the statement, for tiles there are ony different laminaes.