Counting Pythagorean Triples

Problem Description

Pythagorean triples are a very interesting mathematical notion. Three positive integers $a, b, c$ satisfying $a^2 + b^2 = c^2$ with $1 \le a \le b \le c$ form a Pythagorean triple $(a, b, c)$. Can you write a program to count how many such Pythagorean triples satisfy $c \le n$?

Input Format

One line containing a positive integer $n$. It is guaranteed that $1 \le n \le 1000$.

Output Format

Output one line containing an integer $C$, the number of Pythagorean triples satisfying the condition.

Sample Input

Sample Input 1

5

Sample Input 2

13

Sample Output

Sample Output 1

1

Sample Output 2

3

Sample Explanation

For the first sample, the input is $5$, meaning we need to find all Pythagorean triples with $c \le 5$. By enumerating all possible combinations of $a, b, c$ satisfying $a^2 + b^2 = c^2$ and $1 \le a \le b \le c \le 5$, only $(3, 4, 5)$ works, since $3^2 + 4^2 = 9 + 16 = 25 = 5^2$. So the output is $1$.

Constraints

$1 \le n \le 1000$