Problem Statement

Given an integer $n$, find all positive integers $a$, $b$, and $c$ that satisfy the following conditions:

• $1 \leq a \lt b \lt c\leq n$
• $a^{2}+b^{2}=c^{2}$

Constraints

• $1\leq n\leq 10^6$
• $n$ is an integer.

Input

The input is given from Standard Input in the following format:

$\color{#cccccc}\boxed{\color{white}{\large{|}}\color{black}n\color{white}{\large{|}}}$

Output

Output all the values of $a$, $b$, and $c$ that satisfy the conditions, with the values sorted in lexicographical order from smallest to largest. Each of the numbers is separated by space.

Sample Input 1

5

Sample Output 1

3 4 5

Sample Input 2

20

Sample Output 2

3 4 5
5 12 13
6 8 10
8 15 17
9 12 15
12 16 20