Problem F
Any Pythagorean Triple

You are given a circumference $n$ and want to find a right-angled triangle with integer side lengths that has a right angle and this circumference. No side can have length $0$, nor a negative length.

Input

The first and only line of input contains a positive integer $n\le {10}^4$.

Output

Print three positive integers $a,b,c$ separated by spaces. Here $a,b$ should be the lengths of the shorter sides and $c$ the length of the hypotenuse. The sum of the numbers must be $n$ and the triangle must form a right angle. If no solution exists, print three zeros instead.

1000

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