Perfect Squares

A famous theorem in number theory states that every positive integer can be written as the sum of four perfect squares. Usually, though, fewer squares are enough. For example, $27$ needs only three perfect squares: $27 = 5^2 + 1^2 + 1^2$.

A mathematician friend lists these facts about perfect squares:

• An odd prime $p$ is a sum of two squares if and only if $p \equiv 1 \pmod 4$.
• If two positive integers $a$ and $b$ are each a sum of two squares, then their product $ab$ is also a sum of two squares.
• Every positive integer is a sum of three perfect squares, unless it has the form $4^a \cdot (8b + 7)$, where $a$ and $b$ are non-negative integers.

The last fact about sums of three squares interests you, so you decide to write a program that checks the claim and produces the actual squares.

The input is a single integer $n$ ($1 \le n \le 10^{12}$).

If $n$ can be expressed as the sum of three squares, output three integers $x$, $y$, and $z$. An answer is accepted if $0 \le x, y, z \le \sqrt{n}$ and $n = x^2 + y^2 + z^2$. If several choices work, output any of them. Always print exactly three integers, even when $n$ is a sum of two or fewer squares. If $n$ cannot be expressed as the sum of three squares, output $-1$ and nothing else.