P2063 Sum of Two Squares Theorem

For a positive integer $n$, find all pairs of non-negative integers $(x, y)$ such that $x^2+y^2=n$.

There are multiple test cases. The first line contains a positive integer $T$, representing the number of test cases. For each test case, the next line contains a positive integer, which is the value of $n$.

For each test case, first output a single non-negative integer, representing the number of pairs $(x, y)$ that satisfy the condition. Then output all $(x, y)$ in increasing order of $x$. Separate $x$ and $y$ with a space, and separate different pairs with a newline. Insert a blank line between different test cases.

Constraints: For all testdata, $1\le T\le 10^2,1\le n\le 10^{18}$. Translated by ChatGPT 5