Either way square

find how many pairs of integers \((x,y)\) satisfying \( 1 \leq x\leq 100 \) \( 1 \leq y\leq 100 \) are there ,which satisfies following 2 condtions?

1) \(x-y\) is a perfect square.
2) \(x+y \) is a perfect square.

For example, \( (5,4) \) works since \(5-4=1^2\) and \(5+4=3^2\).

Details and Assumptions:

\(0\) is not a perfect square.

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