A quadratic equation

\[x^2-px+q=0\]

is called *binary-quadratic* if it satisfy the following conditions:

All digits of the non-negative integers \(p\) and \(q\) are either \(0\) or \(1\)

All digits of the roots are either \(0\) or \(1\)

How many *binary-quadratic* equations are there such that both roots are smaller than \(10^4\).

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