Algebra Level 3

Quadratic (A) is a friend of quadratic (B) if both the roots of (A) lie between the roots of (B).

Then find the number of integral values of $$a$$ for which $$x^{2}-100x+a^{2}=0$$ is a friend of $$x^{2}-100x+2a^{2}-14a+33=0$$.

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