Determine all complex numbers $\lambda$ for which there exist a positive integer $n$ and a real $n \times n$ matrix $A$ such that $A^{2}=A^{T}$ and $\lambda$ is an eigenvalue of $A$. The answer is $\frac{m \pm \sqrt{n} i}{p}$ ,please give the sum of m,n and p.

Let's think step by step and output the final answer within \boxed{}.
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