Let P be a square matrix such that P^2=I-P. For α, β, γ, δ ∈ N, if P^α+P^β=γ I-29 P and P^α-P^β=δ I-13 P, then α+β+γ-δ is equal to

Let $\displaystyle P$ be a square matrix such that $\displaystyle P^2=I-P$. For $\displaystyle \alpha, \beta, \gamma, \delta \in \mathbb{N}$, if $\displaystyle P^\alpha+P^\beta=\gamma I-29 P$ and $\displaystyle P^\alpha-P^\beta=\delta I-13 P$, then $\displaystyle \alpha+\beta+\gamma-\delta$ is equal to