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