Product of eigenvalues of skew-symmetric P

Let $P = \begin{pmatrix} 0 & 1 & 1 & 1 & 1 \ -1 & 0 & 1 & 1 & 1 \ -1 & -1 & 0 & 1 & 1 \ -1 & -1 & -1 & 0 & 1 \ -1 & -1 & -1 & -1 & 0 \end{pmatrix}$. If $\lambda_1, \lambda_2, \lambda_3, \lambda_4$, and $\lambda_5$ are eigen values of $P$, then $\prod_{i=1}^{5} \lambda_i$ equals __________ (answer in integer).