If \( A = \begin{pmatrix} 1 & 0 \\ 0 & -1 \end{pmatrix} \), \( P = \begin{pmatrix} 1 & 1 \\ 0 & 1 \end{pmatrix} \) and \( X = A P A^T \), then \( A^T X^{50} A = \)