Let \( I \) denote the identity matrix of order 7, and \( A \) be a \( 7 \times 7 \) real matrix having characteristic polynomial \( C_A(\lambda) = \lambda^2 (\lambda - 1)^\alpha (\lambda + 2)^\beta \), where \( \alpha \) and \( \beta \) are positive integers. If \( A \) is diagonalizable and \( \text{rank}(A) = \text{rank}(A + 2I) \), then \( \text{rank}(A - I) \) is \(\underline{\hspace{2cm}}\) (in integer).