If a function $f(x)$ defined by  $f(x) = \begin{cases} ae^x + be^{-x}, & -1 \leq x < 1 \\[6pt] cx^2, & 1 \leq x \leq 3 \\[6pt] ax^2 + 2cx, & 3 < x \leq 4 \end{cases} \\[10pt] $ be continuous for some $ a, b, c \in \mathbb{R} $ and $f'(0) + f'(2) = e,$  then the value of $a$ is