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Algebra Level 3

\[\begin{align} a + 7b + 3c + 5d = 0 \cdots (1) \\ 8a + 4b + 6c + 2d = -16 \cdots (2)\\ 2a + 6b + 4c + 8d = 16 \cdots (3) \\ 5a + 3b + 7c + d = -16 \cdots (4)\end{align}\] If \(a, b, c, d\) satisfiy above equations, then what is the value of \((a + d)(b + c)\)

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