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$\large \begin{aligned} a + 4b + 9c + 16d + 25e & = 1 \\ 4a + 9b + 16c + 25d + 36e & = 8 \\ 9a + 16b + 25c+ 36d + 49e & = 23 \end{aligned}$

Real numbers $a$, $b$, $c$, $d$, and $e$ satisfy the system of equations above. Find $a + b + c+ d + e$.

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