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Algebra Level 2

\[ \begin{eqnarray} a+b+c+d &=& 1 \\ b+c+d+e &=& 2 \\ c+d+e+a &=& 3 \\ d+e+a+b &=& 4 \\ e+a+b+c &=& 6\\ \end{eqnarray} \]

What is the value of \( a^e + b^d + c \)?

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