Go brave or go smart

Algebra Level 4

\[\begin{array}{} & \ \ \ (a+b+c+d)^4+(a+b-c-d)^4 \\ & +(a-b+c-d)^4+(a-b-c+d)^4 \\ & -(a+b+c-d)^4-(a+b-c+d)^4 \\ & -(a-b+c+d)^4-(-a+b+c+d)^4 \end{array}\] Simplify the above expression.

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