14 Angry Numbers!

\[ \large a_1^4+a_2^4+a_3^4+a_4^4+\ldots +a_{14}^4=49999\]

Let there be integers \(a_1,a_2,a_3,\ldots a_{14}\), such that the above equation is satisfied.

How many \(14-\)tuples of \({a_1,a_2,a_3\ldots,a_{14}}\) exist such that the above condition is met?

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