14 Angry Numbers!

a14+a24+a34+a44++a144=49999 \large a_1^4+a_2^4+a_3^4+a_4^4+\ldots +a_{14}^4=49999

Let there be integers a1,a2,a3,a14a_1,a_2,a_3,\ldots a_{14}, such that the above equation is satisfied.

How many 1414-tuples of a1,a2,a3,a14{a_1,a_2,a_3\ldots,a_{14}} exist such that the above condition is met?

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