Find the number of such sequences

Algebra Level 5

Let \({ a }_{ 1 },{ a }_{ 2 },{ a }_{ 3 },{ a }_{ 4 },{ a }_{ 5 }\) be a 5 term geometric sequence satisfying \(0<{ a }_{ 1 }<{ a }_{ 2 }<{ a }_{ 3 }<{ a }_{ 4 }<{ a }_{ 5 }<100\) , where each term is an integer. The number of such 5 terms are

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