Create a custom data type $($suggested name number$\_t)$ that describes numbers and can combine integer and floating$-$point

numbers. Create an array of that data type. Fill the array with the factorial of the index of each element. The factorial value

shall be stored as integer as long as possible and as a floating$-$point value for values that are too large.

Determine the size of the array using operator sizeof.

Advanced question: from which number does the Stirling approximation provide a result that is undistinguishable from the

exact value? Remember that the "exact" value calculated using floating$-$point arithmetic might be not as exact as we hope.

The Stirling approximation is defined as follows:

$n!\sqrt[\phantom{2}]{2n}()\frac{n}{e}$