SP4784 HS09EQ - Diophantine equation

Sometimes solving a Diophantine equation is very hard. But, for example, the equation **a**+**b** $ ^{2} $ +**c** $ ^{3} $ +**d** $ ^{4} $ =**n** has a trivial solution for every value of **n**. Your task is to determine the number of solutions of the equation for each given **n**, assuming that in the equation all the values **a**, **b**, **c** and **d** are non-negative integers.

The first line of input contains an integer **T**, representing the number of test cases (**T** The following **T** lines contain one non-negative integer **n** each, where **n** < 10 $ ^{9} $ .

Output **T** lines, each containing the number of solutions of the respective equation for **n**.