triangle. How many distinct triangles can you make? Two triangles are equal if all the side

lengths are same when sorted in ascending order of length. So $(1, 3, 2)$ is same to $(3, 1, 2)$

because their side lengths are same if we sort them, which is $(1, 2, 3)$. But $(1, 3, 4) $is not

same with $(1, 2, 3)$. Suppose the lengths of three pieces are $ X, Y, Z (X <= Y <= Z) $ respectively.

Following constraints should be maintained:

$

1. X, Y, Z > 0. $

$2. X, Y, Z $ is an integer.

$3. X + Y >= Z$

$4. X + Y + Z = N

$

For example if $ N = 14 $, then there are $7$ triangles: $(1, 6, 7), (2, 5, 7), (2, 6, 6), (3, 4, 7), (3, 5, 6),

(4, 4, 6), (4, 5, 5)$.

**INPUT**

First line will give you the number of test cases,$ T (T<=100) $. Then each line will have an

integer $ N (0< N <= 300000) $

**OUTPUT**

For each test case, print the test case number starting from $1$ and an integer denoting the

number of distinct triangles possible.

**SAMPLE INPUT**

**SAMPLE OUTPUT**