After summoning the next boss — The Brain of Cthulhu, you noticed that it surrounds itself with (n) eyes, numbered from (1) to (n). In one attack, The Brain of Cthulhu chooses a triple of eyes (not necessarily distinct) with numbers ((a, b, c)). The triple of eyes is called crimson if and only if the following property holds: To defeat the boss, you want to know how many ways The Brain of Cthulhu can choose a crimson triple of eyes. The triples of eyes ((a_1, b_1, c_1)) and ((a_2, b_2, c_2)) are considered different if (a_1 \neq a_2), or (b_1 \neq b_2), or (c_1 \neq c_2). (^{\text{∗}})(\gcd(x, y)) denotes the greatest common divisor (GCD) of integers (x) and (y). (^{\text{†}})(\operatorname{lcm}(x, y)) denotes the least common multiple (LCM) of integers (x) and (y). Each test contains multiple test cases. The first line contains the number of test cases (t) ((1 \le t \le 1000)). The description of the test cases follows. The only line of each test case contains one integer (n) ((1 \le n \le 2 \cdot 10^5)) — the number of eyes of The Brain of Cthulhu. It is guaranteed that the sum of (n) across all test cases does not exceed (2 \cdot 10^5). For each test case, output one integer — the number of ways to choose a crimson triple of eyes. In the first test case, there is (1) possible crimson triple: ((1, 1, 1)). In the second test case, there are (5) possible crimson triples: ((1, 1, 1)), ((1, 1, 2)), ((2, 1, 1)), ((2, 1, 2)), ((2, 2, 2)).