G. Hits Differenttime limit per test2.5 secondsmemory limit per test256 megabytesinputstandard inputoutputstandard outputIn a carnival game, there is a huge pyramid of cans with 2023 rows, numbered in a regular pattern as shown. If can 9^2 is hit initially, then all cans colored red in the picture above would fall. You throw a ball at the pyramid, and it hits a single can with number n^2. This causes all cans that are stacked on top of this can to fall (that is, can n^2 falls, then the cans directly above n^2 fall, then the cans directly above those cans, and so on). For example, the picture above shows the cans that would fall if can 9^2 is hit.What is the sum of the numbers on all cans that fall? Recall that n^2 = n \times n.InputThe first line contains an integer t (1 \leq t \leq 1000) — the number of test cases.The only line of each test case contains a single integer n (1 \leq n \leq 10^6) — it means that the can you hit has label n^2.OutputFor each test case, output a single integer — the sum of the numbers on all cans that fall.Please note, that the answer for some test cases won't fit into 32-bit integer type, so you should use at least 64-bit integer type in your programming language (like long long for C++). For all valid inputs, the answer will always fit into 64-bit integer type.ExampleInput
1091234561014341000000Output
156
1
5
10
21
39
46
146
63145186
58116199242129511
NoteThe first test case is pictured in the statement. The sum of the numbers that fall is 1^2 + 2^2 + 3^2 + 5^2 + 6^2 + 9^2 = 1 + 4 + 9 + 25 + 36 + 81 = 156.In the second test case, only the can labeled 1^2 falls, so the answer is 1^2=1.In the third test case, the cans labeled 1^2 and 2^2 fall, so the answer is 1^2+2^2=1+4=5.In the fourth test case, the cans labeled 1^2 and 3^2 fall, so the answer is 1^2+3^2=1+9=10.In the fifth test case, the cans labeled 1^2, 2^2, and 4^2 fall, so the answer is 1^2+2^2+4^2=1+4+16=21.
1091234561014341000000
156 1 5 10 21 39 46 146 63145186 58116199242129511 
['data structures', 'dp', 'implementation', 'math', '*1600']