E. What Is It?time limit per test1 secondmemory limit per test256 megabytesinputstandard inputoutputstandard outputLunar rover finally reached planet X. After landing, he met an obstacle, that contains permutation p of length n. Scientists found out, that to overcome an obstacle, the robot should make p an identity permutation (make p_i = i for all i).Unfortunately, scientists can't control the robot. Thus the only way to make p an identity permutation is applying the following operation to p multiple times:   Select two indices i and j (i \neq j), such that p_j = i and swap the values of p_i and p_j. It takes robot (j - i)^2 seconds to do this operation.  Positions i and j are selected by the robot (scientists can't control it). He will apply this operation while p isn't an identity permutation. We can show that the robot will make no more than n operations regardless of the choice of i and j on each operation.Scientists asked you to find out the maximum possible time it will take the robot to finish making p an identity permutation (i. e. worst-case scenario), so they can decide whether they should construct a new lunar rover or just rest and wait. They won't believe you without proof, so you should build an example of p and robot's operations that maximizes the answer.For a better understanding of the statement, read the sample description.InputThe first line of input contains a single integer t (1 \leq t \leq 10^4) — the number of test cases.Each of next t lines contains the single integer n (2 \leq n \leq 10^5) – the length of p.Note, that p is not given to you. You should find the maximum possible time over all permutations of length n.It is guaranteed, that the total sum of n over all test cases doesn't exceed 10^5.OutputFor each test case in the first line, print how many seconds will the robot spend in the worst case.In the next line, print the initial value of p that you used to construct an answer.In the next line, print the number of operations m \leq n that the robot makes in your example.In the each of next m lines print two integers i and j — indices of positions that the robot will swap on this operation. Note that p_j = i must holds (at the time of operation).ExampleInput
3
2
3
3
Output
1
2 1
1
2 1
5
2 3 1
2
1 3
3 2
5
2 3 1
2
1 3
2 3NoteFor n = 2, p can be either [1, 2] or [2, 1]. In the first case p is already identity, otherwise robot will make it an identity permutation in 1 second regardless of choise i and j on the first operation.For n = 3, p can be equals [2, 3, 1].  If robot will select i = 3, j = 2 on the first operation, p will become [2, 1, 3] in one second. Now robot can select only i = 1, j = 2 or i = 2, j = 1. In both cases, p will become identity in one more second (2 seconds in total). If robot will select i = 1, j = 3 on the first operation, p will become [1, 3, 2] in four seconds. Regardless of choise of i and j on the second operation, p will become identity in five seconds. We can show, that for permutation of length 3 robot will always finish all operation in no more than 5 seconds.
3
2
3
3

1 2 1 1 2 1 5 2 3 1 2 1 3 3 2 5 2 3 1 2 1 3 2 3
['constructive algorithms', 'greedy', '*2500']