B"Lunar 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: 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. The first line of input contains a single integer t ( 1 <= q t <= q 10^4 ) -- the number of test cases. Each of next t lines contains the single integer n ( 2 <= q n <= q 10^5 ) xe2 x80 x93 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 . For 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 <= q 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). For n = 2 , p can be either [1, 2] or [2, 1] . In the first case p is already identity, otherwise robot will mak"...