Given an integer , you need to construct a permutation whose length does not exceed such that there are exactly longest increasing subsequences in .

If multiple solutions exist, print any of them. If no solution exists, report it.

输入描述:

The first line contains an integer  , denoting the number of test cases.
Each test case contains an integer   in one line.

输出描述:

For each test case:
If no solution exists, print "-1" (without quotes) in one line.
Otherwise, print one integer   in the first line denoting the length of the permutation you construct. Then print  integers ,  in the second line denoting the permutation you construct.

2
3
5

4
2 4 1 3
5
3 2 5 1 4

In the first test case, the length of the LIS (longest increasing subsequence) is , and the  LISs are .
In the second test case, the length of the LIS is , and the  LISs are .