The first line contains an integer TTT (1≤T≤1000)(1\le T \le 1\,000)(1≤T≤1000), denoting the number of test cases. Each test case contains an integer mmm (1≤m≤109)(1\le m \le 10^9)(1≤m≤109) in one line.
For each test case: If no solution exists, print "-1" (without quotes) in one line. Otherwise, print one integer nnn (1≤n≤100)(1\le n\le 100)(1≤n≤100) in the first line denoting the length of the permutation you construct. Then print nnn integers p1,p2,⋯,pnp_1, p_2, \cdots, p_np1,p2,⋯,pn, (1≤pi≤n,∀1≤i<j≤n,pi≠pj)(1 \le p_i \le n, \forall \, 1 \le i < j \le n, p_i \neq p_j)(1≤pi≤n,∀1≤i<j≤n,pi=pj) 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 222, and the 333 LISs are {2,4},{2,3},{1,3}\{2, 4\}, \{2, 3\}, \{1, 3\}{2,4},{2,3},{1,3}. In the second test case, the length of the LIS is 222, and the 555 LISs are {3,5},{3,4},{2,5},{2,4},{1,4}\{3, 5\}, \{3, 4\}, \{2, 5\}, \{2, 4\}, \{1, 4\}{3,5},{3,4},{2,5},{2,4},{1,4}.