A permutation (p) of length (n)(^{\text{∗}}) is perfect if, for each index (i) ((1 \le i \le n)), it satisfies the following: The sum of the first (i) elements (p_1 + p_2 + \ldots + p_i) is not a perfect square(^{\text{†}}). You would like things to be perfect. Given a positive integer (n), find a perfect permutation of length (n), or print (-1) if none exists. (^{\text{∗}})A permutation of length (n) is an array consisting of (n) distinct integers from (1) to (n) in arbitrary order. For example, (2,3,1,5,4) is a permutation, but (1,2,2) is not a permutation ((2) appears twice in the array), and (1,3,4) is also not a permutation ((n=3) but there is (4) in the array). (^{\text{†}})A perfect square is an integer that is the square of an integer, e.g., (9=3^2) is a perfect square, but (8) and (14) are not. Each test contains multiple test cases. The first line contains the number of test cases (t) ((1 \le t \le 10^4)). The description of the test cases follows. The first and only line of each test case contains a single integer (n) ((1 \le n \le 5 \cdot 10^5)). It is guaranteed that the sum of (n) over all test cases does not exceed (10^6). For each test case: If no solution exists, print a single integer (-1). Otherwise, print (n) integers (p_1,p_2,\ldots,p_n) — the perfect permutation you find. If there are multiple solutions, print any of them. In the first test case, there is only one permutation with length (n = 1) that is (p = 1), which is not perfect : (p_1 = 1 = x^2) for (x = 1). In the second test case, one possible perfect permutation with length (n = 4) is (p = 2, 4, 1, 3): (p_1 = 2 \neq x^2); (p_1 + p_2 = 2 + 4 = 6 \neq x^2); (p_1 + p_2 + p_3 = 2 + 4 + 1 = 7 \neq x^2); (p_1 + p_2 + p_3 + p_4 = 2 + 4 + 1 + 3 = 10 \neq x^2). In the third test case, one possible p