Penguins are civilized creatures that communicate using permutations. Blackslex, as a penguin researcher, must study their means of communication. For a given integer (n), consider permutations(^{\text{∗}}) (p) of the array (0, 1, \ldots, 2^n - 1). Define ()S(p) \;=\; \sum_{i=0}^{2^n-1} \operatorname{popcount}\!\bigl(p_0 \mathbin{\&} p_1 \mathbin{\&} \cdots \mathbin{\&} p_i\bigr),() where (\operatorname{popcount}(z)) is the number of (1)-bits in the binary representation of (z) (for instance, (\operatorname{popcount}(5) = 2) because (5 = 101_2) has two (1)-bits in the binary representation), and (\&) denotes the bitwise AND operation . . A permutation is considered sacred if it maximizes (S(p)). Find the lexicographically minimal (^{\text{†}}) sacred permutation. (^{\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{†}})An array (a) is lexicographically smaller than an array (b) of the same size if and only if the following holds: in the first position where (a) and (b) differ, the array (a) has a smaller element than the corresponding element in (b). The first line contains a single integer (t) ((1 \le t \le 16)) — the number of test cases. Each test case contains a single integer (n) ((1 \le n \le 16)). It is guaranteed that the sum of (2^n) over all test cases does not exceed (2^{16}). For each test case, output (2^n) integers (p_0, p_1, \ldots, p_{2^n-1}) — the required permutation. For the first test case, there are two possible permutations. (p = 0, 1), (S(p) = 0) (p = 1, 0), (S(p) = 1) For the secon