You are given an integer (n). Call an array (a) of length (n) good if: For all (1 \le i < n), (a_i \cdot a_{i+1} < 0) (i.e., the product of adjacent elements is negative). For all subarrays(^{\text{∗}}) with length at least (2), the sum of all elements in the subarray is positive(^{\text{†}}). Additionally, we say a good array (a) of length (n) is better than another good array (b) of length (n) if (|a_1|, |a_2|, \ldots, |a_n|) is lexicographically smaller(^{\text{‡}}) than (|b_1|, |b_2|, \ldots, |b_n|). Note that (|z|) denotes the absolute value of integer (z). Output a good array of length (n) such that it is better than every other good array of length (n). (^{\text{∗}})An array (c) is a subarray of an array (d) if (c) can be obtained from (d) by the deletion of several (possibly, zero or all) elements from the beginning and several (possibly, zero or all) elements from the end. (^{\text{†}})An integer (x) is positive if (x > 0). (^{\text{‡}})A sequence (a) is lexicographically smaller than a sequence (b) if and only if one of the following holds: (a) is a prefix of (b), but (a \ne b); or in the first position where (a) and (b) differ, the sequence (a) has a smaller element than the corresponding element in (b). The first line contains an integer (t) ((1 \leq t \leq 500)) — the number of test cases. The single line of each test case contains one integer (n) ((2 \le n \le 2 \cdot 10^5)) — the length of your array. It is guaranteed that the sum of (n) over all test cases does not exceed (2 \cdot 10^5). For each test case, output (n) integers (a_1, a_2, \dots, a_n) ((-10^9 \leq a_i \leq 10^9)), the elements of your array on a new line. In the first test case, because (a_1 \cdot a_2 = -2 < 0) and (a_1 + a_2 = 1 > 0), it satisfies the two constraints. In addition, i