A. Suborrays
constructive algorithms; math
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).For a positive integer \(n\), we call a permutation \(p\) of length \(n\) good if the following condition holds for every pair \(i\) and \(j\) (\(1 \le i \le j \le n\)) — \((p_i \text{ OR } p_{i+1} \text{ OR } \ldots \text{ OR } p_{j-1} \text{ OR } p_{j}) \ge j-i+1\), where \(\text{OR}\) denotes the bitwise OR operation. In other words, a permutation \(p\) is good if for every subarray of \(p\), the \(\text{OR}\) of all elements in it is not less than the number of elements in that subarray. Given a positive integer \(n\), output any good permutation of length \(n\). We can show that for the given constraints such a permutation always exists.
Each test contains multiple test cases. The first line contains the number of test cases \(t\) (\(1 \le t \le 100\)). Description of the test cases follows.The first and only line of every test case contains a single integer \(n\) (\(1 \le n \le 100\)).
For every test, output any good permutation of length \(n\) on a separate line.
For \(n = 3\), \([3,1,2]\) is a good permutation. Some of the subarrays are listed below. \(3\text{ OR }1 = 3 \geq 2\) \((i = 1,j = 2)\) \(3\text{ OR }1\text{ OR }2 = 3 \geq 3\) \((i = 1,j = 3)\) \(1\text{ OR }2 = 3 \geq 2\) \((i = 2,j = 3)\) \(1 \geq 1\) \((i = 2,j = 2)\) Similarly, you can verify that \([4,3,5,2,7,1,6]\) is also good.