CF2089A Simple Permutation

Given an integer $ n $ . Construct a permutation $ p_1, p_2, \ldots, p_n $ of length $ n $ that satisfies the following property: For $ 1 \le i \le n $ , define $ c_i = \lceil \frac{p_1+p_2+\ldots +p_i}{i} \rceil $ , then among $ c_1,c_2,\ldots,c_n $ there must be at least $ \lfloor \frac{n}{3} \rfloor - 1 $ prime numbers.

The first line contains an integer $ t $ ( $ 1 \le t \le 10 $ ) — the number of test cases. The description of the test cases follows. In a single line of each test case, there is a single integer $ n $ ( $ 2 \le n \le 10^5) $ — the size of the permutation.

For each test case, output the permutation $ p_1,p_2,\ldots,p_n $ of length $ n $ that satisfies the condition. It is guaranteed that such a permutation always exists.

In the first test case, $ c_1 = \lceil \frac{2}{1} \rceil = 2 $ , $ c_2 = \lceil \frac{2+1}{2} \rceil = 2 $ . Both are prime numbers. In the third test case, $ c_1 = \lceil \frac{2}{1} \rceil = 2 $ , $ c_2 = \lceil \frac{3}{2} \rceil = 2 $ , $ c_3 = \lceil \frac{6}{3} \rceil = 2 $ , $ c_4 = \lceil \frac{10}{4} \rceil = 3 $ , $ c_5 = \lceil \frac{15}{5} \rceil = 3 $ . All these numbers are prime.