| Codeforces Round 1012 (Div. 1) |
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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.
3235
2 12 1 32 1 3 4 5
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.
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