CF2137B Fun Permutation

You are given a permutation$$$^{\\text{∗}}$$$ $$$p$$$ of size $$$n$$$. Your task is to find a permutation $$$q$$$ of size $$$n$$$ such that $$$\\operatorname{GCD}$$$$$$^{\\text{†}}$$$$$$(p\_i+q\_i, p\_{i+1}+q\_{i+1}) \\geq 3$$$ for all $$$1 \\leq i<n$$$. In other words, the greatest common divisor of the sum of any two adjacent positions should be at least $$$3$$$. It can be shown that this is always possible. $$$^{\\text{∗}}$$$A permutation of length $$$m$$$ is an array consisting of $$$m$$$ distinct integers from $$$1$$$ to $$$m$$$ in arbitrary order. For example, $$$\[2,3,1,5,4\]$$$ is a permutation, but $$$\[1,2,2\]$$$ is not a permutation ($$$2$$$ appears twice in the array), and $$$\[1,3,4\]$$$ is also not a permutation ($$$m=3$$$ but there is $$$4$$$ in the array). $$$^{\\text{†}}$$$$$$\\gcd(x, y)$$$ denotes the [greatest common divisor (GCD)](https://en.wikipedia.org/wiki/Greatest_common_divisor) of integers $$$x$$$ and $$$y$$$.

Each test contains multiple test cases. The first line contains the number of test cases $$$t$$$ ($$$1 \\le t \\le 10^4$$$). The description of the test cases follows. The first line of each test case contains an integer $$$n$$$ ($$$2 \\leq n \\leq 2\\cdot 10^5$$$). The second line contains $$$n$$$ integers $$$p\_1,p\_2,\\ldots,p\_n$$$ ($$$1 \\leq p\_i \\leq n$$$). It is guaranteed that the given array forms a permutation. It is guaranteed that the sum of $$$n$$$ over all test cases does not exceed $$$2\\cdot 10^5$$$.

For each test case, output the permutation $$$q$$$ on a new line. If there are multiple possible answers, you may output any.

In the first test case, $$$\\operatorname{GCD}(1+2,3+3)=3\\geq 3$$$ and $$$\\operatorname{GCD}(3+3,2+1)=3\\geq3$$$, so the output is correct.