Fox loves permutations! She came up with the following problem and asked Cat to solve it:

You are given an even positive integer $n$ and a permutation$^\dagger$ $p$ of length $n$.

The score of another permutation $q$ of length $n$ is the number of local maximums in the array $a$ of length $n$, where $a_i = p_i + q_i$ for all $i$ ($1 \le i \le n$). In other words, the score of $q$ is the number of $i$ such that $1 < i < n$ (note the strict inequalities), $a_{i-1} < a_i$, and $a_i > a_{i+1}$ (once again, note the strict inequalities).

Find the permutation $q$ that achieves the maximum score for given $n$ and $p$. If there exist multiple such permutations, you can pick any of them.

$^\dagger$ 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).

The first line of input contains an integer $t$ ($1 \leq t \leq 10^4$) — the number of test cases in the input you will have to solve.

The first line of each test case contains one even integer $n$ ($4 \leq n \leq 10^5$, $n$ is even) — the length of the permutation $p$.

The second line of each test case contains the $n$ integers $p_1, p_2, \ldots, p_n$ ($1 \leq p_i \leq n$). It is guaranteed that $p$ is a permutation of length $n$.

It is guaranteed that the sum of $n$ across all test cases doesn't exceed $10^5$.

For each test case, output one line containing any permutation of length $n$ (the array $q$), such that $q$ maximizes the score under the given constraints.