You are given a permutation$$$^\dagger$$$ $$$a$$$ of length $$$n$$$.

Find any permutation $$$b$$$ of length $$$n$$$ such that $$$a_1+b_1 \le a_2+b_2 \le a_3+b_3 \le \ldots \le a_n+b_n$$$.

It can be proven that a permutation $$$b$$$ that satisfies the condition above always exists.

$$$^\dagger$$$ 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).

Input

Each test contains multiple test cases. The first line of input contains a single integer $$$t$$$ ($$$1 \le t \le 2000$$$) — the number of test cases. The description of test cases follows.

The first line of each test case contains a single integer $$$n$$$ ($$$1 \le n \le 100$$$) — the length of permutations $$$a$$$ and $$$b$$$.

The second line of each test case contains $$$n$$$ distinct integers $$$a_1,a_2,\ldots,a_n$$$ ($$$1 \le a_i \le n$$$) — the elements of permutation $$$a$$$. All elements of $$$a$$$ are distinct.

Note that there is no bound on the sum of $$$n$$$ over all test cases.

Output

For each test case, output any permutation $$$b$$$ which satisfies the constraints mentioned in the statement. It can be proven that a permutation $$$b$$$ that satisfies the condition above always exists.

Note

In the first test case $$$a=[1, 2, 4, 5, 3]$$$. Then the permutation $$$b=[1, 2, 4, 3, 5]$$$ satisfies the condition because $$$1 + 1 \le 2 + 2 \le 4 + 4 \le 5 + 3 \le 3 + 5$$$.

Twin Permutations

Examples