It is known that Farmer John likes Permutations, but I like them too!

— Sun Tzu, The Art of Constructing Permutations

You are given a permutation$$$^{\text{∗}}$$$ $$$p$$$ of length $$$n$$$.

Find a permutation $$$q$$$ of length $$$n$$$ that minimizes the number of pairs ($$$i, j$$$) ($$$1 \leq i \leq j \leq n$$$) such that $$$p_i + p_{i+1} + \ldots + p_j = q_i + q_{i+1} + \ldots + q_j$$$.

$$$^{\text{∗}}$$$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

The first line contains $$$t$$$ ($$$1 \leq t \leq 10^4$$$) — the number of test cases.

The first line of each test case contains $$$n$$$ ($$$1 \leq n \leq 2 \cdot 10^5$$$).

The following line contains $$$n$$$ space-separated integers $$$p_1, p_2, \ldots, p_n$$$ ($$$1 \leq p_i \leq n$$$) — denoting the permutation $$$p$$$ of length $$$n$$$.

It is guaranteed that the sum of $$$n$$$ over all test cases does not exceed $$$2 \cdot 10^5$$$.

Output

For each test case, output one line containing any permutation of length $$$n$$$ (the permutation $$$q$$$) such that $$$q$$$ minimizes the number of pairs.

Note

For the first test, there exists only one pair ($$$i, j$$$) ($$$1 \leq i \leq j \leq n$$$) such that $$$p_i + p_{i+1} + \ldots + p_j = q_i + q_{i+1} + \ldots + q_j$$$, which is ($$$1, 2$$$). It can be proven that no such $$$q$$$ exists for which there are no pairs.

Minimize Equal Sum Subarrays

Examples