Those cling-on troubles that ride my stride — cough up the fee, or step aside.

— SHUN, TAKE IT AWAY

For a permutation$$$^{\text{∗}}$$$ $$$r$$$ of length $$$m$$$, we call an index $$$i$$$ ($$$1\le i\le m$$$) ugly if and only if $$$i=\max(\{r_1,r_2,\ldots,r_i\})$$$.

Simons has a permutation $$$p$$$ of length $$$n$$$, and he can perform the following operation on $$$p$$$ at most once:

Choose two indices $$$i$$$ and $$$j$$$ ($$$1\le i\ne j\le n$$$), then swap $$$p_i$$$ and $$$p_j$$$.

Find a permutation $$$q$$$ that can be obtained from $$$p$$$ by performing the above operation at most once, such that the number of ugly indices in $$$q$$$ is minimized.

$$$^{\text{∗}}$$$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

Each test contains multiple test cases. The first line contains the number of test cases $$$t$$$ ($$$1 \le t \le 100$$$). The description of the test cases follows.

The first line contains an integer $$$n$$$ ($$$1\le n\le 500$$$) — the length of $$$p$$$.

The second line contains $$$n$$$ integers $$$p_1,p_2,\ldots,p_n$$$ ($$$1\le p_i\le n$$$, all $$$p_i$$$-s are distinct) — the elements of $$$p$$$.

Output

For each test case, print $$$n$$$ integers $$$q_1,q_2,\ldots,q_n$$$ — the permutation you found.

If there are multiple possible permutations, you may output any.

Note

In the first test case, Simons can obtain only two possible permutations: $$$[1,2]$$$ and $$$[2,1]$$$.

For permutation $$$[1,2]$$$, we can see $$$1=\max(\{1\})$$$ and $$$2=\max(\{1,2\})$$$. So there are two ugly indices.
For permutation $$$[2,1]$$$, we can see $$$1\ne\max(\{2\})$$$ and $$$2=\max(\{2,1\})$$$. So there is only one ugly index.

Thus, permutation $$$[2,1]$$$ has the minimum count of ugly indices.

In the second test case, Simons can obtain permutation $$$[2,4,1,3]$$$ by choosing indices $$$2$$$ and $$$4$$$ to swap. There is only one ugly index in the permutation:

$$$1\ne \max(\{2\})$$$, so index $$$1$$$ is not ugly;
$$$2\ne \max(\{2,4\})$$$, so index $$$2$$$ is not ugly;
$$$3\ne \max(\{2,4,1\})$$$, so index $$$3$$$ is not ugly;
$$$4=\max(\{2,4,1,3\})$$$, so index $$$4$$$ is ugly.

In the third test case, note that Simons does not perform the operation.

Simons and Making It Beautiful

Examples