Statement : A. Blocked

Given an array $a$ of integers of size $n$, we say that a position $1 \le i \le n$ is blocked if $a_i$ can be expressed as the sum of a subset of $a_1, a_2, \ldots, a_{i-1}$ (i.e. there exist $1 \le j_1 \lt j_2 \lt \ldots \lt j_k \le i-1$ such that $a_{j_1} + a_{j_2} + \ldots + a_{j_k} = a_i$). Reorder $a$ so that no position is blocked or report that it is impossible.

For example, reordering the array [$3, 2, 5$] to [$2, 3, 5$] makes position $3$ blocked, since we can express $5 = 2 + 3$, but if we reorder it to [$3, 5, 2$], no position is blocked.

Each test contains multiple test cases. The first line contains the number of test cases $t$ ($1 \le t \le 400$). The description of the test cases follows.

The first line of each test case contains an integer $n$ ($1 \le n \le 200$).

The second line contains $n$ integers, denoting the array $a$ ($\textbf{1} \le a_i \le 100$).

For each test case, print any order of $a$ such that no position is blocked if it exists, otherwise print $-1$.

Input

4
3
1 5 9
4
1 3 3 2
3
1 2 3
1
1

Output

5 9 1
-1
3 1 2
1

Note

In the third test case, the array [$3, 1, 2$] has no position blocked:

Position $1$ is not blocked since $3$ can’t be expressed as the sum of a subset of [].

Position $2$ is not blocked since $1$ can’t be expressed as the sum of a subset of [$3$].

Position $3$ is not blocked since $2$ can’t be expressed as the sum of a subset of [$3, 1$].