Chef initially had two non-empty arrays A and B, where both arrays contain distinct elements. Moreover, there is no common element in the arrays A and B.

Chef forms another array C from the arrays A and B using the following process :
Let X denote the leftmost element of array A and Y denote the leftmost element of array B.
If Y is smaller than X, delete Y from B and append it to the end of C.
If X is smaller than Y, delete X from A and append it to the end of C.
If either array A or B becomes empty, append all the remaining elements of the other array to the end of C.

Chef forgot the arrays A and B but remembers the array C. Find any two valid non-empty arrays A and B that will yield the given array C. If it is not possible, print -1.

------ Input Format ------

• The first line of input will contain a single integer T, denoting the number of test cases.
• Each test case consists of multiple lines of input.
• The first line of each test case contains a space-separated integer N — the number of elements in array C.
• The next line contains N space-separated integers denoting the elements of the array C.

------ Output Format ------

For each test case, if a solutions exists, print any two valid arrays A and B along with their lengths respectively . For example, if A= [1,7] and B =[4,10,2], then print it as :

2
1 7
3
4 10 2

Else, if answer doesn't exist, print -1 in a single line.

------ Constraints ------

$1 ≤ T ≤ 100$
$1 ≤ N ≤ 10^{5}$
$-10^{5} ≤ C_{i}≤ 10^{5}$
- The sum of $N$ over all test cases won't exceed $10^{6}$.

----- Sample Input 1 ------
2
6
7 6 3 8 2 9
2
2 1

----- Sample Output 1 ------
3
7 6 3
3
8 2 9
-1

----- explanation 1 ------
Test case $1$: We have $A = [7,6,3]$ and $B = [8,2,9]$.
- Move $1$: $X = 7$ and $Y = 8$. Since $X< Y$, we delete $X$ and append it to $C$. Thus, $A = [6, 3], B = [8, 2, 9],$ and $C = [7]$.
- Move $2$: $X = 6$ and $Y = 8$. Since $X< Y$, we delete $X$ and append it to $C$. Thus, $A = [3], B = [8, 2, 9],$ and $C = [7, 6]$.
- Move $3$: $X = 3$ and $Y = 8$. Since $X< Y$, we delete $X$ and append it to $C$. Thus, $A = [], B = [8, 2, 9],$ and $C = [7, 6, 3]$.
- Now, since $A$ is empty, append all elements of $B$ to $C$. Thus, $C = [7, 6, 3, 8, 2, 9]$.

Test case $2$: It can be shown that there exist no valid non-empty arrays $A$ and $B$.

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