Solve the programming task below in a Python markdown code block.
You are given an array A of size N. In one operation, you can:
Choose an index i (1≤ i ≤ N) and increase A_{i} by 1.

Find the minimum number of operations required to convert the array A into a *permutation* of size N. If it is impossible to do so, print -1.

Note that a *permutation* of size N contains each element from 1 to N exactly once.

------ 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 the integer N — the size of the array.
- The next line contains N space-separated integers, the elements of the array A.

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

For each test case, output on a new line, the minimum number of operations required to convert the array A into a *permutation* of size N.  
If it is impossible to do so, print -1.

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

$1 ≤ T ≤ 500$
$1 ≤ N ≤ 1000$
$0 ≤ A_{i} ≤ 1000$

----- Sample Input 1 ------ 
4
4
3 1 1 2
3
0 3 3
3
3 2 1
3
2 0 1

----- Sample Output 1 ------ 
3
-1
0
3
----- explanation 1 ------ 
Test case $1$: We can convert the array $A$ into a permutation using $3$ operations:
- Operation $1$: Choose $i = 3$ and increase $A_{i}$ by $1$. Thus, the array becomes $A = [3, 1, 2, 2]$.
- Operation $2$: Choose $i = 3$ and increase $A_{i}$ by $1$. Thus, the array becomes $A = [3, 1, 3, 2]$.
- Operation $3$: Choose $i = 3$ and increase $A_{i}$ by $1$. Thus, the array becomes $A = [3, 1, 4, 2]$.

It can be shown that this is the minimum number of operations required to convert $A$ into a permutation.

Test case $2$: The given array cannot be converted into a permutation using any number of operations.

Test case $3$: The given array is already a permutation. Thus, we require $0$ operations.

Test case $4$: We can convert the array $A$ into a permutation using $3$ operations:
- Operation $1$: Choose $i = 1$ and increase $A_{i}$ by $1$. Thus, the array becomes $A = [3, 0, 1]$.
- Operation $2$: Choose $i = 2$ and increase $A_{i}$ by $1$. Thus, the array becomes $A = [3, 1, 1]$.
- Operation $3$: Choose $i = 3$ and increase $A_{i}$ by $1$. Thus, the array becomes $A = [3, 1, 2]$.

It can be shown that this is the minimum number of operations required to convert $A$ into a permutation.