Convert to permutation

You are given an array $A$ of size $n$. In one operation, you can choose an index $i(1\le i\le n)$ 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

The first line contains a single integer $T$, denoting the number of test cases.

Each test case consists of multiple lines. The first line of each test case contains the integer $n(1\le n\le 1000)$ — the size of the array. The next line contains $n$ integers, the elements of the array $A(0\le A_i\le 1000)$.

Output

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 $-1$.

Examples