You are given an array A of size n. In one operation, you can choose an index i (1≤i≤n) and increase Ai 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.
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≤n≤1000) — the size of the array. The next line contains n integers, the elements of the array A (0≤Ai≤1000).
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.