C. Paprika and Permutationtime limit per test1 secondmemory limit per test256 megabytesinputstandard inputoutputstandard outputPaprika loves permutations. She has an array a_1, a_2, \dots, a_n. She wants to make the array a permutation of integers 1 to n.In order to achieve this goal, she can perform operations on the array. In each operation she can choose two integers i (1 \le i \le n) and x (x > 0), then perform a_i := a_i \bmod x (that is, replace a_i by the remainder of a_i divided by x). In different operations, the chosen i and x can be different.Determine the minimum number of operations needed to make the array a permutation of integers 1 to n. If it is impossible, output -1.A permutation is an array consisting of n distinct integers from 1 to n in arbitrary order. For example, [2,3,1,5,4] is a permutation, but [1,2,2] is not a permutation (2 appears twice in the array) and [1,3,4] is also not a permutation (n=3 but there is 4 in the array).InputEach test contains multiple test cases. The first line contains a single integer t (1 \le t \le 10^4) — the number of test cases. Description of the test cases follows.The first line of each test case contains an integer n (1 \le n \le 10^5).The second line of each test case contains n integers a_1, a_2, \dots, a_n. (1 \le a_i \le 10^9).It is guaranteed that the sum of n over all test cases does not exceed 2 \cdot 10^5.OutputFor each test case, output the minimum number of operations needed to make the array a permutation of integers 1 to n, or -1 if it is impossible.ExampleInput
4
2
1 7
3
1 5 4
4
12345678 87654321 20211218 23571113
9
1 2 3 4 18 19 5 6 7
Output
1
-1
4
2
NoteFor the first test, the only possible sequence of operations which minimizes the number of operations is:   Choose i=2, x=5. Perform a_2 := a_2 \bmod 5 = 2. For the second test, it is impossible to obtain a permutation of integers from 1 to n.
4
2
1 7
3
1 5 4
4
12345678 87654321 20211218 23571113
9
1 2 3 4 18 19 5 6 7

1 -1 4 2 
['binary search', 'greedy', 'math', 'sortings', '*1300']