B'Paprika loves permutations. She has an array a_1, a_2, ... , 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 <= i <= 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). Each test contains multiple test cases. The first line contains a single integer t ( 1 <= t <= 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 <= n <= 10^5 ). The second line of each test case contains n integers a_1, a_2, ... , a_n . ( 1 <= a_i <= 10^9 ). It is guaranteed that the sum of n over all test cases does not exceed 2 cdot 10^5 . For 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. For the first test, the only possible sequence of operations which minimizes the number of operations is: For the second test, it is impossible to obtain a permutation of integers from 1 to n . '...