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 mod 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).

Input

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 ⋅ 10^5.

Output

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.

Example

Input


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

Note

For 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 mod 5 = 2. 



For the second test, it is impossible to obtain a permutation of integers from 1 to n.
8
2
2 3
3
3 4 5
1
1
1
2
1
3
1
4
1
12071207
5
5 5 5 9 14

1
2
0
-1
1
1
1
4

from sys import stdin, stdout
rd = lambda: list(map(int, stdin.readline().split()))
rds = lambda: stdin.readline().rstrip()
ii = lambda: int(stdin.readline())
INF = 1 << 62
mod = 10**9 + 7

for _ in range(ii()):
    n = ii()
    ar = rd()
    p = set(i for i in range(1, n+1))

    b = []
    for x in ar:
        if x in p:
            p.discard(x)
        else:
            b.append(x)
    
    limits = []
    for x in b:
        if x % 2 == 1:
            limits.append(x // 2)
        else:
            limits.append(x // 2 - 1)
    
    p = list(p)
    p.sort()
    limits.sort()

    res = len(p)
    for x,y in zip(p, limits):
        if y < x:
            res = -1
            break

    print(res)

#stdout.write(' '.join(map(str, ar)))
#stdout.write(f'{res}')

