human
PYTHON3 solution for "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.":


 ... Give me a Python program to determine the minimum number of operations needed to make the array a permutation of integers 1 to n?
assistant
#Here is Python program to determine the minimum number of operations needed to make the array a permutation of integers 1 to n.
 def f(a):
	bad=[]
	n=len(a)
	vis=[-1]*(len(a)+1)
	nt=[]
	for i in a:
		if i>n or vis[i]!=-1:
			bad.append(i)
		else:
			vis[i]=1
	for i in range(1,n+1):
		if vis[i]==-1:
			nt.append(i)
	nt.sort(reverse=True)
	bad.sort(reverse=True)
	ans=len(bad)
	# print(nt,bad)
	for val in bad:
		id=None
		for i in range(len(nt)):
			if val%(val-nt[i])==nt[i]:
				id=i
				break
		if id==None:
			return -1
		nt.pop(id)
	return ans

for _ in range(int(input())):
	a=input()
	l=list(map(int,input().strip().split()))
	print(f(l))