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

import sys
import math as mt
import collections as cc
input = sys.stdin.readline
I = lambda : list(map(int,input().split()))
mod = 10**9+7
def ch(temp):
	tans = 0
	for i in range(len(temp)-k-1,-1,-k):
		tans += 2*abs(temp[i])
	return tans 

for tc in range(int(input())):
	n, =I()
	ar = I()
	ar.sort()
	visi = cc.defaultdict(int)
	temp = []
	x = []
	c = cc.Counter(ar)

	for i in range(1,n+1):
		if c[i]:
			visi[i] = 1
			continue
		else:
			x.append(i)
	#print(visi)
	#print(x)
	xx = []
	for i in ar:
		if visi[i]:
			visi[i] = 0
			continue
		xx.append(i)
	#print(xx)
	tf = 1
	x.sort()
	xx.sort()
	for i in range(len(x)):
		req = x[i]
		hand = (xx[i]-1)//2
		if hand>=req:
			continue
		tf = 0
	if tf:
		print(len(x))
	else:
		print(-1)

	# for i in range(n):
	# 	if ar[i]==i+1:
	# 		visi[i+1] = 1
	# 		continue
	# 	else:
	# 		x.append(i+1)
	# 		req = i+1
	# 		hand = (ar[i]-1)//2
	# 		temp.append((req,hand))
	# temp.sort()
	# print(temp)
	# tf = 1
	# ans = 0
	# for j in range(len(temp)):
	# 	if temp[j][1]>=(x[j]):
	# 		ans+=1
	# 		continue
	# 	tf = 0
	# if tf:
	# 	print(ans)
	# else:
	# 	print(-1)

