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 collections import Counter
from sys import *
from collections import defaultdict as dd
from math import *

# sys.stdin = open('input.txt', 'r')  
# sys.stdout = open('output.txt', 'w')

#input functions
def inp():
    return int(stdin.readline().strip())
def vinp():
    return map(int,stdin.readline().strip().split())
def linp():
    return list(map(int,stdin.readline().strip().split()))
def sinp(n = 1):
    if n==1:
        return stdin.readline().strip()
    elif n==2:
        return list(stdin.readline().strip())
    else:
        return list(stdin.readline().split())

#output function
def pr(*x, end = "\n"):
    print(*x,end = end)

#others
def mod(f, val = 1000000007):
    return f % val
def csort(c):
    sorted(c.items(), key=lambda pair: pair[1], reverse=True)
def indc(l,n):
    c={}
    for i in range(n):
        c[l[i]]=c.get(l[i],[])+[i+1]
    return c

if __name__ =="__main__":
    cou=inp()
    for _ in range(cou):
        n = inp()
        l = linp()
        c = dd(int)
        l2 = []
        for i in range(n):
            if l[i]>=1 and l[i]<=n and not c[l[i]]:
                c[l[i]] = 1
            else:
                l2.append(l[i])
        l2.sort()
        l3 = [0 for i in range(n+1)]
        for i in c.keys():
            l3[i] = 1
        k=0
        p = True
        for i in range(1,n+1):
            if not l3[i]:
                if i <= (l2[k]//2 - (l2[k]%2==0)):
                    k+=1
                    l3[i]=1
                else:
                    p = False
                    break
        if p:
            pr(len(l2))
        else:
            pr(-1)