human
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.

def  Write me a Python code to determine the minimum number of operations needed to make the array a permutation of integers 1 to n?
assistant
#Here is Python code to determine the minimum number of operations needed to make the array a permutation of integers 1 to n.
main():
        
    # if number is even, cannot reach [n // 2, n - 1]
    # if number is odd, cannot reach [n // 2 + 1, n - 1]
    
    t = int(input())
    allans = []
    for _ in range(t):
        n = int(input())
        a = readIntArr()
        
        takenIndexes = set()
        vi = [False] * (n + 1)
        for i, x in enumerate(a):
            if 1 <= x <= n and vi[x] == False:
                vi[x] = True
                takenIndexes.add(i)
        
        remainingItems = []
        for i in range(n):
            if i not in takenIndexes:
                remainingItems.append(a[i])
        remainingItems.sort()
        
        requiredItems = []
        for x in range(1, n + 1):
            if vi[x] == False:
                requiredItems.append(x)
        
        # map remainingItems to requiredItems Greedily in sequence
        m = len(remainingItems)
        possible = True
        for i in range(m):
            if requiredItems[i] * 2 >= remainingItems[i]:
                possible = False
        if possible:
            allans.append(m)
        else:
            allans.append(-1)
        
    multiLineArrayPrint(allans)
    
    return


import sys
input=sys.stdin.buffer.readline #FOR READING PURE INTEGER INPUTS (space separation ok)
# input=lambda: sys.stdin.readline().rstrip("\r\n") #FOR READING STRING/TEXT INPUTS.

def oneLineArrayPrint(arr):
    print(' '.join([str(x) for x in arr]))
def multiLineArrayPrint(arr):
    print('\n'.join([str(x) for x in arr]))
def multiLineArrayOfArraysPrint(arr):
    print('\n'.join([' '.join([str(x) for x in y]) for y in arr]))
 
def readIntArr():
    return [int(x) for x in input().split()]
# def readFloatArr():
#     return [float(x) for x in input().split()]
 
def makeArr(defaultValFactory,dimensionArr): # eg. makeArr(lambda:0,[n,m])
    dv=defaultValFactory;da=dimensionArr
    if len(da)==1:return [dv() for _ in range(da[0])]
    else:return [makeArr(dv,da[1:]) for _ in range(da[0])]
 
def queryInteractive(a, b, c):
    print('? {} {}...