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.
assistant
#Here is Python code to determine the minimum number of operations needed to make the array a permutation of integers 1 to n.

class SegTree:
    def __init__(self, init_val, ide_ele, segfunc):
        self.n = len(init_val)
        self.num = 2**(self.n-1).bit_length()
        self.ide_ele = ide_ele
        self.segfunc = segfunc
        self.seg = [ide_ele]*2*self.num
        # set_val
        for i in range(self.n):
            self.seg[i+self.num] = init_val[i]
        # built
        for i in range(self.num-1, 0, -1):
            self.seg[i] = self.segfunc(self.seg[2*i], self.seg[2*i+1])

    def update(self, k, x):
        k += self.num
        self.seg[k] = x
        while k:
            k = k >> 1
            self.seg[k] = self.segfunc(self.seg[2*k], self.seg[2*k+1])

    def query(self, l, r):
        if r <= l:
            return self.ide_ele
        l += self.num
        r += self.num
        lres = self.ide_ele
        rres = self.ide_ele
        while l < r:
            if r & 1:
                r -= 1
                rres = self.segfunc(self.seg[r], rres)
            if l & 1:
                lres = self.segfunc(lres, self.seg[l])
                l += 1
            l = l >> 1
            r = r >> 1
        res = self.segfunc(lres, rres)
        return res

    def __str__(self): # for debug
        arr = [self.query(i,i+1) for i in range(self.n)]
        return str(arr)

import sys
import io, os
input = sys.stdin.buffer.readline
#input = io.BytesIO(os.read(0,os.fstat(0).st_size)).readline

import heapq
from collections import Counter
INF = 10**18

t = int(input())
for _ in range(t):
    n = int(input())
    A = list(map(int, input().split()))
    ans = 0
    C = Counter(A)
    seg = SegTree(list(range(1, n+1)), -INF, max)
    for a in A:
        if 1 <= a <= n:
            seg.update(a-1, -INF)
    A.sort(reverse=True)
    flag = True
    for a in A:
        if a > n:
            r = (a-1)//2
            b = seg.query(0, min(seg.n, r))
            #print(r, b)
            if b == -INF:
                flag = False
                break
            ans += 1
            seg.update(b-1, -INF)
        else:
            if...