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

#include<bits/stdc++.h>
using namespace std;
 
#define ll            long long int
#define di(x)         ll x;cin>>x
#define dia           di(a)
#define din           di(n)
#define dim           di(m)
#define dik           di(k)
#define dit           di(t)
#define dix           di(x)
#define diy           di(y)
#define diz           di(z)
#define veci          vector<int>
#define vecll         vector<ll>
#define pb            push_back
#define po            pop_back
#define all(x)        x.begin(),x.end()
#define forl(i,l,u,m)   for(ll i=l; i<u; i+=m)
#define for1(i,l,u)    forl(i,l,u,1)
#define fors(n)       forl(i,0,n,1)
#define el            <<"\n"
#define PI            3.14159265359
#define MOD             int(1e9+7)
typedef pair<ll,ll> pairs;
/*****************************/

int main()
{
    ios_base::sync_with_stdio(false);
    cin.tie(NULL);                                                    
    dit;
    while(t--)
    {  din;
    ll a[n];  bool b[n+1]={false}; vecll v,v1;
     fors(n) {cin>>a[i]; if(a[i]<=n && a[i]>0) b[a[i]]=true; else v.pb(a[i]);}
     sort(all(v));
     for1(i,1,n+1) { if(b[i]==false) v1.pb(i);}
     if(v1.size()!=v.size()) cout<<"-1" el;
     else{ ll c=0;
         fors(v.size())
         {  
             if(v[i]<=2*v1[i]) { c=1; break;}
            
         }
          if(c==1) cout<<"-1" el;
             else cout<<v.size() el;
     }
    }
}