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 java.io.*;
import java.util.*;


public class ComdeFormces {
	public static void main(String[] args) throws Exception{
		// TODO Auto-generated method stub
		FastReader sc=new FastReader();
		BufferedWriter log = new BufferedWriter(new OutputStreamWriter(System.out));
		int t=sc.nextInt();
		while(t--!=0) {
		int n=sc.nextInt();
		 long a[]=new long[n];
		 for(int i=0;i<n;i++) {
			 a[i]=sc.nextLong();
		 }
		 boolean vis[]=new boolean[n+1];
		 boolean ans=true;
		 int cnt=0;
		 Arrays.sort(a);
		 for(int i=0;i<n;i++) {
			 int tt=(int)a[i];
			 if(a[i]>=1 && a[i]<=n && !vis[tt]) {
				 vis[tt]=true;
			 }
			 else {
				if(a[i]-(i+1)>i+1) {
					cnt++;
				}
				else {
					ans=false;
					break;
				}
			 }
		 }
		
		if(ans)log.write(cnt+"");
		else log.write("-1");
		 
		 
		log.write("\n");
		log.flush();
		
		}
		
	}
static long find(int s,long a[]) {
	if(s>=a.length)return -1;
	long num=a[s];
	for(int i=s;i<a.length;i+=2) {
		num=gcd(num,a[i]);
		if(num==1 || num==0)return -1;
	}
	return  num;
}	
static long gcd(long a,long b) {
	if(b==0)return a;
	else return gcd(b,a%b);
}	
static long factmod(long n,long mod,long img) {
	if(n==0)return 1;
	long ans=1;
	long temp=1;
	while(n--!=0) {
		if(temp!=img) {
		ans=((ans%mod)*((temp)%mod))%mod;
		}
		temp++;
	}
	return ans%mod;
}	
static long eval(ArrayList<Integer> a, int k) {
	if(a.size()<1 )return 0;
	int i=a.size()-1;
	long ans=0;
	while(i>=0) {
		int temp=k;
		int prev=0;
		while(temp--!=0 && i>=0) {
			ans+=Math.abs(a.get(i)-prev);
			if(temp==0 || i==0)ans+=a.get(i);
			prev=a.get(i);
			i--;
		}
	}
	return ans;
}	
static int bs(LinkedList<Long> a ,long num) {
	int start=0;
	int end=a.size()-1;
	int tempAns=-1;
    while(start<=end) {
    	int mid=start+(end-start)/2;
    	if(a.get(mid)-num>num) {
    		tempAns=mid;
    		end=mid-1;
    	}
    	else if(a.get(mid)-num<=num)start=mid+1;
    
    }
    if(tempAns!=-1)return tempAns;
	return -1;
}	
	
	
//utils	
public static class trip{
	int a,b,c;
	public trip(int a,int b,int c) {
		this.a=a;
		this.b=b;
		this.c=c;
	}
	public int compareTo(trip q) {
		return this.c-q.c;
	}
}	
	static void mergesort(long[] a,int start,int end) {
		if(start>=end)return;
		int mid=start+(end-start)/2;
		mergesort(a,start,mid);
		mergesort(a,mid+1,end);
		merge(a,start,mid,end);
	}
	static void merge(long []a, int start,int mid,int end) {
		int ptr1=start;
		int ptr2=mid+1;
		long b[]=new long[end-start+1];
		int i=0;
		while(ptr1<=mid && ptr2<=end) {
			if(a[ptr1]<=a[ptr2]) {
				b[i]=a[ptr1];
				ptr1++;
				i++;
			}
			else {
				b[i]=a[ptr2];
				ptr2++;
				i++;
			}
		}
		while(ptr1<=mid) {
			b[i]=a[ptr1];
			ptr1++;
			i++;
		}
		while(ptr2<=end) {
			b[i]=a[ptr2];
			ptr2++;
			i++;
		}
		for(int j=start;j<=end;j++) {
			a[j]=b[j-start];
		}
	}
	public static class FastReader {

		BufferedReader b;
		StringTokenizer s;
		public FastReader() {
			b=new BufferedReader(new InputStreamReader(System.in));
		}
		String next() {
			while(s==null ||!s.hasMoreElements()) {
				try {
					s=new StringTokenizer(b.readLine());
				}
				catch(IOException e) {
					e.printStackTrace();
				}
			}
			return s.nextToken();
		}
		public int nextInt() {
			return Integer.parseInt(next());
		}
		public long nextLong() {
			return Long.parseLong(next());
		}
		public double nextDouble() {
			return Double.parseDouble(next());
		}
		String nextLine() {
			String str="";
			try {
				str=b.readLine();
			}
			catch(IOException e) {
				e.printStackTrace();
			}
			return str;
		}
		boolean hasNext() {
		    if (s != null && s.hasMoreTokens()) {
		        return true;
		    }
		    String tmp;
		    try {
		        b.mark(1000);
		        tmp = b.readLine();
		        if (tmp == null) {
		            return false;
		        }
		        b.reset();
		    } catch (IOException e) {
		        return false;
		    }
		    return true;
		}
}
public static class pair{
	int a,b;
	public pair(int a,int b) {
		this.a=a;
		this.b=b;
	}
	public int compareTo(pair b) {
		return this.a-b.a;
	}
}	
}
