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.util.*;

import java.io.*;
public class A1618 
{
	static int md=(int)(1e9);
	
	public static void process()throws IOException
	{
	   int n=I();
	   int a[]=Ai(n);
	   int c=0;
	   for(int i=0;i<n;i++)
	   {
		   if(a[i]<=n){
			  continue;
		   }
		   else
		   {
			   a[i]=a[i]%(a[i]/2+1);
			   c++;
		   }
	   }
	   sort(a);
	   boolean flag=false;
	for(int i=0;i<n;i++)
	{
		if(a[i]>=i+1)
		{
			continue;
		}
		else
		{
			flag=true;
			break;
		}
	}
	if(flag)
	{
		pn(-1);
	}
	else
	{
		pn(c);
	}
			
	}
	static class FastReader {
		BufferedReader br;
		StringTokenizer st;
		
		public FastReader()
		{
			br = new BufferedReader(
					new InputStreamReader(System.in));
		}
		
		String next()
		{
			while (st == null || !st.hasMoreElements()) {
				try {
					st = new StringTokenizer(br.readLine());
				}
				catch (IOException e) {
					e.printStackTrace();
				}
			}
			return st.nextToken();
		}
		
		int nextInt() { return Integer.parseInt(next()); }
		
		long nextLong() { return Long.parseLong(next()); }
		
		double nextDouble()
		{
			return Double.parseDouble(next());
		}
		
		String nextLine()
		{
			String str = "";
			try {
				str = br.readLine();
			}
			catch (IOException e) {
				e.printStackTrace();
			}
			return str;
		}
	}
	static void sort(int[] a) {
		int n = a.length;
		Random r = new Random();
		for (int i = 0; i < a.length; i++) {
			int oi = r.nextInt(n);
			int temp = a[i];
			a[i] = a[oi];
			a[oi] = temp;
		}
		Arrays.sort(a);
	}
	static FastReader sc = new FastReader();
	static PrintWriter out = new PrintWriter(System.out);
	static void pn(Object o){out.println(o);out.flush();}
	static void p(Object o){out.print(o);out.flush();}
	static void pni(Object o){out.println(o);System.out.flush();}
	static int I() throws IOException{return sc.nextInt();}
	static long L() throws IOException{return sc.nextLong();}
	static double D() throws IOException{return sc.nextDouble();}
	static String S() throws IOException{return sc.next();}
	static char C() throws IOException{return sc.next().charAt(0);}
	static int[] Ai(int n) throws IOException{int[] arr = new int[n];for (int i = 0; i < n; i++)arr[i] = I();return arr;}
	static String[] As(int n) throws IOException{String s[] = new String[n];for (int i = 0; i < n; i++)s[i] = S();return s;}
	static long[] Al(int n) throws IOException {long[] arr = new long[n];for (int i = 0; i < n; i++)arr[i] = L();return arr;}
	static void dyn(int dp[][],int n,int m,int z)throws IOException {for(int i=0;i<n;i++){ for(int j=0;j<m;j++){ dp[i][j]=z;}} }
	
//	*--------------------------------------------------------------------------------------------------------------------------------*//
	
	public static void main(String[] args)throws IOException{try{boolean oj=true;if(oj==true)
	{PrintWriter out=new PrintWriter(System.out);}
	else
	{out=new PrintWriter("output.txt");}
	long T=L();while(T-->0)
	{
	process();
	}out.flush();out.close();}catch(Exception e){return;}}}
//*-----------------------------------------------------------------------------------------------------------------------------------*//
	