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.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.*;
public class C{
	public static void main(String[] args){
		FastReader sc = new FastReader();
		int t=sc.nextInt();
		next:while(t-->0){
			int n=sc.nextInt();
			boolean find[]=new boolean [n];
			Map<Integer,Integer> map= new HashMap<Integer, Integer>();
			for(int i=0;i<n;i++) {
				int x=sc.nextInt();
				if(map.containsKey(x))map.put(x, map.get(x)+1);
				else map.put(x, 1);
			}
			ArrayList<Integer> ans = new ArrayList<Integer>();
			for(Integer i:map.keySet()) {
				if(i<=n)find[i-1]=true;
				for(int j=0;j<map.get(i)-1;j++) ans.add(i);
				if(i>n)ans.add(i);
			}
			Collections.sort(ans,Comparator.reverseOrder());
			ArrayList<Integer>want= new ArrayList<Integer>();
			for(int i=n-1;i>=0;i--)if(!find[i])want.add(i+1);
			for(int i=0;i<ans.size();i++) {
				if(ans.get(i)%(Math.abs(ans.get(i)-want.get(i)))!=want.get(i)) {
					System.out.println(-1);
					continue next;
				}
			}
			System.out.println(ans.size());
		}
    }
	static void sort(int a[]) {
		ArrayList<Integer> aa= new ArrayList<>();
		for(int i:a)aa.add(i);
		Collections.sort(aa);
		int j=0;
		for(int i:aa)a[j++]=i;
	}
	static class pair {
		int x;int y;
		 pair(int x,int y){
			this.x=x;
			this.y=y;
		}
		
	}
	static ArrayList<Integer> primeFac(int n){
		ArrayList<Integer>ans = new ArrayList<Integer>();
		int lp[]=new int [n+1];
		Arrays.fill(lp, 0);  	//0-prime
		for(int i=2;i<=n;i++) {
			if(lp[i]==0) {
				for(int j=i;j<=n;j+=i) {
					if(lp[j]==0) lp[j]=i;
				}
			}
		}
		int fac=n;
		while(fac>1) {
			ans.add(lp[fac]);
			fac=fac/lp[fac];
		}
		print(ans);
		return ans;
	}
	static ArrayList<Long> prime_in_given_range(long l,long r){
		ArrayList<Long> ans= new ArrayList<>();
		int n=(int)Math.sqrt(r)+1;
		int prime[]=sieve_of_Eratosthenes(n);
		long res[]=new long [(int)(r-l)+1];
		for(int i=0;i<=r-l;i++) {
			res[i]=i+l;
		}
		for(int i=0;i<prime.length;i++) {
			if(prime[i]==1) {
				System.out.println(2);
				for(int j=Math.max((int)i*i, (int)(l+i-1)/i*i);j<=r;j+=i) {
					res[j-(int)l]=0; 
				}
			}
		}
		for(long i:res) if(i!=0)ans.add(i);
		return ans;
	}
	static int [] sieve_of_Eratosthenes(int n) {
		int prime[]=new int [n];
		Arrays.fill(prime, 1);  // 1-prime | 0-not prime
		prime[0]=prime[1]=0;
		for(int i=2;i<n;i++) {
			if(prime[i]==1) {
				for(int j=i*i;j<n;j+=i) {
					prime[j]=0;
				}
			}
		}
		return prime;
	}
	static long binpow(long a,long b) {
		long res=1;
		if(b==0)return a;
		if(a==0)return 1;
		while(b>0) {
			if((b&1)==1) {
				res*=a;
			}
			a*=a;
			b>>=1;
		}
		return res;
	}
	static void print(int a[]) {
		System.out.println(a.length);
		for(int i:a) {
			System.out.print(i+" ");
		}
		System.out.println();
	}
	static void print(long a[]) {
		System.out.println(a.length);
		for(long i:a) {
			System.out.print(i+" ");
		}
		System.out.println();
	}
	static long rolling_hashcode(String s ,int st,int end,long Hashcode,int n) {
		if(end>=s.length()) return -1;
		int mod=1000000007;
		
		Hashcode=Hashcode-(s.charAt(st-1)*(long)Math.pow(27,n-1));
		Hashcode*=10;
		
		Hashcode=(Hashcode+(long)s.charAt(end))%mod;
		return Hashcode;
		
	}
	static long  hashcode(String s,int n) {
		long code=0;
		for(int i=0;i<n;i++) {
			code+=((long)s.charAt(i)*(long)Math.pow(27, n-i-1)%1000000007);
		}
		return code;
	}
	static void print(ArrayList<Integer> a) {
		System.out.println(a.size());
		for(long i:a) {
			System.out.print(i+" ");
		}
		System.out.println();
	}
	static class FastReader {
		BufferedReader br;
		StringTokenizer st;

		public FastReader()
		{
			br = new BufferedReader(
				new InputStreamReader(System.in));
		}
		int [] fastArray(int n) {
			int a[]=new int [n];
			for(int i=0;i<n;i++) {
				a[i]=nextInt();
			}
			return a;
		}
		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;
		}
	}

}