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 Solution {
	public static void main(String[] args) throws IOException {
		try {
			int t = sc.nextInt();
			while (t-- > 0)
				solve();
		} catch (Exception e) {
			return;
		}
	}

	// SOLUTION STARTS HERE
	// :::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
	static void solve() {
		int n = sc.nextInt();
		int a[] = sc.readIntArray(n);
		Arrays.sort(a);
		int c = 0;
		for (int i = 0; i < n; i++) {
			if (a[i] != i + 1) {
				if (a[i] % (a[i] - (i + 1)) == i + 1)
					c++;
				else {
					System.out.println(-1);
					return;
				}
			}
		}
		System.out.println(c);
	}
	// SOLUTION ENDS HERE
	// :::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::

	static boolean[] seiveOfEratosthenes(int n) {
		boolean[] isPrime = new boolean[n + 1];
		Arrays.fill(isPrime, true);
		for (int i = 2; i * i <= n; i++) {
			for (int j = i * i; j <= n; j += i) {
				isPrime[j] = false;
			}
		}
		return isPrime;
	}

	static int gcd(int a, int b) {
		if (b == 0)
			return a;
		return gcd(b, a % b);
	}

	static boolean isPrime(long n) {
		if (n < 2)
			return false;
		for (int i = 2; i * i <= n; i++) {
			if (n % i == 0)
				return false;
		}
		return true;
	}

	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());
		}

		int[] readIntArray(int n) {
			int a[] = new int[n];
			for (int i = 0; i < n; i++) {
				a[i] = Integer.parseInt(next());
			}
			return a;
		}

		void printIntArray(int a[]) {
			for (int i = 0; i < a.length; i++) {
				System.out.print(a[i] + " ");
			}
		}

		long[] readLongArray(int n) {
			long a[] = new long[n];
			for (int i = 0; i < n; i++) {
				a[i] = Long.parseLong(next());
			}
			return a;
		}

		void printLongArray(long a[]) {
			for (int i = 0; i < a.length; i++) {
				System.out.print(a[i] + " ");
			}
		}

		double nextDouble() {
			return Double.parseDouble(next());
		}

		String nextLine() {
			String str = "";
			try {
				str = br.readLine();
			} catch (IOException e) {
				e.printStackTrace();
			}
			return str;
		}
	}

	static class OutputWriter {
		private final PrintWriter writer;

		public OutputWriter(OutputStream outputStream) {
			writer = new PrintWriter(new BufferedWriter(new OutputStreamWriter(outputStream)));
		}

		public OutputWriter(Writer writer) {
			this.writer = new PrintWriter(writer);
		}

		public void print(Object... objects) {
			for (int i = 0; i < objects.length; i++) {
				if (i != 0)
					writer.print(' ');
				writer.print(objects[i]);
			}
		}

		public void println() {
			writer.print("\n");
		}

		public void printLine(Object... objects) {
			print(objects);
			writer.println();
		}

		public void close() {
			writer.close();
		}

		public void flush() {
			writer.flush();
		}

	}

	private static final FastReader sc = new FastReader();
	private static final OutputWriter out = new OutputWriter(System.out);
}
