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


// package com.company;

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

public final class Main {

    FastReader s;

    public static void main(String[] args) throws java.lang.Exception {

        new Main().run();

    }

    void run() {
        s = new FastReader();
        solve();
    }




    StringBuffer sb;


    void solve() {

        sb = new StringBuffer();

        for (int T = s.nextInt(); T > 0; T--)
        {

            start();


        }


        System.out.print(sb);

    }



    void start()
    {

        int n = s.nextInt();
          long arr[] = longArr(n);
//          sort(arr);
        TreeMap<Long,Long> x = new TreeMap<>();
        for(long i : arr)
        {
            x.put(i,x.getOrDefault(i,0l)+1);
        }
          int cnt = 0;
          for(long i = 1; i<=n; i++)
          {

             if(x.containsKey(i))
             {
                 x.put(i,x.get(i)-1);
                 if(x.get(i) == 0)
                     x.remove(i);
             }
             else if(x.higherKey(2*i) != null)
             {
                 long y = x.higherKey(2*i);
                 x.put(y,x.get(y)-1);
                 if(x.get(y) == 0)
                     x.remove(y);
                 cnt++;
             }
             else
             {
                 sb.append("-1\n");
                 return;
             }



          }
          sb.append(cnt+"\n");

    }






    class Pair {
        int a;
        int b;

        public Pair(int a, int b) {
            this.a = a;
            this.b = b;
        }

        void print() {
            System.out.println(a + " " + b);
        }

    }

    class segmentTree{
         int[] tree;
         int n;
         public segmentTree(int[] nums) {
             if (nums.length > 0) {
                 n = nums.length;
                 tree = new int[n * 2];
                 buildTree(nums);
             }
         }

         private void buildTree(int[] nums) {
             for (int i = n, j = 0;  i < 2 * n; i++,  j++)
                 tree[i] = nums[j];
             for (int i = n - 1; i > 0; --i)
                 tree[i] = tree[i * 2] + tree[i * 2 + 1];
         }

         void update(int pos, int val) {
             pos += n;
             tree[pos] = val;
             while (pos > 0) {
                 int left = pos;
                 int right = pos;
                 if (pos % 2 == 0) {
                     right = pos + 1;
                 } else {
                     left = pos - 1;
                 }
                 // parent is updated after child is updated
                 tree[pos / 2] = tree[left] + tree[right];
                 pos /= 2;
             }
         }

         public int sumRange(int l, int r) {
             // get leaf with value 'l'
             l += n;
             // get leaf with value 'r'
             r += n;
             int sum = 0;
             while (l <= r) {
                 if ((l % 2) == 1) {
                     sum += tree[l];
                     l++;
                 }
                 if ((r % 2) == 0) {
                     sum += tree[r];
                     r--;
                 }
                 l /= 2;
                 r /= 2;
             }
             return sum;
         }

     }

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

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

    long power(long x, long y, long p) {
        long res = 1;


        x = x % p;

        while (y > 0) {

            if ((y & 1) > 0)
                res = (res * x) % p;


            y = y >> 1;
            x = (x * x) % p;
        }
        return res;
    }


    int lower_bound(int[] arr, int key) {

        int i = 0;
        int j = arr.length - 1;
        // if(arr[i] > key)return -1;
        if (arr[j] < key)
            return -1;

        while (i < j) {
            int mid = (i + j) / 2;

            if (arr[mid] == key) {
                j = mid;
            } else if (arr[mid] < key) {
                i = mid + 1;
            } else
                j = mid - 1;
        }

        return i;
    }

    int upper_bound(int[] arr, int key) {

        int i = 0;
        int j = arr.length - 1;
        if (arr[j] <= key)
            return j + 1;

        while (i < j) {
            int mid = (i + j) / 2;

            if (arr[mid] <= key) {
                i = mid + 1;
            } else
                j = mid;
        }

        return i;
    }

    int find(int dsu[], int i) {
        if (dsu[i] == i)
            return i;
        dsu[i] = find(dsu, dsu[i]);
        return dsu[i];
    }

    void union(int dsu[], int i, int j) {
        int a = find(dsu, i);
        int b = find(dsu, j);
        dsu[a] = b;
    }

    static void sort(int[] a) {
        ArrayList<Integer> l = new ArrayList<>();
        for (int i : a)
            l.add(i);
        Collections.sort(l);
        for (int i = 0; i < a.length; i++)
            a[i] = l.get(i);
    }

    static void sort(long[] a) {
        ArrayList<Long> l = new ArrayList<>();
        for (long i : a)
            l.add(i);
        Collections.sort(l);
        for (int i = 0; i < a.length; i++)
            a[i] = l.get(i);
    }

    static String sort(String s) {
        Character ch[] = new Character[s.length()];
        for (int i = 0; i < s.length(); i++) {
            ch[i] = s.charAt(i);
        }
        Arrays.sort(ch);
        StringBuffer st = new StringBuffer("");
        for (int i = 0; i < s.length(); i++) {
            st.append(ch[i]);
        }
        return st.toString();
    }

    // long array input
    public long[] longArr(int len) {
        // long arr input
        long[] arr = new long[len];
        String[] strs = s.nextLine().trim().split("\\s+");
        for (int i = 0; i < len; i++) {
            arr[i] = Long.parseLong(strs[i]);

        }
        return arr;
    }

    // int arr input
    public int[] intArr(int len) {
        // long arr input
        int[] arr = new int[len];
        String[] strs = s.nextLine().trim().split("\\s+");
        for (int i = 0; i < len; i++) {
            arr[i] = Integer.parseInt(strs[i]);

        }
        return arr;
    }

    public void printArray(int[] A) {
        System.out.println(Arrays.toString(A));
    }

    public void printArray(long[] A) {
        System.out.println(Arrays.toString(A));
    }



    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;
        }
    }

}
