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.IOException;

    import java.io.IOException;
    import java.io.InputStream;
    import java.io.PrintWriter;
    import java.util.*;

    public class PaprikaandPermutation {
        static InputReader inputReader=new InputReader(System.in);
        static void solve() {
            int n = inputReader.nextInt();
            TreeMap<Long, Integer> treeMap = new TreeMap<>();
            long arr[] = new long[n];
            for (int i=0;i<n;i++)
            {
                arr[i]=inputReader.nextLong();
            }
            HashSet<Long>present=new HashSet<>();
            for (long ele:arr) {
                if (ele>n) {
                    treeMap.put(ele, treeMap.getOrDefault(ele, 0) + 1);
                }
                else {
                    if (!present.contains(ele)) {
                        present.add(ele);
                    }
                    else
                    {
                        treeMap.put(ele, treeMap.getOrDefault(ele, 0) + 1);
                    }
                }
            }
            int count=0;
            for (long i=1;i<=n;i++)
            {
                if (present.contains(i))
                {
                    continue;
                }
                else
                {
                    long no=2*i+1;
                    Long key=treeMap.ceilingKey(no);
                    if (key==null)
                    {
                        out.println(-1);
                        return;
                    }
                    count++;
                    treeMap.put(key,treeMap.getOrDefault(key,0)-1);
                    if (treeMap.get(key)==0)
                    {
                        treeMap.remove(key);
                    }
                }
            }
            out.println(count);
        }
        static PrintWriter out=new PrintWriter((System.out));
        public static void main(String args[])throws IOException
        {
            int t=inputReader.nextInt();
            while (t-->0) {
                solve();
            }
                out.close();
        }

        static void Sort(int arr[])
        {
            List<Integer>list=new ArrayList<>();
            for (int ele:arr)
            {
                list.add(ele);
            }
            Collections.sort(list);
            for (int i=0;i<list.size();i++)
            {
                arr[i]=list.get(i);
            }
        }
        static void sortDec(int arr[])
        {
            int len=arr.length;
            List<Integer>list=new ArrayList<>();
            for(int ele:arr)
            {
                list.add(ele);
            }
            Collections.sort(list,Collections.reverseOrder());
            for(int i=0;i<len;i++) {
                arr[i] = list.get(i);
            }
        }
        static class InputReader {

            private InputStream stream;
            private byte[] buf = new byte[8192];
            private int curChar, snumChars;
            private SpaceCharFilter filter;

            public InputReader(InputStream stream) {
                this.stream = stream;
            }

            public int snext() {
                if (snumChars == -1)
                    throw new InputMismatchException();
                if (curChar >= snumChars) {
                    curChar = 0;
                    try {
                        snumChars = stream.read(buf);
                    } catch (IOException e) {
                        throw new InputMismatchException();
                    }
                    if (snumChars <= 0)
                        return -1;
                }
                return buf[curChar++];
            }

            public int nextInt() {
                int c = snext();
                while (isSpaceChar(c))
                    c = snext();
                int sgn = 1;
                if (c == '-') {
                    sgn = -1;
                    c = snext();
                }
                int res = 0;
                do {
                    if (c < '0' || c > '9')
                        throw new InputMismatchException();
                    res *= 10;
                    res += c - '0';
                    c = snext();
                } while (!isSpaceChar(c));
                return res * sgn;
            }

            public long nextLong() {
                int c = snext();
                while (isSpaceChar(c))
                    c = snext();
                int sgn = 1;
                if (c == '-') {
                    sgn = -1;
                    c = snext();
                }
                long res = 0;
                do {
                    if (c < '0' || c > '9')
                        throw new InputMismatchException();
                    res *= 10;
                    res += c - '0';
                    c = snext();
                } while (!isSpaceChar(c));
                return res * sgn;
            }

            public int[] nextIntArray(int n) {
                int a[] = new int[n];
                for (int i = 0; i < n; i++)
                    a[i] = nextInt();
                return a;
            }

            public String readString() {
                int c = snext();
                while (isSpaceChar(c))
                    c = snext();
                StringBuilder res = new StringBuilder();
                do {
                    res.appendCodePoint(c);
                    c = snext();
                } while (!isSpaceChar(c));
                return res.toString();
            }

            public boolean isSpaceChar(int c) {
                if (filter != null)
                    return filter.isSpaceChar(c);
                return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
            }

            public interface SpaceCharFilter {
                public boolean isSpaceChar(int ch);
            }
        }
    }
