To help those contestants who struggle a lot in contests, the headquarters of Codeforces are planning to introduce Division 5. In this new division, the tags of all problems will be announced prior to the round to help the contestants.

The contest consists of n problems, where the tag of the i-th problem is denoted by an integer a_i.

You want to AK (solve all problems). To do that, you must solve the problems in some order. To make the contest funnier, you created extra limitations on yourself. You do not want to solve two problems consecutively with the same tag since it is boring. Also, you are afraid of big jumps in difficulties while solving them, so you want to minimize the number of times that you solve two problems consecutively that are not adjacent in the contest order.

Formally, your solve order can be described by a permutation p of length n. The cost of a permutation is defined as the number of indices i (1≤ i<n) where |p_{i+1}-p_i|>1. You have the requirement that a_{p_i}≠ a_{p_{i+1}} for all 1≤ i< n.

You want to know the minimum possible cost of permutation that satisfies the requirement. If no permutations meet this requirement, you should report about it.

Input

The first line contains a single integer t (1≤ t≤ 10^4) — the number of test cases.

The first line of the description of each test case contains a single integer n (1 ≤ n ≤ 10^5) — the number of problems in the contest.

The next line contains n integers a_1,a_2,… a_n (1 ≤ a_i ≤ n) — the tags of the problems.

It is guaranteed that the sum of n over all test cases does not exceed 10^5.

Output

For each test case, if there are no permutations that satisfy the required condition, print -1. Otherwise, print the minimum possible cost of a permutation that satisfies the required condition.

Example

Input


4
6
2 1 2 3 1 1
5
1 1 1 2 2
8
7 7 2 7 7 1 8 7
10
1 2 3 4 1 1 2 3 4 1


Output


1
3
-1
2

Note

In the first test case, let p=[5, 4, 3, 2, 1, 6]. The cost is 1 because we jump from p_5=1 to p_6=6, and |6-1|>1. This permutation is valid because we don't solve problems with the same tag twice in a row. We cannot find a permutation with a cost smaller than 1.

In the second test case, let p=[1,5,2,4,3]. The cost is 3 because |p_2-p_1|>1, |p_3-p_2|>1, and |p_4-p_3|>1. The permutation is valid because we don't solve problems with the same tag twice in a row. We cannot find a permutation with a cost smaller than 3.

In the third test case, for any order of solving the problems, we will solve two problems with the same tag consecutively, so the answer is -1.
import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.io.PrintStream;
import java.util.Arrays;
import java.io.BufferedWriter;
import java.util.InputMismatchException;
import java.io.IOException;
import java.io.File;
import java.util.ArrayList;
import java.io.Writer;
import java.io.OutputStreamWriter;
import java.io.BufferedReader;
import java.io.FileReader;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 *
 * @author lewin
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        OutputWriter out = new OutputWriter(outputStream);
        FTheStrugglingContestant solver = new FTheStrugglingContestant();
        int testCount = Integer.parseInt(in.next());
        for (int i = 1; i <= testCount; i++)
            solver.solve(i, in, out);
        out.close();
    }

    static class FTheStrugglingContestant {
        FTheStrugglingContestant.Interval[] its;
        int sidx;
        int[] ends;

        void addInterval(int s, int e) {
            its[sidx++] = new FTheStrugglingContestant.Interval(s, e);
            ends[s]++;
            ends[e]++;
        }

        int solve(int[] arr) {
            int n = arr.length;
            int[] count = new int[n + 1];
            for (int x : arr) count[x]++;
            for (int i = 0; i <= n; i++) {
                if (count[i] * 2 > n + 1) {
                    return -1;
                }
            }

            int last = arr[0];
            ends = new int[n + 1];
            its = new FTheStrugglingContestant.Interval[n];
            sidx = 0;
            int tot = 0;
            for (int i = 0; i < n - 1; i++) {
                if (arr[i] == arr[i + 1]) {
                    tot++;
                    addInterval(last, arr[i]);
                    last = arr[i];
                }
            }
            addInterval(last, arr[n - 1]);
            int ans = tot;
            Debug.print(tot, ends);
            for (int i = 0; i <= n; i++) {
                ans += Math.max(0, (ends[i] - (2 * (tot + 1) - ends[i]) - 1) / 2);
            }
            return ans;
        }

        public void solve(int testNumber, InputReader in, OutputWriter out) {
            int n = in.nextInt();
            int[] arr = in.readIntArray(n);
            out.println(solve(arr));
        }

        static class Interval {
            public int s;
            public int e;

            public Interval(int s, int e) {
                this.s = s;
                this.e = e;
            }

        }

    }

    static class Debug {
        public static boolean DEBUG;

        static {
            try {
                DEBUG = System.getProperty("user.dir").contains("Dropbox");
            } catch (Exception e) {
                DEBUG = false;
            }
        }

        private static ArrayList<String> getParams() {
            StackTraceElement[] t = Thread.currentThread().getStackTrace();
            StackTraceElement up = t[3];

            ArrayList<String> ret = new ArrayList<>();
            String qqq = up.toString();
            ret.add("." + up.getMethodName() + qqq.substring(qqq.indexOf("("), qqq.length()));
            try {
                BufferedReader br = new BufferedReader(new FileReader(
                        new File("src/" + up.getClassName().replaceAll("\\.", "/") + ".java")));
                int g = up.getLineNumber();
                while (--g > 0) br.readLine();
                String q = br.readLine();
                String[] ss = q.split("Debug\\.print\\(");
                String[] qq = ss[1].substring(0, ss[1].lastIndexOf(")")).split(",");
                for (int i = 0; i < qq.length; i++) {
                    ret.add(qq[i].trim());
                }
            } catch (Exception e) {
            }
            for (int i = 0; i < 50; i++) ret.add("???");
            return ret;
        }

        private static String toString(Object o) {
            if (o == null) {
                return "null";
            } else if (o instanceof Object[]) {
                return Arrays.toString((Object[]) o);
            } else if (o instanceof char[]) {
                return new String((char[]) o);
            } else if (o instanceof int[]) {
                return Arrays.toString((int[]) o);
            } else if (o instanceof long[]) {
                return Arrays.toString((long[]) o);
            } else if (o instanceof double[]) {
                return Arrays.toString((double[]) o);
            } else if (o instanceof boolean[]) {
                return Arrays.toString((boolean[]) o);
            } else {
                return o.toString();
            }
        }

        public static void print(Object... x) {
            if (!DEBUG) return;
            ArrayList<String> s = getParams();
            StringBuilder sb = new StringBuilder();
            sb.append(s.get(0));
            sb.append(": ");
            for (int i = 0; i < x.length; i++) {
                sb.append(s.get(i + 1));
                sb.append(" = ");
                sb.append(toString(x[i]));
                if (i != x.length - 1) sb.append(", ");
            }
            System.out.println(sb.toString());
        }

    }

    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 close() {
            writer.close();
        }

        public void println(int i) {
            writer.println(i);
        }

    }

    static class InputReader {
        private InputStream stream;
        private byte[] buf = new byte[1 << 16];
        private int curChar;
        private int numChars;

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

        public int[] readIntArray(int tokens) {
            int[] ret = new int[tokens];
            for (int i = 0; i < tokens; i++) {
                ret[i] = nextInt();
            }
            return ret;
        }

        public int read() {
            if (this.numChars == -1) {
                throw new UnknownError();
            } else {
                if (this.curChar >= this.numChars) {
                    this.curChar = 0;

                    try {
                        this.numChars = this.stream.read(this.buf);
                    } catch (IOException var2) {
                        throw new InputMismatchException();
                    }

                    if (this.numChars <= 0) {
                        return -1;
                    }
                }

                return this.buf[this.curChar++];
            }
        }

        public int nextInt() {
            int c;
            for (c = this.read(); isSpaceChar(c); c = this.read()) {
                ;
            }

            byte sgn = 1;
            if (c == 45) {
                sgn = -1;
                c = this.read();
            }

            int res = 0;

            while (c >= 48 && c <= 57) {
                res *= 10;
                res += c - 48;
                c = this.read();
                if (isSpaceChar(c)) {
                    return res * sgn;
                }
            }

            throw new InputMismatchException();
        }

        public String next() {
            int c;
            while (isSpaceChar(c = this.read())) {
                ;
            }

            StringBuilder result = new StringBuilder();
            result.appendCodePoint(c);

            while (!isSpaceChar(c = this.read())) {
                result.appendCodePoint(c);
            }

            return result.toString();
        }

        public static boolean isSpaceChar(int c) {
            return c == 32 || c == 10 || c == 13 || c == 9 || c == -1;
        }

    }
}

