The only difference between easy and hard versions is constraints.

You are given a sequence a consisting of n positive integers.

Let's define a three blocks palindrome as the sequence, consisting of at most two distinct elements (let these elements are a and b, a can be equal b) and is as follows: [\underbrace{a, a, ..., a}_{x}, \underbrace{b, b, ..., b}_{y}, \underbrace{a, a, ..., a}_{x}]. There x, y are integers greater than or equal to 0. For example, sequences [], [2], [1, 1], [1, 2, 1], [1, 2, 2, 1] and [1, 1, 2, 1, 1] are three block palindromes but [1, 2, 3, 2, 1], [1, 2, 1, 2, 1] and [1, 2] are not.

Your task is to choose the maximum by length subsequence of a that is a three blocks palindrome.

You have to answer t independent test cases.

Recall that the sequence t is a a subsequence of the sequence s if t can be derived from s by removing zero or more elements without changing the order of the remaining elements. For example, if s=[1, 2, 1, 3, 1, 2, 1], then possible subsequences are: [1, 1, 1, 1], [3] and [1, 2, 1, 3, 1, 2, 1], but not [3, 2, 3] and [1, 1, 1, 1, 2].

Input

The first line of the input contains one integer t (1 ≤ t ≤ 2000) — the number of test cases. Then t test cases follow.

The first line of the test case contains one integer n (1 ≤ n ≤ 2000) — the length of a. The second line of the test case contains n integers a_1, a_2, ..., a_n (1 ≤ a_i ≤ 26), where a_i is the i-th element of a. Note that the maximum value of a_i can be up to 26.

It is guaranteed that the sum of n over all test cases does not exceed 2000 (∑ n ≤ 2000).

Output

For each test case, print the answer — the maximum possible length of some subsequence of a that is a three blocks palindrome.

Example

Input


6
8
1 1 2 2 3 2 1 1
3
1 3 3
4
1 10 10 1
1
26
2
2 1
3
1 1 1


Output


7
2
4
1
1
3
//package CodeforcesJava;

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

public class Main {

    public void solve(InputProvider in, PrintWriter out) throws IOException {
        int testCount = in.nextInt();
        for (int test = 0; test < testCount; test++) {
            int count = in.nextInt();
            int[] numbers = new int[count];
            Map<Integer, List<Integer>> numberPositions = new HashMap<>();
            for (int i = 0; i < numbers.length; i++) {
                numbers[i] = in.nextInt();
                numberPositions.putIfAbsent(numbers[i], new ArrayList<>());
                numberPositions.get(numbers[i]).add(i);
            }
            int maxSize = 0;
            for (Integer baseNumber : numberPositions.keySet()) {
                int size = countMax(numberPositions, baseNumber);
                maxSize = Math.max(maxSize, size);
            }
            out.print(maxSize + "\n");
        }
    }

    private int countMax(Map<Integer, List<Integer>> numberPositions, int baseNumber) {
        int maxSize = numberPositions.get(baseNumber).size();
        for (Integer anotherNumber : numberPositions.keySet()) {
            if (anotherNumber != baseNumber) {
                int size = countMax(numberPositions, baseNumber, anotherNumber);
                maxSize = Math.max(maxSize, size);
            }
        }
        return maxSize;
    }

    private int countMax(Map<Integer, List<Integer>> numberPositions, int baseNumber, int anotherNumber) {
        List<Integer> baseNumberPositions = numberPositions.get(baseNumber);
        int baseForward = 0;
        int baseBackward = baseNumberPositions.size() - 1;
        List<Integer> anotherNumberPositions = numberPositions.get(anotherNumber);
        int anotherForward = 0;
        int anotherBackward = anotherNumberPositions.size() - 1;
        int maxSize = baseNumberPositions.size();
        while (baseForward < baseBackward) {
            while (anotherForward < anotherNumberPositions.size()
                    && anotherNumberPositions.get(anotherForward) < baseNumberPositions.get(baseForward)) {
                anotherForward++;
            }
            while (anotherBackward >= 0
                    && anotherNumberPositions.get(anotherBackward) > baseNumberPositions.get(baseBackward)) {
                anotherBackward--;
            }
            int anotherInnerSize = Math.max(0, anotherBackward - anotherForward + 1);
            maxSize = Math.max(maxSize, 2 * (baseForward + 1) + anotherInnerSize);
            baseForward++;
            baseBackward--;
        }
        return maxSize;
    }

    public static void main(String[] args) throws Exception {
        try (InputProvider input = new InputProvider(System.in);
             PrintWriter output = new PrintWriter(System.out)) {
            new Main().solve(input, output);
        }
    }

    public static class InputProvider implements AutoCloseable {

        private final BufferedReader reader;
        private StringTokenizer tokenizer;

        public InputProvider(Reader reader) {
            this.reader = new BufferedReader(reader);
        }

        public InputProvider(InputStream input) {
            reader = new BufferedReader(new InputStreamReader(input));
        }

        public String next() throws IOException {
            if (Objects.isNull(tokenizer) || !tokenizer.hasMoreTokens())
                tokenizer = new StringTokenizer(reader.readLine());
            return tokenizer.nextToken();
        }

        public int nextInt() throws IOException {
            return Integer.parseInt(next());
        }

        public long nextLong() throws IOException {
            return Long.parseLong(next());
        }

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

        public String nextLine() throws IOException {
            return reader.readLine();
        }

        @Override
        public void close() throws Exception {
            reader.close();
        }

    }

}