Problem: Let's call an array a_1, a_2, ..., a_m of nonnegative integer numbers good if a_1 + a_2 + ... + a_m = 2⋅(a_1 ⊕ a_2 ⊕ ... ⊕ a_m), where ⊕ denotes the [bitwise XOR operation](https://en.wikipedia.org/wiki/Bitwise_operation#XOR).

For example, array [1, 2, 3, 6] is good, as 1 + 2 + 3 + 6 = 12 = 2⋅ 6 = 2⋅ (1⊕ 2 ⊕ 3 ⊕ 6). At the same time, array [1, 2, 1, 3] isn't good, as 1 + 2 + 1 + 3 = 7 ≠ 2⋅ 1 = 2⋅(1⊕ 2 ⊕ 1 ⊕ 3).

You are given an array of length n: a_1, a_2, ..., a_n. Append at most 3 elements to it to make it good. Appended elements don't have to be different. It can be shown that the solution always exists under the given constraints. If there are different solutions, you are allowed to output any of them. Note that you don't have to minimize the number of added elements!. So, if an array is good already you are allowed to not append elements.

Input

Each test contains multiple test cases. The first line contains the number of test cases t (1 ≤ t ≤ 10 000). The description of the test cases follows.

The first line of each test case contains a single integer n (1≤ n ≤ 10^5) — the size of the array.

The second line of each test case contains n integers a_1, a_2, ..., a_n (0≤ a_i ≤ 10^9) — the elements of the array.

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

Output

For each test case, output two lines.

In the first line, output a single integer s (0≤ s≤ 3) — the number of elements you want to append.

In the second line, output s integers b_1, ..., b_s (0≤ b_i ≤ 10^{18}) — the elements you want to append to the array.

If there are different solutions, you are allowed to output any of them.

Example

Input


3
4
1 2 3 6
1
8
2
1 1


Output


0

2
4 4
3
2 6 2

Note

In the first test case of the example, the sum of all numbers is 12, and their ⊕ is 6, so the condition is already satisfied.

In the second test case of the example, after adding 4, 4, the array becomes [8, 4, 4]. The sum of numbers in it is 16, ⊕ of numbers in it is 8.

Solution (in JAVA):

Solution:
import java.io.*;
import java.util.Random;
import java.util.StringTokenizer;

public class A {
    FastScanner in;
    PrintWriter out;

    public static void main(String[] args) {
        new A().runIO();
    }

    Random rnd = new Random(123);

    void solve123() {
        for (int it =0 ; it <123123; it++) {
            System.err.println("it = " + it);
            final int MAX = (int) 100;
            long[] r = solve(rnd.nextInt(MAX), rnd.nextInt(MAX));
            if (r == null) {
                throw new AssertionError();
            }
        }
    }

    void solve() {
        int tc = in.nextInt();
        for (int t = 0; t < tc; t++) {
            int n = in.nextInt();
            long sum = 0;
            long xor = 0;
            for (int i = 0; i < n; i++) {
                long val = in.nextLong();
                sum += val;
                xor ^= val;
            }
            while (true) {
                long[] r = solve(sum, xor);
                if (r != null) {
                    out.println(3);
                    for (long v : r) {
                        out.print(v + " ");
                    }
                    out.println();
                    break;
                }
            }
        }
    }

    long[] solve(long sum, long xor) {
        boolean lastInXor = false;
        long[] res = new long[3];
        for (int bit = 0; bit < 58; bit++) {
            boolean inSum = ((1L << bit) & sum) != 0;
            if (lastInXor != inSum) {
                int cnt = rnd.nextBoolean() ? 1 : 3;
                for (int i = 0; i < cnt; i++) {
                    res[i] ^= 1L << bit;
                    sum += 1L << bit;
                    xor ^= 1L << bit;
                }
            }
            lastInXor = ((1L << bit) & xor) != 0;
        }
        if (xor * 2 == sum) {
            return res;
        } else {
            return null;
        }
    }

    void run() {
        try {
            in = new FastScanner(new File("A.in"));
            out = new PrintWriter(new File("A.out"));

            solve();

            out.close();
        } catch (FileNotFoundException e) {
            e.printStackTrace();
        }
    }

    void runIO() {

        in = new FastScanner(System.in);
        out = new PrintWriter(System.out);

        solve();

        out.close();
    }

    class FastScanner {
        BufferedReader br;
        StringTokenizer st;

        public FastScanner(File f) {
            try {
                br = new BufferedReader(new FileReader(f));
            } catch (FileNotFoundException e) {
                e.printStackTrace();
            }
        }

        public FastScanner(InputStream f) {
            br = new BufferedReader(new InputStreamReader(f));
        }

        String next() {
            while (st == null || !st.hasMoreTokens()) {
                String s = null;
                try {
                    s = br.readLine();
                } catch (IOException e) {
                    e.printStackTrace();
                }
                if (s == null)
                    return null;
                st = new StringTokenizer(s);
            }
            return st.nextToken();
        }

        boolean hasMoreTokens() {
            while (st == null || !st.hasMoreTokens()) {
                String s = null;
                try {
                    s = br.readLine();
                } catch (IOException e) {
                    e.printStackTrace();
                }
                if (s == null)
                    return false;
                st = new StringTokenizer(s);
            }
            return true;
        }

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

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

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