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.BufferedWriter;
import java.io.IOException;
import java.io.InputStream;
import java.io.OutputStream;
import java.io.OutputStreamWriter;
import java.io.PrintWriter;
import java.io.Writer;
import java.util.Arrays;
import java.util.InputMismatchException;
import java.util.*;
import java.io.*;
import java.math.*;
public class Main7{

static class Pair
    { 
        int x;
		int y;
		public Pair(int x, int y) 
        {     
            this.x=x;
			this.y=y;
		}     
        
    @Override
            public int hashCode() 
            { 
                final int temp = 14; 
                int ans = 1; 
                ans =x*31+y*13; 
                return ans; 
            } 
      
            // Equal objects must produce the same 
            // hash code as long as they are equal 
        @Override
        public boolean equals(Object o) 
        { 
            if (this == o) { 
                return true; 
            } 
            if (o == null) { 
                return false; 
            } 
            if (this.getClass() != o.getClass()) { 
                return false; 
            } 
            Pair other = (Pair)o; 
            if (this.x != other.x || this.y!=other.y) { 
                return false; 
            } 
            return true; 
        } 
            
    } 
static class Pair1{
	int x;
	int y;
	long z;
	Pair1(int x, int y, long z)
	{
		this.x=x;
		this.y=y;
		this.z=z;
	}
}
    
    public static long pow(long a, long b)
    {
        long result=1;
        while(b>0)
        {
            if (b % 2 != 0)
            {
                result=(result*a);
                b--;
            } 
            a=(a*a);
            b /= 2;
        }   
        return result;
    }
    public static long fact(long num)
    {
                long value=1;
                long i=1;
                for(i=2;i<=num;i++)
                {
                    value=((value)*(long)i);
                }
                return value;
            }
            public static long gcd(long a, long b)
            {
                if (a == 0)
                    return b;
                return gcd(b%a, a);
            }
            
    /*        public static long lcm(long a,long b)
            {
                return a * (b / gcd(a, b));
            }
        */    public static long sum(int h)
            {
                return (h*(h+1)/2);
            }
      /*     public static void dfs(int parent,boolean[] visited)
            {
                ArrayList<Integer> arr=new ArrayList<Integer>();
                arr=graph.get(parent);
				ts.add(parent);
                visited[parent]=true;
                for(int i=0;i<arr.size();i++)
                {
                    int num=(int)arr.get(i);
                    if(visited[num]==false)
                    {
                        dfs(num,visited);
                    }
                }
            }
			static ArrayList<Integer> ts;
            static int[] dis;*/
            static int mod=1000000007;
            static ArrayList<ArrayList<Integer>> graph;
            static ArrayList<ArrayList<Integer>> g;
            
       /*    public static void bfs(int num,int size)
            {
                boolean[] visited=new boolean[size+1];
                Queue<Integer> q=new LinkedList<>();
                q.add(num);
                ans[num]=1;
                visited[num]=true;
                while(!q.isEmpty())
                {
                    int x=q.poll();
                    ArrayList<Integer> al=graph.get(x);
                    for(int i=0;i<al.size();i++)
                    {
                        int y=al.get(i);    
                        if(visited[y]==false)
                        {
                            q.add(y);
                            ans[y]=ans[x]+1;
                            visited[y]=true;
                        }
                    }
                }
            }
			
            static int[] ans;*/
			static public void main(String args[])throws IOException
            {
				int tt=i();
				StringBuilder sb=new StringBuilder();
				while(tt-->0)
				{
					int n=i();
					long[] a=new long[n];
					long sum=0;
					long xor=0;
					for(int i=0;i<n;i++)
					{
						a[i]=l();
						sum+=a[i];
						xor=xor^a[i];
					}
					if(sum==2*xor)
					{
						pln("0");
						pln("");
					}
					else
					{
						long num1=pow(2,50);
						sum=sum+num1;
						xor=xor^(num1/2);
						long diff=2*xor-sum;
						if(diff%2==0)
						{
							pln("3");
							pln((num1/2)+" "+(diff/2+num1/4)+" "+(diff/2+num1/4));
						
						}
						else
						{
							sum=sum+1;
							xor=xor^1;
							diff=2*xor-sum;
							pln("3");
							pln((num1/2+1)+" "+(diff/2+num1/4)+" "+(diff/2+num1/4));
							//long xorr=(num1/2+1)^1^2;
							//long summ=num1+1+diff+3;
							//pln(2*xorr+" "+summ);
						}
					}
				}
				System.out.print(sb.toString());
			}

            /**/
            static InputReader in=new InputReader(System.in);
                static OutputWriter out=new OutputWriter(System.out);
                public static long l()
                {
                    String s=in.String();
                    return Long.parseLong(s);
                }
                public static void pln(String value)
                {
                    System.out.println(value);
                }
                public static int i()
                {
                    return in.Int();
                }
                public static String s()
                {
                    return in.String();
                }
    }
         
         
         
         
         
         
         
         
         
         
         
         
         
         
         
         
         
         
         
         
         
         
        class InputReader {
             
            private InputStream stream;
            private byte[] buf = new byte[1024];
            private int curChar;
            private int numChars;
            private SpaceCharFilter filter;
         
            public InputReader(InputStream stream) {
                this.stream = stream;
            }
         
            public int read() {
                if (numChars== -1)
                    throw new InputMismatchException();
                if (curChar >= numChars) {
                    curChar = 0;
                    try {
                        numChars = stream.read(buf);
                    } catch (IOException e) {
                        throw new InputMismatchException();
                    }
                    if (numChars <= 0)
                        return -1;
                }
                return buf[curChar++];
            }
         
            public int Int() {
                int c = read();
                while (isSpaceChar(c))
                    c = read();
                int sgn = 1;
                if (c == '-') {
                    sgn = -1;
                    c = read();
                }
                int res = 0;
                do {
                    if (c < '0' || c > '9')
                        throw new InputMismatchException();
                    res *= 10;
                    res += c - '0';
                    c = read();
                } while (!isSpaceChar(c));
                return res * sgn;
            }
         
            public String String() {
                int c = read();
                while (isSpaceChar(c))
                    c = read();
                StringBuilder res = new StringBuilder();
                do {
                    res.appendCodePoint(c);
                    c = read();
                } 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 String next() {
                return String();
            }
         
            public interface SpaceCharFilter {
                public boolean isSpaceChar(int ch);
            }
        }
         
        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 print(Object...objects) {
                for (int i = 0; i < objects.length; i++) {
                    if (i != 0)
                        writer.print(' ');
                    writer.print(objects[i]);
                }
            }
         
            public void printLine(Object...objects) {
                print(objects);
                writer.println();
            }
         
            public void close() {
                writer.close();
            }
         
            public void flush() {
                writer.flush();
            }
         
            }
         
            class IOUtils {
         
            public static int[] readIntArray(InputReader in, int size) {
                int[] array = new int[size];
                for (int i = 0; i < size; i++)
                    array[i] = in.Int();
                return array;
            }
         
            }