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.util.*;
import java.io.*;
public class Solution{
	public static void main(String[] argv)throws Exception {
		new Solver().solve1();
	}
}

class FastReader{
    final private int BUFFER_SIZE = 1<<16;
    private DataInputStream din;
    private byte[] buffer;
    private int bufferPointer, bytesRead;

    public FastReader()throws IOException{
        din=new DataInputStream(System.in);
        bufferPointer=bytesRead=0;
        buffer=new byte[BUFFER_SIZE];
    }
    public FastReader(String filename)throws IOException{
        din=new DataInputStream(new FileInputStream(filename));
        bufferPointer=bytesRead=0;
        buffer=new byte[BUFFER_SIZE];
    }

    public String next()throws IOException{
        String s="";
        byte[] buf = new byte[1<<16];
        byte c;
        int count=0;
        while ((c = read()) != -1)
        {
            if (c == ' ' || c == '\n')
                break;
            buf[count++]=c;
            if(count==1<<16){
                s+=new String(buf,0,count);
                count=0;
                
            }
        }
        s+=new String(buf,0,count);
        return s;
    }

    public String nextLine()throws IOException{
        byte[] buf = new byte[64];
        byte c,count=0;
        while ((c = read()) != -1)
        {
            if (c == '\n')
                break;
            buf[count++]=c;
        }
        return new String(buf,0,count);
    }

    public int nextInt()throws IOException {
        int result=0;
        byte c=read();
        byte c1=c;
        while (c<'0' || c>'9'){
            c1=c;
            c=read();
        }
        boolean neg= (c1=='-');
        do {
            result=result*10 + c-'0';
        }while ((c=read())>='0' && c<='9');
        if(neg)
            return -result;
        return result;
    }
    public long nextLong()throws IOException {
        long result=0;
        byte c=read();
        byte c1=c;
        while (c<'0' || c>'9'){
            c1=c;
            c=read();
        }
        boolean neg= (c1=='-');
        do {
            result=result*10 + c-'0';
        }while ((c=read())>='0' && c<='9');
        if(neg)
            return -result;
        return result;
    }
    public double nextDouble()throws IOException{
        double result=0,divisor=1;
        byte c=read(),c1=c;
        while(c<'0' || c>'9'){
            c1=c;
            c=read();
        }
        boolean neg=(c1=='-');

        do {
            result=result*10 + c-'0';
        }while((c=read())>='0' && c<='9');

        if (c=='.'){
            while ((c=read())>='0' && c<='9'){
                result += (c-'0')/(divisor=divisor*10);
            }
        }
        if(neg)
            return -result;
        return result;
    }
    private void fillBuffer() throws IOException {
        bytesRead = din.read(buffer,bufferPointer=0,BUFFER_SIZE);
        if(bytesRead==-1)
            buffer[0]=-1;
    }
    private byte read()throws IOException {
        if(bufferPointer==bytesRead)
            fillBuffer();
        return buffer[bufferPointer++];
    }
    public void close()throws IOException {
        if(din==null)
            return;
        din.close();
    }
}

class Solver{
	
	public void solve2() throws Exception {
		FastReader sc = new FastReader("input.txt");
		//FastReader sc = new FastReader();
		//Scanner sc = new Scanner(new File("input.txt"));
		//Scanner sc = new Scanner(System.in);
		int t=sc.nextInt();
		while(t-->0) {
			int n=sc.nextInt();
			int[] a=new int[n];
			a[0]=sc.nextInt();
			int max=-1,min=-1,mini=0,maxi=0;
			boolean f=false;
			for(int i=1;i<n;i++) {
				a[i]=sc.nextInt();
				if(!f && Math.abs(a[i] - a[i-1])>1) {
					f=true;
					maxi=i;
					mini=i-1;
				}
			}
			if(f) {
				System.out.println("YES");
				System.out.println((mini+1) + " " + (maxi+1));
			}
			else {
				System.out.println("NO");
			}
			
		}
	}
	public void solve1() throws Exception {
		//FastReader sc = new FastReader("input.txt");
		FastReader sc = new FastReader();
		//Scanner sc = new Scanner(new File("input.txt"));
		//Scanner sc = new Scanner(System.in);
		int t=sc.nextInt();
		while(t-->0) {
			int n=sc.nextInt();
			long[] a= new long[n];
			long sum=0,x=0;
			for(int i=0;i<n;i++) {
				a[i]=sc.nextLong();
				sum+=a[i];
				x = x^a[i];
			}
			if(x*2==sum) {
				System.out.println("0");
				System.out.println();
			}
			else {
				long temp = sum%2==0?2:1,temp2=0;
				while(true) {
					temp2 = x^((sum+temp)/2);
					if(temp2==0) {
						if(temp%2==0) {
							System.out.println("2");
							System.out.println(temp/2 + " " + temp/2);
							break;
						}
					}
					else if(temp2<=temp) {
						if((temp-temp2)%2==0) {
							System.out.println("3");
							System.out.println((temp-temp2)/2 + " " + (temp-temp2)/2 + " " + temp2);
							break;
						}
					}
					temp+=2+20*(10000000000000000l);
				}
			}
		}
		sc.close();
	}
}