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{
  
    static class pair implements Comparable<pair>{
        int a,b;
        pair(int x,int y){
            a=x;b=y;
        }
        public int compareTo(pair t){
          if(t.a==this.a)
          return this.b-t.b;
          return this.a-t.a;
		   
        }
    }
    // public static ArrayList<pair> bfs(String[] a,int r,int c){
    //     ArrayList<pair> ans=new ArrayList<>();
    //     Queue<pair> q=new LinkedList<>();
    //     int[][] dxy={{-1,0,1,0},{0,-1,0,1}};
    //     q.add(new pair(r,c));
    //     HashSet<String> h=new HashSet<>();
    //     while(!q.isEmpty()){
    //         pair f=q.poll();
    //         ans.add(f);h.add(f.a+" "+f.b);
    //         for(int i=0;i<4;i++){
    //             int dx=f.a+dxy[0][i];
    //             int dy=f.b+dxy[1][i];
    //             if(dx<0||dy<0||dx>=a.length||dy>=a.length||h.contains(dx+" "+dy)||
    //             a[dx].charAt(dy)=='1')
    //             continue;
    //             q.add(new pair(dx,dy));
    //             h.add(dx+" "+dy);
    //         }
    //     }
    //     return ans;
    // }    

    /*
    1 1 1 1 1 
3 3 3 
2 3 3 2 1 3 
1 
2 2 2 2 
4 4 4 1 4 
*/
    public static int pow(int a, int n) {
		long ans = 1;
		long base = a;
		while (n != 0) {
			if ((n & 1) == 1) {
				ans *= base;
				ans %= 1000000007;
			}
			base = (base * base) % 1000000007;
			n >>= 1;
		}
		return (int) ans % 1000000007;
	}
	public static int find(int x){
	    int i=1;int f=0;
	    while(x>0){
	        if((x&1)==0)f=i;
	        x>>=1;i++;
	    }
	    return f;
	}
	public static boolean good(int x){
	    
	    if((((x+1)&x))==0)
	    return true;
	    return false;
	}
	public static long f(long n){
	  
	   long val=2;
	   long preval=0;int i=1;
	   while(n>=val){
	       i++;
	       preval=val;
	       val=3*i+val-1;
	       
	   }
	   
	   return preval;
	   
	}
	public static boolean bfs(ArrayList<Integer>[] a,int n,int[] b){
	    Queue<Integer> p=new LinkedList<>();
	    boolean v[]=new boolean[n];
	    v[0]=true;int k=0;
	    if(b[0]!=0)return false;
	    p.add(0);int c=1;
	    HashSet<Integer> h=new HashSet<Integer>();
	    h.add(0);
	    while(!p.isEmpty()){
	        int f=p.poll();k++;
	        if(h.contains(f))h.remove(f);
	        else return false;
	        v[f]=true;
	        c--;
	
	       for(int i:a[f]){
	           if(!v[i]){
	           p.add(i);v[i]=true;}
	       }
	          if(c==0){
	              c=p.size();
	       if(h.size()!=0)return false;
	       for(int j=k;j<k+p.size();j++)
	       h.add(b[j]);
	   }
	    }
	    return true;
	    
	}
	public static int mi(int[] a,int k,int[] dp,int n){
	    int max=0;
	    for(int i=1;i*i<=k;i++){
	      //  System.out.println("fact "+i);
	        if(k%i==0&&(a[i-1]<a[k-1])){
	            
	      //  System.out.println(i+" "+dp[i-1]+" "+a[i-1]+" ");
	        max=Math.max(dp[i-1],max);}
	        if(k%i==0&&(a[k/i-1]<a[k-1])){
	            
	      //  System.out.println(i+" "+dp[i-1]+" "+a[i-1]+" ");
	        max=Math.max(dp[k/i-1],max);}
	        
	    }
	    return max;
	}
	    public static void dfs(ArrayList<Integer> a[],boolean[] v,int n,int llllll){
     v[n]=true;
     llllll=Math.max(n,llllll);
   //   System.out.println(max);
        for(int i=0;i<a[n].size();i++){
            if(!v[a[n].get(i)]){
         dfs(a,v,a[n].get(i),llllll);
            }
           
        }
       
        
    }
    public static void main(String[] args) {
		Scanner s = new Scanner(System.in);
 
			int t = s.nextInt();
 	StringBuilder st=new StringBuilder();
 	
 	
		while(t-- > 0) {
		int n=s.nextInt();
		long[]a=new long[n];
		for(int i=0;i<n;i++)
		a[i]=s.nextLong();
	    long sum=0;
	    long xor=0;
	    String ans="";
	    for(int i=0;i<n;i++){
	        sum+=a[i];
	        xor^=a[i];
	    }
	    if(2*xor==sum)ans="0\n";
	    else{
	        ans="2\n";
	        ans+=xor;
	        sum+=xor;
	        ans+=" "+sum;
	    }
		  st.append(ans+"\n");
		}
 System.out.println(st);
   
/*

2
1
3
1
6


6 23 21
1 1000 0
2 1 2

0
40
41664916690999888

1 
1 2 
2 1 3 
3 1 2 4 
2 4 1 3 5 
3 4 1 5 2 6 

1 11
5 35
3 6
0 42
0 0
1 2
3 4




6 45 46
2 2 1
3 4 2
4 4 3
*/


  
	
        
    }
}