Problem: Omkar has received a message from Anton saying "Your story for problem A is confusing. Just make a formal statement." Because of this, Omkar gives you an array a = [a_1, a_2, …, a_n] of n distinct integers. An array b = [b_1, b_2, …, b_k] is called nice if for any two distinct elements b_i, b_j of b, |b_i-b_j| appears in b at least once. In addition, all elements in b must be distinct. Can you add several (maybe, 0) integers to a to create a nice array b of size at most 300? If a is already nice, you don't have to add any elements.

For example, array [3, 6, 9] is nice, as |6-3|=|9-6| = 3, which appears in the array, and |9-3| = 6, which appears in the array, while array [4, 2, 0, 6, 9] is not nice, as |9-4| = 5 is not present in the array.

For integers x and y, |x-y| = x-y if x > y and |x-y| = y-x otherwise.

Input

Each test contains multiple test cases. The first line contains t (1 ≤ t ≤ 50), the number of test cases. Description of the test cases follows.

The first line of each test case contains a single integer n (2 ≤ n ≤ 100) — the length of the array a.

The second line of each test case contains n distinct integers a_1, a_2, ⋅⋅⋅, a_n (-100 ≤ a_i ≤ 100) — the elements of the array a.

Output

For each test case, output one line containing YES if Omkar can create a nice array b by adding elements to a and NO otherwise. The case of each letter does not matter, so yEs and nO will also be accepted.

If the first line is YES, output a second line containing a single integer k (n ≤ k ≤ 300). 

Then output one line containing k distinct integers b_1, b_2, ⋅⋅⋅, b_k (-10^9 ≤ b_i ≤ 10^9), the elements of the nice array b. b_1, b_2, ⋅⋅⋅, b_k can be in any order. For each a_i in a, a_i must appear at least once in b.

It can be proved that if Omkar can create such an array b, then he can also do so in a way that satisfies the above constraints.

If multiple solutions exist, you can print any. 

Example

Input


4
3
3 0 9
2
3 4
5
-7 3 13 -2 8
4
4 8 12 6


Output


yes
4
6 0 3 9
yEs
5
5 3 1 2 4
NO
Yes
6
8 12 6 2 4 10

Note

For the first case, you can add integers to a to receive the array b = [6, 0, 3, 9]. Note that |6-3| = |9-6| = |3-0| = 3 and 3 is in b, |6-0| = |9-3| = 6 and 6 is in b, and |9-0| = 9 is in b, so b is nice.

For the second case, you can add integers to a to receive the array b = [5, 3, 1, 2, 4]. We have that |2-1| = |3-2| = |4-3| = |5-4| = 1 is in b, |3-1| = |4-2| = |5-3| = 2 is in b, |4-1| = |5-2| = 3 is in b, and |5-1| = 4 is in b, so b is nice.

For the fourth case, you can add integers to a to receive the array b = [8, 12, 6, 2, 4, 10]. We have that |4-2| = |6-4| = |8-6| = |10-8| = |12-10| = 2 is in b, |6-2| = |8-4| = |10-6| = |12-8| = 4 is in b, |8-2| = |10-4| = |12-6| = 6 is in b, |10-2| = |12-4| = 8 is in b, and |12-2| = 10 is in b, so b is nice.

It can be proven that for all other test cases it is impossible to create a nice array b.

Solution (in JAVA):

Solution:
import java.util.*;
import java.io.*;
import java.lang.*;
public class Solution{
    BufferedReader br =new BufferedReader(new InputStreamReader(System.in)); 
    PrintWriter out =new PrintWriter(System.out);
    StringTokenizer st =new StringTokenizer("");
    String next(){
        if(!st.hasMoreTokens()){
            try{
                st=new StringTokenizer(br.readLine());
            }
            catch(Exception e){

            }
        }
        return st.nextToken();
    }
    int nextInt(){
        return Integer.parseInt(next());
    }
    long nextLong(){
        return Long.parseLong(next());
    }
    public static void main(String[] args) throws Exception{
        new Solution().solve();
    }
    void solve() throws Exception{ 
        int t=1; 
        if (System.getProperty("ONLINE_JUDGE") == null) {
          br = new BufferedReader(new FileReader("input.txt"));
          out = new PrintWriter(new FileWriter("output.txt"));
        }
        t = nextInt();
        for(int tt=0;tt<t;tt++){
            int n = nextInt();
            List<Integer> arr = new ArrayList<>();
            Set<Integer> set = new HashSet<>();
            for(int i=0;i<n;i++) {arr.add(nextInt());set.add(arr.get(i));}
            int size =n;
            while(size<=300){
                Set<Integer> temp = new HashSet<>();
                for(int i=0;i<size;i++){
                    for(int j=0;j<size && j!=i;j++){
                        int x = Math.abs(arr.get(i)-arr.get(j));
                        if(!set.contains(x)){
                            temp.add(x);
                        }
                    }
                }
                for(int i:temp){
                    arr.add(i);
                    set.add(i);
                }
                if(temp.size()==0)break;
                size = arr.size();
            }
            if(size<=300){
                out.println("YES");
                out.println(arr.size());
                for(int i:arr){
                    out.print(i+" ");
                }
                out.println();
            }
            else{
                out.println("NO");
            }
        }
        out.close();
    }
}