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.io.*;
import java.math.*;
import java.util.*;
public class a {
	static class FastReader {
		BufferedReader br;
		StringTokenizer st;
		
		public FastReader() {
			br = new BufferedReader(new
					InputStreamReader(System.in));
		}
		
		String next() {
			while (st == null || !st.hasMoreElements()) {
				try {
					st = new StringTokenizer(br.readLine());
				} catch (IOException e) {
					e.printStackTrace();
				}
			}
			return st.nextToken();
		}
		
		int nextInt() {
			return Integer.parseInt(next());
		}
		
		long nextLong() {
			return Long.parseLong(next());
		}
		
		double nextDouble() {
			return Double.parseDouble(next());
		}
		
		String nextLine() {
			String str = "";
			try {
				str = br.readLine();
			} catch (IOException e) {
				e.printStackTrace();
			}
			return str;
		}
	}
	
	static FastReader sc = new FastReader();
	static PrintWriter out = new PrintWriter(System.out);
	
	private static int[] rai(int n) {
		int[] arr = new int[n];
		for (int i = 0; i < n; i++) {
			arr[i] = sc.nextInt();
		}
		return arr;
	}
	
	private static int[][] rai(int n, int m) {
		int[][] arr = new int[n][m];
		for (int i = 0; i < n; i++) {
			for (int j = 0; j < m; j++) {
				arr[i][j] = sc.nextInt();
			}
		}
		return arr;
	}
	
	private static long[] ral(int n) {
		long[] arr = new long[n];
		for (int i = 0; i < n; i++) {
			arr[i] = sc.nextLong();
		}
		return arr;
	}
	
	private static long[][] ral(int n, int m) {
		long[][] arr = new long[n][m];
		for (int i = 0; i < n; i++) {
			for (int j = 0; j < m; j++) {
				arr[i][j] = sc.nextLong();
			}
		}
		return arr;
	}
	
	private static int ri() {
		return sc.nextInt();
	}
	
	private static long rl() {
		return sc.nextLong();
	}
	
	private static String rs() {
		return sc.next();
	}
	
	static void solve()
	{
		int n=sc.nextInt();
		int arr[]=new int[n];
		int h[]=new int[101];
		int a,fg=1,pos=0,neg=0;
		for(int i=0;i<n;i++)
		{
			arr[i]=sc.nextInt();
			h[Math.abs(arr[i])]++;
			if(arr[i]<0)
				neg++;
		}
		if(neg>0)
			System.out.println("NO");
		else
		{
			System.out.println("YES");
			int i,j;
			for( i=0;i<n-1;i++)
			{	for( j=i+1;j<n;j++)
				if(h[Math.abs(arr[i]-arr[j])]==0)
						break;
				if(j<n)
					break;
			}
			if(i==n-1)
			{
				System.out.println(n);
				for( i=0;i<n;i++)
					System.out.print(arr[i]+" ");
				System.out.println();
			}
			else
			{
				System.out.println(101);
				for( i=0;i<=100;i++)
					System.out.print(i*fg+" ");
				System.out.println();
			}
		}
	}
	
	public static void main(String[] args) {
		
		int t;
		t=a.ri();
		while(t-->0)
			solve();
		
	}
}