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.Math;

public class badstory {

	public static int gcd(int a, int b)
	{
		if (a<b){
			int temp =a;
			a = b;
			b=temp;
		}
		if (b==0) {
			return a;
		}
		else{
			return gcd(b,a%b);
		}
	}

	public static boolean execute(int n) {
		int x = console.nextInt();
		if(x<0) {
			for (int j =0;j<(n-1) ;j++ ) {
				int trash = console.nextInt();
			}			
			return false;
		}
		int g= x;
		int max=x;
		boolean zero = false;
		if(x==0){
			zero = true;
		}
		for (int i=1;i<n ;i++ ) {
			x = console.nextInt();				
			if(x==0){
				zero = true;
			}
			if (x<0){
				for (int j =0;j<(n-1-i) ;j++ ) {
					int trash = console.nextInt();
				}
				return false;
			}
			else {
				g = gcd(g,x);
				if (x> max){
					max = x;
				}
			}
		}
		int z=0;
		if(zero){
			z = 1;
		}
		if(max==0){
			System.out.println(1);
			System.out.println(0);
			return true;
		}	

		int num_needed = max/g +z;
		if(num_needed>300){
			return false;
		}
		else {
			System.out.println("YES");

			System.out.println(num_needed);
			if(zero){
				System.out.print(0+" ");
			}
			for (int i=1;i<= max/g ;i++ ) {
				System.out.print(g*i+" ");
			}
			System.out.println();
			return true;
		}
	}
	private static Scanner console = new Scanner(System.in);

	public static void main(String[] args) {

		int t = console.nextInt();
		for (int k=0;k< t ;k++ ) {
			int n = console.nextInt();
			if(!execute(n)){
				System.out.println("NO");
			}
		}


	}

}