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.util.*;

public class main1{

	public void funct1(String s){
		int n = s.length();
		int numbersInBw = n-2;
		System.out.println(s.charAt(0)+ Integer.toString(numbersInBw) +s.charAt(n-1));
	}

	public int funct2(int[] scores, int k){
		int i=0;
		while(i<scores.length){
			if(scores[i]>0){
				if(scores[i] >= scores[k-1]){
					i++;
				}
				else{
					break;
				}
			}
			else{
				break;
			}	
		}
		return i;
	}

	public int funct3(int m, int n){
		int answ = (m*n)/2;
		return answ;
	}

	public int funct4(String first, String second){
		int value = first.compareTo(second);
		if(value<0){
			return -1;
		}else if(value == 0){
			return value;
		}else{
			return 1;
		}

	}
	public Vector<Integer> bucketSort(Vector<Integer> arr){
		int size = arr.size();
		int low = 0, mid = 0,high = size-1;    

		while(mid <= high){
			if(arr.get(mid)==1){
				int temp = arr.get(low);
				arr.set(low, arr.get(mid));
				arr.set(mid, temp);
				mid++;
				low++;
			}
			else if(arr.get(mid) == 2){
				mid++;
			}
			else{
				int temp = arr.get(high);
				arr.set(high,arr.get(mid));
				arr.set(mid,temp);
				high--;
			}

		}
		// System.out.println(arr);
		return arr;
	}
	public static void main(String args[]){
		main1 cf = new main1();
		Scanner scan = new Scanner(System.in);
		int t = scan.nextInt();
		while(t-->0){
			int n = scan.nextInt();
			boolean hasNeg = false;
			int[] arr = new int[n];
			int max = 0;
			for(int i=0;i<n;i++){
				arr[i] = scan.nextInt();
				max = Math.max(arr[i], max);
				if(arr[i]<0){
					hasNeg = true;
				}
			}
			if(hasNeg){
				System.out.println("NO");
			}else{
				System.out.println("YES");
				System.out.print(max+1 + " ");
				for(int i=0;i<max;i++){
					System.out.print(i+" ");
				}
				System.out.print(max);
				System.out.println();
			}

		}
	}
}