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.*;
import java.math.*;
public class Solution {
    InputStream is;
    PrintWriter o;
    /////////////////// CODED++ BY++ ++ ++ ++ BHAVYA++ ARORA++ ++ ++ ++ FROM++ JAYPEE++ INSTITUTE++ OF++ INFORMATION++ TECHNOLOGY++ ////////////////
///////////////////////// Make it work, make it right, make it fast. Make it work, make it right, make it fast. Make it work, make it right, make it fast. Make it work, make it right, make it fast. /////////////////
public static int gcd(int a, int b)
{
    if (a == 0)
        return b;
     
    return gcd(b%a, a);
} 
void solve() {
     int n=ni();
     while(n-->0){
         int m=ni();
         int f=0;
         int arr[]=new int[m];
         int min=Integer.MAX_VALUE;
         int max=Integer.MIN_VALUE;
         for(int i=0;i<m;i++){
             arr[i]=ni();
             if(arr[i]<0){
                 f=1;
             }
             min=Math.min(min,arr[i]);
             max=Math.max(max,arr[i]);
         }
         if(f==1){
             o.println("NO");
             continue;
         }
         int mut=0;
         if(arr.length==1&&arr[0]==0){
             o.println("YES\n1\n0");
             continue;
         }
         for(int i=0;i<m;i++){
            mut=gcd(arr[i], mut);
         }
         o.println("YES");
         o.println(max/mut+1);
         for(int i=0;i<=max;i+=mut){
             o.print(i+" ");
         }
         o.println();
                 

     }

     


}
   //---------- I/O Template ----------
    public static void main(String[] args) { new Solution().run(); }
    void run() { 
        is = System.in; 
        o = new PrintWriter(System.out);
        solve();
        o.flush();
    }
    byte input[] = new byte[1024];
    int len = 0, ptr = 0;
    int readByte() { 
        if(ptr >= len) { ptr = 0; 
            try { len = is.read(input); } 
            catch(IOException e) { throw new InputMismatchException(); } 
            if(len <= 0) { return -1; } 
        } return input[ptr++];
    }
    boolean isSpaceChar(int c) { return !( c >= 33 && c <= 126 ); }
    int skip() { 
        int b = readByte(); 
        while(b != -1 && isSpaceChar(b)) { b = readByte(); } 
        return b;
    }
    char nc() { return (char)skip(); }
    String ns() { 
        int b = skip(); 
        StringBuilder sb = new StringBuilder(); 
        while(!isSpaceChar(b)) { sb.appendCodePoint(b); b = readByte(); } 
        return sb.toString();
    }
    String nLine() { 
        int b = skip(); 
        StringBuilder sb = new StringBuilder(); 
        while( !(isSpaceChar(b) && b != ' ') ) { sb.appendCodePoint(b); b = readByte(); } 
        return sb.toString();
    }
    int ni() { 
        int n = 0, b = readByte(); 
        boolean minus = false;
        while(b != -1 && !( (b >= '0' && b <= '9') || b == '-')) { b = readByte(); } 
        if(b == '-') { minus = true; b = readByte(); } 
        if(b == -1) { return -1; }  //no input 
        while(b >= '0' && b <= '9') { n = n * 10 + (b - '0'); b = readByte(); } 
        return minus ? -n : n;
    }
    long nl() { 
        long n = 0L;    int b = readByte(); 
        boolean minus = false; 
        while(b != -1 && !( (b >= '0' && b <= '9') || b == '-')) { b = readByte(); } 
        if(b == '-') { minus = true; b = readByte(); } 
        while(b >= '0' && b <= '9') { n = n * 10 + (b - '0'); b = readByte(); } 
        return minus ? -n : n;
    }
    double nd() { return Double.parseDouble(ns()); }
    float nf() { return Float.parseFloat(ns()); }
    int[] nia(int n) { 
        int a[] = new int[n]; 
        for(int i = 0; i < n; i++) { a[i] = ni(); } 
        return a;
    }
    long[] nla(int n) { 
        long a[] = new long[n]; 
        for(int i = 0; i < n; i++) { a[i] = nl(); } 
        return a;
    }
    int [][] nim(int n)
    {
        int mat[][]=new int[n][n];
        for(int i=0;i<n;i++)
        {
            for(int j=0;j<n;j++)
            {
                mat[i][j]=ni();
            }
        }
        return mat;
    }
    long [][] nlm(int n)
    {
        long mat[][]=new long[n][n];
        for(int i=0;i<n;i++)
        {
            for(int j=0;j<n;j++)
            {
                mat[i][j]=nl();
            }
        }
        return mat;
    }
    char[] ns(int n) { 
        char c[] = new char[n]; 
        int i, b = skip(); 
        for(i = 0; i < n; i++) { 
            if(isSpaceChar(b)) { break; } 
            c[i] = (char)b; b = readByte(); 
        } return i == n ? c : Arrays.copyOf(c,i);
    }
    void piarr(int arr[])
    {
        for(int i=0;i<arr.length;i++)
        {
            o.print(arr[i]+" ");
        }
        o.println();
    }
    void plarr(long arr[])
    {
        for(int i=0;i<arr.length;i++)
        {
            o.print(arr[i]+" ");
        }
        o.println();
    }
    void pimat(int mat[][])
    {
        for(int i=0;i<mat.length;i++)
        {
            for(int j=0;j<mat[0].length;j++)
            {
                o.print(mat[i][j]+" ");
            }
            o.println();
        }
    }
    void plmat(long mat[][])
    {
        for(int i=0;i<mat.length;i++)
        {
            for(int j=0;j<mat[0].length;j++)
            {
                o.print(mat[i][j]+" ");
            }
            o.println();
        }
    }
   static class DJset
{
int n;
ty1 arr[];
class ty1
{
    int rank;
    int par;
    ty1(int p,int r)
    {
        par=p;
        rank=r;
    }
}
DJset(int nu)
{
    n=nu;
    arr=new ty1[n];
    for(int i=0;i<n;i++)
    {
        arr[i]=new ty1(i,1);
    }
}
int find(int x)
{
    if(arr[x].par!=x)
    {
        arr[x].par=find(arr[x].par);
    }
    return arr[x].par;
}
void union(int x,int y)
{
    x=find(x);
    y=find(y);
    if(x!=y)
    {
        if(arr[x].rank<arr[y].rank)
        {
            arr[x].par=y;
        }
        else if(arr[y].rank<arr[x].rank)
        {
            arr[y].par=x;
        }
        else
        {
            arr[x].rank++;
            arr[y].par=x;
        }
    }
}
public String toString()
{
    String res="";
    for(int i=0;i<n;i++)
    {
        res+=(arr[i].par+" ");
    }
    return res;
}
public int countsets()
{
    int res=0;
    for(int i=0;i<n;i++)
    {
        if(arr[i].par==i)
        {
            res++;
        }
    }
    return res;
}
}
    //////////////////////////////////// template finished //////////////////////////////////////
}