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 CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
#define ll long long
#define vi vector<int>
#define vvi vector<vector<int> >
#define vb vector<bool>
#define vpii vector<pair<int,int> >
#define pii pair<int,int>
#define mii map<int,int>
#define mod 1000000007
#define pb push_back
#define ff first
#define ss second
#define mkp make_pair
#define input(a,b,n) for(i=b;i<n;i++){cin>>a[i];}
#define print(a,b,n) for(i=b;i<n;i++){cout<<a[i]<<" ";}cout<<endl;
#define shadj(n) for(i=1;i<=n;i++){cout<<i<<"->";for(j=0;j<a[i].size();j++){cout<<a[i][j]<<" ";}cout<<endl;}
const int inf=0x3f3f3f3f3f3f3f3f;
ll power(ll a, ll b){
    ll res = 1;
    while(b!=0){
        if(b&1){
            res *= a;
        }
        a = (a * a);
        b = (b / 2);
    }
    return res;
}
ll fac[100001];
void factorial(ll n)
{
    fac[0] = 1;

    for (ll i = 1; i <= n; i++)
    {
        //cout<<"ERRE";
        fac[i] = (fac[i - 1] * i)%mod;
        fac[i] %= mod;
    }
}
ll ncr(ll n, ll r)
{
    if(n<0)
        return (ll)0;
    ll nn=fac[n];
    nn/=fac[r];
    nn/=fac[n-r];
    return nn;
}


int32_t main()
{
	//ios_base::sync_with_stdio(false);
    //cin.tie(NULL);
    //cout.tie(NULL);
   //freopen("input.txt", "r", stdin);freopen("output.txt", "w", stdout);
    ll i,j,k,l,n,m,t;
    t=1;
    cin>>t;
    while(t--)
    {
        cin>>n;
        set<ll> a;
        ll f=0;
        for(i=0;i<n;i++)
        {
            cin>>k;
            a.insert(k);
            if(k<0)
                f=1;
        }
        if(f==1)
        {
            cout<<"NO\n";
            continue;
        }
        ll x,y;
        x=a.size();
        y=0;
        set<ll> ::iterator p,q;
        k=0;
        while(x!=y)
        {
            x=a.size();
            if(k<=300)
                k++;
            else
                break;
            for(p=a.begin();p!=a.end();p++)
            {
                q=p;
                q++;
                for(;q!=a.end();q++)
                {
                    a.insert(abs(*p-*q));
                }
            }
            y=a.size();
        }
        if(a.size()<=300)
        {
            cout<<"YES\n"<<a.size()<<"\n";

            for(p=a.begin();p!=a.end();p++)
            {
                cout<<*p<<" ";
            }
        }
        else
        {
            cout<<"NO";
        }
        cout<<endl;
    }

    return 0;
}