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 <iostream>
#include <algorithm>
#include <bitset>
#include <complex>
#include <deque>
#include <exception>
#include <fstream>
#include <functional>
#include <iomanip>
#include <ios>
#include <iosfwd>
#include <istream>
#include <iterator>
#include <limits>
#include <list>
#include <locale>
#include <map>
#include <memory>
#include <new>
#include <numeric>
#include <ostream>
#include <queue>
#include <set>
#include <sstream>
#include <stack>
#include <stdexcept>
#include <streambuf>
#include <string>
#include <typeinfo>
#include <utility>
#include <valarray>
#include <vector>
#include <climits>
#define vi vector<int>
#define vvi vector<vi>
#define pii pair<int,int>
#define vpii vector<pii>
#define V vector
#define pb push_back
#define all(x) x.begin(),x.end()
#define rall(x) x.rbegin(),x.rend()
#define F first
#define S second
#define sqr(x) (x)*(x)
#define mp make_pair
#define mtp make_tuple
#define tpii tuple<int,int,int>
#define ckmax(a,b) a=max(a,b)
#define ckmin(a,b) a=min(a,b)
#define rep(n) for(int i=0;i<n;i++)
#define inf INT_MAX
#define debug(x) cerr<<x<<'\n';
#define quick ios_base::sync_with_stdio(0),cin.tie(0);long double nownow=clock();
#define total_time cerr<<(clock()-nownow)/CLOCKS_PER_SEC*1000<<" (ms)\n";
using namespace std;
template<typename T>void in(vector<T> &a){for(auto &i:a)cin>>i;}
template<typename T>void in(vector<T> &a,int n){for(auto i=0;i<n;i++)cin>>a[i];}
template<typename T>void out(vector<T> &a){for(auto &i:a)cout<<i<<' ';cout<<'\n';}
#define int long long
#define input freopen("/Users/wangkaiyu/Downloads/Q_6_24_3.in","r",stdin);

void solve(){
    int n;
    cin>>n;
    set<int> s;
    for(int i=0;i<n;i++){
        int x;
        cin>>x;
        s.insert(x);
    }
    int cnt=0;
    int f=1;
    while(f){
        f=0;
        for(auto it=s.begin();it!=s.end();it++){
            for(auto jt=s.begin();jt!=it;jt++){
                if(s.find(abs(*it-*jt))==s.end()){
                    s.insert(abs(*it-*jt));
                    cnt++;
                    f=1;
                }
                if(cnt>300){
                    cout<<"No\n";
                    return;
                }
            }
        }
    }
    cout<<"Yes\n";
    cout<<s.size()<<'\n';
    for(auto it=s.begin();it!=s.end();it++){
        cout<<*it<< ' ';
    }
    cout<<'\n';
}

signed main(){
    quick
    int t;
    cin>>t;
    while(t--){
        solve();
    }
    total_time
    return 0;
}