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 PYTHON3):

Solution:
# for _ in range(int(input())):
#     n=int(input())
#     a=list(map(int,input().split()))
#     arr=[]
#     b=[]
#     op=[]
#     ll=[]
#     rabta=True
#     sss=0
#     for m in range(0,n):
#         b.append(a[m])
#     for i in range(0,n):
#         for j in range(i+1,n):
#             if (a[i]>a[j]):
#                 put=a[i]-a[j]
#             else:
#                 put=a[j]-a[i]
#             arr.append(put)

#     j=0
#     for k in range(len(arr)):
#         if arr[k] in a:
#             continue
#         else:
            
#             if len(b)<=300 :
#                 b.append(arr[k])
#                 while rabta==True :
#                     for o in range(0,len(b)-1):
#                         if (b[-1]>b[o]):
#                             put=b[-1]-b[o]
#                         else:
#                             put=b[o]-b[-1]
#                         if put in b :
#                             if (k==((len(arr)-1)) or k==0) and (j==len(ll) or j==0):
#                                 rabta=False
#                                 print("yes")
#                                 print(len(b))
#                                 print(*b)
#                                 break
                            
#                         else:
#                             if put not in ll:
#                                 ll.append(put)
#                     if len(ll)>0 and j<len(ll):
#                         b.append(ll[j])
#                         j+=1
                        
#                     else:
#                         break
#             else:
#                 print("no")
#                 break

for _ in range(int(input())):
    n=int(input())
    a=list(map(int,input().split()))
    g=[]
    for i in range(0,101):
        g.append(i)
    neg=False
    for j in range(0,n):
        if a[j]<0:
            print("no")
            neg=True
            break
        else:
            continue
    if not neg:
        
        print("yes")
        print(101)
        print(*g)