#P1536A. Omkar and Bad Story

Omkar and Bad Story

Description

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=[a1,a2,,an]a = [a_1, a_2, \ldots, a_n] of nn distinct integers. An array b=[b1,b2,,bk]b = [b_1, b_2, \ldots, b_k] is called nice if for any two distinct elements bi,bjb_i, b_j of bb, bibj|b_i-b_j| appears in bb at least once. In addition, all elements in bb must be distinct. Can you add several (maybe, 00) integers to aa to create a nice array bb of size at most 300300? If aa is already nice, you don't have to add any elements.

For example, array [3,6,9][3, 6, 9] is nice, as 63=96=3|6-3|=|9-6| = 3, which appears in the array, and 93=6|9-3| = 6, which appears in the array, while array [4,2,0,6,9][4, 2, 0, 6, 9] is not nice, as 94=5|9-4| = 5 is not present in the array.

For integers xx and yy, xy=xy|x-y| = x-y if x>yx > y and xy=yx|x-y| = y-x otherwise.

Each test contains multiple test cases. The first line contains tt (1t501 \leq t \leq 50), the number of test cases. Description of the test cases follows.

The first line of each test case contains a single integer nn (2n1002 \leq n \leq 100) — the length of the array aa.

The second line of each test case contains nn distinct integers a1,a2,,ana_1, a_2, \cdots, a_n (100ai100-100 \leq a_i \leq 100) — the elements of the array aa.

For each test case, output one line containing YES if Omkar can create a nice array bb by adding elements to aa 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 kk (nk300n \leq k \leq 300).

Then output one line containing kk distinct integers b1,b2,,bkb_1, b_2, \cdots, b_k (109bi109-10^9 \leq b_i \leq 10^9), the elements of the nice array bb. b1,b2,,bkb_1, b_2, \cdots, b_k can be in any order. For each aia_i in aa, aia_i must appear at least once in bb.

It can be proved that if Omkar can create such an array bb, then he can also do so in a way that satisfies the above constraints.

If multiple solutions exist, you can print any.

Input

Each test contains multiple test cases. The first line contains tt (1t501 \leq t \leq 50), the number of test cases. Description of the test cases follows.

The first line of each test case contains a single integer nn (2n1002 \leq n \leq 100) — the length of the array aa.

The second line of each test case contains nn distinct integers a1,a2,,ana_1, a_2, \cdots, a_n (100ai100-100 \leq a_i \leq 100) — the elements of the array aa.

Output

For each test case, output one line containing YES if Omkar can create a nice array bb by adding elements to aa 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 kk (nk300n \leq k \leq 300).

Then output one line containing kk distinct integers b1,b2,,bkb_1, b_2, \cdots, b_k (109bi109-10^9 \leq b_i \leq 10^9), the elements of the nice array bb. b1,b2,,bkb_1, b_2, \cdots, b_k can be in any order. For each aia_i in aa, aia_i must appear at least once in bb.

It can be proved that if Omkar can create such an array bb, then he can also do so in a way that satisfies the above constraints.

If multiple solutions exist, you can print any.

Samples

样例输入 1

4
3
3 0 9
2
3 4
5
-7 3 13 -2 8
4
4 8 12 6

样例输出 1

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 aa to receive the array b=[6,0,3,9]b = [6, 0, 3, 9]. Note that 63=96=30=3|6-3| = |9-6| = |3-0| = 3 and 33 is in bb, 60=93=6|6-0| = |9-3| = 6 and 66 is in bb, and 90=9|9-0| = 9 is in bb, so bb is nice.

For the second case, you can add integers to aa to receive the array b=[5,3,1,2,4]b = [5, 3, 1, 2, 4]. We have that 21=32=43=54=1|2-1| = |3-2| = |4-3| = |5-4| = 1 is in bb, 31=42=53=2|3-1| = |4-2| = |5-3| = 2 is in bb, 41=52=3|4-1| = |5-2| = 3 is in bb, and 51=4|5-1| = 4 is in bb, so bb is nice.

For the fourth case, you can add integers to aa to receive the array b=[8,12,6,2,4,10]b = [8, 12, 6, 2, 4, 10]. We have that 42=64=86=108=1210=2|4-2| = |6-4| = |8-6| = |10-8| = |12-10| = 2 is in bb, 62=84=106=128=4|6-2| = |8-4| = |10-6| = |12-8| = 4 is in bb, 82=104=126=6|8-2| = |10-4| = |12-6| = 6 is in bb, 102=124=8|10-2| = |12-4| = 8 is in bb, and 122=10|12-2| = 10 is in bb, so bb is nice.

It can be proven that for all other test cases it is impossible to create a nice array bb.