Problem I
Transcribed Books

Long before Gutenberg invented letterpress printing, books have been transcribed by monks. Cloisters wanted to be able to check that a book was transcribed by them (and not by a different cloister). Although watermarked paper would have been an option, the cloister preferred to use a system of hard-to-fake serial numbers for identifying their transcriptions.

Each serial number consists of $10$ single numbers $a_1, a_2, \ldots, a_{10}$ . Valid serial numbers satisfy $a_1 + a_2 + \ldots + a_9 \equiv a_{10} ~({\rm mod}~N)$ with $0 \le a_{10} < N$ . The $N$ is specific to and only known by the cloister that has transcribed this book and is therefore able to check its origin.

You are confronted with a pile of books that presumably have been transcribed by a single cloister. You are asked to write a computer program to determine that cloister, i.e. to calculate the biggest possible $N$ that makes the serial numbers of these books valid. Obviously, no cloister has chosen $N=1$ . So if your calculations yield $N=1$ , there must be something wrong.

Input
Input starts with an integer $t$ on a single line, the number of test cases ( $1 \le t \le 100$ ). Each test case starts with an integer $c$ on a single line, the number of serial numbers you have to consider ( $2 \le c \le 1000$ ). Each of the following $c$ lines holds $10$ integer numbers $a_1, a_2, \ldots, a_{10}$ ( $0 \le a_i < 2^{28}$ ) separated by single spaces.

Output
For each test case, output a single line containing the largest possible $N$ , so that each given serial number for that test case is valid. If you cannot find a $N > 1$ satisfying the condition for all serial numbers or if the numbers are valid independent of the choice of $N$ , output ``impossible'' (without the quotes) on a single line.

Sample Input

4
2
1 1 1 1 1 1 1 1 1 9
2 4 6 8 10 12 14 16 18 90
3
1 1 1 1 1 1 1 1 1 1
5 4 7 2 6 4 2 1 3 2
1 2 3 4 5 6 7 8 9 5
2
1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 0
2
2 2 2 2 2 2 2 2 2 0
1 1 1 1 1 1 1 1 1 1
 

Sample Output

impossible
8
impossible
2