(He who has already studied linear algebra may skip this part) A matrix is composed of n × n elements. Formally, is an n × n matrix. For example, A= Two operations on matrices will be used in this problem: and an1 an2 ··· ann () a11 a12 ··· a1n a21 a22 ··· a2n A= . . ... . is a 2×2 matrix.

- A + k (A is an n × n matrix, k is an integer) all the elements in the MAIN diagonal is added by k. That is For example, A−k is defined A+(−k), so 34 3−1 2. A∗B (both A and B are n×n matrices). Let 12 34 an1 an2 ··· ann+k ()() 12+5=62 34 39 ()() a11 + k a12 · · · a1n a21 a22 + k · · · a2n A+k= . . ... . 12 −42 −5= a11 a12 ··· a1n b11 b12 ··· b1n a21 a22 ··· a2n b21 b22 ··· b2n A=....,B=.... . . .. . . . .. . an1 an2 ··· ann bn1 bn2 ··· bnn c11 c12 ··· c1n c21 c22 ··· c2n C=A×B= . . ... . cn1 cn2 ··· cnn

0 0 0 0 3 4 A= It can be proven that there are infinitely many solutions, however, I do not like trivial answer, so your answer must have at least (n ∗ n)/2 non-zero elements. Input The first line contains the number of tests t (1 ≤ t ≤ 15). Each case contains two lines. The first line contains an integer m (1 ≤ m ≤ 30). The second line contains m integers, representing k1, k2, . . . , km respectively. Absolute values of the integers are no greater than 100. Output For each test case, if no answer can be found, print ‘-1’. Otherwise print n, indicating that you found an n × n matrix root. The following n lines should be the matrix. It is guaranteed that if there is an answer, the smallest possible n is not greater than 50, so your n should also NOT be greater than 50. The absolute value of integers you gave should not be larger than 1000. Sample Input 2 2 1 -5 2 1 -5

10565 – Matrix 3/3 Sample Output 2 14 23 2 14 23