B. Progressive Squaretime limit per test2 secondsmemory limit per test256 megabytesinputstandard inputoutputstandard outputA progressive square of size n is an n \times n matrix. Maxim chooses three integers a_{1,1}, c, and d and constructs a progressive square according to the following rules:a_{i+1,j} = a_{i,j} + ca_{i,j+1} = a_{i,j} + dFor example, if n = 3, a_{1,1} = 1, c=2, and d=3, then the progressive square looks as follows: \begin{pmatrix} 1 & 4 & 7 \\ 3 & 6 & 9 \\ 5 & 8 & 11 \end{pmatrix} Last month Maxim constructed a progressive square and remembered the values of n, c, and d. Recently, he found an array b of n^2 integers in random order and wants to make sure that these elements are the elements of that specific square.It can be shown that for any values of n, a_{1,1}, c, and d, there exists exactly one progressive square that satisfies all the rules.InputThe first line contains an integer t (1 \le t \le {10} ^ 4) — the number of test cases.The first line of each test case contains three integers n, c, and d (2 \le n \le 500, 1 \le c, d \le 10^6) — the size of the square and the values of c and d as described in the statement.The second line of each test case contains n \cdot n integers b_1, b_2, \dots, b_{n \cdot n} (1 \le b_i \le 10^9) — the elements found by Maxim.It is guaranteed that the sum of n ^ 2 over all test cases does not exceed 25 \cdot {10} ^ 4.OutputFor each test case, output "YES" in a separate line if a progressive square for the given n, c, and d can be constructed from the array elements a, otherwise output "NO".You can output each letter in any case (lowercase or uppercase). For example, the strings "yEs", "yes", "Yes", and "YES" will be accepted as a positive answer.ExampleInput
53 2 33 9 6 5 7 1 10 4 83 2 33 9 6 5 7 1 11 4 82 100 100400 300 400 5003 2 33 9 6 6 5 1 11 4 84 4 415 27 7 19 23 23 11 15 7 3 19 23 11 15 11 15Output
NO
YES
YES
NO
NO

53 2 33 9 6 5 7 1 10 4 83 2 33 9 6 5 7 1 11 4 82 100 100400 300 400 5003 2 33 9 6 6 5 1 11 4 84 4 415 27 7 19 23 23 11 15 7 3 19 23 11 15 11 15
NO YES YES NO NO 
['constructive algorithms', 'data structures', 'implementation', 'sortings', '*1000']