You have an array (a) of size (n) — (a_1, a_2, \ldots a_n). You need to divide the (n) elements into (2) sequences (B) and (C), satisfying the following conditions: Each element belongs to exactly one sequence. Both sequences (B) and (C) contain at least one element. (\gcd) ((B_1, B_2, \ldots, B_{|B|}) \ne \gcd(C_1, C_2, \ldots, C_{|C|})) (^{\text{∗}}) (^{\text{∗}})(\gcd(x, y)) denotes the greatest common divisor (GCD) of integers (x) and (y). Each test contains multiple test cases. The first line contains the number of test cases (t) ((1 \le t \le 500)). The description of the test cases follows. The first line of each test case contains an integer (n) ((2 \le n \le 100)). The second line of each test case contains (n) integers (a_1,a_2,\ldots,a_n) ((1 \le a_i \le 10^4)). For each test case, first output (Yes) if a solution exists or (No) if no solution exists. You may print each character in either case, for example (YES) and (yEs) will also be accepted. Only when there is a solution, output (n) integers on the second line. The (i)-th number should be either (1) or (2). (1) represents that the element belongs to sequence (B) and (2) represents that the element belongs to sequence (C). You should guarantee that (1) and (2) both appear at least once. In the first test case, (B = 51, 9) and (C = 1, 20). You can verify (\gcd(B_1, B_2) = 3 \ne 1 = \gcd(C_1, C_2)). In the second test case, it is impossible to find a solution. For example, suppose you distributed the first (3) elements to array (B) and then the last element to array (C). You have (B = 5, 5, 5) and (C = 5), but (\gcd(B_1, B_2, B_3) = 5 = \gcd(C_1)). Hence it is invalid.