You are given an array (a_1, a_2, \ldots, a_n). There exist (3) initially empty multisets (A, B, C), and for each index (i) ((1 \leq i \leq n)), you may put (a_i) into exactly one of (A), (B), or (C). Determine whether it is possible to put the elements into the multisets such that (\operatorname{MEX}(A) + \operatorname{MEX}(B) + \operatorname{MEX}(C) \geq 2 \cdot \max(\operatorname{MEX}(A), \operatorname{MEX}(B), \operatorname{MEX}(C)))(^{\text{∗}}). If so, output a construction that achieves this. (^{\text{∗}})(\operatorname{MEX}(D)) is defined as the smallest non-negative integer that is not present in the set (D). For example, (\operatorname{MEX}(1, 2, 0, 5) = 3), and (\operatorname{MEX}(1, 2, 4, 9) = 0). The (\operatorname{MEX}) of an empty set is (0). The first line of each input contains (t) ((1 \leq t \leq 10^4)) — the number of test cases. The first line of each test case contains (n) ((3 \leq n \leq 2 \cdot 10^5)) — the length of (a). The second line of each test case contains (a_1, a_2, \ldots, a_n) ((0 \leq a_i \leq 10^9)) — the array (a). It is guaranteed that the sum of (n) over all test cases does not exceed (2 \cdot 10^5). If a valid distribution of elements into the multisets exists, output (YES). Otherwise, output (NO). If the answer is (YES), output a string (s) of length (n) on a new line, such that (s_i = A) if the (i)-th element was put into the multiset (A), (s_i = B) if the (i)-th element was put into the multiset (B), and (s_i = C) if the (i)-th element was put into the multiset (C). You can output the answer in any case (upper or lower). For example, the strings (YES), (yes), (yEs), and (Yes) will be recognized as positive responses, and the strings $$$\text