CF1692F 3SUM

Given an array $ a $ of positive integers with length $ n $ , determine if there exist three distinct indices $ i $ , $ j $ , $ k $ such that $ a_i + a_j + a_k $ ends in the digit $ 3 $ .

The first line contains an integer $ t $ ( $ 1 \leq t \leq 1000 $ ) — the number of test cases. The first line of each test case contains an integer $ n $ ( $ 3 \leq n \leq 2 \cdot 10^5 $ ) — the length of the array. The second line of each test case contains $ n $ integers $ a_1, a_2, \dots, a_n $ ( $ 1 \leq a_i \leq 10^9 $ ) — the elements of the array. The sum of $ n $ across all test cases does not exceed $ 2 \cdot 10^5 $ .

Output $ t $ lines, each of which contains the answer to the corresponding test case. Output "YES" if there exist three distinct indices $ i $ , $ j $ , $ k $ satisfying the constraints in the statement, and "NO" otherwise. You can output the answer in any case (for example, the strings "yEs", "yes", "Yes" and "YES" will be recognized as a positive answer).

In the first test case, you can select $ i=1 $ , $ j=4 $ , $ k=3 $ . Then $ a_1 + a_4 + a_3 = 20 + 84 + 19 = 123 $ , which ends in the digit $ 3 $ . In the second test case, you can select $ i=1 $ , $ j=2 $ , $ k=3 $ . Then $ a_1 + a_2 + a_3 = 1 + 11 + 1 = 13 $ , which ends in the digit $ 3 $ . In the third test case, it can be proven that no such $ i $ , $ j $ , $ k $ exist. Note that $ i=4 $ , $ j=4 $ , $ k=4 $ is not a valid solution, since although $ a_4 + a_4 + a_4 = 1111 + 1111 + 1111 = 3333 $ , which ends in the digit $ 3 $ , the indices need to be distinct. In the fourth test case, it can be proven that no such $ i $ , $ j $ , $ k $ exist. In the fifth test case, you can select $ i=4 $ , $ j=3 $ , $ k=1 $ . Then $ a_4 + a_3 + a_1 = 4 + 8 + 1 = 13 $ , which ends in the digit $ 3 $ . In the sixth test case, you can select $ i=1 $ , $ j=2 $ , $ k=6 $ . Then $ a_1 + a_2 + a_6 = 16 + 38 + 99 = 153 $ , which ends in the digit $ 3 $ .