F. 3SUMtime limit per test1 secondmemory limit per test256 megabytesinputstandard inputoutputstandard outputGiven 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.InputThe 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.OutputOutput 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).ExampleInput
6
4
20 22 19 84
4
1 11 1 2022
4
1100 1100 1100 1111
5
12 34 56 78 90
4
1 9 8 4
6
16 38 94 25 18 99
Output
YES
YES
NO
NO
YES
YES
NoteIn 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.
6
4
20 22 19 84
4
1 11 1 2022
4
1100 1100 1100 1111
5
12 34 56 78 90
4
1 9 8 4
6
16 38 94 25 18 99

YES YES NO NO YES YES 
['brute force', 'math', '*1300']