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 $3$ .