AT_abc422_c [ABC422C] AtCoder AAC Contest

Takahashi has some letters. Each letter he has is `A`, `B`, or `C`. Initially, he has $ n _ A $ letters `A`, $ n _ B $ letters `B`, and $ n _ C $ letters `C`. He can hold one contest by using one letter `A`, one letter `C`, and additionally any one letter, for a total of three letters. Specifically, he can hold `AAC` by using two letters `A` and one letter `C`, `ABC` by using one letter each of `A`, `B`, and `C`, and `ACC` by using one letter `A` and two letters `C`. He wants to hold as many contests as possible using the letters he currently has. Find the maximum number of contests he can hold. $ T $ test cases are given, so report the answer for each of them.

The input is given from Standard Input in the following format: > $ T $ $ \mathrm{testcase} _ 1 $ $ \mathrm{testcase} _ 2 $ $ \vdots $ $ \mathrm{testcase} _ T $ $ \mathrm{testcase} _ i\ (1\le i\le T) $ represents the $ i $ -th test case and is given in the following format: > $ n _ A $ $ n _ B $ $ n _ C $

Output over $ T $ lines. On the $ i $ -th line $ (1\le i\le T) $ , output the answer to the $ i $ -th test case.

### Sample Explanation 1 In the first test case, he can hold `AAC` once and `ABC` once, for a total of two contests. Therefore, output `2` on the first line. ### Constraints - $ 1\le T\le2\times10 ^ 5 $ - For each test case, - $ 0\le n _ A\le10 ^ 9 $ - $ 0\le n _ B\le10 ^ 9 $ - $ 0\le n _ C\le10 ^ 9 $ - All input values are integers.