You should know by now that a standard ICPC-style team consists of three students. The best teams, however, have a more precise composition. Students generally specialise into being coders, mathematicians or physicists. A student can only specialise into one category.
A team is considered perfect if it includes at least one coder, at least one mathematician and consists of three members (physicists seem to have a good grasp of both skillsets).
As a coach at a disturbingly large university you know that \(c\) students are coders, \(m\) are mathematicians and \(p\) are physicists.
How many perfect teams can you make?
Some students will be left without a team and obviously no student can be part of two teams.
You need to compute the number of teams for \(Q\) distributions of students.
The first line contains a single integer \(Q (1 \leq Q \leq 10000)\).
The next \(Q\) lines contian three integers \(c, m, p (0 \leq c,m,p \leq 10^8)\)
\(Q\) lines containing a single integer, the number of perfect teams possible.
Sample Input 1
6 1 1 1 0 0 0 0 1 1 3 6 0 100 1 10 4 4 1
Sample Output 1
1 0 0 3 1 3