P15735 [JAG 2024 Summer Camp #2] Give Me a Lot of Triangles

You have $A_1$ sticks of length $1$, $A_2$ sticks of length $2$, and $A_3$ sticks of length $3$. You can perform the following operation any number of times: - Choose 3 sticks such that they can form a triangle. Use these 3 sticks to make a triangle. Once used, these sticks cannot be used to form other triangles. To "form a triangle", the lengths of the chosen sticks $a$, $b$, and $c$ must satisfy the triangle inequality: $a + b > c$, $b + c > a$, and $c + a > b$. Determine the maximum number of triangles that can be made. Given $T$ test cases, compute the answer for each.

The input is given in the following format: $$ \begin{aligned} &T \\ &\text{case}_1 \\ &\text{case}_2 \\ &\vdots \\ &\text{case}_T \end{aligned} $$ Here, $\text{case}_i$ denotes the $i$-th test case. Each test case is given in the following format: $$ A_1 \ A_2 \ A_3 $$ - $1 \leq T \leq 10,000$ - $0 \leq A_i \leq 10^8$ - All input values are integers.

Output $T$ lines. On the $i$-th line, output the answer for the $i$-th test case.