Make 10

AtCoder

IDarc126_a

Time2000ms

Memory256MB

Difficulty—

We have $N_2$ sticks of length $2$ each, $N_3$ sticks of length $3$ each, and $N_4$ sticks of length $4$ each. You can do the following operation any number of times. * Choose two sticks. * Let $x$ and $y$ be the lengths of these sticks. Bond them to form a stick of length $x+y$. Find the maximum number of sticks that can be made whose lengths are exactly $10$. Given $T$ test cases, solve each of them. ## Constraints * $1\leq T\leq 100$ * $0\leq N_2, N_3, N_4\leq 10^{15}$ ## Input Input is given from Standard Input in the following format: $T$ $\text{case}_1$ $\text{case}_2$ $\vdots$ $\text{case}_T$ Each case is in the following format: $N_2$ $N_3$ $N_4$ [samples]

Samples

Input #1

5
3 4 1
7 0 0
0 0 7
0 0 0
1000000000000000 1000000000000000 1000000000000000

Output #1

2
1
0
0
900000000000000

Let us describe the first case. We have three sticks of length $2$, four sticks of length $3$, and one stick of length $4$.
One way to make two sticks of length exactly $10$ is as follows.

*   Bond four sticks of length $2$, $2$, $3$, $3$ in some order to make one stick of length $10$.
*   Bond three sticks of length $3$, $3$, $4$ in some order to make one stick of length $10$.
*   Now we have three sticks of length $2$, $10$, $10$.

API Response (JSON)

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    "name": "Make 10",
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      "content": "We have $N_2$ sticks of length $2$ each, $N_3$ sticks of length $3$ each, and $N_4$ sticks of length $4$ each. You can do the following operation any number of times. *   Choose two sticks. *   Let $",
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    "difficulty": "None",
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    "sync_url": null,
    "sign": "arc126_a"
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  "statements": [
    {
      "statement_type": "Markdown",
      "content": "We have $N_2$ sticks of length $2$ each, $N_3$ sticks of length $3$ each, and $N_4$ sticks of length $4$ each. You can do the following operation any number of times.\n\n*   Choose two sticks.\n*   Let $...",
      "is_translate": false,
      "language": "English"
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}

Full JSON Raw Segments