Hundred Eyes Monster

AtCoder

IDkupc2016_k

Time1000ms

Memory256MB

Difficulty—

## Constraints * $1 \leq T \leq 50000$ * $-10^5 \leq x_A \leq 10^5$ * $-10^5 \leq y_A \leq 10^5$ * $-10^5 \leq x_B \leq 10^5$ * $-10^5 \leq y_B \leq 10^5$ * $1 \leq r_A \leq 10^5$ * $1 \leq r_B \leq 10^5$ * ${r_A}^2 + {r_B}^2 < (x_A - x_B)^2 + (y_A - y_B)^2$ * All values given as input are integers. * It is guaranteed that, when the radiuses of $A$ and $B$ change by $0.0005$, the answer does not change. ## Input The input consists of multiple test cases and is given from Standard Input in the following format: $T$ $testcase_1$ : $testcase_T$ Each test case is given with the following format. $x_A$ $y_A$ $r_A$ $x_B$ $y_B$ $r_B$ ## Story I am a Summoner who can invoke monsters. I can embody the pictures of monsters drawn on sketchbooks. I recently have received a request from Primate Research Institute of Kyoto University to invoke "Hundred Eyes Monster". What an great honor it is to contribute to the prosperity of the primate research of Kyoto University! I decided to paint an extremely high-quarity monster to the best of my ability. I have already painted the forehead and mouth and this time I am going to paint as many eyes as possible between the forehead and mouth. Well...I cannot wait to see the complete painting. ### Problem Statement Two circles $A$, $B$ are given on a two-dimensional plane. The coordinate of the center and radius of circle $A$ is ($x_A$, $y_A$) and $r_A$ respectively. The coordinate of the center and radius of circle $B$ is ($x_B$, $y_B$) and $r_B$ respectively. These two circles have no intersection inside. Here, we consider a set of circles $S$ that satisfies the following conditions. * Each circle in $S$ touches both $A$ and $B$, and does not have common points with them inside the circle. * Any two different circles in $S$ have no common points inside them. Write a program that finds the maximum number of elements in $S$. [samples]

Samples

Input #1

4
0 -3 2 0 3 2
0 0 9 8 8 2
0 0 9 10 10 5
0 0 707 1000 1000 707

Output #1

3
10
21
180

You can arrange circles ,for example, like the following images in Sample 1, 2.  

![image](/img/other/kupc2016/sushi/img00.png) ![image](/img/other/kupc2016/sushi/img01.png)

API Response (JSON)

{
  "problem": {
    "name": "Hundred Eyes Monster",
    "description": {
      "content": "",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 1000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "kupc2016_k"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "## Constraints\n\n*   $1 \\leq T \\leq 50000$\n*   $-10^5 \\leq x_A \\leq 10^5$\n*   $-10^5 \\leq y_A \\leq 10^5$\n*   $-10^5 \\leq x_B \\leq 10^5$\n*   $-10^5 \\leq y_B \\leq 10^5$\n*   $1 \\leq r_A \\leq 10^5$\n*   $1 ...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

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