Compass Walking

AtCoder

IDabc198_c

Time2000ms

Memory256MB

Difficulty—

Takahashi is standing at the origin of a two-dimensional plane. By taking one step, he can move to a point whose Euclidian distance from his current position is exactly $R$ (the coordinates of the destination of a move do not have to be integers). There is no other way to move. Find the minimum number of steps Takahashi has to take before reaching $(X, Y)$. We remind you that the Euclidian distance between points $(x_1,y_1)$ and $(x_2,y_2)$ is $\sqrt{(x_1-x_2)^2+(y_1-y_2)^2}$. ## Constraints * $1 \leq R \leq 10^5$ * $0 \leq X,Y \leq 10^5$ * $(X,Y) \neq (0,0)$ * All values in input are integers. ## Input Input is given from Standard Input in the following format: $R$ $X$ $Y$ [samples]

Samples

Input #1

5 15 0

Output #1

3

He can reach there in three steps: $(0,0) \to (5,0) \to (10,0) \to (15,0)$. This is the minimum number needed: he cannot reach there in two or fewer steps.
![image](https://img.atcoder.jp/ghi/d34bbf4b43d8de5baf54bf589618c64e.png)

Input #2

5 11 0

Output #2

3

One optimal route is $(0,0) \to (5,0) \to (8,4) \to (11,0)$.
![image](https://img.atcoder.jp/ghi/0932ca629f834af5124563f198bb3f9e.png)

Input #3

3 4 4

Output #3

2

One optimal route is $(0,0) \to (2-\frac{\sqrt{2}}{2}, 2+\frac{\sqrt{2}}{2}) \to (4,4)$.
![image](https://img.atcoder.jp/ghi/50d67c401f9aceed8baa130918144597.png)

API Response (JSON)

{
  "problem": {
    "name": "Compass Walking",
    "description": {
      "content": "Takahashi is standing at the origin of a two-dimensional plane. By taking one step, he can move to a point whose Euclidian distance from his current position is exactly $R$ (the coordinates of the des",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc198_c"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "Takahashi is standing at the origin of a two-dimensional plane.\nBy taking one step, he can move to a point whose Euclidian distance from his current position is exactly $R$ (the coordinates of the des...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments