Knight Fork

AtCoder

IDabc239_c

Time2000ms

Memory256MB

Difficulty—

On an $xy$\-coordinate plane, is there a lattice point whose distances from two lattice points $(x_1, y_1)$ and $(x_2, y_2)$ are both $\sqrt{5}$? ## Constraints * $-10^9 \leq x_1 \leq 10^9$ * $-10^9 \leq y_1 \leq 10^9$ * $-10^9 \leq x_2 \leq 10^9$ * $-10^9 \leq y_2 \leq 10^9$ * $(x_1, y_1) \neq (x_2, y_2)$ * All values in input are integers. ## Input Input is given from Standard Input in the following format: $x_1$ $y_1$ $x_2$ $y_2$ [samples] ## Notes A point on an $xy$\-coordinate plane whose $x$ and $y$ coordinates are both integers is called a lattice point. The distance between two points $(a, b)$ and $(c, d)$ is defined to be the Euclidean distance between them, $\sqrt{(a - c)^2 + (b-d)^2}$. The following figure illustrates an $xy$\-plane with a black circle at $(0, 0)$ and white circles at the lattice points whose distances from $(0, 0)$ are $\sqrt{5}$. (The grid shows where either $x$ or $y$ is an integer.) ![image](https://img.atcoder.jp/ghi/2bee701e93a6a0298f73121b85a03f46.jpg)

Samples

Input #1

0 0 3 3

Output #1

Yes

*   The distance between points $(2,1)$ and $(x_1, y_1)$ is $\sqrt{(0-2)^2 + (0-1)^2} = \sqrt{5}$;
*   the distance between points $(2,1)$ and $(x_2, y_2)$ is $\sqrt{(3-2)^2 + (3-1)^2} = \sqrt{5}$;
*   point $(2, 1)$ is a lattice point,

so point $(2, 1)$ satisfies the condition. Thus, `Yes` should be printed.  
One can also assert in the same way that $(1, 2)$ also satisfies the condition.

Input #2

0 1 2 3

Output #2

No

No lattice point satisfies the condition, so `No` should be printed.

Input #3

1000000000 1000000000 999999999 999999999

Output #3

Yes

Point $(10^9 + 1, 10^9 - 2)$ and point $(10^9 - 2, 10^9 + 1)$ satisfy the condition.

API Response (JSON)

{
  "problem": {
    "name": "Knight Fork",
    "description": {
      "content": "On an $xy$\\-coordinate plane, is there a lattice point whose distances from two lattice points $(x_1, y_1)$ and $(x_2, y_2)$ are both $\\sqrt{5}$?",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc239_c"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "On an $xy$\\-coordinate plane, is there a lattice point whose distances from two lattice points $(x_1, y_1)$ and $(x_2, y_2)$ are both $\\sqrt{5}$?\n\n## Constraints\n\n*   $-10^9 \\leq x_1 \\leq 10^9$\n*   $-...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments