Good Distance

AtCoder

IDabc133_b

Time2000ms

Memory256MB

Difficulty—

There are $N$ points in a $D$\-dimensional space. The coordinates of the $i$\-th point are $(X_{i1}, X_{i2}, ..., X_{iD})$. The distance between two points with coordinates $(y_1, y_2, ..., y_D)$ and $(z_1, z_2, ..., z_D)$ is $\sqrt{(y_1 - z_1)^2 + (y_2 - z_2)^2 + ... + (y_D - z_D)^2}$. How many pairs $(i, j)$ $(i < j)$ are there such that the distance between the $i$\-th point and the $j$\-th point is an integer? ## Constraints * All values in input are integers. * $2 \leq N \leq 10$ * $1 \leq D \leq 10$ * $-20 \leq X_{ij} \leq 20$ * No two given points have the same coordinates. That is, if $i \neq j$, there exists $k$ such that $X_{ik} \neq X_{jk}$. ## Input Input is given from Standard Input in the following format: $N$ $D$ $X_{11}$ $X_{12}$ $...$ $X_{1D}$ $X_{21}$ $X_{22}$ $...$ $X_{2D}$ $\vdots$ $X_{N1}$ $X_{N2}$ $...$ $X_{ND}$ [samples]

Samples

Input #1

Output #1

1

The number of pairs with an integer distance is one, as follows:

*   The distance between the first point and the second point is $\sqrt{|1-5|^2 + |2-5|^2} = 5$, which is an integer.
*   The distance between the second point and the third point is $\sqrt{|5-(-2)|^2 + |5-8|^2} = \sqrt{58}$, which is not an integer.
*   The distance between the third point and the first point is $\sqrt{|-2-1|^2+|8-2|^2} = 3\sqrt{5}$, which is not an integer.

Input #2

Output #2

Input #3

Output #3

API Response (JSON)

{
  "problem": {
    "name": "Good Distance",
    "description": {
      "content": "There are $N$ points in a $D$\\-dimensional space. The coordinates of the $i$\\-th point are $(X_{i1}, X_{i2}, ..., X_{iD})$. The distance between two points with coordinates $(y_1, y_2, ..., y_D)$ and ",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc133_b"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "There are $N$ points in a $D$\\-dimensional space.\nThe coordinates of the $i$\\-th point are $(X_{i1}, X_{i2}, ..., X_{iD})$.\nThe distance between two points with coordinates $(y_1, y_2, ..., y_D)$ and ...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments