Problem:
Score : 200 points

Problem Statement

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}

Output

Print the number of pairs (i, j) (i < j) such that the distance between the i-th point and the j-th point is an integer.

Sample Input 1

3 2
1 2
5 5
-2 8

Sample 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.

Sample Input 2

3 4
-3 7 8 2
-12 1 10 2
-2 8 9 3

Sample Output 2

2

Sample Input 3

5 1
1
2
3
4
5

Sample Output 3

10

Solution in Haskell (GHC 7.10.3) (judge verdict: Accepted)

import Control.Monad
import qualified Data.ByteString.Char8 as BS
import Data.Char
import Data.List
import qualified Data.Set as S

toInts :: IO [Int]
toInts = unfoldr (BS.readInt . BS.dropWhile isSpace) <$> BS.getLine

able_dist :: S.Set Int
able_dist = S.fromList [i ^ 2 | i <- [0 .. 130]]

is_good :: Int -> Bool
is_good x = S.member x able_dist

dist_2 :: [Int] -> [Int] -> Int
dist_2 xs ys = sum [(x - y) ^ 2 | (x, y) <- zip xs ys]

solver :: [[Int]] -> Int
solver lss =
  let n = length lss
   in let m = length $ filter is_good [dist_2 a b | a <- lss, b <- lss]
       in div (m - n) 2

main :: IO ()
main = do
  n:d:[] <- toInts
  dat <- forM [1 .. n] (\_ -> toInts)
  print $ solver dat