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)

-- vim: set fdm=marker : -- {{{
{-# OPTIONS_GHC -O2 #-}
{-# LANGUAGE UnboxedTuples #-}
{-# LANGUAGE BangPatterns #-}
import Control.Monad
import Control.Monad.Fix (fix)
import Data.Maybe
import Data.Array.Unboxed
import qualified Data.IntMap as IM
import qualified Data.ByteString.Char8 as BS
-- }}}

-- Input functions with ByteString
-- {{{
tuplify2 (x:y:_) = (x,y)
tuplify2 _ = undefined

readInt :: Num a => BS.ByteString -> a
readInt = fromIntegral . fst . fromJust . BS.readInteger
readIntTuple :: Num a => BS.ByteString -> (a, a)
readIntTuple = tuplify2 . map readInt . BS.words
readIntList :: Num a => BS.ByteString -> [a]
readIntList = map readInt . BS.words

getInt :: Num a => IO a
getInt = readInt <$> BS.getLine
getIntList :: Num a => IO [a]
getIntList = readIntList <$> BS.getLine
getIntN n = map readInt <$> replicateM (fromIntegral n) BS.getLine
getIntNList n = map readIntList <$> replicateM (fromIntegral n) BS.getLine
getIntMatrix = map readIntList . BS.lines <$> BS.getContents
getIntTuple = readIntTuple <$> BS.getLine
getIntNTuples n = map readIntTuple <$> replicateM (fromIntegral n) BS.getLine
getIntTuples = map readIntTuple . BS.lines <$> BS.getContents
-- }}}

main = do
    [n,d] <- getIntList :: IO [Int]
    xss <- getIntNList n :: IO [[Int]]
    print $ solve n xss

solve :: Int -> [[Int]] -> Int
solve n xss = length [() | i <- [0..(n-1)], j <- [(i+1)..(n-1)], isInt (xss!!i) (xss!!j)]

isInt :: [Int] -> [Int] -> Bool
isInt xi xj = isSquare . sum $ zipWith sqMul xi xj where
  sqMul x y = (x - y) * (x - y)

isSquare :: (Integral a) => a -> Bool
isSquare n = (round . sqrt $ fromIntegral n) ^ 2 == n