Problem:
Score : 300 points

Problem Statement

There are N balls in a two-dimensional plane. The i-th ball is at coordinates (x_i, y_i).

We will collect all of these balls, by choosing two integers p and q such that p \neq 0 or q \neq 0 and then repeating the following operation:

Choose a ball remaining in the plane and collect it. Let (a, b) be the coordinates of this ball. If we collected a ball at coordinates (a - p, b - q) in the previous operation, the cost of this operation is 0. Otherwise, including when this is the first time to do this operation, the cost of this operation is 1.

Find the minimum total cost required to collect all the balls when we optimally choose p and q.

Constraints

1 \leq N \leq 50

|x_i|, |y_i| \leq 10^9

If i \neq j, x_i \neq x_j or y_i \neq y_j.

All values in input are integers.

Input

Input is given from Standard Input in the following format:

N
x_1 y_1
:
x_N y_N

Output

Print the minimum total cost required to collect all the balls.

Sample Input 1

2
1 1
2 2

Sample Output 1

1

If we choose p = 1, q = 1, we can collect all the balls at a cost of 1 by collecting them in the order (1, 1), (2, 2).

Sample Input 2

3
1 4
4 6
7 8

Sample Output 2

1

If we choose p = -3, q = -2, we can collect all the balls at a cost of 1 by collecting them in the order (7, 8), (4, 6), (1, 4).

Sample Input 3

4
1 1
1 2
2 1
2 2

Sample Output 3

2

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


import qualified Data.Vector.Unboxed as U
import qualified Data.Vector as V
import qualified Data.ByteString.Char8 as C
import qualified Data.Array.IO as A
import Debug.Trace
import Data.List
import Control.Monad
import Data.Ord


r :: Int -> IO (U.Vector Int)
r n = U.unfoldrN n (C.readInt . C.dropWhile (==' ')) <$> C.getLine

r' :: IO [Int]
r'  =   unfoldr    (C.readInt . C.dropWhile (==' ')) <$> C.getLine

rp :: IO (Int,Int)
rp  = toTup . unfoldr    (C.readInt . C.dropWhile (==' ')) <$> C.getLine

toTup [a,b] = (a,b)

type Point = (Int,Int)
type Dist = (Int,Int)

main :: IO ()
main = do
    n <- readLn
    ws <- replicateM n rp
    --print ws
    let difs = sort $ map (ptNorm . uncurry ptDif) (pair ws)
    --print difs
    let difs' = sortBy (flip (comparing snd)) $ map lenP (group difs)
    --print difs'
    let winDif = fst (head difs')
    --print winDif
    let res = groupCount 0 winDif ws
    print res


groupCount :: Int -> Dist -> [Point] -> Int
groupCount ac _ []  = ac
groupCount ac d ls  = groupCount (ac+1) d (grouperLR d ls)

grouperLR :: Point -> [Point] -> [Point]
grouperLR d ls = intersect (grouper (ptNeg d) ls) (grouper d ls)

grouper :: Dist -> [Point] -> [Point]
grouper d [] = []
grouper d (p:ps) = {-traceShow (d,p:ps) $-} let newp = ptAdd d p in
                    case find ((newp ==)) ps of
                        Nothing -> ps
                        Just r  -> grouper d (newp:(delete r ps))


lenP ls = (head ls, length ls)

ptDif (a,b) (x,y) = (a-x,b-y)
ptAdd (a,b) (x,y) = (a+x,b+y)

ptNorm p@(x,y) = if x<0 then ptNeg p
                else if x==0 && y<0 then ptNeg p
                else p

ptNeg (x,y) = (-x,-y)


pair :: [a] -> [(a,a)]
pair []     = []
pair (a:as) = map (\x->(a,x)) as ++ pair as