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 Ruby (2.3.3) (judge verdict: Accepted)

# util functions

# debug
$debugFlag = ( ARGV[0] != nil )
p "==== DEBUG MODE ====" if $debugFlag

def pd(str)
  p str if $debugFlag
end

def printd(str)
  print str if $debugFlag
end

# input
inputs = []
lc = 0
nn = 0
while l = $stdin.gets do
  if lc == 0
    nn = l.chomp.to_i
  else
    inputs << l.chomp.split(" ").map(&:to_i)
  end
  lc += 1
end

# input check
if $debugFlag
  p "--- INPUT (begin) ---"
  inputs.each do |l_i|
    p l_i
  end
  p "--- INPUT (end) ---"
  print "\n"
end

# body
if $debugFlag
  p nn
  p inputs
end

if nn == 1
  puts 1
  exit
end

inputsy = inputs.clone
inputs.sort_by! {|x, y| x}
inputsy.sort_by! {|x, y| y}

comb = [*(0..nn-1)].combination(2).to_a

pd inputs
pd inputsy
pd comb

$statis = {}
comb.each do |c|
  pv = inputs[c[1]][0] - inputs[c[0]][0]
  qv = inputs[c[1]][1] - inputs[c[0]][1]

  if $statis["#{pv},#{qv}"] != nil
    $statis["#{pv},#{qv}"] += 1
  else
    $statis["#{pv},#{qv}"] = 1
  end
  
end

$statisy = {}
comb.each do |c|
  pv = inputsy[c[1]][0] - inputsy[c[0]][0]
  qv = inputsy[c[1]][1] - inputsy[c[0]][1]

  if $statisy["#{pv},#{qv}"] != nil
    $statisy["#{pv},#{qv}"] += 1
  else
    $statisy["#{pv},#{qv}"] = 1
  end
  
end


pd $statis
pd $statisy

tmp_max = 0
$statis.each do |k, v|
  if v > tmp_max
    tmp_max = v
  end
end

$statisy.each do |k, v|
  if v > tmp_max
    tmp_max = v
  end
end

puts (nn - tmp_max)