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: Wrong Answer)

def main(argv)
  n = gets.chomp.to_i
  
  ps = [nil] * n
  n.times do |i|
    (x, y) = gets.chomp.split(' ').map(&:to_i)
    ps[i] = {:x => x, :y => y}
  end
  
  ans = 1e+9.to_i
  n.times do |i|
    n.times do |j|
      next if i == j
      
      dx = ps[j][:x] - ps[i][:x]
      dy = ps[j][:y] - ps[i][:y]
      
      count = 0
      flag = [false] * n
      n.times do |k|
        next if flag[k]
        flag[k] = true
        count += 1
        
        m = 1
        while true do
          q = {:x => ps[k][:x] + m * dx, :y => ps[k][:y] + m * dy}
          qi = ps.find_index(q)
          if qi == nil then
            break
          else
            if flag[qi] then
              break
            else
              flag[qi] = true
            end
          end
          m += 1
        end
      end
      
      ans = [ans, count].min
    end
  end
  
  puts ans.to_s
end

if self.to_s == 'main' then
  main(ARGV)
end