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
  
  x = [0] * n
  y = [0] * n
  n.times do |i|
    (x[i], y[i]) = gets.chomp.split(' ').map(&:to_i)
  end
  
  table = [nil] * n
  n.times do |i|
	table[i] = [nil] * n
	
    n.times do |j|
      next if i == j
      
			table[i][j] = [i, j]
      
      px = x[j] - x[i]
      py = y[j] - y[i]
      
      n.times do |k|
        next if (i == k) || (j == k)
        
        qx = x[k] - x[i]
        qy = y[k] - y[i]
        
        if px * qy == qx * py then
          table[i][j].push(k)
        end
      end
    end
  end
  
	max1_index = [-1, -1]
	max1_array = []
	max2_index = [-1, -1]
	max2_array = []
	
	n.times do |i|
		n.times do |j|
			next if i == j
			next if table[i][j] == nil
			
			if max1_array.size < table[i][j].size then
				max1_array = table[i][j].dup
				max1_index = [i, j]
			end
		end
	end
	
	n.times do |i|
		n.times do |j|
			next if i == j
			next if table[i][j] == nil
			
			a = max1_array & table[i][j]
			if max2_array.size < (table[i][j].size - a.size) then
				max2_array = table[i][j].dup
				max2_index = [i, j]
			end
		end
	end
	
	puts ((n - (max1_array | max2_array).size) + 1).to_s
end

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