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 Java8 (OpenJDK 1.8.0) (judge verdict: Accepted)

import java.util.Arrays;
import java.util.HashSet;
import java.util.LinkedHashSet;
import java.util.Objects;
import java.util.Scanner;
import java.util.Set;

public class Main {
  public static void main(String[] args) {
    Scanner scanner = new Scanner(System.in);

    int N = scanner.nextInt();
    Ball[] balls = new Ball[N];
    for (int i = 0; i < N; i++) balls[i] = new Ball(scanner.nextInt(), scanner.nextInt());
    Arrays.sort(balls, (b1, b2) -> {
      if (b1.x == b2.x) return b1.y - b2.y;
      return b1.x - b2.x;
    });

    Set<Pair> pqSet = new HashSet<>();
    for (int i = 0; i < N; i++) {
      for (int j = 0; j < N; j++) {
        if (i == j) continue;
        pqSet.add(new Pair(balls[j].x - balls[i].x, balls[j].y - balls[i].y));
      }
    }
    int min = N;
    for (Pair pq : pqSet) {
      Set<Ball> set = new LinkedHashSet<>(Arrays.asList(balls));
      int cost = 0;
      Ball next = null;
      while (!set.isEmpty()) {
        if (next == null || !set.contains(next)) {
          cost++;
          Ball b = set.stream().findFirst().get();
          set.remove(b);
          next = new Ball(b.x + pq.p, b.y + pq.q);
        } else {
          set.remove(next);
          next = new Ball(next.x + pq.p, next.y + pq.q);
        }
      }
      min = Math.min(min, cost);
    }
    System.out.println(min);
  }

  private static class Pair {
    private final int p;
    private final int q;

    private Pair(int p, int q) {
      this.p = p;
      this.q = q;
    }

    @Override public boolean equals(Object o) {
      if (this == o) return true;
      if (o == null || getClass() != o.getClass()) return false;
      Pair pair = (Pair) o;
      return p == pair.p &&
          q == pair.q;
    }

    @Override public int hashCode() {
      return Objects.hash(p, q);
    }
  }

  private static class Ball {
    private final int x;
    private final int y;

    private Ball(int x, int y) {
      this.x = x;
      this.y = y;
    }

    @Override public boolean equals(Object o) {
      if (this == o) return true;
      if (o == null || getClass() != o.getClass()) return false;
      Ball ball = (Ball) o;
      return x == ball.x &&
          y == ball.y;
    }

    @Override public int hashCode() {
      return Objects.hash(x, y);
    }
  }
}