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: Wrong Answer)


import java.util.ArrayList;
import java.util.Collections;
import java.util.List;
import java.util.Scanner;

public class Main {
    public static void main(String[] args) {
        new Main().run();
    }

    private void run(){
        final Scanner scanner = new Scanner(System.in);
        final int count = scanner.nextInt();
        if(count == 1){
            System.out.println(1);
            return;
        }
        final long[][] table = new long[count][2];

        for (int i = 0; i < count; i++) {
            table[i][0] = scanner.nextLong();
            table[i][1] = scanner.nextLong();
        }

        List<Len> lens = new ArrayList<>();
        List<MyInteger> counts = new ArrayList<>();

        for (int i = 0; i < count; i++) {
            for (int j = i + 1; j < count; j++) {
                if (table[i][0] > table[j][0]) {
                    extracted(table, lens, counts, j, i);
                } else {
                    extracted(table, lens, counts, i, j);
                }
            }
        }
        Collections.sort(counts);
        System.out.println(count - counts.get(0).getInteger());
    }

    private void extracted(final long[][] table, final List<Len> lens, final List<MyInteger> counts, final int i, final int j) {
        final Len len = new Len(table[j][0] - table[i][0], table[j][1] - table[i][1]);
        int index;
        if ((index = lens.indexOf(len)) != -1) {
            counts.get(index).increment();
        } else {
            lens.add(len);
            counts.add(new MyInteger());
        }
    }

    class MyInteger implements Comparable {
        private int integer = 1;

        void increment() {
            this.integer++;
        }

        public int getInteger() {
            return integer;
        }

        @Override
        public int compareTo(final Object o) {
            return ((MyInteger) o).getInteger() - this.integer;
        }
    }

    class Len {
        private final long x;
        private final long y;

        Len(final long x, final long y) {
            this.x = x;
            this.y = y;
        }

        @Override
        public boolean equals(final Object obj) {
            return ((Len) obj).getX() == this.getX() && ((Len) obj).getY() == this.getY();
        }

        public long getX() {
            return x;
        }

        long getY() {
            return y;
        }
    }
}