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.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.StringTokenizer;
import java.io.IOException;
import java.io.BufferedReader;
import java.io.InputStreamReader;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 *
 * @author Abhas Jain
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        BPickingUp solver = new BPickingUp();
        solver.solve(1, in, out);
        out.close();
    }

    static class BPickingUp {
        public void solve(int testNumber, InputReader in, PrintWriter out) {
            int n = in.ni();
            if (n == 1) {
                out.print(1);
                return;
            }
            int[] x = new int[n];
            int[] y = new int[n];
            for (int i = 0; i < n; ++i) {
                x[i] = in.ni();
                y[i] = in.ni();
            }
            int pr = Integer.MAX_VALUE;
            for (int i = 0; i < n; ++i) {
                for (int j = 0; j < n; ++j) {
                    int p = x[j] - x[i];
                    int q = y[j] - y[i];
                    DJSet set = new DJSet(n);
                    for (int i1 = 0; i1 < n; ++i1) {
                        for (int j1 = 0; j1 < n; ++j1) {
                            if (x[j1] - x[i1] == p && y[j1] - y[i1] == q) {
                                set.merge(i1, j1);
                            }
                        }
                    }
                    pr = Math.min(pr, set.compo);
                }
            }
            out.print(pr);
        }

        public class DJSet {
            int[] id;
            int[] size;
            int compo;

            DJSet(int n) {
                id = new int[n];
                size = new int[n];
                for (int i = 0; i < n; ++i) {
                    id[i] = i;
                    size[i] = 1;
                }
                compo = n;
            }

            int root(int p) {
                while (id[p] != p) {
                    id[p] = id[id[p]];
                    p = id[p];
                }
                return p;
            }

            void merge(int p, int q) {
                p = root(p);
                q = root(q);
                if (p == q) return;
                compo--;
                if (size[p] > size[q]) {
                    int temp = q;
                    q = p;
                    p = temp;
                }
                id[p] = q;
                size[q] += size[p];
                size[p] = 0;
            }

        }

    }

    static class InputReader {
        public BufferedReader reader;
        public StringTokenizer tokenizer;

        public InputReader(InputStream stream) {
            reader = new BufferedReader(new InputStreamReader(stream), 32768);
            tokenizer = null;
        }

        public String next() {
            while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    tokenizer = new StringTokenizer(reader.readLine());
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return tokenizer.nextToken();
        }

        public int ni() {
            return Integer.parseInt(next());
        }

    }
}