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.BufferedReader;
import java.io.FileNotFoundException;
import java.io.FileReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.StringTokenizer;

public class Main {
    public static void main(String[] args){
        PrintWriter out = new PrintWriter(System.out);
        FastScanner sc = new FastScanner();

        int N = sc.nextInt();
        long x[] = new long[N];
        long y[] = new long[N];
        for (int i=0;i<N;i++) {
            x[i] = sc.nextLong();
            y[i] = sc.nextLong();
        }

        int ans = N;

        for (int i=0;i<N;i++) {
            for (int j=i+1;j<N;j++) {
                long pq[] = calc_pq(x[i], y[i], x[j], y[j]);

                UnionFind uf = new UnionFind(N);

                for (int k=0;k<N;k++) {
                    for (int l=k+1;l<N;l++) {
                        if (check(x[k], y[k], x[l], y[l], pq[0], pq[1]) == false) continue;

                        uf.union(k, l);
                    }
                }

                int cost = 0;
                int groups[] = new int[N];
                for (int k=0;k<N;k++) {
                    int g = uf.find(k);
                    if (groups[g] == 0) {
                        cost++;
                        groups[g] = 1;
                    }
                }

                ans = Math.min(ans, cost);
            }
        }

        out.println(ans);
        out.flush();
    }

    public static long[] calc_pq(long x1, long y1, long x2, long y2) {
        return new long[] { x2 - x1, y2 - y1 };
    }

    public static boolean check(long x1, long y1, long x2, long y2, long p, long q) {
        long dx = x2 - x1;
        long dy = y2 - y1;

        if (dx == p && dy == q) {
            return true;
        }

        if (dx == -p && dy == -q) {
            return true;
        }

        return false;
    }

    public static class FastScanner {
        BufferedReader br;
        StringTokenizer st;

        public FastScanner(String s) {
            try {
                br = new BufferedReader(new FileReader(s));
            } catch (FileNotFoundException e) {
                e.printStackTrace();
            }
        }

        public FastScanner() {
            br = new BufferedReader(new InputStreamReader(System.in));
        }

        String nextToken() {
            while (st == null || !st.hasMoreElements()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }

        int nextInt() {
            return Integer.parseInt(nextToken());
        }

        long nextLong() {
            return Long.parseLong(nextToken());
        }

        double nextDouble() {
            return Double.parseDouble(nextToken());
        }

        int[] nextIntArray(int N) {
            int a[] = new int[N];
            for (int i=0;i<N;i++) {
                a[i] = this.nextInt();
            }

            return a;
        }

        long[] nextLongArray(int N) {
            long a[] = new long[N];
            for (int i=0;i<N;i++) {
                a[i] = this.nextLong();
            }

            return a;
        }

        double[] nextDoubleArray(int N) {
            double a[] = new double[N];
            for (int i=0;i<N;i++) {
                a[i] = this.nextDouble();
            }

            return a;
        }

        String[] nextTokenArray(int N) {
            String a[] = new String[N];
            for (int i=0;i<N;i++) {
                a[i] = this.nextToken();
            }

            return a;
        }
    }
}

class UnionFind {
    int[] parent;
    int[] rank;

    public UnionFind(int size) {
        this.parent = new int[size];
        this.rank = new int[size];

        for (int i = 0; i < size; i++) {
            makeSet(i);
        }
    }

    public void makeSet(int i) {
        parent[i] = i;
        rank[i] = 0;
    }

    public void union(int x, int y) {
        int xRoot = find(x);
        int yRoot = find(y);

        if (rank[xRoot] > rank[yRoot]) {
            parent[yRoot] = xRoot;

        } else if(rank[xRoot] < rank[yRoot]) {
            parent[xRoot] = yRoot;

        } else if (xRoot != yRoot){
            parent[yRoot] = xRoot;
            rank[xRoot]++;
        }
    }

    public int find(int i) {
        if (i != parent[i]) {
            parent[i] = find(parent[i]);
        }
        return parent[i];
    }

    public boolean same(int x, int y) {
        return find(x) == find(y);
    }
}