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.*;
import java.io.*;

public class Main {
    static int N;
    static int[] x;
    static int[] y;
    static int[] parent;
    public static void main(String[] args) {
        N = sc.nextInt();
        parent = new int[N];
        x = new int[N];
        y = new int[N];
        for(int i=0; i < N; i++) {
            x[i] = sc.nextInt();
            y[i] = sc.nextInt();
        }
        int M = N*(N-1)/2;
        int[] vx = new int[M];
        int[] vy = new int[M];
        int index = 0;
        for (int i = 0; i < N; i++) {
            for (int j = i+1; j < N; j++) {
                vx[index] = x[j] - x[i];
                vy[index] = y[j] - y[i];
                index++;
            }
        }
        int ans = N;
        for(int k = 0; k < M; k++) {
            int p = vx[k];
            int q = vy[k];
            UnionFind uf = new UnionFind(N);
            for (int i = 0; i < N; i++) {
                for (int j = i+1; j < N; j++) {
                    int dx = x[j] - x[i];
                    int dy = y[j] - y[i];
                    boolean condPlus = dx == p && dy == q;
                    boolean condMinus = dx == -p && dy == -q;
                    if (condPlus || condMinus) {
                        uf.unite(i,j);
                    }
                }
            }
            ans = Math.min(ans,uf.unionNumber());
        }
        writer.println(ans);
        writer.flush();
    }

    /* class UnionFind
    [Constructor]
    UnionFind(int size)
    [Methods]
    public int root(int x)
    public boolean hasSameRoot(int x, int y)
    public unite(int x, int y)
    public int unionNumber() : returns # of connected components.
    */
    static class UnionFind {
        private int[] parent;
        private int[] rank;
        private int size;
        public UnionFind(int size) {
            this.parent = new int[size];
            this.rank = new int[size];
            this.size = size;
            for(int i = 0; i < size; i++) {
                this.parent[i] = i;
            }
        }
        public int root(int x) {
            int y = this.parent[x];
            if (x==y) return(y);
            return(this.parent[x] = this.root(y));
        }
        public boolean hasSameRoot(int x, int y) {
            return(root(x) == root(y));
        }
        public void unite(int x, int y){
            int rootX = this.root(x);
            int rootY = this.root(y);
            if (rootX == rootY) return;
            if (rank[rootX] > rank[rootY]) {
                parent[rootY] = rootX;
            } else if (rank[rootX] < rank[rootY]) {
                parent[rootX] = rootY;
            } else {
                parent[rootY] = rootX;
                rank[rootX]++;
            }
        }
        public int unionNumber() {
            Set<Integer> s = new HashSet<Integer>();
            for(int i = 0; i < size; i++) {
                s.add(root(i));
            }
            return s.size();
        }
    }

    static final FastScanner sc = new FastScanner(System.in);
    static PrintWriter writer = new PrintWriter(System.out);

    static class FastScanner {
        Reader input;
 
        FastScanner() {
            this(System.in);
        }
 
        FastScanner(InputStream stream) {
            this.input = new BufferedReader(new InputStreamReader(stream));
        }
 
        int nextInt() {
            return (int) nextLong();
        }
 
        long nextLong() {
            try {
                int sign = 1;
                int b = input.read();
                while ((b < '0' || '9' < b) && b != '-' && b != '+') {
                    b = input.read();
                }
                if (b == '-') {
                    sign = -1;
                    b = input.read();
                } else if (b == '+') {
                    b = input.read();
                }
                long ret = b - '0';
                while (true) {
                    b = input.read();
                    if (b < '0' || '9' < b) return ret * sign;
                    ret *= 10;
                    ret += b - '0';
                }
            } catch (IOException e) {
                e.printStackTrace();
                return -1;
            }
        }
 
        double nextDouble() {
            try {
                double sign = 1;
                int b = input.read();
                while ((b < '0' || '9' < b) && b != '-' && b != '+') {
                    b = input.read();
                }
                if (b == '-') {
                    sign = -1;
                    b = input.read();
                } else if (b == '+') {
                    b = input.read();
                }
                double ret = b - '0';
                while (true) {
                    b = input.read();
                    if (b < '0' || '9' < b) break;
                    ret *= 10;
                    ret += b - '0';
                }
                if (b != '.') return sign * ret;
                double div = 1;
                b = input.read();
                while ('0' <= b && b <= '9') {
                    ret *= 10;
                    ret += b - '0';
                    div *= 10;
                    b = input.read();
                }
                return sign * ret / div;
            } catch (IOException e) {
                e.printStackTrace();
                return Double.NaN;
            }
        }
 
        char nextChar() {
            try {
                int b = input.read();
                while (Character.isWhitespace(b)) {
                    b = input.read();
                }
                return (char) b;
            } catch (IOException e) {
                e.printStackTrace();
                return 0;
            }
        }
 
        String nextStr() {
            try {
                StringBuilder sb = new StringBuilder();
                int b = input.read();
                while (Character.isWhitespace(b)) {
                    b = input.read();
                }
                while (b != -1 && !Character.isWhitespace(b)) {
                    sb.append((char) b);
                    b = input.read();
                }
                return sb.toString();
            } catch (IOException e) {
                e.printStackTrace();
                return "";
            }
        }
    }
    //FAST SCANNER END HERE
}