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.OutputStream;
import java.io.BufferedWriter;
import java.util.Set;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.HashSet;
import java.io.UncheckedIOException;
import java.nio.charset.Charset;
import java.util.StringTokenizer;
import java.io.Writer;
import java.io.OutputStreamWriter;
import java.io.BufferedReader;
import java.util.Comparator;
import java.io.InputStream;

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

    static class BPickingUp {
        public void solve(int testNumber, LightScanner in, LightWriter out) {
            // out.setBoolLabel(LightWriter.BoolLabel.YES_NO_FIRST_UP);
            int n = in.ints();
            if (n == 1) {
                out.ans(1).ln();
                return;
            }

            BPickingUp.Point[] points = new BPickingUp.Point[n];
            for (int i = 0; i < n; i++) {
                points[i] = new BPickingUp.Point(in.ints(), in.ints());
            }
            IntroSort.sort(points, Comparator.comparing(p -> p.x));
            Set<BPickingUp.PQ> pqs = new HashSet<>();
            for (int i = 0; i < n; i++) {
                for (int j = 0; j < i; j++) {
                    pqs.add(new BPickingUp.PQ(points[i].x - points[j].x, points[i].y - points[j].y));
                    pqs.add(new BPickingUp.PQ(points[j].x - points[i].x, points[j].y - points[i].y));
                }
            }

            //System.out.println(pqs);

            int ans = Integer.MAX_VALUE;
            Set<BPickingUp.Point> tmp = new HashSet<>();
            for (BPickingUp.PQ pq : pqs) {
                tmp.clear();

                int v = 0;
                for (int i = 0; i < n; i++) {
                    boolean p = tmp.contains(points[i].plus(pq)), q = tmp.contains(points[i].minus(pq));
                    if (p && q) {
                        v--;
                    } else if (!p && !q) {
                        v++;
                    }
                    tmp.add(points[i]);
                }

                //System.out.println(pq + " => " + v);
                ans = Math.min(ans, v);
            }
            out.ans(ans).ln();
        }

        private static class Point {
            long x;
            long y;

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

            BPickingUp.Point minus(BPickingUp.PQ pq) {
                return new BPickingUp.Point(x - pq.p, y - pq.q);
            }

            BPickingUp.Point plus(BPickingUp.PQ pq) {
                return new BPickingUp.Point(x + pq.p, y + pq.q);
            }

            public boolean equals(Object o) {
                if (this == o) return true;
                if (o == null || getClass() != o.getClass()) return false;

                BPickingUp.Point point = (BPickingUp.Point) o;

                if (x != point.x) return false;
                return y == point.y;
            }

            public int hashCode() {
                int result = (int) (x ^ (x >>> 32));
                result = 31 * result + (int) (y ^ (y >>> 32));
                return result;
            }

        }

        private static class PQ {
            long p;
            long q;

            PQ(long p, long q) {
                this.p = p;
                this.q = q;
            }

            public boolean equals(Object o) {
                if (this == o) return true;
                if (o == null || getClass() != o.getClass()) return false;

                BPickingUp.PQ pq = (BPickingUp.PQ) o;

                if (p != pq.p) return false;
                return q == pq.q;
            }

            public int hashCode() {
                int result = (int) (p ^ (p >>> 32));
                result = 31 * result + (int) (q ^ (q >>> 32));
                return result;
            }

            public String toString() {
                return "PQ{" +
                        "p=" + p +
                        ", q=" + q +
                        '}';
            }

        }

    }

    static class IntroSort {
        private static int INSERTIONSORT_THRESHOLD = 16;

        private IntroSort() {
        }

        static <T> void sort(T[] a, int low, int high, int maxDepth, Comparator<T> comparator) {
            while (high - low > INSERTIONSORT_THRESHOLD) {
                if (maxDepth-- == 0) {
                    HeapSort.sort(a, low, high, comparator);
                    return;
                }
                int cut = QuickSort.step(a, low, high, comparator);
                sort(a, cut, high, maxDepth, comparator);
                high = cut;
            }
            InsertionSort.sort(a, low, high, comparator);
        }

        public static <T> void sort(T[] a, Comparator<T> comparator) {
            if (a.length <= INSERTIONSORT_THRESHOLD) {
                InsertionSort.sort(a, 0, a.length, comparator);
            } else {
                sort(a, 0, a.length, 2 * BitMath.msb(a.length), comparator);
            }
        }

    }

    static class HeapSort {
        private HeapSort() {
        }

        private static <T> void heapfy(T[] a, int low, int high, int i, T val, Comparator<? super T> comparator) {
            int child = 2 * i - low + 1;
            while (child < high) {
                if (child + 1 < high && comparator.compare(a[child], a[child + 1]) < 0) {
                    child++;
                }
                if (comparator.compare(val, a[child]) >= 0) {
                    break;
                }
                a[i] = a[child];
                i = child;
                child = 2 * i - low + 1;
            }
            a[i] = val;
        }

        static <T> void sort(T[] a, int low, int high, Comparator<T> comparator) {
            for (int p = (high + low) / 2 - 1; p >= low; p--) {
                heapfy(a, low, high, p, a[p], comparator);
            }
            while (high > low) {
                high--;
                T pval = a[high];
                a[high] = a[low];
                heapfy(a, low, high, low, pval, comparator);
            }
        }

    }

    static class LightWriter implements AutoCloseable {
        private final Writer out;
        private boolean autoflush = false;
        private boolean breaked = true;

        public LightWriter(Writer out) {
            this.out = out;
        }

        public LightWriter(OutputStream out) {
            this(new BufferedWriter(new OutputStreamWriter(out, Charset.defaultCharset())));
        }

        public LightWriter print(char c) {
            try {
                out.write(c);
                breaked = false;
            } catch (IOException ex) {
                throw new UncheckedIOException(ex);
            }
            return this;
        }

        public LightWriter print(String s) {
            try {
                out.write(s, 0, s.length());
                breaked = false;
            } catch (IOException ex) {
                throw new UncheckedIOException(ex);
            }
            return this;
        }

        public LightWriter ans(String s) {
            if (!breaked) {
                print(' ');
            }
            return print(s);
        }

        public LightWriter ans(int i) {
            return ans(Integer.toString(i));
        }

        public LightWriter ln() {
            print(System.lineSeparator());
            breaked = true;
            if (autoflush) {
                try {
                    out.flush();
                } catch (IOException ex) {
                    throw new UncheckedIOException(ex);
                }
            }
            return this;
        }

        public void close() {
            try {
                out.close();
            } catch (IOException ex) {
                throw new UncheckedIOException(ex);
            }
        }

    }

    static class InsertionSort {
        private InsertionSort() {
        }

        static <T> void sort(T[] a, int low, int high, Comparator<? super T> comparator) {
            for (int i = low; i < high; i++) {
                for (int j = i; j > low && comparator.compare(a[j - 1], a[j]) > 0; j--) {
                    ArrayUtil.swap(a, j - 1, j);
                }
            }
        }

    }

    static interface Verified {
    }

    static class LightScanner {
        private BufferedReader reader = null;
        private StringTokenizer tokenizer = null;

        public LightScanner(InputStream in) {
            reader = new BufferedReader(new InputStreamReader(in));
        }

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

        public int ints() {
            return Integer.parseInt(string());
        }

    }

    static final class ArrayUtil {
        private ArrayUtil() {
        }

        public static <T> void swap(T[] a, int x, int y) {
            T t = a[x];
            a[x] = a[y];
            a[y] = t;
        }

    }

    static class QuickSort {
        private QuickSort() {
        }

        private static <T> void med(T[] a, int low, int x, int y, int z, Comparator<? super T> comparator) {
            if (comparator.compare(a[z], a[x]) < 0) {
                ArrayUtil.swap(a, low, x);
            } else if (comparator.compare(a[y], a[z]) < 0) {
                ArrayUtil.swap(a, low, y);
            } else {
                ArrayUtil.swap(a, low, z);
            }
        }

        static <T> int step(T[] a, int low, int high, Comparator<? super T> comparator) {
            int x = low + 1, y = low + (high - low) / 2, z = high - 1;
            if (comparator.compare(a[x], a[y]) < 0) {
                med(a, low, x, y, z, comparator);
            } else {
                med(a, low, y, x, z, comparator);
            }

            int lb = low + 1, ub = high;
            while (true) {
                while (comparator.compare(a[lb], a[low]) < 0) {
                    lb++;
                }
                ub--;
                while (comparator.compare(a[low], a[ub]) < 0) {
                    ub--;
                }
                if (lb >= ub) {
                    return lb;
                }
                ArrayUtil.swap(a, lb, ub);
                lb++;
            }
        }

    }

    static final class BitMath {
        private BitMath() {
        }

        public static int count(int v) {
            v = (v & 0x55555555) + ((v >> 1) & 0x55555555);
            v = (v & 0x33333333) + ((v >> 2) & 0x33333333);
            v = (v & 0x0f0f0f0f) + ((v >> 4) & 0x0f0f0f0f);
            v = (v & 0x00ff00ff) + ((v >> 8) & 0x00ff00ff);
            v = (v & 0x0000ffff) + ((v >> 16) & 0x0000ffff);
            return v;
        }

        public static int msb(int v) {
            if (v == 0) {
                throw new IllegalArgumentException("Bit not found");
            }
            v |= (v >> 1);
            v |= (v >> 2);
            v |= (v >> 4);
            v |= (v >> 8);
            v |= (v >> 16);
            return count(v) - 1;
        }

    }
}