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)

/**
 * Created at 20:44 on 2019-06-15
 */

import java.awt.*;
import java.io.*;
import java.util.*;
import java.math.BigInteger;

public class Main {

  static FastScanner sc = new FastScanner();

  public static void main(String[] args) {

    int N = sc.nextInt();

    Point[] dots = new Point[N];
    for (int i=0; i<N; i++) {
      dots[i] = new Point(sc.nextInt(), sc.nextInt());
    }

    Point[] defs = new Point[N*N];
    for (int i=0; i<N; i++) {
      for (int j=0; j<N; j++) {
        defs[i*N+j] = new Point(dots[j].x-dots[i].x, dots[j].y-dots[i].y);
      }
    }

    int[] counts = new int[N*N];
    for (int i=0; i<N*N; i++) {
      if (defs[i].x == 0 && defs[i].y == 0) continue;
      for (int j=0; j<N*N; j++) {
        if (defs[i].x == defs[j].x && defs[i].y == defs[j].y) {
          counts[i]++;
        }
      }
    }

    Arrays.sort(counts);

    System.out.println(N - counts[counts.length - 1]);

  }

  static class Debugger {

    static long startTime;
    static boolean on = true;

    //入力受け取り後に呼び出す(入力時間をカウントしないため)
    static void start() {
      startTime = System.currentTimeMillis();
    }

    static void printTime() {
      if (on) System.out.println("(" + (System.currentTimeMillis() - startTime) + "ms)");
    }

    static void toggle() {
      on = !on;
    }

  }

  static class BigInt extends BigInteger {

    BigInteger MOD = new BigInteger("1000000007");
    static BigInt ZERO = new BigInt(0);
    static BigInt ONE = new BigInt(1);
    static BigInt TEN = new BigInt(10);

    public BigInt(long l) {
      super(Long.toString(l));
    }

    public BigInt(BigInteger i) {
      super(i.toByteArray());
    }

    public BigInt pow(int i) {
      return new BigInt(super.pow(i));
    }

    public BigInt[] divideAndRemainder(long l) {
      return divideAndRemainder(new BigInt(l));
    }

    public BigInt[] divideAndRemainder(BigInt i) {
      BigInt[] ret = new BigInt[2];
      BigInteger[] dAndR = super.divideAndRemainder(i);
      ret[0] = new BigInt(dAndR[0]);
      ret[1] = new BigInt(dAndR[1]);
      return ret;
    }

    public BigInt mod(long l) {
      return mod(new BigInt(l));
    }

    public BigInt mod(BigInt i) {
      return new BigInt(super.mod(i));
    }

    public BigInt mod() {
      return new BigInt(super.mod(MOD));
    }

    public BigInt add(long l) {
      return add(new BigInt(l));
    }

    public BigInt add(BigInt i) {
      return new BigInt(super.add(i));
    }

    public BigInt subtract(long l) {
      return subtract(new BigInt(l));
    }

    public BigInt subtract(BigInt i) {
      return new BigInt(super.subtract(i));
    }

    public BigInt multiply(long l) {
      return multiply(new BigInt(l));
    }

    public BigInt multiply(BigInt i) {
      return new BigInt(super.multiply(i));
    }

    public BigInt divide(long l) {
      return divide(new BigInt(l));
    }

    public BigInt divide(BigInt i) {
      return new BigInt(super.divide(i));
    }

    public BigInt abs() {
      return new BigInt(super.abs());
    }

  }

  /*
    add()でインデックスを指定しない場合指定されたソート順に違わない位置に追加する
    (ただしソートされていることが前提となる)
    Comparatorが0を返したとき、それらの順序は保証しない
    (TreeSet, TreeMapと違い削除はしない)
   */
  static class TreeList<E> extends ArrayList<E> {

    Comparator<? super E> comparator;

    TreeList(Comparator<? super E> c) {
      super();
      comparator = c;
    }

    /*
      ソート済みのリストに要素を追加する
     */
    public boolean add(E e) {
      int lowIndex = 0;
      int highIndex = size() - 1;
      int index = 0;

      if (size() == 0) {
        super.add(e);
        return true;
      }

      if (comparator.compare(e, get(0)) < 0) {
        index = 0;
      } else if (comparator.compare(e, get(highIndex)) > 0) {
        index = highIndex + 1;
      } else {
        while (lowIndex <= highIndex) {

          if (highIndex == lowIndex + 1 || highIndex == lowIndex) {
            index = highIndex;
            break;
          }

          int midIndex = (lowIndex + highIndex) / 2;
          ;

          if (comparator.compare(e, get(midIndex)) > 0) {
            lowIndex = midIndex;
          } else {
            highIndex = midIndex;
          }

        }
      }

      super.add(index, e);
      return true;
    }

  }

  static class FastScanner {
    private final InputStream in = System.in;
    private final byte[] buffer = new byte[1024];
    private int ptr = 0;
    private int buflen = 0;

    private boolean hasNextByte() {
      if (ptr < buflen) {
        return true;
      } else {
        ptr = 0;
        try {
          buflen = in.read(buffer);
        } catch (IOException e) {
          e.printStackTrace();
        }
        if (buflen <= 0) {
          return false;
        }
      }
      return true;
    }

    private int readByte() {
      if (hasNextByte()) return buffer[ptr++];
      else return -1;
    }

    private static boolean isPrintableChar(int c) {
      return 33 <= c && c <= 126;
    }

    private void skipUnprintable() {
      while (hasNextByte() && !isPrintableChar(buffer[ptr])) ptr++;
    }

    public boolean hasNext() {
      skipUnprintable();
      return hasNextByte();
    }

    public String next() {
      if (!hasNext()) throw new NoSuchElementException();
      StringBuilder sb = new StringBuilder();
      int b = readByte();
      while (isPrintableChar(b)) {
        sb.appendCodePoint(b);
        b = readByte();
      }
      return sb.toString();
    }

    public long nextLong() {
      if (!hasNext()) throw new NoSuchElementException();
      long n = 0;
      boolean minus = false;
      int b = readByte();
      if (b == '-') {
        minus = true;
        b = readByte();
      }
      if (b < '0' || '9' < b) {
        throw new NumberFormatException();
      }
      while (true) {
        if ('0' <= b && b <= '9') {
          n *= 10;
          n += b - '0';
        } else if (b == -1 || !isPrintableChar(b)) {
          return minus ? -n : n;
        } else {
          throw new NumberFormatException();
        }
        b = readByte();
      }
    }

    public int nextInt() {
      return (int) nextLong();
    }
  }

}