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.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.Collections;
import java.util.Comparator;
import java.util.HashMap;
import java.util.InputMismatchException;
import java.util.List;
import java.util.Map.Entry;
import java.util.NoSuchElementException;

public class Main implements Runnable { // クラス名はMain1

	PrintWriter out = new PrintWriter(System.out);
	InputReader sc = new InputReader(System.in);
	static int mod = 1000000000 + 7; //10^9+7
	int[] dx = { 1, 0, -1, 0 }, dy = { 0, 1, 0, -1 }; //4 directions

	public static void main(String[] args) {
		Thread.setDefaultUncaughtExceptionHandler((t, e) -> System.exit(1));
		new Thread(null, new Main(), "", 1024 * 1024 * 1024).start(); // 16MBスタックを確保して実行
	}

	public void run() {

		try {
			/**
			 * 2の累乗一覧
			 * http://www.gaoshukai.com/20/06/0022/
			 *
			 * Bit 全探索
				//Nは要素数 (bit全探索)
				//計算量はO(2^N) Nが0-20~25 (30は多分無理)くらいまでしか使えない
				Out: for (int bit = 0; bit < (1 << N); bit++) {
					out.println(Integer.toBinaryString(bit));
					In: for (int j = 0; j < N; j++) {
						out.println(1 & (bit >> j));
						//1が立ってれば対象。例えば101だったら1桁目と3桁目は選ばれている
						//「二進数iをjだけ右にビットシフトしたときの、iの1桁目と1とでビット論理積をとって、演算結果が1であるなら処理を実行する」
						if ((1 & bit >> j) == 1) {
						}
					}
				}
			 *
			 * 表示系
			 *   out.println();
			 *   out.println("i:" + i + " ,j:" + j);
			 *   out.println(Arrays.toString(A));
			 *
			 * Sort (Arrays)
			 *  Integer[] A = new Integer[N];
			 *    Desc : Arrays.sort(A , Collections.reverseOrder());
			 *    Asc  : Arrays.sort(A);
			 *
			 * 定義系
			 *   int[] s = new int[M];
			 *   ArrayDeque<Integer> deq= new ArrayDeque<>();//先頭と末尾への要素の追加・先頭と末尾の要素の取り出しと削除が定数時間
			 *   ArrayList<Integer> arr = new ArrayList<Integer>();//定数時間
			 *   HashMap<Integer,Integer> hm = new HashMap<>(); //定数時間
			 *
			 *   //要素の追加と、最小の要素の取り出しと削除が対数時間
			 *   PriorityQueue<Integer> pq = new PriorityQueue<>();//昇順
			 *   PriorityQueue<Integer> pq = new PriorityQueue<>(Collections.reverseOrder()); //逆順。降順
			 *
			 *   TreeSet<Integer> ts = new TreeSet<>();//対数時間(重複はできない)
			 *
			 * 文字系
			 *   String S = sc.next().trim();
			 *   for (char i = 'a'; i <= 'z'; i++) {}
			 *   S.substring(1,2);//あいうえお → い
			 *   S.substring(0,1); // 1文字目をとりたいとき
			 *
			 *   //同じ文字の繰り返し
			 *   String goy = String.join("", Collections.nCopies(2, "U")); //Uを２回繰り返し
			 *
			 *   文字列のSort
			 *    String sorted = S.chars().sorted().collect(StringBuilder::new,StringBuilder::appendCodePoint, StringBuilder::append) .toString();
			 */
			// long l = sc.nextLong();
			//String S = sc.next().trim();
			//int N = sc.nextInt();
			//int[] A = new int[N];
			int N = sc.nextInt();
			long[] x = new long[N];
			long[] y = new long[N];
			for (int i = 0; i < N; i++) {
				//A[i] = sc.nextInt();
				x[i] = sc.nextLong();
				y[i] = sc.nextLong();
			}
			//out.println(Arrays.toString(A));

			if (N == 1) {
				out.println(1);
				return;
			}

			int ans = Integer.MAX_VALUE;
			for (int i = 0; i < N; i++) {
				for (int j = 0; j < N; j++) {
					if (i != j) {
						long p = x[i] - x[j];
						long q = y[i] - y[j];
						int count = 0;
						for (int k = 0; k < N; k++) {
							for (int l = 0; l < N; l++) {
								if (k != l) {
									if (p == x[k] - x[l] && q == y[k] - y[l]) {
										count++;
									}
								}
							}
						}
						ans = Math.min(ans, N - count);
					}
				}
			}
			out.println(ans);

		} catch (ArithmeticException ae) {
			//ae.printStackTrace();
			throw new RuntimeException();
		} catch (Exception e) {
			//e.printStackTrace();
			throw new RuntimeException();
		} finally {
			out.flush();
			out.close();
		}

	}

	class Exm implements Comparable<Exm> {

		public int a;
		public int b;

		public Exm(int a, int b) {
			this.a = a;
			this.b = b;
		}

		@Override
		public int compareTo(Exm o) {

			//return this.a - o.a;//昇順
			// return o.a - this.a;//降順

			//複数項目で並び替え。aの降順、aが同じならbの降順
			if (this.a == o.a) {
				return o.b - this.b;
			} else {
				return o.a - this.a;
			}
		}
	}

	/**
	 *
	 * @param n
	 * @param m
	 * @return Combinationの数を返す(mod無しなので、大きい値には使用できない桁溢れする)
	 */
	long calcCombination(int n, int m) {
		if (n < m || m < 0) {
			throw new IllegalArgumentException("引数の値が不正です ( n : " + n + ", m : " + m + ")");
		}
		long c = 1;
		m = (n - m < m ? n - m : m);
		for (int ns = n - m + 1, ms = 1; ms <= m; ns++, ms++) {
			c *= ns;
			c /= ms;
		}
		return c;
	}

	/*
	 * 使用するときはModに注意。Global変数を参照
	 */
	public static long comb(long a, long b) {
		if (a < b)
			return 0;
		long res = 1;
		long inv = pow(fact(Math.min(b, a - b)), mod - 2);
		for (long i = a; i > a - Math.min(b, a - b); i--) {
			res *= i;
			res %= mod;
		}
		res *= inv;
		res %= mod;
		return res;
	}

	public static long pow(long x, long n) {
		long res = 1;
		while (n > 0) {
			if ((n & 1) == 1) {
				res *= x;
				res %= mod;
			}
			x *= x;
			x %= mod;
			n >>= 1;
		}
		return res;
	}

	public static long fact(long n) {
		long res = 1;
		while (n > 0) {
			res *= n;
			res %= mod;
			n--;
		}
		return res;
	}

	/*
	 * HashmapのSort
	 * hmはhashmap
	 * keyvalは"key" or "val"を指定して
	 * ascdescは"asc" or "desc"を指定して
	 */
	private static List<Entry<Integer, Integer>> sortHashMapValue(HashMap<Integer, Integer> hm, String keyval,
			String ascdesc) {
		// 1.Map.Entryのリストを作成する
		List<Entry<Integer, Integer>> list_entries = new ArrayList<Entry<Integer, Integer>>(hm.entrySet());

		// 2.比較関数Comparatorを使用してMap.Entryの値を比較する(昇順)
		Collections.sort(list_entries, new Comparator<Entry<Integer, Integer>>() {
			public int compare(Entry<Integer, Integer> obj1, Entry<Integer, Integer> obj2) {
				if (keyval.equals("val")) {
					if (ascdesc.equals("asc")) {
						// 昇順(value)
						return obj1.getValue().compareTo(obj2.getValue());
					} else {
						// 降順(value)
						return obj2.getValue().compareTo(obj1.getValue());
					}
				} else {
					if (ascdesc.equals("asc")) {
						// 昇順(value)
						return obj1.getKey().compareTo(obj2.getKey());
					} else {
						// 降順(value)
						return obj2.getKey().compareTo(obj1.getKey());
					}
				}
			}
		});
		/*
		// 3. ループで要素順に値を取得する
		for (Entry<Integer, Integer> entry : list_entries) {
			out.println(entry.getKey() + " : " + entry.getValue());
		}
		*/
		return list_entries;
	}

	// 高速なScanner
	static class InputReader {
		private InputStream in;
		private byte[] buffer = new byte[1024];
		private int curbuf;
		private int lenbuf;

		public InputReader(InputStream in) {
			this.in = in;
			this.curbuf = this.lenbuf = 0;
		}

		public boolean hasNextByte() {
			if (curbuf >= lenbuf) {
				curbuf = 0;
				try {
					lenbuf = in.read(buffer);
				} catch (IOException e) {
					throw new InputMismatchException();
				}
				if (lenbuf <= 0)
					return false;
			}
			return true;
		}

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

		private boolean isSpaceChar(int c) {
			return !(c >= 33 && c <= 126);
		}

		private void skip() {
			while (hasNextByte() && isSpaceChar(buffer[curbuf]))
				curbuf++;
		}

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

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

		public int nextInt() {
			if (!hasNext())
				throw new NoSuchElementException();
			int c = readByte();
			while (isSpaceChar(c))
				c = readByte();
			boolean minus = false;
			if (c == '-') {
				minus = true;
				c = readByte();
			}
			int res = 0;
			do {
				if (c < '0' || c > '9')
					throw new InputMismatchException();
				res = res * 10 + c - '0';
				c = readByte();
			} while (!isSpaceChar(c));
			return (minus) ? -res : res;
		}

		public long nextLong() {
			if (!hasNext())
				throw new NoSuchElementException();
			int c = readByte();
			while (isSpaceChar(c))
				c = readByte();
			boolean minus = false;
			if (c == '-') {
				minus = true;
				c = readByte();
			}
			long res = 0;
			do {
				if (c < '0' || c > '9')
					throw new InputMismatchException();
				res = res * 10 + c - '0';
				c = readByte();
			} while (!isSpaceChar(c));
			return (minus) ? -res : res;
		}

		public double nextDouble() {
			return Double.parseDouble(next());
		}

		public int[] nextIntArray(int n) {
			int[] a = new int[n];
			for (int i = 0; i < n; i++)
				a[i] = nextInt();
			return a;
		}

		public long[] nextLongArray(int n) {
			long[] a = new long[n];
			for (int i = 0; i < n; i++)
				a[i] = nextLong();
			return a;
		}

		public char[][] nextCharMap(int n, int m) {
			char[][] map = new char[n][m];
			for (int i = 0; i < n; i++)
				map[i] = next().toCharArray();
			return map;
		}
	}
}