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 Scala (2.11.7) (judge verdict: Accepted)

object Main {
  import java.io.{BufferedReader, InputStream, InputStreamReader}
  import java.util.StringTokenizer
  import scala.reflect.ClassTag

  def main(args: Array[String]): Unit = {
    val out = new java.io.PrintWriter(System.out)
    new Main(out, new InputReader(System.in)).solve()
    out.flush()
  }

  private val oj = System.getenv("ATCODER_DEBUG") == null
  def DEBUG(f: => Unit): Unit = {
    if (!oj){ f }
  }
  def debug(as: Array[Boolean]): Unit = if (!oj){ debug(as.map(x => if(x) "1" else "0").mkString) }
  def debug(as: Array[Int]): Unit = if (!oj){ debug(as.mkString(" ")) }
  def debug(as: Array[Long]): Unit =if (!oj){ debug(as.mkString(" ")) }
  def debugDim(m: Array[Array[Long]]): Unit = if (!oj){
    REP(m.length) { i =>
      debug(m(i))
    }
  }
  def debugDimFlip(m: Array[Array[Long]]): Unit = if (!oj){
    REP(m(0).length) { j =>
      REP(m.length) { i =>
        System.err.print(m(i)(j))
        System.err.print(" ")
      }
      System.err.println()
    }
  }
  def debug(s: => String): Unit = DEBUG {
    System.err.println(s)
  }
  def debugL(num: => Long): Unit = DEBUG {
    System.err.println(num)
  }

  class InputReader(val stream: InputStream) {
    private val reader = new BufferedReader(new InputStreamReader(stream), 32768)
    private var tokenizer: StringTokenizer = _

    def next(): String = {
      while (tokenizer == null || !tokenizer.hasMoreTokens)
        tokenizer = new StringTokenizer(reader.readLine)
      tokenizer.nextToken
    }

    def nextInt(): Int = Integer.parseInt(next())
    def nextLong(): Long = java.lang.Long.parseLong(next())
    def nextChar(): Char = next().charAt(0)

    def ni(): Int = nextInt()
    def nl(): Long = nextLong()
    def nc(): Char = nextChar()
    def ns(): String = next()
    def ns(n: Int): Array[Char] = ns().toCharArray
    def na(n: Int, offset: Int = 0): Array[Int] = map(n)(_ => ni() + offset)
    def na2(n: Int, offset: Int = 0): (Array[Int], Array[Int]) = {
      val A1, A2 = Array.ofDim[Int](n)
      REP(n) { i =>
        A1(i) = ni() + offset
        A2(i) = ni() + offset
      }
      (A1, A2)
    }
    def nm(n: Int, m: Int): Array[Array[Int]] = {
      val A = Array.ofDim[Int](n, m)
      REP(n) { i =>
        REP(m) { j =>
          A(i)(j) = ni()
        }
      }
      A
    }
    def nal(n: Int): Array[Long] = map(n)(_ => nl())
    def nm_c(n: Int, m: Int): Array[Array[Char]] = map(n) (_ => ns(m))
  }

  def REP(n: Int, offset: Int = 0)(f: Int => Unit): Unit = {
    var i = offset
    val N = n + offset
    while(i < N) { f(i); i += 1 }
  }
  def REP_r(n: Int, offset: Int = 0)(f: Int => Unit): Unit = {
    var i = n - 1 + offset
    while(i >= offset) { f(i); i -= 1 }
  }
  def TO(from: Int, to: Int)(f: Int => Unit): Unit = {
    REP(to - from + 1, from) { i =>
      f(i)
    }
  }
  def map[@specialized A: ClassTag](n: Int, offset: Int = 0)(f: Int => A): Array[A] = {
    val res = Array.ofDim[A](n)
    REP(n)(i => res(i) = f(i + offset))
    res
  }

  def sumL(as: Array[Int]): Long = {
    var s = 0L
    REP(as.length)(i => s += as(i))
    s
  }
  def cumSum(as: Array[Int]): Array[Long] = {
    val cum = Array.ofDim[Long](as.length + 1)
    REP(as.length) { i =>
      cum(i + 1) = cum(i) + as(i)
    }
    cum
  }
}

case class Key(x: Int, y: Int)

class Main(out: java.io.PrintWriter, sc: Main.InputReader) {
  import sc._
  import Main._
  import java.util.Arrays.sort

  import scala.collection.mutable
  import math.{abs, max, min}
  import mutable.ArrayBuffer

  // toIntとか+7とかするならvalにしろ
  @inline private def MOD = 1000000007

  def solve(): Unit = {
    val N = ni()
    val (x, y) = na2(N)
    val D = mutable.Map[Key, Int]().withDefaultValue(0)
    if (N == 1) {
      out.println(1)
      return
    }

    REP(N - 1) { i =>
      TO(i + 1, N - 1) { j =>
        var a = x(i) - x(j)
        var b = y(i) - y(j)
        if (a < 0) {
          a *= -1
          b *= -1
        }
        if (a == 0 & b < 0) {
          b *= -1
        }
        D(Key(a, b)) += 1
      }
    }

    debug(D.mkString(" "))

    val ans = N - D.values.max
    out.println(ans)

  }
}