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 Go (1.6) (judge verdict: Wrong Answer)

package main

import (
	"bufio"
	"fmt"
	"math"
	"os"
	"sort"
	"strconv"
)

var N, ans int

func main() {
	fmt.Scan(&N)

	reader := bufio.NewScanner(os.Stdin)
	reader.Split(bufio.ScanWords)
	m := make(b, N)

	for i := 0; i < N; i++ {
		reader.Scan()
		m[i].x, _ = strconv.Atoi(reader.Text())
		reader.Scan()
		m[i].y, _ = strconv.Atoi(reader.Text())
	}

	n := make(b, N*N)
	var k int
	for i := 0; i < N; i++ {
		for j := i; j < N; j++ {
			n[k].x = m[i].x - m[j].x
			n[k].y = m[i].y - m[j].y
			k++
		}
	}

	sort.Sort(n)

	for i := 1; i < N; i++ {
		if n[i].x == 0 && n[i].y == 0 {
			break
		}
		if n[i].x != n[i-1].x || n[i].y != n[i-1].y {
			ans++
		}

	}
	if N == 2 {
		fmt.Println(1)
	} else {
		fmt.Println(ans)
	}

}

/*  ----------------------------------------  */

func combination(x, y int) int {
	return permutation(x, y) / permutation(y, y)
}

func permutation(x, y int) int {
	var ans int = 1
	for i := x - y; 0 < i; i-- {
		ans *= i
	}
	return ans
}

func max(x ...int) int {
	var res int = x[0]
	for i := 1; i < len(x); i++ {
		res = int(math.Max(float64(x[i]), float64(res)))
	}
	return res
}

func min(x ...int) int {
	var res int = x[0]
	for i := 1; i < len(x); i++ {
		res = int(math.Min(float64(x[i]), float64(res)))
	}
	return res
}
func pow(x, y int) int { return int(math.Pow(float64(x), float64(y))) }
func abs(x int) int    { return int(math.Abs(float64(x))) }
func floor(x int) int  { return int(math.Floor(float64(x))) }

type XY struct {
	x int
	y int
}
type b []XY

func (a b) Len() int      { return len(a) }
func (a b) Swap(i, j int) { a[i], a[j] = a[j], a[i] }
func (a b) Less(i, j int) bool {
	if a[i].x == a[j].x {
		return a[i].y < a[j].y
	}
	return a[i].x < a[j].x
}