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 Rust (1.15.1) (judge verdict: Accepted)

#[allow(unused_macros)]
macro_rules! input_byline {
    ($($r:tt)* ) => {
        let stdin = std::io::stdin();
        let mut q = std::collections::VecDeque::new();
        let mut next = || {
            if q.is_empty() {
                let mut s = String::new();
                stdin.read_line(&mut s);
                for v in s.split_whitespace() {
                    q.push_back(v.to_string());
                }
            }
            q.pop_front().unwrap()
        };
        input_inner!{next, $($r)*}
    };

}

#[allow(unused_macros)]
macro_rules! input {
    ($($r:tt)*) => {
        let stdin = std::io::stdin();
        let mut bytes = std::io::Read::bytes(std::io::BufReader::new(stdin.lock()));
        let mut next = move || -> String{
            bytes
                .by_ref()
                .map(|r|r.unwrap() as char)
                .skip_while(|c|c.is_whitespace())
                .take_while(|c|!c.is_whitespace())
                .collect()
        };
        input_inner!{next, $($r)*}
    };
}

#[allow(unused_macros)]
macro_rules! input_inner {
    ($next:expr) => {};
    ($next:expr, ) => {};

    ($next:expr, $var:ident : $t:tt $($r:tt)*) => {
        let $var = read_value!($next, $t);
        input_inner!{$next $($r)*}
    };

    ($next:expr, mut $var:ident : $t:tt $($r:tt)*) => {
        let mut $var = read_value!($next, $t);
        input_inner!{$next $($r)*}
    };
}

#[allow(unused_macros)]
macro_rules! read_value {
    ($next:expr, ( $($t:tt),* )) => {
        ( $(read_value!($next, $t)),* )
    };

    ($next:expr, [ $t:tt ; $len:expr ]) => {
        (0..$len).map(|_| read_value!($next, $t)).collect::<Vec<_>>()
    };

    ($next:expr, chars) => {
        read_value!($next, String).chars().collect::<Vec<char>>()
    };

    ($next:expr, bytes) => {
        read_value!($next, String).into_bytes()
    };

    ($next:expr, usize1) => {
        read_value!($next, usize) - 1
    };

    ($next:expr, $t:ty) => {
        $next().parse::<$t>().expect("Parse error")
    };
}

trait Printable {
    fn p(&self);
}

impl<T: std::fmt::Display> Printable for T {
    fn p(&self) {
        println!("{}", self);
    }
}

impl<T: std::fmt::Display> Printable for [T] {
    fn p(&self) {
        for i in 0..self.len() {
            if i != 0 {
                print!(" ");
            }
            print!("{}", self[i]);
        }
        println!("");
    }
}

#[allow(unused_imports)]
use std::cmp::{max, min};
#[allow(unused_imports)]
use std::collections::{BinaryHeap, HashMap};

#[allow(dead_code)]
type Graph = Vec<Vec<usize>>;
#[allow(dead_code)]
const M: usize = 1e9 as usize + 9;

struct UnionFind {
    parent: Vec<usize>,
    size: Vec<usize>,
    rank: Vec<usize>,
}

impl UnionFind {
    pub fn new(n: usize) -> UnionFind {
        let mut parent = vec![];
        for i in 0..n {
            parent.push(i);
        }
        UnionFind {
            parent: parent,
            size: vec![1; n],
            rank: vec![0; n],
        }
    }

    pub fn root(&mut self, x: usize) -> usize {
        if self.parent[x] == x {
            x
        } else {
            let parent = self.parent[x];
            self.parent[x] = self.root(parent);
            self.parent[x]
        }
    }

    pub fn unite(&mut self, x: usize, y: usize) {
        let x_root = self.root(x);
        let y_root = self.root(y);

        if x_root == y_root {
            return;
        }

        let sum = self.size[x_root] + self.size[y_root];
        self.size[x_root] = sum;
        self.size[y_root] = sum;

        if self.rank[x_root] < self.rank[y_root] {
            self.parent[x_root] = y_root;
        } else {
            self.parent[y_root] = x_root;
            if self.rank[x_root] == self.rank[y_root] {
                self.rank[x_root] += 1;
            }
        }
    }

    pub fn same(&mut self, x: usize, y: usize) -> bool {
        self.root(x) == self.root(y)
    }

    pub fn size(&mut self, x: usize) -> usize {
        let root = self.root(x);
        self.size[root]
    }
}

fn main() {
    input! {
        n :usize,
        xy: [(isize, isize); n],
    }

    if n == 1 {
        println!("1");
        return;
    }

    let mut ans = 50;

    for i in 0..n {
        for j in 0..n {
            if i == j {
                continue;
            }
            let p = xy[i].0 - xy[j].0;
            let q = xy[i].1 - xy[j].1;

            let mut uf = UnionFind::new(n);
            for k in 0..n {
                for l in 0..n {
                    if k == l {
                        continue;
                    }
                    if xy[k].0 - xy[l].0 == p && xy[k].1 - xy[l].1 == q {
                        uf.unite(k, l);
                    }
                }
            }
            let mut set = std::collections::HashSet::new();
            for i in 0..n {
                set.insert(uf.root(i));
            }
            ans = min(ans, set.len());
        }
    }
    println!("{}", ans);
}