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 C++14 (GCC 5.4.1) (judge verdict: Wrong Answer)

#define _CRT_SECURE_NO_WARNINGS
#define _USE_MATH_DEFINES
#include <iostream>
#include <iomanip>
#include <cstdio>
#include <cstring>
#include <cmath>
#include <cstdlib>
#include <algorithm>
#include <string>
#include <vector>
#include <stack>
#include <queue>
#include <set>
#include <map>
#include <unordered_map>
#include <functional>
#include <utility>
#include <tuple>
#include <cctype>
#include <bitset>
#include <complex>
#include <cmath>
#include <array>
#include <numeric>
using namespace std;
#define INF 0x3f3f3f3f
#define INFLL 0x3f3f3f3f3f3f3f3fLL
//#define mod 998244353
#define MOD 1000000007
#define mp make_pair
#define mt make_tuple
#define pb push_back
#define eb emplace_back
typedef long long ll;
typedef unsigned long long ull;
typedef long double ld;
typedef pair<int, int> pint;
typedef pair<ll,ll> pll;
typedef tuple<int,int,int> tint;
typedef vector<int> vint;
typedef vector<ll> vll;
typedef vector<ull> vull;
typedef vector<pint> vpint;
int dx[8]={0,0,-1,1,1,1,-1,-1};
int dy[8]={-1,1,0,0,1,-1,1,-1};
const int SIZE=100050;
int main() {
	int N;
	cin>>N;
	vint X,Y;
	map<pint, int> pam;
	for(int i=0;i<N;i++){
		int x,y;
		cin>>x>>y;
		X.pb(x);
		Y.pb(y);
		pam[mp(x,y)]=1;
	}
	int ans=INF;
	for(int i=0;i<N;i++){
		for(int j=0;j<N;j++){
			if(i==j)
				continue;
			int p=X[i]-X[j],q=Y[i]-Y[j];
			int temp=0;
			for(int k=0;k<N;k++){
				int x=X[k], y=Y[k];
				if(pam.find(mp(x+p, y+q))==pam.end())
					temp++;
			}
			ans=min(ans, temp);
		}
	}
	cout<<max(ans,1)<<endl;
	return 0;
}