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 (GCC 5.4.1) (judge verdict: Accepted)

#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#define ll long long
#define rep(i,l,r)for(ll i=(l);i<(r);i++)
#define repp(i,l,r,k)for(ll i=(l);i<(r);i+=(k))
#define INF ((1LL<<62)-(1LL<<31))
#define max(p,q)((p)>(q)?(p):(q))
#define min(p,q)((p)<(q)?(p):(q))
#define bit(n,m)(((n)>>(m))&1)
int upll(const void*a, const void*b){return*(ll*)a<*(ll*)b?-1:*(ll*)a>*(ll*)b?1:0;}
int downll(const void*a, const void*b){return*(ll*)a<*(ll*)b?1:*(ll*)a>*(ll*)b?-1:0;}
void sortup(ll*a,int n){qsort(a,n,sizeof(ll),upll);}
void sortdown(ll*a,int n){qsort(a,n,sizeof(ll),downll);}
ll pom(ll a,ll n,int m){ll x=1;for(a%=m;n;n/=2)n&1?x=x*a%m:0,a=a*a%m;return x;}
//#define MOD 998244353
#define MOD 1000000007
#define invp(a,p)pom(a,p-2,p)

ll n;
ll x[99],y[99];
ll idx[99];
ll idx2[99];

int c(const void*a,const void*b){
	ll p=*(ll*)a,q=*(ll*)b;
	ll ppp=x[p]*2000000001+y[p];
	ll qqq=x[q]*2000000001+y[q];
	if(ppp<qqq)return -1;
	return 1;
}
int c2(const void*a,const void*b){
	ll p=*(ll*)a,q=*(ll*)b;
	ll ppp=x[p]*2000000001-y[p];
	ll qqq=x[q]*2000000001-y[q];
	if(ppp<qqq)return -1;
	return 1;
}

int main(){
	scanf("%lld",&n);
	rep(i,0,n)scanf("%lld %lld",x+i,y+i);
	rep(i,0,n)idx[i]=idx2[i]=i;
	qsort(idx,n,sizeof(ll),c);
	qsort(idx2,n,sizeof(ll),c2);
	ll ans=n;
	
	rep(aaa,0,n)rep(bbb,0,n)if(aaa!=bbb){
		//aaa,bbb間の移動を(p,q)に指定する
		ll p=x[aaa]-x[bbb];
		ll q=y[aaa]-y[bbb];
		ll tempx[99]={};
		ll tempy[99]={};

		if(p*q>=0){
			if(p>0||q>0){
				//左下から右下へ
				rep(i,0,n){
					tempx[i]=x[idx[i]];
					tempy[i]=y[idx[i]];
				}
			}else{
				//右上から左下へ
				for(ll i=n-1;i>=0;i--){
					tempx[i]=x[idx[i]];
					tempy[i]=y[idx[i]];
				}
			}
		}else{
			if(p<0){
				//左上から右下へ
				rep(i,0,n){
					tempx[i]=x[idx2[i]];
					tempy[i]=y[idx2[i]];
				}
			}else{
				//右下から左上へ
				for(ll i=n-1;i>=0;i--){
					tempx[i]=x[idx2[i]];
					tempy[i]=y[idx2[i]];
				}
			}
		}
		
		ll cnt=0;
		rep(i,0,n){
			if(tempx[i]!=INF){
				cnt++;
				int flag=1;
				ll crrx=tempx[i];
				ll crry=tempy[i];
				tempx[i]=INF;
				tempy[i]=INF;
				
				while(flag){
					flag=0;
					crrx+=p;
					crry+=q;
					rep(j,0,n){
						if(crrx==tempx[j]&&crry==tempy[j]){
							flag=1;
							tempx[j]=INF;
							tempy[j]=INF;
							break;
						}
					}
				}
			}
		}
		ans=min(ans,cnt);
	}
	printf("%lld",ans);
}