破防了，遂刷一節課圓錐曲線放鬆大腦，原因如圖

來個有緣人

#include<bits/stdc++.h>
using namespace std;
#define int __int128
void _print(__int128 x,bool first=true){
	if(x<0){
		putchar('-');
		_print(-x,false);
		return;
	}
	if(x==0){
		if(first) putchar('0');
		return;
	}
	_print(x/10,false);
	putchar((int)(x%10)+'0');
}
#define abs(x) (x>0?x:-x)
class frac{
    private:
        int z,m;
    public:
        frac(int x=0,int y=1){
            z=x,m=y;
            fixed();
        }
        frac fixed(){
            int gcd=__gcd(abs(z),abs(m));
            if(m<0){
                m*=-1;z*=-1;
            }
            if(z==0){
                m=1;return *this;
            }
            if(gcd==0) return *this;
            z/=gcd;m/=gcd;
            return *this;
        }
        frac upside(){
            return frac(m,z);
        }
        frac operator = (pair<int,int>A){
            z=A.first;m=A.second;fixed();
            return *this;
        }
        frac operator + (frac A){
            return (frac(z*A.m+m*A.z,m*A.m)).fixed();
        }
        frac operator * (frac A){
            // cout<<"multi ";this->print();putchar(' ');
            // A.print();putchar('=');
            int gcd1=__gcd(z,A.m);
            int gcd2=__gcd(A.z,m);
            frac ans=(frac((z/gcd1)*(A.z/gcd2),(m/gcd2)*(A.m/gcd1))).fixed();
            // ans.print();putchar('\n');
            return ans;
        }
        frac operator / (frac A){
            return (*this*A.upside()).fixed();
        }
        frac operator -(){
            return frac(-z,m);
        }
        frac operator -(frac A){
            return *this+(-A);
        }
        bool operator <(frac A){
            return z*A.m<A.z*m;
        }
        bool operator ==(frac A){
            return z*A.m==A.z*m;
        }
        bool operator >(frac A){
            return !(*this==A and *this<A);
        }
        void print(){
            fixed();
            _print(z);putchar('/');_print(m);
            // cout<<z<<"/"<<m<<endl;
        }
        frac _abs(){
            return frac(abs(z),abs(m));
        }
        long double it(){
            return z*1.0/m;
        }
};
struct node{
    signed x,y;
}p[1000001],s[1000001];
signed n;
double ans,mid;
double multi(node a1,node a2,node b1,node b2){
    return (a2.x-a1.x)*(b2.y-b1.y)-(b2.x-b1.x)*(a2.y-a1.y);
}
double dis(node p1,node p2){
    return sqrt((double)(p2.y-p1.y)*(p2.y-p1.y)*1.0+(double)(p2.x-p1.x)*(p2.x-p1.x)*1.0);
}
bool cmp(node p1,node p2){
    double tmp=multi(p[1],p1,p[1],p2);
    if(tmp>0) return true;
    if(tmp==0 and dis(p[0],p1)<dis(p[0],p2)) return true;
    return false;
}
int sqr_vector_dis(node a){
    return (__int128)a.x*a.x+(__int128)a.y*a.y;
}
int vector_multi(node a,node b){
    return abs((__int128)a.x*b.x+(__int128)a.y*b.y);
}
void print_node(node a){
    // cout<<"("<<a.x<<","<<a.y<<") ";
}
frac dist(node a,node b,node c){
    // cout<<"dist ";print_node(a);print_node(b);print_node(c);putchar(' ');
    //distance from c to line ab
    node vector1={b.x-a.x,b.y-a.y};
    node vector2={b.x-c.x,b.y-c.y};
    // cout<<"::";print_node(vector1);print_node(vector2);
    frac ans=
    frac(vector_multi(vector1,vector2)*vector_multi(vector1,vector2)
    ,sqr_vector_dis(vector1)*sqr_vector_dis(vector2));
    ans=-ans+1;ans=ans*sqr_vector_dis(vector2);ans=ans*frac(1,4);
    // cout<<"= ";ans.print();putchar('\n');
    return ans;
}
signed main(){
    freopen("a.in","r",stdin);
    freopen("a.out","w",stdout);
    scanf("%d",&n);
    for(int i=1;i<=n;++i){
        scanf("%d%d",&p[i].x,&p[i].y);
        if(i!=1 and p[i].y<p[1].y){
            mid=p[1].y;p[1].y=p[i].y;p[i].y=mid;
            mid=p[1].x;p[1].x=p[i].x;p[i].x=mid;
        }
    } 
    sort(p+2,p+1+n,cmp);
    s[1]=p[1];
    int tot=1;
    for(int i=2;i<=n;i++){
        while(tot>1 and multi(s[tot-1],s[tot],s[tot],p[i])<=0) tot--;
        tot++;
        s[tot]=p[i];
    }
    s[tot+1]=p[1];int now=1;
    frac ans;
    for(int i=1;i<=tot;i++){
        //s[i] s[i+1]
        while(dist(s[i],s[i+1],s[now]).it()<dist(s[i],s[i+1],s[(now==tot?1:now+1)]).it()){
            now=(now==tot?1:now+1);
        }
        if(dist(s[i],s[i+1],s[now]).it()>ans.it()){
            ans=dist(s[i],s[i+1],s[now]);
        }
    }
    ans.print();
}