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ID题目提交者结果用时内存语言文件大小提交时间测评时间
#315892#8168. Spacecraftucup-team087#AC ✓735ms4952kbC++2023.3kb2024-01-27 16:21:382024-01-27 16:21:39

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你现在查看的是最新测评结果

  • [2024-01-27 16:21:39]
  • 评测
  • 测评结果:AC
  • 用时:735ms
  • 内存:4952kb
  • [2024-01-27 16:21:38]
  • 提交

answer

#ifndef LOCAL
#pragma GCC optimize ("Ofast")
#pragma GCC optimize ("unroll-loops")
#endif

#include <bits/stdc++.h>
using namespace std;

using ll=long long;
#define int ll

#define rng(i,a,b) for(int i=int(a);i<int(b);i++)
#define rep(i,b) rng(i,0,b)
#define gnr(i,a,b) for(int i=int(b)-1;i>=int(a);i--)
#define per(i,b) gnr(i,0,b)
#define pb push_back
#define eb emplace_back
#define a first
#define b second
#define bg begin()
#define ed end()
#define all(x) x.bg,x.ed
#define si(x) int(x.size())
#ifdef LOCAL
#define dmp(x) cerr<<__LINE__<<" "<<#x<<" "<<x<<endl
#else
#define dmp(x) void(0)
#endif

template<class t,class u> bool chmax(t&a,u b){if(a<b){a=b;return true;}else return false;}
template<class t,class u> bool chmin(t&a,u b){if(b<a){a=b;return true;}else return false;}

template<class t> using vc=vector<t>;
template<class t> using vvc=vc<vc<t>>;

using pi=pair<int,int>;
using vi=vc<int>;

template<class t,class u>
ostream& operator<<(ostream& os,const pair<t,u>& p){
	return os<<"{"<<p.a<<","<<p.b<<"}";
}

template<class t> ostream& operator<<(ostream& os,const vc<t>& v){
	os<<"{";
	for(auto e:v)os<<e<<",";
	return os<<"}";
}

#define mp make_pair
#define mt make_tuple
#define one(x) memset(x,-1,sizeof(x))
#define zero(x) memset(x,0,sizeof(x))
#ifdef LOCAL
void dmpr(ostream&os){os<<endl;}
template<class T,class... Args>
void dmpr(ostream&os,const T&t,const Args&... args){
	os<<t<<" ";
	dmpr(os,args...);
}
#define dmp2(...) dmpr(cerr,__LINE__,##__VA_ARGS__)
#else
#define dmp2(...) void(0)
#endif

using uint=unsigned;
using ull=unsigned long long;

template<class t,size_t n>
ostream& operator<<(ostream&os,const array<t,n>&a){
	return os<<vc<t>(all(a));
}

template<int i,class T>
void print_tuple(ostream&,const T&){
}

template<int i,class T,class H,class ...Args>
void print_tuple(ostream&os,const T&t){
	if(i)os<<",";
	os<<get<i>(t);
	print_tuple<i+1,T,Args...>(os,t);
}

template<class ...Args>
ostream& operator<<(ostream&os,const tuple<Args...>&t){
	os<<"{";
	print_tuple<0,tuple<Args...>,Args...>(os,t);
	return os<<"}";
}

ll read(){
	ll i;
	cin>>i;
	return i;
}

vi readvi(int n,int off=0){
	vi v(n);
	rep(i,n)v[i]=read()+off;
	return v;
}

pi readpi(int off=0){
	int a,b;cin>>a>>b;
	return pi(a+off,b+off);
}

template<class t>
void print_single(t x,int suc=1){
	cout<<x;
	if(suc==1)
		cout<<"\n";
	if(suc==2)
		cout<<" ";
}

template<class t,class u>
void print_single(const pair<t,u>&p,int suc=1){
	print_single(p.a,2);
	print_single(p.b,suc);
}

template<class T>
void print_single(const vector<T>&v,int suc=1){
	rep(i,v.size())
		print_single(v[i],i==int(v.size())-1?suc:2);
}

template<class T>
void print_offset(const vector<T>&v,ll off,int suc=1){
	rep(i,v.size())
		print_single(v[i]+off,i==int(v.size())-1?suc:2);
}

template<class T,size_t N>
void print_single(const array<T,N>&v,int suc=1){
	rep(i,N)
		print_single(v[i],i==int(N)-1?suc:2);
}

template<class T>
void print(const T&t){
	print_single(t);
}

template<class T,class ...Args>
void print(const T&t,const Args&...args){
	print_single(t,2);
	print(args...);
}

string readString(){
	string s;
	cin>>s;
	return s;
}

template<class T>
T sq(const T& t){
	return t*t;
}

void YES(bool ex=true){
	cout<<"YES\n";
	if(ex)exit(0);
	#ifdef LOCAL
	cout.flush();
	#endif
}
void NO(bool ex=true){
	cout<<"NO\n";
	if(ex)exit(0);
	#ifdef LOCAL
	cout.flush();
	#endif
}
void Yes(bool ex=true){
	cout<<"Yes\n";
	if(ex)exit(0);
	#ifdef LOCAL
	cout.flush();
	#endif
}
void No(bool ex=true){
	cout<<"No\n";
	if(ex)exit(0);
	#ifdef LOCAL
	cout.flush();
	#endif
}
//#define CAPITAL
/*
void yes(bool ex=true){
	#ifdef CAPITAL
	cout<<"YES"<<"\n";
	#else
	cout<<"Yes"<<"\n";
	#endif
	if(ex)exit(0);
	#ifdef LOCAL
	cout.flush();
	#endif
}
void no(bool ex=true){
	#ifdef CAPITAL
	cout<<"NO"<<"\n";
	#else
	cout<<"No"<<"\n";
	#endif
	if(ex)exit(0);
	#ifdef LOCAL
	cout.flush();
	#endif
}*/
void possible(bool ex=true){
	#ifdef CAPITAL
	cout<<"POSSIBLE"<<"\n";
	#else
	cout<<"Possible"<<"\n";
	#endif
	if(ex)exit(0);
	#ifdef LOCAL
	cout.flush();
	#endif
}
void impossible(bool ex=true){
	#ifdef CAPITAL
	cout<<"IMPOSSIBLE"<<"\n";
	#else
	cout<<"Impossible"<<"\n";
	#endif
	if(ex)exit(0);
	#ifdef LOCAL
	cout.flush();
	#endif
}

constexpr ll ten(int n){
	return n==0?1:ten(n-1)*10;
}

const ll infLL=LLONG_MAX/3;

#ifdef int
const int inf=infLL;
#else
const int inf=INT_MAX/2-100;
#endif

int topbit(signed t){
	return t==0?-1:31-__builtin_clz(t);
}
int topbit(ll t){
	return t==0?-1:63-__builtin_clzll(t);
}
int topbit(ull t){
	return t==0?-1:63-__builtin_clzll(t);
}
int botbit(signed a){
	return a==0?32:__builtin_ctz(a);
}
int botbit(ll a){
	return a==0?64:__builtin_ctzll(a);
}
int botbit(ull a){
	return a==0?64:__builtin_ctzll(a);
}
int popcount(signed t){
	return __builtin_popcount(t);
}
int popcount(ll t){
	return __builtin_popcountll(t);
}
int popcount(ull t){
	return __builtin_popcountll(t);
}
int bitparity(ll t){
	return __builtin_parityll(t);
}
bool ispow2(int i){
	return i&&(i&-i)==i;
}
ll mask(int i){
	return (ll(1)<<i)-1;
}
ull umask(int i){
	return (ull(1)<<i)-1;
}
ll minp2(ll n){
	if(n<=1)return 1;
	else return ll(1)<<(topbit(n-1)+1);
}

bool inc(int a,int b,int c){
	return a<=b&&b<=c;
}

template<class t> void mkuni(vc<t>&v){
	sort(all(v));
	v.erase(unique(all(v)),v.ed);
}

template<class t> bool isuni(vc<t> v){
	int s=si(v);
	mkuni(v);
	return si(v)==s;
}

ll rand_int(ll l, ll r) { //[l, r]
	//#ifdef LOCAL
	static mt19937_64 gen;
	/*#else
	static mt19937_64 gen(chrono::steady_clock::now().time_since_epoch().count());
	#endif*/
	return uniform_int_distribution<ll>(l, r)(gen);
}

ll rand_int(ll k){ //[0,k)
	return rand_int(0,k-1);
}

template<class t>
void myshuffle(vc<t>&a){
	rep(i,si(a))swap(a[i],a[rand_int(0,i)]);
}

template<class t,class u>
int lwb(const vc<t>&v,const u&a){
	return lower_bound(all(v),a)-v.bg;
}
template<class t,class u>
bool bis(const vc<t>&v,const u&a){
	return binary_search(all(v),a);
}

vvc<int> readGraph(int n,int m){
	vvc<int> g(n);
	rep(i,m){
		int a,b;
		cin>>a>>b;
		//sc.read(a,b);
		a--;b--;
		g[a].pb(b);
		g[b].pb(a);
	}
	return g;
}

vvc<int> readTree(int n){
	return readGraph(n,n-1);
}

template<class t>
vc<t> presum(const vc<t>&a){
	vc<t> s(si(a)+1);
	rep(i,si(a))s[i+1]=s[i]+a[i];
	return s;
}
vc<ll> presum(const vi&a){
	vc<ll> s(si(a)+1);
	rep(i,si(a))s[i+1]=s[i]+a[i];
	return s;
}
//BIT で数列を管理するときに使う (CF850C)
template<class t>
vc<t> predif(vc<t> a){
	gnr(i,1,si(a))a[i]-=a[i-1];
	return a;
}
template<class t>
vvc<ll> imos(const vvc<t>&a){
	int n=si(a),m=si(a[0]);
	vvc<ll> b(n+1,vc<ll>(m+1));
	rep(i,n)rep(j,m)
		b[i+1][j+1]=b[i+1][j]+b[i][j+1]-b[i][j]+a[i][j];
	return b;
}

//verify してないや
void transvvc(int&n,int&m){
	swap(n,m);
}
template<class t,class... Args>
void transvvc(int&n,int&m,vvc<t>&a,Args&...args){
	assert(si(a)==n);
	vvc<t> b(m,vi(n));
	rep(i,n){
		assert(si(a[i])==m);
		rep(j,m)b[j][i]=a[i][j];
	}
	a.swap(b);
	transvvc(n,m,args...);
}
//CF854E
void rotvvc(int&n,int&m){
	swap(n,m);
}
template<class t,class... Args>
void rotvvc(int&n,int&m,vvc<t>&a,Args&...args){
	assert(si(a)==n);
	vvc<t> b(m,vi(n));
	rep(i,n){
		assert(si(a[i])==m);
		rep(j,m)b[m-1-j][i]=a[i][j];
	}
	a.swap(b);
	rotvvc(n,m,args...);
}

//ソートして i 番目が idx[i]
//CF850C
template<class t>
vi sortidx(const vc<t>&a){
	int n=si(a);
	vi idx(n);iota(all(idx),0);
	sort(all(idx),[&](int i,int j){return a[i]<a[j];});
	return idx;
}
//vs[i]=a[idx[i]]
//例えば sortidx で得た idx を使えば単にソート列になって返ってくる
//CF850C
template<class t>
vc<t> a_idx(const vc<t>&a,const vi&idx){
	int n=si(a);
	assert(si(idx)==n);
	vc<t> vs(n);
	rep(i,n)vs[i]=a[idx[i]];
	return vs;
}
//CF850C
vi invperm(const vi&p){
	int n=si(p);
	vi q(n);
	rep(i,n)q[p[i]]=i;
	return q;
}

template<class t,class s=t>
s SUM(const vc<t>&a){
	return accumulate(all(a),s(0));
}
template<class t,size_t K,class s=t>
s SUM(const array<t,K>&a){
	return accumulate(all(a),s(0));
}

template<class t>
t MAX(const vc<t>&a){
	return *max_element(all(a));
}

template<class t>
pair<t,int> MAXi(const vc<t>&a){
	auto itr=max_element(all(a));
	return mp(*itr,itr-a.bg);
}

template<class A>
auto MIN(const A&a){
	return *min_element(all(a));
}

template<class t>
pair<t,int> MINi(const vc<t>&a){
	auto itr=min_element(all(a));
	return mp(*itr,itr-a.bg);
}

vi vid(int n){
	vi res(n);iota(all(res),0);
	return res;
}

template<class S>
void soin(S&s){
	sort(all(s));
}

template<class S,class F>
void soin(S&s,F&&f){
	sort(all(s),forward<F>(f));
}

template<class S>
S soout(S s){
	soin(s);
	return s;
}

template<class S>
void rein(S&s){
	reverse(all(s));
}

template<class S>
S reout(S s){
	rein(s);
	return s;
}

template<class t,class u>
pair<t,u>&operator+=(pair<t,u>&a,pair<t,u> b){
	a.a+=b.a;a.b+=b.b;return a;}
template<class t,class u>
pair<t,u>&operator-=(pair<t,u>&a,pair<t,u> b){
	a.a-=b.a;a.b-=b.b;return a;}
template<class t,class u>
pair<t,u> operator+(pair<t,u> a,pair<t,u> b){return mp(a.a+b.a,a.b+b.b);}
template<class t,class u>
pair<t,u> operator-(pair<t,u> a,pair<t,u> b){return mp(a.a-b.a,a.b-b.b);}
template<class t,class u>
pair<t,u> operator-(pair<t,u> a){return mp(-a.a,-a.b);}
template<class t,class u>
istream&operator>>(istream&is,pair<t,u>&a){
	return is>>a.a>>a.b;
}

template<class t>
t gpp(vc<t>&vs){
	assert(si(vs));
	t res=move(vs.back());
	vs.pop_back();
	return res;
}

template<class t,class u>
void pb(vc<t>&a,const vc<u>&b){
	a.insert(a.ed,all(b));
}

template<class t,class...Args>
vc<t> cat(vc<t> a,Args&&...b){
	(pb(a,forward<Args>(b)),...);
	return a;
}

template<class t,class u>
vc<t>& operator+=(vc<t>&a,u x){
	for(auto&v:a)v+=x;
	return a;
}

template<class t,class u>
vc<t> operator+(vc<t> a,u x){
	return a+=x;
}

template<class t>
vc<t> operator+(const vc<t>&a,const vc<t>&b){
	vc<t> c(max(si(a),si(b)));
	rep(i,si(a))c[i]+=a[i];
	rep(i,si(b))c[i]+=b[i];
	return c;
}

template<class t,class u>
vc<t>& operator-=(vc<t>&a,u x){
	for(auto&v:a)v-=x;
	return a;
}

template<class t,class u>
vc<t>& operator-(vc<t> a,u x){
	return a-=x;
}

template<class t,class u>
void remval(vc<t>&a,const u&v){
	a.erase(remove(all(a),v),a.ed);
}
//消した要素の個数を返してくれる
//UCUP 2-8-F
template<class t,class F>
int remif(vc<t>&a,F f){
	auto itr=remove_if(all(a),f);
	int res=a.ed-itr;
	a.erase(itr,a.ed);
	return res;
}

template<class VS,class u>
void fila(VS&vs,const u&a){
	fill(all(vs),a);
}

template<class t,class u>
int findid(const vc<t>&vs,const u&a){
	auto itr=find(all(vs),a);
	if(itr==vs.ed)return -1;
	else return itr-vs.bg;
}

template<class t>
void rtt(vc<t>&vs,int i){
	rotate(vs.bg,vs.bg+i,vs.ed);
}

//copied from yosupo's library
//PARTLY VERIFIED

//USACO 2022 January ptlatinum C

#define GEOF

#ifdef GEOF
using ld=long double;
//using ld=double;
const ld PI=acos(ld(-1));
#else
using ld=ll;
#endif
const ld eps=1e-12;
int sgn(ld a){return a<-eps?-1:(a>eps?1:0);}
int sgn(ld a,ld b){return sgn(a-b);}
/*
using pt=complex<ld>;
#define x real()
#define y imag()
*/
namespace geo2d{

struct pt {
    ld x,y;
    //pt(ld _x = ld(0), ld _y = ld(0)) : x(_x), y(_y) {}
    pt():x(0),y(0){}
    pt(ld xx,ld yy):x(xx),y(yy){}
    pt operator+(const pt& r) const { return {x + r.x, y + r.y}; }
    pt operator-(const pt& r) const { return {x - r.x, y - r.y}; }
    pt operator*(const pt& r) const {
        return {x * r.x - y * r.y, x * r.y + y * r.x};
    }
    pt inv()const{
		ld d=norm();
		return {x/d,-y/d};
	}
    pt operator/(const pt&r)const{
		return operator*(r.inv());
	}

    pt operator*(const ld& r) const { return {x * r, y * r}; }
    pt operator/(const ld& r) const { return {x / r, y / r}; }

    pt& operator+=(const pt& r) { return *this = *this + r; }
    pt& operator-=(const pt& r) { return *this = *this - r; }
    pt& operator*=(const pt& r) { return *this = *this * r; }
    pt& operator/=(const pt& r) { return *this = *this / r; }
    pt& operator*=(const ld& r) { return *this = *this * r; }
    pt& operator/=(const ld& r) { return *this = *this / r; }

    pt operator-() const { return {-x, -y}; }

	static int cmp(const pt&a,const pt&b){
		int v=sgn(a.x,b.x);
		return v?v:sgn(a.y,b.y);
	}
    bool operator<(const pt& r) const {
        return cmp(*this,r)<0;
    }
    bool operator<=(const pt& r) const {
        return cmp(*this,r)<=0;
    }
    bool operator>(const pt& r) const {
        return cmp(*this,r)>0;
    }
    bool operator==(const pt& r) const { return sgn((*this - r).rabs()) == 0; }
    bool operator!=(const pt& r) const { return !(*this == r); }

    ld norm() const { return x * x + y * y; }
    ld rabs() const { return max(std::abs(x), std::abs(y)); }  // robust abs
    pair<ld, ld> to_pair() const { return {x, y}; }
    #ifdef GEOF
    ld abs() const { return sqrt(norm()); }
    ld arg() const { return atan2(y, x); }
    static pt polar(ld le, ld th) { return {le * cos(th), le * sin(th)}; }
	#endif
};
istream& operator>>(istream& is, pt& p){
	return is>>p.x>>p.y;
}
ostream& operator<<(ostream& os, const pt& p) {
    return os << "pt(" << p.x << ", " << p.y << ")";
}
ld norm(const pt&a){
	return a.norm();
}
ld rabs(const pt&a){
	return a.rabs();
}
#ifdef GEOF
ld abs(const pt&a){
	return sqrt(norm(a));
}
//XXII Opencup Gpt of Ural K
pt normalized(const pt&a){
	return a/abs(a);
}
ld arg(const pt&a){return a.arg();}
//normalize to [-PI,PI)
//Contest 2: ptKU Contest 1, ptTZ Summer 2022 Day 4
ld normarg(ld a){
	ld res=fmod(a+PI,2*PI);
	if(res<0)res+=PI;
	else res-=PI;
	return res;
}
//normalize to [0,2*PI)
//Multiuni2023-10-E
ld normarg_nonnegative(ld a){
	ld res=fmod(a,2*PI);
	if(res<0)res+=2*PI;
	return res;
}
//AOJ1183
//arg between ab
//assume given lengths are valid
ld arg(ld a,ld b,ld c){
	return acos(min(max((a*a+b*b-c*c)/(2*a*b),ld(-1)),ld(1)));
}
#endif
ld norm(const pt&a,const pt&b){
	return (a-b).norm();
}
ld dot(const pt&a,const pt&b){return a.x*b.x+a.y*b.y;}
ld crs(const pt& a,const pt& b){return a.x*b.y-a.y*b.x;}
ld crs(const pt& a,const pt& b,const pt& c){return crs(b-a,c-a);}
int ccw(const pt& a,const pt& b){return sgn(crs(a,b));}
int ccw(const pt& a,const pt& b,const pt& c){return ccw(b-a,c-a);}
//(-pi,0](0,pi]
int argtype(const pt&a){
	if(sgn(a.y)==0)return a.x<0?1:0;
	return a.y<0?0:1;
}
int argcmp(const pt&a,const pt&b){
	int at=argtype(a),bt=argtype(b);
	if(at!=bt)return at<bt?-1:1;
	return -ccw(a,b);
};
bool argless(const pt&a,const pt&b){return argcmp(a,b)<0;}
//(-2)[a,-1](0)[b,1](2)
int bet(pt a,pt b,pt c){
	pt d=b-a;
	ld e=dot(d,c-a);
	if(sgn(e)<=0)return sgn(e)-1;
	return sgn(e-norm(d))+1;
}
//AOJ0153
//三角形 abc に d が含まれるか?0-no,1-edge,2-in
int cont(pt a,pt b,pt c,pt d){
	if(ccw(a,b,c)==-1) swap(b,c);
	return min({ccw(a,b,d),ccw(b,c,d),ccw(c,a,d)})+1;
}
//(a,b) を結ぶ直線を考え,x 座標との交点の y 座標を求める
//(分子,分母)を返す
pair<ld,ld> xcut(const pt&a,const pt&b,ld x){
	return mp(a.y*(b.x-x)-b.y*(a.x-x),b.x-a.x);
}
//XXII Opencup Gpt of Ural K
pt rot90(pt a){
	return pt(-a.y,a.x);
}
#ifdef GEOF
ld xcutval(const pt&a,const pt&b,ld x){
	auto [p,q]=xcut(a,b,x);
	return p/q;
}
//AOJ1183
//Xmas2010 E
//-+ の 順で返す
//a の符号により,small/large が決まる
int qeq(ld a,ld b,ld c,ld&d,ld&e){
	if(sgn(a)==0){
		if(sgn(b)==0)return 0;
		d=-c/b;
		return 1;
	}
	ld f=b*b-4*a*c;
	if(sgn(f)<0)return 0;
	ld g=sqrt(max(f,ld(0)));
	d=(-b-g)/(2*a);
	e=(-b+g)/(2*a);
	return sgn(f)+1;
}
#else
pt normdir(pt a){
	if(a==pt(0,0))return a;
	int g=gcd(a.x,a.y);
	return pt(a.x/g,a.y/g);
}
#endif

ld area2(const vc<pt>&ps){
	ld res=0;
	rep(i,si(ps))res+=crs(ps[i],ps[(i+1)%si(ps)]);
	return res;
}

using ln=pair<pt,pt>;
pt dir(ln a){return a.b-a.a;}
pt eval(ln a,ld b){return a.a+dir(a)*b;}
ld crs(ln a,pt b){return crs(a.a,a.b,b);}
int ccw(ln a,pt b){return ccw(a.a,a.b,b);}
int bet(ln a,pt b){return bet(a.a,a.b,b);}
ld projt(ln a,pt b){
	pt c=dir(a);
	return dot(c,b-a.a)/norm(c);
}
pt proj(ln a,pt b){
	pt c=dir(a);
	return a.a+c*dot(c,b-a.a)/norm(c);
}
pt refl(ln a,pt b){
	return proj(a,b)*2-b;
}
//AOJ1157
//0-no,1-yes(endpoint),2-yes(innner),3-overelap
//if the two line touch like this
// x----x----x
//it returns 1
int iss(ln a,ln b){
	int c1=ccw(a.a,a.b,b.a),c2=ccw(a.a,a.b,b.b);
	int d1=ccw(b.a,b.b,a.a),d2=ccw(b.a,b.b,a.b);
	if(c1||c2||d1||d2)return 1-max(c1*c2,d1*d2);
	int f=bet(a.a,a.b,b.a),g=bet(a.a,a.b,b.b);
	if(max(f,g)==-2||min(f,g)==2)return 0;
	if(max(f,g)==-1||min(f,g)==1)return 1;
	return 3;
}
//segment a intersects line b?
//endpoints inclusive
bool isl(ln a,ln b){
	int d1=ccw(b.a,b.b,a.a),d2=ccw(b.a,b.b,a.b);
	return d1*d2<=0;
}
//並行でない->true, というだけ
//直線が一致とかは考えてないことに注意
bool ill(ln a,ln b){
	return ccw(dir(a),dir(b));
}
ld cllt(ln a,ln b){
	return crs(b.a,b.b,a.a)/crs(dir(a),dir(b));
}
//ICPC Yokohama 2022 J
pair<ld,ld> clltf(ln a,ln b){
	return mp(crs(b.a,b.b,a.a),crs(dir(a),dir(b)));
}
//AOJ1033
pt cll(ln a,ln b){
	return eval(a,crs(b.a,b.b,a.a)/crs(dir(a),dir(b)));
}

vc<pt> halfpint(vc<ln> s){
	sort(all(s),[&](ln a,ln b){
		int c=argcmp(dir(a),dir(b));
		if(c)return c<0;
		return ccw(b,a.a)>0;
	});
	s.erase(unique(all(s),[&](ln a,ln b){
		return argcmp(dir(a),dir(b))==0;
	}),s.ed);
	int n=si(s);
	vi cur;
	rep(ii,n*2){
		int i=ii%n,m;
		while((m=si(cur))>=2){
			if(ccw(s[i],cll(s[cur[m-2]],s[cur[m-1]]))>0)break;
			cur.pop_back();
		}
		cur.pb(i);
	}
	vi cnt(n);
	for(auto i:cur)cnt[i]++;
	vc<ln> t;
	rep(i,n)if(cnt[i]==2)t.pb(s[i]);
	int m=si(t);
	vc<pt> res(m);
	rep(i,m)res[i]=cll(t[i],t[(i+1)%m]);
	return res;
}

}


//VERIFY: yosupo
//KUPC2017J
//AOJDSL1A
//without rank
struct unionfind{
	vi p,s;
	int c;
	unionfind(int n):p(n,-1),s(n,1),c(n){}
	void clear(){
		fill(all(p),-1);
		fill(all(s),1);
		c=si(p);
	}
	int find(int a){
		return p[a]==-1?a:(p[a]=find(p[a]));
	}
	//set b to a child of a
	bool unite(int a,int b){
		a=find(a);
		b=find(b);
		if(a==b)return false;
		p[b]=a;
		s[a]+=s[b];
		c--;
		return true;
	}
	bool same(int a,int b){
		return find(a)==find(b);
	}
	int sz(int a){
		return s[find(a)];
	}
};

bool dbg=false;

/*
using ld=long double;
const ld eps=1e-12;
int sgn(ld a){return a<-eps?-1:(a>eps?1:0);}
int sgn(ld a,ld b){return sgn(a-b);}
*/

//ll で verify (TTPC2022 N)
//frac<ll>約分なしで verify (ABC301)
struct pt{
	ld x,y,z;
	pt():x(0),y(0),z(0){}
	pt(ld xx,ld yy,ld zz):x(xx),y(yy),z(zz){}
	pt operator-()const{return pt(-x,-y,-z);}
	pt&operator+=(pt r){x+=r.x;y+=r.y;z+=r.z;return *this;}
	pt&operator-=(pt r){x-=r.x;y-=r.y;z-=r.z;return *this;}
	pt&operator*=(ld r){x*=r;y*=r;z*=r;return *this;}
	pt&operator/=(ld r){x/=r;y/=r;z/=r;return *this;}
	pt operator+(pt r)const{return pt(*this)+=r;}
	pt operator-(pt r)const{return pt(*this)-=r;}
	pt operator*(ld r)const{return pt(*this)*=r;}
	pt operator/(ld r)const{return pt(*this)/=r;}
	//ld length(){return sqrt(length2());}
	ld length2(){return sq(x)+sq(y)+sq(z);}
	int cmp(const pt&a,const pt&b)const{
		int sx=sgn(a.x-b.x),sy=sgn(a.y-b.y),sz=sgn(a.z-b.z);
		return sx?sx:sy?sy:sz;
	}
	bool operator<(pt r)const{return cmp(*this,r)<0;}
	bool operator==(pt r)const{return cmp(*this,r)==0;}
};
ostream& operator<<(ostream&os, pt a){
	return os<<"("<<a.x<<","<<a.y<<","<<a.z<<")";
}
istream& operator>>(istream&is, pt&a){
	return is>>a.x>>a.y>>a.z;
}
ld dot(pt a,pt b){
	return a.x*b.x+a.y*b.y+a.z*b.z;
}
ld norm(pt a){
	return dot(a,a);
}
ld norm(pt a,pt b){
	return norm(a-b);
}
bool is0(pt a){
	return sgn(a.x)==0&&sgn(a.y)==0&&sgn(a.z)==0;
}
pt crs(pt a,pt b){
	return pt(
		a.y*b.z-a.z*b.y,
		a.z*b.x-a.x*b.z,
		a.x*b.y-a.y*b.x
	);
}
pt crs(pt a,pt b,pt c){
	return crs(b-a,c-a);
}
ld det(pt a,pt b,pt c){
	return dot(crs(a,b),c);
}
//vol>0 -> a から見て b,c,d が時計まわり
ld det(pt a,pt b,pt c,pt d){
	return det(b-a,c-a,d-a);
}
//TTPC2022 N
using T=tuple<pt,pt,pt>;
//面を返す; 全部三角形
//外側から見たとき,反時計まわりに列挙
//UCUP-2-20-D

//UCUP2-3-J
pt anotheraxis(pt v){
	ld ax=abs(v.x),ay=abs(v.y),az=abs(v.z);
	if(ax<=ay&&ax<=az)return pt(0,-v.z,v.y);
	else if(ay<=az)return pt(v.z,0,-v.x);
	else return pt(-v.y,v.x,0);
}

ld abs(pt v){
	return sqrt(norm(v));
}
vc<T> halfpint(vc<pair<pt,ld>> hps){
	//assume bounded
	
	vc<T> res;
	
	rep(root,si(hps)){
		auto [X,off]=hps[root];
		auto Y=anotheraxis(X);
		Y/=abs(Y);
		auto Z=crs(X,Y);
		assert(sgn(abs(Z),1)==0);
		
		vc<geo2d::ln> ls;
		//for(auto [dir,thre]:hps){
		rep(i,si(hps))if(i!=root){
			auto [dir,thre]=hps[i];
			ld x=dot(dir,X);
			ld y=dot(dir,Y);
			ld z=dot(dir,Z);
			
			geo2d::pt u(y,z);
			//dot(u,v)+x*off<=thre
			if(u==geo2d::pt(0,0)){
				if(x*off>thre)goto done;
			}else{
				geo2d::pt a=u*((thre-x*off)/norm(u));
				auto b=a+geo2d::rot90(u);
				ls.eb(a,b);
			}
		}
		{
			//dmp2(X,off);
			//dmp(ls);
			auto w=geo2d::halfpint(ls);
			
			auto ch=[&](geo2d::pt q){
				return X*off+Y*q.x+Z*q.y;
			};
			
			rng(i,1,si(w)-1){
				res.eb(ch(w[i+1]),ch(w[i]),ch(w[0]));
			}
		}
		
		done:;
	}
	
	vc<pt> vs;
	for(auto [a,b,c]:res){
		vs.pb(a);
		vs.pb(b);
		vs.pb(c);
	}
	mkuni(vs);
	
	auto rectify=[&](pt v){
		int i=lwb(vs,v);
		assert(i<si(vs)&&vs[i]==v);
		return vs[i];
	};
	
	vc<T> tmp;
	for(auto [a,b,c]:res){
		if(a==b||b==c||c==a)continue;
		tmp.eb(rectify(a),rectify(b),rectify(c));
	}
	
	return tmp;
}


//AOJ1183
//arg between ab
//assume given lengths are valid
ld arg(ld a,ld b,ld c){
	return acos(min(max((a*a+b*b-c*c)/(2*a*b),ld(-1)),ld(1)));
}

ld heron(ld a,ld b,ld c){
	ld s=(a+b+c)/2;
	return sqrt(s*(s-a)*(s-b)*(s-c));
}

void slv(){
	int n;cin>>n;
	ld R;cin>>R;
	//R=sqrt(R);
	
	vc<pair<pt,ld>> hps;
	
	{
		const int V=R*2;
		hps.eb(pt(+1,0,0),V);
		hps.eb(pt(-1,0,0),V);
		hps.eb(pt(0,+1,0),V);
		hps.eb(pt(0,-1,0),V);
		hps.eb(pt(0,0,+1),V);
		hps.eb(pt(0,0,-1),V);
	}
	
	rep(_,n){
		pt v;cin>>v;
		ld len=abs(v);
		
		pt dir=-v/len;
		ld thre=sqrt(sq(len)-sq(R))/len*R;
		
		hps.eb(dir,thre);
	}
	
	auto bound=halfpint(hps);
	//dmp(bound);
	
	vc<pt> vs;
	for(auto [a,b,c]:bound){
		vs.pb(a);
		vs.pb(b);
		vs.pb(c);
	}
	mkuni(vs);
	
	unionfind uf(si(vs));
	
	auto in=[&](pt v){
		return sgn(abs(v)-R)<=0;
	};
	
	auto work=[&](pt a,pt b){
		if(in(a)||in(b))return;
		if(dot(a,b-a)<0&&dot(b,a-b)<0){
			ld p=abs(a);
			ld q=abs(b);
			ld r=abs(a-b);
			ld h=heron(p,q,r)*2/r;
			if(sgn(h-R)<=0)return;
		}
		uf.unite(lwb(vs,a),lwb(vs,b));
	};
	for(auto [a,b,c]:bound){
		work(a,b);
		work(b,c);
		work(c,a);
	}
	
	int ans=0;
	rep(i,si(vs))if(uf.find(i)==i&&!in(vs[i])){
		ans++;
	}
	print(ans);
}

signed main(){
	cin.tie(0);
	ios::sync_with_stdio(0);
	cout<<fixed<<setprecision(20);
	
	if(dbg){
		while(1)slv();
	}else{
		int t;cin>>t;rep(_,t)
		slv();
	}
}

详细

Test #1:

score: 100
Accepted
time: 1ms
memory: 3840kb

input:

3
4 12
13 0 0
0 15 0
0 -15 0
0 0 15
6 100
0 0 101
0 0 -101
0 101 0
0 -101 0
101 0 0
-101 0 0
20 333
328 -160 -572
-165 417 -847
-319 -45 271
359 -467 -625
-355 -451 658
-280 -424 687
-65 -224 573
475 -371 373
-246 -54 -903
595 -196 -305
622 -570 -250
386 -541 -566
647 455 -424
734 117 -405
830 -10 -...

output:

1
0
3

result:

ok 3 tokens

Test #2:

score: 0
Accepted
time: 15ms
memory: 4212kb

input:

10
21 252
0 0 280
0 0 -280
0 553 0
163 528 0
311 457 0
432 345 0
514 202 0
539 -123 0
479 -276 0
376 -405 0
240 -498 0
82 -546 0
-82 -546 0
-240 -498 0
-376 -405 0
-479 -276 0
-539 -123 0
-551 41 0
-432 345 0
-311 457 0
-163 528 0
24 290
0 0 323
0 0 -323
0 638 0
180 612 0
345 537 0
482 418 0
581 265...

output:

32
44
46
48
50
20
30
23
15
2

result:

ok 10 tokens

Test #3:

score: 0
Accepted
time: 13ms
memory: 4016kb

input:

10
1 64
-152 679 262
1 61
-555 536 -388
20 41
20 62 -75
-20 -62 75
40 124 -150
-40 -124 150
60 186 -225
-60 -186 225
80 248 -300
-80 -248 300
100 310 -375
-100 -310 375
120 372 -450
-120 -372 450
140 434 -525
-140 -434 525
160 496 -600
-160 -496 600
180 558 -675
-180 -558 675
200 620 -750
-200 -620 ...

output:

1
1
1
1
1
3
1
1
4
13

result:

ok 10 tokens

Test #4:

score: 0
Accepted
time: 18ms
memory: 4020kb

input:

10
23 238
0 0 265
0 0 -265
0 522 0
154 499 0
294 431 0
408 325 0
486 191 0
520 39 0
509 -116 0
452 -261 0
355 -383 0
226 -470 0
78 -516 0
-78 -516 0
-226 -470 0
-355 -383 0
-452 -261 0
-509 -116 0
-520 39 0
-486 191 0
-408 325 0
-294 431 0
-154 499 0
24 232
0 0 258
0 0 -258
0 511 0
144 490 0
276 430...

output:

42
44
46
48
50
22
28
20
11
6

result:

ok 10 tokens

Test #5:

score: 0
Accepted
time: 70ms
memory: 4228kb

input:

10
1 78
-342 22 -830
1 22
753 206 51
28 67
-37 32 52
37 -32 -52
-74 64 104
74 -64 -104
-111 96 156
111 -96 -156
-148 128 208
148 -128 -208
-185 160 260
185 -160 -260
-222 192 312
222 -192 -312
-259 224 364
259 -224 -364
-296 256 416
296 -256 -416
-333 288 468
333 -288 -468
-370 320 520
370 -320 -520...

output:

1
1
1
1
1
1
17
1
4
14

result:

ok 10 tokens

Test #6:

score: 0
Accepted
time: 19ms
memory: 4052kb

input:

10
23 260
0 0 289
0 0 -289
0 570 0
168 545 0
321 471 0
446 355 0
531 208 0
569 43 0
556 -127 0
494 -285 0
388 -418 0
247 -514 0
85 -564 0
-85 -564 0
-247 -514 0
-388 -418 0
-494 -285 0
-556 -127 0
-569 43 0
-531 208 0
-446 355 0
-321 471 0
-168 545 0
24 205
0 0 228
0 0 -228
0 451 0
127 433 0
244 380...

output:

42
44
46
48
50
18
29
20
15
1

result:

ok 10 tokens

Test #7:

score: 0
Accepted
time: 80ms
memory: 4084kb

input:

10
1 84
-208 367 629
10 15
-53 53 -65
-106 106 -130
-159 159 -195
-212 212 -260
-265 265 -325
-318 318 -390
-371 371 -455
-424 424 -520
-477 477 -585
-530 530 -650
20 50
-61 15 72
61 -15 -72
-122 30 144
122 -30 -144
-183 45 216
183 -45 -216
-244 60 288
244 -60 -288
-305 75 360
305 -75 -360
-366 90 4...

output:

1
1
1
1
1
3
23
1
6
10

result:

ok 10 tokens

Test #8:

score: 0
Accepted
time: 23ms
memory: 4164kb

input:

10
26 190
-273 590 -183
96 -197 50
-334 465 87
134 -254 203
-39 239 -151
-192 96 -200
95 -236 50
-466 -601 406
-483 -461 -336
262 -291 -148
-317 -250 -59
-54 54 212
-117 632 116
281 168 -107
467 240 -295
527 -348 143
437 301 -86
251 132 -304
-171 -515 -335
198 83 -133
-92 -195 -274
107 325 171
231 2...

output:

4
5
8
14
6
0
4
3
4
7

result:

ok 10 tokens

Test #9:

score: 0
Accepted
time: 43ms
memory: 4208kb

input:

10
52 130
114 284 -163
651 -474 -209
-120 183 -203
-236 -268 151
-152 -124 75
-123 502 215
-403 99 350
-106 199 -154
377 664 -403
-325 -379 218
58 83 -238
484 648 -208
74 -111 323
78 201 56
53 166 40
-137 177 215
498 -426 675
-222 69 -26
161 39 166
-210 243 37
174 236 216
117 -107 -287
-127 -152 -70...

output:

4
5
7
9
5
2
19
0
1
0

result:

ok 10 tokens

Test #10:

score: 0
Accepted
time: 37ms
memory: 4004kb

input:

10
73 296
-85 518 -425
709 224 484
669 -180 601
296 376 -600
-660 -373 500
55 -783 -472
192 -835 -147
310 -153 -207
-494 -188 -102
-686 480 -246
-626 -457 -564
105 63 699
-460 527 427
-594 23 -510
-251 572 -130
765 203 -47
250 385 -138
-211 785 417
192 -767 -155
-75 111 -382
655 -398 -557
16 -74 -86...

output:

4
8
4
6
1
4
4
0
5
0

result:

ok 10 tokens

Test #11:

score: 0
Accepted
time: 31ms
memory: 3952kb

input:

10
125 133
579 746 180
135 752 -291
42 -651 -652
94 -313 801
207 154 -772
118 279 923
-385 -407 49
355 -35 -723
292 52 352
-865 -230 99
-698 -43 143
-476 -838 117
-10 -633 -452
-97 -475 301
667 479 467
356 188 777
107 94 627
423 -670 -103
578 -48 -300
320 715 -483
433 -269 -771
223 -758 543
19 -87 1...

output:

9
5
8
1
7
7
5
10
9
0

result:

ok 10 tokens

Test #12:

score: 0
Accepted
time: 699ms
memory: 4072kb

input:

10
500 104
61 296 49
-313 -843 -229
348 516 46
84 -102 196
-272 -94 -274
424 437 -115
-77 -606 194
-194 -138 -102
412 284 102
-580 123 -393
183 -618 102
234 867 -159
242 -237 883
95 -11 -298
-62 203 196
-454 -851 -136
393 -484 618
-52 94 61
-310 -105 -42
55 -16 141
-14 156 -8
-151 18 93
-176 -550 17...

output:

0
0
0
0
0
0
0
0
0
0

result:

ok 10 tokens

Test #13:

score: 0
Accepted
time: 698ms
memory: 4076kb

input:

10
500 114
93 -268 -242
-148 -268 -291
-199 69 110
-165 -178 77
76 34 -453
-246 -443 291
-144 337 636
-402 35 -718
22 -79 97
-845 259 -159
-157 -463 328
304 564 -164
-90 -438 -112
-223 -38 29
-26 322 72
-628 114 -754
307 -265 -229
-772 -181 -197
-212 377 132
700 2 -16
-719 31 -151
372 41 564
142 25 ...

output:

0
0
0
0
0
0
0
0
0
0

result:

ok 10 tokens

Test #14:

score: 0
Accepted
time: 3ms
memory: 3952kb

input:

10
15 10
431 -214 -126
564 55 16
-5 192 -599
566 753 76
406 -573 549
47 589 -568
-505 -389 -486
-505 243 260
-650 -220 -411
-890 302 -327
-176 737 -422
103 502 -121
-223 -312 -648
291 -523 -45
-184 90 -636
20 19
675 149 -602
713 -539 -253
283 618 442
-187 662 -680
177 -844 60
163 148 264
158 505 -77...

output:

1
1
1
1
1
1
1
1
1
1

result:

ok 10 tokens

Test #15:

score: 0
Accepted
time: 0ms
memory: 3900kb

input:

10
24 17
521 286 -776
-115 -70 193
-211 -388 -38
255 -586 -309
-443 809 49
637 -278 -195
926 -206 183
598 642 -479
-825 55 404
208 -106 240
-745 -344 -547
194 225 -442
-61 533 -149
-648 608 386
-640 14 517
412 -309 184
537 42 685
731 353 238
300 -14 -227
-810 153 -486
-510 -28 -828
-454 424 293
497 ...

output:

1
1
1
1
1
1
1
1
1
1

result:

ok 10 tokens

Test #16:

score: 0
Accepted
time: 1ms
memory: 4056kb

input:

3
4 100
111 0 0
101 0 0
1000 0 0
628 0 0
3 314
0 431 0
0 999 0
0 341 0
7 7
0 0 77
0 0 777
0 0 70
0 0 770
0 0 707
0 0 700
0 0 -777

output:

1
1
1

result:

ok 3 tokens

Test #17:

score: 0
Accepted
time: 1ms
memory: 4032kb

input:

3
16 64
32 64 0
2 256 0
128 8 0
512 0 0
4 -128 0
256 -8 0
128 -2 0
0 -256 0
-4 -128 0
-32 -64 0
-512 -1 0
-128 0 0
-512 1 0
-8 512 0
-128 4 0
0 128 0
6 123
0 666 0
0 -666 0
0 333 576
0 333 -576
0 -333 576
0 -333 -576
4 999
707 0 707
707 0 -707
-707 0 707
-707 0 -707

output:

1
1
2

result:

ok 3 tokens

Test #18:

score: 0
Accepted
time: 266ms
memory: 4240kb

input:

10
300 121
-973 -95 -199
-561 -803 189
652 -552 -517
421 315 848
-208 -741 635
357 776 516
-423 -901 73
-894 52 440
-473 -799 365
605 503 614
622 743 238
84 -189 976
759 -118 638
-69 891 444
-497 -52 864
293 604 -739
-409 900 134
211 959 -180
434 -566 698
621 -34 780
-997 -8 -48
568 -12 -820
-678 -1...

output:

317
317
317
317
317
317
317
317
317
317

result:

ok 10 tokens

Test #19:

score: 0
Accepted
time: 735ms
memory: 4952kb

input:

10
500 95
-99 38 -992
-182 -153 -969
-693 -632 342
-828 556 39
-146 925 344
600 -779 -174
-589 -796 126
86 797 -594
-626 -260 -732
843 451 -286
366 -928 -31
-822 267 498
-747 485 450
-334 82 -937
-214 177 -959
681 -265 680
9 -953 -297
488 -834 -250
-818 -542 -183
-99 -613 781
-818 -481 -310
-964 -45...

output:

457
457
457
457
457
457
457
457
457
457

result:

ok 10 tokens

Test #20:

score: 0
Accepted
time: 616ms
memory: 4800kb

input:

10
411 96
970 0 -235
51 54 995
-125 -907 -397
835 190 512
-463 648 -601
71 949 300
326 743 -581
-699 -646 -300
925 118 -356
907 -378 175
-442 561 697
-743 632 211
842 -516 -146
-286 -227 929
-197 895 395
-258 -910 -318
908 381 -163
-643 382 -661
557 635 532
-961 -251 -102
-565 787 -241
714 490 -497
...

output:

283
410
89
12
6
2
407
297
460
0

result:

ok 10 tokens

Test #21:

score: 0
Accepted
time: 605ms
memory: 4880kb

input:

10
429 91
-143 867 -473
-835 545 -54
-829 -325 -452
930 100 -348
-282 -274 -917
-494 456 -738
-932 154 -322
-996 32 -47
-428 -893 124
256 698 -666
-227 -131 963
919 -230 313
641 747 -165
-913 -383 -125
476 161 -863
-408 -665 -623
-912 -286 289
-405 479 776
-974 6 -218
607 553 568
-371 770 515
-139 -...

output:

199
377
358
486
40
133
377
327
3
340

result:

ok 10 tokens

Extra Test:

score: 0
Extra Test Passed