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#634339#9455. Getting Lostucup-team087#WA 88ms4404kbC++2332.2kb2024-10-12 17:07:082024-10-12 17:07:08

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  • [2024-10-12 17:07:08]
  • 评测
  • 测评结果：WA
  • 用时：88ms
  • 内存：4404kb
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  • [2024-10-12 17:07:08]
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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

bool dbg=false;

#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>;
using vvi=vc<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));
}

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);
}
string rand_string(int n,char lw,char up){
	string s(n,'?');
	rep(i,n)s[i]=rand_int(lw,up);
	return s;
}

int current_run_id,run_batch_size=1000;
int calc_random_limit(){
	return current_run_id/run_batch_size+1;
}
template<class t>
void generate_single(t&a){
	a=rand_int(1,calc_random_limit());
}
void generate_single(string&a){
	int n;generate_single(n);
	a=rand_string(n,'a','b');
}
template<class t,class u>
void generate_single(pair<t,u>&a){
	generate_single(a.a);
	generate_single(a.b);
}
//https://trap.jp/post/1224/
template<class... Args>
void input(Args&... a){
	if(dbg){
		(generate_single(a),...);
	}else{
		#ifdef USE_FAST_IO
		sc.read(a...);
		#else
		(cin >> ... >> a);
		#endif
	}
}
#define INT(...) int __VA_ARGS__;input(__VA_ARGS__)
#define LL(...) ll __VA_ARGS__;input(__VA_ARGS__)
#define ULL(...) ull __VA_ARGS__;input(__VA_ARGS__)
#define STR(...) string __VA_ARGS__;input(__VA_ARGS__)
#define CHR(...) char __VA_ARGS__;input(__VA_ARGS__)
#define DBL(...) double __VA_ARGS__;input(__VA_ARGS__)
#define LD(...) ld __VA_ARGS__;input(__VA_ARGS__)
#define overload3(a,b,c,d,...) d
#define VI2(name,size) vi name(size);rep(i_##name,size)input(name[i_##name]);
#define VI3(name,size,offset) vi name(size);rep(i_##name,size)input(name[i_##name]),name[i_##name]+=offset;
#define VI(...) overload3(__VA_ARGS__,VI3,VI2)(__VA_ARGS__)
#define VPI(name,size) vc<pi> name(size);rep(i_##name,size)input(name[i_##name]);
#define VVI(name,sizeN,sizeM) vvi name(sizeN,vi(sizeM));\
rep(i_##name,sizeN)rep(j_##name,sizeM)input(name[i_##name][j_##name]);
#define VS(name,size) vc<string> name(size);rep(i_##name,size)input(name[i_##name]);

#define overload5(a,b,c,d,e,f,...) f
#define VVC4(type,name,sizeN,sizeM) vvc<type> name(sizeN,vc<type>(sizeM));
#define VVC5(type,name,sizeN,sizeM,ini) vvc<type> name(sizeN,vc<type>(sizeM,ini));
#define VVC(...) overload5(__VA_ARGS__,VVC5,VVC4)(__VA_ARGS__)

template<class T>
T vvvc(T v){
	return v;
}

template<class T,class...Args>
auto vvvc(int n,T v,Args...args){
	return vector(n,vvvc(v,args...));
}

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<<"}";
}

void printsuc(int suc){
	#ifdef USE_FAST_IO
		if(suc==1)pr.write('\n');
		if(suc==2)pr.write(' ');
	#else
		if(suc==1){
			if(dbg)cout<<endl;
			else{
				#ifdef LOCAL
				cout<<endl;
				#else
				cout<<"\n";
				#endif
			}
		}
		if(suc==2)
			cout<<" ";
	#endif
}

template<class t>
void print_single(t x,int suc=1){
	#ifdef USE_FAST_IO
	pr.write(x);
	#else
	cout<<x;
	#endif
	printsuc(suc);
}

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?3:2);
	printsuc(suc);
}

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?3:2);
	printsuc(suc);
}

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...);
}

template<class T>
void printvv(const vvc<T>&vs){
	for(const auto&row:vs)print(row);
}

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 S> void mkuni(S&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;
}

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

template<class S,class u>
int lwb(const S&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);
}

//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)];
	}
};

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> rand_tree(int n){
	vvc<int> t(n);
	unionfind uf(n);
	while(uf.c>1){
		int a=rand_int(n);
		int b=rand_int(n);
		if(uf.unite(a,b)){
			t[a].pb(b);
			t[b].pb(a);
		}
	}
	return t;
}

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

vi readRooted(int n){
	assert(!dbg);
	vi par(n,-1);
	rng(i,1,n){
		input(par[i]);
		par[i]--;
		assert(inc(0,par[i],i-1));
	}
	return par;
}

void printTree(const vvc<int> t){
	int n=si(t);
	int degsum=0;
	rep(i,n)degsum+=si(t[i]);
	if(degsum==n-1){
		//directed
		rep(i,si(t))for(auto j:t[i]){
			print(i+1,j+1);
		}
	}else if(degsum==2*(n-1)){
		//undirected
		rep(i,si(t))for(auto j:t[i])if(i<j){
			print(i+1,j+1);
		}
	}else{
		assert(false);
	}
}

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,class v>
pair<t,u>&operator*=(pair<t,u>&a,v b){
	a.a*=b;a.b*=b;return a;}
template<class t,class u,class v>
pair<t,u> operator*(pair<t,u> a,v b){return a*=b;}
template<class t,class u>
pair<t,u> operator-(pair<t,u> a){return mp(-a.a,-a.b);}
namespace std{
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+=(vc<t>&a,const vc<t>&b){
	a.resize(max(si(a),si(b)));
	rep(i,si(b))a[i]+=b[i];
	return a;
}

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>
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>
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<<=(vc<t>&a,int k){
	assert(k>=0);
	a.insert(a.bg,k,t(0));
	return a;
}
template<class t>
vc<t> operator<<(vc<t> a,int k){
	return a<<=k;
}

template<class t>
vc<t>& operator>>=(vc<t>&a,int k){
	if(si(a)<=k)a.clear();
	else a.erase(a.bg,a.bg+k);
	return a;
}
template<class t>
vc<t> operator>>(vc<t> a,int k){
	return a>>=k;
}

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 t>
void rempos(vc<t>&a,int i){
	assert(inc(0,i,si(a)-1));
	a.erase(a.bg+i);
}

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);
}

//Multiuni2023-8 C
//f(lw)=false,...,f(n-1)=false,f(n)=true,...,f(up)=true,
//のときに n を返す
template<class F>
int find_min_true(int lw,int up,F f){
	while(up-lw>1){
		const int mid=(lw+up)/2;
		if(f(mid))up=mid;
		else lw=mid;
	}
	return up;
}
//f(lw)=true,f(up)=false
template<class F>
int find_max_true(int lw,int up,F f){
	while(up-lw>1){
		const int mid=(lw+up)/2;
		if(f(mid))lw=mid;
		else up=mid;
	}
	return lw;
}

template<class t> using pqmin=priority_queue<t,vc<t>,greater<t>>;
template<class t> using pqmax=priority_queue<t>;
using T=tuple<int,int,int>;

//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-9;
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()
*/
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)));
}
//UCUP 2-20-D
ld heron(ld a,ld b,ld c){
	ld s=(a+b+c)/2;
	return sqrt(s*(s-a)*(s-b)*(s-c));
}
#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;}
//c の位置を聞く関数です，b じゃないです
//(-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
//Multiuni 2024-6-C
pt rot(pt a,ld b){
	ld c=cos(b),s=sin(b);
	return pt(a.x*c-a.y*s,a.x*s+a.y*c);
}
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)));
}
//UCUP3-4-H
bool isp(ln a,pt b){
	return ccw(a,b)==0&&inc(-1,bet(a.a,a.b,b),1);
}
#ifdef GEOF
//AOJ2201
ld dlp(ln a,pt b){
	return abs(crs(a,b)/abs(dir(a)));
}
//AOJ0153
ld dsp(ln a,pt b){
	pt c=proj(a,b);
	if(abs(bet(a.a,a.b,c))<=1)return abs(b-c);
	return min(abs(b-a.a),abs(b-a.b));
}
//ABC314H
//b から最も近い a 上の点を返す
pt dsp_tar(ln a,pt b){
	pt c=proj(a,b);
	if(abs(bet(a.a,a.b,c))<=1)return c;
	return abs(b-a.a)<abs(b-a.b)?a.a:a.b;
}
//AOJ1157
ld dss(ln a,ln b){
	if(iss(a,b))return 0;
	return min({dsp(a,b.a),dsp(a,b.b),dsp(b,a.a),dsp(b,a.b)});
}
//AOJ2160
//反時計回り方向に伸びる垂直二等分線
ln vbis(pt a,pt b){
	pt c=(a+b)*ld(0.5),d=b-a;
	return ln(c,pt(c.x-d.y,c.y+d.x));
}
ld cutareat(ln z,ld l,ld r){
	pt a=eval(z,l);
	pt b=eval(z,r);
	return -(b.x-a.x)*(a.y+b.y)/2;
}
#endif
//ABC286H
//simple polygon と線分が交わるか
//接している場合も true
/*
bool icl(const vc<pt>&ps,ln z){
	int n=si(ps);
	rep(i,n){
		pt p=ps[i],q=ps[(i+1)%n];
		if(iss(z,ln(p,q)))return true;
	}
	return cont(ps,z.a);
}*/

//cm,cr を pt,C に書き換えたあとコンパイルだけ通した，verify はしてない(バカ？)
//Contest 2: PKU Contest 1, PTZ Summer 2022 Day 4
struct C{
	pt c;
	ld r;
	pt eval(ld a){
		return c+pt::polar(r,a);
	}
	bool operator==(const C&rhs)const{
		return c==rhs.c&&sgn(r,rhs.r)==0;
	}
};
istream& operator>>(istream& is,C& c){
	return is>>c.c>>c.r;
}
ostream& operator<<(ostream& os,const C& c){
	return os<<"C{"<<c.c<<","<<c.r<<"}";
}

//AOJ0153
//0-no,1-edge,2-in
int cont(C a,pt b){
	return sgn(a.r-abs(b-a.c))+1;
}
//AOJ0153 円じゃなくて円盤
//0-no,1-touch,2-cross
int ids(C a,ln b){
	return sgn(a.r-dsp(b,a.c))+1;
}
//AOJ0129 (touch以外)
//0-no(in),1-touch(in),2-cross,3-touch(out),4-no(out)
int ics(C a,ln b){
	int c=ids(a,b);
	if(c<=1)return 4-c;
	return sgn(max(abs(b.a-a.c),abs(b.b-a.c))-a.r)+1;
}
//AOJ1183
//eval(b,t) が a と重なる t を c,d に入れる
//解の個数を返す
int ccl(C a,ln b,ld&c,ld&d){
	pt e=dir(b);
	pt f=b.a-a.c;
	return qeq(norm(e),2*dot(e,f),norm(f)-a.r*a.r,c,d);
}
//AOJ0023
//Contest 2: PKU Contest 1, PTZ Summer 2022 Day 4 (2,7)
//0-apart,1-coincide,2-a<b,3-a<=b,4-a>b,5-a>=b,6-a touch b,7-a cross b
int icc(C a,C b){
	ld c=abs(a.c-b.c);
	if(sgn(c)==0&&sgn(a.r-b.r)==0)return 1;
	int d=sgn(c+a.r-b.r);
	if(d<=0)return d+3;
	int e=sgn(c+b.r-a.r);
	if(e<=0)return e+5;
	int f=sgn(a.r+b.r-c);
	if(f>=0)return f+6;
	return 0;
}
//AOJ2572
//Contest 2: PKU Contest 1, PTZ Summer 2022 Day 4
//args of two intersections r,l seen by a.c
//assume two circles cross
pair<ld,ld> ccc(C a,C b){
	ld c=arg(b.c-a.c);
	ld d=arg(a.r,abs(b.c-a.c),b.r);
	return make_pair(c-d,c+d);
}
//XXI Opencup GP of Siberia 5
vc<pt> ccc_list(C a,C b){
	int v=icc(a,b);
	if(v==0||v==1||v==2||v==4)return {};
	auto z=ccc(a,b);
	if(v==3||v==5||v==6){
		return {a.c+pt::polar(a.r,z.a)};
	}else{
		return {a.c+pt::polar(a.r,z.a),a.c+pt::polar(a.r,z.b)};
	}
}
//Contest 2: PKU Contest 1, PTZ Summer 2022 Day 4
//単位円で偏角 0-x で y*(-dx) を積分した値
ld cutareaarg(ld x){
	return (x-sin(2*x)/2)/2;
}
//Contest 2: PKU Contest 1, PTZ Summer 2022 Day 4
ld cutareaarg(ld l,ld r){
	return cutareaarg(r)-cutareaarg(l);
}
//Contest 4, PTZ 2022 Winter Day 6 (ICPC Camp Day 1) J
ld cutareaarg(C c,ld l,ld r){
	l=normarg(l);
	r=normarg(r);
	return (l<=r?cutareaarg(l,r):cutareaarg(l,PI)+cutareaarg(-PI,r))
			*sq(c.r)-c.c.y*c.r*(cos(r)-cos(l));
}
//Osijek Day9 E
//a から c への接線
//a から見たときの arg
pair<ld,ld> tangent_args(C c,pt a){
	assert(!cont(c,a));
	pt dif=c.c-a;
	ld w=asin(max<ld>(-1,min<ld>(1,c.r/abs(dif))));
	ld k=arg(dif);
	return mp(normarg(k-w),normarg(k+w));
}
//円 a の偏角 b の位置で接する直線
ln tanln(C a,ld b){
	pt c=a.eval(b);
	return ln(c,c+pt::polar(1,b+PI/2));
}
//AOJ2201
//Contest 4, PTZ 2022 Winter Day 6 (ICPC Camp Day 1)
//a と b の共通外接線を引く
//a の接点の偏角を返す
pair<ld,ld> tangent_points_ext(C a,C b){
	pt dif=b.c-a.c;
	ld w=acos(max<ld>(-1,min<ld>(1,(a.r-b.r)/abs(dif))));
	ld k=arg(dif);
	return mp(normarg(k-w),normarg(k+w));
}
pair<ln,ln> tangent_line_ext(C a,C b){
	auto [p,q]=tangent_points_ext(a,b);
	return mp(tanln(a,p),tanln(a,q));
}
//AOJ2201
//内接線
pair<ld,ld> tangent_points_in(C a,C b){
	pt dif=b.c-a.c;
	ld w=acos(min<ld>(1,(a.r+b.r)/abs(dif)));
	ld k=arg(dif);
	return mp(normarg(k-w),normarg(k+w));
}
pair<ln,ln> tangent_line_in(C a,C b){
	auto [p,q]=tangent_points_in(a,b);
	return mp(tanln(a,p),tanln(a,q));
}
//AOJ2201(内接外接あたりの verify はできてない)
vc<ln> tangent_lines(C a,C b){
	vc<ln> res;
	int v=icc(a,b);
	if(v==0||v==3||v==5||v==6||v==7){//out
		auto [p,q]=tangent_line_ext(a,b);
		res.pb(p);
		if(v!=3&&v!=5)res.pb(q); //内接しているときは外接線は 1 つ
	}
	if(v==0||v==6){//in
		auto [p,q]=tangent_line_in(a,b);
		res.pb(p);
		if(v!=6)res.pb(q); //外接しているときは内接線は 1 つ
	}
	return res;
}

//極大な円だけ残す，重複も消す
//AOJ1047
//Contest 4, PTZ 2022 Winter Day 6 (ICPC Camp Day 1) J
//Contest 5, PTZ 2021 Summer Day 2, NAC 2021 B
vc<C> simplify_circle_sets(const vc<C>&rw){
	vc<C> cs;
	for(auto cur:rw){
		bool ok=true;
		rep(j,si(cs)){
			int w=icc(cs[j],cur);
			if(w==1||w==4||w==5){
				ok=false;
			}
		}
		if(ok){
			rep(j,si(cs)){
				int w=icc(cs[j],cur);
				if(w==1||w==2||w==3){
					cs.erase(cs.bg+j--);
				}
			}
			cs.pb(cur);
		}
	}
	return cs;
}

//ByteCamp 2022 Day3 A
//原点中心,半径 r の円の x 座標 a 以下の領域の面積
ld cutarea_sub(ld r,ld a){
	ld theta=acos(max(min(a/r,ld(1)),ld(-1)));
	return sq(r)*(PI-theta)+a*r*sin(theta);
}
//2020 Multi-Uni Day5 J
//x座標 b 以上 c 以下の部分だけ取ってきて，その面積
ld cutarea(C a,ld b,ld c){
	chmax(b,a.c.x-a.r);
	chmin(c,a.c.x+a.r);
	b-=a.c.x;
	c-=a.c.x;
	if(sgn(c-b)<=0)return 0;
	return cutarea_sub(a.r,c)-cutarea_sub(a.r,b);
}

//dist の初期値が long long になってる
template<class E,class D=ll>
pair<vc<D>,vi> dijkstra(const vvc<E>& g,int s){
	const int n=g.size();
	using P=pair<D,int>;
	priority_queue<P,vc<P>,greater<P>> pq;
	vc<D> dist(n,infLL);
	vi from(n,-1);
	const auto ar=[&](int v,D d,int f){
		if(chmin(dist[v],d)){
			pq.emplace(d,v);
			from[v]=f;
		}
	};
	ar(s,0,-1);
	while(pq.size()){
		auto [d,v]=pq.top();pq.pop();
		if(dist[v]!=d)continue;
		for(auto e:g[v])
			ar(e.to,d+e.cost,v);
	}
	return mp(dist,from);
}

struct E{
	int to;
	ld cost;
	operator int()const{return to;}
};
ostream&operator<<(ostream&os,const E&e){
	return os<<"E{"<<e.to<<","<<e.cost<<"}";
}

void slv(){
	INT(cnum);
	pt A,B;
	cin>>A>>B;
	LD(R);
	
	vc<C> cs(cnum);
	rep(i,cnum)cin>>cs[i];
	
	vc<pt> vs;
	auto clear=[&](){
		mkuni(vs);
		remif(vs,[&](pt p){
			for(auto c:cs){
				if(cont(c,p)==2)return true;
			}
			return false;
		});
	};
	
	{
		vs.pb(A);
		vs.pb(B);
		
		auto tryline=[&](ld w){
			pt dir=pt::polar(1,w);
			ln z(B,B+dir);
			
			{
				ld d=dot(A-B,dir);
				vs.pb(eval(z,d));
			}
			for(auto c:cs){
				ld d=dot(c.c-B,dir);
				vs.pb(eval(z,d-c.r));
				vs.pb(eval(z,d+c.r));
			}
			
			vs.pb(eval(z,R));
			for(auto c:cs){
				ld u[2];
				int num=ccl(c,z,u[0],u[1]);
				rep(i,num)vs.pb(eval(z,u[i]));
			}
		};
		
		if(A!=B)tryline(arg(A-B));
		for(auto c:cs)if(cont(c,B)==0){
			auto [a,b]=tangent_args(c,B);
			tryline(a);
			tryline(b);
		}
	}
	
	{
		clear();
		vc<pt> tmp;
		
		for(auto p:vs){
			tmp.pb(p);
			for(auto c:cs){
				int z=cont(c,p);
				if(z==0){
					auto [a,b]=tangent_args(c,p);
					ld d=sqrt(norm(p-c.c)-norm(c.r));
					tmp.pb(p+pt::polar(d,a));
					tmp.pb(p+pt::polar(d,b));
				}
			}
		}
		rep(i,cnum)rep(j,cnum)if(i!=j){
			{
				auto [a,b]=tangent_points_ext(cs[i],cs[j]);
				tmp.pb(cs[i].eval(a));
				tmp.pb(cs[i].eval(b));
			}
			{
				auto [a,b]=tangent_points_in(cs[i],cs[j]);
				tmp.pb(cs[i].eval(a));
				tmp.pb(cs[i].eval(b));
			}
		}
		
		vs.swap(tmp);
	}
	
	auto ok=[&](pt a,pt b){
		for(auto c:cs){
			//0-no,1-touch,2-cross
			if(ids(c,ln(a,b))==2)return false;
		}
		return true;
	};
	
	{
		clear();
		
		int n=si(vs);
		vvc<E> g(n);
		
		rep(i,n)rep(j,n)if(i!=j){
			if(ok(vs[i],vs[j])){
				g[i].pb({j,abs(vs[i]-vs[j])});
			}else{
				for(auto c:cs){
					if(cont(c,vs[i])==1&&cont(c,vs[j])==1){
						ld u=arg(vs[i]-c.c);
						ld v=arg(vs[j]-c.c);
						ld dif=fmodl(abs(u-v),2*PI);
						g[i].pb({j,min(dif,2*PI-dif)*c.r});
					}
				}
			}
		}
		if(0){
			dmp(vs);
			rep(i,n){
				dmp(g[i]);
			}
		}
		
		auto [dist,from]=dijkstra<E,ld>(g,lwb(vs,A));
		ld ans=infLL;
		int goal=-1;
		rep(i,n){
			pt v=vs[i];
			if(v==B||(sgn(abs(v-B),R)<=0&&ok(v,B))){
				dmp2(vs[i],dist[i]);
				if(chmin(ans,dist[i]))goal=i;
			}
		}
		
		if(1)while(vs[goal]!=A){
			dmp2(vs[goal],dist[goal]);
			goal=from[goal];
		}
		
		print(ans);
	}
}

signed main(signed argc,char*argv[]){
	if(argc>1&&strcmp(argv[1],"D")==0)dbg=true;
	
	cin.tie(0);
	ios::sync_with_stdio(0);
	cout<<fixed<<setprecision(20);
	
	if(dbg){
		while(1){
			if(current_run_id%run_batch_size==0){
				cerr<<"Current Run "<<current_run_id<<endl;
			}
			slv();
			current_run_id++;
		}
	}else{
		int t;cin>>t;rep(_,t)
		slv();
	}
}
Source code, Language: C++23

Details

Tip: Click on the bar to expand more detailed information

Test #1:

score: 100
Accepted
time: 1ms
memory: 4008kb

input:

2
1
10 0
0 0 2
6 0 1
0
0 10
0 0 5

output:

8.20919146366880091159
5.00000000000000000000

result:

ok 2 numbers

Test #2:

score: -100
Wrong Answer
time: 88ms
memory: 4404kb

input:

52
0
0 10
0 0 5
0
10 0
0 0 5
1
10 0
0 0 2
6 0 1
1
10 0
4 0 2
6 0 1
1
10 0
3 0 4
6 0 2
1
10 0
3 0 2
6 0 3
1
10 0
3 0 4
6 0 3
2
10 0
-2 0 4
6 4 3
6 -4 3
2
10 0
-2 0 7
6 4 3
6 -4 3
2
10 6
-2 0 7
6 4 3
6 -4 3
2
10 2
-2 0 14
6 4 3
6 -4 3
2
14 4
-2 0 14
6 4 3
6 -4 3
2
12 -10
-2 0 14
2 2 3
6 -4 3
2
8 -8
-2...

output:

5.00000000000000000000
5.00000000000000000000
8.20919146366880091159
4.39361279378061824526
4.82286889931749292127
9.90232652839372347233
9.90232652839372347233
8.00000000000000000000
5.00000000000000000000
7.97483976967475756805
0.52954009072945654619
3.11802043481301209430
4.30451298836671195081
1...

result:

wrong answer 6th numbers differ - expected: '8.3743109', found: '9.9023265', error = '0.1824646'
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