#include<bits/stdc++.h>
#include<atcoder/all>
#define all(a) begin(a),end(a)
#define eb emplace_back
#define ep emplace
#define ef(...) else if(__VA_ARGS__)
#define wh(...) while(__VA_ARGS__)
#define fin(...) rr pp(__VA_ARGS__)
#define RD(T,...) T __VA_ARGS__;li(__VA_ARGS__)
#define LL(...) RD(ll,__VA_ARGS__)
#define ST(...) RD(str,__VA_ARGS__)
#define UL(n,...) u1 __VA_ARGS__;resize({n},__VA_ARGS__);li(__VA_ARGS__)
#define UV(n,...) u1 __VA_ARGS__;resize({n},__VA_ARGS__);vi(__VA_ARGS__)
#define SS(n,...) strs __VA_ARGS__;resize({n},__VA_ARGS__);li(__VA_ARGS__)
#define U2(n,m,...) u2 __VA_ARGS__;resize({n,m},__VA_ARGS__);li(__VA_ARGS__)
#define fe(v,e,...) for(auto&&__VA_OPT__([)e __VA_OPT__(,__VA_ARGS__)__VA_OPT__(]):v)
#define fo(i,...) for(auto[i,i##stop,i##step]=rng_fo(__VA_ARGS__);i<i##stop;i+=i##step)
#define of(i,...) for(auto[i,i##stop,i##step]=rng_of(__VA_ARGS__);i>=i##stop;i-=i##step)
#define debug(...) pp(#__VA_ARGS__,__VA_ARGS__)
#define I(...) template<__VA_ARGS__>
#define J typename
#define O operator
#define ce constexpr
#define cs const
#define rr return
#define uu using
namespace my{uu vo=void;vo main();vo solve();}int main(){my::main();}namespace my{uu namespace std;uu namespace atcoder;
uu is=istream;uu os=ostream;uu bo=bool;uu dd=long double;uu ll=long long;uu i128=__int128_t;uu ul=unsigned long long;uu u128=__uint128_t;
I(J T)uu v1=vector<T>;I(J T)uu v2=v1<v1<T>>;uu u1=v1<ll>;uu u2=v2<ll>;uu str=string;uu strs=v1<str>;str sp=" ",nc="",nl="\n";
uu ml=modint998244353;is&O>>(is&i,ml&x){ll t;i>>t;x=t;rr i;}os&O<<(os&o,cs ml&x){rr o<<x.val();}uu m1=v1<ml>;uu m2=v2<ml>;
I(J A,J B=A)struct cp{A a={};B b={};cp(){}cp(A a,B b):a(a),b(b){}cp(pair<A,B>p):a(p.first),b(p.second){}
  cp&O+=(cs cp&c){a+=c.a,b+=c.b;rr*this;}cp O+(cs cp&c)cs{rr cp{*this}+=c;}bo O==(cs cp&c)cs{rr a==c.a&&b==c.b;}
  cp&O-=(cs cp&c){a-=c.a,b-=c.b;rr*this;}cp O-(cs cp&c)cs{rr cp{*this}-=c;}bo O!=(cs cp&c)cs{rr a!=c.a||b!=c.b;}cp O-()cs{rr cp(-a,-b);}
  bo O<(cs cp&c)cs{rr a!=c.a?a<c.a:b<c.b;}bo O>(cs cp&c)cs{rr a!=c.a?a>c.a:b>c.b;}friend os&O<<(os&o,cs cp&c){rr o<<c.a<<sp<<c.b;}
};uu cl=cp<ll>;uu cls=v1<cl>;I(J T)uu qmax=priority_queue<T>;I(J T)uu qmin=priority_queue<T,v1<T>,greater<T>>;
I(J T)struct set:std::set<T>{set(v1<T>a={}){fe(a,e)this->ep(e);}};I(J T)struct uset:unordered_set<T>{uset(v1<T>a={}){fe(a,e)this->ep(e);}};
I(J T)struct mset:multiset<T>{mset(v1<T>a={}){fe(a,e)this->ep(e);}
  vo erase(cs T&x){if(auto p=this->find(x);p!=this->end())multiset<T>::erase(p);}};
I(J T,J U=T)uu map=std::map<T,U>;I(J T,J U=T)uu umap=unordered_map<T,U>;ll ppc(ll x){rr __builtin_popcountll(x);}
ce ll oo=3e18;dd ee=1e-12,pi=acosl(-1);u1 dx{-1,0,1,0,-1,1,1,-1},dy{0,-1,0,1,-1,-1,1,1};str Yes(bo y=1){rr y?"Yes":"No";}str No(){rr"No";}
ll rnd(ll l,ll r=oo){static ul x=76,y=53,z=20,w=41;ul t=x^(x<<11);x=y,y=z,z=w,w=(w^(w>>19))^(t^(t>>8));if(r==oo)r=l,l=0;rr w%(r-l)+l;}
ll l2(u128 x){x|=1;ll r=0;wh(x)x>>=1,++r;rr r;}bo odd(ll x){rr x&1;}ll pwm1(ll x){rr 1-2*(x&1);}I(J T)bo at(T x,ll i){rr x>>i&1;}
ll l10(u128 x){x|=1;ll r=0;wh(x)x/=10,++r;rr r;}bo eve(ll x){rr~x&1;}ll pw2(ll n){rr 1LL<<n;}I(J T,J U,J V)bo in(T l,U m,V r){rr l<=m&&m<r;}
I(J T)T flo(T x,T y){rr y<0?x=-x,y=-y:x>=0?x/y:(x+1)/y-1;}array<ll,3>rng_fo(ll a,ll b=oo,ll c=1){if(b==oo)b=a,a=0;rr{a,b,c};}
I(J T)T cei(T x,T y){rr y<0?x=-x,y=-y:x<=0?x/y:(x-1)/y+1;}array<ll,3>rng_of(ll a,ll b=0,ll c=1){rr{a-1,b,c};}I(J T)T abs(T x){rr x<0?-x:x;}

I(J T)auto&O++(v1<T>&v){fe(v,e)++e;rr v;}I(J T)auto&O^=(v1<T>&v,cs v1<T>&u){copy(all(u),back_inserter(v));rr v;}
I(J T)auto&O--(v1<T>&v){fe(v,e)--e;rr v;}I(J T)auto O^(v1<T>v,cs v1<T>&u){rr v^=u;}u1 io(ll n,ll x=0){u1 a(n);fo(i,n)a[i]=i+x;rr a;}
I(J T)T&srt(T&a){sort(all(a));rr a;}I(J T)T&rv(T&a){reverse(all(a));rr a;}I(J T)T slice(cs T&a,ll l,ll r){rr T(begin(a)+l,begin(a)+r);}
I(J T)T&rsr(T&a){srt(a),rv(a);rr a;}I(J T)T&uq(T&a){srt(a),a.erase(unique(all(a)),end(a));rr a;}I(J T)ll len(cs T&a){rr a.size();}
I(J T)decltype(auto)bg(T&a){assert(len(a));rr*begin(a);}I(J T)T pof(deque<T>&q){T r=bg(q);q.pop_front();rr r;}I(J T)ce bo is_vec=0;
I(J T)decltype(auto)rb(T&a){assert(len(a));rr*rbegin(a);}I(J T)T pob(deque<T>&q){T r=rb(q);q.pop_back();rr r;}I(J T)ce bo is_vec<v1<T>> =1;
I(J T)auto pop(T&a){if ce(is_vec<T>||is_same_v<T,str>){auto r=rb(a);a.pop_back();rr r;}else{auto r=a.top();a.pop();rr r;}}
I(J...A)auto max(cs A&...a){rr max(initializer_list<common_type_t<A...>>{a...});}I(J T,J U=T)vo af(v1<T>&a,U e={}){a.ep(begin(a),e);}
I(J...A)auto min(cs A&...a){rr min(initializer_list<common_type_t<A...>>{a...});}I(J T)vo df(T&a){a.erase(begin(a));}
I(J T,J U)ll arglb(cs v1<T>&a,cs U&b){rr lower_bound(all(a),b)-begin(a);}I(J T,J U)bo amax(T&a,cs U&b){rr a<b?a=b,1:0;}
I(J T,J U)ll argub(cs v1<T>&a,cs U&b){rr upper_bound(all(a),b)-begin(a);}I(J T,J U)bo amin(T&a,cs U&b){rr a>b?a=b,1:0;}
I(J V)auto recval(cs V&){if ce(is_vec<V>)rr recval(J V::value_type());else rr V();}I(J T)bo add(T&a,cs T&b){rr a+=b,0;}
I(J S,bo f(S&,cs S&),J V)cp<S,bo>scan(cs v1<V>&v){
  S r{};bo b=0;fe(v,x)if ce(is_same_v<V,S>)b?f(r,x):(r=x,b=1);ef(auto[y,c]=scan<S,f>(x);c)b?f(r,y):(r=y,b=1);rr{r,b};}
I(J V,J T=decltype(recval(V())))T max(cs v1<V>&v){rr scan<T,amax<T>>(v).a;}
I(J V,J T=decltype(recval(V())))T min(cs v1<V>&v){rr scan<T,amin<T>>(v).a;}
I(J V,J T=decltype(recval(V())))T sum(cs v1<V>&v){rr scan<T,add<T>>(v).a;}
I(J T=ll,ll n,ll i=0)auto vec(cs ll(&l)[n],T x={}){if ce(i==n-1)rr vector(l[i],x);else rr vector(l[i],vec<T,n,i+1>(l,x));}
I(ll n,J...A)vo resize(cs ll(&l)[n],A&...a){((a=vec(l,recval(a))),...);}
I(J V,J T=decltype(recval(V())))vo fill(v1<V>&v,T x={}){if ce(is_vec<V>)fe(v,e)fill(e,x);else fe(v,e)e=x;}

struct fio{fio(){ios::sync_with_stdio(0);cin.tie(0);cout<<fixed<<setprecision(l10(1/ee)+1);}}fio;
os&O<<(os&o,cs u128&x){if(x<10)rr o<<char(x+'0');rr o<<x/10<<char(x%10+'0');}os&O<<(os&o,cs i128&x){rr o<<str(x<0,'-')<<u128(abs(x));}
I(J V)os&O<<(os&o,cs v1<V>&v){str s=nl;if ce(is_vec<V>){if ce(is_vec<J V::value_type>)s+=nl;}else s=sp;fe(v,e)o<<e<<(&e==&rb(v)?nc:s);rr o;}
I(J T)os&O<<(os&o,cs set<T>&v){fe(v,e)o<<e<<sp;rr o;}I(J T,J U)os&O<<(os&o,cs map<T,U>&m){fe(m,e)o<<cp(e)<<nl;rr o;}
I(J T)os&O<<(os&o,cs mset<T>&v){fe(v,e)o<<e<<sp;rr o;}I(J T)is&O>>(is&i,v1<T>&v){fe(v,e)i>>e;rr i;}
I(J...A)vo li(A&...a){(cin>>...>>a);}I(J...A)vo vi(A&...a){fo(i,(len(a)&...))(cin>>...>>a[i]);}
I(J...A)vo pp(cs A&...a){ll i=0;((cout<<a<<(++i==sizeof...(a)?nc:sp)),...);cout<<nl;}

struct edg{ll t,w;edg(){}edg(ll t,ll w=1):t(t),w(w){}};uu graph=v2<edg>;
graph tog(cs u2&a){graph g;fe(a,e){g.eb();fe(e,v)rb(g).eb(v);}rr g;}u2 tou(cs graph&g){u2 a;fe(g,e){a.eb();fe(e,v,w)rb(a).eb(v);}rr a;}
I(J G)auto ygi(G&g,ll m,bo f=1){if ce(is_same_v<G,graph>){UV(m,a,b,c);if(f)--a,--b;fo(i,m)g[a[i]].eb(b[i],c[i]);rr tuple{a,b,c};}
  else{UV(m,a,b);if(f)--a,--b;fo(i,m)g[a[i]].eb(b[i]);rr tuple{a,b};}}
I(J G)auto mgi(G&g,ll m,bo f=1){if ce(is_same_v<G,graph>){auto[a,b,c]=ygi(g,m,f);fo(i,m)g[b[i]].eb(a[i],c[i]);rr tuple{a,b,c};}
  else{auto[a,b]=ygi(g,m,f);fo(i,m)g[b[i]].eb(a[i]);rr tuple{a,b};}}I(J G)auto ti(G&g,bo f=1){rr mgi(g,len(g)-1,f);}
u1 en(cs str&s,cs str&b="a"){ll n=len(s);u1 r(n,-1);fo(i,n)if(len(b)==1)r[i]=s[i]-b[0];else fo(j,len(b))if(s[i]==b[j])r[i]=j;rr r;}
str de(cs u1&a,cs str&b="a"){ll n=len(a);str r(n,'|');fo(i,n)if(len(b)==1)r[i]=a[i]+b[0];else fo(j,len(b))if(a[i]==j)r[i]=b[j];rr r;}
u2 en(cs strs&s,cs str&b="a"){u2 r;fe(s,e)r.eb(en(e,b));rr r;}str ins(){ST(s);rr s;}strs inss(ll n){SS(n,s);rr s;}
strs de(cs u2&a,cs str&b="a"){strs r;fe(a,e)r.eb(de(e,b));rr r;}u1 abc(){rr en(ins());}u2 abcs(ll n){rr en(inss(n));}

I(J...A)u1 zp(A&...a){u1 v=(a^...);uq(v);([&](u1&u){fe(u,e)e=arglb(v,e);}(a),...);rr v;}I(J...A)vo dec(A&...a){((--a),...);}
I(J F,J...A)u1 vs(cs F&f,A&...a){u1 o=io((len(a)&...));sort(all(o),f);([&](auto&e){auto c=e;fo(i,len(e))e[i]=c[o[i]];}(a),...);rr o;}
I(J F)ll bsl(cs F&f,ll o,ll n){wh(abs(o-n)>1)(f((o+n)/2)?o:n)=(o+n)/2;rr o;}ll sqr(ll x){ll r=max(sqrtl(x)-1,0.);wh(r+1<=x/(r+1))++r;rr r;}
I(J F)dd bsd(cs F&f,dd o,dd n){fo(t,l2(abs(o-n)/ee)+5)(f((o+n)/2)?o:n)=(o+n)/2;rr o;}I(J T)auto zt(v1<T>a){fo(i,1,len(a))a[i]+=a[i-1];rr a;}
cls rle(cs u1&a){cls r;fe(a,e)len(r)&&e==rb(r).a?++rb(r).b:r.eb(e,1).b;rr r;}cls rce(u1 a){rr rle(srt(a));}
i128 pow(i128 x,u128 n,u128 m=0){i128 r=1;wh(n){if(n&1)r*=x;x*=x;if(m)r%=m,x%=m;n>>=1;}rr r;}I(J T)T sq(cs T&a){rr a*a;}
u1 divs(ll n){u1 r;for(ll i=1;i*i<=n;++i)if(n%i==0)r.eb(i),r.eb(n/i);rr uq(r);}I(J T)T cb(cs T&a){rr a*a*a;}
cls fact(ll n){umap<ll>m;for(ll i=2;i*i<=n;++i)wh(n%i==0)++m[i],n/=i;if(n>1)++m[n];cls r;fe(m,e)r.eb(e);rr srt(r);}

I(J T)struct cv1:v1<T>{uu v1<T>::v1;cv1(cs v1<T>&v){fe(v,e)this->eb(e);}T&O[](ll i){ll n=len(*this);rr this->begin()[(i%n+n)%n];}};
I(J T)ll sgn(cs T&a){rr(a>=ee)-(a<=-ee);}//-ee<a<eeの値は0とみなす．すなわちeeが最小単位
I(J T,J U)ll sgn(cs T&a,cs U&b){rr sgn(a-b);}//ee=1e-nとすると，aとbの小数点以下n桁まで一致していれば等しいと判定．

I(J T)struct pt{
  T x,y;
  pt():x(),y(){}
  pt(T x,T y):x(x),y(y){}
  pt O+()const{rr*this;}
  pt O-()const{rr pt(-x,-y);}
  pt&O+=(const pt&p){x+=p.x;y+=p.y;rr*this;}
  pt&O-=(const pt&p){x-=p.x;y-=p.y;rr*this;}
  pt&O*=(const T&d){x*=d;y*=d;rr *this;}
  pt&O/=(const T&d){x/=d;y/=d;rr*this;}
  pt O+(const pt&p)const{rr pt(*this)+=p;}
  pt O-(const pt&p)const{rr pt(*this)-=p;}
  pt O*(const T&d)const{rr pt(*this)*=d;}
  pt O/(const T&d)const{rr pt(*this)/=d;}
  
  bo O==(const pt&p)const{rr sgn(x,p.x)==0&&sgn(y,p.y)==0;}
  bo O!=(const pt&p)const{rr !(*this==p);}
  bo O<(const pt&p)const{rr sgn(x,p.x)?sgn(x,p.x)<0:sgn(y,p.y)<0;}
  bo O>(const pt&p)const{rr sgn(x,p.x)?sgn(x,p.x)>0:sgn(y,p.y)>0;}
  bo O<=(const pt&p)const{rr !(*this>p);}
  bo O>=(const pt&p)const{rr !(*this<p);}
  
  T dot(const pt&a)const{rr x*a.x+y*a.y;}//内積
  T norm()const{rr dot(*this);}//長さの2乗
  T abs()const{rr sqrtl(norm());}//長さ
  T crs(const pt&a)const{rr x*a.y-a.x*y;}//外積
  T cos(const pt&a)const{rr dot(a)/(abs()*a.abs());}//cos
  T arg()const{T r=atan2l(y,x);rr sgn(r)<0?r+pi*2:r;}//偏角.0≦θ<2π
  T arg(const pt&a)const{rr rot(-a.arg()).arg();}//aを基準とした偏角.0≦θ<2π
  T ang(const pt&a)const{rr atan2l(x*a.y-y*a.x,x*a.x+y*a.y);}//thisを基準としたaとのなす角.-π≦θ<π
  pt rot(const T&t)const{rr{cosl(t)*x-sinl(t)*y,sinl(t)*x+cosl(t)*y};}
  pt rot90()const{rr{-y,x};}
  
  friend is&O>>(is&i,pt&p){rr i>>p.x>>p.y;}
  friend os&O<<(os&o,const pt&p){rr o<<p.x<<sp<<p.y;}
};

I(J T)uu pts=v1<pt<T>>;
I(J T)uu ply=cv1<pt<T>>;
uu ptl=pt<ll>;
uu ptls=pts<ll>;
uu ptd=pt<dd>;
uu ptds=pts<dd>;

I(J T)T to_rad(const T&deg){rr deg*pi/180;}
I(J T)T to_deg(const T&rad){rr rad*180/pi;}
I(J T)T dot(const pt<T>&a,const pt<T>&b){rr a.dot(b);}
I(J T)T norm(const pt<T>&a){rr a.norm();}
I(J T)T abs(const pt<T>&a){rr a.abs();}
I(J T)T crs(const pt<T>&a,const pt<T>&b){rr a.crs(b);}
I(J T)T cos(const pt<T>&a,const pt<T>&b){rr a.cos(b);}
I(J T)T arg(const pt<T>&a){rr a.arg();}
I(J T)T arg(const pt<T>&a,const pt<T>&b){rr a.arg(b);}
I(J T)T ang(const pt<T>&a,const pt<T>&b){rr a.ang(b);}
I(J T)pt<T>rot(const pt<T>&a,const T&t){rr a.rot(t);}
I(J T)pt<T>rot90(const pt<T>&a){rr a.rot90();}


I(J T)struct line{
  T p,q,r;//px+qy+r=0
  pt<T>a,b;//a,bを通る
  line():p(0),q(0),r(0){}
  line(T zp,T zq,T zr):p(zp),q(zq),r(zr){
    if(sgn(p)<0||(sgn(p)==0&&sgn(q)<0))p=-p,q=-q,r=-r;
    T g=(T)ee?(p?p:q?q:r):std::gcd((ll)p,std::gcd((ll)q,(ll)r));
    p/=g,q/=g,r/=g;
    
    if(sgn(p)==0)a={0,-r/q},b={1,-r/q};
    ef(sgn(q)==0)a={-r/p,0},b={-r/p,1};
    else a={0,-r/q},b={-r/p,0};
  }
  line(pt<T>za,pt<T>zb):a(za),b(zb){
    p=b.y-a.y;q=a.x-b.x;r=a.y*b.x-a.x*b.y;
    if(sgn(p)<0||(sgn(p)==0&&sgn(q)<0))p=-p,q=-q,r=-r;
    T g=(T)ee?(p?p:q?q:r):std::gcd((ll)p,std::gcd((ll)q,(ll)r));
    p/=g,q/=g,r/=g;
  }
  
  auto coef()const{rr tr(p,q,r);}
  auto pts()const{rr cp(a,b);}
};


I(J T)struct seg:line<T>{
  seg():line<T>(){}
  seg(pt<T>a,pt<T>b):line<T>(a,b){}
  friend is&O>>(is&i,seg&s){pt<T>a,b;i>>a>>b;s={a,b};rr i;}
  friend os&O<<(os&o,const seg&s){rr o<<s.a<<sp<<s.b;}
};


I(J T)struct cir{
  pt<T>p;
  T r;
  cir():p(pt<T>()),r(0){}
  cir(T x,T y,T r):p(x,y),r(r){}
  cir(pt<T>p,T r):p(p),r(r){}
  friend is&O>>(is&i,cir&c){rr i>>c.p>>c.r;}
  friend os&O<<(os&o,const cir&c){rr o<<c.p<<sp<<c.r;}
};

I(J T)uu lines=v1<line<T>>;
I(J T)uu segs=v1<seg<T>>;
I(J T)uu cirs=v1<cir<T>>;


I(J T)ll ccw(const pt<T>&a,pt<T>b,pt<T>c){//ベクトルabに対するcの位置
  b-=a;c-=a;
  if(sgn(crs(b,c))>0)rr 1;       //COUNTER_CLOCKWISE
  if(sgn(crs(b,c))<0)rr -1;      //CLOCKWISE
  if(sgn(dot(b,c))<0)rr 2;       //ONLINE_BACK =c-a-b
  if(sgn(abs(b),abs(c))<0)rr -2; //ONLINE_FRONT=a-b-c
  rr 0;                          //ON_SEGMENT  =a-c-b
}


I(J T)bo para(const line<T>&l,const line<T>&m){
  rr sgn(crs(l.b-l.a,m.b-m.a))==0;
}
I(J T)bo orth(const line<T>&l,const line<T>&m){
  rr sgn(dot(l.b-l.a,m.b-m.a))==0;
}
I(J T)auto prj(const line<T>&l,const pt<T>&p){
  T t=dot(p-l.a,l.b-l.a)/norm(l.a-l.b);
  rr l.a+(l.b-l.a)*t;
}
I(J T)auto ref(const line<T>&l,const pt<T>&p){rr p+(prj(l,p)-p)*T(2);}


I(J T)bo intersect(const line<T>&l,const pt<T>&p){rr abs(ccw(l.a,l.b,p))!=1;}
I(J T)bo intersect(const line<T>&l,const line<T>&m){
  rr sgn(crs(l.b-l.a,m.b-m.a))||sgn(crs(l.b-l.a,m.b-l.a))==0;
}
I(J T)bo intersect(const seg<T>&s,const pt<T>&p){rr ccw(s.a,s.b,p)==0;}
I(J T)bo intersect(const line<T>&l,const seg<T>&s){
  rr sgn(crs(l.b-l.a,s.a-l.a)*crs(l.b-l.a,s.b-l.a))<=0;
}
I(J T)bo intersect(const seg<T>&s,const seg<T>&t){
  rr ccw(s.a,s.b,t.a)*ccw(s.a,s.b,t.b)<=0&&ccw(t.a,t.b,s.a)*ccw(t.a,t.b,s.b)<=0;
}
I(J T)T dist(const line<T>&l,const pt<T>&p);
I(J T)bo intersect(const cir<T>&c,const line<T>&l){rr sgn(dist(l,c.p),c.r)<=0;}
I(J T)bo intersect(const cir<T>&c,const pt<T>&p){
  rr sgn(abs(abs(p-c.p)-c.r))<=0;
}
I(J T)ll intersect(const cir<T>&c,const seg<T>&s){
  if(sgn(norm(prj(s,c.p)-c.p)-c.r*c.r)>0)rr 0;
  T d1=abs(c.p-s.a),d2=abs(c.p-s.b);
  if(sgn(d1,c.r)<=0&&sgn(d2,c.r)<=0)rr 0;
  if(sgn(d1,c.r)<0&&sgn(d2,c.r)>0)rr 1;
  if(sgn(d1,c.r)>0&&sgn(d2,c.r)<0)rr 1;
  pt h=prj(s,c.p);
  if(sgn(dot(s.a-h,s.b-h))<0)rr 2;
  rr 0;
}
I(J T)ll intersect(cir<T>c1,cir<T>c2){//共通接線の本数
  if(c1.r<c2.r)swap(c1,c2);
  T d=abs(c1.p-c2.p);
  if(c1.r+c2.r<d)rr 4;//離れている
  if(sgn(c1.r+c2.r,d)==0)rr 3;//外接
  if(c1.r-c2.r<d)rr 2;//交わる
  if(sgn(c1.r-c2.r,d)==0)rr 1;//内接
  rr 0;//一方が一方を包含
}


//xptはintersectが真である時使用
I(J T)auto xpt(const line<T>&l,const line<T>&m){
  T A=crs(l.b-l.a,m.b-m.a);
  T B=crs(l.b-l.a,l.b-m.a);
  if(sgn(A)==0&&sgn(B)==0)rr m.a;
  rr m.a+(m.b-m.a)*B/A;
}
I(J T)auto xpt(const seg<T>&s,const seg<T>&t){rr xpt(line(s),line(t));}

I(J T)auto xpt(const cir<T>&c,const line<T>&l){
  pt h=prj(l,c.p);
  pt e=(l.b-l.a)/abs(l.b-l.a);
  if(sgn(dist(l,c.p),c.r)==0)rr cp(h,h);
  T t=sqrtl(c.r*c.r-norm(c.p-h));
  rr cp(h-e*t,h+e*t);
}
I(J T)auto xpt(const cir<T>&c,const seg<T>&s){
  if(intersect(c,s)==2)rr xpt(c,line(s));
  auto[a,b]=xpt(c,line(s));
  sgn(dot(s.a-a,s.b-a))<0?b=a:a=b;
  rr cp(a,b);
}
I(J T)auto xpt(const cir<T>&c1,const cir<T>&c2){
  T d=abs(c1.p-c2.p);
  T a=acosl((sq(c1.r)+sq(d)-sq(c2.r))/(c1.r*d*2));
  T t=atan2l(c2.p.y-c1.p.y,c2.p.x-c1.p.x);
  pt p1=c1.p+pt(cosl(t+a)*c1.r,sinl(t+a)*c1.r);
  pt p2=c1.p+pt(cosl(t-a)*c1.r,sinl(t-a)*c1.r);
  rr cp(p1,p2);
}


//「pを通るcへの接線」とcの交点
I(J T)auto tan(const cir<T>&c,const pt<T>&p){
  rr xpt(c,cir(p,sqrtl(norm(c.p-p)-sq(c.r))));
}

I(J T)auto tan(cir<T>c1,cir<T>c2){
  lines<T>res;
  ll f=0;
  if(c1.r<c2.r)swap(c1,c2),f=1;
  T g=norm(c1.p-c2.p);
  if(sgn(g)==0)rr res;
  auto u=(c2.p-c1.p)/sqrtl(g);
  auto v=u.rot(pi/2);
  for(ll s:{-1,1}){
    T h=(c1.r+c2.r*s)/sqrtl(g);
    if(sgn(1-h*h)==0){
      res.eb(c1.p+u*c1.r,c1.p+u*c1.r);
    }ef(sgn(1-h*h)>0){
      auto uh=u*h,vh=v*sqrtl(1-h*h);
      res.eb(c1.p+(uh+vh)*c1.r,c2.p-(uh+vh)*c2.r*s);
      res.eb(c1.p+(uh-vh)*c1.r,c2.p-(uh-vh)*c2.r*s);
    }
  }
  if(f)fe(res,l)swap(l.a,l.b);
  rr res;
}


I(J T)auto convex_hull(pts<T>p);
I(J T)ll contain(const ply<T>&g,const pt<T>&p);

I(J T)auto tan(ply<T>g,const pt<T>&p){
  assert(!contain(g,p));
  g.eb(p);
  auto ch=convex_hull(g);
  fo(i,len(ch))if(ch[i]==p)rr cp{ch[i-1],ch[i+1]};
  rr cp<pt<T>,pt<T>>{};
}


I(J T)T dist(const pt<T>&a,const pt<T>&b){rr abs(a-b);}
I(J T)T dist(const line<T>&l,const pt<T>&p){rr abs(p-prj(l,p));}
I(J T)T dist(const line<T>&l,const line<T>&m){rr intersect(l,m)?0:dist(l,m.a);}
I(J T)T dist(const seg<T>&s,const pt<T>&p){
  pt r=prj(s,p);
  rr intersect(s,r)?abs(r-p):min(abs(s.a-p),abs(s.b-p));
}
I(J T)T dist(const seg<T>&s,const seg<T>&t){
  rr intersect(s,t)?0:min(dist(s,t.a),dist(s,t.b),dist(t,s.a),dist(t,s.b));
}
I(J T)T dist(const line<T>&l,const seg<T>&s){
  rr intersect(l,s)?0:min(dist(l,s.a),dist(l,s.b));
}

//角二等分線
I(J T)auto bsc_ang(const pt<T>&a,const pt<T>&b,const pt<T>&c){
  rr line(a,a+(b-a).rot(ang(b-a,c-a)/2));
}
//垂直二等分線
I(J T)auto bsc_perp(const pt<T>&a,const pt<T>&b){
  pt m=(a+b)/2;
  rr line(m,m+(a-m).rot(pi/2));
}


I(J T)auto incir(const pt<T>&a,const pt<T>&b,const pt<T>&c){
  pt p=xpt(bsc_ang(a,b,c),bsc_ang(b,a,c));
  rr cir(p,dist(line(a,b),p));
}
I(J T)auto outcir(const pt<T>&a,const pt<T>&b,const pt<T>&c){
  pt p=xpt(bsc_perp(a,b),bsc_perp(a,c));
  rr cir(p,dist(p,a));
}


I(J T)auto center(const pts<T>&p){pt<T>g;fe(p,a)g+=a;rr g/len(p);}


I(J T)T area(const ply<T>&g){
  T S=0;
  fo(i,len(g))S+=crs(g[i],g[i+1]);
  rr abs(S)/2;
}
I(J T,J...A)T area(const A&...a){ply<T>g;fe({a...},e)g.eb(e);rr area(g);}

I(J T)T area(const ply<T>&g,const cir<T>&c){
  auto f=rec([&](auto&&f,const cir<T>&c,const pt<T>&a,const pt<T>&b)->T{
    pt pa=a-c.p,pb=b-c.p;
    T t=ang(pa,pb),r=0;
    if(sgn(t)==0)rr r;
    if(sgn(max(abs(pa),abs(pb)),c.r)<=0)rr crs(pa,pb)/2;
    if(sgn(dist(seg(a,b),c.p),c.r)>=0)rr sq(c.r)*t/2;
    auto u=xpt(c,seg(a,b));
    pts<T>v={a,u.a,u.b,b};
    fo(i,len(v)-1)r+=f(c,v[i],v[i+1]);
    rr r;
  });
  T S=0;
  fo(i,len(g))S+=f(c,g[i],g[i+1]);
  rr S;
}
I(J T)T area(const cir<T>&c1,const cir<T>&c2){
  ll f=intersect(c1,c2);
  if(f==3||f==4)rr 0;
  if(f==0||f==1)rr pi*sq(min(c1.r,c2.r));
  auto xs=xpt(c1,c2);
  pt x1=(ccw(c1.p,c2.p,xs.a)==-1?xs.a:xs.b);
  pt x2=(ccw(c1.p,c2.p,xs.a)==-1?xs.b:xs.a);
  T t1=(x2-c1.p).arg(x1-c1.p);
  T t2=(x1-c2.p).arg(x2-c2.p);
  rr sq(c1.r)*t1/2+sq(c2.r)*t2/2-area<T>(c1.p,x1,c2.p,x2);
}


I(J T)bo is_convex(const ply<T>&g){
  fo(i,len(g))if(ccw(g[i-1],g[i],g[i+1])==-1)rr 0;
  rr 1;
}


I(J T)ll contain(const cir<T>&c,const pt<T>&p){
  rr sgn(abs(p-c.p)-c.r)<=0;
}

I(J T)ll contain(const ply<T>&g,const pt<T>&p){
  enum{out,on,in};
  ll f=0;
  fo(i,len(g)){
    auto a=g[i]-p,b=g[i+1]-p;
    if(sgn(a.y,b.y)>0)swap(a,b);
    if(sgn(a.y)<=0&&sgn(b.y)>0&&sgn(crs(a,b))<0)f=!f;
    if(sgn(crs(a,b))==0&&sgn(dot(a,b))<=0)rr on;
  }
  rr f?in:out;
}


I(J T)auto convex_upper(pts<T>p){
  uq(p);
  ply<T>u;
  fe(p,a){wh(len(u)>=2&&ccw(u.end()[-2],u.end()[-1],a)==1)pop(u);u.eb(a);}
  rr u;
}
I(J T)auto convex_lower(pts<T>p){
  uq(p);
  ply<T>l;
  fe(p,a){wh(len(l)>=2&&ccw(l.end()[-2],l.end()[-1],a)==-1)pop(l);l.eb(a);}
  rr l;
}
I(J T)auto convex_hull(pts<T>p){
  uq(p);
  ply<T>u=convex_upper(p),l=convex_lower(p);
  ply<T>ch;
  if(len(u))pop(u);
  rv(u);
  if(len(u))pop(u);
  fe(l,a)ch.eb(a);
  fe(u,a)ch.eb(a);
  rr ch;
}


I(J T)T convex_dia(const ply<T>&g){
  ll n=len(g);
  ll is=0,js=0;
  fo(i,1,n){
    if(sgn(g[i].y,g[is].y)>0)is=i;
    if(sgn(g[i].y,g[js].y)<0)js=i;
  }
  T ma=abs(g[is]-g[js]);
  
  ll i,j,mi,mj;
  i=mi=is;
  j=mj=js;
  do{
    sgn(crs(g[i+1]-g[i],g[j+1]-g[j]))>=0?j=(j+1)%n:i=(i+1)%n;
    if(amax(ma,abs(g[i]-g[j]))){mi=i;mj=j;}
  }wh(i!=is||j!=js);
  rr ma;
}

//ベクトル(l.a,lb)の左側にできる凸多角形
I(J T)auto convex_cut(const ply<T>&g,const line<T>l){
  ply<T>g2;
  ll n=len(g);
  fo(i,n){
    auto cu=g[i],nx=g[i+1];
    line<T>m(cu,nx);
    if(ccw(l.a,l.b,cu)!=-1)g2.eb(cu);
    if(ccw(l.a,l.b,cu)*ccw(l.a,l.b,nx)==-1)g2.eb(xpt(m,l));
  }
  rr g2;
}

I(J T)T closest_pair(pts<T>p){
  srt(p);
  auto cy=[](const pt<T>&a,const pt<T>&b){rr sgn(a.y,b.y)<0;};
  
  rr rec([&](auto&&f,ll l,ll r)->T{
    if(r-l<=1)rr oo;
    ll m=(l+r)/2;
    T x=p[m].x;
    T res=min(f(l,m),f(m,r));
    inplace_merge(bgn(p)+l,bgn(p)+m,bgn(p)+r,cy);
    
    pts<T>b;
    fo(i,l,r){
      if(sgn(abs(p[i].x-x),res)>=0)continue;
      of(j,len(b)){
        if(sgn(p[i].y-b[j].y,res)>=0)break;
        amin(res,abs(p[i]-b[j]));
      }
      b.eb(p[i]);
    }
    rr res;
  })(0,len(p));
}

I(J T)vo floyd_warshall(v2<T>&d){ll n=len(d);fo(k,n)fo(i,n)fo(j,n)amin(d[i][j],d[i][k]+d[k][j]);}

vo main(){ll T=1;fo(t,T)solve();}
vo solve(){
  LL(N,M);
  auto p=vec({N,2},ptd());li(p);
  
  auto dist=vec<dd>({N,2,N,2},oo);
  fo(i,N)fo(j,2)dist[i][j][i][j]=0;
  
  fo(i,N)fo(j,2){
    fo(k,i+1,N)fo(l,2){
      ll f=0;
      fo(s,N)if(s!=i&&s!=k)if(intersect(seg(p[i][j],p[k][l]),seg(p[s][0],p[s][1])))f=1;
      if(!f)dist[i][j][k][l]=dist[k][l][i][j]=(p[i][j]-p[k][l]).abs();
    }
  }
  
  fo(s,N)fo(t,2)fo(i,N)fo(j,2)fo(k,N)fo(l,2){
    amin(dist[i][j][k][l],dist[i][j][s][t]+dist[s][t][k][l]);
  }
  
  fo(i,M){
    LL(a,b,c,d);dec(a,b,c,d);
    pp(dist[a][b][c][d]);
  }
}}