結果
問題 | No.2892 Lime and Karin |
ユーザー |
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提出日時 | 2024-09-22 20:16:11 |
言語 | C++17(gcc12) (gcc 12.3.0 + boost 1.87.0) |
結果 |
AC
|
実行時間 | 196 ms / 8,000 ms |
コード長 | 55,616 bytes |
コンパイル時間 | 6,573 ms |
コンパイル使用メモリ | 326,688 KB |
実行使用メモリ | 79,708 KB |
最終ジャッジ日時 | 2024-09-22 20:16:27 |
合計ジャッジ時間 | 14,537 ms |
ジャッジサーバーID (参考情報) |
judge3 / judge1 |
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ファイルパターン | 結果 |
---|---|
sample | AC * 3 |
other | AC * 52 |
ソースコード
#if !defined(MYLOCAL)//提出時用テンプレート#pragma GCC optimize("Ofast")#if defined(NDEBUG)#undef NDEBUG#endif#include "bits/stdc++.h"#if __has_include(<atcoder/all>)#include <atcoder/all>using namespace atcoder;#endifusing namespace std;using ll=long long;using dd=long double;using pll=pair<ll,ll>;using tll=tuple<ll,ll,ll>;using qll=tuple<ll,ll,ll,ll>;using ll2=array<ll,2>;using ll3=array<ll,3>;using ll4=array<ll,4>;using namespace chrono;constexpr ll INF = 1201001001001001001;struct Fast{ Fast(){ cin.tie(0); ios::sync_with_stdio(false); cout<<fixed<<setprecision(numeric_limits<double>::max_digits10); } } fast;#define EXPAND( x ) x//VS用おまじない#define overload3(_1,_2,_3,name,...) name#define overload4(_1,_2,_3,_4,name,...) name#define overload5(_1,_2,_3,_4,_5,name,...) name#define rep1(N) for (ll dmyi = 0; dmyi < (N); dmyi++)#define rep2(i, N) for (ll i = 0; i < (N); i++)#define rep3(i, S, E) for (ll i = (S); i <= (E); i++)#define rep4(i, S, E, t) for (ll i = (S); i <= (E); i+=(t))#define rep(...) EXPAND(overload4(__VA_ARGS__,rep4,rep3,rep2,rep1)(__VA_ARGS__))#define dep3(i, E, S) for (ll i = (E); i >= (S); i--)#define dep4(i, E, S, t) for (ll i = (E); i >= (S); i-=(t))#define dep(...) EXPAND(overload4(__VA_ARGS__, dep4, dep3,_,_)(__VA_ARGS__))#define ALL1(v) (v).begin(), (v).end()#define ALL2(v,E) (v).begin(), (v).begin()+((E)+1)#define ALL3(v,S,E) (v).begin()+(S), (v).begin()+((E)+1)#define all(...) EXPAND(overload3(__VA_ARGS__, ALL3, ALL2, ALL1)(__VA_ARGS__))#define RALL1(v) (v).rbegin(), (v).rend()#define RALL2(v,E) (v).rbegin(), (v).rbegin()+((E)+1)#define RALL3(v,S,E) (v).rbegin()+(S), (v).rbegin()+((E)+1)#define rall(...) EXPAND(overload3(__VA_ARGS__, RALL3, RALL2, RALL1)(__VA_ARGS__))template<class T> inline bool chmax(T &a, T b) { if (a < b) { a = b; return true; }return false; }template<class T> inline bool chmin(T &a, T b) { if (a > b) { a = b; return true; }return false; }template<class T> inline auto maxe(T &&v,ll S,ll E){ return *max_element(all(v,S,E)); }template<class T> inline auto maxe(T &&v){ return *max_element(all(v)); }template<class T> inline auto mine(T &&v,ll S,ll E){ return *min_element(all(v,S,E)); }template<class T> inline auto mine(T &&v){ return *min_element(all(v)); }template<class T,class U=typename remove_reference<T>::type::value_type>inline U sum(T &&v,ll S,ll E) {return accumulate(all(v,S,E),U());}template<class T> inline auto sum(T &&v) {return sum(v,0,v.end()-v.begin()-1);}template<class T> inline ll sz(T &&v){ return (ll)v.size(); }inline ll Ceil(ll a,ll b){ return (a<0) ? -(-a/b) : (a+b-1)/b; } //負もOKinline ll Floor(ll a,ll b){ return -Ceil(-a,b); } //負もOKinline ll Floormod(ll a,ll m){ return Floor(a,m)*m; } //負もOKinline ll Ceilmod(ll a,ll m){ return Ceil(a,m)*m; } //負もOKinline ll Mod(ll a,ll m){ ll r=a%m; if(r<0)r+=m; return r; } //負もOKtemplate<class T> inline T Pow(T a,ll n){ T r=1; for(; n>0; n>>=1,a*=a){ if(n&1)r*=a; } return r; }inline ll Pow(int a,ll n){ return Pow((ll)a,n); }inline ll limitmul(ll a,ll b,ll u){ return b==0||a<=u/b ? a*b : u; }//min(a*b,u) a,b,u≧0//pair用テンプレートtemplate<class T,class S> inline pair<T,S>& operator+=(pair<T,S> &a,const pair<T,S> &b){ a.first+=b.first; a.second+=b.second; return a; }template<class T,class S> inline pair<T,S>& operator-=(pair<T,S> &a,const pair<T,S> &b){ a.first-=b.first; a.second-=b.second; return a; }template<class T,class S> inline pair<T,S>& operator*=(pair<T,S> &a,const pair<T,S> &b){ a.first*=b.first; a.second*=b.second; return a; }template<class T,class S> inline pair<T,S>& operator/=(pair<T,S> &a,const pair<T,S> &b){ a.first/=b.first; a.second/=b.second; return a; }template<class T,class S> inline pair<T,S>& operator%=(pair<T,S> &a,const pair<T,S> &b){ a.first%=b.first; a.second%=b.second; return a; }template<class T,class S,class R> inline pair<T,S>& operator+=(pair<T,S> &a,R b){ a.first+=b; a.second+=b; return a; }template<class T,class S,class R> inline pair<T,S>& operator-=(pair<T,S> &a,R b){ a.first-=b; a.second-=b; return a; }template<class T,class S,class R> inline pair<T,S>& operator*=(pair<T,S> &a,R b){ a.first*=b; a.second*=b; return a; }template<class T,class S,class R> inline pair<T,S>& operator/=(pair<T,S> &a,R b){ a.first/=b; a.second/=b; return a; }template<class T,class S,class R> inline pair<T,S>& operator%=(pair<T,S> &a,R b){ a.first%=b; a.second%=b; return a; }template<class T,class S,class R> inline pair<T,S> operator+(const pair<T,S> &a,R b){ pair<T,S> c=a; return c+=b; }template<class T,class S,class R> inline pair<T,S> operator-(const pair<T,S> &a,R b){ pair<T,S> c=a; return c-=b; }template<class T,class S,class R> inline pair<T,S> operator*(const pair<T,S> &a,R b){ pair<T,S> c=a; return c*=b; }template<class T,class S,class R> inline pair<T,S> operator/(const pair<T,S> &a,R b){ pair<T,S> c=a; return c/=b; }template<class T,class S,class R> inline pair<T,S> operator%(const pair<T,S> &a,R b){ pair<T,S> c=a; return c%=b; }template<class T,class S,class R> inline pair<T,S> operator-(R b,const pair<T,S> &a){ pair<T,S> c=-a; return c+=b; }template<class T,class S> inline pair<T,S> operator-(const pair<T,S> &a,const pair<T,S> &b){ pair<T,S> c=a; return c-=b; }template<class T,class S> inline pair<T,S> operator-(const pair<T,S> &a){ pair<T,S> c=a; return c*=(-1); }template<class T,class S> inline ostream &operator<<(ostream &os,const pair<T,S> &a){ return os << a.first << ' ' << a.second; }//tuple用テンプレート 出力用のみtemplate<class T,class S,class R> inline ostream &operator<<(ostream &os,const tuple<T,S,R> &a){ return os << get<0>(a) << ' ' << get<1>(a) << ' '<< get<2>(a); }template<class T,class S,class R,class Q> inline ostream &operator<<(ostream &os,const tuple<T,S,R,Q> &a){ return os << get<0>(a) << ' ' << get<1>(a) << ' ' << get<2>(a) << ' ' << get<3>(a); }//vector用テンプレートtemplate<class T> inline ostream &operator<<(ostream &os,const vector<T> &a){ for (ll i=0; i<(ll)a.size(); i++) os<<(i>0?" ":"")<<a[i]; return os;}//array用テンプレートtemplate<class T,size_t S> inline array<T,S>& operator+=(array<T,S> &a,const array<T,S> &b){ for (ll i=0; i<(ll)S; i++) a[i]+=b[i]; return a; }template<class T,size_t S> inline array<T,S>& operator-=(array<T,S> &a,const array<T,S> &b){ for (ll i=0; i<(ll)S; i++) a[i]-=b[i]; return a; }template<class T,size_t S> inline array<T,S>& operator*=(array<T,S> &a,const array<T,S> &b){ for (ll i=0; i<(ll)S; i++) a[i]*=b[i]; return a; }template<class T,size_t S> inline array<T,S>& operator/=(array<T,S> &a,const array<T,S> &b){ for (ll i=0; i<(ll)S; i++) a[i]/=b[i]; return a; }template<class T,size_t S> inline array<T,S>& operator%=(array<T,S> &a,const array<T,S> &b){ for (ll i=0; i<(ll)S; i++) a[i]%=b[i]; return a; }template<class T,size_t S,class R> inline array<T,S>& operator+=(array<T,S> &a,R b){ for (T &e: a) e+=b; return a; }template<class T,size_t S,class R> inline array<T,S>& operator-=(array<T,S> &a,R b){ for (T &e: a) e-=b; return a; }template<class T,size_t S,class R> inline array<T,S>& operator*=(array<T,S> &a,R b){ for (T &e: a) e*=b; return a; }template<class T,size_t S,class R> inline array<T,S>& operator/=(array<T,S> &a,R b){ for (T &e: a) e/=b; return a; }template<class T,size_t S,class R> inline array<T,S>& operator%=(array<T,S> &a,R b){ for (T &e: a) e%=b; return a; }template<class T,size_t S,class R> inline array<T,S> operator+(const array<T,S> &a,R b){ array<T,S> c=a; return c+=b; }template<class T,size_t S,class R> inline array<T,S> operator-(const array<T,S> &a,R b){ array<T,S> c=a; return c-=b; }template<class T,size_t S,class R> inline array<T,S> operator*(const array<T,S> &a,R b){ array<T,S> c=a; return c*=b; }template<class T,size_t S,class R> inline array<T,S> operator/(const array<T,S> &a,R b){ array<T,S> c=a; return c/=b; }template<class T,size_t S,class R> inline array<T,S> operator%(const array<T,S> &a,R b){ array<T,S> c=a; return c%=b; }template<class T,size_t S,class R> inline array<T,S> operator-(R b,const array<T,S> &a){ array<T,S> c=-a; return c+=b; }template<class T,size_t S> inline array<T,S> operator-(const array<T,S> &a,const array<T,S> &b){ array<T,S> c=a; return c-=b; }template<class T,size_t S> inline array<T,S> operator-(const array<T,S> &a){ array<T,S> c=a; return c*=(-1); }template<class T,size_t S> inline ostream &operator<<(ostream &os,const array<T,S> &a){ for (ll i=0; i<(ll)S; i++) os<<(i>0?" ":"")<<a[i]; returnos; }inline struct{system_clock::time_point st = system_clock::now();ll operator()()const{return duration_cast<microseconds>(system_clock::now()-st).count()/1000;}} timeget;struct cinutil{template<class T> static void cin1core(T &a){ cin>>a; }template<class T,class S> static void cin1core(pair<T,S> &a){cin1core(a.first), cin1core(a.second);}template<class... Args> static void cin1core(tuple<Args...> &a){cinTplRec<tuple<Args...>,sizeof...(Args)-1>()(a);}template<class T,size_t N>static void cin1core(array<T,N> &a){for(int i=0;i<(int)N;++i) cin>>a[i];}private:template<class Tpl,int i> struct cinTplRec{void operator()(Tpl &a){ cinTplRec<Tpl,i-1>()(a); cin1core(get<i>(a)); }};template<class Tpl> struct cinTplRec<Tpl,0>{void operator()(Tpl &a){ cin1core(get<0>(a)); }};};template<class T> T cin1(){ T a; cinutil::cin1core(a); return a; }template<class... Args> tuple<Args...> cins(){ return cin1<tuple<Args...>>(); }template<long long MOD> struct mll_{using Int = long long;using ll = long long;ll val_=0;/*---- utility ----*/mll_ &norm(){ return normR().normS(); }//正規化mll_ &normR(){ val_%=MOD; return *this; }//剰余正規化のみmll_ &normS(){ if (val_<0) val_+=MOD; return *this; }//正負正規化のみmll_ &normP(){ if (val_>=MOD) val_-=MOD; return *this; }//加算時正規化mll_ &invsg(){ val_=-val_; return normS(); }//正負反転ll modinv(int a){//a^-1 mod MODint ypre=0,y=1,apre=MOD;while (a>1){int t=apre/a;apre-=a*t,swap(a,apre);ypre-=y*t,swap(y,ypre);}return y<0 ? y+MOD: y;}/*---- I/F ----*/mll_(){}mll_(ll v): val_(v){ norm(); }mll_(ll v,bool b): val_(v){} //正規化無のコンストラクタInt val()const{ return (Int)val_; }bool isnone() const { return val_==-1; } //true:値なしmll_ &none() { val_=-1; return *this; } //値なしにするmll_ &inv(){ val_=modinv((int)val_); return *this; }mll_ &operator+=(mll_ b){ val_+=b.val_; return normP(); }mll_ &operator-=(mll_ b){ val_-=b.val_; return normS(); }mll_ &operator*=(mll_ b){ val_*=b.val_; return normR(); }mll_ &operator/=(mll_ b){ return *this*=b.inv(); }mll_ &operator+=(ll b){ return *this+=mll_(b); }mll_ &operator-=(ll b){ return *this-=mll_(b); }mll_ &operator*=(ll b){ return *this*=mll_(b); }mll_ &operator/=(ll b){ return *this/=mll_(b); }mll_ operator-()const{ return mll_(*this).invsg(); }mll_ operator+(mll_ b)const{ return mll_(*this)+=b; }mll_ operator-(mll_ b)const{ return mll_(*this)-=b; }mll_ operator*(mll_ b)const{ return mll_(*this)*=b; }mll_ operator/(mll_ b)const{ return mll_(*this)/=b; }mll_ operator+(ll b)const{ return mll_(*this)+=b; }mll_ operator-(ll b)const{ return mll_(*this)-=b; }mll_ operator*(ll b)const{ return mll_(*this)*=b; }mll_ operator/(ll b)const{ return mll_(*this)/=b; }friend mll_ operator+(ll a,mll_ b){ return b+a; }friend mll_ operator-(ll a,mll_ b){ return -b+a; }friend mll_ operator*(ll a,mll_ b){ return b*a; }friend mll_ operator/(ll a,mll_ b){ return mll_(a)/b; }bool operator==(mll_ b)const{ return val_==b.val_; }bool operator!=(mll_ b)const{ return val_!=b.val_; }bool operator==(ll b)const{ return *this==mll_(b); }bool operator!=(ll b)const{ return *this!=mll_(b); }friend bool operator==(ll a,mll_ b){ return mll_(a)==b; }friend bool operator!=(ll a,mll_ b){ return mll_(a)!=b; }friend ostream &operator<<(ostream &os,mll_ a){ return os << a.val_; }friend istream &operator>>(istream &is,mll_ &a){ return is >> a.val_; }mll_ pow(ll k)const{mll_ ret(1,false),a(*this);for (; k>0; k>>=1,a*=a) if (k&1)ret*=a;return ret;}static constexpr int mod() { return MOD; }//enum{ modll=MOD };};struct bll{ //第0~62bitまで対応ll s=0;bll(ll s_=0): s(s_){}bll(int s_): s(s_){}bll(const string &bitstr): s(str2val(bitstr)){}bll(const char *bitstr): s(str2val(bitstr)){}struct ref {bll &b; const ll msk;ref(bll &b_,ll pos):b(b_),msk(1LL<<pos){}operator ll() const { return (b.s&msk)!=0; }ref &operator=(bool x){ if(x) b.s|=msk; else b.s&=~msk; return *this; }};ref operator[](ll pos){ return ref(*this,pos); }ll operator[](ll pos) const { return (s>>pos)&1; }bll &operator=(int b){ s=b; return *this; }bll &operator=(ll b){ s=b; return *this; }bll &operator=(const string &bitstr){ s=str2val(bitstr); return *this; }bll &operator=(const char *bitstr){ s=str2val(bitstr); return *this; }bll operator++(int){ bll b(*this); s++; return b; }bll operator--(int){ bll b(*this); s--; return b; }operator ll() const noexcept { return s; }bll &operator&=(ll b){ s&=b; return *this; }bll &operator|=(ll b){ s|=b; return *this; }bll &operator^=(ll b){ s^=b; return *this; }bll &operator+=(ll b){ s+=b; return *this; }bll &operator-=(ll b){ s-=b; return *this; }bll &operator<<=(ll i){ s<<=i; return *this; }bll &operator>>=(ll i){ s>>=i; return *this; }bool contains(ll b)const{ return (s&b)==b; }bll &oneq (ll l,ll r){ s|= rangemask(l,r); return *this; }//l>=rbll &offeq (ll l,ll r){ s&=~rangemask(l,r); return *this; }//l>=rbll &flipeq(ll l,ll r){ s^= rangemask(l,r); return *this; }//l>=rbll &oneq (ll i){ s|= (1LL<<i); return *this; }bll &offeq (ll i){ s&=~(1LL<<i); return *this; }bll &flipeq(ll i){ s^= (1LL<<i); return *this; }bll on (ll l,ll r)const{ return bll(s).oneq (l,r); }//l>=rbll off (ll l,ll r)const{ return bll(s).offeq (l,r); }//l>=rbll flip(ll l,ll r)const{ return bll(s).flipeq(l,r); }//l>=rbll on (ll i)const{ return bll(s).oneq (i); }bll off (ll i)const{ return bll(s).offeq (i); }bll flip(ll i)const{ return bll(s).flipeq(i); }bll substr(ll l,ll r)const{ return (s&rangemask(l,r))>>r; }//l>=rstatic ll rangemask(ll l,ll r){ return (1LL<<(l+1))-(1LL<<r); }//l>=rll msbit()const{for(ll o=63,x=-1;;){ll m=(o+x)/2;if(s < (1LL<<m)) o=m; else x=m;if(o-x==1) return x;}}ll lsbit()const{ return bll(lsb()).msbit(); }ll msb()const{ ll pos=msbit(); return (pos<0) ? 0LL : 1LL<<pos; }ll lsb()const{ return s&-s; }ll count()const{ return bitset<64>(s).count(); }vector<ll> idxes()const{vector<ll> v;for(ll i=0,t=s; t; t>>=1,i++) if(t&1)v.push_back(i);return v;}string to_string()const{string ret;for(ll i=msbit();i>=0;--i) ret += '0'+char((s>>i)&1);return ret;}private:ll str2val(const string &bitstr){ll val=0, len=(ll)bitstr.size();for(ll i=0;i<len;++i) val|=ll(bitstr[i]-'0')<<(len-1-i);return val;}};template<class T> struct SET: set<T>{using P=set<T>;typename P::iterator it=P::end();template<class...Args> SET(Args...args): P(args...){}SET(initializer_list<T> a): P(a.begin(),a.end()){}ll size() const { return (ll)P::size(); }bool insert(const T &x){ bool r; tie(it,r)=P::insert(x); return r; }template <class It> void insert(It st,It en){ P::insert(st,en); }void insert(initializer_list<T> a){ P::insert(a.begin(),a.end()); }template<class...A> bool emplace(A&&...a){ bool r; tie(it,r)=P::emplace(a...); return r; }void eraseit(){ it=P::erase(it); }void find(const T &x){ it=P::find(x); }bool contains(const T &x){ return P::count(x)==1; }void lower_bound(const T &x){ it=P::lower_bound(x); }void upper_bound(const T &x){ it=P::upper_bound(x); }bool isend() { return it==P::end(); }T getit() { return *it; }T next() { return *(++it); }T prev() { return *(--it); }bool nextok() { return !isend() && it!=--P::end(); }bool prevok() { return it!=P::begin(); }T front() { return *(it=P::begin()); }T back() { return *(it=--P::end()); }void pop_front(){ front(); eraseit(); }void pop_back(){ back(); eraseit(); }void push_front(const T &x){ it=P::insert(P::begin(),x); }void push_back (const T &x){ it=P::insert(P::end(),x); }void push_out(SET &b){ b.push_front(back()); pop_back(); }void pull_in(SET &b){ push_back(b.front()); b.pop_front(); }};template<class T> struct cumulativesum{using Int = long long;using ll = long long;ll n=0; vector<T> c;cumulativesum():c(1){}template<class S> cumulativesum(S &&v): n((ll)v.size()),c(n+1) { Ini(v); }template<class S> void init(S &&v){ n=(ll)v.size(); c.resize(n+1); Ini(v); }void add(T x) { n++; c.push_back(c.back()+x); }T operator()(Int l,Int r){ return c[max(min(n,r+1),0LL)]-c[min(max(0LL,l),n)]; }pair<Int,T> group(T i){ll g=upper_bound(c.begin(),c.end(),i)-c.begin()-1;T r = g>=0 ? i-c[g] : i;return {g,r};}T mx(){//区間和maxT mn=T(),samx=0;for(ll i=1;i<=n;++i){chmax(samx,c[i]-mn);chmin(mn,c[i]);}return samx;}template<class S> void Ini(S &&v) { for(ll i=0;i<n;++i) c[i+1]=c[i]+v[i]; }};template<class S> cumulativesum(S) -> cumulativesum<typename remove_reference<S>::type::value_type>;template<class T> vector<T> powers(T m,ll n){vector<T> ret(n+1,1);for(ll i=1;i<=n;++i) ret[i]=ret[i-1]*m;return ret;}template <class T> auto runlength(T &&v){vector<pair<typename remove_reference<T>::type::value_type,ll>> ret;for(auto&&e:v){if(ret.empty() or ret.back().first!=e) ret.emplace_back(e,1);else ret.back().second++;}return ret;}inline vector<ll> str2num(string &s,char base,const string &etc){vector<ll> v(s.size());for(ll i=0;i<(ll)s.size();++i){size_t pos=etc.find(s[i]);if(pos==etc.npos) v[i]=s[i]-(ll)base;else v[i]=-((ll)pos+1);}return v;}template<class T> struct combination{vector<T> f,g; ll mxN=0;combination(){}combination(ll maxN): f(maxN+1,1),g(maxN+1),mxN(maxN) {for (ll i=1;i<=mxN;++i) { f[i]=f[i-1]*i; }g[mxN]=1/f[mxN];for (ll i=mxN;i>=1;--i) { g[i-1]=g[i]*i; }}T P(ll n,ll r){ return (n<0 || r<0 || n<r) ? T(0) : f[n]*g[n-r]; } //nPrT H(ll n,ll r){ return operator()(n+r-1,n-1); }//nHrT inv(ll n) { return f[n-1] * g[n]; } //1/nT fact(ll n) { return f[n]; } //n!T finv(ll n) { return g[n]; } //1/n!T operator()(ll n,ll r){if (r<0) return 0;if (n<0) return operator()(-n+r-1,r) * ((r&1)?-1:1); //-nCr = (-1)^r * n+r-1Crif (n<r) return 0;if (n<=mxN) return f[n]*g[n-r]*g[r]; //通常//n巨大、rかn-r小if (n-r<r) r=n-r;T bunsi=1,bunbo=1;for (ll i=0;i<r;++i) bunsi*=n-i;for (ll i=0;i<r;++i) bunbo*=i+1;return bunsi/bunbo;}template<class SP>vector<T> CnLnR(long long nL,long long nR,long long r,SP sp){if (nR-nL+1<=0) return vector<T>();if (r<0) return vector<T>(nR-nL+1,0);vector<T> v=sp(nL-r+1,nR-r+1,r);for (T& e: v) e*=finv(r);return v;}template<class SP>vector<T> HrLrR(long long n,long long rL,long long rR,SP sp){//r<0不可return CnLnR(n-1+rL,n-1+rR,n-1,sp);}};template<class T> struct wrapVector1d{using S=typename T::value_type;using Int = long long;const T *v;S Ini;wrapVector1d(const T &v_,S ini_=S()):v(&v_),Ini(ini_){}S operator[](Int i)const{ return (i<0 || (Int)v->size()<=i) ? Ini : (*v)[i]; }};template<class T> struct wrapVector2d{using S=typename T::value_type;using Int = long long;const vector<T> *v;S Ini;T dmy;wrapVector2d(const vector<T> &v_,S ini_=S()):v(&v_),Ini(ini_){}wrapVector1d<T> operator[](ll i)const{return (i<0 || (Int)v->size()<=i) ?wrapVector1d(dmy,Ini) : wrapVector1d((*v)[i],Ini);}};namespace dumpstring{//dummystruct args{using Int = long long;args(){}args &wd(Int wd__){ (void)wd__; return *this; }template<size_t DIM> args &rngs(array<array<Int,DIM>,2> rngs){ return *this; }args &tr(vector<Int> tr__){ (void)tr__; return *this; }args &tr(){ return *this; }args &labels(vector<string> labels__){ (void)labels__; return *this; }args &xrev(){ return *this; }args &yrev(){ return *this; }args &zrev(){ return *this; }args &wrev(){ return *this; }};template<class NdT>void dumpNd(const string &h,const NdT &fd,const args &p=args(),ostream &os=cerr){}};using dumpstring::args; using dumpstring::dumpNd;#endif//テンプレートendtemplate<class T> struct Vector: vector<T>{using Int = long long;using vT=vector<T>;using cvT=const vector<T>;using cT=const T;using vT::vT; //親クラスのコンストラクタの隠蔽を回避using vT::begin,vT::end,vT::insert,vT::erase;auto it(Int i){ return begin()+i; }auto it(Int i)const{ return begin()+i; }Vector(cvT& b):vT(b){}Vector(vT&& b):vT(move(b)){}Vector(Int n,cT& x):vT(n,x){}//型推論のためラッパー作成template<class S> Vector(const Vector<S>& b):vT(b.begin(),b.end()){}template<class S> Vector(const vector<S>& b):vT(b.begin(),b.end()){}Vector(Int n,T s,T d){ iota(n,s,d); }Vector(Int n,function<T(Int)> g):vT(n){ for(Int i=0;i<n;++i) (*this)[i]=g(i); }template<class S> Vector &operator+=(S x){ for(T &e: *this) e+=x; return *this; }template<class S> Vector &operator-=(S x){ for(T &e: *this) e-=x; return *this; }template<class S> Vector &operator*=(S x){ for(T &e: *this) e*=x; return *this; }template<class S> Vector &operator/=(S x){ for(T &e: *this) e/=x; return *this; }template<class S> Vector &operator%=(S x){ for(T &e: *this) e%=x; return *this; }template<class S> Vector operator+(S x)const{ return Vector(*this)+=x; }template<class S> Vector operator-(S x)const{ return Vector(*this)-=x; }template<class S> Vector operator*(S x)const{ return Vector(*this)*=x; }template<class S> Vector operator/(S x)const{ return Vector(*this)/=x; }template<class S> Vector operator%(S x)const{ return Vector(*this)%=x; }Vector &operator--(int){ return *this-=T(1); }Vector &operator++(int){ return *this+=T(1); }Vector operator-()const{ return Vector(*this)*=-1; }template<class S> friend Vector operator-(S x,const Vector &a){ return -a+=x; }Vector slice(Int l,Int r,Int d=1)const{Vector ret;for(Int i=l;(d>0&&i<=r)||(d<0&&r<=i);i+=d) ret.push_back((*this)[i]);return ret;}Int size()const{ return (Int)vT::size(); }Vector &push_back(cT& x,Int n=1){ for(Int i=0;i<n;++i){ vT::push_back(x); } return *this; }Vector &pop_back(Int n=1){ for(Int i=0;i<n;++i){ vT::pop_back(); } return *this; }Vector &push_front(cT& x,Int n=1){ this->insert(0,x,n); return *this; }Vector &pop_front(Int n=1){ erase(0,n-1); return *this; }T pull_back(){ T x=move(vT::back()); vT::pop_back(); return x; }T pull_front(){ T x=move(vT::front()); erase(0); return x; }Vector &insert(Int i,cT& x,Int n=1){ insert(it(i),n,x); return *this; }Vector &insert(Int i,cvT& b){ insert(it(i),b.begin(),b.end()); return *this; }Vector &erase(Int i){ erase(it(i)); return *this; }Vector &erase(Int l,Int r){ erase(it(l),it(r+1)); return *this; }Vector &concat(cvT &b,Int n=1){cvT B = (&b==this) ? *this : vT{};for(int i=0;i<n;++i) this->insert(size(),(&b==this)?B:b);return *this;}Vector repeat(Int n){ return Vector{}.concat(*this,n); }Vector &reverse(Int l=0,Int r=-1){ r+=r<0?size():0; std::reverse(it(l),it(r+1)); return *this; }Vector &rotate(Int m){ return rotate(0,size()-1,m); }Vector &rotate(Int l,Int r,Int m){ std::rotate(it(l),it(m),it(r+1)); return *this; }Vector &sort(Int l=0,Int r=-1){ r+=r<0?size():0; std::sort(it(l),it(r+1)); return *this; }Vector &rsort(Int l=0,Int r=-1){ return sort(l,r).reverse(l,r); }template<class Pr> Vector &sort(Pr pr){ return sort(0,size()-1,pr); }template<class Pr> Vector &sort(Int l,Int r,Pr pr){ std::sort(it(l),it(r+1),pr); return *this; }Vector &uniq(){ erase(unique(begin(),end()),end()); return *this; }Vector &sortq(){ return sort().uniq(); }Vector &fill(cT& x){ return fill(0,size()-1,x); }Vector &fill(Int l,Int r,cT& x){ std::fill(it(l),it(r+1),x); return *this; }template<class S=Int> Vector &iota(Int n,T s=0,S d=1){vT::resize(n);if(n==0) return *this;(*this)[0]=s;for(int i=1;i<n;++i) (*this)[i]=(*this)[i-1]+d;return *this;}Int count(cT& x)const{ return count(0,size()-1,x); }Int count(Int l,Int r,cT& x)const{ return Int(std::count(it(l),it(r+1),x)); }template<class Pr> Int countif(Pr pr)const{ return countif(0,size()-1,pr); }template<class Pr> Int countif(Int l,Int r,Pr pr)const{ return Int(count_if(it(l),it(r+1),pr)); }Int find(cT& x)const{ return find(0,size()-1,x); }Int find(Int l,Int r,cT& x)const{ return Int(std::find(it(l),it(r+1),x)-begin()); }template<class Pr> Int findif(Pr pr)const{ return findif(0,size()-1,pr); }template<class Pr> Int findif(Int l,Int r,Pr pr)const{ return Int(find_if(it(l),it(r+1),pr)-begin()); }Vector<Int> findall(cT& x)const{ return findall(0,size()-1,x); }Vector<Int> findall(Int l,Int r,cT& x)const{ return findallif(l,r,[&](cT& y){return y==x;}); }template<class Pr> Vector<Int> findallif(Pr pr)const{ return findallif(0,size()-1,pr); }template<class Pr> Vector<Int> findallif(Int l,Int r,Pr pr)const{Vector<Int> ret;for(Int i=l;i<=r;++i) if(pr((*this)[i])) ret.push_back(i);return ret;}Int flooridx(cT& x)const{ return Int(upper_bound(begin(),end(),x)-begin()-1); }Int ceilidx(cT& x)const{ return Int(lower_bound(begin(),end(),x)-begin()); }Int leftnmof(cT& x)const{ return flooridx(x)+1; }Int rightnmof(cT& x)const{ return size()-ceilidx(x); }bool contains(cT& x)const{ Int i=flooridx(x); return i>=0 && (*this)[i]==x; }template<class Pr> Int flooridx(cT& x,Pr pr)const{ return Int(upper_bound(begin(),end(),x,pr)-begin()-1); }template<class Pr> Int ceilidx(cT& x,Pr pr)const{ return Int(lower_bound(begin(),end(),x,pr)-begin()); }template<class Pr> Int leftnmof(cT& x,Pr pr)const{ return flooridx(x,pr)+1; }template<class Pr> Int rightnmof(cT& x,Pr pr)const{ return size()-ceilidx(x,pr); }template<class Pr> bool contains(cT& x,Pr pr)const{ Int i=flooridx(x,pr); return i>=0 && (*this)[i]==x; }template<class S> using VV = Vector<Vector<S>>; template<class S> using sVV = vector<vector<S>>;template<class S> using VVV = Vector<VV<S>>; template<class S> using sVVV = vector<sVV<S>>;template<class S> using VVVV = Vector<VVV<S>>; template<class S> using sVVVV = vector<sVVV<S>>;template<class S> using VVVVV = Vector<VVVV<S>>; template<class S> using sVVVVV = vector<sVVVV<S>>;auto tostd()const{ return tov(*this); }template <class S> static vector<S> tov(const Vector<S>&v){ return v; }template <class S> static sVV<S> tov(const VV<S> &v){ sVV<S> ret; for(auto&& e:v) ret.push_back(e); return ret; }template <class S> static sVVV<S> tov(const VVV<S> &v){ sVVV<S> ret; for(auto&& e:v) ret.push_back(e.tostd()); return ret; }template <class S> static sVVVV<S> tov(const VVVV<S> &v){ sVVVV<S> ret; for(auto&& e:v) ret.push_back(e.tostd()); return ret; }template <class S> static sVVVVV<S> tov(const VVVVV<S> &v){ sVVVVV<S> ret; for(auto&& e:v) ret.push_back(e.tostd()); return ret; }};/*vll a={9,8,7},b={1,2,3};vpll p={{5,3},{7,8},{0,2},};- -------- 操作系 --------a+=x a-=x a*=x a/=x a%=x a+x a-x a*x a/x a%x -a x-a a++ a-- //∀i a[i]にxを演算a.push_front(x,n); //n個先頭追加 省略時1a.push_back(x,n); //n個末尾追加 省略時1a.pop_front(n); //n個先頭削除 省略時1a.pop_back(n); //n個末尾削除 省略時1ll x=a.pull_front(); //pop_front()と同時に値取得ll x=a.pull_back(); //pop_back()と同時に値取得a.insert(i,x,n); //a[i]にn個x挿入 n省略時1a.insert(i,b); //a[i]にvll b挿入a.erase(i); //a[i]削除a.erase(l,r); //区間[l,r]削除a.concat(b); //aにbを結合 b=a可a.concat(b,n); //aにbをn回結合 b=a可a.reverse(l,r); //[l,r]を反転 l,r省略可a.rotate(m); //a[m]を先頭にするrotatea.rotate(l,r,m); //a[m]を先頭にするrotate 範囲[l,r]a.sort(l,r); //[l,r]をソート l,r省略可a.rsort(l,r); //[l,r]を逆順ソート l,r省略可p.sort(l,r,[&](pll x,pll y){return x.second<y.second;});//比較関数指定sort l,r省略可a.uniq(); //連続同値を1つにするa.sortq(); //ソートしてユニークa.fill(l,r,x); //[l,r]にx代入 l,r省略可a.iota(n,s,d); //aを等差数列にする 長さn,初項s,公差dvll a(n,s,d); //コンストラクタ版iotavll b=a.slice(st,en,d); //a[st:en:d] d省略時1vll b=a.repeat(n); //aをn回繰り返す- -------- 検索系 --------auto pr=[&](auto &x){ return x>0; }; //検索条件ll m=a.count(x); //xの個数ll m=a.count(l,r,x); //xの個数in[l,r]ll m=a.countif(pr); //条件満たす個数ll m=a.countif(l,r,pr); //条件満たす個数in[l,r]ll i=a.find(x); //xの最左位置i ない時N(配列長)ll i=a.find(l,r,x); //xの最左位置i in[l,r] ない時r+1ll i=a.findif(pr); //条件満たす最左位置i ない時N(配列長)ll i=a.findif(l,r,pr); //条件満たす最左位置i in[l,r] ない時r+1vll is=a.findall(x); //xの位置i列挙vll is=a.findall(l,r,x); //xの位置i列挙in[l,r]vll is=a.findallif(pr); //条件満たす位置i列挙vll is=a.findallif(l,r,pr); //条件満たす位置i列挙in[l,r]- -------- 昇順sort済み配列用 --------ll i=a.flooridx(x); //x以下の最近傍位置i ない時-1ll i=a.ceilidx(x); //x以上の最近傍位置i ない時N(配列長)ll m=a.leftnmof(x); //x以下の個数ll m=a.rightnmof(x); //x以上の個数bool b=a.contains(x); //xを含む- -------- 比較関数prでsort済みの配列用 --------auto pr=[&](auto &x,auto &y){ return x>y; }; //降順ソート時ll i=a.flooridx(x,pr); //x以左の最近傍位置i ない時-1ll i=a.ceilidx(x,pr); //x以右の最近傍位置i ない時N(配列長)ll m=a.leftnmof(x,pr); //x以左の個数ll m=a.rightnmof(x,pr); //x以右の個数bool b=a.contains(x,pr); //xを含むa.concat(b,n).pop_back().rsort().uniq(); //連続適用できるauto aa=a.tostd(); //N次元VectorをN次元vectorに変換(N≦5)*/#if 0#define MODLL (1000000007LL)#else#define MODLL (998244353LL)#endifusing mll = mll_<MODLL>;//using mll = fraction;// 1//0┼2// 3 左 上 右 下vector<pll> dxys={{0,-1},{-1,0},{0,1},{1,0},};namespace SolvingSpace{template<class T> using vector = Vector<T>;using vll=vector< ll>; using vmll=vector< mll>; using vdd=vector< dd>;using vvll=vector< vll>; using vvmll=vector< vmll>; using vvdd=vector< vdd>;using vvvll=vector< vvll>; using vvvmll=vector< vvmll>; using vvvdd=vector< vvdd>;using vvvvll=vector<vvvll>; using vvvvmll=vector<vvvmll>; using vvvvdd=vector<vvvdd>;using vpll=vector< pll>; using vtll=vector< tll>; using vqll=vector< qll>;using vvpll=vector< vpll>; using vvtll=vector< vtll>; using vvqll=vector< vqll>;using vll2=vector< ll2>; using vll3=vector< ll3>; using vll4=vector< ll4>;using vvll2=vector< vll2>; using vvll3=vector< vll3>; using vvll4=vector< vll4>;using vvvll2=vector<vvll2>; using vvvll3=vector< vvll3>; using vvvll4=vector<vvll4>;using vss=vector<string>;template<class T> vector<T> cinv(ll nm){ return vector<T>(nm,[](ll i){ (void)i; return cin1<T>(); }); }template<class T> vector<vector<T>> cinvv(ll H,ll W){ return vector<vector<T>>(H,[&](ll i){ (void)i; return cinv<T>(W); }); }template<class E> struct HeavyLightDecomposition{using Int = long long;vector<vector<E>> *to=nullptr; //グラフvector<Int> head; //head[v] 頂点vの属する重パスの根側端頂点vector<Int> id; //id[v] 頂点vの行きがけ順番号 0-originvector<Int> rev; //rev[ID] 行きがけ順番号IDの頂点vvector<Int> lst; //lst[v] 頂点vのサブ木内頂点の行きがけ順番号最大値vector<Int> par; //par[v] 頂点vの親頂点 par[根]は-1vector<Int> siz; //siz[v] 頂点vのサブ木内頂点数(v含む)vector<Int> dpt; //dpt[v] 頂点vの深さ(根が0)HeavyLightDecomposition(){}HeavyLightDecomposition(vector<vector<E>> &to_,Int root=0):to(&to_),head(size(),root),id(size()),rev(size()),lst(size()),par(size()),siz(size(),1),dpt(size()){assert(!to_.empty());dfsSz(root);dfsHld(root);}Int size()const{ return to->size(); } //頂点数Int vof(Int id_)const{ return rev[id_]; }Int idof(Int v)const{ return id[v]; }Int parentof(Int v)const{ return par[v]; }Int subszof(Int v)const{ return siz[v]; }Int depthof(Int v)const{ return dpt[v]; }bool isleaf(Int v)const{return id[v]==size()-1 || head[v]!=head[rev[id[v]+1]];}vector<pair<Int,Int>> preorder()const{ //行きがけ順の(頂点,親頂点)列vector<pair<Int,Int>> ret;for(int i=0;i<size();++i) ret.emplace_back(rev[i],par[rev[i]]);return ret;}Int lcaorg(Int u,Int v)const{ //u,vのLCAwhile(head[u]!=head[v]){if(id[u]>id[v]) swap(u,v);v=par[head[v]];}return id[u]<id[v] ? u : v;}Int lca(Int u,Int v)const{ //u,vのLCAif(id[u]>id[v])swap(u,v);while(head[u]!=head[v] && id[u]<id[v]) v=par[head[v]];return id[u]<id[v] ? u : v;}Int dist(Int u,Int v)const{ return dpt[u]+dpt[v]-2*dpt[lca(u,v)]; }Int jump(Int v,Int k)const{ //vのk個上 なければ-1while(id[v]-k<id[head[v]]){k-=id[v]-id[head[v]]+1;v=par[head[v]];if(v==-1) return -1;}return rev[id[v]-k];}vector<pair<Int,Int>> heavypaths()const{ //[stID0,enID0],[stID1,enID1],…vector<pair<Int,Int>> ret;Int enID=to->size()-1;while(enID!=-1){Int stID=id[head[rev[enID]]];ret.emplace_back(stID,enID);enID=stID-1;}reverse(ret.begin(),ret.end());return ret;}vector<pair<Int,Int>> uv2idranges(Int u,Int v,bool isedge=false)const{ //パスu→vを重パス分解Int a=lca(u,v);//aを含む重パス上まで移動auto func=[&](Int &t){vector<pair<Int,Int>> t2a;while(head[t]!=head[a]){t2a.emplace_back(id[t],id[head[t]]);t=par[head[t]];}return t2a;};vector<pair<Int,Int>> u2a=func(u),v2a=func(v);//aを含む重パス上の追加if(!isedge){//頂点if(u!=a) u2a.emplace_back(id[u],id[a]);else if(v!=a) v2a.emplace_back(id[v],id[a]);else u2a.emplace_back(id[a],id[a]);}else{//辺if(u!=a) u2a.emplace_back(id[u],id[a]-1);else if(v!=a) v2a.emplace_back(id[v],id[a]-1);}//v2aを反転して結合while(!v2a.empty()){auto [st,en]=v2a.back(); v2a.pop_back();u2a.emplace_back(en,st);}return u2a;}vector<Int> path(Int u,Int v)const{ //パスu→v 頂点列Int a=lca(u,v);auto func=[&](Int t){vector<Int> t2a;for(;t!=a;t=par[t]) t2a.push_back(t);return t2a;};vector<Int> u2a=func(u),v2a=func(v);u2a.push_back(a);while(!v2a.empty()){u2a.push_back(v2a.back()); v2a.pop_back();}return u2a;}pair<Int,Int> subtree2idrange(Int v)const{ //サブ木ID範囲return {id[v],lst[v]};}private:void dfsSz(Int v,Int p=-1){par[v]=p;for(auto&& u: (*to)[v]){if(u==p)continue;dpt[u]=dpt[v]+1;dfsSz(u,v);siz[v]+=siz[u];}}Int idcnt=0;void dfsHld(Int v,Int p=-1){vector<E> &tov=(*to)[v];id[v]=idcnt++;rev[id[v]]=v;//重パスの子を先頭へInt mxsz=-1;for(auto&& u: tov){if(u==p)continue;if(mxsz<siz[u]) mxsz=siz[u],swap(tov[0],u);}//head決めるdfsfor(auto&& u: tov){if(u==p)continue;head[u] = (u==(*to)[v][0]) ? head[v] : u;dfsHld(u,v);}lst[v]=idcnt-1;}Int root()const{ return rev[0]; }};/*- 定義 ↓木グラフ to[v][0]が重パスになるよう変更されるHeavyLightDecomposition hld(to);HeavyLightDecomposition hld(to,root);- 行きがけ順番号id ⇔ 頂点vll v=hld.vof(id);ll id=hld.idof(v);- 親頂点ll p=hld.parentof(v);- サブ木内頂点数(v含む)ll s=hld.subszof(v);- 深さ(根が0)ll d=hld.depthof(v);- 葉?bool b=hld.isleaf(v);- 行きがけ順の頂点列vpll vp=hld.preorder();for (auto&&[v,p]:vp){for (ll u:to[v]){if (u==p)continue;//}}- LCAll a=hld.lca(u,v);- k個上の親頂点 なければ-1ll u=hld.jump(v,k);- 距離ll d=hld.dist(u,v);- ID列上の重パス列挙 [stID0,enID0],[stID1,enID1],…vpll hs=hld.heavypaths();- パスu→vを重パス分解 [uID,enID0],[stID1,enID1],…,[stID*,vID]. u→vの順のためstID>enIDもありvpll hs=hld.uv2idranges(u,v);vpll hs=hld.uv2idranges(u,v,true); //辺の値を乗せる時(LCA含まない)- パスu→vの頂点列vll path=hld.path(u,v);- ID列上のサブ木範囲auto[l,r]=hld.subtree2idrange(v);*/struct binarytrie{struct node{ll nm;node *c[2];//vll accept;node():nm(0),c{nullptr,nullptr} {}};ll B=59;//ビット数-1(第Bビットが最上位bit)node *root=nullptr;binarytrie(){}binarytrie(ll B_){ init(B_); }void init(ll B_){ B=B_-1; root=NewNode(); }ll size(){ return root->nm; }//要素数bool empty(){ return root->nm==0; }void insert(ll x,ll delta=1,ll idx=-1){ assert(IsIn(x)); Add(root,x,idx,B,delta); }void erase(ll x){ insert(x,-1); }bool contains(ll x){ return (*this)[x]>0; }ll rank(ll x,ll xorval=0){return leftnumof(x-1,xorval)+1;} //xの順位(昇順) 1-originll rrank(ll x,ll xorval=0){return rightnumof(x+1,xorval)+1;}//xの順位(降順) 1-originll leftnumof(ll x,ll xorval=0){ //x以下の個数if (x<0) return 0;if (x+1 >= 1LL<<B<<1) return size();return CountLess(root,x+1,B,xorval);}ll rightnumof(ll x,ll xorval=0){ //x以上の個数if (x<=0) return size();if (x >= 1LL<<B<<1) return 0;return size()-CountLess(root,x,B,xorval); }ll operator[](ll x) { node *v=find(x); return v?v->nm:0; }//xの個数ll min(ll xorval=0){ assert(!empty()); return nthsmall(1,xorval); }//最小値ll max(ll xorval=0){ assert(!empty()); return nthbig(1,xorval); }//最大値ll nthsmall(ll r,ll xorval=0){return nthnode(r,xorval).first;}//r番目(昇順) 1-originll nthbig(ll r,ll xorval=0){return nthnode(size()+1-r,xorval).first;}//r番目(降順) 1-originnode *find(ll x){ return IsIn(x) ? Find(root,x,B) : nullptr; }//なければnullptrpair<ll,node*> nthnode(ll r,ll xorval=0){//r番目(昇順)の要素とnode 1-originif (r<=0)return{-INF,nullptr};if (r>root->nm)return{INF,nullptr};return NthNode(root,r-1,B,xorval);}void Add(node *v,ll x,ll idx,ll depth,ll delta){if (depth==-1){//if (idx>=0)t->accept.push_back(idx);}else{node *&c = v->c[(x>>depth)&1];if (!c) c=NewNode();Add(c,x,idx,depth-1,delta);}v->nm+=delta; assert(v->nm>=0);}node *Find(node *v,ll x,ll depth){if (depth==-1) return v;node *c = v->c[(x>>depth)&1];return c ? Find(c,x,depth-1) : nullptr;}pair<ll,node*> NthNode(node *v,ll r,ll depth,ll xorval){//サブ木v内r番目の要素 0-originif (depth==-1) return{0,v};bool f=(xorval>>depth)&1;ll cnm = v->c[f] ? v->c[f]->nm : 0;if (cnm<=r){auto ret=NthNode(v->c[f^1],r-cnm,depth-1,xorval);ret.first|=1LL<<depth;return ret;}else return NthNode(v->c[f],r,depth-1,xorval);}ll CountLess(node *v,ll x,ll depth,ll xorval){//サブ木v内x未満個数if (depth==-1)return 0;ll ret=0;bool f=(xorval>>depth)&1, g=(x>>depth)&1;if (g && v->c[f]) ret+=v->c[f]->nm;if (v->c[f^g]) ret+=CountLess(v->c[f^g],x,depth-1,xorval);return ret;}bool IsIn(ll x){ return 0<=x && x<(1LL<<B<<1); }#if defined(MYLOCAL)//メモリ管理有vector<node*> buf;node *NewNode(){ buf.push_back(new node()); return buf.back(); }~binarytrie(){ for (node *p:buf) delete p; }#else//メモリ管理無node *NewNode(){ return new node(); }#endifvoid dump(){ for(int r=1;r<=size();r++)cerr<<nthsmall(r)<<' '; cerr<<'\n'; }};/*binarytrie bt(n); //0≦x<2^nならnをセットll s=bt.size();bool b=bt.empty();bt.insert(x); //xを1つ挿入bt.insert(x,nm); //xをnm個挿入bt.erase(x); //xを1つ削除bool b=bt.contains(x); //x∈集合ならtruell r=bt.rank(x); //xの順位(昇順) 1-originll r=bt.rank(x,xorval); //xの順位(昇順) 1-origin (集合にxorvalをかけた時)ll r=bt.rrank(x); //xの順位(降順) 1-originll r=bt.rrank(x,xorval); //xの順位(降順) 1-origin (集合にxorvalをかけた時)ll nm=bt.leftnumof(x); //x以下の個数ll nm=bt.leftnumof(x,xorval); //x以下の個数 (集合にxorvalをかけた時)ll nm=bt.rightnumof(x); //x以上の個数ll nm=bt.rightnumof(x,xorval); //x以上の個数 (集合にxorvalをかけた時)ll nm=bt[x]; //xの個数ll x=bt.min(); //最小値ll x=bt.min(xorval); //最小値 (集合にxorvalをかけた時の最小値。xorがかかったものを返す)ll x=bt.max(); //最大値ll x=bt.max(xorval); //最大値 (集合にxorvalをかけた時の最大値。xorがかかったものを返す)ll x=bt.nthsmall(r); //r番目の要素(昇順) 1-origin ない時はINFll x=bt.nthsmall(r,xorval); // 〃 (集合にxorvalをかけた時)ll x=bt.nthbig(r); //r番目の要素(降順) 1-origin ない時は-INFll x=bt.nthbig(r,xorval); // 〃 (集合にxorvalをかけた時)*/template<class T,class Ope,class F> struct dynamicSegTree{using Int=long long;using ll=long long;using cT= const T;Ope ope;F f;T e;ll B;//ビット数int rootid=-1;ll offset,offsetOrg;struct Node{T x;array<int,2> cids={-1,-1};Node(T e):x(e){}ll nChild()const{ return 2-(cids[0]==-1)-(cids[1]==-1); }};vector<Node> pool;dynamicSegTree(T,Int B,T e,Ope ope,F f,Int offset=0) //B:ビット数:ope(ope),f(f),e(e),B(B),offset(offset),offsetOrg(offset){rootid=newNode();}void clear(){pool.clear();rootid=newNode();offset=offsetOrg;}ll imin()const{ return offset; }ll imax()const{ return (1LL<<B)-1+offset; }void set(ll i,cT &x){ apply(i,x,[](cT &va,cT &x){ return x; }); }//a[i]←xtemplate<class E> void apply(ll i,const E &y){ apply(i,y,f); }//a[i]←f(a[i],y)template<class E,class G> void apply(ll i,const E &y,G g){//a[i]←g(a[i],y)assert(IsIn(i));Apply(rootid,i-offset,B,y,g);}T operator[](ll i)const{ return prod(i,i); }T get(ll i)const{ return prod(i,i); }T prod(ll l,ll r)const{l=clamp(l-offset,0LL,1LL<<B);r=clamp(r-offset,-1LL,(1LL<<B)-1);if(r<l) return e;return Prod(l,r,rootid,B);}T allprod()const{ return Val(rootid); }/*isOK([l,r])==trueとなる最右のrを得る l○→○→ⓡ×××××rmx存在しないときmax(l,offset)未満の値を返す要件:isOK(e)==true*/template<class IsOK> ll maxRight(ll l,ll rmx,IsOK isOK)const{assert(isOK(e));auto [pos,ignore]=SearchR(normalizeL(l),rootid,0,1LL<<B,B,e,isOK,true);return min(pos-1,normalizeR(rmx))+offset;}/*isOK([l,r])==trueとなる最左のrを得る l×→×→×ⓡ○○○○rmx存在しないときmin(rmx,2^B-1+offset)超の値を返す要件:isOK(e)==false*/template<class IsOK> ll minRight(ll l,ll rmx,IsOK isOK)const{assert(!isOK(e));auto [pos,ignore]=SearchR(normalizeL(l),rootid,0,1LL<<B,B,e,isOK,false);return min(pos,normalizeR(rmx)+1)+offset;}/*isOK([l,r])==trueとなる最左のlを得る lmn××××ⓛ←○←○r存在しないとき min(r,2^B-1+offset)超の値を返す要件:isOK(e)==true*/template<class IsOK> ll minLeft(ll lmn,ll r,IsOK isOK)const{assert(isOK(e));auto [pos,ignore]=SearchL(normalizeR(r)+1,rootid,0,1LL<<B,B,e,isOK,true);return max(pos+1,normalizeL(lmn))+offset;}/*isOK([l,r])==trueとなる最右のlを得る lmn○○○ⓛ×←×←×r存在しないとき max(lmn,offset)未満の値を返す要件:isOK(e)==false*/template<class IsOK> ll maxLeft(ll lmn,ll r,IsOK isOK)const{assert(!isOK(e));auto [pos,ignore]=SearchL(normalizeR(r)+1,rootid,0,1LL<<B,B,e,isOK,false);return max(pos,normalizeL(lmn)-1)+offset;}vector<pair<ll,T>> enumerate()const{vector<pair<ll,T>> ret;auto dfs=[&](auto dfs,int id,ll i,ll d)->void{//ノードid(第d bit,開始位置i)内を列挙while(node(id).nChild()==1){ll bit=node(id).cids[1]!=-1;id=node(id).cids[bit];i|=bit<<(d-1);d--;}if(node(id).nChild()==0){ret.emplace_back(i+offset,node(id).x);}else{for(ll bit=0;bit<=1;++bit){dfs(dfs,node(id).cids[bit],i|(bit<<(d-1)),d-1);}}};dfs(dfs,rootid,0,B);return ret;}vector<T> tov()const{vector<T> ret;for(ll i=0;i<1LL<<B;++i) ret.push_back(get(i+offset));return ret;}private:int newNode(){ pool.emplace_back(e); return (int)pool.size()-1; }Node &node(int id){ return pool[id]; }const Node &node(int id)const{ return pool[id]; }cT& Val(int id)const{ return id==-1 ? e : node(id).x; }bool IsIn(ll i)const{ return imin()<=i && i<=imax(); }ll normalizeL(ll l)const{ return clamp(l-offset,0LL,1LL<<B); }ll normalizeR(ll r)const{ return clamp(r-offset,-1LL,(1LL<<B)-1); }/* 第dビットに相当するノードidのapply処理 */template<class E,class G> cT &Apply(int id,ll i,ll d,const E &y,G g){if(d==0) return node(id).x = g(node(id).x,y); //葉のときelse{ //葉以外のとき//子を再帰的に更新int cid=node(id).cids[(i>>(d-1))&1];if(cid==-1) cid=node(id).cids[(i>>(d-1))&1]=newNode();//node実体の再配置に注意cT &cx=Apply(cid,i,d-1,y,g);//自身の値を更新Node &v=node(id);#if 0if(v.cids[0]==-1) v.x=node(v.cids[1]).x;else if(v.cids[1]==-1) v.x=node(v.cids[0]).x;else v.x=ope(node(v.cids[0]).x,node(v.cids[1]).x);#elif 0T x0 = (v.cids[0]==-1) ? e : node(v.cids[0]).x;T x1 = (v.cids[1]==-1) ? e : node(v.cids[1]).x;v.x=ope(x0,x1);#elseif(v.cids[0]==-1 || v.cids[1]==-1) return v.x=cx;else return v.x=ope(node(v.cids[0]).x,node(v.cids[1]).x);#endif}}/*!第dビットに相当するノードid内部の[l,r]の値を得る要件 (1)ノードidは[l,r]を中に含む (2)l≦r*/T Prod(ll l,ll r,int id,ll d)const{if(id==-1) return e;//ノード未生成時const Node &v=node(id);if(d==0) return v.x; //葉のときif(((r>>(d-1))&1)==0) return Prod(l,r,v.cids[0],d-1);//左のみelse if(((l>>(d-1))&1)==1) return Prod(l,r,v.cids[1],d-1);//右のみelse if(IsLEdge(l,d) && IsREdge(r,d)) return v.x;//全区間else{//左右T lx=Prod(l,l|mask(d-2),v.cids[0],d-1);T rx=Prod(r&~mask(d-2),r,v.cids[1],d-1);return ope(lx,rx);}}/*isOKがlに近いとき×、遠いとき○の場合、ノードid内部で、位置l以降で[l,pos]が初めて○になるposと[l,pos-1]の値prdを得る(isOKの○×が反対の場合はその逆)@return <pos,prd> pos==en:ノードid内に○がない*/template<class IsOK> pair<ll,T> SearchR(ll l,int id,ll st,ll en,ll d,//ノードidは区間[st,en)で第dビットに対応T prePrd,//[l,st)の値 st<=lならeIsOK isOK,bool b //b=true:isOKの○×が反対(近いとき○、遠いとき×))const{if(id==-1) return {en,prePrd};//ノード未作成のとき prdは変化しない→必ずall×const Node &v=node(id);//ノードがlより左のときif(en<=l) return {en,e};//ノードが丸ごとl以降かつall×のときif(T prd=ope(prePrd,v.x); l<=st && isOK(prd)==b) return {en,prd};//葉のとき(○であることは上で確定済み)if(d==0) return {st,prePrd};//それ以外ならノードがlかposをまたぐ→分割して再帰ll md = st | 1LL<<(d-1);ll pos; T prd=prePrd; tie(pos,prd)=SearchR(l,v.cids[0],st,md,d-1,prd,isOK,b);if(pos==md) tie(pos,prd)=SearchR(l,v.cids[1],md,en,d-1,prd,isOK,b);return {pos,prd};}/*isOKがrに近いとき×、遠いとき○の場合、ノードid内部で、位置r未満で[pos,r)が初めて○になるposと[pos+1,r)の値prdを得る(isOKの○×が反対の場合はその逆)@return <pos,prd> pos==st-1:ノードid内に○がない*/template<class IsOK> pair<ll,T> SearchL(ll r,int id,ll st,ll en,ll d,//ノードidは区間[st,en)で第dビットに対応T prePrd,//[en,r)の値 r<=enならeIsOK isOK,bool b //b=true:isOKの○×が反対(近いとき○、遠いとき×))const{if(id==-1) return {st-1,prePrd};//ノード未作成のとき prdは変化しない→必ずall×const Node &v=node(id);//ノードがrより右のときif(r<=st) return {st-1,e};//ノードが丸ごとr未満かつall×のときif(T prd=ope(v.x,prePrd); en<=r && isOK(prd)==b) return {st-1,prd};//葉のとき(○であることは上で確定済み)if(d==0) return {st,prePrd};//それ以外ならノードがrかposをまたぐ→分割して再帰ll md = st | 1LL<<(d-1);ll pos; T prd=prePrd; tie(pos,prd)=SearchL(r,v.cids[1],md,en,d-1,prd,isOK,b);if(pos==md-1) tie(pos,prd)=SearchL(r,v.cids[0],st,md,d-1,prd,isOK,b);return {pos,prd};}static bool IsLEdge(ll l,ll d){ return (l&mask(d-1))==0; }//true:lがノード内なら左端static bool IsREdge(ll r,ll d){ return(~r&mask(d-1))==0; }//true:rがノード内なら右端static ll mask(ll depth){ return (1LL<<(depth+1))-1; }//第depthビット以下all1};/*offset、Nは広めにとる(広くしてもほとんど処理時間変わらない)- 定義dynamicSegTree dsg(ll(),B,-INF,ope,[](ll x,ll y){return y;});//一点代入、区間maxvpll ixs=enumerate(); //葉を位置昇順に列挙 {<位置i,値x>,…}*/struct binarytrieMultiset: public dynamicSegTree<long long,plus<long long>,plus<long long>>{using Int=long long;using ll=long long;binarytrieMultiset(Int B,Int offset=0):dynamicSegTree(ll(),B,0,plus<ll>(),plus<ll>(),offset){}ll size()const{ return allprod(); }bool empty()const{ return allprod()==0; }void insert(ll x,ll nm=1){ apply(x,nm); }void erase(ll x,ll nm=1){ apply(x,-nm); }bool contains(ll x)const{ return get(x)>0; }ll min()const{ return nthsmall(0); }ll max()const{ return nthbig(0); }ll leftcount(ll x)const{ return prod(imin(),x); }ll rightcount(ll x)const{ return prod(x,imax()); }ll operator[](ll x)const{ return get(x); }ll nthsmall(ll r)const{return minRight(imin(),imax(),[&](ll cmx){return cmx>=r+1;});}ll nthbig(ll r)const{return maxLeft(imin(),imax(),[&](ll cmx){return cmx>=r+1;});}void shift(ll x){ offset+=x; }void merge(binarytrieMultiset &b){if(size()<b.size()) swap(*this,b);vector<pair<ll,ll>> xs=b.enumerate();for(auto&&[x,nm]:xs) insert(x,nm);b.clear();}void dump()const{vpll b;for(ll r=0;r<size();){ll x=nthsmall(r);ll nm=(*this)[x];b.emplace_back(x,nm);r+=nm;}cerr<<"---\n";for(auto&&[x,ct]:b) cerr<<x<<' '<<ct<<endl;cerr<<"---\n";}};/*binarytrieMultiset btm(B); //要素値の範囲 0 ~ 2^B-1binarytrieMultiset btm(B,-10000); //要素値の範囲 -10000 ~ -10000+2^B-1ll s=btm.size(); //要素数bool btm.empty();btm.clear();btm.insert(x); //xを1つ追加btm.insert(x,nm); //xをnm個追加btm.erase(x); //xを1つ削除btm.erase(x,nm); //xをnm個削除bool b=btm.contains(x); //true:x∈集合ll nm=btm.leftcount(x); //x以下の個数ll nm=btm.rightcount(x); //x以上の個数ll nm=btm[x]; //xの個数ll x=btm.min(); //最小値 ないときはbtm.imax()+1を返すll x=btm.max(); //最大値 ないときはbtm.imin()-1を返すll x=btm.nthsmall(r); //昇順r番目の値 0-origin ないときはbtm.imax()+1を返すll x=btm.nthbig(r); //降順r番目の値 0-origin ないときはbtm.imin()-1を返すbtm.shift(x); //全要素にx加算btm.merge(btm2); //btmにbtm2をマージ btm2は空になるvpll xs=btm.enumerate(); //x昇順に列挙 {<要素x,個数ct>,…}*/void cin2solve(){auto N=cin1<ll>();auto uv=cinv<pair<ll,ll>>(N-1);for(auto&&[u,v]:uv) u--,v--;auto S_=cin1<string>();vll S=str2num(S_,'0',"");S*=2; S--;auto makeGraph=[](ll n,vector<pair<ll,ll>> &ab,bool isDirected){vvll to(n);for(auto [a,b]:ab){to[a].push_back(b);if(!isDirected) to[b].push_back(a);}return to;};vvll to=makeGraph(N,uv,false);HeavyLightDecomposition hld(to);if(N==1){cout << S_[0] << '\n'; return;}Vector dp(N,binarytrieMultiset(bll(2*N+10).msbit()+1,-N));auto overnmget=[&](binarytrieMultiset &b,ll x){return b.rightcount(x);};ll ans=0;vpll vp=hld.preorder().reverse();for (auto&&[v,p]:vp){if(hld.isleaf(v)){dp[v].insert(S[v]);if(S[v]==1) ans++;}else{vll us;for(ll u:to[v]){if(u==p)continue;us.push_back(u);}ll U=sz(us);us.sort([&](ll u,ll uu){return hld.subszof(u)>hld.subszof(uu);});//vが片端のパスをカウントif(S[v]==1) ans++;for(auto&& u: us){binarytrieMultiset &b =dp[u];ll overnm=overnmget(b,-S[v]+1);ans+=overnm;}//us[0]に集約しながら、異なる子をまたぐパスをカウントrep(i,1,U-1){ll u=us[0];ll uu=us[i];binarytrieMultiset &b =dp[u];binarytrieMultiset &bb=dp[uu];vpll bf=bb.enumerate();bb.clear();//まずカウントfor(auto&&[x,nm]:bf){ll va=x+S[v];ll overnm=overnmget(b,-va+1);ans+=nm*overnm;}//集約for(auto&&[x,nm]:bf) b.insert(x,nm);}//vへmove,vを追加{ll u=us[0];dp[v]=move(dp[u]);dp[v].shift(S[v]);dp[v].insert(S[v]);}}}cout << ans << '\n';return;}};//SolvingSpace//////////////////////////////////////////int main(){#if 1//SolvingSpace::labo();SolvingSpace::cin2solve();//SolvingSpace::generand();#elsell t; cin >> t;rep(i,0,t-1){SolvingSpace::cin2solve();//SolvingSpace::generand();}#endifcerr << timeget() <<"ms"<< '\n';return 0;}