#include "dungeons.h"
#include <vector>
#ifndef LOCAL
#pragma GCC optimize ("Ofast")
#pragma GCC optimize ("unroll-loops")
#endif
#include <bits/stdc++.h>
using namespace std;
using ll=long long;
//#define int ll
#define rng(i,a,b) for(int i=int(a);i<int(b);i++)
#define rep(i,b) rng(i,0,b)
#define gnr(i,a,b) for(int i=int(b)-1;i>=int(a);i--)
#define per(i,b) gnr(i,0,b)
#define pb push_back
#define eb emplace_back
#define a first
#define b second
#define bg begin()
#define ed end()
#define all(x) x.bg,x.ed
#define si(x) int(x.size())
#ifdef LOCAL
#define dmp(x) cerr<<__LINE__<<" "<<#x<<" "<<x<<endl
#else
#define dmp(x) void(0)
#endif
template<class t,class u> bool chmax(t&a,u b){if(a<b){a=b;return true;}else return false;}
template<class t,class u> bool chmin(t&a,u b){if(b<a){a=b;return true;}else return false;}
template<class t> using vc=vector<t>;
template<class t> using vvc=vc<vc<t>>;
using pi=pair<int,int>;
using vi=vc<int>;
template<class t,class u>
ostream& operator<<(ostream& os,const pair<t,u>& p){
return os<<"{"<<p.a<<","<<p.b<<"}";
}
template<class t> ostream& operator<<(ostream& os,const vc<t>& v){
os<<"{";
for(auto e:v)os<<e<<",";
return os<<"}";
}
#define mp make_pair
#define mt make_tuple
#define one(x) memset(x,-1,sizeof(x))
#define zero(x) memset(x,0,sizeof(x))
#ifdef LOCAL
void dmpr(ostream&os){os<<endl;}
template<class T,class... Args>
void dmpr(ostream&os,const T&t,const Args&... args){
os<<t<<" ";
dmpr(os,args...);
}
#define dmp2(...) dmpr(cerr,__LINE__,##__VA_ARGS__)
#else
#define dmp2(...) void(0)
#endif
using uint=unsigned;
using ull=unsigned long long;
template<class t,size_t n>
ostream& operator<<(ostream&os,const array<t,n>&a){
return os<<vc<t>(all(a));
}
template<int i,class T>
void print_tuple(ostream&,const T&){
}
template<int i,class T,class H,class ...Args>
void print_tuple(ostream&os,const T&t){
if(i)os<<",";
os<<get<i>(t);
print_tuple<i+1,T,Args...>(os,t);
}
template<class ...Args>
ostream& operator<<(ostream&os,const tuple<Args...>&t){
os<<"{";
print_tuple<0,tuple<Args...>,Args...>(os,t);
return os<<"}";
}
template<class t>
void print(t x,int suc=1){
cout<<x;
if(suc==1)
cout<<"\n";
if(suc==2)
cout<<" ";
}
ll read(){
ll i;
cin>>i;
return i;
}
vi readvi(int n,int off=0){
vi v(n);
rep(i,n)v[i]=read()+off;
return v;
}
pi readpi(int off=0){
int a,b;cin>>a>>b;
return pi(a+off,b+off);
}
template<class t,class u>
void print(const pair<t,u>&p,int suc=1){
print(p.a,2);
print(p.b,suc);
}
template<class T>
void print(const vector<T>&v,int suc=1){
rep(i,v.size())
print(v[i],i==int(v.size())-1?suc:2);
}
template<class T>
void print_offset(const vector<T>&v,ll off,int suc=1){
rep(i,v.size())
print(v[i]+off,i==int(v.size())-1?suc:2);
}
template<class T,size_t N>
void print(const array<T,N>&v,int suc=1){
rep(i,N)
print(v[i],i==int(N)-1?suc:2);
}
string readString(){
string s;
cin>>s;
return s;
}
template<class T>
T sq(const T& t){
return t*t;
}
//#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 botbit(signed a){
return a==0?32:__builtin_ctz(a);
}
int botbit(ll a){
return a==0?64:__builtin_ctzll(a);
}
int popcount(signed t){
return __builtin_popcount(t);
}
int popcount(ll t){
return __builtin_popcountll(t);
}
bool ispow2(int i){
return i&&(i&-i)==i;
}
ll mask(int i){
return (ll(1)<<i)-1;
}
bool inc(int a,int b,int c){
return a<=b&&b<=c;
}
template<class t> void mkuni(vc<t>&v){
sort(all(v));
v.erase(unique(all(v)),v.ed);
}
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);
}
template<class t>
void myshuffle(vc<t>&a){
rep(i,si(a))swap(a[i],a[rand_int(0,i)]);
}
template<class t>
int lwb(const vc<t>&v,const t&a){
return lower_bound(all(v),a)-v.bg;
}
vvc<int> readGraph(int n,int m){
vvc<int> g(n);
rep(i,m){
int a,b;
cin>>a>>b;
//sc.read(a,b);
a--;b--;
g[a].pb(b);
g[b].pb(a);
}
return g;
}
vvc<int> readTree(int n){
return readGraph(n,n-1);
}
#ifdef LOCAL
const int nmax=1000;
const int B=50;
#else
const int nmax=400000;
const int B=1000;
#endif
const int L=40;
const ll M=mask(L);
struct N{
ll sum;
int mn;
};
#ifdef LOCAL
vc<N> buf[nmax/B];
#else
N* buf[nmax/B];
#endif
//sum に変な情報をもたせていない
void mg(N&a,const N&b){
if(b.mn!=inf)
chmin(a.mn,max(b.mn-a.sum,0LL));
a.sum+=b.sum;
}
vi ls;
int n,to[nmax+1],gain[nmax+1],cap[nmax+1],dep[nmax+1];
void load2buf(int tar){
static int cnt[nmax+1],qbuf[nmax+1];
rep(i,n+1)cnt[i]=0;
rep(i,n+1)if(to[i]!=-1)cnt[to[i]]++;
int head=0;
rep(i,n+1)if(cnt[i]==0)qbuf[head++]=i;
rep(i,head){
int v=qbuf[i];
if(to[v]!=-1&&--cnt[to[v]]==0)
qbuf[head++]=to[v];
}
rep(i,n+1)if(cnt[i]){
int x=i,last=-1;
do{
assert(cnt[x]==1);
cnt[x]=0;
qbuf[head++]=x;
last=x;
x=to[x];
}while(x!=i);
to[last]=-1;
}
assert(head==n+1);
per(i,n+1){
int v=qbuf[i];
if(to[v]!=-1&&dep[to[v]]==B-1)to[v]=-1;
if(to[v]==-1){
buf[tar][v]={ll(v)<<L,inf};
dep[v]=0;
}else{
buf[tar][v].sum=buf[tar][to[v]].sum+gain[v];
int w=buf[tar][to[v]].mn;
buf[tar][v].mn=min(cap[v],w==inf?inf:max(w-gain[v],0));
dep[v]=dep[to[v]]+1;
}
}
}
int addup[nmax],addlw[nmax],goup[nmax],golw[nmax];
void init(int n_, std::vector<int> s, std::vector<int> p, std::vector<int> w, std::vector<int> l) {
n=n_;
#ifdef LOCAL
rep(i,nmax/B)buf[i].resize(n+1,{-infLL,-1});
#else
N*ptr=new N[(n+1)*(nmax/B)];
rep(i,nmax/B)buf[i]=ptr+i*(n+1);
#endif
ls=s;mkuni(ls);
for(int i=0;i<si(ls);i+=B){
int j=min(i+B,si(ls));
int lw=ls[i],up=ls[j-1];
rep(k,n){
if(inc(lw,s[k],up))to[k]=-1;
else if(s[k]<lw){
to[k]=w[k];
gain[k]=s[k];
cap[k]=inf;
}else{
to[k]=l[k];
gain[k]=p[k];
cap[k]=s[k];
}
}
to[n]=-1;
load2buf(i/B);
}
rep(i,n){
addup[i]=s[i];
addlw[i]=p[i];
goup[i]=w[i];
golw[i]=l[i];
}
}
int lastvis[nmax],pos[nmax],idx[nmax];
N work[nmax];
int curtime;
long long simulate(int x,int z_){
ll z=z_;
while(x!=n){
curtime++;
int tar=lower_bound(all(ls),z)-ls.bg;
if(tar==si(ls))tar--;
tar/=B;
ll ini=z;
auto advance=[&](){
while(1){
dmp(x);
assert(x!=n);
if(addup[x]<=ini){
dmp2(x,addup[x],ls[B],ini,goup[x]);
z+=addup[x];
x=goup[x];
}else if(z<addup[x]){
z+=addlw[x];
x=golw[x];
}else{
z+=addup[x];
x=goup[x];
break;
}
}
};
int s=0;
while(x!=n){
if(lastvis[x]==curtime){
int p=pos[x];
N cur={0,inf};
rng(i,p,s)mg(cur,work[i]);
if(cur.mn>z){
z+=(cur.mn-z+cur.sum-1)/cur.sum*cur.sum;
}
bool did=false;
rng(i,p,s){
if(work[i].mn>z){
z+=work[i].sum;
}else{
x=idx[i];
advance();
did=true;
break;
}
}
assert(did);
break;
}else{
lastvis[x]=curtime;
pos[x]=s++;
idx[s-1]=x;
work[s-1]=buf[tar][x];
int y=buf[tar][x].sum>>L;
work[s-1].sum&=M;
dmp(y);
if(y<n){
mg(work[s-1],addup[y]<=ini?N{addup[y],inf}:N{addlw[y],addup[y]});
y=addup[y]<=ini?goup[y]:golw[y];
}
if(work[s-1].mn<=z){
dmp(x);
dmp(y);
advance();
break;
}
z+=work[s-1].sum;
x=y;
}
}
}
return z;
}
