This submission is migrated from previous version of oj.uz, which used different machine for grading. This submission may have different result if resubmitted.
#include <bits/stdc++.h>
#define MAX 105000
std::vector<int> con[MAX];
typedef std::pair<int,int> pii;
using ll = long long;
std::vector<pii> frutas[MAX];
int N,M,K;
typedef std::pair<int,ll> pil;
typedef std::pair<pil,int> ppi;
const int nodes = 2e7;
int left[nodes],right[nodes];
ll max[nodes],lazy[nodes];
int cur=3;
int aloca(){return cur++;}
class SparseTree {
public:
int inicio;
int size;
void iniciar(){
inicio=aloca();
size=0;
}
void propag(int pos){
max[pos]+=lazy[pos];
if(!left[pos])left[pos]=aloca();
lazy[left[pos]]+=lazy[pos];
if(!right[pos])right[pos]=aloca();
lazy[right[pos]]+=lazy[pos];
lazy[pos]=0;
}
ll query(int l,int r,int pos,int la=0,int ra=MAX-1){
propag(pos);
assert(pos);
if(la>r||ra<l)return 0;
if(la>=l&&ra<=r){
return max[pos];
}
int m = (la+ra)/2;
return std::max(query(l,r,left[pos],la,m),query(l,r,right[pos],m+1,ra));
}
void add(int l,int r,ll k,int pos,int la=0,int ra=MAX-1){
// std::cout<<"Envia "<<k<<"\n";
propag(pos);
assert(pos);
if(la>r||ra<l)return;
if(la>=l&&ra<=r){
lazy[pos]+=k;
propag(pos);
// std::cout<<"Somou "<<k<<"\n";
return;
}
int m = (la+ra)/2;
add(l,r,k,left[pos],la,m);
add(l,r,k,right[pos],m+1,ra);
max[pos]=std::max(max[left[pos]],max[right[pos]]);
//std::cout<<"Val:"<<max[pos]<<" "<<k<<"\n";
}
void add(int l,int r,ll k){
add(l,r,k,inicio);
}
ll query(int l,int r){
return query(l,r,inicio);
}
};
std::map<int,bool> acumulados[MAX];
SparseTree dfs(int pos){
SparseTree st;
st.iniciar();
st.size=1;
for(auto&x:con[pos]){
SparseTree res = dfs(x);
///Garante que st eh maior
if(res.size>st.size){std::swap(res,st);acumulados[pos].swap(acumulados[x]);}
st.size+=res.size;
std::vector<int> vals;
for(auto&y:acumulados[x]){
vals.push_back(y.first);
acumulados[pos][y.first]=1;
}
std::sort(vals.begin(),vals.end());
{
std::vector<int> garante;
ll best=0;
for(auto&x:vals){
ll as = res.query(x,x);
if(as>best){
best=as;
garante.push_back(x);
}
}
vals=garante;
}
std::reverse(vals.begin(),vals.end());
int last = MAX-50;
for(auto&y:vals){
ll val = res.query(y,y);
ll left = st.query(0,y);
// std::cout<<"Insere "<<left<<" "<<y<<"\n";
///right
st.add(y,last,val);
ll pos = st.query(y,y);
val+=left;
if(pos<val){
ll delta = val-pos;
st.add(y,y,delta);
}
last=y-1;
}
}
assert(frutas[pos].size()<=1);
for(auto&x:frutas[pos]){
int dia = x.first;
ll left = st.query(0,dia);
ll value = x.second+left;
ll prev = st.query(dia,dia);
// std::cout<<"add "<<dia<<" "<<left<<" "<<value<<" "<<prev<<"\n";
if(prev<value){
ll delta = value-prev;
st.add(dia,dia,delta);
}
acumulados[pos][dia]=1;
++st.size;
}
// std::cout<<"Respostas "<<pos<<"\n";
// for(int i=0;i!=K;++i){
// std::cout<<st.query(i,i)<<"\n";
// }
return st;
}
int main(){
std::ios::sync_with_stdio(false);
std::cin.tie(0);
std::cout.tie(0);
std::cin>>N>>M>>K;
for(int i=1;i!=N;++i){
int a;
std::cin>>a;--a;
con[a].push_back(i);
}
for(int i=0;i!=M;++i){
int v,d,w;
std::cin>>v>>d>>w;--v;
std::sort(frutas[v].begin(),frutas[v].end());
frutas[v].push_back({d,w});
}
auto ans = dfs(0);
std::cout<<ans.query(0,K+5)<<"\n";
}
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