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>
using namespace std;
const int MN = 2e5 + 5;
#define lc ind<<1
#define rc ind<<1|1
struct Node { //range add, range set, some kind of walking
	long long mx,alz,slz;
	Node () {mx = alz = 0; slz = -1;}
} tree[MN << 2];
void push_down (int ind, int l, int r) {
	if (tree[ind].slz >= 0) {
		tree[ind].mx = tree[ind].slz;
		if (l != r) {
			tree[lc].slz = tree[rc].slz = tree[ind].slz;
			tree[lc].alz = tree[rc].alz = 0;
		}
		tree[ind].slz = -1;
	}
	if (tree[ind].alz) {
		tree[ind].mx += tree[ind].alz;
		if (l != r) {
			tree[lc].alz += tree[ind].alz;
			tree[rc].alz += tree[ind].alz;
		}
		tree[ind].alz = 0;
	}
}
void update (int ind, int tl, int tr, int l, int r, long long v) {
	push_down(ind,tl,tr);
	if (tl > r || tr < l) return;
	if (l <= tl && tr <= r) {
		tree[ind].alz += v;
		push_down(ind,tl,tr);
		return;
	}
	int mid = (tl + tr) / 2;
	update(lc,tl,mid,l,r,v); update(rc,mid+1,tr,l,r,v);
	tree[ind].mx = max(tree[lc].mx,tree[rc].mx);
}
void setv (int ind, int tl, int tr, int r, long long v) { //everything in [1,r] > v gets set to v
	push_down(ind,tl,tr);
	if (tree[ind].mx <= v) return;
	if (tl == tr) {
		tree[ind].mx = v; tree[ind].slz = -1; tree[ind].alz = 0;
		return;
	}
	int mid = (tl + tr) / 2;
	if (r <= mid) {
		push_down(rc,mid+1,tr);
		setv(lc,tl,mid,r,v);
	} else if (r < tr) {
		setv(lc,tl,mid,r,v); setv(rc,mid+1,tr,r,v);
	} else {
		push_down(lc,tl,mid);
		if (tree[lc].mx > v) {
			tree[rc].slz = v; tree[rc].alz = 0;
			push_down(rc,mid+1,tr);
			setv(lc,tl,mid,r,v);
		} else {
			push_down(lc,tl,mid); 
			setv(rc,mid+1,tr,r,v);
		}
	}
	tree[ind].mx = max(tree[lc].mx,tree[rc].mx);
}
long long query (int ind, int tl, int tr, int l, int r) {
	push_down(ind,tl,tr);
	if (tl > r || tr < l) return LLONG_MIN;
	if (l <= tl && tr <= r) return tree[ind].mx;
	int mid = (tl + tr) / 2;
	return max(query(lc,tl,mid,l,r),query(rc,mid+1,tr,l,r));
}
int a[MN], h[MN], c[MN], sz[MN], st[MN], ed[MN], at[MN], big[MN], tt;
vector<int> adj[MN], xs;
int getx (int x) {return lower_bound(xs.begin(),xs.end(),x) - xs.begin() + 1;}
void getsz (int cur) {
	sz[cur] = 1; st[cur] = ++tt; at[tt] = cur;
	for (int i : adj[cur]) {
		getsz(i);
		sz[cur] += sz[i];
		if (sz[i] > sz[big[cur]]) big[cur] = i;
	}
	ed[cur] = tt;
}
map<int,long long> dp[MN];
void dfs (int cur, bool del = true) {
	for (int i : adj[cur]) if (i != big[cur]) dfs(i,true);
	if (big[cur]) dfs(big[cur],false);
	for (int i : adj[cur]) if (i != big[cur]) {
		int lst = 1;
		for (auto [j,v] : dp[i]) {
			if (lst <= j) update(1,1,(int)xs.size(),lst,j,v);
			lst = j+1;
		}
	}
	update(1,1,(int)xs.size(),1,(int)xs.size(),c[cur]);
	//if (cur == 1) printf ("%lld\n",query(1,1,(int)xs.size(),h[cur],h[cur])-c[cur]);
	setv(1,1,(int)xs.size(),h[cur],query(1,1,(int)xs.size(),h[cur],h[cur])-c[cur]);
	//for (int i = 1; i <= (int)xs.size(); i++) printf ("dp[%d][%d] = %lld\n",cur,i,query(1,1,(int)xs.size(),i,i));
	if (del) {
		for (int j = st[cur]; j <= ed[cur]; j++) {
			int v = h[at[j]];
			if (!dp[cur].count(v)) dp[cur][v] = query(1,1,(int)xs.size(),v,v);
		}
		int v = (int)xs.size();
		if (!dp[cur].count(v)) dp[cur][v] = query(1,1,(int)xs.size(),v,v);
		tree[1].slz = tree[1].alz = 0;
	}
}
int main () {
	int n; scanf ("%d",&n);
	for (int i = 1; i <= n; i++) {
		scanf ("%d %d %d",&a[i],&h[i],&c[i]);
		xs.push_back(h[i]);
		if (i > 1) adj[a[i]].push_back(i);
	}
	sort(xs.begin(),xs.end()); xs.erase(unique(xs.begin(),xs.end()),xs.end());
	for (int i = 1; i <= n; i++) h[i] = getx(h[i]);
	getsz(1);
	dfs(1);
	long long ret = 1e18;
	for (auto [j,v] : dp[1]) ret = min(ret,v);
	printf ("%lld\n",ret);
	return 0;
}
Compilation message (stderr)
worst_reporter2.cpp: In function 'int main()':
worst_reporter2.cpp:111:15: warning: ignoring return value of 'int scanf(const char*, ...)', declared with attribute warn_unused_result [-Wunused-result]
  111 |  int n; scanf ("%d",&n);
      |         ~~~~~~^~~~~~~~~
worst_reporter2.cpp:113:9: warning: ignoring return value of 'int scanf(const char*, ...)', declared with attribute warn_unused_result [-Wunused-result]
  113 |   scanf ("%d %d %d",&a[i],&h[i],&c[i]);
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