#include <bits/stdc++.h>
using namespace std;
//long long MOD = 1e9 + 7;
const long long MOD = 998244353;
// const long long MOD = 100000007 ;
#define fast ios_base::sync_with_stdio(0);cin.tie(0);cout.tie(0)
#define popCnt(x) (__builtin_popcountll(x))
#define int long long
#define ld long double
#define F first
#define S second
#define pi M_PI
#define all(x) x.begin() , x.end()
#define ll long long
#define SZ(v) (int)(v.size())
int dx[] = {1, -1, 0, 0};
int dy[] = {0, 0, 1, -1};
const long long OO = LLONG_MAX / 4, N = 1e9 + 5, M = 1e5 + 5, K = 505;
// A line: y = m * x + c
struct Line {
ll m, c;
Line(ll _m = 0, ll _c = OO) : m(_m), c(_c) {}
// safe evaluation using __int128 and clamp to avoid undefined behavior
ll eval(ll x) const {
__int128 val = (__int128)m * (__int128)x + (__int128)c;
if (val > ( (__int128)LLONG_MAX / 2 )) return LLONG_MAX;
if (val < ( (__int128)LLONG_MIN / 2 )) return LLONG_MIN;
return (ll)val;
}
ll operator()(ll x) const { return eval(x); }
};
struct Node {
Line line;
Node* left = nullptr;
Node* right = nullptr;
Node(const Line &L = Line()) : line(L) {}
};
// change record (either pointer change or a line content change)
struct Change {
bool isLineChange;
// pointer change:
Node** ptrAddr = nullptr;
Node* oldPtr = nullptr;
// line change:
Node* node = nullptr;
Line oldLine;
// constructors
Change(Node** p, Node* old) : isLineChange(false), ptrAddr(p), oldPtr(old) {}
Change(Node* nd, const Line &oldL) : isLineChange(true), node(nd), oldLine(oldL) {}
};
vector<Change> changeLog;
vector<int> insertCheckpoints;
// record pointer change (address of the Node* variable and its old value)
inline void record_ptr(Node*& p) {
changeLog.emplace_back(&p, p);
}
// record a node->line change
inline void record_line(Node* node) {
changeLog.emplace_back(node, node->line);
}
void rollbackTo(int checkpoint) {
while ((int)changeLog.size() > checkpoint) {
Change ch = changeLog.back();
changeLog.pop_back();
if (!ch.isLineChange) {
// pointer change: restore pointer
*ch.ptrAddr = ch.oldPtr;
} else {
// line change: restore node->line
ch.node->line = ch.oldLine;
}
}
}
void rollbackLastInsert() {
if (!insertCheckpoints.empty()) {
rollbackTo(insertCheckpoints.back());
insertCheckpoints.pop_back();
}
}
// Insert implementation (min Li Chao)
void insert_impl(Line newLine, Node*& root, ll l, ll r) {
if (!root) {
record_ptr(root); // record change to this pointer
root = new Node(newLine);
return;
}
ll m = (l + r) / 2;
bool lef = newLine.eval(l) < root->line.eval(l);
bool mid = newLine.eval(m) < root->line.eval(m);
if (mid) {
record_line(root); // record old line BEFORE swapping
swap(root->line, newLine);
}
if (r - l == 1) return;
if (lef != mid) insert_impl(newLine, root->left, l, m);
else insert_impl(newLine, root->right, m, r);
}
// Public API for tracked insertion
void insert(Line newLine, Node*& root, ll l = -N, ll r = +N) {
insertCheckpoints.push_back((int)changeLog.size());
insert_impl(newLine, root, l, r);
}
// query min at x
ll query(ll x, Node* root, ll l = -N, ll r = +N) {
if (!root) return OO;
ll m = (l + r) / 2;
ll res = root->line.eval(x);
if (r - l == 1) return res;
if (x < m) return min(res, query(x, root->left, l, m));
else return min(res, query(x, root->right, m, r));
}
Node *root = nullptr;
int n;
vector<int> v, c;
vector<vector<pair<int, int>>> adj;
vector<int> dp;
void dfs(int node , int p = -1 , int d = 0)
{
if(p == -1) dp[node] = 0;
else dp[node] = query(v[node] , root) + v[node] * d + c[node];
insert(Line(-d , dp[node]) , root);
for(auto [child , len] : adj[node])
{
if(child == p)continue;
dfs(child , node , d + len);
}
rollbackLastInsert();
}
signed main() {
fast;
// freopen("in.txt", "r", stdin);
// freopen("out.txt", "w", stdout);
cin >> n;
dp = v = c = vector<int>(n);
adj.resize(n);
for (int i = 0; i < n - 1; ++i) {
int u, vv, d;
cin >> u >> vv >> d;
u--;
vv--;
adj[u].emplace_back(vv, d);
adj[vv].emplace_back(u, d);
}
for (int i = 1; i < n; ++i) {
cin >> c[i] >> v[i];
}
dfs(0);
for(int i = 1 ; i < n ; i++) cout << dp[i] << " ";
cout<<'\n';
}
