#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 = 3e5 + 5, M = 1e5 + 5, K = 505;
using ll = long long;
const long double NINF = -1e300L;
const long double PINF = 1e300L;
struct Line {
ll a, b; // y = a*x + b
Line(ll a = 0, ll b = LLONG_MIN) : a(a), b(b) {}
inline ll eval(ll x) const { return a * x + b; }
};
struct Op {
bool added; // whether we actually added a line
vector<Line> removed_lines; // lines removed from the back while adding
vector<long double> removed_xs; // their associated intersection x-values
};
struct RollbackableCHT {
// lines[i] is active line for interval x >= xs[i]
vector<Line> lines;
vector<long double> xs; // xs[0] = -inf
vector<Op> ops; // operation log for rollback
// compute intersection x-coordinate where line l becomes better than r
long double inter(const Line &l, const Line &r) {
if (l.a == r.a) {
// parallel lines: whichever has larger intercept wins everywhere
return (l.b > r.b) ? PINF : NINF; // if l better => +inf (l dominates to +inf)
}
return (long double)(r.b - l.b) / (long double)(l.a - r.a);
}
void clear() { lines.clear(); xs.clear(); ops.clear(); }
// add line with slope strictly greater than previous line's slope
void add_line(const Line &ln) {
Op op;
op.added = true;
if (lines.empty()) {
// first line
lines.push_back(ln);
xs.push_back(NINF);
ops.push_back(std::move(op));
return;
}
// equal slope handling: if new line is never better, do nothing.
if (ln.a == lines.back().a) {
if (ln.b <= lines.back().b) {
// new line worse or equal: record no-op so rollback matches calls
op.added = false;
ops.push_back(std::move(op));
return;
} else {
// new line strictly better: remove last line (store it)
op.removed_lines.push_back(lines.back());
op.removed_xs.push_back(xs.back());
lines.pop_back();
xs.pop_back();
if (lines.empty()) {
lines.push_back(ln);
xs.push_back(NINF);
ops.push_back(std::move(op));
return;
}
}
}
// compute intersection with current back, and pop while intersection
// is <= previous intersection (meaning back is useless)
long double x = inter(lines.back(), ln);
while (!xs.empty() && x <= xs.back()) {
// remove the last line and record it
op.removed_lines.push_back(lines.back());
op.removed_xs.push_back(xs.back());
lines.pop_back();
xs.pop_back();
if (lines.empty()) break;
x = inter(lines.back(), ln);
}
// finally add new line; its valid region starts at x
lines.push_back(ln);
xs.push_back(x);
ops.push_back(std::move(op));
}
// query max at arbitrary x
ll query(ll x) const {
if (lines.empty()) return LLONG_MIN; // or some sentinel
// find last index i with xs[i] <= x
int l = 0, r = (int)xs.size()-1, ans = 0;
while (l <= r) {
int m = (l + r) >> 1;
if (xs[m] <= (long double)x) {
ans = m;
l = m + 1;
} else r = m - 1;
}
return lines[ans].eval(x);
}
// rollback last add_line() call
bool rollback() {
if (ops.empty()) return false;
Op op = std::move(ops.back());
ops.pop_back();
if (!op.added) {
// no-op add: nothing changed
return true;
}
// remove the line we added
if (!lines.empty()) {
lines.pop_back();
xs.pop_back();
}
// restore removed lines in reverse order
for (int i = (int)op.removed_lines.size() - 1; i >= 0; --i) {
lines.push_back(op.removed_lines[i]);
xs.push_back(op.removed_xs[i]);
}
return true;
}
};
RollbackableCHT cht;
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] = cht.query(v[node]) + v[node] * d + c[node];
cht.add_line(Line(-d , dp[node]));
for(auto [child , len] : adj[node])
{
if(child == p)continue;
dfs(child , node , d + len);
}
cht.rollback();
}
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';
}
