/*
Author: Nguyen Chi Thanh - High School for the Gifted - VNU.HCM (i2528)
*/
#include <bits/stdc++.h>
using namespace std;
/* START OF TEMPALTE */
// #define int long long
#define ll long long
#define ull unsigned long long
#define ld long double
#define pii pair<int, int>
#define pll pair<ll, ll>
#define fi first
#define se second
#define popcount __builtin_popcountll
#define all(x) (x).begin(), (x).end()
#define BIT(x, i) (((x) >> (i)) & 1)
#define MASK(x) (1ll << (x))
#define SZ(a) ((int32_t)a.size())
#define debug(a, l, r) {for (int _i = (l); _i <= (r); ++_i) cout << (a)[_i] << ' '; cout << '\n';}
template<class X, class Y>
bool minimize(X &x, const Y &y) {
if (x > y) {
x = y;
return true;
} else return false;
}
template<class X, class Y>
bool maximize(X &x, const Y &y) {
if (x < y) {
x = y;
return true;
} else return false;
}
/* END OF TEMPALTE */
const ll INF = (ll)1e18 + 5;
struct Line {
ll a, b;
Line(ll _a = 0, ll _b = INF) : a(_a), b(_b) {}
ll get(ll x) const { return a * x + b; }
};
ll ceil_div(ll a, ll b) {
assert(b > 0);
if (a >= 0) return (a + b - 1) / b;
return a / b;
}
struct RollbackCHT {
struct State {
int old_top, pos;
Line old_line;
ll old_start;
bool overwritten;
};
vector<Line> hull;
vector<ll> start;
vector<State> history;
int top;
RollbackCHT() {
hull.assign(1, Line());
start.assign(1, -INF);
top = 0;
}
int checkpoint() {
return (int)history.size();
}
void rollback(int snap) {
while ((int)history.size() > snap) {
State cur = history.back();
history.pop_back();
if (cur.overwritten) {
hull[cur.pos] = cur.old_line;
start[cur.pos] = cur.old_start;
}
top = cur.old_top;
}
}
ll first_better(const Line &old, const Line &nw) {
return ceil_div(nw.b - old.b, old.a - nw.a);
}
bool keep_pos(int pos, const Line &nw) {
if (pos == 1) return true;
return hull[pos].get(start[pos]) < nw.get(start[pos]);
}
void add_line(Line nw) {
if (top == 0) {
history.push_back({top, 1, Line(), 0, false});
if ((int)hull.size() <= 1) {
hull.push_back(nw);
start.push_back(-INF);
} else {
hull[1] = nw;
start[1] = -INF;
}
top = 1;
return;
}
int l = 1, r = top, ans = 1;
while (l <= r) {
int mid = (l + r) >> 1;
if (keep_pos(mid, nw)) {
ans = mid;
l = mid + 1;
} else r = mid - 1;
}
int pos = ans + 1;
ll st = first_better(hull[ans], nw);
State cur;
cur.old_top = top;
cur.pos = pos;
cur.overwritten = (pos <= top);
if (cur.overwritten) {
cur.old_line = hull[pos];
cur.old_start = start[pos];
}
history.push_back(cur);
if ((int)hull.size() <= pos) {
hull.push_back(nw);
start.push_back(st);
} else {
hull[pos] = nw;
start[pos] = st;
}
top = pos;
}
ll query(ll x) {
int l = 1, r = top, ans = 1;
while (l <= r) {
int mid = (l + r) >> 1;
if (start[mid] <= x) {
ans = mid;
l = mid + 1;
} else r = mid - 1;
}
return hull[ans].get(x);
}
};
const int MAXN = 1e5 + 5;
int n, s[MAXN], v[MAXN], parent[MAXN];
ll dp[MAXN], distToRoot[MAXN];
vector<pii> adj[MAXN];
RollbackCHT cht;
void init() {
cin >> n;
for (int i = 1; i < n; ++i) {
int u, v, w; cin >> u >> v >> w;
adj[u].push_back({v, w});
adj[v].push_back({u, w});
}
for (int i = 2; i <= n; ++i) {
cin >> s[i] >> v[i];
}
cht.add_line(Line(0, 0));
}
void dfsPrepare(int u, int par = 0) {
parent[u] = par;
for (auto &e : adj[u]) {
int v = e.fi, w = e.se;
if (v == par) continue;
distToRoot[v] = distToRoot[u] + w;
dfsPrepare(v, u);
}
}
void dfsDP(int u, int par = 0) {
int snapshot = cht.checkpoint();
if (u != 1) {
// int pre = parent[u];
// while (pre) {
// minimize(dp[u], s[u] + 1ll * v[u] * (distToRoot[u] - distToRoot[pre]) + dp[pre]);
// // s[u] + v[u] * distToRoot[u] (fixed)
// // -distToRoot[pre] * v[u] + dp[pre]
// pre = parent[pre];
// }
dp[u] = s[u] + 1ll * v[u] * distToRoot[u] + cht.query(v[u]);
cht.add_line(Line(-distToRoot[u], dp[u]));
}
for (auto &e : adj[u]) {
int v = e.fi;
if (v == par) continue;
dfsDP(v, u);
}
cht.rollback(snapshot);
}
void solve() {
dfsPrepare(1);
fill(dp + 1, dp + n + 1, INF);
dp[1] = 0;
dfsDP(1);
for (int i = 2; i <= n; ++i)
cout << dp[i] << ' ';
}
signed main() {
#ifdef NCTHANH
freopen("input.txt", "r", stdin);
freopen("output.txt", "w", stdout);
#endif
ios_base::sync_with_stdio(0);
cin.tie(nullptr); cout.tie(nullptr);
init();
solve();
return 0;
}
