#include <bits/stdc++.h>
#define ll long long
using namespace std;
const ll N = 2e5+10, oo = 4e18;
vector<pair<int, int>> edges[N];
ll p[N], s[N], v[N], sum[N], dp[N], n;
void mini(ll &x, ll y) {
if(x > y) {
x = y;
}
}
struct line {
ll k, b;
line(ll _k, ll _b) : k(_k), b(_b) {}
line() : line(0, 4e18) {}
ll f(ll x) {
return k*x + b;
}
};
struct lichao {
vector<array<int, 2>> children;
vector<line> t;
stack<pair<int, line>> ops;
int nodes, size;
lichao(int _size = 1e9) {
size = _size;
nodes = 0;
create_node();
}
int create_node() {
children.push_back({-1, -1});
t.push_back(line());
return nodes++;
}
void rollback(int T) {
while((int)ops.size() > T) {
pair<int, line> p = ops.top(); ops.pop();
t[p.first] = p.second;
}
}
int add_line(ll l, ll r, line ln, int pos) {
if(pos == -1) {
pos = create_node();
}
ll m = l + r >> 1;
bool lft = t[pos].f(l) < ln.f(l);
bool mid = t[pos].f(m) < ln.f(m);
if(lft == mid && !lft) {
ops.push({pos, t[pos]});
swap(t[pos], ln);
}
if(lft != mid && !mid) {
ops.push({pos, t[pos]});
swap(t[pos], ln);
}
if(l == r) return pos;
if(lft == mid) {
children[pos][1] = add_line(m+1, r, ln, children[pos][1]);
} else {
children[pos][0] = add_line(l, m, ln, children[pos][0]);
}
return pos;
}
ll get_min(ll l, ll r, ll x, int pos) {
if(pos == -1 || l > x || r < x) return oo;
ll me = t[pos].f(x);
if(l == r) return me;
ll m = l + r >> 1;
ll lft = get_min(l, m, x, children[pos][0]);
ll rgh = get_min(m+1, r, x, children[pos][1]);
return min({me, lft, rgh});
}
void add_line(line l) {
add_line(1, size, l, 0);
}
ll get_min(ll x) {
return get_min(1, size, x, 0);
}
} t;
void dfs(int x, int p) {
int T = (int)t.ops.size();
if(x == 1) {
dp[x] = 0;
} else {
dp[x] = t.get_min(v[x]) + sum[x] * v[x] + s[x];
}
t.add_line(line(-sum[x], dp[x]));
for(pair<int, int> to : edges[x]) {
if(to.first != p) {
sum[to.first] = sum[x] + to.second;
dfs(to.first, x);
}
}
t.rollback(T);
}
int main() {
ios::sync_with_stdio(0); cin.tie(0);
cin >> n;
for(int i = 0; i < n-1; ++i) {
int u, v, w; cin >> u >> v >> w;
edges[u].push_back({v, w});
edges[v].push_back({u, w});
}
for(int i = 2; i <= n; ++i) {
cin >> s[i] >> v[i];
}
dfs(1, 0);
for(int i = 2; i <= n; ++i) {
cout << dp[i] << ' ';
}
}
