#include<bits/stdc++.h>
using namespace std;
#define ll long long
#define ed << "\n";
#define el cout<<'\n';
#define ALL(s) s.begin(),s.end()
#define fi first
#define se second
#define task "a"
#define SQ(a) (a)*(a)
#define A(a) abs(a)
#define SZ(a) ((int)(a.size()))
#define REP(i,a,b) for (int i = (a), _b = (b); i < _b; i++)
#define FOR(i,a,b) for (int i = (a), _b = (b); i <= _b; i++)
#define FOD(i,r,l) for(int i=r; i>=l; i--)
#define MASK(x) (1LL << (x))
#define pii pair<int,int>
#define BIT(x, i) ((x) >> (i) & 1)
#define int ll
const int mod = 1e9 + 7;
mt19937 rd(chrono::steady_clock::now().time_since_epoch().count());
int random(int l, int r) {
return l + rd() % (r - l + 1);
}
int mul(ll a, ll b) {
if(a >= mod) a %= mod;
if(b >= mod) b %= mod;
return 1LL * a * b % mod;
}
void ADD(int &x, int y) {
x += y;
if (x >= mod) x -= mod;
}
int add(int a, int b) {
a += b;
if(a >= mod) a -= mod;
return a;
}
int pw(int a, int b) {
int res = 1;
while(b) {
if(b & 1)
res = mul(res, a);
b = b >> 1;
a = mul(a, a);
}
return res;
}
template <class T> inline bool minimize(T &a, const T &b) {
return (a > b ? (a = b),1 : 0);
}
template <class T> inline bool maximize(T &a, const T &b) {
return (a < b ? (a = b),1 : 0);
}
void ReadInp() {
if(fopen(task".inp","r")) {
freopen(task".inp","r",stdin);
freopen(task".out","w",stdout);
}
#define task "ACQUIRE"
if(fopen(task".inp","r")) {
freopen(task".inp","r",stdin);
freopen(task".out","w",stdout);
}
}
//struct CHT{
// struct LINE{
// int slope, yInter;
// LINE(int slope, int yInter) : slope(slope) , yInter(yInter){}
//
// int val(int x) const{
// return slope * x + yInter;
// }
//
// double intersect(const LINE &l) const{
// double ds = slope - l.slope;
// double dy = l.yInter - yInter;
// return dy / ds;
// }
// };
// vector <double> x;
// vector <LINE> l ;
//
// void init(int slope, int yInter){
// x.push_back(- 1e12);
// l.push_back(LINE(slope, yInter));
// }
//
// void addLine(int slope, int yInter){
// LINE p (slope, yInter);
// while(SZ(l) > 1 && p.intersect(l[l.size() - 2]) <= x.back()){
// x.pop_back();
// l.pop_back();
// }
//
// if(l.size()) x.push_back(p.intersect(l.back()));
// l.push_back(p);
// }
//
// long long query(long long qx) const{
// int id = upper_bound(x.begin(), x.end(), qx) - x.begin();
// id --;
// return l[id].val(qx);
// }
//};
struct CHT {
struct LINE {
int slope, yInter;
LINE(int slope = 0, int yInter = 0) : slope(slope), yInter(yInter) {}
int val(int x) const{
return slope * x + yInter;
}
double intersect(const LINE &l) const{
double ds = slope - l.slope;
double dy = l.yInter - yInter;
return dy / ds;
}
} lines[100000];
struct PAST {
int pos, top;
LINE past;
PAST(int _pos, int _top, LINE _p) : pos(_pos), top(_top), past(_p) {}
};
vector <PAST> undo;
int top;
bool bad(LINE a, LINE b, LINE c) const {
return b.intersect(a) >= c.intersect(a);
}
void addLine(int slope, int yInter) {
int l = 2, r = top;
int k = top + 1;
LINE p (slope, yInter);
while(l <= r) {
int m = (l + r) / 2;
if(bad(lines[m - 1], lines[m], p)) {
k = m;
r = m - 1;
} else l = m + 1;
}
undo.push_back({k, top, lines[k]});
lines[k] = p;
top = k;
}
void roll_back() {
if(undo.empty()) return;
PAST p = undo.back();
undo.pop_back();
lines[p.pos] = p.past; top = p.top;
}
long long query(long long qx) {
int l = 1, r = top;
ll ans = 1e18;
while(l <= r) {
int m = (l + r) / 2;
ll x = lines[m].val(qx);
ll y = 1e18;
if(m < top) y = lines[m + 1].val(qx);
if(x > y) l = m + 1;
else r = m - 1;
ans = min(ans, min(x, y));
}
return ans ;
}
} dp;
int n, m, k;
int a[100005];
int s[100005];
int d[100005];
int V[100005];
int f[100005];
vector <pair<int,int>> g[100005];
void dfs(int u, int p) {
for(auto [v, c] : g[u]) if(v != p){
d[v] = d[u] + c;
f[v] = dp.query(V[v]) + d[v] * V[v] + s[v];
dp.addLine(- d[v], f[v]);
dfs(v, u);
dp.roll_back();
}
}
void sol() {
cin >> n;
FOR(i, 1, n - 1) {
int u, v, d;
cin >> u >> v >> d;
g[u].push_back({v, d});
g[v].push_back({u, d});
}
FOR(i, 2, n) cin >> s[i] >> V[i];
dp.addLine(0, 0);
dfs(1, 1);
FOR(i, 2, n) cout << f[i] << ' ';
}
signed main() {
ios_base::sync_with_stdio(false);
cin.tie(NULL), cout.tie(NULL);
ReadInp();
int t = 1; //cin >> t;
while(t --) sol();
return 0;
}
