#include <bits/stdc++.h>
#define FOR(i, a, b) for(int i = (a); i <= (b); i++)
using namespace std;
using ll = long long;
const int N = 1e5+1;
struct LichaoOptMem{
struct Line{
int a; ll b;
Line(int a = 0, ll b = LLONG_MAX): a(a), b(b) {}
ll f(ll x){return 1ll*a*x + b;}
ll slope(){return a;}
bool operator != (const Line& x) const{
return (a != x.a || b != x.b);
}
};
vector<bool> rekt;
vector<int> compress; int global_version = 0;
vector<vector<pair<Line, int>>> st; int trsz;
LichaoOptMem(int n = 0, vector<int> comp = vector<int>()): trsz(n){
compress = comp;
rekt.resize((n<<1|1));
st.assign(n+1, vector<pair<Line,int>>(1, make_pair(Line(), 0)));
return;
}
void roll_back(vector<pair<Line,int>>& tr){
while(rekt[tr.back().second]) tr.pop_back();
return;
}
void update(int l, int r, Line curLine){
if(l > r) return;
if(l == r){
Line version = st[l].back().first;
version = (version.f(compress[l]) < curLine.f(compress[l]) ? version : curLine);
if(version != st[l].back().first)
return st[l].push_back(make_pair(version, global_version)), void();
}
else{
int mid = l+r>>1;
roll_back(st[mid]);
Line version = st[mid].back().first;
if(version.f(compress[mid]) > curLine.f(compress[mid])) swap(curLine, version);
if(version.slope() < curLine.slope()) update(l, mid-1, curLine);
if(version.slope() > curLine.slope()) update(mid+1, r, curLine);
if(version != st[mid].back().first) st[mid].push_back(make_pair(version, global_version));
}
return;
}
ll query(int l, int r, ll x){
if(l > r) return LLONG_MAX;
int mid = l+r>>1;
roll_back(st[mid]);
ll cur = st[mid].back().first.f(x);
if(x == compress[mid]) return cur;
if(x < compress[mid]) return min(cur, query(l, mid-1, x));
if(x > compress[mid]) return min(cur, query(mid+1, r, x));
return -1;
}
ll query(ll x){
return query(0, trsz, x);
}
int addLine(int a, ll b){return ++global_version, update(0, trsz, Line(a, b)), global_version;}
void rmvLine(int version){return rekt[version] = true, void();}
};
int n, wait_time[N], speed[N];
ll dp[N];
vector<pair<int,int>> adj[N];
void dfs(int x, int p, ll cur_dist, LichaoOptMem& lichao){
if(x) dp[x] = lichao.query(speed[x]) + (1ll * cur_dist * speed[x]) + (1ll * wait_time[x]);
int rem_version = lichao.addLine(-cur_dist, dp[x]);
for(pair<int,int> e : adj[x]){
int v = e.first, w = e.second;
if(v != p){
dfs(v, x, cur_dist + 1ll*w, lichao);
}
}
lichao.rmvLine(rem_version);
return;
}
void solve()
{
int n; cin >> n;
FOR(i, 1, n-1){
int u,v,w; cin >> u >> v >> w;
u--, v--;
adj[u].emplace_back(v, w);
adj[v].emplace_back(u, w);
}
vector<int> compress;
FOR(i, 1, n-1){
cin >> wait_time[i] >> speed[i];
compress.push_back(speed[i]);
}
sort(compress.begin(), compress.end());
compress.erase(unique(compress.begin(), compress.end()), compress.end());
LichaoOptMem lichao((int)compress.size()-1, compress);
dfs(0, -1, 0, lichao);
FOR(i, 1, n-1) cout << dp[i] <<" \n"[i == n-1];
}
signed main()
{
ios_base::sync_with_stdio(0);
cin.tie(0);
cout.tie(0);
#define name "InvMOD"
if(fopen(name".INP", "r")){
freopen(name".INP","r",stdin);
freopen(name".OUT","w",stdout);
}
int t = 1; //cin >> t;
while(t--) solve();
return 0;
}
