#include<bits/stdc++.h>
#define ll long long
#define MAXN 100003
using namespace std;
vector<vector<pair<int,int>>>T(MAXN);
int s[MAXN], v[MAXN];
struct line
{
//int node;
ll k,n;
};
ll eval(ll x, line *l)
{
return l->k*x+l->n;
}
ll depth[MAXN];
void depth_dfs(int node, int p)
{
for(auto i:T[node])
{
if(i.first!=p)
{
depth[i.first]=(ll)i.second+depth[node];
depth_dfs(i.first, node);
}
}
}
vector<vector<line*>>lichao(262151);
map<line*,vector<int>>loc;
vector<int>xx;
int sz;
void make_lichao(int n)
{
sz = (1<<((int)ceil(log2(n))));
for(int i=1;i<=n;i++) xx.push_back(v[i]);
while(xx.size()<sz) xx.push_back(0);
sort(xx.begin(),xx.end());
}
void add_line(line *ln, int node, int l, int r)
{
if(lichao[node].empty())
{
lichao[node].push_back(ln);
loc[ln].push_back(node);
return;
}
line *lo = lichao[node].back();
ll lold = eval(xx[l], lo), rold = eval(xx[r], lo);
ll lnew = eval(xx[l], ln), rnew = eval(xx[r], ln);
if(lnew>=lold && rnew>=rold) return;
if(lnew<=lold && rnew<=rold)
{
lichao[node].push_back(ln);
loc[ln].push_back(node);
return;
}
int mid = (l+r)/2;
ll mold = eval(xx[mid], lo), mnew = eval(xx[mid], ln);
if(lnew<=lold)
{
if(mnew<=mold)
{
lichao[node].push_back(ln);
loc[ln].push_back(node);
add_line(lo, 2*node+1, mid+1, r);
return;
}
else
{
add_line(ln, 2*node, l, mid);
return;
}
}
else
{
if(mnew<=mold)
{
lichao[node].push_back(ln);
loc[ln].push_back(node);
add_line(lo, 2*node, l, mid);
return;
}
else
{
add_line(ln, 2*node+1, mid+1, r);
return;
}
}
return;
}
void pop_line(line *ln)
{
while(!loc[ln].empty())
{
lichao[loc[ln].back()].pop_back();
loc[ln].pop_back();
}
return;
}
ll get_val(int x)
{
ll res = 100000000000000000;
int l=0, r=sz-1, node=1;
while(l<=r)
{
if(!lichao[node].empty()) res=min(res, eval(x, lichao[node].back()));
int mid=(l+r)/2;
if(xx[mid]<=x)
{
l=mid+1;
node=node*2+1;
}
else
{
r=mid-1;
node=node*2;
}
}
return res;
}
ll dp[MAXN];
void dp_dfs(int node, int p)
{
if(node != 1 ) dp[node]=(ll)(s[node])+(ll)(v[node])*depth[node]+get_val(v[node]);
line l;
//l.node=node;
l.k=-depth[node];
l.n=dp[node];
add_line(&l, 1, 0, sz-1);
for(auto i:T[node])
{
if(i.first!=p)
{
dp_dfs(i.first,node);
}
}
pop_line(&l);
}
int main()
{
ios_base::sync_with_stdio(false);
cin.tie(0);cout.tie(0);
int n;
cin>>n;
for(int i=1;i<n;i++)
{
int u1,v1;
ll w;
cin>>u1>>v1>>w;
T[u1].emplace_back(v1,w);
T[v1].emplace_back(u1,w);
}
s[1]=0, v[1]=0;
for(int i=2;i<=n;i++)
cin>>s[i]>>v[i];
depth[1]=0;
depth_dfs(1,1);
make_lichao(n);
dp[1]=0;
dp_dfs(1,1);
for(int i=2;i<=n;i++)
cout<<dp[i]<<" ";
cout<<endl;
return 0;
}
