#include<bits/stdc++.h>
#define ll long long
#define MAXN 100007
using namespace std;
vector<vector<pair<int,ll>>>T(MAXN);
ll s[MAXN], v[MAXN];
struct line
{
int node;
ll k,n;
ll eval(ll x)
{
return k*x+n;
}
};
ll depth[MAXN];
void depth_dfs(int node, int p)
{
for(auto i:T[node])
{
if(i.first!=p)
{
depth[i.first]=i.second+depth[node];
depth_dfs(i.first, node);
}
}
}
vector<stack<line>>lichao;
vector<vector<int>>loc(MAXN);
map<int,int>xfind;
vector<ll>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());
for(int i=0;i<sz;i++) xfind[xx[i]]=i;
stack<line>st;
for(int i=0;i<2*sz+5;i++) lichao.push_back(st);
}
void add_line(line ln, int node, int l, int r)
{
if(lichao[node].empty())
{
lichao[node].push(ln);
loc[ln.node].push_back(node);
return;
}
line lo = lichao[node].top();
ll lold = lo.eval(xx[l]), rold = lo.eval(xx[r]);
ll lnew = ln.eval(xx[l]), rnew = ln.eval(xx[r]);
if(lnew>=lold && rnew>=rold) return;
if(lnew<=lold && rnew<=rold)
{
lichao[node].push(ln);
loc[ln.node].push_back(node);
return;
}
int mid = (l+r)/2;
ll mold = lo.eval(xx[mid]), mnew = ln.eval(xx[mid]);
if(lnew<=lold)
{
if(mnew<=mold)
{
lichao[node].push(ln);
loc[ln.node].push_back(node);
add_line(ln, 2*node+1, mid+1, r);
return;
}
else
{
add_line(ln, 2*node, l, mid);
return;
}
}
else
{
if(mnew<=mold)
{
lichao[node].push(ln);
loc[ln.node].push_back(node);
add_line(ln, 2*node, l, mid);
return;
}
else
{
add_line(ln, 2*node+1, mid+1, r);
return;
}
}
return;
}
void pop_line(line l)
{
for(auto i:loc[l.node]) lichao[i].pop();
return;
}
ll get_val(ll x)
{
ll res = 10000000000000; //PROVERITI JOS
ll t = xfind[x] + sz;
while(t>0)
{
if(!lichao[t].empty()) res = min(res, lichao[t].top().eval(x));
t/=2;
}
return res;
}
ll dp[MAXN];
void dp_dfs(int node, int p)
{
if(node != 1 ) dp[node]=s[node]+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;
}
