#include<bits/stdc++.h>
using namespace std;
#define int long long
#define faster ios_base::sync_with_stdio(0);cin.tie(0);cout.tie(0);
#define fi first
#define se second
#define pb push_back
typedef pair<int , int> pii;
const int inf = 1e18;
const int mod = 1e9 + 7;
const int maxn = 1e5 + 5;
int n , V[maxn] , S[maxn] , dp[maxn] , d[maxn] , len = 0;
pii cvh[maxn];
vector<pii> adj[maxn];
struct line
{
pii last_line;
int pos , last_len;
};
vector<line> cur;
int cal(int m , int x , int b)
{
return m * x + b;
}
int get(int x)
{
int l = 0 , r = len - 1;
int minn = cal(cvh[0].fi , x , cvh[0].se);
while(l < r)
{
int mid = (l + r) >> 1;
if(cal(cvh[mid].fi , x , cvh[mid].se) < cal(cvh[mid + 1].fi , x , cvh[mid + 1].se))
{
r = mid;
minn = min(minn , cal(cvh[mid].fi , x , cvh[mid].se));
}
else
{
l = mid + 1;
minn = min(minn , cal(cvh[mid + 1].fi , x , cvh[mid + 1].se));
}
}
return minn;
}
bool check(pii l1 , pii l2 , pii l3)
{
return (double)(l3.se - l1.se) / (double)(l1.fi - l3.fi) <= (double)(l2.se - l1.se) / (double)(l1.fi - l2.fi);
}
void add(int m , int b)
{
int l = 1 , r = len - 1 , p = len;
while(l <= r)
{
int mid = (l + r) >> 1;
if(check(cvh[mid - 1] , cvh[mid] , {m , b}))
{
p = mid;
r = mid - 1;
}
else l = mid + 1;
}
cur.pb({cvh[p] , p , len});
len = p + 1;
cvh[p] = {m , b};
}
void remove()
{
line gan = cur.back();
cur.pop_back();
cvh[gan.pos] = gan.last_line;
len = gan.last_len;
}
void dfs(int u , int par)
{
if(u != 1) dp[u] = get(V[u]) + d[u] * V[u] + S[u];
add(-d[u] , dp[u]);
for(auto v : adj[u])
{
if(v.fi != par)
{
d[v.fi] = d[u] + v.se;
dfs(v.fi , u);
}
}
remove();
}
main()
{
faster
cin >> n;
for(int i = 1 ; i <= n - 1 ; ++i)
{
int u , v , d;
cin >> u >> v >> d;
adj[u].pb({v , d});
adj[v].pb({u , d});
}
for(int i = 2 ; i <= n ; ++i) cin >> S[i] >> V[i];
dfs(1 , -1);
for(int i = 2 ; i <= n ; ++i) cout << dp[i] << " ";
}
