#include <bits/stdc++.h>
using namespace std;
void setup()
{
ios_base::sync_with_stdio(0);
cin.tie(0);
cout.tie(0);
}
struct LINE
{
double a, b;
inline LINE()
{
a = 1e9;
b = 1e18;
}
inline LINE(long long new_a, long long new_b)
{
a = new_a;
b = new_b;
}
inline long long Val(long long x)
{
return a * x + b;
}
};
struct CONVEX_HULL
{
vector<LINE> v;
inline bool Check(LINE x, LINE y, LINE z)
{
double i1 = (x.b - y.b) / (y.a - x.a);
double i2 = (x.b - z.b) / (z.a - x.a);
return i1 > i2;
}
inline vector<LINE> Add(LINE inp)
{
vector<LINE> removed;
while (v.size() > 1 && Check(v[v.size() - 2], v[v.size() - 1], inp))
{
removed.push_back(v.back());
v.pop_back();
}
v.push_back(inp);
return removed;
}
inline void Revive(vector<LINE> & inp)
{
v.pop_back();
reverse(inp.begin(), inp.end());
for (auto & i : inp)
{
v.push_back(i);
}
}
inline long long Get(long long x)
{
int l = 0, r = v.size() - 1, m;
long long res = 9e18;
while (l <= r)
{
m = (l + r) >> 1;
res = min(res, v[m].Val(x));
if (m + 1 < v.size() && v[m].Val(x) > v[m + 1].Val(x))
{
l = m + 1;
}
else
{
r = m - 1;
}
}
return res;
}
} cht;
int id[100000], n, a, b, c, s[100000], v[100000];
long long f[100000];
vector<pair<int, int>> g[100000];
inline void DFS(int node, int par, int road)
{
vector<LINE> keep;
if (node == 0)
{
keep = cht.Add(LINE(0, 0));
}
else
{
f[node] = cht.Get(v[node]) + (long long)road * v[node] + s[node];
keep = cht.Add(LINE(-road, f[node]));
}
for (auto & i : g[node])
{
if (i.first != par)
{
DFS(i.first, node, road + i.second);
}
}
cht.Revive(keep);
keep.clear();
}
int main()
{
setup();
cin >> n;
for (int i = 0; i < n - 1; ++i)
{
cin >> a >> b >> c;
g[a - 1].push_back({b - 1, c});
g[b - 1].push_back({a - 1, c});
}
for (int i = 1; i < n; ++i)
{
cin >> s[i] >> v[i];
}
DFS(0, 0, 0);
for (int i = 1; i < n; ++i)
{
cout << f[i] << " ";
}
return 0;
}
