#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;
}
};
int n, a, b, c, s[100000], v[100000], pre[20][100000];
long long f[100000];
LINE l[100000];
vector<pair<int, int>> g[100000];
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 long long GetVal(int ind, long long x)
{
for (int i = 19; i >= 0; --i)
{
if (pre[i][ind] != -1 && pre[0][pre[i][ind]] != -1 &&
l[pre[i][ind]].Val(x) > l[pre[0][pre[i][ind]]].Val(x))
{
ind = pre[i][ind];
}
}
return (pre[0][ind] == -1 ? l[ind].Val(x) : min(l[ind].Val(x), l[pre[0][ind]].Val(x)));
}
inline int GetPar(int ind, LINE inp)
{
for (int i = 19; i >= 0; --i)
{
if (pre[i][ind] != -1 && pre[0][pre[i][ind]] != -1 &&
Check(l[pre[0][pre[i][ind]]], l[pre[i][ind]], inp))
{
ind = pre[i][ind];
}
}
if (pre[0][ind] == -1 || !Check(l[pre[0][ind]], l[ind], inp))
{
return ind;
}
return pre[0][ind];
}
inline void DFS(int node, int par, int road)
{
f[node] = (node == 0 ? 0 : GetVal(par, v[node])) + (long long)road * v[node] + s[node];
l[node] = LINE(-road, f[node]);
pre[0][node] = (node == 0 ? -1 : GetPar(par, l[node]));
for (int i = 1; i < 20; ++i)
{
pre[i][node] = (pre[i - 1][node] == -1 ? -1 : pre[i - 1][pre[i - 1][node]]);
}
for (auto & i : g[node])
{
if (i.first != par)
{
DFS(i.first, node, road + i.second);
}
}
}
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, -1, 0);
for (int i = 1; i < n; ++i)
{
cout << f[i] << " ";
}
return 0;
}
