#include <bits/stdc++.h>
using namespace std;
void setup()
{
ios_base::sync_with_stdio(0);
cin.tie(0);
cout.tie(0);
}
struct LINE
{
long long 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 NODE
{
LINE v;
int l, r;
};
struct LICHAOTREE
{
int sz = 0;
NODE tree[4000000];
inline int Update(int ind, int l, int r, LINE inp)
{
int new_ind = sz++;
if (ind == -1)
{
tree[new_ind].v = inp;
tree[new_ind].l = tree[new_ind].r = -1;
}
else
{
tree[new_ind] = tree[ind];
int m = (l + r) >> 1;
if (tree[new_ind].v.Val(m) > inp.Val(m))
{
swap(tree[new_ind].v, inp);
}
if (l < r)
{
if (tree[new_ind].v.Val(l) > inp.Val(l))
{
tree[new_ind].l = Update(tree[ind].l, l, m, inp);
}
if (tree[new_ind].v.Val(r) > inp.Val(r))
{
tree[new_ind].r = Update(tree[ind].r, m + 1, r, inp);
}
}
}
return new_ind;
}
inline long long Get(int ind, int l, int r, int x)
{
if (ind == -1)
{
return 9e18;
}
if (l == r)
{
return tree[ind].v.Val(x);
}
int m = (l + r) >> 1;
if (x <= m)
{
return min(tree[ind].v.Val(x), Get(tree[ind].l, l, m, x));
}
return min(tree[ind].v.Val(x), Get(tree[ind].r, m + 1, r, x));
}
} lct;
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)
{
if (node == 0)
{
id[node] = lct.Update(-1, 1, 1e9, LINE(0, 0));
}
else
{
f[node] = (long long)v[node] * road + s[node] + lct.Get(id[par], 1, 1e9, v[node]);
id[node] = lct.Update(id[par], 1, 1e9, LINE(-road, f[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, 0, 0);
for (int i = 1; i < n; ++i)
{
cout << f[i] << " ";
}
return 0;
}
