#include <bits/stdc++.h>
#define int long long
using namespace std;
typedef array<int, 2> pr;
const int MAX = 100010;
const int INF = 1'000'000'000;
struct Line {
int A, B;
int get(int X) { return A * X + B; }
Line(int A, int B) : A(A), B(B) {}
};
struct Node {
int s, e, l = -1, r = -1;
Line line;
Node(int s, int e, Line line) : s(s), e(e), line(line) {}
};
int S[MAX], V[MAX], depth[MAX], dp[MAX];
vector<pr> adj[MAX];
vector<Node> tree;
vector<vector<pair<int, Line>>> st;
void update(int n, Line v) {
st.back().push_back({n, tree[n].line});
int s = tree[n].s, e = tree[n].e, m = s + e >> 1;
Line low = tree[n].line, high = v;
if (low.get(s) > high.get(s))
swap(low, high);
if (low.get(e) <= high.get(e)) {
tree[n].line = low;
return;
}
if (low.get(m) < high.get(m)) {
tree[n].line = low;
if (tree[n].r == -1) {
tree[n].r = tree.size();
tree.push_back(Node(m + 1, e, Line(0, INF)));
}
update(tree[n].r, high);
} else {
tree[n].line = high;
if (tree[n].l == -1) {
tree[n].l = tree.size();
tree.push_back(Node(s, m, Line(0, INF)));
}
update(tree[n].l, low);
}
}
int query(int n, int x) {
if (n == -1)
return INF;
int s = tree[n].s, e = tree[n].e, m = s + e >> 1;
if (x <= m)
return min(tree[n].line.get(x), query(tree[n].l, x));
return min(tree[n].line.get(x), query(tree[n].r, x));
}
void rollback() {
for (pair<int, Line> i : st.back())
tree[i.first].line = i.second;
st.pop_back();
}
void dfs(int node, int par) {
if (node != 1)
dp[node] = S[node] + V[node] * depth[node] + query(0, V[node]);
st.push_back({});
update(0, Line(-depth[node], dp[node]));
for (pr i : adj[node]) {
if (i[0] == par)
continue;
depth[i[0]] = depth[node] + i[1];
dfs(i[0], node);
}
rollback();
}
signed main() {
ios_base::sync_with_stdio(false);
cin.tie(0), cout.tie(0);
int N, X, Y, Z;
cin >> N;
for (int i = 1; i < N; i++) {
cin >> X >> Y >> Z;
adj[X].push_back({Y, Z}), adj[Y].push_back({X, Z});
}
for (int i = 2; i <= N; i++)
cin >> S[i] >> V[i];
tree.push_back(Node(0, INF, Line(0, INF)));
dfs(1, 0);
for (int i = 2; i <= N; i++)
cout << dp[i] << ' ';
cout << '\n';
return 0;
}
