// Author: Muhammed Khaled Shoeib
#include <bits/stdc++.h>
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>
using namespace __gnu_pbds;
using namespace std;
//....................................................
// struct to speed-up the unordered data structures like map/set.
struct hash_function // unordered + modified hash >> ordered
{ static uint64_t splitmix64(uint64_t x) {
x += 0x9e3779b97f4a7c15; x = (x ^ (x >> 30)) * 0xbf58476d1ce4e5b9;
x = (x ^ (x >> 27)) * 0x94d049bb133111eb; return x ^ (x >> 31); }
size_t operator()(uint64_t x) const {
static const uint64_t FIXED_RANDOM = chrono::steady_clock::now().time_since_epoch().count();
return splitmix64(x + FIXED_RANDOM); } };
//....................................................
template < typename T, typename Compare = less < T > > // O(logn)
using ordered_set = tree < T, null_type, Compare, rb_tree_tag, tree_order_statistics_node_update>;
// less_equal: asc. not_unique, st.order_of_key(k) --> no. of items < k, less: unique
// greater_equal: desc. not_unique, st.order_of_key(k) --> no. of items > k, greater: unique
// *st.find_by_order(k) --> st[k] (Zero-indexed)
// less_equal (u can't erase here!) == multi-set
template < typename T > using maxpq = priority_queue < T >;
template < typename T > using minpq = priority_queue < T, vector< T >, greater< T > >;
//....................................................
#define boost ios_base::sync_with_stdio(false); cin.tie(0); cout.tie(0)
#define precision(a) cout << fixed << setprecision(a)
#define alo cout << "alooooooooooo!" << endl
#define YES cout << "YES" << endl
#define Yes cout << "Yes" << endl
#define yes cout << "yes" << endl
#define NO cout << "NO" << endl
#define No cout << "No" << endl
#define no cout << "no" << endl
#define ne cout << -1 << endl
#define endl "\n"
#define mem(mat, val) memset(mat, val, sizeof(mat))
#define ones(x) __builtin_popcountll(x)
#define msb(x) 63ll - __builtin_clzll(x)
#define lsb(x) __builtin_ffsll(x) - 1ll
//....................................................
#define all(x) x.begin(), x.end()
#define rall(x) x.rbegin(),x.rend()
#define _ceil(a, b) (((ll)(a) + (ll)(b - 1)) / (ll)(b)) // up
#define _floor(a, b) (a / b) // down
#define _round(a, b) ((a + (b / 2ll)) / b) // nearest
//....................................................
// using ll = int; // take care of this shit!
using ll = long long;
using i64 = long long; using i32 = int; using lli = long long int; using LL = __int128;
using ld = long double; using LD = __float128; using ull = unsigned long long;
using cld = complex < long double >; using cd = complex < double >;
//......................................................
ll _gcd(ll x, ll y) { return y ? _gcd(y, x % y) : x; } // O(log(min(x, y)))
ll _lcm(ll a, ll b) { ll g = _gcd(a, b); return (a * b) / g; }
//mt19937 rng(chrono::steady_clock::now().time_since_epoch().count());
//#define getrand(l, r) uniform_int_distribution<long long>(l, r)(rng)
//......................................................
int dx[4] = {-1, 0, 1, 0}, dy[4] = {0, 1, 0, -1};
int dx_diag[4] = { 1, 1, -1, -1 }, dy_diag[4] = { 1, -1, -1, 1 };
int dx_all[8] = {-1, -1, -1, 0, 1, 1, 1, 0}, dy_all[8] = {-1, 0, 1, 1, 1, 0, -1, -1};
int dx_knight[8] = {2, 2, 1, 1, -2, -2, -1, -1}, dy_knight[8] = {1, -1, 2, -2, 1, -1, 2, -2};
const ld pi = acos(-1); // 3.141592653589793238462643383279
const ld eps = 1e-9;
const ll inf = (ll)INT32_MAX; // 2e9
const ll oo = (ll)1e18; // 1e15 (may cause OF in DP, Binary Search, ...)
const ll OO = (ll)INT64_MAX; // 9e18
const ll mod = (ll)1e9 + 7; // 1e9 + 7, 998244353
//..................................................... // string(len, char);
/*
* think twice, code once.
* think of different approaches to tackle a problem, write them down.
* think of different views of the problem, don't look from only one side.
* don't get stuck in one approach/problem.
* common mistakes: line 49, overflow (sum of many numbers), corner cases (n = 1), over/under count, infinite loops,
* TLE, MLE (int instead of ll, using memset, Recursive DP, ...), RTE (out of bounds indexing), ....
*/
///____________________________________________ Shoeib __________________________________________________________
/* Persistent CHT */
// insert & eval in O(log(n)), rollback (undoes the most recent insertion) in O(1).
// All lines should be added in strictly increasing slope order.
// it's max, to make it min --> pcht.add_line(-m, -c), -1*pcht.eval(x)
class PersistentCHT
{
struct Line
{
ll m, c;
Line() { }
Line(ll _m, ll _c) : m(_m), c(_c) { }
};
vector < vector < Line > > hull;
vector < ll > version_idx;
vector < ll > version_sz;
ll SZ = 0;
ld inter(Line t1, Line t2)
{
ld ret;
ret = (ld)(t2.c - t1.c - .0)/(t1.m - t2.m - .0);
return ret;
}
void insert_line(Line curr)
{
Line temp, temp2;
version_sz.push_back(SZ);
if(SZ > 1)
{
ll s = 0, e = SZ - 1;
while(s < e)
{
ll p = (s + e) / 2;
temp = hull[p + 1].back();
temp2 = hull[p].back();
ld point = inter(temp, temp2);
ld point2 = inter(temp, curr);
if(point < point2) s = p+1;
else e = p;
}
SZ = s + 1;
}
if(hull.size() == SZ)
{
vector<Line> x;
hull.push_back(x);
}
hull[SZ].push_back(curr);
version_idx.push_back(SZ);
SZ++;
}
public:
void insert_line(ll m, ll c){ insert_line(Line(m, c)); }
ll eval(ll find)
{
ll s = 0, e = SZ - 1;
while(s < e)
{
ll p = (s + e) / 2;
ld point = inter(hull[p].back(), hull[p + 1].back());
if(point < find) s = p + 1;
else e = p;
}
ll ret = (hull[s].back().m * find) + hull[s].back().c;
return ret;
}
void rollback()
{
SZ = version_sz.back();
version_sz.pop_back();
hull[version_idx.back()].pop_back();
version_idx.pop_back();
}
ll size() { return SZ; }
};
ll n;
vector < vector < pair < ll, ll > > > graph;
vector < ll > s, v, dp;
// dp[l] = min(s[l] + v[l]*(dist[l] - dist[j]) + dp[j])
// dp[l] = min(s[l] + v[l]*dist[l] - dist[j]*v[l] + dp[j])
// dp[l] = min(s[l] + v[l]*dist[l] + m * x + c
PersistentCHT pcht;
void dfs(ll root, ll par, ll dist)
{
if(root != 1)
{
ll x = v[root];
dp[root] = s[root] + v[root]*dist + -pcht.eval(x);
}
ll m = -dist, c = dp[root];
pcht.insert_line(-m, -c);
for(const auto &i : graph[root])
{
if(i.first == par) continue;
dfs(i.first, root, dist + i.second);
}
pcht.rollback();
}
void solve()
{
cin >> n;
graph.resize(n + 1);
for(ll i = 1; i <= n - 1; i++)
{
ll u, v, d; cin >> u >> v >> d;
graph[u].push_back({v, d});
graph[v].push_back({u, d});
}
s.resize(n + 1); v.resize(n + 1);
for(ll i = 2; i <= n; i++) cin >> s[i] >> v[i];
dp.resize(n + 1); dp[1] = 0;
dfs(1, 0, 0);
for(ll i = 2; i <= n; i++) cout << dp[i] << ' ';
cout << endl;
return;
}
signed main()
{
boost;
// freopen("bank.in", "r", stdin);
// freopen("bank.out", "w", stdout);
// precision(15);
i32 _ = 1; //cin >> _;
// cout.flush();
while(_--) solve();
return 0;
}
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