#include<bits/stdc++.h>
using namespace std;
using vi = vector<int>;
using pi = pair<int,int>;
typedef long long ll;
#define debug(x) cout << #x << " = " << x << "\n";
#define vdebug(a) cout << #a << " = "; for(auto x: a) cout << x << " "; cout << "\n";
const int MOD = 1e9 + 7;
const int INF = 1e9;
template<ll mod>
struct modnum {
static constexpr bool is_big_mod = mod > numeric_limits<int>::max();
using S = conditional_t<is_big_mod, ll, int>;
using L = conditional_t<is_big_mod, __int128, ll>;
S x;
modnum() : x(0) {}
modnum(ll _x) {
_x %= static_cast<ll>(mod);
if (_x < 0) { _x += mod; }
x = _x;
}
modnum pow(ll n) const {
modnum res = 1;
modnum cur = *this;
while (n > 0) {
if (n & 1) res *= cur;
cur *= cur;
n /= 2;
}
return res;
}
modnum inv() const { return (*this).pow(mod-2); }
modnum& operator+=(const modnum& a){
x += a.x;
if (x >= mod) x -= mod;
return *this;
}
modnum& operator-=(const modnum& a){
if (x < a.x) x += mod;
x -= a.x;
return *this;
}
modnum& operator*=(const modnum& a){
x = static_cast<L>(x) * a.x % mod;
return *this;
}
modnum& operator/=(const modnum& a){ return *this *= a.inv(); }
friend modnum operator+(const modnum& a, const modnum& b){ return modnum(a) += b; }
friend modnum operator-(const modnum& a, const modnum& b){ return modnum(a) -= b; }
friend modnum operator*(const modnum& a, const modnum& b){ return modnum(a) *= b; }
friend modnum operator/(const modnum& a, const modnum& b){ return modnum(a) /= b; }
friend bool operator==(const modnum& a, const modnum& b){ return a.x == b.x; }
friend bool operator!=(const modnum& a, const modnum& b){ return a.x != b.x; }
friend bool operator<(const modnum& a, const modnum& b){ return a.x < b.x; }
friend ostream& operator<<(ostream& os, const modnum& a){ os << a.x; return os; }
friend istream& operator>>(istream& is, modnum& a) { ll x; is >> x; a = modnum(x); return is; }
};
using mint = modnum<MOD>;
template <class T> class SumSegmentTree {
private:
const T DEFAULT = 0;
vector<T> segtree;
int len;
public:
SumSegmentTree(int len) : len(len), segtree(len * 2, DEFAULT) {}
void set(int ind, T val) {
ind += len;
segtree[ind] = val;
for (; ind > 1; ind /= 2) {
segtree[ind / 2] = segtree[ind] + segtree[ind ^ 1];
}
}
T range_sum(int start, int end) {
T sum = DEFAULT;
for (start += len, end += len; start < end; start /= 2, end /= 2) {
if (start % 2 == 1) { sum += segtree[start++]; }
if (end % 2 == 1) { sum += segtree[--end]; }
}
return sum;
}
};
/*
const int N = 250005;
struct BIT {
ll b[N], n;
void init(int _n) {
n = _n ;
for(int i = 0 ; i <= n ; ++i) b[i] = 0;
}
inline int lowbit(int x) { return x & (-x); }
void update(int x, ll v) {
for(int i = x ; i <= n ; i += lowbit(i)) b[i] += v;
}
ll query(int x) {
ll ans = 0;
for(int i = x ; i > 0 ; i -= lowbit(i)) ans += b[i];
return ans;
}
} bit[2]; */
int gcd(int a, int b, int& x, int& y) { // x*a + y*b = a1
x = 1, y = 0;
int x1 = 0, y1 = 1, a1 = a, b1 = b;
while (b1) {
int q = a1 / b1;
tie(x, x1) = make_tuple(x1, x - q * x1);
tie(y, y1) = make_tuple(y1, y - q * y1);
tie(a1, b1) = make_tuple(b1, a1 - q * b1);
}
return a1;
}
int inv_ecd(int a, int m) {
int x, y;
int g = gcd(a, m, x, y);
if(g != 1) return -1;
x = (x + m) % m;
return x;
}
const int maxn = 1e5 + 1;
using ld = long double;
struct Line {
ll m, b;
Line(ll m = 0, ll b = 0) : m(m), b(b) {}
ll operator()(ll x) { return m * x + b; }
friend ld intersect(Line l1, Line l2) {
return (ld)(l2.b - l1.b) / (ld)(l1.m - l2.m);
}
};
int n, siz;
Line stk[maxn];
vector<pi>adjL[maxn];
vi v, s;
vector<ll>ans;
int remove_pos(Line line) {
if(siz < 2 or intersect(line, stk[siz-1]) >= intersect(stk[siz-1], stk[siz-2])) return siz;
int l=1, r=siz-1;
while(l<r) {
int m = (l+r)/2;
if(intersect(line, stk[m]) < intersect(stk[m], stk[m-1])) r=m;
else l=m+1;
}
return l;
}
ll get_min(ll x) {
int l=0, r=siz-1;
while(l<r) {
int m = (l+r)/2;
if(intersect(stk[m], stk[m+1]) < x) l = m+1;
else r = m;
}
return stk[l](x);
}
void dfs(int pos, ll d, int prev=0) {
int prev_siz, prev_pos;
Line prev_line;
if(!pos) {
ans[pos] = 0;
stk[siz++] = {0,0};
} else {
ans[pos] = get_min(v[pos]) + 1LL * d * v[pos] + s[pos];
Line tmp(-d, ans[pos]);
prev_siz = siz;
prev_pos = siz = remove_pos(tmp);
prev_line = stk[siz];
stk[siz++] = tmp;
}
for(auto [V,W]: adjL[pos]) {
if(V == prev) continue;
dfs(V, d+W, pos);
}
if(pos) {
siz = prev_siz;
stk[prev_pos] = prev_line;
}
}
void solve() {
cin >> n;
v.resize(n);
s.resize(n);
ans.resize(n);
for(int i=0; i<n-1; ++i) {
int u,v,d;
cin >> u >> v >> d;
--u, --v;
adjL[u].push_back({v,d});
adjL[v].push_back({u,d});
}
for(int i=1; i<n; ++i) cin >> s[i] >> v[i];
dfs(0, 0);
for(int i=1; i<n; ++i) cout << ans[i] << endl;
}
int main(){
ios::sync_with_stdio(0);
cin.tie(0); cout.tie(0);
//freopen("strange_file.txt", "r", stdin);
//freopen("strange_file3.txt", "w", stdout);
int tc = 1;
while (tc--) solve();
}
