#include <bits/stdc++.h>
#pragma GCC optimize("Ofast")
#pragma GCC target("sse,sse2,sse3,ssse3,sse4,popcnt,abm,mmx,avx,tune=native")
#pragma GCC target ("avx2")
#pragma GCC optimization ("O3")
#pragma GCC optimization ("unroll-loops")
using namespace std;
#define int long long
const int N = 5e5;
vector<pair<int, long long>> adj[N];
int n, m;
/*int first[N], last[N], l2[N * 2], p2[N * 2];
long long dep[N];
int sparse[N * 2][22];
int c = 0;*/
int sub[N], par[N];
long long ans[N];
bool isCen[N];
int size = 0;
int block_size, block_cnt;
vector<int> first_visit;
vector<int> euler_tour;
vector<int> height;
vector<int> log_2;
vector<vector<int>> st;
vector<vector<vector<int>>> blocks;
vector<int> block_mask;
long long dep[N];
void dfs(int v, int p, int h, long long de = 0) {
first_visit[v] = euler_tour.size();
euler_tour.push_back(v);
height[v] = h;
dep[v] = de;
for (auto u : adj[v]) {
if (u.first == p)
continue;
dfs(u.first, v, h + 1, de + u.second);
euler_tour.push_back(v);
}
}
int min_by_h(int i, int j) {
return height[euler_tour[i]] < height[euler_tour[j]] ? i : j;
}
void precompute_lca(int root) {
// get euler tour & indices of first occurences
first_visit.assign(n, -1);
height.assign(n, 0);
euler_tour.reserve(2 * n);
dfs(root, -1, 0);
// precompute all log values
int m = euler_tour.size();
log_2.reserve(m + 1);
log_2.push_back(-1);
for (int i = 1; i <= m; i++)
log_2.push_back(log_2[i / 2] + 1);
block_size = max(1ll, log_2[m] / 2ll);
block_cnt = (m + block_size - 1) / block_size;
// precompute minimum of each block and build sparse table
st.assign(block_cnt, vector<int>(log_2[block_cnt] + 1));
for (int i = 0, j = 0, b = 0; i < m; i++, j++) {
if (j == block_size)
j = 0, b++;
if (j == 0 || min_by_h(i, st[b][0]) == i)
st[b][0] = i;
}
for (int l = 1; l <= log_2[block_cnt]; l++) {
for (int i = 0; i < block_cnt; i++) {
int ni = i + (1 << (l - 1));
if (ni >= block_cnt)
st[i][l] = st[i][l-1];
else
st[i][l] = min_by_h(st[i][l-1], st[ni][l-1]);
}
}
// precompute mask for each block
block_mask.assign(block_cnt, 0);
for (int i = 0, j = 0, b = 0; i < m; i++, j++) {
if (j == block_size)
j = 0, b++;
if (j > 0 && (i >= m || min_by_h(i - 1, i) == i - 1))
block_mask[b] += 1 << (j - 1);
}
// precompute RMQ for each unique block
int possibilities = 1 << (block_size - 1);
blocks.resize(possibilities);
for (int b = 0; b < block_cnt; b++) {
int mask = block_mask[b];
if (!blocks[mask].empty())
continue;
blocks[mask].assign(block_size, vector<int>(block_size));
for (int l = 0; l < block_size; l++) {
blocks[mask][l][l] = l;
for (int r = l + 1; r < block_size; r++) {
blocks[mask][l][r] = blocks[mask][l][r - 1];
if (b * block_size + r < m)
blocks[mask][l][r] = min_by_h(b * block_size + blocks[mask][l][r],
b * block_size + r) - b * block_size;
}
}
}
}
int lca_in_block(int b, int l, int r) {
return blocks[block_mask[b]][l][r] + b * block_size;
}
int lca(int v, int u) {
int l = first_visit[v];
int r = first_visit[u];
if (l > r)
swap(l, r);
int bl = l / block_size;
int br = r / block_size;
if (bl == br)
return euler_tour[lca_in_block(bl, l % block_size, r % block_size)];
int ans1 = lca_in_block(bl, l % block_size, block_size - 1);
int ans2 = lca_in_block(br, 0, r % block_size);
int ans = min_by_h(ans1, ans2);
if (bl + 1 < br) {
int l = log_2[br - bl - 1];
int ans3 = st[bl+1][l];
int ans4 = st[br - (1 << l)][l];
ans = min_by_h(ans, min_by_h(ans3, ans4));
}
return euler_tour[ans];
}
// LCA begins
/*void pre(int v, int p = -1, long long d = 0, int de = 0) {
first[v] = c++;
dep[v] = d;
euler[c - 1] = v;
depth[c - 1] = de;
for (auto i : adj[v]) {
if (i.first != p) {
pre(i.first, v, d + i.second, de + 1);
euler[c] = v;
depth[c++] = de;
}
}
last[v] = c - 1;
}
int merge(int a, int b) {
return depth[a] < depth[b] ? a : b;
}
void build_sparse() {
int es = n * 2 - 1;
assert(es < N * 2);
assert(l2[es] <= 22);
for (int i = 0; i < es; i++)
sparse[i][0] = i;
for (int i = 1; i <= l2[es]; i++) {
for (int j = 0; j < es && j - 1 + (p2[i]) < es; j++)
sparse[j][i] = depth[sparse[j][i - 1]] < depth[sparse[j + (p2[i - 1])][i - 1]] ? sparse[j][i - 1] : sparse[j + (p2[i - 1])][i - 1];
}
}
int lca(int u, int v) {
if (u == v) return u;
int f1 = min(first[u], first[v]), f2 = max(first[v], first[u]), diff = f2 - f1;
int dx = l2[diff];
return euler[merge(sparse[f1][dx], sparse[f2 - (p2[dx])][dx])];
}*/
long long dist(int u, int v) {
return dep[u] + dep[v] - 2 * dep[lca(u, v)];
}
// LCA ends
// Centroid decomposition begins
void calc(int v, int p = -1) { // Pre calculate subtree sizes
sub[v] = 1;
size++;
for (auto i : adj[v]) {
if (i.first != p && !isCen[v])
calc(i.first, v), sub[v] += sub[i.first];
}
}
int find(int v, int p = -1) { // Find the centroid in current subtree
for (auto i : adj[v]) {
if (i.first != p && !isCen[i.first] && sub[i.first] > size / 2)
return find(i.first, v);
}
return v;
}
void decompose(int v, int p = -1) {
size = 0; // Stores size of current subtree
calc(v);
int centroid = find(v);
par[centroid] = p;
isCen[centroid] = true;
for (auto i : adj[centroid]) {
if (i.first != p && !isCen[i.first])
decompose(i.first, centroid);
}
}
// Centroid decomposition ends
void update(int v) {
int p = v, co = 0;
while (p != -1) {
ans[p] = min(ans[p], dist(p, v));
p = par[p];
}
assert(co <= 22);
}
long long query(int v) {
int p = v, co = 0;
long long val = 1e18;
while (p != -1) {
val = min(val, ans[p] + dist(p, v));
p = par[p];
}
assert(co <= 22);
return val;
}
void revert(int v) {
int p = v;
while (p != -1) {
ans[p] = 1e18;
p = par[p];
}
}
#undef int
int qc = 0;
long long Query(int S, int X[], int T, int Y[]) {
if (S <= 10 && T <= 10) {
long long ans = dist(X[0], Y[0]);
for (int i = 0; i < S; i++) {
for (int j = 0; j < T; j++)
ans = min(ans, dist(X[i], Y[j]));
}
qc++;
return ans;
} else for(;;);
for (int i = 0; i < S; i++)
update(X[i]);
long long ans = 1e18;
for (int i = 0; i < T; i++)
ans = min(ans, query(Y[i]));
for (int i = 0; i < S; i++)
revert(X[i]);
return ans;
}
void Init(int N, int A[], int B[], int D[]) {
n = N;
for (int i = 0; i < n - 1; i++) {
adj[A[i]].emplace_back(B[i], D[i]);
adj[B[i]].emplace_back(A[i], D[i]);
}
precompute_lca(0);
//decompose(0);
fill(ans, ans + N, 1e18);
}
