#pragma GCC optimize ("O3")
#pragma GCC target ("sse4")
#include <bits/stdc++.h>
#include <ext/pb_ds/tree_policy.hpp>
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/rope>
#include "factories.h"
using namespace std;
using namespace __gnu_pbds;
using namespace __gnu_cxx;
random_device(rd);
mt19937 rng(rd());
const long long FIXED_RANDOM = chrono::steady_clock::now().time_since_epoch().count();
struct custom_hash
{
template<class T>
unsigned long long operator()(T v) const
{
unsigned long long x = v;
x += FIXED_RANDOM;
// x += 11400714819323198485ull;
// x = (x ^ (x >> 30)) * 13787848793156543929ull;
x = (x ^ (x >> 27)) * 10723151780598845931ull;
return x ^ (x >> 31);
}
};
template<class T> using ordered_set = tree<T, null_type, less<T>, rb_tree_tag, tree_order_statistics_node_update>;
template<class T, class U> using hash_table = gp_hash_table<T, U, custom_hash>;
template<class T>
T randomize(T mod)
{
return (uniform_int_distribution<T>(0, mod - 1))(rng);
}
template<class T>
void readi(T &x)
{
x = 0;
bool negative = false;
char c = ' ';
while (c < '-')
{
c = getchar();
}
if (c == '-')
{
negative = true;
c = getchar();
}
while (c >= '0')
{
x = x * 10 + (c - '0');
c = getchar();
}
if (negative)
{
x = -x;
}
}
template<class T>
void printi(T output)
{
if (output == 0)
{
putchar('0');
return;
}
if (output < 0)
{
putchar('-');
output = -output;
}
int buf[20], n = 0;
while(output)
{
buf[n] = ((output % 10));
output /= 10;
n++;
}
for (n--; n >= 0; n--)
{
putchar(buf[n] + '0');
}
return;
}
template<class T>
void ckmin(T &a, T b)
{
a = min(a, b);
}
template<class T>
void ckmax(T &a, T b)
{
a = max(a, b);
}
long long expo(long long a, long long e, long long mod)
{
return ((e == 0) ? 1 : ((expo(a * a % mod, e >> 1, mod)) * ((e & 1) ? a : 1) % mod));
}
template<class T, class U>
void nmod(T &x, U mod)
{
if (x >= mod) x -= mod;
}
template<class T>
T gcd(T a, T b)
{
return (b ? gcd(b, a % b) : a);
}
#define y0 ___y0
#define y1 ___y1
#define MP make_pair
#define PB push_back
#define LB lower_bound
#define UB upper_bound
#define fi first
#define se second
#define DBG(x) cerr << #x << " = " << (x) << endl
#define SZ(x) ((int) ((x).size()))
#define FOR(i, a, b) for (auto i = (a); i < (b); i++)
#define FORD(i, a, b) for (auto i = (a) - 1; i >= (b); i--)
#define ALL(x) (x).begin(), (x).end()
const long double PI = 4.0 * atan(1.0);
const long double EPS = 1e-9;
#define MAGIC 347
#define SINF 10007
#define CO 1000007
#define INF 1000000007
#define BIG 1000000931
#define LARGE 1696969696967ll
#define GIANT 2564008813937411ll
#define LLINF 2696969696969696969ll
#define MAXN 500013
typedef long long ll;
typedef long double ld;
typedef pair<int, int> pii;
typedef pair<ll, ll> pll;
typedef pair<ld, ld> pdd;
typedef vector<int> vi;
typedef vector<ll> vl;
typedef vector<ld> vd;
typedef vector<pii> vpi;
typedef vector<pll> vpl;
typedef vector<pdd> vpd;
int N, M, T;
vpl edge[MAXN], edge1[MAXN];
int parent[MAXN], depth[MAXN];
int parent1[MAXN];
int mintable[25][2 * MAXN];
int ord[2 * MAXN], rord[2 * MAXN];
int st[MAXN], ft[MAXN];
ll dis[MAXN];
ll dp[2][MAXN];
vi L, R, V;
vpi pts;
ll ans;
int comb1(int a, int b)
{
return (depth[ord[a]] < depth[ord[b]] ? a : b);
}
int lca(int u, int v)
{
u = rord[u]; v = rord[v];
if (u > v) swap(u, v);
int sz = 31 - __builtin_clz(v - u + 1);
int res = ord[comb1(mintable[sz][u], mintable[sz][v - (1 << sz) + 1])];
return res;
}
void dfs(int u)
{
ord[M] = u;
rord[u] = M;
M++;
st[u] = T;
ft[u] = T;
T++;
for (pii p : edge[u])
{
int v = p.se;
if (v == parent[u]) continue;
parent[v] = u;
depth[v] = depth[u] + 1;
dis[v] = dis[u] + p.fi;
dfs(v);
ft[u] = ft[v];
ord[M] = u;
M++;
}
}
ll dist(int u, int v)
{
// cerr << u << ' ' << v << ' ' << lca(u, v) << endl;
return dis[u] + dis[v] - 2 * dis[lca(u, v)];
}
void Init(int n, int A[], int B[], int D[])
{
N = n;
FOR(i, 0, N - 1)
{
int u = A[i], v = B[i], d = D[i];
edge[u].PB({d, v});
edge[v].PB({d, u});
}
parent[0] = N;
dfs(0);
FOR(i, 0, M)
{
mintable[0][i] = i;
}
FOR(j, 1, 21)
{
FOR(i, 0, M)
{
mintable[j][i] = mintable[j - 1][i];
if (i + (1 << (j - 1)) < M)
{
mintable[j][i] = comb1(mintable[j][i], mintable[j - 1][i + (1 << (j - 1))]);
}
}
}
FOR(i, 0, N)
{
dp[0][i] = dp[1][i] = LLINF;
parent1[i] = N;
}
}
bool cmp(int a, int b)
{
return st[a] < st[b];
}
bool cmp1(pii a, pii b)
{
return st[a.fi] < st[b.fi];
}
int ok(int idx)
{
int u = V[idx];
int e;
for (e = idx + 1; e < SZ(V) && st[u] <= st[V[e]] && st[V[e]] <= ft[u]; )
{
int v = V[e];
ll d = dist(u, v);
edge1[u].PB({d, v});
edge1[v].PB({d, u});
parent1[v] = u;
e = ok(e);
}
return e;
}
long long Query(int S, int X[], int T, int Y[])
{
FOR(i, 0, S)
{
L.PB(X[i]);
}
FOR(i, 0, T)
{
R.PB(Y[i]);
}
for (int u : L)
{
pts.PB({u, 0});
}
for (int u : R)
{
pts.PB({u, 1});
}
sort(ALL(pts), cmp1);
FOR(i, 0, SZ(pts))
{
V.PB(pts[i].fi);
if (i)
{
V.PB(lca(pts[i - 1].fi, pts[i].fi));
}
}
sort(ALL(V), cmp);
V.erase(unique(ALL(V)), V.end());
ok(0);
priority_queue<pll, vector<pll>, greater<pll> > pq;
for (int u : L)
{
dp[0][u] = 0;
pq.push({0, u});
}
while(!pq.empty())
{
ll d = pq.top().fi, u = pq.top().se;
pq.pop();
if (d != dp[0][u]) continue;
for (pll p : edge1[u])
{
int u = p.se; ll nd = d + p.fi;
if (nd < dp[0][u])
{
dp[0][u] = nd;
pq.push({nd, u});
}
}
}
for (int u : R)
{
dp[1][u] = 0;
pq.push({0, u});
}
while(!pq.empty())
{
ll d = pq.top().fi, u = pq.top().se;
pq.pop();
if (d != dp[1][u]) continue;
for (pll p : edge1[u])
{
int u = p.se; ll nd = d + p.fi;
if (nd < dp[1][u])
{
dp[1][u] = nd;
pq.push({nd, u});
}
}
}
ans = LLINF;
for (int u : V)
{
ckmin(ans, dp[0][u] + dp[1][u]);
}
for (int u : V)
{
dp[0][u] = LLINF;
dp[1][u] = LLINF;
}
for (int u : V)
{
edge1[u].clear();
parent1[u] = N;
}
L.clear();
R.clear();
pts.clear();
V.clear();
//u need to build the tree!
return ans;
}
/* READ READ READ
* int overflow, maxn too small, special cases (n=1?, two distinct?), cin.tie() interactive
* reread the problem, try small cases
* note down possible sources of error as you go
* do smth instead of nothing
*/
