#line 1 "verify/verify-unit-test/dynamic-diameter.test.cpp"
#define PROBLEM "https://judge.yosupo.jp/problem/aplusb"
//
#line 2 "template/template.hpp"
using namespace std;
// intrinstic
#include <immintrin.h>
#include <algorithm>
#include <array>
#include <bitset>
#include <cassert>
#include <cctype>
#include <cfenv>
#include <cfloat>
#include <chrono>
#include <cinttypes>
#include <climits>
#include <cmath>
#include <complex>
#include <cstdarg>
#include <cstddef>
#include <cstdint>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <deque>
#include <fstream>
#include <functional>
#include <initializer_list>
#include <iomanip>
#include <ios>
#include <iostream>
#include <istream>
#include <iterator>
#include <limits>
#include <list>
#include <map>
#include <memory>
#include <new>
#include <numeric>
#include <ostream>
#include <queue>
#include <random>
#include <set>
#include <sstream>
#include <stack>
#include <streambuf>
#include <string>
#include <tuple>
#include <type_traits>
#include <typeinfo>
#include <unordered_map>
#include <unordered_set>
#include <utility>
#include <vector>
// utility
#line 1 "template/util.hpp"
namespace Nyaan {
using ll = long long;
using i64 = long long;
using u64 = unsigned long long;
using i128 = __int128_t;
using u128 = __uint128_t;
template <typename T>
using V = vector<T>;
template <typename T>
using VV = vector<vector<T>>;
using vi = vector<int>;
using vl = vector<long long>;
using vd = V<double>;
using vs = V<string>;
using vvi = vector<vector<int>>;
using vvl = vector<vector<long long>>;
template <typename T>
using minpq = priority_queue<T, vector<T>, greater<T>>;
template <typename T, typename U>
struct P : pair<T, U> {
template <typename... Args>
P(Args... args) : pair<T, U>(args...) {}
using pair<T, U>::first;
using pair<T, U>::second;
P &operator+=(const P &r) {
first += r.first;
second += r.second;
return *this;
}
P &operator-=(const P &r) {
first -= r.first;
second -= r.second;
return *this;
}
P &operator*=(const P &r) {
first *= r.first;
second *= r.second;
return *this;
}
template <typename S>
P &operator*=(const S &r) {
first *= r, second *= r;
return *this;
}
P operator+(const P &r) const { return P(*this) += r; }
P operator-(const P &r) const { return P(*this) -= r; }
P operator*(const P &r) const { return P(*this) *= r; }
template <typename S>
P operator*(const S &r) const {
return P(*this) *= r;
}
P operator-() const { return P{-first, -second}; }
};
using pl = P<ll, ll>;
using pi = P<int, int>;
using vp = V<pl>;
constexpr int inf = 1001001001;
constexpr long long infLL = 4004004004004004004LL;
template <typename T>
int sz(const T &t) {
return t.size();
}
template <typename T, typename U>
inline bool amin(T &x, U y) {
return (y < x) ? (x = y, true) : false;
}
template <typename T, typename U>
inline bool amax(T &x, U y) {
return (x < y) ? (x = y, true) : false;
}
template <typename T>
inline T Max(const vector<T> &v) {
return *max_element(begin(v), end(v));
}
template <typename T>
inline T Min(const vector<T> &v) {
return *min_element(begin(v), end(v));
}
template <typename T>
inline long long Sum(const vector<T> &v) {
return accumulate(begin(v), end(v), 0LL);
}
template <typename T>
int lb(const vector<T> &v, const T &a) {
return lower_bound(begin(v), end(v), a) - begin(v);
}
template <typename T>
int ub(const vector<T> &v, const T &a) {
return upper_bound(begin(v), end(v), a) - begin(v);
}
constexpr long long TEN(int n) {
long long ret = 1, x = 10;
for (; n; x *= x, n >>= 1) ret *= (n & 1 ? x : 1);
return ret;
}
template <typename T, typename U>
pair<T, U> mkp(const T &t, const U &u) {
return make_pair(t, u);
}
template <typename T>
vector<T> mkrui(const vector<T> &v, bool rev = false) {
vector<T> ret(v.size() + 1);
if (rev) {
for (int i = int(v.size()) - 1; i >= 0; i--) ret[i] = v[i] + ret[i + 1];
} else {
for (int i = 0; i < int(v.size()); i++) ret[i + 1] = ret[i] + v[i];
}
return ret;
};
template <typename T>
vector<T> mkuni(const vector<T> &v) {
vector<T> ret(v);
sort(ret.begin(), ret.end());
ret.erase(unique(ret.begin(), ret.end()), ret.end());
return ret;
}
template <typename F>
vector<int> mkord(int N, F f) {
vector<int> ord(N);
iota(begin(ord), end(ord), 0);
sort(begin(ord), end(ord), f);
return ord;
}
template <typename T>
vector<int> mkinv(vector<T> &v) {
int max_val = *max_element(begin(v), end(v));
vector<int> inv(max_val + 1, -1);
for (int i = 0; i < (int)v.size(); i++) inv[v[i]] = i;
return inv;
}
vector<int> mkiota(int n) {
vector<int> ret(n);
iota(begin(ret), end(ret), 0);
return ret;
}
template <typename T>
T mkrev(const T &v) {
T w{v};
reverse(begin(w), end(w));
return w;
}
template <typename T>
bool nxp(T &v) {
return next_permutation(begin(v), end(v));
}
// 返り値の型は入力の T に依存
// i 要素目 : [0, a[i])
template <typename T>
vector<vector<T>> product(const vector<T> &a) {
vector<vector<T>> ret;
vector<T> v;
auto dfs = [&](auto rc, int i) -> void {
if (i == (int)a.size()) {
ret.push_back(v);
return;
}
for (int j = 0; j < a[i]; j++) v.push_back(j), rc(rc, i + 1), v.pop_back();
};
dfs(dfs, 0);
return ret;
}
// F : function(void(T&)), mod を取る操作
// T : 整数型のときはオーバーフローに注意する
template <typename T>
T Power(T a, long long n, const T &I, const function<void(T &)> &f) {
T res = I;
for (; n; f(a = a * a), n >>= 1) {
if (n & 1) f(res = res * a);
}
return res;
}
// T : 整数型のときはオーバーフローに注意する
template <typename T>
T Power(T a, long long n, const T &I = T{1}) {
return Power(a, n, I, function<void(T &)>{[](T &) -> void {}});
}
template <typename T>
T Rev(const T &v) {
T res = v;
reverse(begin(res), end(res));
return res;
}
template <typename T>
vector<T> Transpose(const vector<T> &v) {
using U = typename T::value_type;
if(v.empty()) return {};
int H = v.size(), W = v[0].size();
vector res(W, T(H, U{}));
for (int i = 0; i < H; i++) {
for (int j = 0; j < W; j++) {
res[j][i] = v[i][j];
}
}
return res;
}
template <typename T>
vector<T> Rotate(const vector<T> &v, int clockwise = true) {
using U = typename T::value_type;
int H = v.size(), W = v[0].size();
vector res(W, T(H, U{}));
for (int i = 0; i < H; i++) {
for (int j = 0; j < W; j++) {
if (clockwise) {
res[W - 1 - j][i] = v[i][j];
} else {
res[j][H - 1 - i] = v[i][j];
}
}
}
return res;
}
} // namespace Nyaan
#line 58 "template/template.hpp"
// bit operation
#line 1 "template/bitop.hpp"
namespace Nyaan {
__attribute__((target("popcnt"))) inline int popcnt(const u64 &a) {
return __builtin_popcountll(a);
}
inline int lsb(const u64 &a) { return a ? __builtin_ctzll(a) : 64; }
inline int ctz(const u64 &a) { return a ? __builtin_ctzll(a) : 64; }
inline int msb(const u64 &a) { return a ? 63 - __builtin_clzll(a) : -1; }
template <typename T>
inline int gbit(const T &a, int i) {
return (a >> i) & 1;
}
template <typename T>
inline void sbit(T &a, int i, bool b) {
if (gbit(a, i) != b) a ^= T(1) << i;
}
constexpr long long PW(int n) { return 1LL << n; }
constexpr long long MSK(int n) { return (1LL << n) - 1; }
} // namespace Nyaan
#line 61 "template/template.hpp"
// inout
#line 1 "template/inout.hpp"
namespace Nyaan {
template <typename T, typename U>
ostream &operator<<(ostream &os, const pair<T, U> &p) {
os << p.first << " " << p.second;
return os;
}
template <typename T, typename U>
istream &operator>>(istream &is, pair<T, U> &p) {
is >> p.first >> p.second;
return is;
}
template <typename T>
ostream &operator<<(ostream &os, const vector<T> &v) {
int s = (int)v.size();
for (int i = 0; i < s; i++) os << (i ? " " : "") << v[i];
return os;
}
template <typename T>
istream &operator>>(istream &is, vector<T> &v) {
for (auto &x : v) is >> x;
return is;
}
istream &operator>>(istream &is, __int128_t &x) {
string S;
is >> S;
x = 0;
int flag = 0;
for (auto &c : S) {
if (c == '-') {
flag = true;
continue;
}
x *= 10;
x += c - '0';
}
if (flag) x = -x;
return is;
}
istream &operator>>(istream &is, __uint128_t &x) {
string S;
is >> S;
x = 0;
for (auto &c : S) {
x *= 10;
x += c - '0';
}
return is;
}
ostream &operator<<(ostream &os, __int128_t x) {
if (x == 0) return os << 0;
if (x < 0) os << '-', x = -x;
string S;
while (x) S.push_back('0' + x % 10), x /= 10;
reverse(begin(S), end(S));
return os << S;
}
ostream &operator<<(ostream &os, __uint128_t x) {
if (x == 0) return os << 0;
string S;
while (x) S.push_back('0' + x % 10), x /= 10;
reverse(begin(S), end(S));
return os << S;
}
void in() {}
template <typename T, class... U>
void in(T &t, U &...u) {
cin >> t;
in(u...);
}
void out() { cout << "\n"; }
template <typename T, class... U, char sep = ' '>
void out(const T &t, const U &...u) {
cout << t;
if (sizeof...(u)) cout << sep;
out(u...);
}
struct IoSetupNya {
IoSetupNya() {
cin.tie(nullptr);
ios::sync_with_stdio(false);
cout << fixed << setprecision(15);
cerr << fixed << setprecision(7);
}
} iosetupnya;
} // namespace Nyaan
#line 64 "template/template.hpp"
// debug
#line 1 "template/debug.hpp"
namespace DebugImpl {
template <typename U, typename = void>
struct is_specialize : false_type {};
template <typename U>
struct is_specialize<
U, typename conditional<false, typename U::iterator, void>::type>
: true_type {};
template <typename U>
struct is_specialize<
U, typename conditional<false, decltype(U::first), void>::type>
: true_type {};
template <typename U>
struct is_specialize<U, enable_if_t<is_integral<U>::value, void>> : true_type {
};
void dump(const char& t) { cerr << t; }
void dump(const string& t) { cerr << t; }
void dump(const bool& t) { cerr << (t ? "true" : "false"); }
void dump(__int128_t t) {
if (t == 0) cerr << 0;
if (t < 0) cerr << '-', t = -t;
string S;
while (t) S.push_back('0' + t % 10), t /= 10;
reverse(begin(S), end(S));
cerr << S;
}
void dump(__uint128_t t) {
if (t == 0) cerr << 0;
string S;
while (t) S.push_back('0' + t % 10), t /= 10;
reverse(begin(S), end(S));
cerr << S;
}
template <typename U,
enable_if_t<!is_specialize<U>::value, nullptr_t> = nullptr>
void dump(const U& t) {
cerr << t;
}
template <typename T>
void dump(const T& t, enable_if_t<is_integral<T>::value>* = nullptr) {
string res;
if (t == Nyaan::inf) res = "inf";
if constexpr (is_signed<T>::value) {
if (t == -Nyaan::inf) res = "-inf";
}
if constexpr (sizeof(T) == 8) {
if (t == Nyaan::infLL) res = "inf";
if constexpr (is_signed<T>::value) {
if (t == -Nyaan::infLL) res = "-inf";
}
}
if (res.empty()) res = to_string(t);
cerr << res;
}
template <typename T, typename U>
void dump(const pair<T, U>&);
template <typename T>
void dump(const pair<T*, int>&);
template <typename T>
void dump(const T& t,
enable_if_t<!is_void<typename T::iterator>::value>* = nullptr) {
cerr << "[ ";
for (auto it = t.begin(); it != t.end();) {
dump(*it);
cerr << (++it == t.end() ? "" : ", ");
}
cerr << " ]";
}
template <typename T, typename U>
void dump(const pair<T, U>& t) {
cerr << "( ";
dump(t.first);
cerr << ", ";
dump(t.second);
cerr << " )";
}
template <typename T>
void dump(const pair<T*, int>& t) {
cerr << "[ ";
for (int i = 0; i < t.second; i++) {
dump(t.first[i]);
cerr << (i == t.second - 1 ? "" : ", ");
}
cerr << " ]";
}
void trace() { cerr << endl; }
template <typename Head, typename... Tail>
void trace(Head&& head, Tail&&... tail) {
cerr << " ";
dump(head);
if (sizeof...(tail) != 0) cerr << ",";
trace(std::forward<Tail>(tail)...);
}
} // namespace DebugImpl
#ifdef NyaanDebug
#define trc(...) \
do { \
cerr << "## " << #__VA_ARGS__ << " = "; \
DebugImpl::trace(__VA_ARGS__); \
} while (0)
#else
#define trc(...) (void(0))
#endif
#ifdef NyaanLocal
#define trc2(...) \
do { \
cerr << "## " << #__VA_ARGS__ << " = "; \
DebugImpl::trace(__VA_ARGS__); \
} while (0)
#else
#define trc2(...) (void(0))
#endif
#line 67 "template/template.hpp"
// macro
#line 1 "template/macro.hpp"
#define each(x, v) for (auto&& x : v)
#define each2(x, y, v) for (auto&& [x, y] : v)
#define all(v) (v).begin(), (v).end()
#define rep(i, N) for (long long i = 0; i < (long long)(N); i++)
#define repr(i, N) for (long long i = (long long)(N)-1; i >= 0; i--)
#define rep1(i, N) for (long long i = 1; i <= (long long)(N); i++)
#define repr1(i, N) for (long long i = (N); (long long)(i) > 0; i--)
#define reg(i, a, b) for (long long i = (a); i < (b); i++)
#define regr(i, a, b) for (long long i = (b)-1; i >= (a); i--)
#define fi first
#define se second
#define ini(...) \
int __VA_ARGS__; \
in(__VA_ARGS__)
#define inl(...) \
long long __VA_ARGS__; \
in(__VA_ARGS__)
#define ins(...) \
string __VA_ARGS__; \
in(__VA_ARGS__)
#define in2(s, t) \
for (int i = 0; i < (int)s.size(); i++) { \
in(s[i], t[i]); \
}
#define in3(s, t, u) \
for (int i = 0; i < (int)s.size(); i++) { \
in(s[i], t[i], u[i]); \
}
#define in4(s, t, u, v) \
for (int i = 0; i < (int)s.size(); i++) { \
in(s[i], t[i], u[i], v[i]); \
}
#define die(...) \
do { \
Nyaan::out(__VA_ARGS__); \
return; \
} while (0)
#line 70 "template/template.hpp"
namespace Nyaan {
void solve();
}
int main() { Nyaan::solve(); }
#line 4 "verify/verify-unit-test/dynamic-diameter.test.cpp"
//
#line 2 "tree/dynamic-diameter.hpp"
#line 9 "tree/dynamic-diameter.hpp"
using namespace std;
#line 2 "graph/graph-template.hpp"
template <typename T>
struct edge {
int src, to;
T cost;
edge(int _to, T _cost) : src(-1), to(_to), cost(_cost) {}
edge(int _src, int _to, T _cost) : src(_src), to(_to), cost(_cost) {}
edge &operator=(const int &x) {
to = x;
return *this;
}
operator int() const { return to; }
};
template <typename T>
using Edges = vector<edge<T>>;
template <typename T>
using WeightedGraph = vector<Edges<T>>;
using UnweightedGraph = vector<vector<int>>;
// Input of (Unweighted) Graph
UnweightedGraph graph(int N, int M = -1, bool is_directed = false,
bool is_1origin = true) {
UnweightedGraph g(N);
if (M == -1) M = N - 1;
for (int _ = 0; _ < M; _++) {
int x, y;
cin >> x >> y;
if (is_1origin) x--, y--;
g[x].push_back(y);
if (!is_directed) g[y].push_back(x);
}
return g;
}
// Input of Weighted Graph
template <typename T>
WeightedGraph<T> wgraph(int N, int M = -1, bool is_directed = false,
bool is_1origin = true) {
WeightedGraph<T> g(N);
if (M == -1) M = N - 1;
for (int _ = 0; _ < M; _++) {
int x, y;
cin >> x >> y;
T c;
cin >> c;
if (is_1origin) x--, y--;
g[x].emplace_back(x, y, c);
if (!is_directed) g[y].emplace_back(y, x, c);
}
return g;
}
// Input of Edges
template <typename T>
Edges<T> esgraph([[maybe_unused]] int N, int M, int is_weighted = true,
bool is_1origin = true) {
Edges<T> es;
for (int _ = 0; _ < M; _++) {
int x, y;
cin >> x >> y;
T c;
if (is_weighted)
cin >> c;
else
c = 1;
if (is_1origin) x--, y--;
es.emplace_back(x, y, c);
}
return es;
}
// Input of Adjacency Matrix
template <typename T>
vector<vector<T>> adjgraph(int N, int M, T INF, int is_weighted = true,
bool is_directed = false, bool is_1origin = true) {
vector<vector<T>> d(N, vector<T>(N, INF));
for (int _ = 0; _ < M; _++) {
int x, y;
cin >> x >> y;
T c;
if (is_weighted)
cin >> c;
else
c = 1;
if (is_1origin) x--, y--;
d[x][y] = c;
if (!is_directed) d[y][x] = c;
}
return d;
}
/**
* @brief グラフテンプレート
* @docs docs/graph/graph-template.md
*/
#line 2 "tree/static-top-tree-vertex-based.hpp"
#line 6 "tree/static-top-tree-vertex-based.hpp"
using namespace std;
#line 2 "tree/convert-tree.hpp"
#line 4 "tree/convert-tree.hpp"
template <typename T>
struct has_cost {
private:
template <typename U>
static auto confirm(U u) -> decltype(u.cost, std::true_type());
static auto confirm(...) -> std::false_type;
public:
enum : bool { value = decltype(confirm(std::declval<T>()))::value };
};
template <typename T>
vector<vector<T>> inverse_tree(const vector<vector<T>>& g) {
int N = (int)g.size();
vector<vector<T>> rg(N);
for (int i = 0; i < N; i++) {
for (auto& e : g[i]) {
if constexpr (is_same<T, int>::value) {
rg[e].push_back(i);
} else if constexpr (has_cost<T>::value) {
rg[e].emplace_back(e.to, i, e.cost);
} else {
assert(0);
}
}
}
return rg;
}
template <typename T>
vector<vector<T>> rooted_tree(const vector<vector<T>>& g, int root = 0) {
int N = (int)g.size();
vector<vector<T>> rg(N);
vector<char> v(N, false);
v[root] = true;
queue<int> que;
que.emplace(root);
while (!que.empty()) {
auto p = que.front();
que.pop();
for (auto& e : g[p]) {
if (v[e] == false) {
v[e] = true;
que.push(e);
rg[p].push_back(e);
}
}
}
return rg;
}
/**
* @brief 根付き木・逆辺からなる木への変換
*/
#line 2 "tree/heavy-light-decomposition.hpp"
#line 4 "tree/heavy-light-decomposition.hpp"
template <typename G>
struct HeavyLightDecomposition {
private:
void dfs_sz(int cur) {
size[cur] = 1;
for (auto& dst : g[cur]) {
if (dst == par[cur]) {
if (g[cur].size() >= 2 && int(dst) == int(g[cur][0]))
swap(g[cur][0], g[cur][1]);
else
continue;
}
depth[dst] = depth[cur] + 1;
par[dst] = cur;
dfs_sz(dst);
size[cur] += size[dst];
if (size[dst] > size[g[cur][0]]) {
swap(dst, g[cur][0]);
}
}
}
void dfs_hld(int cur) {
down[cur] = id++;
for (auto dst : g[cur]) {
if (dst == par[cur]) continue;
nxt[dst] = (int(dst) == int(g[cur][0]) ? nxt[cur] : int(dst));
dfs_hld(dst);
}
up[cur] = id;
}
// [u, v)
vector<pair<int, int>> ascend(int u, int v) const {
vector<pair<int, int>> res;
while (nxt[u] != nxt[v]) {
res.emplace_back(down[u], down[nxt[u]]);
u = par[nxt[u]];
}
if (u != v) res.emplace_back(down[u], down[v] + 1);
return res;
}
// (u, v]
vector<pair<int, int>> descend(int u, int v) const {
if (u == v) return {};
if (nxt[u] == nxt[v]) return {{down[u] + 1, down[v]}};
auto res = descend(u, par[nxt[v]]);
res.emplace_back(down[nxt[v]], down[v]);
return res;
}
public:
G& g;
int root, id;
vector<int> size, depth, down, up, nxt, par;
HeavyLightDecomposition(G& _g, int _root = 0)
: g(_g),
root(_root),
id(0),
size(g.size(), 0),
depth(g.size(), 0),
down(g.size(), -1),
up(g.size(), -1),
nxt(g.size(), root),
par(g.size(), root) {
dfs_sz(root);
dfs_hld(root);
}
pair<int, int> idx(int i) const { return make_pair(down[i], up[i]); }
template <typename F>
void path_query(int u, int v, bool vertex, const F& f) {
int l = lca(u, v);
for (auto&& [a, b] : ascend(u, l)) {
int s = a + 1, t = b;
s > t ? f(t, s) : f(s, t);
}
if (vertex) f(down[l], down[l] + 1);
for (auto&& [a, b] : descend(l, v)) {
int s = a, t = b + 1;
s > t ? f(t, s) : f(s, t);
}
}
template <typename F>
void path_noncommutative_query(int u, int v, bool vertex, const F& f) {
int l = lca(u, v);
for (auto&& [a, b] : ascend(u, l)) f(a + 1, b);
if (vertex) f(down[l], down[l] + 1);
for (auto&& [a, b] : descend(l, v)) f(a, b + 1);
}
template <typename F>
void subtree_query(int u, bool vertex, const F& f) {
f(down[u] + int(!vertex), up[u]);
}
int lca(int a, int b) {
while (nxt[a] != nxt[b]) {
if (down[a] < down[b]) swap(a, b);
a = par[nxt[a]];
}
return depth[a] < depth[b] ? a : b;
}
int dist(int a, int b) { return depth[a] + depth[b] - depth[lca(a, b)] * 2; }
};
/**
* @brief Heavy Light Decomposition(重軽分解)
* @docs docs/tree/heavy-light-decomposition.md
*/
#line 10 "tree/static-top-tree-vertex-based.hpp"
namespace StaticTopTreeVertexBasedImpl {
enum Type { Vertex, Compress, Rake, Add_Edge, Add_Vertex };
template <typename G>
struct StaticTopTreeVertexBased {
const HeavyLightDecomposition<G>& hld;
vector<vector<int>> g;
int root; // 元の木の root
int tt_root; // top tree の root
vector<int> P, L, R;
vector<Type> T;
StaticTopTreeVertexBased(const HeavyLightDecomposition<G>& _hld) : hld(_hld) {
root = hld.root;
g = rooted_tree(hld.g, root);
int n = g.size();
P.resize(n, -1), L.resize(n, -1), R.resize(n, -1);
T.resize(n, Type::Vertex);
build();
}
private:
int add(int l, int r, Type t) {
if (t == Type::Compress or t == Type::Rake) {
assert(l != -1 and r != -1);
}
if (t == Type::Add_Edge) {
assert(l != -1 and r == -1);
}
assert(t != Type::Vertex and t != Type::Add_Vertex);
int k = P.size();
P.push_back(-1), L.push_back(l), R.push_back(r), T.push_back(t);
if (l != -1) P[l] = k;
if (r != -1) P[r] = k;
return k;
}
int add2(int k, int l, int r, Type t) {
assert(k < (int)g.size());
assert(t == Type::Vertex or t == Type::Add_Vertex);
if (t == Type::Vertex) {
assert(l == -1 and r == -1);
} else {
assert(l != -1 and r == -1);
}
P[k] = -1, L[k] = l, R[k] = r, T[k] = t;
if (l != -1) P[l] = k;
if (r != -1) P[r] = k;
return k;
}
pair<int, int> merge(const vector<pair<int, int>>& a, Type t) {
assert(!a.empty());
if (a.size() == 1) return a[0];
int sum_s = 0;
for (auto& [_, s] : a) sum_s += s;
vector<pair<int, int>> b, c;
for (auto& [i, s] : a) {
(sum_s > s ? b : c).emplace_back(i, s);
sum_s -= s * 2;
}
auto [i, si] = merge(b, t);
auto [j, sj] = merge(c, t);
return {add(i, j, t), si + sj};
}
pair<int, int> compress(int i) {
vector<pair<int, int>> chs;
while (true) {
chs.push_back(add_vertex(i));
if (g[i].empty()) break;
i = g[i][0];
}
return merge(chs, Type::Compress);
}
pair<int, int> rake(int i) {
vector<pair<int, int>> chs;
for (int j = 1; j < (int)g[i].size(); j++) chs.push_back(add_edge(g[i][j]));
if (chs.empty()) return {-1, 0};
return merge(chs, Type::Rake);
}
pair<int, int> add_edge(int i) {
auto [j, sj] = compress(i);
return {add(j, -1, Type::Add_Edge), sj};
}
pair<int, int> add_vertex(int i) {
auto [j, sj] = rake(i);
return {add2(i, j, -1, j == -1 ? Type::Vertex : Type::Add_Vertex), sj + 1};
}
void build() {
auto [i, n] = compress(root);
assert((int)g.size() == n);
tt_root = i;
}
};
template <typename G, typename Path, typename Point, typename Vertex,
typename Compress, typename Rake, typename Add_edge,
typename Add_vertex>
struct DPonStaticTopTreeVertexBased {
const StaticTopTreeVertexBased<G> tt;
vector<Path> path;
vector<Point> point;
const Vertex vertex;
const Compress compress;
const Rake rake;
const Add_edge add_edge;
const Add_vertex add_vertex;
DPonStaticTopTreeVertexBased(const HeavyLightDecomposition<G>& hld,
const Vertex& _vertex, const Compress& _compress,
const Rake& _rake, const Add_edge& _add_edge,
const Add_vertex& _add_vertex)
: tt(hld),
vertex(_vertex),
compress(_compress),
rake(_rake),
add_edge(_add_edge),
add_vertex(_add_vertex) {
int n = tt.P.size();
path.resize(n), point.resize(n);
dfs(tt.tt_root);
}
Path get() { return path[tt.tt_root]; }
void update(int k) {
while (k != -1) _update(k), k = tt.P[k];
}
private:
void _update(int k) {
if (tt.T[k] == Type::Vertex) {
path[k] = vertex(k);
} else if (tt.T[k] == Type::Compress) {
path[k] = compress(path[tt.L[k]], path[tt.R[k]]);
} else if (tt.T[k] == Type::Rake) {
point[k] = rake(point[tt.L[k]], point[tt.R[k]]);
} else if (tt.T[k] == Type::Add_Edge) {
point[k] = add_edge(path[tt.L[k]]);
} else {
path[k] = add_vertex(point[tt.L[k]], k);
}
}
void dfs(int k) {
if (tt.L[k] != -1) dfs(tt.L[k]);
if (tt.R[k] != -1) dfs(tt.R[k]);
_update(k);
}
};
} // namespace StaticTopTreeVertexBasedImpl
using StaticTopTreeVertexBasedImpl::DPonStaticTopTreeVertexBased;
using StaticTopTreeVertexBasedImpl::StaticTopTreeVertexBased;
/*
// template
using Path = ;
using Point = ;
auto vertex = [&](int i) -> Path {
};
auto compress = [&](const Path& p, const Path& c) -> Path {
};
auto rake = [&](const Point& a, const Point& b) -> Point {
};
auto add_edge = [&](const Path& a) -> Point {
};
auto add_vertex = [&](const Point& a, int i) -> Path {
};
HeavyLightDecomposition hld{g};
DPonStaticTopTreeVertexBased<vector<vector<int>>, Path, Point,
decltype(vertex), decltype(compress), decltype(rake), decltype(add_edge),
decltype(add_vertex)>
dp(hld, vertex, compress, rake, add_edge, add_vertex);
*/
/**
* @brief Static Top Tree
*/
#line 13 "tree/dynamic-diameter.hpp"
namespace DynamicDiameterImpl {
template <typename T>
struct HalfPath {
T d;
int u;
friend HalfPath max(const HalfPath& lhs, const HalfPath& rhs) {
if (lhs.d != rhs.d) return lhs.d > rhs.d ? lhs : rhs;
return lhs.u > rhs.u ? lhs : rhs;
}
};
template <typename T>
struct Path {
T d;
int u, v;
friend Path max(const Path& lhs, const Path& rhs) {
if (lhs.d != rhs.d) return lhs.d > rhs.d ? lhs : rhs;
if (lhs.u != rhs.u) return lhs.u > rhs.u ? lhs : rhs;
return lhs.v > rhs.v ? lhs : rhs;
}
};
template <typename T>
struct L {
Path<T> dia;
HalfPath<T> d1, d2;
};
template <typename T>
struct H {
Path<T> dia;
HalfPath<T> pd, cd;
T p_to_c;
int p, c;
};
template <typename T>
H<T> vertex(T x, int i) {
H<T> r;
r.dia = {x, i, i};
r.pd = r.cd = {x, i};
r.p_to_c = x;
r.p = r.c = i;
return r;
}
template <typename T>
H<T> compress(const H<T>& p, const H<T>& c) {
H<T> r;
r.dia = max(max(p.dia, c.dia), {p.cd.d + c.pd.d, p.cd.u, c.pd.u});
r.pd = max(p.pd, {p.p_to_c + c.pd.d, c.pd.u});
r.cd = max(c.cd, {c.p_to_c + p.cd.d, p.cd.u});
r.p_to_c = p.p_to_c + c.p_to_c;
r.p = p.p, r.c = c.c;
return r;
}
template <typename T>
L<T> rake(const L<T>& a, const L<T>& b) {
L<T> r;
r.dia = max(a.dia, b.dia);
if (a.d1.d > b.d1.d) {
r.d1 = a.d1;
r.d2 = max(a.d2, b.d1);
} else {
r.d1 = b.d1;
r.d2 = max(b.d2, a.d1);
}
return r;
}
template <typename T>
L<T> add_edge(const H<T>& a) {
L<T> r;
r.dia = a.dia;
r.d1 = a.pd;
r.d2 = {0, -1};
return r;
}
template <typename T>
H<T> add_vertex(const L<T>& a, T x, int i) {
H<T> r;
r.dia = max(a.dia, {a.d1.d + x + a.d2.d, a.d1.u, a.d2.u});
r.pd = r.cd = {a.d1.d + x, a.d1.u};
r.p_to_c = x;
r.p = r.c = i;
return r;
}
template <typename T>
struct Aux_Tree {
int N, _buf;
const WeightedGraph<T>& g;
vector<vector<int>> aux;
vector<T> w;
map<pair<int, int>, int> e_to_id;
Aux_Tree(const WeightedGraph<T>& _g) : g(_g) {
N = g.size();
aux.resize(2 * N - 1);
w.resize(2 * N - 1);
_buf = N;
dfs(0, -1);
assert(_buf == 2 * N - 1);
}
void dfs(int c, int p) {
for (auto& d : g[c]) {
if (d == p) continue;
int id = _buf++;
aux[id].push_back(c), aux[c].push_back(id);
aux[id].push_back(d), aux[d].push_back(id);
w[id] = d.cost;
e_to_id[minmax<int>(c, d)] = id;
dfs(d, c);
}
}
};
template <typename T>
struct DynamicDiameter {
const WeightedGraph<T>& g;
int n;
Aux_Tree<T> aux;
HeavyLightDecomposition<vector<vector<int>>> hld;
DPonStaticTopTreeVertexBased<
vector<vector<int>>, H<T>, L<T>, function<H<T>(int)>,
function<H<T>(const H<T>&, const H<T>&)>,
function<L<T>(const L<T>&, const L<T>&)>, function<L<T>(const H<T>&)>,
function<H<T>(const L<T>&, int)>>
dp;
DynamicDiameter(const WeightedGraph<T>& _g)
: g(_g),
n(g.size()),
aux(g),
hld(aux.aux),
dp(
hld, [&](int i) { return vertex(aux.w[i], i < n ? i : -1); },
[&](const H<T>& p, const H<T>& c) { return compress(p, c); },
[&](const L<T>& a, const L<T>& b) { return rake(a, b); },
[&](const H<T>& a) { return add_edge(a); },
[&](const L<T>& a, int i) {
return add_vertex(a, aux.w[i], i < n ? i : -1);
}) {}
pair<T, pair<int, int>> get() {
auto [d, u, v] = dp.get().dia;
return make_pair(d, make_pair(u, v));
}
void update(int u, int v, T x) {
assert(aux.e_to_id.count(minmax(u, v)));
int i = aux.e_to_id[minmax(u, v)];
aux.w[i] = x;
dp.update(i);
}
};
} // namespace DynamicDiameterImpl
using DynamicDiameterImpl::DynamicDiameter;
#line 6 "verify/verify-unit-test/dynamic-diameter.test.cpp"
using namespace Nyaan;
//
#line 2 "graph/graph-utility.hpp"
#line 4 "graph/graph-utility.hpp"
// 一般のグラフのstからの距離！！！！
// unvisited nodes : d = -1
vector<int> Depth(const UnweightedGraph &g, int start = 0) {
int n = g.size();
vector<int> ds(n, -1);
ds[start] = 0;
queue<int> q;
q.push(start);
while (!q.empty()) {
int c = q.front();
q.pop();
int dc = ds[c];
for (auto &d : g[c]) {
if (ds[d] == -1) {
ds[d] = dc + 1;
q.push(d);
}
}
}
return ds;
}
// Depth of Rooted Weighted Tree
// unvisited nodes : d = -1
template <typename T>
vector<T> Depth(const WeightedGraph<T> &g, int start = 0) {
vector<T> d(g.size(), -1);
auto dfs = [&](auto rec, int cur, T val, int par = -1) -> void {
d[cur] = val;
for (auto &dst : g[cur]) {
if (dst == par) continue;
rec(rec, dst, val + dst.cost, cur);
}
};
dfs(dfs, start, 0);
return d;
}
// Diameter of Tree
// return value : { {u, v}, length }
pair<pair<int, int>, int> Diameter(const UnweightedGraph &g) {
auto d = Depth(g, 0);
int u = max_element(begin(d), end(d)) - begin(d);
d = Depth(g, u);
int v = max_element(begin(d), end(d)) - begin(d);
return make_pair(make_pair(u, v), d[v]);
}
// Diameter of Weighted Tree
// return value : { {u, v}, length }
template <typename T>
pair<pair<int, int>, T> Diameter(const WeightedGraph<T> &g) {
auto d = Depth(g, 0);
int u = max_element(begin(d), end(d)) - begin(d);
d = Depth(g, u);
int v = max_element(begin(d), end(d)) - begin(d);
return make_pair(make_pair(u, v), d[v]);
}
// nodes on the path u-v ( O(N) )
template <typename G>
vector<int> Path(G &g, int u, int v) {
vector<int> ret;
int end = 0;
auto dfs = [&](auto rec, int cur, int par = -1) -> void {
ret.push_back(cur);
if (cur == v) {
end = 1;
return;
}
for (int dst : g[cur]) {
if (dst == par) continue;
rec(rec, dst, cur);
if (end) return;
}
if (end) return;
ret.pop_back();
};
dfs(dfs, u);
return ret;
}
/**
* @brief グラフユーティリティ
* @docs docs/graph/graph-utility.md
*/
#line 9 "verify/verify-unit-test/dynamic-diameter.test.cpp"
//
#line 2 "shortest-path/dijkstra.hpp"
#line 4 "shortest-path/dijkstra.hpp"
// unreachable -> -1
template <typename T>
vector<T> dijkstra(WeightedGraph<T> &g, int start = 0) {
using P = pair<T, int>;
int N = (int)g.size();
vector<T> d(N, T(-1));
priority_queue<P, vector<P>, greater<P> > Q;
d[start] = 0;
Q.emplace(0, start);
while (!Q.empty()) {
P p = Q.top();
Q.pop();
int cur = p.second;
if (d[cur] < p.first) continue;
for (auto dst : g[cur]) {
if (d[dst] == T(-1) || d[cur] + dst.cost < d[dst]) {
d[dst] = d[cur] + dst.cost;
Q.emplace(d[dst], dst);
}
}
}
return d;
}
/**
* @brief ダイクストラ法
* @docs docs/shortest-path/dijkstra.md
*/
#line 11 "verify/verify-unit-test/dynamic-diameter.test.cpp"
//
#line 2 "misc/rng.hpp"
#line 2 "internal/internal-seed.hpp"
#line 4 "internal/internal-seed.hpp"
using namespace std;
namespace internal {
unsigned long long non_deterministic_seed() {
unsigned long long m =
chrono::duration_cast<chrono::nanoseconds>(
chrono::high_resolution_clock::now().time_since_epoch())
.count();
m ^= 9845834732710364265uLL;
m ^= m << 24, m ^= m >> 31, m ^= m << 35;
return m;
}
unsigned long long deterministic_seed() { return 88172645463325252UL; }
// 64 bit の seed 値を生成 (手元では seed 固定)
// 連続で呼び出すと同じ値が何度も返ってくるので注意
// #define RANDOMIZED_SEED するとシードがランダムになる
unsigned long long seed() {
#if defined(NyaanLocal) && !defined(RANDOMIZED_SEED)
return deterministic_seed();
#else
return non_deterministic_seed();
#endif
}
} // namespace internal
#line 4 "misc/rng.hpp"
namespace my_rand {
using i64 = long long;
using u64 = unsigned long long;
// [0, 2^64 - 1)
u64 rng() {
static u64 _x = internal::seed();
return _x ^= _x << 7, _x ^= _x >> 9;
}
// [l, r]
i64 rng(i64 l, i64 r) {
assert(l <= r);
return l + rng() % u64(r - l + 1);
}
// [l, r)
i64 randint(i64 l, i64 r) {
assert(l < r);
return l + rng() % u64(r - l);
}
// choose n numbers from [l, r) without overlapping
vector<i64> randset(i64 l, i64 r, i64 n) {
assert(l <= r && n <= r - l);
unordered_set<i64> s;
for (i64 i = n; i; --i) {
i64 m = randint(l, r + 1 - i);
if (s.find(m) != s.end()) m = r - i;
s.insert(m);
}
vector<i64> ret;
for (auto& x : s) ret.push_back(x);
sort(begin(ret), end(ret));
return ret;
}
// [0.0, 1.0)
double rnd() { return rng() * 5.42101086242752217004e-20; }
// [l, r)
double rnd(double l, double r) {
assert(l < r);
return l + rnd() * (r - l);
}
template <typename T>
void randshf(vector<T>& v) {
int n = v.size();
for (int i = 1; i < n; i++) swap(v[i], v[randint(0, i + 1)]);
}
} // namespace my_rand
using my_rand::randint;
using my_rand::randset;
using my_rand::randshf;
using my_rand::rnd;
using my_rand::rng;
#line 13 "verify/verify-unit-test/dynamic-diameter.test.cpp"
void test() {
ll wmax = TEN(9);
rep1(N, 50) {
rep(_, 100) {
WeightedGraph<ll> g;
Edges<ll> es;
rep1(i, N - 1) {
int j = rng(0, i - 1);
es.emplace_back(j, i, rng(0, wmax));
}
auto gen = [&]() {
g.clear();
g.resize(N);
each(e, es) {
g[e.src].emplace_back(e.src, e.to, e.cost);
g[e.to].emplace_back(e.to, e.src, e.cost);
}
};
gen();
auto DP = DynamicDiameter(g);
rep(t, 100) {
// check
auto [d, uv] = DP.get();
ll d2 = -1;
{
int u = 0;
auto du = dijkstra(g, u);
int v = max_element(all(du)) - begin(du);
auto dv = dijkstra(g, v);
int w = max_element(all(dv)) - begin(dv);
d2 = dv[w];
}
assert(uv.first != -1 and uv.second != -1);
assert(d == d2);
assert(d == dijkstra(g, uv.first)[uv.second]);
if (N >= 2) {
// update
int e_num = rng(0, N - 2);
int u = es[e_num].src, v = es[e_num].to;
ll x = rng(0, wmax);
DP.update(u, v, x);
es[e_num].cost = x;
gen();
}
}
}
}
trc2("OK");
}
void q() {
test();
int a, b;
cin >> a >> b;
cout << a + b << endl;
}
void Nyaan::solve() {
int t = 1;
// in(t);
while (t--) q();
}
verify/verify-unit-test/dynamic-diameter.test.cpp