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#line 1 "swap.h"
#include <vector>
void init(int N, int M,
std::vector<int> U, std::vector<int> V, std::vector<int> W);
int getMinimumFuelCapacity(int X, int Y);
#line 2 "/Users/kaage/Desktop/ProgrammingWorkspace/library/other/template.hpp"
#define _CRT_SECURE_NO_WARNINGS
#ifndef __clang__
#ifdef ONLINE_JUDGE
#pragma GCC target("avx512f")
#elif defined EVAL
#else
#pragma GCC target("avx2")
#endif
#pragma GCC optimize("O3")
#pragma GCC optimize("unroll-loops")
#endif
#include <string.h>
#include <algorithm>
#include <array>
#include <bitset>
#include <cassert>
#include <cfloat>
#include <climits>
#include <cmath>
#include <complex>
#include <ctime>
#include <deque>
#include <fstream>
#include <functional>
#include <iomanip>
#include <iostream>
#include <iterator>
#include <list>
#include <map>
#include <memory>
#include <queue>
#include <random>
#include <set>
#include <stack>
#include <string>
#include <unordered_map>
#include <unordered_set>
#include <utility>
#line 41 "/Users/kaage/Desktop/ProgrammingWorkspace/library/other/template.hpp"
#define rep(i, n) for (int i = 0; i < int(n); i++)
#define REP(i, n) for (int i = 1; i <= int(n); i++)
#define all(V) V.begin(), V.end()
using i128 = __int128_t;
using u128 = __uint128_t;
using uint = unsigned int;
using lint = long long;
using ulint = unsigned long long;
using IP = std::pair<int, int>;
using LP = std::pair<lint, lint>;
constexpr int INF = INT_MAX / 2;
constexpr lint LINF = LLONG_MAX / 2;
constexpr double eps = DBL_EPSILON;
constexpr double PI = 3.141592653589793238462643383279;
template <class T>
class prique : public std::priority_queue<T, std::vector<T>, std::greater<T>> {
};
int popcount(uint x) {
#if __cplusplus >= 202002L
return std::popcount(x);
#else
#ifndef __clang__
return __builtin_popcount(x);
#endif
#endif
x = (x & 0x55555555) + (x >> 1 & 0x55555555);
x = (x & 0x33333333) + (x >> 2 & 0x33333333);
x = (x & 0x0f0f0f0f) + (x >> 4 & 0x0f0f0f0f);
x = (x & 0x00ff00ff) + (x >> 8 & 0x00ff00ff);
return (x & 0x0000ffff) + (x >> 16 & 0x0000ffff);
}
template <class F>
inline constexpr decltype(auto) lambda_fix(F&& f) {
return [f = std::forward<F>(f)](auto&&... args) {
return f(f, std::forward<decltype(args)>(args)...);
};
}
template <class T>
constexpr std::vector<T> make_vec(size_t n) {
return std::vector<T>(n);
}
template <class T, class... Args>
constexpr auto make_vec(size_t n, Args&&... args) {
return std::vector<decltype(make_vec<T>(args...))>(
n, make_vec<T>(std::forward<Args>(args)...));
}
template <class T, class U>
std::istream& operator>>(std::istream& ist, std::pair<T, U>& x) {
return ist >> x.first >> x.second;
}
template <class T, class U>
std::ostream& operator<<(std::ostream& ost, const std::pair<T, U>& x) {
return ost << x.first << " " << x.second;
}
template <class T, class U>
constexpr inline bool chmax(T& lhs, const U& rhs) noexcept {
if (lhs < rhs) {
lhs = rhs;
return true;
}
return false;
}
template <class T, class U>
constexpr inline bool chmin(T& lhs, const U& rhs) noexcept {
if (lhs > rhs) {
lhs = rhs;
return true;
}
return false;
}
constexpr inline lint gcd(lint a, lint b) noexcept {
while (b) {
lint c = a;
a = b;
b = c % b;
}
return a;
}
inline lint lcm(lint a, lint b) noexcept { return a / gcd(a, b) * b; }
constexpr bool isprime(lint n) noexcept {
if (n == 1) return false;
for (int i = 2; i * i <= n; i++) {
if (n % i == 0) return false;
}
return true;
}
template <class T>
constexpr T mypow(T a, lint b) noexcept {
T res(1);
while (true) {
if (b & 1) res *= a;
b >>= 1;
if (!b) break;
a *= a;
}
return res;
}
constexpr lint modpow(lint a, lint b, lint m) noexcept {
a %= m;
lint res(1);
while (b) {
if (b & 1) {
res *= a;
res %= m;
}
a *= a;
a %= m;
b >>= 1;
}
return res;
}
template <class T>
constexpr void printArray(const std::vector<T>& vec, char split = ' ') {
rep(i, vec.size()) {
std::cout << vec[i];
std::cout << (i == (int)vec.size() - 1 ? '\n' : split);
}
}
template <class InputIter>
constexpr void printArray(InputIter l, InputIter r, char split = ' ') {
auto rprev = std::prev(r);
for (auto i = l; i != r; i++) {
std::cout << *i;
std::cout << (i == rprev ? '\n' : split);
}
}
LP extGcd(lint a, lint b) noexcept {
if (b == 0) return {1, 0};
LP s = extGcd(b, a % b);
std::swap(s.first, s.second);
s.second -= a / b * s.first;
return s;
}
LP ChineseRem(const lint& b1, const lint& m1, const lint& b2,
const lint& m2) noexcept {
auto p = extGcd(m1, m2);
lint g = gcd(m1, m2), l = m1 / g * m2;
lint tmp = (b2 - b1) / g * p.first % (m2 / g);
lint r = (b1 + m1 * tmp + l) % l;
return {r, l};
}
int LCS(const std::string& a, const std::string& b) {
auto dp = make_vec<int>(a.size() + 1, b.size() + 1);
rep(i, a.size()) {
rep(j, b.size()) {
chmax(dp[i + 1][j], dp[i][j]);
chmax(dp[i][j + 1], dp[i][j]);
if (a[i] == b[j]) chmax(dp[i + 1][j + 1], dp[i][j] + 1);
}
chmax(dp[i + 1][b.size()], dp[i][b.size()]);
}
rep(j, b.size()) chmax(dp[a.size()][j + 1], dp[a.size()][j]);
return dp[a.size()][b.size()];
}
template <class T, std::enable_if_t<std::is_convertible<int, T>::value,
std::nullptr_t> = nullptr>
void compress(std::vector<T>& vec) {
auto tmp = vec;
std::sort(all(tmp));
tmp.erase(std::unique(all(tmp)), tmp.end());
for (T& i : vec) i = std::lower_bound(all(tmp), i) - tmp.begin();
}
template <class T>
void compress(T* l, T* r) {
std::vector<T> tmp(l, r);
std::sort(all(tmp));
tmp.erase(std::unique(all(tmp)), tmp.end());
for (auto i = l; i < r; i++) {
*i = std::lower_bound(all(tmp), *i) - tmp.begin();
}
}
template <class InputIter>
void compress(InputIter l, InputIter r) {
std::vector<typename InputIter::value_type> tmp(l, r);
std::sort(all(tmp));
tmp.erase(std::unique(all(tmp)), tmp.end());
for (auto i = l; i < r; i++) {
*i = std::lower_bound(all(tmp), *i) - tmp.begin();
}
}
#line 3 "swap.cpp"
class PersistentUnionFind {
std::vector<IP> notparent;
std::vector<std::vector<std::pair<int, int>>> sizevec;
std::vector<int> ok_vec;
int opcount = 0;
public:
PersistentUnionFind(unsigned int size) {
notparent.resize(size);
sizevec.resize(size);
ok_vec.resize(size, INF);
rep(i, size) {
sizevec[i].push_back(std::make_pair(-1, 1));
notparent[i] = std::make_pair(INF, i);
}
}
int find(int n, int t = INF) {
if (t < notparent[n].first || notparent[n].second == n) return n;
return find(notparent[n].second, t);
}
void unite(int n, int m, bool f = false) {
n = find(n), m = find(m);
if (n == m) {
if (f && ok_vec[n] == INF) ok_vec[n] = opcount;
opcount++;
return;
}
if (sizevec[n].back().second > sizevec[m].back().second)
std::swap(n, m);
notparent[n] = {opcount, m};
if (ok_vec[m] == INF && (f || ok_vec[n] != INF)) ok_vec[m] = opcount;
sizevec[m].emplace_back(
opcount, sizevec[m].back().second + sizevec[n].back().second);
opcount++;
}
bool same(int n, int m, int t = INF) { return find(n, t) == find(m, t); }
bool ok(int x, int t = INF - 1) { return ok_vec[x] <= t; }
int get_opcount() { return opcount; }
};
int N, M;
std::vector<std::pair<int, IP>> edges;
std::vector<int> avail_edges;
PersistentUnionFind uf(100010);
void init(int n, int m, std::vector<int> U, std::vector<int> V,
std::vector<int> W) {
N = n, M = m;
edges.reserve(M);
rep(i, M) edges.push_back({W[i], {U[i], V[i]}});
std::sort(all(edges));
std::vector<int> degree(N);
rep(i, M) {
degree[edges[i].second.first]++;
degree[edges[i].second.second]++;
int X = uf.find(edges[i].second.first),
Y = uf.find(edges[i].second.second);
if (X == Y) {
if (!uf.ok(X)) {
uf.unite(X, Y, true);
avail_edges.emplace_back(i);
}
} else {
uf.unite(X, Y,
degree[edges[i].second.first] >= 3 ||
degree[edges[i].second.second] >= 3);
avail_edges.emplace_back(i);
}
}
}
int getMinimumFuelCapacity(int X, int Y) {
int min = -1, max = avail_edges.size();
while (min + 1 < max) {
int mid = (min + max) / 2;
int root_x = uf.find(X, mid), root_y = uf.find(Y, mid);
if (root_x != root_y)
min = mid;
else if (uf.ok(root_x, mid))
max = mid;
else
min = mid;
}
if (max != M) return edges[avail_edges[max]].first;
return -1;
}
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