#include "game.h"
#include <bits/stdc++.h>
#include <ext/pb_ds/assoc_container.hpp>
#pragma GCC optimize("O3")
#pragma GCC target("avx,avx2,fma")
//#pragma GCC optimization ("unroll-loops")
#pragma GCC target("avx,avx2,sse,sse2,sse3,sse4,popcnt")
using namespace std;
using namespace __gnu_pbds;
#define float long double
#define elif else if
#define endl "\n"
#define mod 1000000007
#define pi acos(-1)
#define eps 0.000000001
#define inf 1000'000'000'000'000'000LL
#define FIXED(a) cout << fixed << setprecision(a)
#define all(x) x.begin(), x.end()
#define rall(x) x.rbegin(), x.rend()
#define time_init auto start = std::chrono::high_resolution_clock::now()
#define time_report \
auto end = std::chrono::high_resolution_clock::now(); \
std::cout << std::chrono::duration_cast<std::chrono::milliseconds>(end - start).count() << " ms" << endl
#define debug(x) \
{ cerr << #x << " = " << x << endl; }
#define len(x) (int) x.size()
#define sqr(x) ((x) * (x))
#define cube(x) ((x) * (x) * (x))
#define bit(x, i) (((x) >> (i)) & 1)
#define set_bit(x, i) ((x) | (1LL << (i)))
#define clear_bit(x, i) ((x) & (~(1LL << (i))))
#define toggle_bit(x, i) ((x) ^ (1LL << (i)))
#define low_bit(x) ((x) & (-(x)))
#define count_bit(x) __builtin_popcountll(x)
#define srt(x) sort(all(x))
#define rsrt(x) sort(rall(x))
#define mp make_pair
#define maxel(x) (*max_element(all(x)))
#define minel(x) (*min_element(all(x)))
#define maxelpos(x) (max_element(all(x)) - x.begin())
#define minelpos(x) (min_element(all(x)) - x.begin())
#define sum(x) (accumulate(all(x), 0LL))
#define product(x) (accumulate(all(x), 1LL, multiplies<int>()))
#define gcd __gcd
#define lcm(a, b) ((a) / gcd(a, b) * (b))
#define rev(x) (reverse(all(x)))
#define shift_left(x, k) (rotate(x.begin(), x.begin() + k, x.end()))
#define shift_right(x, k) (rotate(x.rbegin(), x.rbegin() + k, x.rend()))
#define is_sorted(x) (is_sorted_until(all(x)) == x.end())
#define is_even(x) (((x) &1) == 0)
#define is_odd(x) (((x) &1) == 1)
#define pow2(x) (1LL << (x))
struct custom_hash {
static uint64_t splitmix64(uint64_t x) {
// http://xorshift.di.unimi.it/splitmix64.c
x += 0x9e3779b97f4a7c15;
x = (x ^ (x >> 30)) * 0xbf58476d1ce4e5b9;
x = (x ^ (x >> 27)) * 0x94d049bb133111eb;
return x ^ (x >> 31);
}
size_t operator()(uint64_t x) const {
static const uint64_t FIXED_RANDOM = chrono::steady_clock::now().time_since_epoch().count();
return splitmix64(x + FIXED_RANDOM);
}
};
template<typename T>
using min_heap = priority_queue<T, vector<T>, greater<T>>;
template<typename T>
using max_heap = priority_queue<T, vector<T>, less<T>>;
template<typename T>
using ordered_set = tree<T, null_type, less<T>, rb_tree_tag, tree_order_statistics_node_update>;
template<typename T>
using ordered_multiset = tree<T, null_type, less_equal<T>, rb_tree_tag, tree_order_statistics_node_update>;
template<typename T>
using matrix = vector<vector<T>>;
template<typename T>
using graph = vector<vector<T>>;
using hashmap = gp_hash_table<int, int, custom_hash>;
template<typename T>
vector<T> vect(int n, T val) {
return vector<T>(n, val);
}
template<typename T>
vector<vector<T>> vect(int n, int m, T val) {
return vector<vector<T>>(n, vector<T>(m, val));
}
template<typename T>
vector<vector<vector<T>>> vect(int n, int m, int k, T val) {
return vector<vector<vector<T>>>(n, vector<vector<T>>(m, vector<T>(k, val)));
}
template<typename T>
vector<vector<vector<vector<T>>>> vect(int n, int m, int k, int l, T val) {
return vector<vector<vector<vector<T>>>>(n, vector<vector<vector<T>>>(m, vector<vector<T>>(k, vector<T>(l, val))));
}
template<typename T>
matrix<T> new_matrix(int n, int m, T val) {
return matrix<T>(n, vector<T>(m, val));
}
template<typename T>
graph<T> new_graph(int n) {
return graph<T>(n);
}
template<class T, class S>
inline bool chmax(T &a, const S &b) {
return (a < b ? a = b, 1 : 0);
}
template<class T, class S>
inline bool chmin(T &a, const S &b) {
return (a > b ? a = b, 1 : 0);
}
using i8 = int8_t;
using i16 = int16_t;
using i32 = int32_t;
using i64 = int64_t;
using i128 = __int128_t;
using u8 = uint8_t;
using u16 = uint16_t;
using u32 = uint32_t;
using u64 = uint64_t;
using u128 = __uint128_t;
template<typename T>
using vec = vector<T>;
using pII = pair<int, int>;
template<typename T>
using enumerated = pair<T, int>;
vec<bitset<1501>> a;
vec<set<int>> g_mst;
set<pair<int, int>> edges;
set<pair<int, int>> MST_edges;
mt19937 rng(10235);
void initialize(int n) {
g_mst.resize(n);
a.resize(n);
vec<int> p(n);
iota(all(p), 0);
shuffle(all(p), rng);
for (int i = 1; i < n; i++) {
MST_edges.insert({p[i], p[i - 1]});
MST_edges.insert({p[i - 1], p[i]});
g_mst[p[i]].insert(p[i - 1]);
g_mst[p[i - 1]].insert(p[i]);
}
for (int i = 0; i < n; i++) {
for (int j = 0; j < n; j++) {
if (i == j) continue;
if (MST_edges.count({i, j}) == 0)
edges.insert({i, j});
a[i][j] = true;
}
}
}
int hasEdge(int u, int v) {
if (edges.count({u, v})) {
edges.erase({u, v});
edges.erase({v, u});
a[v][u] = false;
a[u][v] = false;
return false;
}
a[u][v] = false;
a[v][u] = false;
g_mst[u].erase(v);
g_mst[v].erase(u);
bitset<1501> right;
function<void(int, int)> dfs = [&](int v, int p) {
right[v] = true;
for (auto u: g_mst[v]) {
if (u == p) continue;
dfs(u, v);
}
};
int n = len(g_mst);
dfs(0, -1);
if (len(edges) < n * n / 100) {
int a_ = -1;
int b_ = -1;
for (auto [x, y]: edges) {
if (right[x] xor right[y]) {
a_ = x;
b_ = y;
}
}
if (a_ == -1) {
a[u][v] = true;
a[v][u] = true;
g_mst[u].insert(v);
g_mst[v].insert(u);
return true;
}
edges.erase({a_, b_});
edges.erase({b_, a_});
g_mst[a_].insert(b_);
g_mst[b_].insert(a_);
return false;
}
for (int i = 0; i < n; i++) {
if (right[i]) continue;
bitset<1501> t = a[i] & right;
if (t.count() != 0) {
for (int j = 0; j < n; j++) {
if (t[j]) {
edges.erase({i, j});
edges.erase({j, i});
g_mst[i].insert(j);
g_mst[j].insert(i);
return false;
}
}
}
}
a[u][v] = true;
a[v][u] = true;
g_mst[u].insert(v);
g_mst[v].insert(u);
return true;
}
