#include "incursion.h"
#include <bits/stdc++.h>
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>
#define ll long long
#define ld long double
#define ull unsigned long long
#define ff first
#define ss second
#define pii pair<int,int>
#define pll pair<long long, long long>
#define vi vector<int>
#define vl vector<long long>
#define pb push_back
#define rep(i, b) for(int i = 0; i < (b); ++i)
#define rep2(i,a,b) for(int i = a; i <= (b); ++i)
#define rep3(i,a,b,c) for(int i = a; i <= (b); i+=c)
#define count_bits(x) __builtin_popcountll((x))
#define all(x) (x).begin(),(x).end()
#define siz(x) (int)(x).size()
#define forall(it,x) for(auto& it:(x))
using namespace __gnu_pbds;
using namespace std;
typedef tree<int, null_type, less<int>, rb_tree_tag,tree_order_statistics_node_update> ordered_set;
//mt19937 mt;void random_start(){mt.seed(chrono::time_point_cast<chrono::milliseconds>(chrono::high_resolution_clock::now()).time_since_epoch().count());}
//ll los(ll a, ll b) {return a + (mt() % (b-a+1));}
const int INF = 1e9+50;
const ll INF_L = 1e18+40;
const ll MOD = 1e9+7;
int n;
vi graph[45001];
int sub[45001];
int P[45001];
vi marks;
void dfs(int v, int pop)
{
sub[v] = 1;
P[v] = pop;
forall(it,graph[v])
{
if(it != pop)
{
dfs(it,v);
sub[v] += sub[it];
}
}
}
void dfs_mark(int v, int pop)
{
if(v == pop) marks[v-1] = 0;
else
{
int best_ = 0;
forall(it,graph[v])
{
if(it != P[v])
{
best_ = max(best_,sub[it]);
}
else
{
best_ = max(best_,n-sub[v]);
}
}
if(best_ == n-sub[v]) marks[v-1] = 1;
else marks[v-1] = 0;
}
forall(it,graph[v])
{
if(it != pop)
{
dfs_mark(it,v);
}
}
}
vi mark(vector<pii> F, int safe)
{
n = siz(F)+1;
rep2(i,1,n) graph[i] = {};
forall(it,F)
{
graph[it.ff].pb(it.ss);
graph[it.ss].pb(it.ff);
}
dfs(safe,safe);
marks.resize(n,0);
dfs_mark(safe,safe);
return marks;
}
void locate(vector<pii> F, int curr, int t)
{
n = siz(F)+1;
rep2(i,1,n) graph[i] = {};
forall(it,F)
{
graph[it.ff].pb(it.ss);
graph[it.ss].pb(it.ff);
}
dfs(1,1);
int prev = curr;
while(true)
{
if(t == 1)
{
int best_ = 0;
vi bests;
forall(it,graph[curr])
{
if(it == prev) continue;
if(it != P[curr])
{
if(best_ == sub[it])
{
bests.pb(it);
}
else if(best_ < sub[it])
{
best_ = sub[it];
bests = {it};
}
}
else
{
if(best_ == n-sub[curr])
{
bests.pb(it);
}
else if(best_ < n-sub[curr])
{
best_ = n-sub[curr];
bests = {it};
}
}
}
rep(i,siz(bests))
{
t = visit(bests[i]);
if(i == siz(bests)-1)
{
prev = curr;
curr = bests[i];
break;
}
else
{
if(t == 1)
{
t = visit(curr);
}
else
{
prev = curr;
curr = bests[i];
break;
}
}
}
}
else
{
vector<pii> rest;
int best_ = 0;
forall(it,graph[curr])
{
int d = sub[it];
if(P[curr] == it) d = n - sub[curr];
best_ = max(best_,d);
}
forall(it,graph[curr])
{
if(it == prev) continue;
int d = sub[it];
if(P[curr] == it) d = n - sub[curr];
if(d != best_) rest.pb({d,it});
}
sort(all(rest));
reverse(all(rest));
bool is = 0;
rep(i,siz(rest))
{
t = visit(rest[i].ss);
if(t == 0)
{
prev = curr;
curr = rest[i].ss;
is = 1;
break;
}
else
{
t = visit(curr);
}
}
if(!is) break;
}
}
}
