#include <bits/stdc++.h>
#include "incursion.h"
#define respagold ios_base::sync_with_stdio(0), cin.tie(0);
//#define int long long
#define ll long long
#define int2 __int128_t
#define FOR( i, x, n, d ) for( int i = x; i <= n; i += d )
#define FORR( i, x, n, d ) for( int i = x; i >= n; i -= d )
#define F first
#define S second
#define all(x) x.begin(), x.end()
#define sz(x) (int)(x.size())
#define pb push_back
#define ins insert
#define lb lower_bound
#define ub upper_bound
#define pii pair <int, int>
#define ppi pair <pair <int, int>, int>
#define pip pair <int, pair <int, int>>
#define mkp make_pair
using namespace std;
const int N = 1e6 + 12;
const int inf = 1e18;
const int mod = 1e9 + 7;
const double eps = 1e-20;
const int dx[4] = {1, 0, -1, 0};
const int dy[4] = {0, 1, 0, -1};
vector <int> g[N], t, siz, pa, used;
int nn;
mt19937 rng( chrono::steady_clock::now().time_since_epoch().count());
void dfs( int v, int p )
{
pa[v] = p;
for( auto to : g[v] )
{
if( to != p )
{
dfs(to, v);
siz[v] += siz[to];
}
}
}
int find_centroid( int v, int p = 0 )
{
for( auto to : g[v] )
{
if( to != p && siz[to] > nn / 2 ) return find_centroid(to, v);
}
return v;
}
vector <int> mark( vector <pair <int, int>> f, int s )
{
set <int> st;
for( auto i : f )
{
g[i.F].pb(i.S);
g[i.S].pb(i.F);
st.ins(i.F), st.ins(i.S);
}
nn = sz(st);
t = vector <int> (nn, 0);
siz = vector <int> (nn + 1, 1);
pa = vector <int> (nn + 1, 0);
dfs(s, 0); int c2 = 0;
int c = find_centroid(s, 0);
for( auto v : g[c] )
{
bool centroid_2 = 1;
for( auto to : g[v] ) centroid_2 &= (siz[to] <= nn / 2);
if( centroid_2 ) {c2 = v; break;}
}
dfs(c, c2);
if(c2) dfs(c2, c);
while(1)
{
t[s - 1] = 1;
s = pa[s];
if( s == c || s == c2 )
{
t[s - 1] = 1;
break;
}
}
for( auto v : st ) g[v].clear();
return t;
}
void locate( vector <pair <int, int>> f, int cur, int t )
{
set <int> st;
for( auto i : f )
{
g[i.F].pb(i.S);
g[i.S].pb(i.F);
st.ins(i.F), st.ins(i.S);
}
nn = sz(st);
int par = 0;
siz = vector <int> (nn + 1, 1);
pa = vector <int> (nn + 1, 0);
dfs(cur, 0); int c2 = 0;
int c = find_centroid(cur, 0);
for( auto v : g[c] )
{
bool centroid_2 = 1;
for( auto to : g[v] ) centroid_2 &= (siz[to] <= nn / 2);
if( centroid_2 ) {c2 = v; break;}
}
dfs(c, c2); used = vector <int> (nn + 1, 0);
if(c2) dfs(c2, c); used[cur] = 1;
while( t != 1 )
{
t = visit(pa[cur]);
cur = pa[cur]; used[cur] = 1;
}
siz = vector <int> (nn + 1, 1);
dfs(cur, 0);
while(1)
{
vector <pii> ord;
for( auto to : g[cur] )
{
if( to == pa[cur] || used[to] ) continue;
ord.pb({siz[to], to});
}
if( ord.empty() ) break;
sort( all(ord) );
t = visit(ord[0].S);
if( t == 1 )
{
par = cur;
cur = ord[0].S;
continue;
}
if( sz(ord) > 1 )
{
t = visit(cur);
t = visit(ord[1].S);
if( t == 1 )
{
par = cur;
cur = ord[1].S;
continue;
}
}
visit(cur);
break;
}
return;
}
