#include <bits/stdc++.h>
using namespace std;
#include "incursion.h"
int n;
vector<int> adj[45010];
vector<int> cen;
int siz[45010];
int par[45010];
void f(int x, int p) {
bool ok = 1;
siz[x] = 1;
for (int y : adj[x]) {
if (y == p) continue;
f(y, x);
siz[x] += siz[y];
if (siz[y] > n / 2) ok = 0;
}
if (n - siz[x] > n / 2) ok = 0;
if (ok) cen.push_back(x);
}
void g(int x, int p) {
par[x] = p;
siz[x] = 1;
for (int y : adj[x]) {
if (y == p) continue;
g(y, x);
siz[x] += siz[y];
}
}
void init(vector<pair<int, int>>& F) {
n = (int)F.size() + 1;
for (auto [x, y] : F) {
adj[x].push_back(y);
adj[y].push_back(x);
}
f(1, -1);
if ((int)cen.size() == 1) cen.push_back(-1);
assert((int)cen.size() == 2);
g(cen[0], cen[1]);
if (cen[1] != -1) g(cen[1], cen[0]);
}
vector<int> mark(vector<pair<int, int>> F, int safe) {
init(F);
vector<int> res(n);
int x = safe;
while (1) {
res[x - 1] = 1;
if (x == cen[0] || x == cen[1]) break;
x = par[x];
}
return res;
}
void locate(vector<pair<int, int>> F, int curr, int t) {
init(F);
int x = curr;
while (t == 0) {
t = visit(par[x]);
x = par[x];
}
while (1) {
vector<pair<int, int>> nx;
for (int y : adj[x]) {
if (y == par[x]) continue;
nx.push_back({siz[y], y});
}
sort(nx.rbegin(), nx.rend());
bool ok = 1;
for (auto [_, y] : nx) {
if (visit(y)) {
ok = 0;
x = y;
break;
}
visit(x);
}
if (ok) return;
}
}
