/*************************************
* author: marvinthang *
* created: 25.08.2023 10:13:26 *
*************************************/
#include "incursion.h"
#include <bits/stdc++.h>
using namespace std;
#define fi first
#define se second
#define left ___left
#define right ___right
#define TIME (1.0 * clock() / CLOCKS_PER_SEC)
#define MASK(i) (1LL << (i))
#define BIT(x, i) ((x) >> (i) & 1)
#define __builtin_popcount __builtin_popcountll
#define ALL(v) (v).begin(), (v).end()
#define REP(i, n) for (int i = 0, _n = (n); i < _n; ++i)
#define REPD(i, n) for (int i = (n); i-- > 0; )
#define FOR(i, a, b) for (int i = (a), _b = (b); i < _b; ++i)
#define FORD(i, b, a) for (int i = (b), _a = (a); --i >= _a; )
#define FORE(i, a, b) for (int i = (a), _b = (b); i <= _b; ++i)
#define FORDE(i, b, a) for (int i = (b), _a = (a); i >= _a; --i)
#define scan_op(...) istream & operator >> (istream &in, __VA_ARGS__ &u)
#define print_op(...) ostream & operator << (ostream &out, const __VA_ARGS__ &u)
#ifdef LOCAL
#include "debug.h"
#else
#define file(name) if (fopen(name".inp", "r")) { freopen(name".inp", "r", stdin); freopen(name".out", "w", stdout); }
#define DB(...) 23
#define db(...) 23
#define debug(...) 23
#endif
template <class U, class V> scan_op(pair <U, V>) { return in >> u.first >> u.second; }
template <class T> scan_op(vector <T>) { for (size_t i = 0; i < u.size(); ++i) in >> u[i]; return in; }
template <class U, class V> print_op(pair <U, V>) { return out << '(' << u.first << ", " << u.second << ')'; }
template <size_t i, class T> ostream & print_tuple_utils(ostream &out, const T &tup) { if constexpr(i == tuple_size<T>::value) return out << ")"; else return print_tuple_utils<i + 1, T>(out << (i ? ", " : "(") << get<i>(tup), tup); }
template <class ...U> print_op(tuple<U...>) { return print_tuple_utils<0, tuple<U...>>(out, u); }
template <class Con, class = decltype(begin(declval<Con>()))> typename enable_if <!is_same<Con, string>::value, ostream&>::type operator << (ostream &out, const Con &con) { out << '{'; for (__typeof(con.begin()) it = con.begin(); it != con.end(); ++it) out << (it == con.begin() ? "" : ", ") << *it; return out << '}'; }
// end of template
vector<int> mark(vector<pair<int, int>> F, int safe) {
int N = F.size() + 1;
vector <int> sz(N), par(N, -1);
vector <vector <int>> adj(N);
for (auto [u, v]: F) {
--u; --v;
adj[u].push_back(v);
adj[v].push_back(u);
}
function<void(int)> dfs = [&] (int u) {
sz[u] = 1;
for (int v: adj[u]) if (v != par[u]) {
par[v] = u;
dfs(v);
sz[u] += sz[v];
}
};
dfs(--safe);
vector <int> res(N);
REP(u, N) if (u != safe) {
vector <int> val;
res[u] = 1;
for (int v: adj[u]) if (v != par[u] && N - sz[u] < sz[v]) {
res[u] = 0;
break;
}
}
return res;
}
void locate(vector<pair<int, int>> F, int u, int t) {
int N = F.size() + 1;
vector <int> sz(N + 1), par(N + 1, -1);
vector <vector <int>> adj(N + 1);
for (auto [u, v]: F) {
adj[u].push_back(v);
adj[v].push_back(u);
}
function<void(int)> dfs = [&] (int u) {
sz[u] = 1;
for (int v: adj[u]) if (v != par[u]) {
par[v] = u;
dfs(v);
sz[u] += sz[v];
}
};
dfs(1);
auto get_size = [&] (int u, int p) {
return par[p] == u ? N - sz[p] : sz[u];
};
int last = u;
vector <pair <int, int>> nxt;
for (int v: adj[u]) nxt.emplace_back(get_size(v, u), v);
sort(ALL(nxt));
if (!t && nxt[0].fi == nxt.back().fi) return;
if (adj[u].size() == 1) {
t = visit(u = adj[u][0]);
} else {
if (t) {
if (nxt.size() == 1 || nxt.back().fi != nxt.end()[-2].fi) {
u = nxt.back().se;
t = visit(u);
} else {
for (auto [sz, v]: nxt) if (sz == nxt.back().fi) {
if (visit(v)) {
visit(u);
} else {
u = v;
t = 0;
break;
}
}
}
} else {
if (nxt[1].fi == nxt.back().fi) {
if (visit(nxt[0].se)) {
visit(u);
return;
}
u = nxt[0].se;
t = 0;
} else {
if (visit(nxt[1].se)) {
visit(u);
if (visit(nxt[0].se)) {
visit(u);
return;
}
u = nxt[0].se;
t = 0;
} else {
u = nxt[1].se;
t = 0;
}
}
}
}
while (true) {
vector <pair <int, int>> nxt_move, nxt;
for (int v: adj[u]) {
nxt.emplace_back(get_size(v, u), v);
if (v != last) nxt_move.push_back(nxt.back());
}
sort(ALL(nxt));
sort(ALL(nxt_move));
last = u;
if (!t && (nxt_move.empty() || nxt[0].fi == nxt.back().fi)) return;
assert(nxt.size() > 1);
if (t) {
if (nxt_move.size() == 1 || nxt_move[1].fi > nxt_move[0].fi) {
u = nxt_move.back().se;
t = visit(u);
} else {
for (auto [sz, v]: nxt_move) {
if (visit(v)) {
visit(u);
} else {
u = v;
t = 0;
break;
}
}
}
} else {
if (nxt_move.size() == 1 || nxt_move[1].fi == nxt.back().fi) {
if (nxt_move[0].fi == nxt.back().fi) return;
if (visit(nxt_move[0].se)) {
visit(u);
return;
}
u = nxt_move[0].se;
t = 0;
} else {
if (visit(nxt_move[1].se)) {
visit(u);
if (visit(nxt_move[0].se)) {
visit(u);
return;
}
u = nxt_move[0].se;
t = 0;
} else {
u = nxt_move[1].se;
t = 0;
}
}
}
}
}
