#include "werewolf.h"
#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef long double ld;
typedef double db;
typedef string str;
typedef pair<int,int> pi;
typedef pair<ll,ll> pl;
typedef pair<db,db> pd;
typedef vector<int> vi;
typedef vector<ll> vl;
typedef vector<db> vd;
typedef vector<str> vs;
typedef vector<pi> vpi;
typedef vector<pl> vpl;
typedef vector<pd> vpd;
#define mp make_pair
#define f first
#define s second
#define sz(x) (int)x.size()
#define all(x) begin(x), end(x)
#define rall(x) (x).rbegin(), (x).rend()
#define rsz resize
#define ins insert
#define ft front()
#define bk back()
#define pf push_front
#define pb push_back
#define eb emplace_back
#define lb lower_bound
#define ub upper_bound
#define FOR(i,a,b) for (int i = (a); i < (b); ++i)
#define F0R(i,a) FOR(i,0,a)
#define ROF(i,a,b) for (int i = (b)-1; i >= (a); --i)
#define R0F(i,a) ROF(i,0,a)
#define trav(a,x) for (auto& a: x)
const int MOD = 1e9+7; // 998244353;
const int MX = 2e5+5;
const ll INF = 1e18;
const ld PI = acos((ld)-1);
const int xd[4] = {1,0,-1,0}, yd[4] = {0,1,0,-1};
template<class T> bool ckmin(T& a, const T& b) {
return b < a ? a = b, 1 : 0; }
template<class T> bool ckmax(T& a, const T& b) {
return a < b ? a = b, 1 : 0; }
int pct(int x) { return __builtin_popcount(x); }
int bit(int x) { return 31-__builtin_clz(x); } // floor(log2(x))
int cdiv(int a, int b) { return a/b+!(a<0||a%b == 0); } // division of a by b rounded up, assumes b > 0
// INPUT
template<class A> void re(complex<A>& c);
template<class A, class B> void re(pair<A,B>& p);
template<class A> void re(vector<A>& v);
template<class A, size_t SZ> void re(array<A,SZ>& a);
template<class T> void re(T& x) { cin >> x; }
void re(db& d) { str t; re(t); d = stod(t); }
void re(ld& d) { str t; re(t); d = stold(t); }
template<class H, class... T> void re(H& h, T&... t) { re(h); re(t...); }
template<class A> void re(complex<A>& c) { A a,b; re(a,b); c = {a,b}; }
template<class A, class B> void re(pair<A,B>& p) { re(p.f,p.s); }
template<class A> void re(vector<A>& x) { trav(a,x) re(a); }
template<class A, size_t SZ> void re(array<A,SZ>& x) { trav(a,x) re(a); }
// TO_STRING
#define ts to_string
template<class A, class B> str ts(pair<A,B> p);
template<class A> str ts(complex<A> c) { return ts(mp(c.real(),c.imag())); }
str ts(bool b) { return b ? "true" : "false"; }
str ts(char c) { str s = ""; s += c; return s; }
str ts(str s) { return s; }
str ts(const char* s) { return (str)s; }
str ts(vector<bool> v) {
bool fst = 1; str res = "{";
F0R(i,sz(v)) {
if (!fst) res += ", ";
fst = 0; res += ts(v[i]);
}
res += "}"; return res;
}
template<size_t SZ> str ts(bitset<SZ> b) {
str res = ""; F0R(i,SZ) res += char('0'+b[i]);
return res; }
template<class T> str ts(T v) {
bool fst = 1; str res = "{";
for (const auto& x: v) {
if (!fst) res += ", ";
fst = 0; res += ts(x);
}
res += "}"; return res;
}
template<class A, class B> str ts(pair<A,B> p) {
return "("+ts(p.f)+", "+ts(p.s)+")"; }
// OUTPUT
template<class A> void pr(A x) { cout << ts(x); }
template<class H, class... T> void pr(const H& h, const T&... t) {
pr(h); pr(t...); }
void ps() { pr("\n"); } // print w/ spaces
template<class H, class... T> void ps(const H& h, const T&... t) {
pr(h); if (sizeof...(t)) pr(" "); ps(t...); }
// DEBUG
void DBG() { cerr << "]" << endl; }
template<class H, class... T> void DBG(H h, T... t) {
cerr << to_string(h); if (sizeof...(t)) cerr << ", ";
DBG(t...); }
#ifdef LOCAL // compile with -DLOCAL
#define dbg(...) cerr << "[" << #__VA_ARGS__ << "]: [", DBG(__VA_ARGS__)
#else
#define dbg(...) 42
#endif
// FILE I/O
void setIn(string s) { freopen(s.c_str(),"r",stdin); }
void setOut(string s) { freopen(s.c_str(),"w",stdout); }
void unsyncIO() { ios_base::sync_with_stdio(0); cin.tie(0); }
void setIO(string s = "") {
unsyncIO();
// cin.exceptions(cin.failbit);
// throws exception when do smth illegal
// ex. try to read letter into int
if (sz(s)) { setIn(s+".in"), setOut(s+".out"); } // for USACO
}
mt19937 rng((uint32_t)chrono::steady_clock::now().time_since_epoch().count());
/**
* Description: point add and rectangle sum with offline 2D BIT. $x\in (0,SZ)$.
* Time: O(N\log^2 N)
* Memory: O(N\log N)
* Source: Own
* Verification:
* https://dmoj.ca/problem/occ19g4
* http://www.usaco.org/index.php?page=viewproblem2&cpid=722 (753 ms)
* http://www.usaco.org/index.php?page=viewproblem2&cpid=601 (679 ms)
*/
template<class T, int SZ> struct OffBIT2D {
bool mode = 0; // mode = 1 -> initialized
vpi todo;
int cnt[SZ], st[SZ];
vi val, bit;
void init() {
assert(!mode); mode = 1;
int lst[SZ]; F0R(i,SZ) lst[i] = cnt[i] = 0;
sort(all(todo),[](const pi& a, const pi& b) {
return a.s < b.s; });
trav(t,todo) for (int x = t.f; x < SZ; x += x&-x)
if (lst[x] != t.s) lst[x] = t.s, cnt[x] ++;
int sum = 0;
F0R(i,SZ) { lst[i] = 0; st[i] = sum; sum += cnt[i]; }
val.rsz(sum); bit.rsz(sum); // store BITs in single vector
trav(t,todo) for (int x = t.f; x < SZ; x += x&-x)
if (lst[x] != t.s) lst[x] = t.s, val[st[x]++] = t.s;
}
int rank(int y, int l, int r) {
return ub(begin(val)+l,begin(val)+r,y)-begin(val)-l; }
void UPD(int x, int y, int t) {
int z = st[x]-cnt[x]; // x-BIT = range from z to st[x]-1
for (y = rank(y,z,st[x]); y <= cnt[x]; y += y&-y)
bit[z+y-1] += t;
}
void upd(int x, int y, int t) {
if (!mode) todo.pb({x,y});
else for (; x < SZ; x += x&-x) UPD(x,y,t);
}
int QUERY(int x, int y) {
int z = st[x]-cnt[x], res = 0;
for (y = rank(y,z,st[x]); y; y -= y&-y) res += bit[z+y-1];
return res;
}
int query(int x, int y) {
assert(mode);
int res = 0; for (; x; x -= x&-x) res += QUERY(x,y);
return res;
}
int query(int xl, int xr, int yl, int yr) {
return query(xr,yr)-query(xl-1,yr)
-query(xr,yl-1)+query(xl-1,yl-1); }
};
/**
* Description: 1D range minimum query. Can also do queries
* for any associative operation in $O(1)$ with D\&C
* Source: KACTL
* Verification:
* https://cses.fi/problemset/stats/1647/
* http://wcipeg.com/problem/ioi1223
* https://pastebin.com/ChpniVZL
* Memory: O(N\log N)
* Time: O(1)
*/
template<class T> struct RMQ { // floor(log_2(x))
int level(int x) { return 31-__builtin_clz(x); }
vector<T> v; vector<vi> jmp;
int comb(int a, int b) { // index of min
return v[a]==v[b]?min(a,b):(v[a]<v[b]?a:b); }
void init(const vector<T>& _v) {
v = _v; jmp = {vi(sz(v))}; iota(all(jmp[0]),0);
for (int j = 1; 1<<j <= sz(v); ++j) {
jmp.pb(vi(sz(v)-(1<<j)+1));
F0R(i,sz(jmp[j])) jmp[j][i] = comb(jmp[j-1][i],
jmp[j-1][i+(1<<(j-1))]);
}
}
int index(int l, int r) { // get index of min element
int d = level(r-l+1);
return comb(jmp[d][l],jmp[d][r-(1<<d)+1]); }
T query(int l, int r) { return v[index(l,r)]; }
};
/**
* Description: Euler Tour LCA w/ O(1) query. Compress takes a subset $S$
* of nodes and computes the minimal subtree that contains all the nodes
* pairwise LCA's and compressing edges. Returns a list of (par, orig\_index)
* representing a tree rooted at 0. The root points to itself.
* Source: USACO, Simon Lindholm (KACTL)
* Verification: USACO Debug the Bugs
* https://codeforces.com/contest/1320/problem/E
*/
template<int SZ> struct LCA {
int N, R = 1, depth[SZ], st[SZ], en[SZ];
vi adj[SZ]; vpi tmp; RMQ<pi> r;
void ae(int u, int v) { adj[u].pb(v), adj[v].pb(u); }
void dfs(int u, int prev){
en[u] = st[u] = sz(tmp), depth[u] = depth[prev]+1;
tmp.pb({depth[u],u});
trav(v,adj[u]) if (v != prev){
dfs(v,u);
en[u] = sz(tmp);
tmp.pb({depth[u],u});
}
}
void init(int _N) { N = _N; dfs(R,0); r.init(tmp); }
int lca(int u, int v){
u = st[u], v = st[v]; if (u > v) swap(u,v);
return r.query(u,v).s; }
/// int dist(int u, int v) {
/// return depth[u]+depth[v]-2*depth[lca(u,v)]; }
vpi compress(vi S) {
static vi rev; rev.rsz(N+1);
auto cmp = [&](int a, int b) { return st[a] < st[b]; };
sort(all(S),cmp);
int m = sz(S)-1; F0R(i,m) S.pb(lca(S[i],S[i+1]));
sort(all(S),cmp); S.erase(unique(all(S)),end(S));
F0R(i,sz(S)) rev[S[i]] = i;
vpi ret = {pi(0,S[0])};
F0R(i,sz(S)-1) ret.eb(rev[lca(S[i],S[i+1])],S[i+1]);
return ret;
}
};
/**
* Description: Disjoint Set Union with path compression.
* Add edges and test connectivity. Use for Kruskal's
* minimum spanning tree.
* Time: O(\alpha(N))
* Source: CSAcademy, KACTL
* Verification: USACO superbull
*/
struct DSU {
vi e; void init(int n) { e = vi(n,-1); }
int get(int x) { return e[x] < 0 ? x : e[x] = get(e[x]); }
bool sameSet(int a, int b) { return get(a) == get(b); }
int size(int x) { return -e[get(x)]; }
bool unite(int x, int y) { // Attach y to x
x = get(x), y = get(y); if (x == y) return 0;
e[x] += e[y]; e[y] = x; return 1;
}
};
/**template<class T> T kruskal(int n, vector<pair<T,pi>> ed) {
sort(all(ed));
T ans = 0; DSU D; D.init(n+1); // edges that unite are in MST
trav(a,ed) if (D.unite(a.s.f,a.s.s)) ans += a.f;
return ans;
}*/
const int mx = 200005;
vi uadj[mx];
vi dadj[mx];
int par1[mx][25];
int par2[mx][25];
LCA<mx> lca1;
LCA<mx> lca2;
OffBIT2D<int, 2*mx+10> points;
vector<int> check_validity(int N, vector<int> X, vector<int> Y, vector<int> S, vector<int> E, vector<int> L, vector<int> R) {
int Q = S.size();
int M = X.size();
for(int i = 0; i < M; i++){
X[i]++;
Y[i]++;
}
for(int i = 0; i < Q; i++){
S[i]++;
E[i]++;
L[i]++;
R[i]++;
}
for(int i = 0; i < M; i++){
int a = X[i];
int b = Y[i];
if(a > b) swap(a, b);
uadj[a].pb(b);
dadj[b].pb(a);
}
DSU dsu;
dsu.init(N+5);
for(int i = N; i >= 1; i--){
for(auto u: uadj[i]){
if(dsu.sameSet(i, u)) continue;
u = dsu.get(u);
par1[u][0] = i;
//ps(u, i);
lca1.ae(u, i);
dsu.unite(i, u);
}
}
//ps("SEP");
dsu.init(N+5);
for(int i = 1; i <= N; i++){
for(auto u: dadj[i]){
if(dsu.sameSet(i, u)) continue;
u = dsu.get(u);
par2[u][0] = i;
lca2.ae(u, i);
//ps(u, i);
dsu.unite(i, u);
}
}
for(int j = 1; j <= 20; j++){
for(int i = 1; i <= N; i++){
par1[i][j] = par1[par1[i][j-1]][j-1];
par2[i][j] = par2[par2[i][j-1]][j-1];
}
}
lca1.init(N);
lca2.R = N;
lca2.init(N);
//ps(par1[4][0]);
vpi a;
for(int i = 1; i <= N; i++){
points.upd(lca1.st[i]+1, lca2.st[i]+1, 1);
a.pb(mp(lca1.st[i]+1, lca2.st[i]+1));
//ps(i, lca1.st[i]+1, lca2.st[i]+1, 1);
}
points.init();
for(auto u: a){
//ps(u.f, u.s, 1);
points.upd(u.f, u.s, 1);
}
vi A;
for(int i = 0; i < Q; i++){
int ind1 = L[i];
int pos1 = S[i];
//ps(i, ind1, pos1);
for(int j = 20; j >= 0; j--){
if(par1[pos1][j] == 0) continue;
if(par1[pos1][j] >= ind1){
//ps(pos1, par1[pos1][j]);
pos1 = par1[pos1][j];
}
}
int ind2 = R[i];
int pos2 = E[i];
for(int j = 20; j >= 0; j--){
if(par2[pos2][j] == 0) continue;
if(par2[pos2][j] <= ind2){
pos2 = par2[pos2][j];
}
}
//ps(pos1, pos2);
//subtree of pos1 in tree1
int st1 = lca1.st[pos1];
int en1 = lca1.en[pos1];
//subtree of pos2 in tree2
int st2 = lca2.st[pos2];
int en2 = lca2.en[pos2];
//ps(st1+1, en1+1, st2+1, en2+1);
if(points.query(st1+1, en1+1, st2+1, en2+1) == 0){
A.pb(0);
}
else A.pb(1);
}
return A;
}
/*int main(){
int N, M, Q;
cin >> N >> M >> Q;
vector<int> X(M), Y(M), S(Q), E(Q), L(Q), R(Q);
for (int j = 0; j < M; ++j) {
cin >> X[j];
cin >> Y[j];
}
for (int i = 0; i < Q; ++i) {
cin >> S[i];
cin >> E[i];
cin >> L[i];
cin >> R[i];
}
vi a = (check_validity(N, X, Y, S, E, L, R));
for(auto u: a){
ps(u);
}
}*/
