#include "island.h"
#include <bits/stdc++.h>
#include <ext/pb_ds/tree_policy.hpp>
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/rope>
using namespace std;
using namespace __gnu_pbds;
using namespace __gnu_cxx;
typedef long long ll;
typedef long double ld;
typedef complex<ld> cd;
typedef pair<int, int> pi;
typedef pair<ll,ll> pl;
typedef pair<ld,ld> pd;
typedef vector<int> vi;
typedef vector<ld> vd;
typedef vector<ll> vl;
typedef vector<pi> vpi;
typedef vector<pl> vpl;
typedef vector<cd> vcd;
template <class T> using Tree = tree<T, null_type, less<T>, rb_tree_tag,tree_order_statistics_node_update>;
#define FOR(i, a, b) for (int i = (a); i < (b); i++)
#define F0R(i, a) for (int i = 0; i < (a); i++)
#define FORd(i,a,b) for (int i = (b)-1; i >= (a); i--)
#define F0Rd(i,a) for (int i = (a)-1; i >= 0; i--)
#define trav(a, x) for (auto& a : x)
#define mp make_pair
#define pb push_back
#define f first
#define s second
#define lb lower_bound
#define ub upper_bound
#define sz(x) (int)x.size()
#define all(x) begin(x), end(x)
#define rsz resize
const int MOD = 1000000007; // 998244353
const ll INF = 1e18;
const int MX = 100005;
const ld PI = 4*atan((ld)1);
template<class T> void ckmin(T &a, T b) { a = min(a, b); }
template<class T> void ckmax(T &a, T b) { a = max(a, b); }
namespace input {
template<class T> void re(complex<T>& x);
template<class T1, class T2> void re(pair<T1,T2>& p);
template<class T> void re(vector<T>& a);
template<class T, size_t SZ> void re(array<T,SZ>& a);
template<class T> void re(T& x) { cin >> x; }
void re(double& x) { string t; re(t); x = stod(t); }
void re(ld& x) { string t; re(t); x = stold(t); }
template<class Arg, class... Args> void re(Arg& first, Args&... rest) {
re(first); re(rest...);
}
template<class T> void re(complex<T>& x) { T a,b; re(a,b); x = cd(a,b); }
template<class T1, class T2> void re(pair<T1,T2>& p) { re(p.f,p.s); }
template<class T> void re(vector<T>& a) { F0R(i,sz(a)) re(a[i]); }
template<class T, size_t SZ> void re(array<T,SZ>& a) { F0R(i,SZ) re(a[i]); }
}
using namespace input;
namespace output {
template<class T1, class T2> void pr(const pair<T1,T2>& x);
template<class T, size_t SZ> void pr(const array<T,SZ>& x);
template<class T> void pr(const vector<T>& x);
template<class T> void pr(const set<T>& x);
template<class T1, class T2> void pr(const map<T1,T2>& x);
template<class T> void pr(const T& x) { cout << x; }
template<class Arg, class... Args> void pr(const Arg& first, const Args&... rest) {
pr(first); pr(rest...);
}
template<class T1, class T2> void pr(const pair<T1,T2>& x) {
pr("{",x.f,", ",x.s,"}");
}
template<class T> void prContain(const T& x) {
pr("{");
bool fst = 1; for (const auto& a: x) pr(!fst?", ":"",a), fst = 0; // const needed for vector<bool>
pr("}");
}
template<class T, size_t SZ> void pr(const array<T,SZ>& x) { prContain(x); }
template<class T> void pr(const vector<T>& x) { prContain(x); }
template<class T> void pr(const set<T>& x) { prContain(x); }
template<class T1, class T2> void pr(const map<T1,T2>& x) { prContain(x); }
void ps() { pr("\n"); }
template<class Arg> void ps(const Arg& first) {
pr(first); ps(); // no space at end of line
}
template<class Arg, class... Args> void ps(const Arg& first, const Args&... rest) {
pr(first," "); ps(rest...); // print w/ spaces
}
}
using namespace output;
namespace io {
void setIn(string s) { freopen(s.c_str(),"r",stdin); }
void setOut(string s) { freopen(s.c_str(),"w",stdout); }
void setIO(string s = "") {
ios_base::sync_with_stdio(0); cin.tie(0); // fast I/O
if (sz(s)) { setIn(s+".in"), setOut(s+".out"); } // for USACO
}
}
using namespace io;
template<class T> T invGeneral(T a, T b) {
a %= b; if (a == 0) return b == 1 ? 0 : -1;
T x = invGeneral(b,a);
return x == -1 ? -1 : ((1-(ll)b*x)/a+b)%b;
}
template<class T> struct modular {
T val;
explicit operator T() const { return val; }
modular() { val = 0; }
modular(const ll& v) {
val = (-MOD <= v && v <= MOD) ? v : v % MOD;
if (val < 0) val += MOD;
}
// friend ostream& operator<<(ostream& os, const modular& a) { return os << a.val; }
friend void pr(const modular& a) { pr(a.val); }
friend void re(modular& a) { ll x; re(x); a = modular(x); }
friend bool operator==(const modular& a, const modular& b) { return a.val == b.val; }
friend bool operator!=(const modular& a, const modular& b) { return !(a == b); }
friend bool operator<(const modular& a, const modular& b) { return a.val < b.val; }
modular operator-() const { return modular(-val); }
modular& operator+=(const modular& m) { if ((val += m.val) >= MOD) val -= MOD; return *this; }
modular& operator-=(const modular& m) { if ((val -= m.val) < 0) val += MOD; return *this; }
modular& operator*=(const modular& m) { val = (ll)val*m.val%MOD; return *this; }
friend modular pow(modular a, ll p) {
modular ans = 1; for (; p; p /= 2, a *= a) if (p&1) ans *= a;
return ans;
}
friend modular inv(const modular& a) {
auto i = invGeneral(a.val,MOD); assert(i != -1);
return i;
} // equivalent to return exp(b,MOD-2) if MOD is prime
modular& operator/=(const modular& m) { return (*this) *= inv(m); }
friend modular operator+(modular a, const modular& b) { return a += b; }
friend modular operator-(modular a, const modular& b) { return a -= b; }
friend modular operator*(modular a, const modular& b) { return a *= b; }
friend modular operator/(modular a, const modular& b) { return a /= b; }
};
typedef modular<int> mi;
typedef pair<mi,mi> pmi;
typedef vector<mi> vmi;
typedef vector<pmi> vpmi;
mt19937 rng(chrono::steady_clock::now().time_since_epoch().count());
template<class T, int SZ> struct RMQ {
constexpr static int level(int x) { return 31-__builtin_clz(x); } // floor(log_2(x))
int stor[SZ][level(SZ)+1];
vector<T> v;
int comb(int a, int b) { return v[a] == v[b] ? min(a,b) : (v[a] < v[b] ? a : b); } // index of minimum
void init(const vector<T>& _v) {
v = _v; F0R(i,sz(v)) stor[i][0] = i;
FOR(j,1,level(sz(v))+1) F0R(i,sz(v)-(1<<(j-1)))
stor[i][j] = comb(stor[i][j-1],stor[i+(1<<(j-1))][j-1]);
}
int index(int l, int r) { // get index of min element
int x = level(r-l+1);
return comb(stor[l][x],stor[r-(1<<x)+1][x]);
}
T query(int l, int r) { return v[index(l,r)]; }
};
pi nex[MX];
template<int SZ> struct DSU {
int par[SZ], sz[SZ], fst[SZ], lst[SZ];
DSU() {
F0R(i,SZ) {
par[i] = i, sz[i] = 1;
fst[i] = lst[i] = i;
}
}
int get(int x) { // path compression
if (par[x] != x) par[x] = get(par[x]);
return par[x];
}
bool unite(int x, int y, int w) { // union-by-rank
if (sz[x] < sz[y]) swap(x,y);
sz[x] += sz[y], par[y] = x;
nex[lst[x]] = {fst[y],w};
lst[x] = lst[y];
return 1;
}
};
const int BLOCK = 320;
RMQ<int,MX> R;
vi ans[MX], pos[MX];
DSU<MX> D;
int getMin(int l, int r) {
if (l > r) swap(l,r);
return R.query(l,r-1);
}
void Init(int K, std::vector<int> F, std::vector<int> S, std::vector<int> E){
int N = F.size(), M = S.size();
F0R(i,N) nex[i] = {-1,-1};
F0Rd(i,M) {
int s = D.get(S[i]), e = D.get(E[i]);
if (s == e) continue;
D.unite(s,e,i+1);
}
int st = D.fst[D.get(0)];
/*ps(st);
F0R(i,N) ps(i,nex[i]);
exit(0);*/
vi wei, label;
F0R(i,N) {
//ps("CUR",i,st,F[st]);
pos[F[st]].pb(i);
label.pb(F[st]);
if (i != N-1) {
wei.pb(nex[st].s);
st = nex[st].f; assert(st != -1);
}
}
// ps("HUH",label,wei);
R.init(wei);
F0R(i,K) if (sz(pos[i]) > BLOCK) {
ans[i] = vi(K,-1);
int ind = 0;
F0R(j,N) {
while (ind < sz(pos[i]) && pos[i][ind] <= j) ind ++;
if (label[j] == i) continue;
if (ind > 0) ckmax(ans[i][label[j]],getMin(pos[i][ind-1],j));
if (ind < sz(pos[i])) ckmax(ans[i][label[j]],getMin(pos[i][ind],j));
}
}
// ps("HUH",wei);
// F0R(i,K) ps(i,pos[i]);
// ToDo
}
int Separate(int A, int B){
if (sz(pos[A]) < sz(pos[B])) swap(A,B);
if (sz(pos[A]) > BLOCK) return ans[A][B];
int ia = 0, ib = 0, res = -1;
while (ia < sz(pos[A]) && ib < sz(pos[B])) {
ckmax(res,getMin(pos[A][ia],pos[B][ib]));
if (pos[A][ia] < pos[B][ib]) ia ++;
else ib ++;
}
return res;
}
