#include "plants.h"
#include<bits/stdc++.h>
using namespace std;
using ll = long long;
#define pll pair <ll,ll>
#define fi first
#define se second
#define MP make_pair
#define sz(a) (ll((a).size()))
#define BIT(mask,i) (((mask) >> (i))&1)
#define MASK(i) (1LL<<(i))
namespace trung{
const ll MAXN = 2e5+100;
const ll INF = 1e9+7;
ll n,k;
vector <int> val;
namespace seg{
pll tree[MAXN*4];
ll lazy[MAXN*4];
pll combine(pll x,pll y){
if (x.fi > y.fi)return y;
else return x;
}
void build(ll id=1,ll l=0,ll r=n-1){
if (l==r){tree[id] = MP(val[l],l);}
else{
ll mid = (l + r) >> 1;
build(id<<1,l,mid);
build(id<<1|1,mid+1,r);
tree[id] = combine(tree[id<<1],tree[id<<1|1]);
}
}
void push(ll id,ll x){
tree[id].fi+=x;
lazy[id]+=x;
}
void lz(ll id){
push(id<<1,lazy[id]);
push(id<<1|1,lazy[id]);
lazy[id] = 0;
}
void update(ll l1,ll r1,ll id=1,ll l=0,ll r=n-1){
// if (id==1)cout<<"UPD "<<l1<<' '<<r1<<endl;
if (l1 > r || l > r1 || l1 > r1)return;
if (l1 <= l && r <= r1){
// cout<<"UPD2 "<<l<<' '<<r<<endl;
push(id,-1);
return;
}
lz(id);
ll mid = (l + r) >> 1;
update(l1,r1,id<<1,l,mid);
update(l1,r1,id<<1|1,mid+1,r);
tree[id] = combine(tree[id<<1],tree[id<<1|1]);
}
void del(ll i,ll id=1,ll l=0,ll r=n-1){
if (l > i || i > r)return;
if (l==r){
// cout<<"BRUH "<<i<<endl;
tree[id].fi = INF;
return;
}
lz(id);
ll mid = (l + r) >> 1;
del(i,id<<1,l,mid);
del(i,id<<1|1,mid+1,r);
tree[id] = combine(tree[id<<1],tree[id<<1|1]);
}
ll get(ll l1,ll r1,ll id=1,ll l=0,ll r=n-1){
if (l1 > r || l > r1 || l1 > r1)return n+1;
if (tree[id].fi!=0)return n+1;
if (l1 <= l && r <= r1)return tree[id].se;
lz(id);
ll mid = (l + r) >> 1;
ll res = get(l1,r1,id<<1,l,mid);
if (res==n+1)res = get(l1,r1,id<<1|1,mid+1,r);
return res;
}
ll sus(ll i,ll id=1,ll l=0,ll r=n-1){
if (i > r || l > i)return INF+1;
if (l == r)return tree[id].fi;
lz(id);
ll mid = (l + r) >> 1;
return min(sus(i,id<<1,l,mid),sus(i,id<<1|1,mid+1,r));
}
}
vector <ll> h;
ll label;
bool in[MAXN];
void solve(ll x){
// assert(in[x] == 0);
// in[x] = 1;
ll l = x-k+1,r=x-1;
// cout<<x<<' '<<l<<' '<<r<<endl;
ll tmp;
while ((tmp=seg::get(l,r)) != n+1){
solve(tmp);
}
while ((tmp=seg::get(l+n,r+n)) != n+1){
// cout<<x<<' '<<tmp<<endl;
solve(tmp);
}
seg::del(x);
h[x] = --label;
seg::update(l,r);
seg::update(l+n,r+n);
}
const ll MAXK = 20;
ll sp_nxt[MAXK][MAXN*2];
ll sp_pre[MAXK][MAXN*2];
bool solve_nxt(ll x,ll y){
for (ll j = MAXK-1;j>=0;j--){
if (sp_nxt[j][x] <= y)x = sp_nxt[j][x];
}
return (y-x<k&&h[y]>=h[x]);
}
bool solve_pre(ll x,ll y){
for (ll j = MAXK-1;j>=0;j--){
if (sp_pre[j][x] >= y)x = sp_pre[j][x];
}
return (x-y<k&&h[y]>=h[x]);
}
}
void init(int K, std::vector<int> r){
using namespace trung;
val = r;
n=sz(r);
h.resize(n);
k=K;
seg::build();
// cout<<"OK"<<endl;
ll cur;
label = n;
while ((cur=seg::get(0,n-1)) != n+1){
// cout<<"CUR "<<cur<<endl;
solve(cur);
}
for (ll i = 0;i < n;i ++){
h.push_back(h[i]);
}
h.insert(h.begin(),INF);
h.push_back(INF);
{
set <pll> s;
for (ll i = 1;i <= k - 1;i ++){
s.insert(MP(h[i],i));
}
for (ll i = 1;i <= 2 * n;i ++){
s.erase(MP(h[i],i));
if (i + k - 1 <= 2 * n)s.insert(MP(h[i+k-1],i+k-1));
auto tmp = s.lower_bound(MP(h[i],i)); ;
if (tmp != s.end())sp_nxt[0][i] = (*tmp).se;
else sp_nxt[0][i] = i;
}
s.clear();
for (ll i = 2*n;i>=2*n-k+2;i--)s.insert(MP(h[i],i));
for (ll i = 2*n;i >= 1;i--){
s.erase(MP(h[i],i));
if (i - k + 1 >= 1)s.insert(MP(h[i - k + 1],i - k + 1));
auto tmp = s.lower_bound(MP(h[i],i)); ;
if (tmp != s.end())sp_pre[0][i] = (*tmp).se;
else sp_pre[0][i] = i;
}
// for (ll i = 1;i <= 2 * n;i ++){
// cout<<h[i]<<' ';
// }
// cout<<endl;
// for (ll i = 1;i <= 2 * n;i ++){
// cout<<sp_nxt[0][i]<<' ';
// }
// cout<<endl;
// for (ll i = 1;i <= 2 * n;i ++){
// cout<<sp_pre[0][i]<<' ';
// }
// cout<<endl;
}
for (ll j = 1;j<MAXK;j ++){
for (ll i = 1;i <= 2 * n;i ++){
sp_nxt[j][i] = sp_nxt[j-1][sp_nxt[j-1][i]];
sp_pre[j][i] = sp_pre[j-1][sp_pre[j-1][i]];
}
}
}
int compare_plants(int x, int y){
using namespace trung;
x++,y++;
if (h[x] > h[y]){
if (solve_nxt(y,x+n)||solve_pre(y,x))return 1;
else return 0;
}
else{
if (solve_nxt(x,y)||solve_pre(x+n,y))return -1;
else return 0;
}
// return (h[x] > h[y] ? 1 : -1);
}
