#include <bits/stdc++.h>
using namespace std;
using ll = long long;
#define all(x) x.begin(), x.end()
#define mp make_pair
#define mt make_tuple
#define x first
#define y second
#include "plants.h"
#define cerr if (0) cout
namespace my {
const int L = 18;
const int N = 1 << L;
int n, k, kth[N], can[N];
struct tree_t {
pair<int, int> mi[2 * N];
int pu[2 * N];
int ls(int v) {
return 2 * v + 1;
}
int rs(int v) {
return 2 * v + 2;
}
void build(int v, int l, int r) {
if (r - l == 1) {
mi[v] = mp(kth[l], l);
} else {
int m = (l + r) / 2;
build(ls(v), l, m);
build(rs(v), m, r);
mi[v] = min(mi[ls(v)], mi[rs(v)]);
}
}
void build() {
build(0, 0, N);
}
void push(int v) {
mi[ls(v)].x += pu[v];
mi[rs(v)].x += pu[v];
pu[ls(v)] += pu[v];
pu[rs(v)] += pu[v];
pu[v] = 0;
}
void upd(int v, int vl, int vr, int ql, int qr, int d) {
if (ql <= vl && vr <= qr) {
mi[v].x += d;
pu[v] += d;
return;
}
if (qr <= vl || vr <= ql) {
return;
}
push(v);
int vm = (vl + vr) / 2;
upd(ls(v), vl, vm, ql, qr, d);
upd(rs(v), vm, vr, ql, qr, d);
mi[v] = min(mi[ls(v)], mi[rs(v)]);
}
void range_add(int l, int r, int value) {
upd(0, 0, N, l, r, value);
}
void cycle_add(int from, int value) {
from %= n; from += n; from %= n;
if (from + k <= n) {
range_add(from, from + k, value);
} else {
range_add(from, n, value), range_add(0, from + k - n, value);
}
}
pair<int, int> query(int v, int vl, int vr, int ql, int qr) {
if (ql <= vl && vr <= qr) {
return mi[v];
}
if (qr <= vl || vr <= ql) {
return mp(N, -1);
}
int vm = (vl + vr) / 2;
push(v);
return min(query(ls(v), vl, vm, ql, qr), query(rs(v), vm, vr, ql, qr));
}
pair<int, int> range_min(int l, int r) {
return query(0, 0, N, l, r);
}
pair<int, int> cycle_min(int from) {
from %= n; from += n; from %= n;
if (from + k <= n) {
return range_min(from, from + k);
} else {
return min(range_min(from, n), range_min(0, from + k - n));
}
}
} tree;
vector<int> topsort;
void extract(int v) {
tree.range_add(v, v + 1, N);
while (1) {
auto e = tree.cycle_min(v - k + 1);
if (e.x) break;
extract(e.y);
}
tree.cycle_add(v - k + 1, -1);
topsort.push_back(v);
}
const int BAD = -1;
int lef[L][N], rig[L][N];
}
bool btw(int l, int r, int w) {
if (l <= r) {
return l <= w && w <= r;
} else {
return l <= w || w <= r;
}
}
void init(int _k, vector<int> _r) {
using namespace my;
n = (int)_r.size();
k = _k;
copy(all(_r), kth);
tree.build();
while (1) {
auto e = tree.range_min(0, n);
if (e.x) break;
extract(e.y);
}
assert((int)topsort.size() == n);
reverse(all(topsort));
for (int i = 0; i < n; ++i) {
can[topsort[i]] = i;
}
set<pair<int, int>> iset;
for (int i = 0; i < k - 1; ++i) {
iset.emplace(can[i], i);
}
fill_n(lef[0], L * N, BAD), fill_n(rig[0], L * N, BAD);
for (int i = k - 1;;) {
auto it = iset.lower_bound(mp(can[i], i));
if (it != iset.begin()) {
--it;
lef[0][i] = it->y;
}
iset.erase({can[(i + n - k + 1) % n], (i + n - k + 1) % n});
iset.emplace(can[i], i);
(i += 1) %= n;
if (i == k - 1) break;
}
iset.clear();
for (int i = 0; i < k - 1; ++i) {
iset.emplace(can[i], i);
}
for (int i = n - 1; i >= 0; --i) {
auto it = iset.lower_bound(mp(can[i], i));
if (it != iset.begin()) {
--it;
rig[0][i] = it->y;
}
iset.erase({can[(i + k - 1) % n], (i + k - 1) % n});
iset.emplace(can[i], i);
}
for (int i = 0; i < n; ++i) {
cerr << i << " " << lef[0][i] << " " << rig[0][i] << endl;
}
for (int i = 0; i < n; ++i) {
cerr << can[i] << " ";
}
cerr << endl;
for (int it = 1; it < L; ++it) {
for (int i = 0; i < n; ++i) {
if (lef[it - 1][i] != BAD) {
int j = lef[it - 1][i];
if (j == BAD || btw(lef[it - 1][j], j, i)) {
continue;
}
lef[it][i] = lef[it - 1][j];
}
}
}
for (int it = 1; it < L; ++it) {
for (int i = 0; i < n; ++i) {
if (rig[it - 1][i] != BAD) {
int j = rig[it - 1][i];
if (j == BAD || btw(j, rig[it - 1][j], i)) {
continue;
}
rig[it][i] = rig[it - 1][j];
}
}
}
}
bool taller(int x, int y) {
using namespace my;
cerr << "taller " << x << " " << y << endl;
int z = x;
for (int it = L - 1; it >= 0; --it) {
int v = lef[it][z];
cerr << it << " " << z << " " << v << endl;
if (v == BAD || btw(v, z, y)) {
continue;
}
z = v;
}
cerr << "z = " << z << " " << y << endl;
assert(lef[0][z] == BAD || btw(lef[0][z], z, y));
if (lef[0][z] != BAD && btw(lef[0][z], z, y) && can[z] >= can[y]) {
return true;
}
z = x;
for (int it = L - 1; it >= 0; --it) {
int v = rig[it][z];
if (v == BAD || btw(z, v, y)) {
continue;
}
z = v;
}
assert(rig[0][z] == BAD || btw(z, rig[0][z], y));
cerr << "z = " << z << endl;
if (rig[0][z] != BAD && btw(z, rig[0][z], y) && can[z] >= can[y]) {
return true;
}
return false;
}
int compare_plants(int x, int y) {
if (taller(x, y)) {
return 1;
} else if (taller(y, x)) {
return -1;
} else {
return 0;
}
}
#ifdef LC
#include "grader.cpp"
#endif
