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#include "ds/segtree/sortable_segtree.hpp"
#include "ds/fastset.hpp"
#include "ds/segtree/segtree.hpp"
template <typename Monoid>
struct Sortable_SegTree {
using MX = Monoid;
using X = typename MX::value_type;
const int N, KEY_MAX;
struct Node {
X x, rev_x;
int size;
Node *l, *r;
};
Node* pool;
const int NODES;
int pid;
using np = Node*;
FastSet ss; // 区間の左端全体を表す fastset
SegTree<MX> seg; // 区間を集約した値を区間の左端にのせた segtree
vector<np> root; // 区間の左端に、dynamic segtree の node を乗せる
vector<bool> rev;
Sortable_SegTree(int NODES, int KEY_MAX, vector<int> key, vector<X> dat) : N(key.size()), KEY_MAX(KEY_MAX), NODES(NODES), pid(0), ss(key.size()), seg(dat) {
pool = new Node[NODES];
init(key, dat);
}
~Sortable_SegTree() { delete[] pool; }
void set(int i, int key, const X& x) {
assert(key < KEY_MAX);
split_at(i), split_at(i + 1);
rev[i] = 0, root[i] = new_node();
set_rec(root[i], 0, KEY_MAX, key, x);
seg.set(i, x);
}
X prod_all() { return seg.prod_all(); }
X prod(int l, int r) {
if (pid > NODES * 0.9) rebuild();
split_at(l), split_at(r);
return seg.prod(l, r);
}
void sort_inc(int l, int r) {
split_at(l), split_at(r);
while (1) {
if (pid > NODES * 0.9) rebuild();
np c = root[l];
int i = ss.next(l + 1);
if (i == r) break;
root[l] = merge(c, root[i]);
ss.erase(i), seg.set(i, MX::unit());
}
rev[l] = 0, seg.set(l, root[l]->x);
};
void sort_dec(int l, int r) {
if (pid > NODES * 0.9) rebuild();
sort_inc(l, r), rev[l] = 1;
seg.set(l, root[l]->rev_x);
};
pair<vc<int>, vc<X>> get_all() {
vector<int> key;
vector<X> dat;
key.reserve(N);
dat.reserve(N);
auto dfs = [&](auto& dfs, np n, int l, int r, bool rev) -> void {
if (!n) return;
if (r == l + 1) {
key.eb(l), dat.eb(n->x);
return;
}
int m = (l + r) / 2;
if (!rev) { dfs(dfs, n->l, l, m, rev), dfs(dfs, n->r, m, r, rev); }
if (rev) { dfs(dfs, n->r, m, r, rev), dfs(dfs, n->l, l, m, rev); }
};
for (int i = 0; i < N; ++i) {
if (ss[i]) dfs(dfs, root[i], 0, KEY_MAX, rev[i]);
}
return {key, dat};
}
private:
void init(vector<int>& key, vector<X>& dat) {
rev.assign(N, 0), root.clear(), root.reserve(N);
seg.build(N, [&](int i) -> X { return dat[i]; });
for (int i = 0; i < N; ++i) {
ss.insert(i);
root.eb(new_node(MX::unit()));
assert(key[i] < KEY_MAX);
set_rec(root[i], 0, KEY_MAX, key[i], dat[i]);
}
}
// x が左端になるようにする
void split_at(int x) {
if (x == N || ss[x]) return;
int a = ss.prev(x), b = ss.next(a + 1);
ss.insert(x);
if (!rev[a]) {
auto [nl, nr] = split(root[a], x - a);
root[a] = nl, root[x] = nr;
rev[a] = rev[x] = 0;
seg.set(a, root[a]->x), seg.set(x, root[x]->x);
} else {
auto [nl, nr] = split(root[a], b - x);
root[a] = nr, root[x] = nl;
rev[a] = rev[x] = 1;
seg.set(a, root[a]->rev_x), seg.set(x, root[x]->rev_x);
}
}
void rebuild() {
auto [key, dat] = get_all();
pid = 0;
init(key, dat);
}
np new_node(X x = MX::unit()) {
assert(pid < NODES);
pool[pid].x = pool[pid].rev_x = x;
pool[pid].l = pool[pid].r = nullptr;
pool[pid].size = 1;
return &(pool[pid++]);
}
pair<np, np> split(np n, int k) {
if (k == 0) { return {nullptr, n}; }
if (k == n->size) { return {n, nullptr}; }
int s = (n->l ? n->l->size : 0);
Node* b = new_node();
if (k <= s) {
auto [nl, nr] = split(n->l, k);
b->l = nr, b->r = n->r, n->l = nl, n->r = nullptr;
}
if (k > s) {
auto [nl, nr] = split(n->r, k - s);
n->l = n->l, n->r = nl, b->l = nullptr, b->r = nr;
}
update(n), update(b);
return {n, b};
}
np merge(np a, np b) {
if (!a) return b;
if (!b) return a;
a->l = merge(a->l, b->l), a->r = merge(a->r, b->r);
update(a);
return a;
}
void update(np n) {
if (!(n->l) && !(n->r)) { return; }
if (!(n->l)) {
n->x = n->r->x, n->rev_x = n->r->rev_x, n->size = n->r->size;
return;
}
if (!(n->r)) {
n->x = n->l->x, n->rev_x = n->l->rev_x, n->size = n->l->size;
return;
}
n->x = MX::op(n->l->x, n->r->x);
n->rev_x = MX::op(n->r->rev_x, n->l->rev_x);
n->size = n->l->size + n->r->size;
}
void set_rec(np n, int l, int r, int k, const X& x) {
if (r == l + 1) {
n->x = n->rev_x = x;
return;
}
int m = (l + r) / 2;
if (k < m) {
if (!(n->l)) n->l = new_node();
set_rec(n->l, l, m, k, x);
}
if (m <= k) {
if (!(n->r)) n->r = new_node();
set_rec(n->r, m, r, k, x);
}
update(n);
}
};
#line 2 "ds/fastset.hpp"
// 64-ary tree
// space: (N/63) * u64
struct FastSet {
static constexpr u32 B = 64;
int n, log;
vvc<u64> seg;
FastSet() {}
FastSet(int n) { build(n); }
int size() { return n; }
template <typename F>
FastSet(int n, F f) {
build(n, f);
}
void build(int m) {
seg.clear();
n = m;
do {
seg.push_back(vc<u64>((m + B - 1) / B));
m = (m + B - 1) / B;
} while (m > 1);
log = len(seg);
}
template <typename F>
void build(int n, F f) {
build(n);
FOR(i, n) { seg[0][i / B] |= u64(f(i)) << (i % B); }
FOR(h, log - 1) {
FOR(i, len(seg[h])) { seg[h + 1][i / B] |= u64(bool(seg[h][i])) << (i % B); }
}
}
bool operator[](int i) const { return seg[0][i / B] >> (i % B) & 1; }
void insert(int i) {
assert(0 <= i && i < n);
for (int h = 0; h < log; h++) { seg[h][i / B] |= u64(1) << (i % B), i /= B; }
}
void add(int i) { insert(i); }
void erase(int i) {
assert(0 <= i && i < n);
u64 x = 0;
for (int h = 0; h < log; h++) {
seg[h][i / B] &= ~(u64(1) << (i % B));
seg[h][i / B] |= x << (i % B);
x = bool(seg[h][i / B]);
i /= B;
}
}
void remove(int i) { erase(i); }
// min[x,n) or n
int next(int i) {
assert(i <= n);
chmax(i, 0);
for (int h = 0; h < log; h++) {
if (i / B == seg[h].size()) break;
u64 d = seg[h][i / B] >> (i % B);
if (!d) {
i = i / B + 1;
continue;
}
i += lowbit(d);
for (int g = h - 1; g >= 0; g--) {
i *= B;
i += lowbit(seg[g][i / B]);
}
return i;
}
return n;
}
// max [0,x], or -1
int prev(int i) {
assert(i >= -1);
if (i >= n) i = n - 1;
for (int h = 0; h < log; h++) {
if (i == -1) break;
u64 d = seg[h][i / B] << (63 - i % B);
if (!d) {
i = i / B - 1;
continue;
}
i -= __builtin_clzll(d);
for (int g = h - 1; g >= 0; g--) {
i *= B;
i += topbit(seg[g][i / B]);
}
return i;
}
return -1;
}
bool any(int l, int r) { return next(l) < r; }
// [l, r)
template <typename F>
void enumerate(int l, int r, F f) {
for (int x = next(l); x < r; x = next(x + 1)) f(x);
}
string to_string() {
string s(n, '?');
for (int i = 0; i < n; ++i) s[i] = ((*this)[i] ? '1' : '0');
return s;
}
};
#line 2 "ds/segtree/segtree.hpp"
template <class Monoid>
struct SegTree {
using MX = Monoid;
using X = typename MX::value_type;
using value_type = X;
vc<X> dat;
int n, log, size;
SegTree() {}
SegTree(int n) { build(n); }
template <typename F>
SegTree(int n, F f) {
build(n, f);
}
SegTree(const vc<X>& v) { build(v); }
void build(int m) {
build(m, [](int i) -> X { return MX::unit(); });
}
void build(const vc<X>& v) {
build(len(v), [&](int i) -> X { return v[i]; });
}
template <typename F>
void build(int m, F f) {
n = m, log = 1;
while ((1 << log) < n) ++log;
size = 1 << log;
dat.assign(size << 1, MX::unit());
FOR(i, n) dat[size + i] = f(i);
FOR_R(i, 1, size) update(i);
}
X get(int i) { return dat[size + i]; }
vc<X> get_all() { return {dat.begin() + size, dat.begin() + size + n}; }
void update(int i) { dat[i] = Monoid::op(dat[2 * i], dat[2 * i + 1]); }
void set(int i, const X& x) {
assert(i < n);
dat[i += size] = x;
while (i >>= 1) update(i);
}
void multiply(int i, const X& x) {
assert(i < n);
i += size;
dat[i] = Monoid::op(dat[i], x);
while (i >>= 1) update(i);
}
X prod(int L, int R) {
assert(0 <= L && L <= R && R <= n);
X vl = Monoid::unit(), vr = Monoid::unit();
L += size, R += size;
while (L < R) {
if (L & 1) vl = Monoid::op(vl, dat[L++]);
if (R & 1) vr = Monoid::op(dat[--R], vr);
L >>= 1, R >>= 1;
}
return Monoid::op(vl, vr);
}
X prod_all() { return dat[1]; }
template <class F>
int max_right(F check, int L) {
assert(0 <= L && L <= n && check(Monoid::unit()));
if (L == n) return n;
L += size;
X sm = Monoid::unit();
do {
while (L % 2 == 0) L >>= 1;
if (!check(Monoid::op(sm, dat[L]))) {
while (L < size) {
L = 2 * L;
if (check(Monoid::op(sm, dat[L]))) { sm = Monoid::op(sm, dat[L++]); }
}
return L - size;
}
sm = Monoid::op(sm, dat[L++]);
} while ((L & -L) != L);
return n;
}
template <class F>
int min_left(F check, int R) {
assert(0 <= R && R <= n && check(Monoid::unit()));
if (R == 0) return 0;
R += size;
X sm = Monoid::unit();
do {
--R;
while (R > 1 && (R % 2)) R >>= 1;
if (!check(Monoid::op(dat[R], sm))) {
while (R < size) {
R = 2 * R + 1;
if (check(Monoid::op(dat[R], sm))) { sm = Monoid::op(dat[R--], sm); }
}
return R + 1 - size;
}
sm = Monoid::op(dat[R], sm);
} while ((R & -R) != R);
return 0;
}
// prod_{l<=i<r} A[i xor x]
X xor_prod(int l, int r, int xor_val) {
static_assert(Monoid::commute);
X x = Monoid::unit();
for (int k = 0; k < log + 1; ++k) {
if (l >= r) break;
if (l & 1) { x = Monoid::op(x, dat[(size >> k) + ((l++) ^ xor_val)]); }
if (r & 1) { x = Monoid::op(x, dat[(size >> k) + ((--r) ^ xor_val)]); }
l /= 2, r /= 2, xor_val /= 2;
}
return x;
}
};
#line 3 "ds/segtree/sortable_segtree.hpp"
template <typename Monoid>
struct Sortable_SegTree {
using MX = Monoid;
using X = typename MX::value_type;
const int N, KEY_MAX;
struct Node {
X x, rev_x;
int size;
Node *l, *r;
};
Node* pool;
const int NODES;
int pid;
using np = Node*;
FastSet ss; // 区間の左端全体を表す fastset
SegTree<MX> seg; // 区間を集約した値を区間の左端にのせた segtree
vector<np> root; // 区間の左端に、dynamic segtree の node を乗せる
vector<bool> rev;
Sortable_SegTree(int NODES, int KEY_MAX, vector<int> key, vector<X> dat) : N(key.size()), KEY_MAX(KEY_MAX), NODES(NODES), pid(0), ss(key.size()), seg(dat) {
pool = new Node[NODES];
init(key, dat);
}
~Sortable_SegTree() { delete[] pool; }
void set(int i, int key, const X& x) {
assert(key < KEY_MAX);
split_at(i), split_at(i + 1);
rev[i] = 0, root[i] = new_node();
set_rec(root[i], 0, KEY_MAX, key, x);
seg.set(i, x);
}
X prod_all() { return seg.prod_all(); }
X prod(int l, int r) {
if (pid > NODES * 0.9) rebuild();
split_at(l), split_at(r);
return seg.prod(l, r);
}
void sort_inc(int l, int r) {
split_at(l), split_at(r);
while (1) {
if (pid > NODES * 0.9) rebuild();
np c = root[l];
int i = ss.next(l + 1);
if (i == r) break;
root[l] = merge(c, root[i]);
ss.erase(i), seg.set(i, MX::unit());
}
rev[l] = 0, seg.set(l, root[l]->x);
};
void sort_dec(int l, int r) {
if (pid > NODES * 0.9) rebuild();
sort_inc(l, r), rev[l] = 1;
seg.set(l, root[l]->rev_x);
};
pair<vc<int>, vc<X>> get_all() {
vector<int> key;
vector<X> dat;
key.reserve(N);
dat.reserve(N);
auto dfs = [&](auto& dfs, np n, int l, int r, bool rev) -> void {
if (!n) return;
if (r == l + 1) {
key.eb(l), dat.eb(n->x);
return;
}
int m = (l + r) / 2;
if (!rev) { dfs(dfs, n->l, l, m, rev), dfs(dfs, n->r, m, r, rev); }
if (rev) { dfs(dfs, n->r, m, r, rev), dfs(dfs, n->l, l, m, rev); }
};
for (int i = 0; i < N; ++i) {
if (ss[i]) dfs(dfs, root[i], 0, KEY_MAX, rev[i]);
}
return {key, dat};
}
private:
void init(vector<int>& key, vector<X>& dat) {
rev.assign(N, 0), root.clear(), root.reserve(N);
seg.build(N, [&](int i) -> X { return dat[i]; });
for (int i = 0; i < N; ++i) {
ss.insert(i);
root.eb(new_node(MX::unit()));
assert(key[i] < KEY_MAX);
set_rec(root[i], 0, KEY_MAX, key[i], dat[i]);
}
}
// x が左端になるようにする
void split_at(int x) {
if (x == N || ss[x]) return;
int a = ss.prev(x), b = ss.next(a + 1);
ss.insert(x);
if (!rev[a]) {
auto [nl, nr] = split(root[a], x - a);
root[a] = nl, root[x] = nr;
rev[a] = rev[x] = 0;
seg.set(a, root[a]->x), seg.set(x, root[x]->x);
} else {
auto [nl, nr] = split(root[a], b - x);
root[a] = nr, root[x] = nl;
rev[a] = rev[x] = 1;
seg.set(a, root[a]->rev_x), seg.set(x, root[x]->rev_x);
}
}
void rebuild() {
auto [key, dat] = get_all();
pid = 0;
init(key, dat);
}
np new_node(X x = MX::unit()) {
assert(pid < NODES);
pool[pid].x = pool[pid].rev_x = x;
pool[pid].l = pool[pid].r = nullptr;
pool[pid].size = 1;
return &(pool[pid++]);
}
pair<np, np> split(np n, int k) {
if (k == 0) { return {nullptr, n}; }
if (k == n->size) { return {n, nullptr}; }
int s = (n->l ? n->l->size : 0);
Node* b = new_node();
if (k <= s) {
auto [nl, nr] = split(n->l, k);
b->l = nr, b->r = n->r, n->l = nl, n->r = nullptr;
}
if (k > s) {
auto [nl, nr] = split(n->r, k - s);
n->l = n->l, n->r = nl, b->l = nullptr, b->r = nr;
}
update(n), update(b);
return {n, b};
}
np merge(np a, np b) {
if (!a) return b;
if (!b) return a;
a->l = merge(a->l, b->l), a->r = merge(a->r, b->r);
update(a);
return a;
}
void update(np n) {
if (!(n->l) && !(n->r)) { return; }
if (!(n->l)) {
n->x = n->r->x, n->rev_x = n->r->rev_x, n->size = n->r->size;
return;
}
if (!(n->r)) {
n->x = n->l->x, n->rev_x = n->l->rev_x, n->size = n->l->size;
return;
}
n->x = MX::op(n->l->x, n->r->x);
n->rev_x = MX::op(n->r->rev_x, n->l->rev_x);
n->size = n->l->size + n->r->size;
}
void set_rec(np n, int l, int r, int k, const X& x) {
if (r == l + 1) {
n->x = n->rev_x = x;
return;
}
int m = (l + r) / 2;
if (k < m) {
if (!(n->l)) n->l = new_node();
set_rec(n->l, l, m, k, x);
}
if (m <= k) {
if (!(n->r)) n->r = new_node();
set_rec(n->r, m, r, k, x);
}
update(n);
}
};