This documentation is automatically generated by online-judge-tools/verification-helper
#include "ds/wavelet_matrix/wavelet_matrix.hpp"
#include "ds/bit_vector.hpp"
#include "ds/index_compression.hpp"
#include "alg/monoid/add.hpp"
// 静的メソッドinverseの存在をチェックするテンプレート
template <typename, typename = std::void_t<>>
struct has_inverse : std::false_type {};
template <typename T>
struct has_inverse<T, std::void_t<decltype(
T::inverse(std::declval<typename T::value_type>()))>>
: std::true_type {};
struct Dummy_Data_Structure {
using MX = Monoid_Add<bool>;
void build(const vc<bool>& A) {}
};
template <typename Y, bool SMALL_Y, typename SEGTREE = Dummy_Data_Structure>
struct Wavelet_Matrix {
using Mono = typename SEGTREE::MX;
using T = typename Mono::value_type;
static_assert(Mono::commute);
int n, log, K;
Index_Compression<Y, true, SMALL_Y> IDX;
vc<Y> ItoY;
vc<int> mid;
vc<Bit_Vector> bv;
vc<SEGTREE> seg;
Wavelet_Matrix() {}
Wavelet_Matrix(const vc<Y>& A) { build(A); }
Wavelet_Matrix(const vc<Y>& A, vc<T>& SUM_Data) { build(A, SUM_Data); }
template <typename F>
Wavelet_Matrix(int n, F f) {
build(n, f);
}
template <typename F>
void build(int m, F f) {
vc<Y> A(m);
vc<T> S(m);
for (int i = 0; i < m; ++i) tie(A[i], S[i]) = f(i);
build(A, S);
}
void build(const vc<Y>& A) { build(A, vc<T>(len(A), Mono::unit())); }
void build(const vc<Y>& A, vc<T> S) {
n = len(A);
vc<int> B = IDX.build(A);
K = 0;
for (auto& x: B) chmax(K, x + 1);
ItoY.resize(K);
FOR(i, n) ItoY[B[i]] = A[i];
log = 0;
while ((1 << log) < K) ++log;
mid.resize(log), bv.assign(log, Bit_Vector(n));
vc<int> B0(n), B1(n);
vc<T> S0(n), S1(n);
seg.resize(log + 1);
seg[log].build(S);
for (int d = log - 1; d >= 0; --d) {
int p0 = 0, p1 = 0;
for (int i = 0; i < n; ++i) {
bool f = (B[i] >> d & 1);
if (!f) { B0[p0] = B[i], S0[p0] = S[i], p0++; }
if (f) { bv[d].set(i), B1[p1] = B[i], S1[p1] = S[i], p1++; }
}
swap(B, B0), swap(S, S0);
move(B1.begin(), B1.begin() + p1, B.begin() + p0);
move(S1.begin(), S1.begin() + p1, S.begin() + p0);
mid[d] = p0, bv[d].build(), seg[d].build(S);
}
}
// [L,R) x [0,y)
int prefix_count(int L, int R, Y y) {
int p = IDX(y);
if (L == R || p == 0) return 0;
if (p == K) return R - L;
int cnt = 0;
for (int d = log - 1; d >= 0; --d) {
int l0 = bv[d].count_prefix(L, 0), r0 = bv[d].count_prefix(R, 0);
int l1 = L + mid[d] - l0, r1 = R + mid[d] - r0;
if (p >> d & 1) cnt += r0 - l0, L = l1, R = r1;
if (!(p >> d & 1)) L = l0, R = r0;
}
return cnt;
}
// [L,R) x [y1,y2)
int count(int L, int R, Y y1, Y y2) {
return prefix_count(L, R, y2) - prefix_count(L, R, y1);
}
// [L,R) x [0,y)
pair<int, T> prefix_count_and_prod(int L, int R, Y y) {
int p = IDX(y);
if (p == 0) return {0, Mono::unit()};
if (p == K) return {R - L, seg[log].prod(L, R)};
int cnt = 0;
T t = Mono::unit();
for (int d = log - 1; d >= 0; --d) {
int l0 = bv[d].count_prefix(L, 0), r0 = bv[d].count_prefix(R, 0);
int l1 = L + mid[d] - l0, r1 = R + mid[d] - r0;
if (p >> d & 1) {
cnt += r0 - l0, t = Mono::op(t, seg[d].prod(l0, r0)), L = l1, R = r1;
}
if (!(p >> d & 1)) L = l0, R = r0;
}
return {cnt, t};
}
// [L,R) x [y1,y2)
pair<int, T> count_and_prod(int L, int R, Y y1, Y y2) {
if constexpr (has_inverse<Mono>::value) {
auto [c1, t1] = prefix_count_and_prod(L, R, y1);
auto [c2, t2] = prefix_count_and_prod(L, R, y2);
return {c2 - c1, Mono::op(Mono::inverse(t1), t2)};
}
int lo = IDX(y1), hi = IDX(y2), cnt = 0;
T t = Mono::unit();
auto dfs = [&](auto& dfs, int d, int L, int R, int a, int b) -> void {
assert(b - a == (1 << d));
if (hi <= a || b <= lo) return;
if (lo <= a && b <= hi) {
cnt += R - L, t = Mono::op(t, seg[d].prod(L, R));
return;
}
--d;
int c = (a + b) / 2;
int l0 = bv[d].count_prefix(L, 0), r0 = bv[d].count_prefix(R, 0);
int l1 = L + mid[d] - l0, r1 = R + mid[d] - r0;
dfs(dfs, d, l0, r0, a, c), dfs(dfs, d, l1, r1, c, b);
};
dfs(dfs, log, L, R, 0, 1 << log);
return {cnt, t};
}
// [L,R) x [y1,y2)
T prefix_prod(int L, int R, Y y) { return prefix_count_and_prod(L, R, y).se; }
// [L,R) x [y1,y2)
T prod(int L, int R, Y y1, Y y2) { return count_and_prod(L, R, y1, y2).se; }
T prod_all(int L, int R) { return seg[log].prod(L, R); }
Y kth(int L, int R, int k) {
assert(0 <= k && k < R - L);
int p = 0;
for (int d = log - 1; d >= 0; --d) {
int l0 = bv[d].count_prefix(L, 0), r0 = bv[d].count_prefix(R, 0);
int l1 = L + mid[d] - l0, r1 = R + mid[d] - r0;
if (k < r0 - l0) {
L = l0, R = r0;
} else {
k -= r0 - l0, L = l1, R = r1, p |= 1 << d;
}
}
return ItoY[p];
}
// y 以上最小 OR infty<Y>
Y next(int L, int R, Y y) {
int k = IDX(y);
int p = K;
auto dfs = [&](auto& dfs, int d, int L, int R, int a, int b) -> void {
if (p <= a || L == R || b <= k) return;
if (d == 0) {
chmin(p, a);
return;
}
--d;
int c = (a + b) / 2;
int l0 = bv[d].count_prefix(L, 0), r0 = bv[d].count_prefix(R, 0);
int l1 = L + mid[d] - l0, r1 = R + mid[d] - r0;
dfs(dfs, d, l0, r0, a, c), dfs(dfs, d, l1, r1, c, b);
};
dfs(dfs, log, L, R, 0, 1 << log);
return (p == K ? infty<Y> : ItoY[p]);
}
// y 以下最大 OR -infty<T>
Y prev(int L, int R, Y y) {
int k = IDX(y + 1);
int p = -1;
auto dfs = [&](auto& dfs, int d, int L, int R, int a, int b) -> void {
if (b - 1 <= p || L == R || k <= a) return;
if (d == 0) {
chmax(p, a);
return;
}
--d;
int c = (a + b) / 2;
int l0 = bv[d].count_prefix(L, 0), r0 = bv[d].count_prefix(R, 0);
int l1 = L + mid[d] - l0, r1 = R + mid[d] - r0;
dfs(dfs, d, l1, r1, c, b), dfs(dfs, d, l0, r0, a, c);
};
dfs(dfs, log, L, R, 0, 1 << log);
return (p == -1 ? -infty<Y> : ItoY[p]);
}
Y median(bool UPPER, int L, int R) {
assert(0 <= L && L < R && R <= n);
int k = (UPPER ? (R - L) / 2 : (R - L - 1) / 2);
return kth(L, R, k);
}
pair<Y, T> kth_value_and_prod(int L, int R, int k) {
assert(0 <= k && k <= R - L);
if (k == R - L) return {infty<Y>, seg[log].prod(L, R)};
int p = 0;
T t = Mono::unit();
for (int d = log - 1; d >= 0; --d) {
int l0 = bv[d].count_prefix(L, 0), r0 = bv[d].count_prefix(R, 0);
int l1 = L + mid[d] - l0, r1 = R + mid[d] - r0;
if (k < r0 - l0) {
L = l0, R = r0;
} else {
t = Mono::op(t, seg[d].prod(l0, r0)), k -= r0 - l0, L = l1, R = r1,
p |= 1 << d;
}
}
t = Mono::op(t, seg[0].prod(L, L + k));
return {ItoY[p], t};
}
T prod_index_range(int L, int R, int k1, int k2) {
static_assert(has_inverse<Mono>::value);
T t1 = kth_value_and_prod(L, R, k1).se;
T t2 = kth_value_and_prod(L, R, k2).se;
return Mono::op(Mono::inverse(t1), t2);
}
// [L,R) x [0,y) での check(cnt, prod) が true となる最大の (cnt,prod)
template <typename F>
pair<int, T> max_right(F check, int L, int R) {
int cnt = 0;
T t = Mono::unit();
assert(check(0, Mono::unit()));
if (check(R - L, seg[log].prod(L, R))) {
return {R - L, seg[log].prod(L, R)};
}
for (int d = log - 1; d >= 0; --d) {
int l0 = bv[d].count_prefix(L, 0), r0 = bv[d].count_prefix(R, 0);
int l1 = L + mid[d] - l0, r1 = R + mid[d] - r0;
int cnt1 = cnt + r0 - l0;
T t1 = Mono::op(t, seg[d].prod(l0, r0));
if (check(cnt1, t1)) {
cnt = cnt1, t = t1, L = l1, R = r1;
} else {
L = l0, R = r0;
}
}
return {cnt, t};
}
void set(int i, T t) {
assert(0 <= i && i < n);
int L = i, R = i + 1;
seg[log].set(L, t);
for (int d = log - 1; d >= 0; --d) {
int l0 = bv[d].count_prefix(L, 0), r0 = bv[d].count_prefix(R, 0);
int l1 = L + mid[d] - l0, r1 = R + mid[d] - r0;
if (l0 < r0) L = l0, R = r0;
if (l0 == r0) L = l1, R = r1;
seg[d].set(L, t);
}
}
void multiply(int i, T t) {
assert(0 <= i && i < n);
int L = i, R = i + 1;
seg[log].multiply(L, t);
for (int d = log - 1; d >= 0; --d) {
int l0 = bv[d].count_prefix(L, 0), r0 = bv[d].count_prefix(R, 0);
int l1 = L + mid[d] - l0, r1 = R + mid[d] - r0;
if (l0 < r0) L = l0, R = r0;
if (l0 == r0) L = l1, R = r1;
seg[d].multiply(L, t);
}
}
};
#line 1 "ds/bit_vector.hpp"
struct Bit_Vector {
int n;
bool prepared = 0;
vc<pair<u64, u32>> dat;
Bit_Vector(int n) : n(n) { dat.assign((n + 127) >> 6, {0, 0}); }
void set(int i) {
assert(!prepared);
dat[i >> 6].fi |= u64(1) << (i & 63);
}
void reset() {
fill(all(dat), pair<u64, u32>{0, 0});
prepared = 0;
}
void build() {
prepared = 1;
FOR(i, len(dat) - 1) dat[i + 1].se = dat[i].se + popcnt(dat[i].fi);
}
// [0, k) 内の 1 の個数
bool operator[](int i) { return dat[i >> 6].fi >> (i & 63) & 1; }
int count_prefix(int k, bool f = true) {
assert(prepared);
auto [a, b] = dat[k >> 6];
int ret = b + popcnt(a & ((u64(1) << (k & 63)) - 1));
return (f ? ret : k - ret);
}
int count(int L, int R, bool f = true) { return count_prefix(R, f) - count_prefix(L, f); }
string to_string() {
string ans;
FOR(i, n) ans += '0' + (dat[i / 64].fi >> (i % 64) & 1);
return ans;
}
};
#line 1 "ds/index_compression.hpp"
template <typename T>
struct Index_Compression_DISTINCT_SMALL {
static_assert(is_same_v<T, int>);
int mi, ma;
vc<int> dat;
vc<int> build(vc<int> X) {
mi = 0, ma = -1;
if (!X.empty()) mi = MIN(X), ma = MAX(X);
dat.assign(ma - mi + 2, 0);
for (auto& x: X) dat[x - mi + 1]++;
FOR(i, len(dat) - 1) dat[i + 1] += dat[i];
for (auto& x: X) { x = dat[x - mi]++; }
FOR_R(i, 1, len(dat)) dat[i] = dat[i - 1];
dat[0] = 0;
return X;
}
int operator()(ll x) { return dat[clamp<ll>(x - mi, 0, ma - mi + 1)]; }
};
template <typename T>
struct Index_Compression_SAME_SMALL {
static_assert(is_same_v<T, int>);
int mi, ma;
vc<int> dat;
vc<int> build(vc<int> X) {
mi = 0, ma = -1;
if (!X.empty()) mi = MIN(X), ma = MAX(X);
dat.assign(ma - mi + 2, 0);
for (auto& x: X) dat[x - mi + 1] = 1;
FOR(i, len(dat) - 1) dat[i + 1] += dat[i];
for (auto& x: X) { x = dat[x - mi]; }
return X;
}
int operator()(ll x) { return dat[clamp<ll>(x - mi, 0, ma - mi + 1)]; }
};
template <typename T>
struct Index_Compression_SAME_LARGE {
vc<T> dat;
vc<int> build(vc<T> X) {
vc<int> I = argsort(X);
vc<int> res(len(X));
for (auto& i: I) {
if (!dat.empty() && dat.back() == X[i]) {
res[i] = len(dat) - 1;
} else {
res[i] = len(dat);
dat.eb(X[i]);
}
}
dat.shrink_to_fit();
return res;
}
int operator()(T x) { return LB(dat, x); }
};
template <typename T>
struct Index_Compression_DISTINCT_LARGE {
vc<T> dat;
vc<int> build(vc<T> X) {
vc<int> I = argsort(X);
vc<int> res(len(X));
for (auto& i: I) { res[i] = len(dat), dat.eb(X[i]); }
dat.shrink_to_fit();
return res;
}
int operator()(T x) { return LB(dat, x); }
};
template <typename T, bool SMALL>
using Index_Compression_DISTINCT =
typename std::conditional<SMALL, Index_Compression_DISTINCT_SMALL<T>,
Index_Compression_DISTINCT_LARGE<T>>::type;
template <typename T, bool SMALL>
using Index_Compression_SAME =
typename std::conditional<SMALL, Index_Compression_SAME_SMALL<T>,
Index_Compression_SAME_LARGE<T>>::type;
// SAME: [2,3,2] -> [0,1,0]
// DISTINCT: [2,2,3] -> [0,2,1]
// (x): lower_bound(X,x) をかえす
template <typename T, bool SAME, bool SMALL>
using Index_Compression =
typename std::conditional<SAME, Index_Compression_SAME<T, SMALL>,
Index_Compression_DISTINCT<T, SMALL>>::type;
#line 2 "alg/monoid/add.hpp"
template <typename E>
struct Monoid_Add {
using X = E;
using value_type = X;
static constexpr X op(const X &x, const X &y) noexcept { return x + y; }
static constexpr X inverse(const X &x) noexcept { return -x; }
static constexpr X power(const X &x, ll n) noexcept { return X(n) * x; }
static constexpr X unit() { return X(0); }
static constexpr bool commute = true;
};
#line 4 "ds/wavelet_matrix/wavelet_matrix.hpp"
// 静的メソッドinverseの存在をチェックするテンプレート
template <typename, typename = std::void_t<>>
struct has_inverse : std::false_type {};
template <typename T>
struct has_inverse<T, std::void_t<decltype(
T::inverse(std::declval<typename T::value_type>()))>>
: std::true_type {};
struct Dummy_Data_Structure {
using MX = Monoid_Add<bool>;
void build(const vc<bool>& A) {}
};
template <typename Y, bool SMALL_Y, typename SEGTREE = Dummy_Data_Structure>
struct Wavelet_Matrix {
using Mono = typename SEGTREE::MX;
using T = typename Mono::value_type;
static_assert(Mono::commute);
int n, log, K;
Index_Compression<Y, true, SMALL_Y> IDX;
vc<Y> ItoY;
vc<int> mid;
vc<Bit_Vector> bv;
vc<SEGTREE> seg;
Wavelet_Matrix() {}
Wavelet_Matrix(const vc<Y>& A) { build(A); }
Wavelet_Matrix(const vc<Y>& A, vc<T>& SUM_Data) { build(A, SUM_Data); }
template <typename F>
Wavelet_Matrix(int n, F f) {
build(n, f);
}
template <typename F>
void build(int m, F f) {
vc<Y> A(m);
vc<T> S(m);
for (int i = 0; i < m; ++i) tie(A[i], S[i]) = f(i);
build(A, S);
}
void build(const vc<Y>& A) { build(A, vc<T>(len(A), Mono::unit())); }
void build(const vc<Y>& A, vc<T> S) {
n = len(A);
vc<int> B = IDX.build(A);
K = 0;
for (auto& x: B) chmax(K, x + 1);
ItoY.resize(K);
FOR(i, n) ItoY[B[i]] = A[i];
log = 0;
while ((1 << log) < K) ++log;
mid.resize(log), bv.assign(log, Bit_Vector(n));
vc<int> B0(n), B1(n);
vc<T> S0(n), S1(n);
seg.resize(log + 1);
seg[log].build(S);
for (int d = log - 1; d >= 0; --d) {
int p0 = 0, p1 = 0;
for (int i = 0; i < n; ++i) {
bool f = (B[i] >> d & 1);
if (!f) { B0[p0] = B[i], S0[p0] = S[i], p0++; }
if (f) { bv[d].set(i), B1[p1] = B[i], S1[p1] = S[i], p1++; }
}
swap(B, B0), swap(S, S0);
move(B1.begin(), B1.begin() + p1, B.begin() + p0);
move(S1.begin(), S1.begin() + p1, S.begin() + p0);
mid[d] = p0, bv[d].build(), seg[d].build(S);
}
}
// [L,R) x [0,y)
int prefix_count(int L, int R, Y y) {
int p = IDX(y);
if (L == R || p == 0) return 0;
if (p == K) return R - L;
int cnt = 0;
for (int d = log - 1; d >= 0; --d) {
int l0 = bv[d].count_prefix(L, 0), r0 = bv[d].count_prefix(R, 0);
int l1 = L + mid[d] - l0, r1 = R + mid[d] - r0;
if (p >> d & 1) cnt += r0 - l0, L = l1, R = r1;
if (!(p >> d & 1)) L = l0, R = r0;
}
return cnt;
}
// [L,R) x [y1,y2)
int count(int L, int R, Y y1, Y y2) {
return prefix_count(L, R, y2) - prefix_count(L, R, y1);
}
// [L,R) x [0,y)
pair<int, T> prefix_count_and_prod(int L, int R, Y y) {
int p = IDX(y);
if (p == 0) return {0, Mono::unit()};
if (p == K) return {R - L, seg[log].prod(L, R)};
int cnt = 0;
T t = Mono::unit();
for (int d = log - 1; d >= 0; --d) {
int l0 = bv[d].count_prefix(L, 0), r0 = bv[d].count_prefix(R, 0);
int l1 = L + mid[d] - l0, r1 = R + mid[d] - r0;
if (p >> d & 1) {
cnt += r0 - l0, t = Mono::op(t, seg[d].prod(l0, r0)), L = l1, R = r1;
}
if (!(p >> d & 1)) L = l0, R = r0;
}
return {cnt, t};
}
// [L,R) x [y1,y2)
pair<int, T> count_and_prod(int L, int R, Y y1, Y y2) {
if constexpr (has_inverse<Mono>::value) {
auto [c1, t1] = prefix_count_and_prod(L, R, y1);
auto [c2, t2] = prefix_count_and_prod(L, R, y2);
return {c2 - c1, Mono::op(Mono::inverse(t1), t2)};
}
int lo = IDX(y1), hi = IDX(y2), cnt = 0;
T t = Mono::unit();
auto dfs = [&](auto& dfs, int d, int L, int R, int a, int b) -> void {
assert(b - a == (1 << d));
if (hi <= a || b <= lo) return;
if (lo <= a && b <= hi) {
cnt += R - L, t = Mono::op(t, seg[d].prod(L, R));
return;
}
--d;
int c = (a + b) / 2;
int l0 = bv[d].count_prefix(L, 0), r0 = bv[d].count_prefix(R, 0);
int l1 = L + mid[d] - l0, r1 = R + mid[d] - r0;
dfs(dfs, d, l0, r0, a, c), dfs(dfs, d, l1, r1, c, b);
};
dfs(dfs, log, L, R, 0, 1 << log);
return {cnt, t};
}
// [L,R) x [y1,y2)
T prefix_prod(int L, int R, Y y) { return prefix_count_and_prod(L, R, y).se; }
// [L,R) x [y1,y2)
T prod(int L, int R, Y y1, Y y2) { return count_and_prod(L, R, y1, y2).se; }
T prod_all(int L, int R) { return seg[log].prod(L, R); }
Y kth(int L, int R, int k) {
assert(0 <= k && k < R - L);
int p = 0;
for (int d = log - 1; d >= 0; --d) {
int l0 = bv[d].count_prefix(L, 0), r0 = bv[d].count_prefix(R, 0);
int l1 = L + mid[d] - l0, r1 = R + mid[d] - r0;
if (k < r0 - l0) {
L = l0, R = r0;
} else {
k -= r0 - l0, L = l1, R = r1, p |= 1 << d;
}
}
return ItoY[p];
}
// y 以上最小 OR infty<Y>
Y next(int L, int R, Y y) {
int k = IDX(y);
int p = K;
auto dfs = [&](auto& dfs, int d, int L, int R, int a, int b) -> void {
if (p <= a || L == R || b <= k) return;
if (d == 0) {
chmin(p, a);
return;
}
--d;
int c = (a + b) / 2;
int l0 = bv[d].count_prefix(L, 0), r0 = bv[d].count_prefix(R, 0);
int l1 = L + mid[d] - l0, r1 = R + mid[d] - r0;
dfs(dfs, d, l0, r0, a, c), dfs(dfs, d, l1, r1, c, b);
};
dfs(dfs, log, L, R, 0, 1 << log);
return (p == K ? infty<Y> : ItoY[p]);
}
// y 以下最大 OR -infty<T>
Y prev(int L, int R, Y y) {
int k = IDX(y + 1);
int p = -1;
auto dfs = [&](auto& dfs, int d, int L, int R, int a, int b) -> void {
if (b - 1 <= p || L == R || k <= a) return;
if (d == 0) {
chmax(p, a);
return;
}
--d;
int c = (a + b) / 2;
int l0 = bv[d].count_prefix(L, 0), r0 = bv[d].count_prefix(R, 0);
int l1 = L + mid[d] - l0, r1 = R + mid[d] - r0;
dfs(dfs, d, l1, r1, c, b), dfs(dfs, d, l0, r0, a, c);
};
dfs(dfs, log, L, R, 0, 1 << log);
return (p == -1 ? -infty<Y> : ItoY[p]);
}
Y median(bool UPPER, int L, int R) {
assert(0 <= L && L < R && R <= n);
int k = (UPPER ? (R - L) / 2 : (R - L - 1) / 2);
return kth(L, R, k);
}
pair<Y, T> kth_value_and_prod(int L, int R, int k) {
assert(0 <= k && k <= R - L);
if (k == R - L) return {infty<Y>, seg[log].prod(L, R)};
int p = 0;
T t = Mono::unit();
for (int d = log - 1; d >= 0; --d) {
int l0 = bv[d].count_prefix(L, 0), r0 = bv[d].count_prefix(R, 0);
int l1 = L + mid[d] - l0, r1 = R + mid[d] - r0;
if (k < r0 - l0) {
L = l0, R = r0;
} else {
t = Mono::op(t, seg[d].prod(l0, r0)), k -= r0 - l0, L = l1, R = r1,
p |= 1 << d;
}
}
t = Mono::op(t, seg[0].prod(L, L + k));
return {ItoY[p], t};
}
T prod_index_range(int L, int R, int k1, int k2) {
static_assert(has_inverse<Mono>::value);
T t1 = kth_value_and_prod(L, R, k1).se;
T t2 = kth_value_and_prod(L, R, k2).se;
return Mono::op(Mono::inverse(t1), t2);
}
// [L,R) x [0,y) での check(cnt, prod) が true となる最大の (cnt,prod)
template <typename F>
pair<int, T> max_right(F check, int L, int R) {
int cnt = 0;
T t = Mono::unit();
assert(check(0, Mono::unit()));
if (check(R - L, seg[log].prod(L, R))) {
return {R - L, seg[log].prod(L, R)};
}
for (int d = log - 1; d >= 0; --d) {
int l0 = bv[d].count_prefix(L, 0), r0 = bv[d].count_prefix(R, 0);
int l1 = L + mid[d] - l0, r1 = R + mid[d] - r0;
int cnt1 = cnt + r0 - l0;
T t1 = Mono::op(t, seg[d].prod(l0, r0));
if (check(cnt1, t1)) {
cnt = cnt1, t = t1, L = l1, R = r1;
} else {
L = l0, R = r0;
}
}
return {cnt, t};
}
void set(int i, T t) {
assert(0 <= i && i < n);
int L = i, R = i + 1;
seg[log].set(L, t);
for (int d = log - 1; d >= 0; --d) {
int l0 = bv[d].count_prefix(L, 0), r0 = bv[d].count_prefix(R, 0);
int l1 = L + mid[d] - l0, r1 = R + mid[d] - r0;
if (l0 < r0) L = l0, R = r0;
if (l0 == r0) L = l1, R = r1;
seg[d].set(L, t);
}
}
void multiply(int i, T t) {
assert(0 <= i && i < n);
int L = i, R = i + 1;
seg[log].multiply(L, t);
for (int d = log - 1; d >= 0; --d) {
int l0 = bv[d].count_prefix(L, 0), r0 = bv[d].count_prefix(R, 0);
int l1 = L + mid[d] - l0, r1 = R + mid[d] - r0;
if (l0 < r0) L = l0, R = r0;
if (l0 == r0) L = l1, R = r1;
seg[d].multiply(L, t);
}
}
};