verify/ds/range_query/range_lis_query.test.cpp

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• Last update: 2026-10-06 01:57:24+09:00
• Problem: https://judge.yosupo.jp/problem/static_range_lis_query

Depends on

• Static Range LIS Query (ds/range_query/range_lis_query.hpp)
• Wavelet Matrix (ds/wavelet_matrix/wavelet_matrix.hpp)
• Fast IO (utilities/fast_io.hpp)

Code

#define PROBLEM "https://judge.yosupo.jp/problem/static_range_lis_query"

#include "../../../ds/range_query/range_lis_query.hpp"
#include "../../../utilities/fast_io.hpp"

#include <algorithm>
#include <cassert>
#include <cstdint>
#include <vector>

namespace {

int brute(const std::vector<int>& values, int left, int right) {
    std::vector<int> tails;
    for (int i = left; i < right; i++) {
        auto position = std::lower_bound(
            tails.begin(),
            tails.end(),
            values[i]
        );
        if (position == tails.end()) {
            tails.push_back(values[i]);
        } else {
            *position = values[i];
        }
    }
    return int(tails.size());
}

void test_randomized() {
    m1une::ds::RangeLisQuery<int> empty(std::vector<int>{});
    assert(empty.empty());
    assert(empty.query(0, 0) == 0);

    std::uint64_t state = 3141592653ULL;
    auto random = [&]() {
        state ^= state << 7;
        state ^= state >> 9;
        return state;
    };

    for (int trial = 0; trial < 500; trial++) {
        int n = int(random() % 36);
        std::vector<int> values(n);
        for (int& value : values) value = int(random() % 11) - 5;
        m1une::ds::RangeLisQuery<int> structure(values);
        assert(structure.size() == n);
        assert(structure.empty() == (n == 0));

        for (int left = 0; left <= n; left++) {
            for (int right = left; right <= n; right++) {
                int expected = brute(values, left, right);
                assert(structure.query(left, right) == expected);
                assert(structure.lis_length(left, right) == expected);
            }
        }
    }
}

}  // namespace

int main() {
    test_randomized();

    m1une::utilities::FastInput input;
    m1une::utilities::FastOutput output;

    int n = 0, query_count = 0;
    input.read(n, query_count);
    std::vector<int> permutation(n);
    for (int& value : permutation) input.read(value);

    m1une::ds::RangeLisQuery<int> structure(permutation);
    while (query_count--) {
        int left = 0, right = 0;
        input.read(left, right);
        output.println(structure.query(left, right));
    }
}

#line 1 "verify/ds/range_query/range_lis_query.test.cpp"
#define PROBLEM "https://judge.yosupo.jp/problem/static_range_lis_query"

#line 1 "ds/range_query/range_lis_query.hpp"



#line 1 "ds/wavelet_matrix/wavelet_matrix.hpp"



#include <algorithm>
#include <bit>
#include <cassert>
#include <concepts>
#include <cstdint>
#include <limits>
#include <optional>
#include <type_traits>
#include <utility>
#include <vector>

#if defined(__AVX2__) || defined(__BMI2__)
#include <immintrin.h>
#endif

namespace m1une {
namespace ds {

// A static wavelet matrix for integral values.
template <std::integral T>
requires(!std::same_as<std::remove_cv_t<T>, bool>)
struct WaveletMatrix {
    using value_type = T;
    using unsigned_type = std::make_unsigned_t<T>;

   private:
    static constexpr int value_bit_width =
        std::numeric_limits<unsigned_type>::digits;
    static constexpr unsigned_type sign_mask = [] {
        if constexpr (std::signed_integral<T>) {
            return unsigned_type(1) << (value_bit_width - 1);
        } else {
            return unsigned_type(0);
        }
    }();

    struct BitVector {
        std::vector<std::uint64_t> bits;
        std::vector<int> prefix;

        BitVector() = default;

        explicit BitVector(int n)
            : bits(((std::size_t(n) + 63) >> 6) + 1, 0),
              prefix(bits.size(), 0) {}

        void build() {
            for (std::size_t i = 0; i + 1 < bits.size(); i++) {
                prefix[i + 1] = prefix[i] + std::popcount(bits[i]);
            }
        }

        bool get(int p) const {
            return (bits[std::size_t(p) >> 6] >> (p & 63)) & 1;
        }

        int rank1(int r) const {
            std::size_t word = std::size_t(r) >> 6;
            int offset = r & 63;
            int result = prefix[word];
#if defined(__BMI2__)
            result += std::popcount(
                _bzhi_u64(bits[word], static_cast<unsigned int>(offset))
            );
#else
            if (offset != 0) {
                result += std::popcount(
                    bits[word] & ((std::uint64_t(1) << offset) - 1)
                );
            }
#endif
            return result;
        }
    };

    int _n;
    int _log;
    unsigned_type _key_prefix;
    unsigned_type _min_key;
    unsigned_type _max_key;
    std::vector<BitVector> _matrix;
    std::vector<int> _zero_count;

    static unsigned_type encode(T value) {
        unsigned_type bits;
        if constexpr (std::signed_integral<T>) {
            bits = std::bit_cast<unsigned_type>(value);
        } else {
            bits = value;
        }
        return bits ^ sign_mask;
    }

    static T decode(unsigned_type key) {
        unsigned_type bits = key ^ sign_mask;
        if constexpr (std::signed_integral<T>) {
            return std::bit_cast<T>(bits);
        } else {
            return bits;
        }
    }

    bool bit(unsigned_type value, int level) const {
        return (value >> (_log - 1 - level)) & unsigned_type(1);
    }

    static std::uint64_t extract_bits(
        const unsigned_type* values,
        int count,
        int shift
    ) {
        std::uint64_t result = 0;
        int i = 0;
#if defined(__AVX2__)
        if constexpr (sizeof(unsigned_type) == 8) {
            __m128i left = _mm_cvtsi32_si128(63 - shift);
            for (; i + 4 <= count; i += 4) {
                __m256i data = _mm256_loadu_si256(
                    reinterpret_cast<const __m256i*>(values + i)
                );
                data = _mm256_sll_epi64(data, left);
                int mask = _mm256_movemask_pd(_mm256_castsi256_pd(data));
                result |= std::uint64_t(mask) << i;
            }
        } else if constexpr (sizeof(unsigned_type) == 4) {
            __m128i left = _mm_cvtsi32_si128(31 - shift);
            for (; i + 8 <= count; i += 8) {
                __m256i data = _mm256_loadu_si256(
                    reinterpret_cast<const __m256i*>(values + i)
                );
                data = _mm256_sll_epi32(data, left);
                int mask = _mm256_movemask_ps(_mm256_castsi256_ps(data));
                result |= std::uint64_t(mask) << i;
            }
        }
#endif
        for (; i < count; i++) {
            result |= std::uint64_t((values[i] >> shift) & unsigned_type(1))
                      << i;
        }
        return result;
    }

    int count_less_encoded(int l, int r, unsigned_type upper) const {
        if (_n == 0 || upper <= _min_key) return 0;
        if (upper > _max_key) return r - l;

        int result = 0;
        for (int level = 0; level < _log; level++) {
            int l1 = _matrix[level].rank1(l);
            int r1 = _matrix[level].rank1(r);
            if (bit(upper, level)) {
                result += (r - l) - (r1 - l1);
                l = _zero_count[level] + l1;
                r = _zero_count[level] + r1;
            } else {
                l -= l1;
                r -= r1;
            }
        }
        return result;
    }

   public:
    WaveletMatrix()
        : _n(0),
          _log(0),
          _key_prefix(0),
          _min_key(0),
          _max_key(0) {}

    explicit WaveletMatrix(const std::vector<T>& values)
        : _n(int(values.size())),
          _log(0),
          _key_prefix(0),
          _min_key(0),
          _max_key(0) {
        std::vector<unsigned_type> current(_n);
        std::vector<unsigned_type> next(_n);
        for (int i = 0; i < _n; i++) current[i] = encode(values[i]);
        if (_n == 0) return;

        _min_key = current[0];
        _max_key = current[0];
        for (unsigned_type key : current) {
            if (key < _min_key) _min_key = key;
            if (_max_key < key) _max_key = key;
        }
        _log = int(std::bit_width(unsigned_type(_min_key ^ _max_key)));
        if (_log != value_bit_width) {
            _key_prefix = unsigned_type((_min_key >> _log) << _log);
        }
        _zero_count.assign(_log, 0);

        _matrix.reserve(_log);
        for (int level = 0; level < _log; level++) {
            _matrix.emplace_back(_n);
            BitVector& bit_vector = _matrix.back();
            int shift = _log - 1 - level;
            int zeros = 0;
            for (int base = 0; base < _n; base += 64) {
                int count = std::min(64, _n - base);
                std::uint64_t word = extract_bits(
                    current.data() + base,
                    count,
                    shift
                );
                bit_vector.bits[std::size_t(base) >> 6] = word;
                zeros += count - std::popcount(word);
            }
            bit_vector.build();

            _zero_count[level] = zeros;
            int zero_pos = 0;
            int one_pos = zeros;
            for (int base = 0; base < _n; base += 64) {
                int count = std::min(64, _n - base);
                std::uint64_t ones = bit_vector.bits[std::size_t(base) >> 6];
                std::uint64_t valid = count == 64
                                          ? ~std::uint64_t(0)
                                          : (std::uint64_t(1) << count) - 1;
                std::uint64_t zeroes = (~ones) & valid;
                while (zeroes != 0) {
                    int offset = std::countr_zero(zeroes);
                    next[zero_pos++] = current[base + offset];
                    zeroes &= zeroes - 1;
                }
                while (ones != 0) {
                    int offset = std::countr_zero(ones);
                    next[one_pos++] = current[base + offset];
                    ones &= ones - 1;
                }
            }
            current.swap(next);
        }
    }

    int size() const {
        return _n;
    }

    bool empty() const {
        return _n == 0;
    }

    T access(int p) const {
        assert(0 <= p && p < _n);
        unsigned_type key = _key_prefix;
        for (int level = 0; level < _log; level++) {
            int ones_before = _matrix[level].rank1(p);
            bool one = _matrix[level].get(p);
            if (one) {
                key |= unsigned_type(1) << (_log - 1 - level);
                p = _zero_count[level] + ones_before;
            } else {
                p -= ones_before;
            }
        }
        return decode(key);
    }

    T operator[](int p) const {
        return access(p);
    }

    int rank(T value, int r) const {
        assert(0 <= r && r <= _n);
        return rank(value, 0, r);
    }

    int rank(T value, int l, int r) const {
        assert(0 <= l && l <= r && r <= _n);
        unsigned_type key = encode(value);
        if (_n == 0 || key < _min_key || _max_key < key) return 0;
        for (int level = 0; level < _log; level++) {
            int l1 = _matrix[level].rank1(l);
            int r1 = _matrix[level].rank1(r);
            if (bit(key, level)) {
                l = _zero_count[level] + l1;
                r = _zero_count[level] + r1;
            } else {
                l -= l1;
                r -= r1;
            }
        }
        return r - l;
    }

    T kth_smallest(int l, int r, int k) const {
        assert(0 <= l && l <= r && r <= _n);
        assert(0 <= k && k < r - l);
        unsigned_type key = _key_prefix;
        for (int level = 0; level < _log; level++) {
            int l1 = _matrix[level].rank1(l);
            int r1 = _matrix[level].rank1(r);
            int l0 = l - l1;
            int r0 = r - r1;
            int zeros = r0 - l0;
            if (k < zeros) {
                l = l0;
                r = r0;
            } else {
                k -= zeros;
                key |= unsigned_type(1) << (_log - 1 - level);
                l = _zero_count[level] + l1;
                r = _zero_count[level] + r1;
            }
        }
        return decode(key);
    }

    T kth_largest(int l, int r, int k) const {
        assert(0 <= l && l <= r && r <= _n);
        assert(0 <= k && k < r - l);
        return kth_smallest(l, r, r - l - 1 - k);
    }

    int range_freq(int l, int r, T upper) const {
        assert(0 <= l && l <= r && r <= _n);
        return count_less_encoded(l, r, encode(upper));
    }

    int range_freq(int l, int r, T lower, T upper) const {
        assert(0 <= l && l <= r && r <= _n);
        if (upper <= lower) return 0;
        return range_freq(l, r, upper) - range_freq(l, r, lower);
    }

    std::optional<T> prev_value(int l, int r, T upper) const {
        assert(0 <= l && l <= r && r <= _n);
        int count = range_freq(l, r, upper);
        if (count == 0) return std::nullopt;
        return kth_smallest(l, r, count - 1);
    }

    std::optional<T> next_value(int l, int r, T lower) const {
        assert(0 <= l && l <= r && r <= _n);
        int count = range_freq(l, r, lower);
        if (count == r - l) return std::nullopt;
        return kth_smallest(l, r, count);
    }
};

}  // namespace ds
}  // namespace m1une


#line 5 "ds/range_query/range_lis_query.hpp"

#line 8 "ds/range_query/range_lis_query.hpp"
#include <numeric>
#line 11 "ds/range_query/range_lis_query.hpp"

namespace m1une {
namespace ds {

namespace range_lis_query_internal {

constexpr int none = -1;
using Permutation = std::vector<int>;
using Iterator = Permutation::iterator;

inline Permutation inverse(const Permutation& permutation) {
    int n = int(permutation.size());
    Permutation result(n, none);
    for (int i = 0; i < n; i++) {
        if (permutation[i] != none) result[permutation[i]] = i;
    }
    return result;
}

// Distance multiplication of two unit-Monge matrices, represented by their
// permutations. `workspace` must have the size used by subunit_monge_product.
inline void unit_monge_product(
    int n,
    Iterator workspace,
    Iterator first,
    Iterator second
) {
    if (n == 1) {
        workspace[0] = 0;
        return;
    }

    Iterator result_row = workspace;
    workspace += n;
    Iterator result_column = workspace;
    workspace += n;

    auto map_half = [=](int length, const auto& belongs, const auto& map) {
        Iterator first_half = workspace;
        Iterator first_position = workspace + length;
        Iterator second_half = workspace + 2 * length;
        Iterator second_position = workspace + 3 * length;

        auto split = [=](Iterator source, Iterator half, Iterator position) {
            for (int i = 0; i < n; i++) {
                if (belongs(source[i])) {
                    *half++ = map(source[i]);
                    *position++ = i;
                }
            }
        };
        split(first, first_half, first_position);
        split(second, second_half, second_position);

        Iterator product = workspace + 4 * length;
        unit_monge_product(
            length,
            product,
            first_half,
            second_half
        );
        for (int i = 0; i < length; i++) {
            int row = first_position[i];
            int column = second_position[product[i]];
            result_row[row] = column;
            result_column[column] = row;
        }
    };

    int middle = n / 2;
    map_half(
        middle,
        [middle](int value) { return value < middle; },
        [](int value) { return value; }
    );
    map_half(
        n - middle,
        [middle](int value) { return value >= middle; },
        [middle](int value) { return value - middle; }
    );

    struct DiagonalIterator {
        int delta = 0;
        int column = 0;
    };

    int row = n;
    auto move_right = [&](DiagonalIterator& iterator) {
        if (second[iterator.column] < middle) {
            if (result_column[iterator.column] >= row) iterator.delta++;
        } else {
            if (result_column[iterator.column] < row) iterator.delta++;
        }
        iterator.column++;
    };
    auto move_up = [&](DiagonalIterator& iterator) {
        if (first[row] < middle) {
            if (result_row[row] >= iterator.column) iterator.delta--;
        } else {
            if (result_row[row] < iterator.column) iterator.delta--;
        }
    };

    DiagonalIterator negative;
    DiagonalIterator positive;
    while (row != 0) {
        while (positive.column != n) {
            DiagonalIterator next = positive;
            move_right(next);
            if (next.delta != 0) break;
            positive = next;
        }
        row--;
        move_up(negative);
        move_up(positive);
        while (negative.delta != 0) move_right(negative);
        if (negative.column > positive.column) {
            result_row[row] = positive.column;
        }
    }
}

inline int workspace_size(int n) {
    int result = 1;
    while (n > 1) {
        result += 2 * n;
        n = (n + 1) / 2;
        result += 4 * n;
    }
    return result;
}

inline Permutation subunit_monge_product(
    Permutation first,
    Permutation second
) {
    int n = int(first.size());
    Permutation first_inverse = inverse(first);
    Permutation second_inverse = inverse(second);
    std::swap(second, second_inverse);

    Permutation first_map;
    Permutation second_map;
    for (int i = n - 1; i >= 0; i--) {
        if (first[i] != none) {
            first_map.push_back(i);
            first[n - int(first_map.size())] = first[i];
        }
    }
    std::reverse(first_map.begin(), first_map.end());

    int missing = 0;
    for (int i = 0; i < n; i++) {
        if (first_inverse[i] == none) first[missing++] = i;
    }
    for (int i = 0; i < n; i++) {
        if (second[i] != none) {
            second[int(second_map.size())] = second[i];
            second_map.push_back(i);
        }
    }
    missing = int(second_map.size());
    for (int i = 0; i < n; i++) {
        if (second_inverse[i] == none) second[missing++] = i;
    }

    Permutation workspace(workspace_size(n));
    unit_monge_product(
        n,
        workspace.begin(),
        first.begin(),
        second.begin()
    );

    Permutation result(n, none);
    int first_count = int(first_map.size());
    int second_count = int(second_map.size());
    for (int i = 0; i < first_count; i++) {
        int mapped = workspace[n - first_count + i];
        if (mapped < second_count) {
            result[first_map[i]] = second_map[mapped];
        }
    }
    return result;
}

inline Permutation seaweed_doubling(const Permutation& permutation) {
    int n = int(permutation.size());
    if (n == 1) return Permutation(1, none);

    int middle = n / 2;
    Permutation lower;
    Permutation upper;
    Permutation lower_map;
    Permutation upper_map;
    for (int i = 0; i < n; i++) {
        int value = permutation[i];
        if (value < middle) {
            lower.push_back(value);
            lower_map.push_back(i);
        } else {
            upper.push_back(value - middle);
            upper_map.push_back(i);
        }
    }

    lower = seaweed_doubling(lower);
    upper = seaweed_doubling(upper);
    Permutation lower_padded(n);
    Permutation upper_padded(n);
    std::iota(lower_padded.begin(), lower_padded.end(), 0);
    std::iota(upper_padded.begin(), upper_padded.end(), 0);

    for (int i = 0; i < middle; i++) {
        lower_padded[lower_map[i]] =
            lower[i] == none ? none : lower_map[lower[i]];
    }
    for (int i = 0; middle + i < n; i++) {
        upper_padded[upper_map[i]] =
            upper[i] == none ? none : upper_map[upper[i]];
    }
    return subunit_monge_product(
        std::move(lower_padded),
        std::move(upper_padded)
    );
}

template <class T>
Permutation make_permutation(const std::vector<T>& values) {
    int n = int(values.size());
    Permutation order(n);
    std::iota(order.begin(), order.end(), 0);
    std::sort(order.begin(), order.end(), [&](int first, int second) {
        if (values[first] < values[second]) return true;
        if (values[second] < values[first]) return false;
        return first > second;
    });

    Permutation permutation(n);
    for (int rank = 0; rank < n; rank++) {
        permutation[order[rank]] = rank;
    }
    return permutation;
}

}  // namespace range_lis_query_internal

// Static strict-LIS lengths for arbitrary subarrays.
template <class T>
struct RangeLisQuery {
   private:
    int _n;
    WaveletMatrix<int> _seaweed;

   public:
    RangeLisQuery() : _n(0), _seaweed() {}

    explicit RangeLisQuery(const std::vector<T>& values)
        : _n(int(values.size())), _seaweed() {
        if (_n == 0) return;
        std::vector<int> row = range_lis_query_internal::seaweed_doubling(
            range_lis_query_internal::make_permutation(values)
        );
        for (int& value : row) {
            if (value == range_lis_query_internal::none) value = _n;
        }
        _seaweed = WaveletMatrix<int>(row);
    }

    int size() const {
        return _n;
    }

    bool empty() const {
        return _n == 0;
    }

    // Returns the strict LIS length of values[left, right).
    int query(int left, int right) const {
        assert(0 <= left && left <= right && right <= _n);
        if (left == right) return 0;
        return right - left - _seaweed.range_freq(left, _n, right);
    }

    int lis_length(int left, int right) const {
        return query(left, right);
    }
};

}  // namespace ds
}  // namespace m1une


#line 1 "utilities/fast_io.hpp"



#line 5 "utilities/fast_io.hpp"
#include <array>
#include <cerrno>
#include <charconv>
#include <cstddef>
#include <cstdio>
#include <cstdlib>
#line 12 "utilities/fast_io.hpp"
#include <cstring>
#include <iterator>
#include <string>
#include <sys/stat.h>
#line 18 "utilities/fast_io.hpp"
#include <unistd.h>
#line 20 "utilities/fast_io.hpp"

namespace m1une {
namespace utilities {

struct FastOutput;

namespace internal {

// Shared with the convenience helpers in template.hpp.
inline FastOutput* standard_output_instance = nullptr;

// Detect std::begin(x), std::end(x).
template <class T, class = void>
struct is_range : std::false_type {};

template <class T>
struct is_range<T, std::void_t<
    decltype(std::begin(std::declval<T&>())),
    decltype(std::end(std::declval<T&>()))
>> : std::true_type {};

template <class T>
inline constexpr bool is_range_v = is_range<T>::value;

template <class T>
using range_reference_t = decltype(*std::begin(std::declval<T&>()));

template <class T>
using range_value_t = std::remove_cv_t<std::remove_reference_t<range_reference_t<T>>>;

template <class T, class = void>
struct range_stored_value {
    using type = range_value_t<T>;
};

template <class T>
struct range_stored_value<T, std::void_t<typename std::remove_cv_t<std::remove_reference_t<T>>::value_type>> {
    using type = typename std::remove_cv_t<std::remove_reference_t<T>>::value_type;
};

template <class T>
using range_stored_value_t = typename range_stored_value<T>::type;

// Treat strings and C strings as scalar output objects, not as ranges.
template <class T>
struct is_char_array : std::false_type {};

template <class T, std::size_t N>
struct is_char_array<T[N]>
    : std::bool_constant<std::is_same_v<std::remove_cv_t<T>, char>> {};

template <class T>
struct is_string_like
    : std::bool_constant<
          std::is_same_v<std::decay_t<T>, std::string>
          || std::is_same_v<std::decay_t<T>, const char*>
          || std::is_same_v<std::decay_t<T>, char*>
          || is_char_array<std::remove_reference_t<T>>::value
      > {};

template <class T>
inline constexpr bool is_string_like_v = is_string_like<T>::value;

// ModInt-like type: x.val() is printable, and x can be assigned from long long.
template <class T, class = void>
struct has_val_method : std::false_type {};

template <class T>
struct has_val_method<T, std::void_t<decltype(std::declval<const T&>().val())>>
    : std::true_type {};

template <class T>
inline constexpr bool has_val_method_v = has_val_method<T>::value;

template <class T, class = void>
struct has_static_mod_raw : std::false_type {};

template <class T>
struct has_static_mod_raw<
    T, std::void_t<decltype(T::mod()), decltype(T::raw(std::declval<uint32_t>()))>>
    : std::true_type {};

template <class T>
inline constexpr bool has_static_mod_raw_v = has_static_mod_raw<T>::value;

// libstdc++ before GCC 16 does not classify __int128 as an integral type in
// strict ISO modes such as -std=c++23. Keep the fast-I/O interface independent
// of that implementation detail.
template <class T>
inline constexpr bool is_integral_v =
    std::is_integral_v<T>
    || std::is_same_v<std::remove_cv_t<T>, __int128_t>
    || std::is_same_v<std::remove_cv_t<T>, __uint128_t>;

template <class T>
inline constexpr bool is_signed_v =
    std::is_signed_v<T>
    || std::is_same_v<std::remove_cv_t<T>, __int128_t>;

template <class T>
struct make_unsigned {
    using type = std::make_unsigned_t<T>;
};

template <>
struct make_unsigned<__int128_t> {
    using type = __uint128_t;
};

template <>
struct make_unsigned<__uint128_t> {
    using type = __uint128_t;
};

template <class T>
using make_unsigned_t = typename make_unsigned<std::remove_cv_t<T>>::type;

}  // namespace internal

struct FastInput {
    static constexpr int buffer_size = 1 << 20;

   private:
    std::FILE* _stream;
    char _buffer[buffer_size];
    int _position;
    int _length;
    int _file_descriptor;
    bool _streaming;

    bool refill() {
        _position = 0;
        if (_streaming) {
            ssize_t length;
            do {
                length = ::read(_file_descriptor, _buffer, buffer_size);
            } while (length < 0 && errno == EINTR);
            if (length <= 0) {
                _length = 0;
                return false;
            }
            _length = int(length);
        } else {
            _length = int(std::fread(_buffer, 1, buffer_size, _stream));
        }
        return _length != 0;
    }

    template <class T>
    bool read_integer_from_stream(T& value) {
        if (!skip_spaces()) return false;
        int c = read_char_raw();

        bool negative = false;
        if (c == '-') {
            negative = true;
            c = read_char_raw();
        }

        if constexpr (internal::is_signed_v<T>) {
            T result = 0;
            while ('0' <= c && c <= '9') {
                result = negative ? result * 10 - (c - '0')
                                  : result * 10 + (c - '0');
                c = read_char_raw();
            }
            value = result;
        } else {
            T result = 0;
            while ('0' <= c && c <= '9') {
                result = result * 10 + T(c - '0');
                c = read_char_raw();
            }
            value = negative ? T(0) - result : result;
        }
        return true;
    }

    bool prepare_number() {
        if (_length - _position >= 64) return true;
        const int remaining = _length - _position;
        if (remaining > 0) std::memmove(_buffer, _buffer + _position, remaining);
        const int added = int(std::fread(_buffer + remaining, 1, buffer_size - remaining, _stream));
        _position = 0;
        _length = remaining + added;
        if (_length < buffer_size) _buffer[_length] = '\0';
        return _length != 0;
    }

   public:
    explicit FastInput(std::FILE* stream = stdin)
        : _stream(stream),
          _position(0),
          _length(0),
          _file_descriptor(::fileno(stream)),
          _streaming([&] {
              struct stat status;
              return _file_descriptor >= 0
                     && ::fstat(_file_descriptor, &status) == 0
                     && !S_ISREG(status.st_mode);
          }()) {}

    FastInput(const FastInput&) = delete;
    FastInput& operator=(const FastInput&) = delete;

    int read_char_raw() {
        if (_position == _length && !refill()) return EOF;
        return _buffer[_position++];
    }

    bool skip_spaces() {
        int c = read_char_raw();
        while (c != EOF && c <= ' ') c = read_char_raw();
        if (c == EOF) return false;
        --_position;
        return true;
    }

    bool read(char& value) {
        if (!skip_spaces()) return false;
        value = char(read_char_raw());
        return true;
    }

    bool read(std::string& value) {
        if (!skip_spaces()) return false;
        value.clear();
        while (true) {
            const int begin = _position;
            while (_position < _length &&
                   static_cast<unsigned char>(_buffer[_position]) > ' ') {
                ++_position;
            }
            value.append(_buffer + begin, _position - begin);
            if (_position < _length) {
                ++_position;
                return true;
            }
            if (!refill()) return true;
        }
    }

    bool read(bool& value) {
        int x;
        if (!read(x)) return false;
        value = x != 0;
        return true;
    }

    template <class T>
    std::enable_if_t<
        internal::is_integral_v<T>
            && !std::is_same_v<std::remove_cv_t<T>, bool>
            && !std::is_same_v<std::remove_cv_t<T>, char>,
        bool
    >
    read(T& value) {
        if (_streaming) return read_integer_from_stream(value);
        if (!prepare_number()) return false;
        int c = static_cast<unsigned char>(_buffer[_position++]);
        while (c <= ' ') c = static_cast<unsigned char>(_buffer[_position++]);

        bool negative = false;
        if (c == '-') {
            negative = true;
            c = static_cast<unsigned char>(_buffer[_position++]);
        }

        if constexpr (internal::is_signed_v<T>) {
            T result = 0;
            while ('0' <= c && c <= '9') {
                const int first = c - '0';
                const int second = static_cast<unsigned char>(_buffer[_position]) - '0';
                if (0 <= second && second <= 9) {
                    result = negative ? result * 100 - (first * 10 + second)
                                      : result * 100 + (first * 10 + second);
                    ++_position;
                } else {
                    result = negative ? result * 10 - first : result * 10 + first;
                }
                c = static_cast<unsigned char>(_buffer[_position++]);
            }
            value = result;
        } else {
            T result = 0;
            while ('0' <= c && c <= '9') {
                const unsigned first = unsigned(c - '0');
                const int second = static_cast<unsigned char>(_buffer[_position]) - '0';
                if (0 <= second && second <= 9) {
                    result = result * 100 + T(first * 10 + unsigned(second));
                    ++_position;
                } else {
                    result = result * 10 + T(first);
                }
                c = static_cast<unsigned char>(_buffer[_position++]);
            }
            value = negative ? T(0) - result : result;
        }
        if (_position > _length) _position = _length;
        return true;
    }

    template <class T>
    std::enable_if_t<std::is_floating_point_v<T>, bool>
    read(T& value) {
        if (!skip_spaces()) return false;
        int c = read_char_raw();
        bool negative = false;
        if (c == '-' || c == '+') {
            negative = c == '-';
            c = read_char_raw();
        }

        long double result = 0;
        while ('0' <= c && c <= '9') {
            result = result * 10 + (c - '0');
            c = read_char_raw();
        }
        if (c == '.') {
            long double place = 0.1L;
            c = read_char_raw();
            while ('0' <= c && c <= '9') {
                result += (c - '0') * place;
                place *= 0.1L;
                c = read_char_raw();
            }
        }
        if (c == 'e' || c == 'E') {
            c = read_char_raw();
            bool exponent_negative = false;
            if (c == '-' || c == '+') {
                exponent_negative = c == '-';
                c = read_char_raw();
            }
            int exponent = 0;
            while ('0' <= c && c <= '9') {
                exponent = exponent * 10 + (c - '0');
                c = read_char_raw();
            }
            long double scale = 1;
            long double power = 10;
            while (exponent > 0) {
                if (exponent & 1) scale *= power;
                power *= power;
                exponent >>= 1;
            }
            result = exponent_negative ? result / scale : result * scale;
        }
        value = static_cast<T>(negative ? -result : result);
        return true;
    }

    template <class T>
    std::enable_if_t<
        internal::has_val_method_v<T>
            && !internal::is_integral_v<T>
            && !internal::is_range_v<T>,
        bool
    >
    read(T& value) {
        long long x;
        if (!read(x)) return false;
        if constexpr (internal::has_static_mod_raw_v<T>) {
            if (x >= 0 && uint64_t(x) < uint64_t(T::mod())) {
                value = T::raw(uint32_t(x));
            } else {
                value = T(x);
            }
        } else {
            value = T(x);
        }
        return true;
    }

    template <class First, class Second>
    bool read(std::pair<First, Second>& value) {
        if (!read(value.first)) return false;
        return read(value.second);
    }

    template <class Range>
    std::enable_if_t<
        internal::is_range_v<Range>
            && !internal::is_string_like_v<Range>,
        bool
    >
    read(Range& range) {
        using StoredValue = internal::range_stored_value_t<Range>;
        constexpr bool nested = internal::is_range_v<StoredValue>
                                && !internal::is_string_like_v<StoredValue>;

        for (auto&& value : range) {
            if constexpr (std::is_same_v<StoredValue, bool> && !nested) {
                bool x;
                if (!read(x)) return false;
                value = x;
            } else {
                if (!read(value)) return false;
            }
        }
        return true;
    }

    template <class First, class Second, class... Rest>
    bool read(First& first, Second& second, Rest&... rest) {
        if (!read(first)) return false;
        return read(second, rest...);
    }

    template <class T>
    FastInput& operator>>(T& value) {
        if (!read(value)) std::abort();
        return *this;
    }
};

struct FastOutput {
    static constexpr int buffer_size = 1 << 20;

   private:
    inline static const auto digit_quads = [] {
        std::array<char, 40000> result{};
        for (int i = 0; i < 10000; i++) {
            int value = i;
            for (int j = 3; j >= 0; j--) {
                result[4 * i + j] = char('0' + value % 10);
                value /= 10;
            }
        }
        return result;
    }();

    std::FILE* _stream;
    char _buffer[buffer_size];
    int _position;
    int _precision;
    std::chars_format _float_format;
    char _range_separator;
    std::string* _capture = nullptr;

    template <class T>
    std::string format_cell(const T& value) {
        std::string result;
        struct CaptureGuard {
            std::string*& target;
            std::string* previous;
            ~CaptureGuard() { target = previous; }
        } guard{_capture, _capture};
        _capture = &result;
        write(value);
        return result;
    }

    template <class Matrix>
    void write_aligned_matrix(const Matrix& matrix) {
        std::vector<std::vector<std::string>> rows;
        std::vector<std::size_t> widths;
        for (const auto& row : matrix) {
            auto& cells = rows.emplace_back();
            std::size_t column = 0;
            for (const auto& value : row) {
                cells.push_back(format_cell(value));
                if (column == widths.size()) widths.push_back(0);
                widths[column] = std::max(widths[column], cells.back().size());
                ++column;
            }
        }
        bool first = true;
        for (const auto& row : rows) {
            if (!first) write_char('\n');
            first = false;
            for (std::size_t column = 0; column < row.size(); ++column) {
                if (column != 0) write_char(_range_separator);
                for (std::size_t padding = row[column].size();
                     padding < widths[column]; ++padding) {
                    write_char(' ');
                }
                write(row[column]);
            }
        }
    }

   public:
    explicit FastOutput(std::FILE* stream = stdout)
        : _stream(stream),
          _position(0),
          _precision(6),
          _float_format(std::chars_format::general),
          _range_separator(' ') {
        if (_stream == stdout
            && internal::standard_output_instance == nullptr) {
            internal::standard_output_instance = this;
        }
    }

    FastOutput(const FastOutput&) = delete;
    FastOutput& operator=(const FastOutput&) = delete;

    ~FastOutput() {
        flush();
        if (internal::standard_output_instance == this) {
            internal::standard_output_instance = nullptr;
        }
    }

    void flush() {
        if (_position != 0) {
            std::fwrite(_buffer, 1, _position, _stream);
            _position = 0;
        }
        std::fflush(_stream);
    }

    void write_char(char c) {
        if (_capture != nullptr) {
            _capture->push_back(c);
            return;
        }
        if (_position == buffer_size) flush();
        _buffer[_position++] = c;
    }

    void write(const char* s) {
        while (*s != '\0') write_char(*s++);
    }

    void write(const std::string& s) {
        if (_capture != nullptr) {
            _capture->append(s);
            return;
        }
        std::size_t position = 0;
        while (position < s.size()) {
            if (_position == buffer_size) flush();
            const std::size_t copied =
                std::min<std::size_t>(buffer_size - _position, s.size() - position);
            std::memcpy(_buffer + _position, s.data() + position, copied);
            _position += int(copied);
            position += copied;
        }
    }

    void write(char c) {
        write_char(c);
    }

    void write(bool value) {
        write_char(value ? '1' : '0');
    }

    template <class T>
    std::enable_if_t<std::is_floating_point_v<T>>
    write(T value) {
        char digits[128];
        auto [end, error] = std::to_chars(
            digits,
            digits + sizeof(digits),
            value,
            _float_format,
            _precision
        );
        if (error != std::errc()) std::abort();
        for (const char* pointer = digits; pointer != end; pointer++) {
            write_char(*pointer);
        }
    }

    template <class T>
    std::enable_if_t<
        internal::is_integral_v<T>
            && !std::is_same_v<std::remove_cv_t<T>, bool>
            && !std::is_same_v<std::remove_cv_t<T>, char>
    >
    write(T value) {
        using Raw = std::remove_cv_t<T>;
        using Unsigned = internal::make_unsigned_t<Raw>;

        Unsigned magnitude;
        if constexpr (internal::is_signed_v<Raw>) {
            if (value < 0) {
                write_char('-');
                magnitude = Unsigned(0) - Unsigned(value);
            } else {
                magnitude = Unsigned(value);
            }
        } else {
            magnitude = value;
        }

        if (magnitude == 0) {
            write_char('0');
            return;
        }

        unsigned chunks[16];
        int count = 0;
        while (magnitude >= 10000) {
            const Unsigned quotient = magnitude / 10000;
            chunks[count++] = unsigned(magnitude - quotient * 10000);
            magnitude = quotient;
        }
        if (_capture == nullptr && _position > buffer_size - 64) flush();
        char captured[64];
        char* const begin = _capture != nullptr ? captured : _buffer + _position;
        char* destination = begin;
        const unsigned leading = unsigned(magnitude);
        const char* first = digit_quads.data() + 4 * leading;
        int skip = leading < 10 ? 3 : leading < 100 ? 2 : leading < 1000 ? 1 : 0;
        for (; skip < 4; skip++) *destination++ = first[skip];
        while (count--) {
            const char* digits = digit_quads.data() + 4 * chunks[count];
            std::memcpy(destination, digits, 4);
            destination += 4;
        }
        if (_capture != nullptr) {
            _capture->append(begin, destination - begin);
        } else {
            _position += int(destination - begin);
        }
    }

    template <class T>
    std::enable_if_t<
        internal::has_val_method_v<T>
            && !internal::is_integral_v<T>
            && !internal::is_range_v<T>
    >
    write(const T& value) {
        write(value.val());
    }

    template <class First, class Second>
    void write(const std::pair<First, Second>& value) {
        write(value.first);
        write_char(' ');
        write(value.second);
    }

    template <class Range>
    std::enable_if_t<
        internal::is_range_v<Range>
            && !internal::is_string_like_v<Range>
    >
    write(const Range& range) {
        using StoredValue = internal::range_stored_value_t<const Range>;
        constexpr bool nested = internal::is_range_v<StoredValue>
                                && !internal::is_string_like_v<StoredValue>;

        bool first = true;
        for (const auto& value : range) {
            if (!first) write_char(nested ? '\n' : _range_separator);
            first = false;
            if constexpr (std::is_same_v<StoredValue, bool> && !nested) {
                write(static_cast<bool>(value));
            } else {
                write(value);
            }
        }
    }

    template <class First, class... Rest>
    void print(const First& first, const Rest&... rest) {
        write(first);
        ((write_char(' '), write(rest)), ...);
    }

    void println() {
        write_char('\n');
    }

    void set_precision(int precision) {
        _precision = precision;
    }

    void set_fixed(int precision = 6) {
        _float_format = std::chars_format::fixed;
        _precision = precision;
    }

    void set_general(int precision = 6) {
        _float_format = std::chars_format::general;
        _precision = precision;
    }

    void set_range_separator(char separator) {
        _range_separator = separator;
    }

    template <class Matrix>
    void write_aligned(const Matrix& matrix) {
        using Row = internal::range_stored_value_t<const Matrix>;
        using Cell = internal::range_stored_value_t<const Row>;
        static_assert(internal::is_range_v<Row> && !internal::is_string_like_v<Row>,
                      "write_aligned requires a two-dimensional range");
        static_assert(!internal::is_range_v<Cell> || internal::is_string_like_v<Cell>,
                      "write_aligned requires scalar cells");
        write_aligned_matrix(matrix);
    }

    template <class Matrix>
    void println_aligned(const Matrix& matrix) {
        write_aligned(matrix);
        write_char('\n');
    }

    template <class... Args>
    void println(const Args&... args) {
        print(args...);
        write_char('\n');
    }

    template <class T>
    FastOutput& operator<<(const T& value) {
        write(value);
        return *this;
    }
};

}  // namespace utilities
}  // namespace m1une


#line 5 "verify/ds/range_query/range_lis_query.test.cpp"

#line 10 "verify/ds/range_query/range_lis_query.test.cpp"

namespace {

int brute(const std::vector<int>& values, int left, int right) {
    std::vector<int> tails;
    for (int i = left; i < right; i++) {
        auto position = std::lower_bound(
            tails.begin(),
            tails.end(),
            values[i]
        );
        if (position == tails.end()) {
            tails.push_back(values[i]);
        } else {
            *position = values[i];
        }
    }
    return int(tails.size());
}

void test_randomized() {
    m1une::ds::RangeLisQuery<int> empty(std::vector<int>{});
    assert(empty.empty());
    assert(empty.query(0, 0) == 0);

    std::uint64_t state = 3141592653ULL;
    auto random = [&]() {
        state ^= state << 7;
        state ^= state >> 9;
        return state;
    };

    for (int trial = 0; trial < 500; trial++) {
        int n = int(random() % 36);
        std::vector<int> values(n);
        for (int& value : values) value = int(random() % 11) - 5;
        m1une::ds::RangeLisQuery<int> structure(values);
        assert(structure.size() == n);
        assert(structure.empty() == (n == 0));

        for (int left = 0; left <= n; left++) {
            for (int right = left; right <= n; right++) {
                int expected = brute(values, left, right);
                assert(structure.query(left, right) == expected);
                assert(structure.lis_length(left, right) == expected);
            }
        }
    }
}

}  // namespace

int main() {
    test_randomized();

    m1une::utilities::FastInput input;
    m1une::utilities::FastOutput output;

    int n = 0, query_count = 0;
    input.read(n, query_count);
    std::vector<int> permutation(n);
    for (int& value : permutation) input.read(value);

    m1une::ds::RangeLisQuery<int> structure(permutation);
    while (query_count--) {
        int left = 0, right = 0;
        input.read(left, right);
        output.println(structure.query(left, right));
    }
}

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