#991763 (C++23) No.2798 Multiple Chain

• 問題: No.2798 Multiple Chain
• ユーザー: ebi_fly
• 提出日時: 2024-06-28 23:21:48
• 言語: C++23 (gcc 13.3.0 + boost 1.87.0)
• 結果: AC
• 実行時間: 2 ms / 2,000 ms
• コード長: 14,957 bytes
• コンパイル時間: 3,530 ms
• コンパイル使用メモリ: 270,144 KB
• 実行使用メモリ: 6,948 KB
• 最終ジャッジ日時: 2024-06-28 23:21:53
• 合計ジャッジ時間: 4,290 ms
• ジャッジサーバーID （参考情報）: judge4 / judge5

ファイルパターン	結果
sample	AC * 3
other	AC * 51

ソースコード

#line 1 "template/template.hpp"
#include <bits/stdc++.h>

#define rep(i, a, n) for (int i = (int)(a); i < (int)(n); i++)
#define rrep(i, a, n) for (int i = ((int)(n)-1); i >= (int)(a); i--)
#define Rep(i, a, n) for (i64 i = (i64)(a); i < (i64)(n); i++)
#define RRep(i, a, n) for (i64 i = ((i64)(n)-i64(1)); i >= (i64)(a); i--)
#define all(v) (v).begin(), (v).end()
#define rall(v) (v).rbegin(), (v).rend()

#line 2 "template/debug_template.hpp"

#line 4 "template/debug_template.hpp"

namespace ebi {

#ifdef LOCAL
#define debug(...)                                                      \
    std::cerr << "LINE: " << __LINE__ << "  [" << #__VA_ARGS__ << "]:", \
        debug_out(__VA_ARGS__)
#else
#define debug(...)
#endif

void debug_out() {
    std::cerr << std::endl;
}

template <typename Head, typename... Tail> void debug_out(Head h, Tail... t) {
    std::cerr << " " << h;
    if (sizeof...(t) > 0) std::cerr << " :";
    debug_out(t...);
}

}  // namespace ebi
#line 2 "template/int_alias.hpp"

#line 4 "template/int_alias.hpp"

namespace ebi {

using ld = long double;
using std::size_t;
using i8 = std::int8_t;
using u8 = std::uint8_t;
using i16 = std::int16_t;
using u16 = std::uint16_t;
using i32 = std::int32_t;
using u32 = std::uint32_t;
using i64 = std::int64_t;
using u64 = std::uint64_t;
using i128 = __int128_t;
using u128 = __uint128_t;

}  // namespace ebi
#line 2 "template/io.hpp"

#line 5 "template/io.hpp"
#include <optional>
#line 7 "template/io.hpp"

namespace ebi {

template <typename T1, typename T2>
std::ostream &operator<<(std::ostream &os, const std::pair<T1, T2> &pa) {
    return os << pa.first << " " << pa.second;
}

template <typename T1, typename T2>
std::istream &operator>>(std::istream &os, std::pair<T1, T2> &pa) {
    return os >> pa.first >> pa.second;
}

template <typename T>
std::ostream &operator<<(std::ostream &os, const std::vector<T> &vec) {
    for (std::size_t i = 0; i < vec.size(); i++)
        os << vec[i] << (i + 1 == vec.size() ? "" : " ");
    return os;
}

template <typename T>
std::istream &operator>>(std::istream &os, std::vector<T> &vec) {
    for (T &e : vec) std::cin >> e;
    return os;
}

template <typename T>
std::ostream &operator<<(std::ostream &os, const std::optional<T> &opt) {
    if (opt) {
        os << opt.value();
    } else {
        os << "invalid value";
    }
    return os;
}

void fast_io() {
    std::cout << std::fixed << std::setprecision(15);
    std::cin.tie(nullptr);
    std::ios::sync_with_stdio(false);
}

}  // namespace ebi
#line 2 "template/utility.hpp"

#line 5 "template/utility.hpp"

#line 2 "graph/base.hpp"

#line 5 "graph/base.hpp"
#include <ranges>
#line 7 "graph/base.hpp"

#line 2 "data_structure/simple_csr.hpp"

#line 6 "data_structure/simple_csr.hpp"

namespace ebi {

template <class E> struct simple_csr {
    simple_csr() = default;

    simple_csr(int n, const std::vector<std::pair<int, E>>& elements)
        : start(n + 1, 0), elist(elements.size()) {
        for (auto e : elements) {
            start[e.first + 1]++;
        }
        for (auto i : std::views::iota(0, n)) {
            start[i + 1] += start[i];
        }
        auto counter = start;
        for (auto [i, e] : elements) {
            elist[counter[i]++] = e;
        }
    }

    simple_csr(const std::vector<std::vector<E>>& es)
        : start(es.size() + 1, 0) {
        int n = es.size();
        for (auto i : std::views::iota(0, n)) {
            start[i + 1] = (int)es[i].size() + start[i];
        }
        elist.resize(start.back());
        for (auto i : std::views::iota(0, n)) {
            std::copy(es[i].begin(), es[i].end(), elist.begin() + start[i]);
        }
    }

    int size() const {
        return (int)start.size() - 1;
    }

    const auto operator[](int i) const {
        return std::ranges::subrange(elist.begin() + start[i],
                                     elist.begin() + start[i + 1]);
    }
    auto operator[](int i) {
        return std::ranges::subrange(elist.begin() + start[i],
                                     elist.begin() + start[i + 1]);
    }

    const auto operator()(int i, int l, int r) const {
        return std::ranges::subrange(elist.begin() + start[i] + l,
                                     elist.begin() + start[i + 1] + r);
    }
    auto operator()(int i, int l, int r) {
        return std::ranges::subrange(elist.begin() + start[i] + l,
                                     elist.begin() + start[i + 1] + r);
    }

  private:
    std::vector<int> start;
    std::vector<E> elist;
};

}  // namespace ebi
#line 9 "graph/base.hpp"

namespace ebi {

template <class T> struct Edge {
    int from, to;
    T cost;
    int id;
};

template <class E> struct Graph {
    using cost_type = E;
    using edge_type = Edge<cost_type>;

    Graph(int n_) : n(n_) {}

    Graph() = default;

    void add_edge(int u, int v, cost_type c) {
        buff.emplace_back(u, edge_type{u, v, c, m});
        edges.emplace_back(edge_type{u, v, c, m++});
    }

    void add_undirected_edge(int u, int v, cost_type c) {
        buff.emplace_back(u, edge_type{u, v, c, m});
        buff.emplace_back(v, edge_type{v, u, c, m});
        edges.emplace_back(edge_type{u, v, c, m});
        m++;
    }

    void read_tree(int offset = 1, bool is_weighted = false) {
        read_graph(n - 1, offset, false, is_weighted);
    }

    void read_parents(int offset = 1) {
        for (auto i : std::views::iota(1, n)) {
            int p;
            std::cin >> p;
            p -= offset;
            add_undirected_edge(p, i, 1);
        }
        build();
    }

    void read_graph(int e, int offset = 1, bool is_directed = false,
                    bool is_weighted = false) {
        for (int i = 0; i < e; i++) {
            int u, v;
            std::cin >> u >> v;
            u -= offset;
            v -= offset;
            if (is_weighted) {
                cost_type c;
                std::cin >> c;
                if (is_directed) {
                    add_edge(u, v, c);
                } else {
                    add_undirected_edge(u, v, c);
                }
            } else {
                if (is_directed) {
                    add_edge(u, v, 1);
                } else {
                    add_undirected_edge(u, v, 1);
                }
            }
        }
        build();
    }

    void build() {
        assert(!prepared);
        csr = simple_csr<edge_type>(n, buff);
        buff.clear();
        prepared = true;
    }

    int size() const {
        return n;
    }

    int node_number() const {
        return n;
    }

    int edge_number() const {
        return m;
    }

    edge_type get_edge(int i) const {
        return edges[i];
    }

    std::vector<edge_type> get_edges() const {
        return edges;
    }

    const auto operator[](int i) const {
        return csr[i];
    }
    auto operator[](int i) {
        return csr[i];
    }

  private:
    int n, m = 0;

    std::vector<std::pair<int,edge_type>> buff;

    std::vector<edge_type> edges;
    simple_csr<edge_type> csr;
    bool prepared = false;
};

}  // namespace ebi
#line 8 "template/utility.hpp"

namespace ebi {

template <class T> inline bool chmin(T &a, T b) {
    if (a > b) {
        a = b;
        return true;
    }
    return false;
}

template <class T> inline bool chmax(T &a, T b) {
    if (a < b) {
        a = b;
        return true;
    }
    return false;
}

template <class T> T safe_ceil(T a, T b) {
    if (a % b == 0)
        return a / b;
    else if (a >= 0)
        return (a / b) + 1;
    else
        return -((-a) / b);
}

template <class T> T safe_floor(T a, T b) {
    if (a % b == 0)
        return a / b;
    else if (a >= 0)
        return a / b;
    else
        return -((-a) / b) - 1;
}

constexpr i64 LNF = std::numeric_limits<i64>::max() / 4;

constexpr int INF = std::numeric_limits<int>::max() / 2;

const std::vector<int> dy = {1, 0, -1, 0, 1, 1, -1, -1};
const std::vector<int> dx = {0, 1, 0, -1, 1, -1, 1, -1};

}  // namespace ebi
#line 2 "a.cpp"

#line 6 "a.cpp"
#include <initializer_list>
#line 10 "a.cpp"

namespace fast_factorize {

/*
    See : https://judge.yosupo.jp/submission/189742
*/

// ---- gcd ----

uint64_t gcd_stein_impl( uint64_t x, uint64_t y ) {
    if( x == y ) { return x; }
    const uint64_t a = y - x;
    const uint64_t b = x - y;
    const int n = __builtin_ctzll( b );
    const uint64_t s = x < y ? a : b;
    const uint64_t t = x < y ? x : y;
    return gcd_stein_impl( s >> n, t );
}

uint64_t gcd_stein( uint64_t x, uint64_t y ) {
    if( x == 0 ) { return y; }
    if( y == 0 ) { return x; }
    const int n = __builtin_ctzll( x );
    const int m = __builtin_ctzll( y );
    return gcd_stein_impl( x >> n, y >> m ) << ( n < m ? n : m );
}

// ---- is_prime ----

uint64_t mod_pow( uint64_t x, uint64_t y, uint64_t mod ) {
    uint64_t ret = 1;
    uint64_t acc = x;
    for( ; y; y >>= 1 ) {
        if( y & 1 ) {
            ret = __uint128_t(ret) * acc % mod;
        }
        acc = __uint128_t(acc) * acc % mod;
    }
    return ret;
}

bool miller_rabin( uint64_t n, const std::initializer_list<uint64_t>& as ) {
    return std::all_of( as.begin(), as.end(), [n]( uint64_t a ) {
        if( n <= a ) { return true; }

        int e = __builtin_ctzll( n - 1 );
        uint64_t z = mod_pow( a, ( n - 1 ) >> e, n );
        if( z == 1 || z == n - 1 ) { return true; }

        while( --e ) {
            z = __uint128_t(z) * z % n;
            if( z == 1 ) { return false; }
            if( z == n - 1 ) { return true; }
        }

        return false;
    });
}

bool is_prime( uint64_t n ) {
    if( n == 2 ) { return true; }
    if( n % 2 == 0 ) { return false; }
    if( n < 4759123141 ) { return miller_rabin( n, { 2, 7, 61 } ); }
    return miller_rabin( n, { 2, 325, 9375, 28178, 450775, 9780504, 1795265022 } );
}

// ---- Montgomery ----

class Montgomery {
    uint64_t mod;
    uint64_t R;
public:
    Montgomery( uint64_t n ) : mod(n), R(n) {
       for( size_t i = 0; i < 5; ++i ) {
          R *= 2 - mod * R;
       }
    }

    uint64_t fma( uint64_t a, uint64_t b, uint64_t c ) const {
        const __uint128_t d = __uint128_t(a) * b;
        const uint64_t    e = c + mod + ( d >> 64 );
        const uint64_t    f = uint64_t(d) * R;
        const uint64_t    g = ( __uint128_t(f) * mod ) >> 64;
        return e - g;
    }

    uint64_t mul( uint64_t a, uint64_t b ) const {
        return fma( a, b, 0 );
    }
};

// ---- Pollard's rho algorithm ----

uint64_t pollard_rho( uint64_t n ) {
    if( n % 2 == 0 ) { return 2; }
    const Montgomery m( n );

    constexpr uint64_t C1 = 1;
    constexpr uint64_t C2 = 2;
    constexpr uint64_t M = 512;

    uint64_t Z1 = 1;
    uint64_t Z2 = 2;
retry:
    uint64_t z1 = Z1;
    uint64_t z2 = Z2;
    for( size_t k = M; ; k *= 2 ) {
        const uint64_t x1 = z1 + n;
        const uint64_t x2 = z2 + n;
        for( size_t j = 0; j < k; j += M ) {
            const uint64_t y1 = z1;
            const uint64_t y2 = z2;

            uint64_t q1 = 1;
            uint64_t q2 = 2;
            z1 = m.fma( z1, z1, C1 );
            z2 = m.fma( z2, z2, C2 );
            for( size_t i = 0; i < M; ++i ) {
                const uint64_t t1 = x1 - z1;
                const uint64_t t2 = x2 - z2;
                z1 = m.fma( z1, z1, C1 );
                z2 = m.fma( z2, z2, C2 );
                q1 = m.mul( q1, t1 );
                q2 = m.mul( q2, t2 );
            }
            q1 = m.mul( q1, x1 - z1 );
            q2 = m.mul( q2, x2 - z2 );

            const uint64_t q3 = m.mul( q1, q2 );
            const uint64_t g3 = gcd_stein( n, q3 );
            if( g3 == 1 ) { continue; }
            if( g3 != n ) { return g3; }

            const uint64_t g1 = gcd_stein( n, q1 );
            const uint64_t g2 = gcd_stein( n, q2 );

            const uint64_t C = g1 != 1 ? C1 : C2;
            const uint64_t x = g1 != 1 ? x1 : x2;
            uint64_t       z = g1 != 1 ? y1 : y2;
            uint64_t       g = g1 != 1 ? g1 : g2;

            if( g == n ) {
                do {
                    z = m.fma( z, z, C );
                    g = gcd_stein( n, x - z );
                } while( g == 1 );
            }
            if( g != n ) {
                return g;
            }

            Z1 += 2;
            Z2 += 2;
            goto retry;
        }
    }
}

void factorize_impl( uint64_t n, std::vector<uint64_t>& ret ) {
    if( n <= 1 ) { return; }
    if( is_prime( n ) ) { ret.push_back( n ); return; }

    const uint64_t p = pollard_rho( n );

    factorize_impl( p, ret );
    factorize_impl( n / p, ret );
}

std::vector<uint64_t> factorize( uint64_t n ) {
    std::vector<uint64_t> ret;
    factorize_impl( n, ret );
    std::sort( ret.begin(), ret.end() );
    return ret;
}

} // namespace fast_factorize

namespace noya2 {

std::vector<std::pair<long long, int>> factorize(long long n){
    std::vector<std::pair<long long, int>> ans;
    auto ps = fast_factorize::factorize(n);
    int sz = ps.size();
    for (int l = 0, r = 0; l < sz; l = r){
        while (r < sz && ps[l] == ps[r]) r++;
        ans.emplace_back(ps[l], r-l);
    }
    return ans;
}

std::vector<long long> divisors(long long n){
    auto ps = fast_factorize::factorize(n);
    int sz = ps.size();
    std::vector<long long> ans = {1};
    for (int l = 0, r = 0; l < sz; l = r){
        while (r < sz && ps[l] == ps[r]) r++;
        int e = r - l;
        int len = ans.size();
        ans.reserve(len*(e+1));
        long long mul = ps[l];
        while (true){
            for (int i = 0; i < len; i++){
                ans.emplace_back(ans[i]*mul);
            }
            if (--e == 0) break;
            mul *= ps[l];
        }
    }
    return ans;
}

std::vector<long long> divisors(const std::vector<std::pair<long long, int>> &pes){
    std::vector<long long> ans = {1};
    for (auto [p, e] : pes){
        int len = ans.size();
        ans.reserve(len*(e+1));
        long long mul = p;
        while (true){
            for (int i = 0; i < len; i++){
                ans.emplace_back(ans[i]*mul);
            }
            if (--e == 0) break;
            mul *= p;
        }
    }
    return ans;
}

} // namespace noya2

namespace ebi {

void main_() {
    i64 n;
    std::cin >> n;
    auto ps = noya2::factorize(n);
    const int sz = 70;
    std::vector dp(sz, std::vector<i64>(sz, 0));
    rep(i,1,sz) {
        dp[i][i] = 1;
    }
    rep(i,0,sz) rep(j,0,sz) {
        rep(k,i,sz) {
            if(j + k < sz) {
                dp[k][j + k] += dp[i][j];
            }
        }
    }
    i64 ans = 1;
    for(auto [p, c]: ps) {
        i64 ret = 0;
        rep(i,0,sz) {
            ret += dp[i][c];
        }
        ans *= ret;
    }
    std::cout << ans << '\n';
}

}  // namespace ebi

int main() {
    ebi::fast_io();
    int t = 1;
    // std::cin >> t;
    while (t--) {
        ebi::main_();
    }
    return 0;
}