結果

問題 No.2902 ZERO!!
ユーザー apricityapricity
提出日時 2024-09-28 07:04:50
言語 C++17
(gcc 12.3.0 + boost 1.83.0)
結果
AC  
実行時間 216 ms / 2,000 ms
コード長 8,756 bytes
コンパイル時間 1,467 ms
コンパイル使用メモリ 140,060 KB
実行使用メモリ 42,376 KB
最終ジャッジ日時 2024-09-28 07:04:56
合計ジャッジ時間 6,117 ms
ジャッジサーバーID
（参考情報） 		judge4 / judge3
このコードへのチャレンジ
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テストケース

テストケース表示
入力 結果 実行時間
実行使用メモリ
testcase_00 AC 11 ms
27,008 KB
testcase_01 AC 12 ms
27,008 KB
testcase_02 AC 205 ms
42,376 KB
testcase_03 AC 12 ms
26,880 KB
testcase_04 AC 52 ms
30,464 KB
testcase_05 AC 102 ms
34,604 KB
testcase_06 AC 202 ms
41,668 KB
testcase_07 AC 64 ms
31,360 KB
testcase_08 AC 216 ms
40,924 KB
testcase_09 AC 181 ms
40,380 KB
testcase_10 AC 134 ms
36,648 KB
testcase_11 AC 111 ms
35,080 KB
testcase_12 AC 23 ms
27,904 KB
testcase_13 AC 185 ms
40,676 KB
testcase_14 AC 140 ms
37,156 KB
testcase_15 AC 204 ms
38,516 KB
testcase_16 AC 95 ms
33,964 KB
testcase_17 AC 186 ms
40,320 KB
testcase_18 AC 167 ms
39,240 KB
testcase_19 AC 151 ms
37,872 KB
testcase_20 AC 127 ms
36,268 KB
testcase_21 AC 136 ms
36,900 KB
testcase_22 AC 72 ms
32,000 KB
testcase_23 AC 99 ms
34,356 KB
testcase_24 AC 12 ms
27,008 KB
testcase_25 AC 13 ms
27,008 KB
testcase_26 AC 12 ms
27,008 KB
testcase_27 AC 12 ms
27,136 KB
testcase_28 AC 12 ms
27,136 KB
testcase_29 AC 12 ms
26,880 KB
testcase_30 AC 12 ms
27,008 KB
testcase_31 AC 12 ms
27,096 KB
testcase_32 AC 12 ms
27,008 KB
testcase_33 AC 11 ms
27,008 KB
testcase_34 AC 12 ms
27,136 KB
testcase_35 AC 11 ms
27,040 KB
testcase_36 AC 12 ms
27,136 KB
testcase_37 AC 12 ms
27,008 KB
testcase_38 AC 12 ms
27,044 KB
testcase_39 AC 12 ms
27,008 KB
testcase_40 AC 12 ms
27,008 KB
testcase_41 AC 19 ms
27,008 KB
testcase_42 AC 12 ms
26,880 KB
testcase_43 AC 12 ms
27,008 KB
権限があれば一括ダウンロードができます

ソースコード

diff # 

#include<iostream>
#include<string>
#include<vector>
#include<algorithm>
#include<numeric>
#include<cmath>
#include<utility>
#include<tuple>
#include<cstdint>
#include<cstdio>
#include<iomanip>
#include<map>
#include<queue>
#include<set>
#include<stack>
#include<deque>
#include<unordered_map>
#include<unordered_set>
#include<bitset>
#include<cctype>
#include<chrono>
#include<random>
#include<cassert>
#include<cstddef>
#include<iterator>
#include<string_view>
#include<type_traits>

#ifdef LOCAL
#  include "debug_print.hpp"
#  define debug(...) debug_print::multi_print(#__VA_ARGS__, __VA_ARGS__)
#else
#  define debug(...) (static_cast<void>(0))
#endif

using namespace std;
#define rep1(a)          for(int i = 0; i < a; i++)
#define rep2(i, a)       for(int i = 0; i < a; i++)
#define rep3(i, a, b)    for(int i = a; i < b; i++)
#define rep4(i, a, b, c) for(int i = a; i < b; i += c)
#define overload4(a, b, c, d, e, ...) e
#define rep(...) overload4(__VA_ARGS__, rep4, rep3, rep2, rep1)(__VA_ARGS__)
#define rrep1(a)          for(int i = (a)-1; i >= 0; i--)
#define rrep2(i, a)       for(int i = (a)-1; i >= 0; i--)
#define rrep3(i, a, b)    for(int i = (b)-1; i >= a; i--)
#define rrep4(i, a, b, c) for(int i = (b)-1; i >= a; i -= c)
#define rrep(...) overload4(__VA_ARGS__, rrep4, rrep3, rrep2, rrep1)(__VA_ARGS__)
#define ALL(v) v.begin(), v.end()
#define RALL(v) v.rbegin(), v.rend()
#define UNIQUE(v) v.erase( unique(v.begin(), v.end()), v.end() );
#define pb push_back
using ll = long long;
using D = double;
using LD = long double;
using P = pair<int, int>;
using vi = vector<int>;
using vl = vector<ll>;
template <class T> using vc = vector<T>;
template <class T> using vvc = vector<vc<T>>;
template <class T> using vvvc = vector<vvc<T>>;
template <class T> using vvvvc = vector<vvvc<T>>;
template <class T> using vvvvvc = vector<vvvvc<T>>;
#define vv(type, name, h, ...) \
  vector<vector<type>> name(h, vector<type>(__VA_ARGS__))
#define vvv(type, name, h, w, ...)   \
  vector<vector<vector<type>>> name( \
      h, vector<vector<type>>(w, vector<type>(__VA_ARGS__)))
#define vvvv(type, name, a, b, c, ...)       \
  vector<vector<vector<vector<type>>>> name( \
      a, vector<vector<vector<type>>>(       \
             b, vector<vector<type>>(c, vector<type>(__VA_ARGS__))))
template<typename T> using PQ = priority_queue<T,vector<T>>;
template<typename T> using minPQ = priority_queue<T, vector<T>, greater<T>>;
template<class T>bool chmax(T &a, const T &b) { if (a<b) { a=b; return 1; } return 0; }
template<class T>bool chmin(T &a, const T &b) { if (b<a) { a=b; return 1; } return 0; }
void yesno(bool flag) {cout << (flag?"Yes":"No") << "\n";}

template<typename T, typename U>
ostream &operator<<(ostream &os, const pair<T, U> &p) {
    os << p.first << " " << p.second;
    return os;
}
template<typename T, typename U>
istream &operator>>(istream &is, pair<T, U> &p) {
    is >> p.first >> p.second;
    return is;
}

template<typename T>
ostream &operator<<(ostream &os, const vector<T> &v) {
    int s = (int)v.size();
    for (int i = 0; i < s; i++) os << (i ? " " : "") << v[i];
    return os;
}
template<typename T>
istream &operator>>(istream &is, vector<T> &v) {
    for (auto &x : v) is >> x;
    return is;
}
void in() {}
template<typename T, class... U>
void in(T &t, U &...u) {
    cin >> t;
    in(u...);
}
void out() { cout << "\n"; }
template<typename T, class... U, char sep = ' '>
void out(const T &t, const U &...u) {
    cout << t;
    if (sizeof...(u)) cout << sep;
    out(u...);
}
void outr() {}
template<typename T, class... U, char sep = ' '>
void outr(const T &t, const U &...u) {
    cout << t;
    outr(u...);
}

template<int mod> struct Fp {
    long long val;
    constexpr Fp(long long v = 0) noexcept : val(v % mod) {
        if (val < 0) val += mod;
    }
    constexpr int getmod() { return mod; }
    constexpr Fp operator - () const noexcept {
        return val ? mod - val : 0;
    }
    constexpr Fp operator + (const Fp& r) const noexcept { return Fp(*this) += r; }
    constexpr Fp operator - (const Fp& r) const noexcept { return Fp(*this) -= r; }
    constexpr Fp operator * (const Fp& r) const noexcept { return Fp(*this) *= r; }
    constexpr Fp operator / (const Fp& r) const noexcept { return Fp(*this) /= r; }
    constexpr Fp& operator += (const Fp& r) noexcept {
        val += r.val;
        if (val >= mod) val -= mod;
        return *this;
    }
    constexpr Fp& operator -= (const Fp& r) noexcept {
        val -= r.val;
        if (val < 0) val += mod;
        return *this;
    }
    constexpr Fp& operator *= (const Fp& r) noexcept {
        val = val * r.val % mod;
        return *this;
    }
    constexpr Fp& operator /= (const Fp& r) noexcept {
        long long a = r.val, b = mod, u = 1, v = 0;
        while (b) {
            long long t = a / b;
            a -= t * b; swap(a, b);
            u -= t * v; swap(u, v);
        }
        val = val * u % mod;
        if (val < 0) val += mod;
        return *this;
    }
    constexpr bool operator == (const Fp& r) const noexcept {
        return this->val == r.val;
    }
    constexpr bool operator != (const Fp& r) const noexcept {
        return this->val != r.val;
    }
    friend constexpr istream& operator >> (istream &is, const Fp<mod>& x) noexcept {
        int val; is >> val;
        x = Fp<mod>(val);
        return is;
    }
    friend constexpr ostream& operator << (ostream &os, const Fp<mod>& x) noexcept {
        return os << x.val;
    }
    friend constexpr Fp<mod> modpow(const Fp<mod> &a, long long n) noexcept {
        if (n == 0) return 1;
        auto t = modpow(a, n / 2);
        t = t * t;
        if (n & 1) t = t * a;
        return t;
    }
};

//const int mod = 1e9+7;
const int mod = 998244353;
using mint = Fp<mod>;

struct eratosthenes{
    vector<bool> isprime;
    vector<int> minfactor;
    vector<int> mobius;
    eratosthenes(int n) : isprime(n+1,true), minfactor(n+1, -1), mobius(n+1,1){
        isprime[1] = false;
        minfactor[1] = 1;
 
        for(int i = 2; i <= n; i++){
            if(!isprime[i]) continue;
            minfactor[i] = i;
            mobius[i] = -1;
            for(int j = i+i; j <= n; j += i){
                isprime[j] = false;
                if(minfactor[j] == -1) minfactor[j] = i;
                if((j/i)%i == 0) mobius[j] = 0;
                else mobius[j] *= -1;
            }
        }
    }
 
    vector<pair<int, int>> factorize(int n){
        vector<pair<int, int>> res;
        while(n > 1){
            int p = minfactor[n];
            int e = 0;
            while(minfactor[n] == p){
                n /= p;
                e++;
            }
            res.push_back({p,e});
        }
        return res;
    }
 
    vector<int> divisor(int n){
        vector<int> res;
        res.pb(1);
        auto v = factorize(n);
        for(auto x : v){
            int s = res.size();
            rep(i,s){
                int m = 1;
                rep(j,x.second){
                    m *= x.first;
                    res.push_back(res[i]*m);
                }
            }
        }
        return res;
    }
 
    template<class T> void fzt(vector<T> &f){
        int n = f.size();
        for(int p = 2; p < n; p++){
            if(!isprime[p]) continue;
            for(int q = (n-1)/p; q > 0; q--){
                f[q] += f[p*q];
            }
        }
    }
 
 
    template<class T> void fmt(vector<T> &f){
        int n = f.size();
        for(int p = 2; p < n; p++){
            if(!isprime[p]) continue;
            for(int q = 1; q*p < n; q++){
                f[q] -= f[p*q];
            }
        }
    }
 
    template<class T> vector<T> conv(const vector<T> &f, const vector<T> &g){
        int n = max(f.size(), g.size());
        vector<T> nf(n), ng(n), h(n);
        rep(i,f.size()) nf[i] = f[i];
        rep(i,g.size()) ng[i] = g[i];
        fzt(nf); fzt(ng);
        rep(i,n) h[i] = nf[i]*ng[i];
        fmt(h);
        return h;
    }
};

vector<pair<int,int>> v[1010101];

int main(){
    ios_base::sync_with_stdio(false);
    cin.tie(nullptr);
    int n; in(n);
    eratosthenes si(n+1);
    vector<int> cnt(n+1);
    rep(i,2,n+1){
        for(auto [p,e] : si.factorize(i)) cnt[p] += e;
    }
    rep(i,2,n+1)if(cnt[i]>0){
        int r = cnt[i];
        while(r){
            ll q = cnt[i]/r;
            ll l = cnt[i]/(q+1);
            v[l+1].emplace_back(i,q);
            r = l;
        }
        v[cnt[i]+1].emplace_back(i,0);
    }
    mint ans = 0;
    mint cur = 1;
    rep(i,n+1) cur *= (cnt[i]+1);
    rep(i,1,n+1){
        for(auto [idx, q] : v[i]){
            cur /= (cnt[idx]+1);
            cur *= q+1;
            cnt[idx] = q;
        }
        ans += cur-1;
    }
    out(ans);
}
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