Submission #67535615

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Source Code Expand

#include <algorithm>
#include <bitset>
#include <cassert>
#include <cmath>
#include <complex>
#include <cstdio>
#include <fstream>
#include <functional>
#include <iomanip>
#include <iostream>
#include <iterator>
#include <map>
#include <numeric>
#include <queue>
#include <random>
#include <set>
#include <sstream>
#include <stack>
#include <unordered_set>
using namespace std;
#if __has_include(<atcoder/all>)
#include <atcoder/all>
#endif
#define GET_MACRO(_1, _2, _3, NAME, ...) NAME
#define _rep(i, n) _rep2(i, 0, n)
#define _rep2(i, a, b) for (int i = (int)(a); i < (int)(b); i++)
#define rep(...) GET_MACRO(__VA_ARGS__, _rep2, _rep)(__VA_ARGS__)
#define all(x) (x).begin(), (x).end()
#define rall(x) (x).rbegin(), (x).rend()
#define UNIQUE(x)                      \
    std::sort((x).begin(), (x).end()); \
    (x).erase(std::unique((x).begin(), (x).end()), (x).end())
using i64 = long long;
using u64 = unsigned long long;
using u32 = unsigned int;
using i32 = int;
using ld = long double;
using f64 = double;
template <class T, class U>
bool chmin(T& a, const U& b) {
    return (b < a) ? (a = b, true) : false;
}
template <class T, class U>
bool chmax(T& a, const U& b) {
    return (b > a) ? (a = b, true) : false;
}
template <class T = std::string, class U = std::string>
inline void YesNo(bool f = 0, const T yes = "Yes", const U no = "No") {
    if (f)
        std::cout << yes << "\n";
    else
        std::cout << no << "\n";
}
namespace io {

template <class T, class U>
istream& operator>>(istream& i, pair<T, U>& p) {
    i >> p.first >> p.second;
    return i;
}

template <class T, class U>
ostream& operator<<(ostream& o, pair<T, U>& p) {
    o << p.first << " " << p.second;
    return o;
}

template <typename T>
istream& operator>>(istream& i, vector<T>& v) {
    rep(j, v.size()) i >> v[j];
    return i;
}
template <typename T>
string join(vector<T>& v) {
    stringstream s;
    rep(i, v.size()) s << ' ' << v[i];
    return s.str().substr(1);
}
template <typename T>
ostream& operator<<(ostream& o, vector<T>& v) {
    if (v.size()) o << join(v);
    return o;
}
template <typename T>
string join(vector<vector<T>>& vv) {
    string s = "\n";
    rep(i, vv.size()) s += join(vv[i]) + "\n";
    return s;
}
template <typename T>
ostream& operator<<(ostream& o, vector<vector<T>>& vv) {
    if (vv.size()) o << join(vv);
    return o;
}

void OUT() { std::cout << "\n"; }

template <class Head, class... Tail>
void OUT(Head&& head, Tail&&... tail) {
    std::cout << head;
    if (sizeof...(tail)) std::cout << ' ';
    OUT(std::forward<Tail>(tail)...);
}

void OUTL() { std::cout << std::endl; }

template <class Head, class... Tail>
void OUTL(Head&& head, Tail&&... tail) {
    std::cout << head;
    if (sizeof...(tail)) std::cout << ' ';
    OUTL(std::forward<Tail>(tail)...);
}

void IN() {}

template <class Head, class... Tail>
void IN(Head&& head, Tail&&... tail) {
    cin >> head;
    IN(std::forward<Tail>(tail)...);
}

}  // namespace io
using namespace io;

namespace useful {
long long modpow(long long a, long long b, long long mod) {
    long long res = 1;
    while (b) {
        if (b & 1) res *= a, res %= mod;
        a *= a;
        a %= mod;
        b >>= 1;
    }
    return res;
}

bool is_pow2(long long x) { return x > 0 && (x & (x - 1)) == 0; }

template <class T>
void rearrange(vector<T>& a, vector<int>& p) {
    vector<T> b = a;
    for (int i = 0; i < int(a.size()); i++) {
        a[i] = b[p[i]];
    }
    return;
}

template <std::forward_iterator I>
std::vector<std::pair<typename std::iterator_traits<I>::value_type, int>>
run_length_encoding(I s, I t) {
    if (s == t) return {};
    std::vector<std::pair<typename std::iterator_traits<I>::value_type, int>>
        res;
    res.emplace_back(*s, 1);
    for (auto it = ++s; it != t; it++) {
        if (*it == res.back().first)
            res.back().second++;
        else
            res.emplace_back(*it, 1);
    }
    return res;
}

vector<int> linear_sieve(int n) {
    vector<int> primes;
    vector<int> res(n + 1);
    iota(all(res), 0);
    for (int i = 2; i <= n; i++) {
        if (res[i] == i) primes.emplace_back(i);
        for (auto j : primes) {
            if (j * i > n) break;
            res[j * i] = j;
        }
    }
    return res;
    // return primes;
}

template <class T>
vector<long long> dijkstra(vector<vector<pair<int, T>>>& graph, int start) {
    int n = graph.size();
    vector<long long> res(n, 2e18);
    res[start] = 0;
    priority_queue<pair<long long, int>, vector<pair<long long, int>>,
                   greater<pair<long long, int>>>
        que;
    que.push({0, start});
    while (!que.empty()) {
        auto [c, v] = que.top();
        que.pop();
        if (res[v] < c) continue;
        for (auto [nxt, cost] : graph[v]) {
            auto x = c + cost;
            if (x < res[nxt]) {
                res[nxt] = x;
                que.push({x, nxt});
            }
        }
    }
    return res;
}

}  // namespace useful
using namespace useful;

template <class T, T l, T r>
struct RandomIntGenerator {
    std::random_device seed;
    std::mt19937_64 engine;
    std::uniform_int_distribution<T> uid;

    RandomIntGenerator() {
        engine = std::mt19937_64(seed());
        uid = std::uniform_int_distribution<T>(l, r);
    }

    T gen() { return uid(engine); }
};

using mint = atcoder::modint998244353;
mint inv2 = mint(2).inv();

mint range_sum(mint l, mint r) {
    return r * (r - 1) * inv2 - l * (l - 1) * inv2;
}

int main() {
    std::cout << fixed << setprecision(15);
    cin.tie(nullptr);
    ios::sync_with_stdio(false);
    i64 n;
    IN(n);
    vector<pair<i64, i64>> v;
    {
        i64 x = 1;
        while (x <= n) {
            v.emplace_back(x, n / x);
            x = n / (n / x) + 1;
        }
    }
    v.emplace_back(n + 1, 0);
    int m = v.size() - 1;
    mint ans = 0;
    rep(i, m) {
        mint L = v[i].first, R = v[i + 1].first;
        mint x = v[i].second;
        mint len = R - L;
        // OUT(L.val(), R.val(), len.val(), x.val());
        ans += len * (n + 1 - x) - range_sum(L, R);
    }
    OUT(ans.val());
}

Submission Info

Judge Result