結果
| 問題 | No.3505 Sum of Prod of Root |
| コンテスト | |
| ユーザー |
 ryoku
|
| 提出日時 | 2026-04-18 11:11:03 |
| 言語 | C++23 (gcc 15.2.0 + boost 1.89.0) |
| 結果 |
AC
|
| 実行時間 | 326 ms / 2,000 ms |
| コード長 | 24,514 bytes |
| 記録 | |
| コンパイル時間 | 2,919 ms |
| コンパイル使用メモリ | 314,736 KB |
| 実行使用メモリ | 7,808 KB |
| 最終ジャッジ日時 | 2026-04-18 11:11:11 |
| 合計ジャッジ時間 | 6,877 ms |
|
ジャッジサーバーID （参考情報） |
judge1_0 / judge2_1 |
（要ログイン）
| ファイルパターン | 結果 |
|---|---|
| sample | AC * 1 |
| other | AC * 13 |
ソースコード
#line 1 "a.cpp"
#line 1 "a.cpp"
#line 2 "lib/template.hpp"
# pragma GCC optimize("unroll-loops")
#pragma GCC optimize("O3")
using namespace std;
#include <iostream>
#include <iomanip>
#include <cstdio>
#include <string>
#include <cstring>
#include <vector>
#include <list>
#include <queue>
#include <stack>
#include <deque>
#include <set>
#include <map>
#include <unordered_set>
#include <unordered_map>
#include <algorithm>
#include <numeric>
#include <cmath>
#include <climits>
#include <cassert>
#include <functional>
#include <iterator>
#include <utility>
#include <complex>
#include <bitset>
#include <chrono>
#include <random>
#include <limits>
#include <optional>
#include <variant>
#include <any>
#include <array>
#include <bit>
#include <compare>
#include <concepts>
#include <format>
#include <numbers>
#include <ranges>
#include <span>
#include <string_view>
#include <tuple>
#include <type_traits>
#include <version>
using uint=unsigned;
using ll=long long;
using ull=unsigned long long;
using ld=long double;
using pii=pair<int,int>;
using pll=pair<ll,ll>;
using i128=__int128;
template<class T>using vc=vector<T>;
template<class T>using vvc=vc<vc<T>>;
template<class T>using vvvc=vvc<vc<T>>;
#define vec(d,T,n,...) vec_##d(T,n,__VA_ARGS__)
#define vec_1(T,n,a) vector<T> n(a)
#define vec_2(T,n,a,b) vector<vector<T>> n(a,vector<T>(b))
#define vec_3(T,n,a,b,c) vector<vector<vector<T>>> n(a,vector<vector<T>>(b,vector<T>(c)))
#define vec_4(T,n,a,b,c,d) vector<vector<vector<vector<T>>>> n(a,vector<vector<vector<T>>>(b,vector<vector<T>>(c,vector<T>(d))))
#define vec_5(T,n,a,b,c,d,e) vector<vector<vector<vector<vector<T>>>>> n(a,vector<vector<vector<vector<T>>>>(b,vector<vector<vector<T>>>(c,vector<vector<T>>(d,vector<T>(e)))))
#define vec_6(T,n,a,b,c,d,e,f) vector<vector<vector<vector<vector<vector<T>>>>>> n(a,vector<vector<vector<vector<vector<T>>>>>(b,vector<vector<vector<vector<T>>>>(c,vector<vector<vector<T>>>(d,vector<vector<T>>(e,vector<T>(f))))))
#define vec_7(T,n,a,b,c,d,e,f,g) vector<vector<vector<vector<vector<vector<vector<T>>>>>>> n(a,vector<vector<vector<vector<vector<vector<T>>>>>>(b,vector<vector<vector<vector<vector<T>>>>>(c,vector<vector<vector<vector<T>>>>(d,vector<vector<vector<T>>>(e,vector<vector<T>>(f,vector<T>(g)))))))
template<class T>using smpq=priority_queue<T,vector<T>,greater<T>>;
template<class T>using bipq=priority_queue<T>;
#define rep(i,n) for(ll i=0;i<(ll)(n);i++)
#define REP(i,j,n) for(ll i=(j);i<(ll)(n);i++)
#define DREP(i,n,m) for(ll i=(n);i>=(m);i--)
#define drep(i,n) for(ll i=((n)-1);i>=0;i--)
#define all(x) x.begin(),x.end()
#define rall(x) x.rbegin(),x.rend()
#define mp make_pair
#define pb push_back
#define fi first
#define se second
#define is insert
#define bg begin()
#define ed end()
void scan(int&a) { cin >> a; }
void scan(ll&a) { cin >> a; }
void scan(string&a) { cin >> a; }
void scan(char&a) { cin >> a; }
void scan(uint&a) { cin >> a; }
void scan(ull&a) { cin >> a; }
void scan(bool&a) { cin >> a; }
void scan(ld&a){ cin>> a;}
template<class T> void scan(vector<T>&a) { for(auto&x:a) scan(x); }
void read() {}
template<class Head, class... Tail> void read(Head&head, Tail&... tail) { scan(head); read(tail...); }
#define INT(...) int __VA_ARGS__; read(__VA_ARGS__);
#define LL(...) ll __VA_ARGS__; read(__VA_ARGS__);
#define ULL(...) ull __VA_ARGS__; read(__VA_ARGS__);
#define STR(...) string __VA_ARGS__; read(__VA_ARGS__);
#define CHR(...) char __VA_ARGS__; read(__VA_ARGS__);
#define DBL(...) double __VA_ARGS__; read(__VA_ARGS__);
#define LD(...) ld __VA_ARGS__; read(__VA_ARGS__);
#define VC(type, name, ...) vector<type> name(__VA_ARGS__); read(name);
#define VVC(type, name, size, ...) vector<vector<type>> name(size, vector<type>(__VA_ARGS__)); read(name);
template<class T>void print(T a) { cout << a; }
template<class T> void print(vector<T>a) { for(int i=0;i<(int)a.size();i++){if(i)cout<<" ";print(a[i]);}cout<<endl;}
void PRT() { cout <<endl; return ; }
template<class T> void PRT(T a) { print(a); cout <<endl; return; }
template<class Head, class... Tail> void PRT(Head head, Tail ... tail) { print(head); cout << " "; PRT(tail...); return; }
template<class T,class F>
bool chmin(T &x, F y){
if(x>y){
x=y;
return true;
}
return false;
}
template<class T, class F>
bool chmax(T &x, F y){
if(x<y){
x=y;
return true;
}
return false;
}
template <typename T>
T floor(T a, T b) {
return a / b - (a % b && (a ^ b) < 0);
}
template <typename T>
T ceil(T x, T y) {
return floor(x + y - 1, y);
}
template <typename T>
T bmod(T x, T y) {
return x - y * floor(x, y);
}
template <typename T>
pair<T, T> divmod(T x, T y) {
T q = floor(x, y);
return {q, x - q * y};
}
void YesNo(bool b){
cout<<(b?"Yes":"No")<<endl;
}
void Yes(){
cout<<"Yes"<<endl;
}
void No(){
cout<<"No"<<endl;
}
template<class T=ll>
T isqrt(T x){
T F=sqrtl(x);
while((F+1)*(F+1)<=x)F++;
while(F*F>x)F--;
return F;
}
template<class T>
int popcount(T n){
return __builtin_popcountll(n);
}
template<class T,class L=ll>
L sum(vc<T>&a){
return accumulate(all(a),L(0));
}
template<class T>
vc<T>subset(T S){
vc<T>ans;
for(T x=S;x>0;x=(x-1)&S)ans.pb(x);
ans.pb(0);
return ans;
}
template<class T>
T max(vc<T>&a){
return *max_element(all(a));
}
template<class T>
T min(vc<T>&a){
return *min_element(all(a));
}
vvc<int>readgraph(int n,int m,int off = -1){
vvc<int> g(n);
rep(i, m){
int u,v;
cin>>u>>v;
u+=off,v+=off;
g[u].push_back(v);
g[v].push_back(u);
}
return g;
}
vvc<int> readtree(int n,int off=-1){
return readgraph(n,n-1,off);
}
template<class T,class L=ll>
vc<L> presum(vc<T> &a){
vc<L> ret(a.size()+1);
rep(i,a.size())ret[i+1]=ret[i]+a[i];
return ret;
}
template<class T, class F>
vc<T> &operator+=(vc<T> &a,F b){
for (auto&v:a)v += b;
return a;
}
template<class T, class F>
vc<T> &operator-=(vc<T>&a,F b){
for (auto&v:a)v-=b;
return a;
}
template<class T, class F>
vc<T> &operator*=(vc<T>&a,F b){
for (auto&v:a)v*=b;
return a;
}
template<class T=ll>
constexpr T POW(T a,T b){
T res=1;
while(b){
if(b&1)res*=a;
a*=a;
b/=2;
}
return res;
}
constexpr ll ten(ll a){
return POW<ll>(10,a);
}
template<class T>
struct Compress{
vc<T>v;
bool worked;
Compress(){worked=0;}
Compress(int n){v.reserve(n);worked=0;}
void push(T x){
v.push_back(x);
}
void work(){
if(worked)return;
worked=1;
sort(all(v));
v.erase(unique(all(v)),v.end());
}
int find(T x){
work();
auto itr=lower_bound(all(v),x);
if((*itr)==x)return itr-v.begin();
return -1;
}
int find_next(T x){
work();
return lower_bound(all(v),x)-v.begin();
}
int find_prev(T x){
work();
return lower_bound(all(v),x)-v.begin()-1;
}
};
int tbit(int32_t x){return x==0?-1:31-__builtin_clz((uint32_t)x);}
int lbit(int32_t x){return x==0?-1:__builtin_ctz((uint32_t)x);}
int tbit(uint32_t x){return x==0?-1:31-__builtin_clz(x);}
int lbit(uint32_t x){return x==0?-1:__builtin_ctz(x);}
int tbit(int64_t x){return x==0?-1:63-__builtin_clzll((uint64_t)x);}
int lbit(int64_t x){return x==0?-1:__builtin_ctzll((uint64_t)x);}
int tbit(uint64_t x){return x==0?-1:63-__builtin_clzll(x);}
int lbit(uint64_t x){return x==0?-1:__builtin_ctzll(x);}
int tbit(int32_t x,int p){return p<0?-1:tbit((int32_t)(x&(p>=31?~0u:(1u<<(p+1))-1)));}
int lbit(int32_t x,int p){return p>31?-1:lbit((int32_t)(x&(~0u<<p)));}
int tbit(uint32_t x,int p){return p<0?-1:tbit((uint32_t)(x&(p>=31?~0u:(1u<<(p+1))-1)));}
int lbit(uint32_t x,int p){return p>31?-1:lbit((uint32_t)(x&(~0u<<p)));}
int tbit(int64_t x,int p){return p<0?-1:tbit((int64_t)(x&(p>=63?~0ULL:(1ULL<<(p+1))-1)));}
int lbit(int64_t x,int p){return p>63?-1:lbit((int64_t)(x&(~0ULL<<p)));}
int tbit(uint64_t x,int p){return p<0?-1:tbit((uint64_t)(x&(p>=63?~0ULL:(1ULL<<(p+1))-1)));}
int lbit(uint64_t x,int p){return p>63?-1:lbit((uint64_t)(x&(~0ULL<<p)));}
std::istream& operator>>(std::istream& is, __int128& x) {
std::streambuf* sb = is.rdbuf();
int c = sb->sgetc();
while (c <= ' ') c = sb->snextc();
bool neg = false;
if (c == '-') {
neg = true;
c = sb->snextc();
}
unsigned __int128 v = 0;
while ((unsigned)(c - '0') < 10) {
v = v * 10 + (c - '0');
c = sb->snextc();
}
x = neg ? -(__int128)v : (__int128)v;
return is;
}
std::ostream& operator<<(std::ostream& os, __int128 x) {
std::streambuf* sb = os.rdbuf();
if (x == 0) {
sb->sputc('0');
return os;
}
char buf[40];
int pos = 39;
bool neg = x < 0;
unsigned __int128 v = neg ? -(unsigned __int128)x : (unsigned __int128)x;
while (v) {
buf[--pos] = char('0' + (v % 10));
v /= 10;
}
if (neg) buf[--pos] = '-';
sb->sputn(buf + pos, 39 - pos);
return os;
}
#ifdef LOCAL
template<typename T, typename U> std::ostream& operator<<(std::ostream& os, const std::pair<T, U>& p);
template<typename T> std::ostream& operator<<(std::ostream& os, const std::vector<T>& v);
template<typename T> std::ostream& operator<<(std::ostream& os, const std::deque<T>& dq);
template<typename T> std::ostream& operator<<(std::ostream& os, const std::list<T>& lst);
template<typename T> std::ostream& operator<<(std::ostream& os, const std::set<T>& s);
template<typename T> std::ostream& operator<<(std::ostream& os, const std::unordered_set<T>& s);
template<typename K, typename V> std::ostream& operator<<(std::ostream& os, const std::map<K, V>& m);
template<typename K, typename V> std::ostream& operator<<(std::ostream& os, const std::unordered_map<K, V>& m);
template<typename T> std::ostream& operator<<(std::ostream& os, std::stack<T> st);
template<typename T> std::ostream& operator<<(std::ostream& os, std::queue<T> q);
template<typename T, std::size_t N> std::ostream& operator<<(std::ostream& os, const std::array<T, N>& a);
template <typename T, typename Container, typename Compare>
std::ostream& operator<<(std::ostream& os, std::priority_queue<T, Container, Compare> pq);
#define dbg(...) debug_func(0, #__VA_ARGS__, __VA_ARGS__)
template <typename T>
void debug_func(int i, T name) {
cout << endl;
}
template <typename T1, typename T2, typename... T3>
void debug_func(int i, const T1 &name, const T2 &a, const T3 &...b) {
for ( ; name[i] != ',' && name[i] != '\0'; i++ ) cout << name[i];
cout << ":" << a << " ";
debug_func(i + 1, name, b...);
}
// pair
template<typename T, typename U>
std::ostream& operator<<(std::ostream& os, const std::pair<T, U>& p) {
return os << "(" << p.first << ", " << p.second << ")";
}
// vector
template<typename T>
std::ostream& operator<<(std::ostream& os, const std::vector<T>& v) {
os << "[";
for (size_t i = 0; i < v.size(); ++i) {
if (i > 0) os << ", ";
os << v[i];
}
os << "]";
return os;
}
template<typename T>
std::ostream& operator<<(std::ostream& os, const std::deque<T>& dq) {
os << "[";
for (size_t i = 0; i < dq.size(); ++i) {
if (i > 0) os << ", ";
os << dq[i];
}
os << "]";
return os;
}
template<typename T>
std::ostream& operator<<(std::ostream& os, const std::list<T>& lst) {
os << "[";
bool first = true;
for (const auto& x : lst) {
if (!first) os << ", ";
os << x;
first = false;
}
os << "]";
return os;
}
template<typename T>
std::ostream& operator<<(std::ostream& os, const std::set<T>& s) {
os << "{";
bool first = true;
for (const auto& x : s) {
if (!first) os << ", ";
os << x;
first = false;
}
os << "}";
return os;
}
template<typename T>
std::ostream& operator<<(std::ostream& os, const std::unordered_set<T>& s) {
os << "{";
bool first = true;
for (const auto& x : s) {
if (!first) os << ", ";
os << x;
first = false;
}
os << "}";
return os;
}
template<typename K, typename V>
std::ostream& operator<<(std::ostream& os, const std::map<K, V>& m) {
os << "{";
bool first = true;
for (const auto& kv : m) {
if (!first) os << ", ";
os << kv;
first = false;
}
os << "}";
return os;
}
template<typename K, typename V>
std::ostream& operator<<(std::ostream& os, const std::unordered_map<K, V>& m) {
os << "{";
bool first = true;
for (const auto& kv : m) {
if (!first) os << ", ";
os << kv;
first = false;
}
os << "}";
return os;
}
template<typename T>
std::ostream& operator<<(std::ostream& os, std::stack<T> st) {
os << "[";
bool first = true;
while (!st.empty()) {
if (!first) os << ", ";
os << st.top();
st.pop();
first = false;
}
os << "]";
return os;
}
template<typename T>
std::ostream& operator<<(std::ostream& os, std::queue<T> q) {
os << "[";
bool first = true;
while (!q.empty()) {
if (!first) os << ", ";
os << q.front();
q.pop();
first = false;
}
os << "]";
return os;
}
template<typename T, typename Container, typename Compare>
std::ostream& operator<<(std::ostream& os, std::priority_queue<T, Container, Compare> pq) {
os << "[";
while (!pq.empty()) {
os << pq.top() << (pq.size() > 1 ? ", " : "");
pq.pop();
}
return os << "]";
}
template<typename T, std::size_t N>
std::ostream& operator<<(std::ostream& os, const std::array<T, N>& a) {
os << "[";
for (std::size_t i = 0; i < N; ++i) {
if (i > 0) os << ", ";
os << a[i];
}
os << "]";
return os;
}
#else
#define dbg(...) 1111
#endif
#line 3 "lib/math/barrett.hpp"
struct Barrett{
using u64=uint64_t;
using u32=uint32_t;
using i128=__int128_t;
u64 m;
int mod;
void set(int mod_){
mod=mod_;
m=(i128(1)<<64)/mod;
}
unsigned reduce(uint64_t x){
x-=(((i128)x*m)>>64)*mod;
return x<mod?x:x-mod;
}
};
#line 4 "lib/math/d_mint.hpp"
template<int id>
struct DynamicModInt{
using u32=uint32_t;
using u64=uint64_t;
u32 val;
DynamicModInt():val(0){}
DynamicModInt(ll x){
int v=x%get_mod();
if(v<0)v+=get_mod();
val=v;
}
static DynamicModInt raw(int v){
assert(v>=0);
DynamicModInt mi;
mi.val=v;
return mi;
}
DynamicModInt &operator+=(const DynamicModInt&m){
if((val+=m.val)>=get_mod())val-=get_mod();
return *this;
}
DynamicModInt &operator-=(const DynamicModInt&m){
if((val+=(get_mod()-m.val))>=get_mod())val-=get_mod();
return *this;
}
DynamicModInt &operator*=(const DynamicModInt&m){
val=rem(u64(val)*m.val);
return *this;
}
DynamicModInt &operator/=(const DynamicModInt&m){
val=rem(u64(val)*m.inv().val);
return *this;
}
DynamicModInt operator-() const{
return DynamicModInt(-val);
}
DynamicModInt operator+() const {
return *this;
}
friend DynamicModInt operator+(DynamicModInt lhs, const DynamicModInt& rhs){
return lhs+=rhs;
}
friend DynamicModInt operator-(DynamicModInt lhs, const DynamicModInt& rhs){
return lhs-=rhs;
}
friend DynamicModInt operator*(DynamicModInt lhs, const DynamicModInt& rhs){
return lhs*=rhs;
}
friend DynamicModInt operator/(DynamicModInt lhs,const DynamicModInt&rhs){
return lhs/=rhs;
}
bool operator==(const DynamicModInt&p) const{
return p.val==val;
}
bool operator!=(const DynamicModInt&p) const{
return p.val!=val;
}
DynamicModInt pow(int64_t n) const{
DynamicModInt res(1),mul(val);
while(n){
if(n%2)res*=mul;
mul*=mul;
n/=2;
}
return res;
}
friend ostream&operator<<(ostream&os,const DynamicModInt&p){
os<<p.val;
return os;
}
friend istream&operator>>(istream&is,DynamicModInt&p){
int64_t x;
is>>x;
p=DynamicModInt(x);
return is;
}
DynamicModInt inv()const{
int a=val,b=get_mod(),u=1,v=0,t;
#ifdef LOCAL
assert(gcd(a,b)==1);
#endif
while(b>0){
t=a/b;
swap(a-=t*b,b);
swap(u-=t*v,v);
}
return DynamicModInt(u);
}
inline static u32 rem(u64 x){return BarrettReduction().reduce(x);}
static inline int &get_mod(){
static int mod=0;
return mod;
}
static void set_mod(int md){
assert(0<md&&md<=(1ll<<30)-1);
get_mod()=md;
BarrettReduction().set(md);
}
static inline Barrett&BarrettReduction(){
static Barrett b;
return b;
}
};
#line 4 "lib/math/mod.hpp"
template<class mint>
struct Binom{
inline static vector<mint>fact={1},invfact={1};
static void build(int n){
if(n<(int)fact.size())return;
fact=invfact=vector<mint>(n+1);
fact[0]=1;
for(int i=1;i<=n;i++)fact[i]=fact[i-1]*i;
invfact[n]=(1/fact[n]);
for(int i=n-1;i>=0;i--)invfact[i]=invfact[i+1]*(i+1);
}
static mint C(int a,int b){//aCb
if(a<0||b<0||a-b<0)return mint(0);
while((int)fact.size()<=a){
fact.push_back(fact.back()*(fact.size()));
}
while((int)invfact.size()<=a){
invfact.push_back(invfact.back()/invfact.size());
}
return fact[a]*invfact[b]*invfact[a-b];
}
static mint P(int a,int b){
if(a<b||b<0)return 0;
return fact[a]*invfact[a-b];
}
static mint H(int a,int b){
return C(a+b-1,b);
}
};
template<class T>
pair<T,T> inv(T x,T m){
T a1,a2;
T res=extgcd(x,m,a1,a2);
return {a1,m/res};
}
template<class T>
pair<T,T> mod_solve(T a,T b,T m){//return x s.t. ax=b mod m
a%=m,b%=m;if(a<0)a+=m;if(b<0)b+=m;
T g=gcd(gcd(a,b),m);
a/=g,b/=g,m/=g;
if(gcd(a,m)>1)return {-1,-1};
return {(inv(a,m).first*b)%m,inv(a,m).second};
}
//https://nyaannyaan.github.io/library/modulo/mod-sqrt.hpp.html
int64_t mod_sqrt(const int64_t &a, const int64_t &p) {
assert(0 <= a && a < p);
if (a < 2) return a;
using Mint = DynamicModInt<409075245>;
Mint::set_mod(p);
if (Mint(a).pow((p - 1) >> 1) != 1) return -1;
Mint b = 1, one = 1;
while (b.pow((p - 1) >> 1) == 1) b += one;
int64_t m = p - 1, e = 0;
while (m % 2 == 0) m >>= 1, e += 1;
Mint x = Mint(a).pow((m - 1) >> 1);
Mint y = Mint(a) * x * x;
x *= a;
Mint z = Mint(b).pow(m);
while (y != 1) {
int64_t j = 0;
Mint t = y;
while (t != one) {
j += 1;
t *= t;
}
z = z.pow(int64_t(1) << (e - j - 1));
x *= z;
z *= z;
y *= z;
e = j;
}
return x.val;
}
#line 4 "lib/math/s_mint.hpp"
template<uint32_t mod>
struct StaticModInt{
using u32=uint32_t;
using u64=uint64_t;
u32 val;
StaticModInt():val(0){}
StaticModInt(ll x){
int v=x%mod;
if(v<0)v+=mod;
val=v;
}
constexpr static uint32_t get_mod(){
return mod;
}
static StaticModInt raw(int v){
assert(v>=0);
StaticModInt mi;
mi.val=v;
return mi;
}
StaticModInt &operator+=(const StaticModInt&m){
if((val+=m.val)>=mod)val-=mod;
return *this;
}
StaticModInt &operator-=(const StaticModInt&m){
if((val+=(mod-m.val))>=mod)val-=mod;
return *this;
}
StaticModInt &operator*=(const StaticModInt&m){
val=u64(val)*m.val%mod;
return *this;
}
StaticModInt &operator/=(const StaticModInt&m){
val=u64(val)*m.inv().val%mod;
return *this;
}
StaticModInt operator-() const{
return StaticModInt(mod-val);
}
StaticModInt operator+() const {
return *this;
}
friend StaticModInt operator+(StaticModInt lhs, const StaticModInt& rhs){
return lhs+=rhs;
}
friend StaticModInt operator-(StaticModInt lhs, const StaticModInt& rhs){
return lhs-=rhs;
}
friend StaticModInt operator*(StaticModInt lhs, const StaticModInt& rhs){
return lhs*=rhs;
}
friend StaticModInt operator/(StaticModInt lhs,const StaticModInt&rhs){
return lhs/=rhs;
}
bool operator==(const StaticModInt&p) const{
return p.val==val;
}
bool operator!=(const StaticModInt&p) const{
return p.val!=val;
}
StaticModInt pow(int64_t n) const{
StaticModInt res(1),mul(val);
while(n){
if(n%2)res*=mul;
mul*=mul;
n/=2;
}
return res;
}
friend ostream&operator<<(ostream&os,const StaticModInt&p){
os<<p.val;
return os;
}
friend istream&operator>>(istream&is,StaticModInt&p){
int64_t x;
is>>x;
p=StaticModInt(x);
return is;
}
StaticModInt inv()const{
int a=val,b=mod,u=1,v=0,t;
#ifdef LOCAL
assert(gcd(a,b)==1);
#endif
while(b>0){
t=a/b;
swap(a-=t*b,b);
swap(u-=t*v,v);
}
return StaticModInt(u);
}
};
#line 3 "lib/math/kth_root.hpp"
//floor(a^{1/b})
ull kth_root(ull a,ull b){
if(a==0)return 0;
if(b==1)return a;
if(b>=64)return 1;
auto my_pow=[&](ull A,ull B)->ull{
ull res=1;
while(B){
if(B%2){
if(i128(res)*A>a)return 0;
res*=A;
}
B/=2;
if(B){
if(i128(A)*A>a)return 0;
A*=A;
}
}
return res;
};
ull ac=1,wa=(ull(1)<<(64/b+1))+1;
while(wa-ac>1){
ull wj=ac+wa>>1;
auto res=my_pow(wj,b);
if(res&&res<=a){
ac=wj;
}else wa=wj;
}
return ac;
}
#line 4 "a.cpp"
using mint=StaticModInt<998244353>;
mint inv2=499122177;
mint i20=149736653;
inline mint sm(mint l){
return mint(l)*(l-1)*inv2;
}
int cnt=0;
inline mint get_sum(ll l,ll r){
ll li=sqrt(l);if(li*li>l)li--;
ll ri=sqrt(r);if(ri*ri>r)ri--;
mint ans=0;
if(li==ri){
ans+=mint(li)*(sm(r+1)-sm(l));
return ans;
}
ans+=mint(li)*(sm((li+1)*(li+1))-sm(l));
ans+=mint(ri)*(sm(r+1)-sm(ri*ri));
mint L1=(li+1);
mint R1=ri;
ans+=L1*(sm(R1*R1)-sm(L1*L1));
//REP(i,L1.val+1,R1.val+1)ans+=(sm(R1*R1)-sm(i*i))*coef;
auto L2=L1*L1;
auto L3=L1*L2;
auto L4=L1*L3;
auto L5=L1*L4;
auto R2=R1*R1;
auto R3=R1*R2;
auto R4=R1*R3;
auto R5=R1*R4;
ans+=(2*L5+5*L4-5*L2-2*L1*(5*R4-5*R2+1)+R1*(8*R4-5*R3-10*R2+5*R1+2))*i20;
return ans;
}
void solve(){
LL(n);
vc<mint>inv(1e6);REP(i,1,1e6)inv[i]=1/mint(i);
mint ans=0;
vvc<ll>put(63);
REP(i,4,63){
for(int j=1;;j++){
i128 P=POW<i128>(j,i);
if(P>n)break;
put[i].push_back(P);
}
}
smpq<array<ll,3>>que;REP(i,4,63){
if(put[i].size()>1)que.push({put[i][1],i,1});
cnt+=put[i].size();
}
vc<ll>coef(63,1);
for(ll K=1;K<=1e6;K++){
ll L=ll(K)*K*K;
ll R=min(n+1,ll(K+1)*(K+1)*(K+1));
if(L>R)break;
mint all_coef=K;REP(i,4,63)all_coef*=coef[i];
//[L,R)
array<ll,3>tmp{-1,-1,-1};
auto get_top=[&](){
return que.top();
};
while(que.size()&&get_top()[0]<R){
auto [p,q,r]=que.top();que.pop();tmp={-1,-1,-1};
ans+=get_sum(L,p-1)*all_coef;
L=p;
auto update=[&](int p,int q,int r){
all_coef*=inv[coef[q]++];
all_coef*=coef[q];
++cnt;
if(put[q].size()>r+1)que.push({put[q][r+1],q,r+1});
};
update(p,q,r);
while(que.size()&&get_top()[0]==p){
auto[np,nq,nr]=que.top();que.pop();tmp={-1,-1,-1};
++cnt;
update(np,nq,nr);
}
}
ans+=get_sum(L,R-1)*all_coef;
}
PRT(ans);
}
signed main(){
dbg("==============="s);
#ifdef LOCAL
freopen("input.txt","r",stdin);
freopen("output.txt","w",stdout);
#endif
cin.tie(0)->sync_with_stdio(0);
cout<<fixed<<setprecision(20);
int t=1;
// cin >> t;
while(t--)solve();
}