結果

問題 No.2902 ZERO!!
ユーザー RubikunRubikun
提出日時 2024-09-27 20:10:22
言語 C++17
(gcc 12.3.0 + boost 1.83.0)
結果
AC  
実行時間 175 ms / 2,000 ms
コード長 26,342 bytes
コンパイル時間 3,700 ms
コンパイル使用メモリ 246,396 KB
実行使用メモリ 24,212 KB
最終ジャッジ日時 2024-09-27 20:10:29
合計ジャッジ時間 6,857 ms
ジャッジサーバーID
(参考情報)
judge5 / 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 5 ms
16,544 KB
testcase_01 AC 4 ms
16,744 KB
testcase_02 AC 175 ms
24,212 KB
testcase_03 AC 5 ms
16,536 KB
testcase_04 AC 42 ms
18,280 KB
testcase_05 AC 86 ms
21,456 KB
testcase_06 AC 167 ms
24,188 KB
testcase_07 AC 51 ms
19,544 KB
testcase_08 AC 159 ms
24,060 KB
testcase_09 AC 172 ms
23,820 KB
testcase_10 AC 115 ms
21,676 KB
testcase_11 AC 102 ms
20,632 KB
testcase_12 AC 15 ms
17,032 KB
testcase_13 AC 155 ms
23,936 KB
testcase_14 AC 118 ms
22,384 KB
testcase_15 AC 135 ms
23,056 KB
testcase_16 AC 83 ms
20,916 KB
testcase_17 AC 152 ms
24,192 KB
testcase_18 AC 144 ms
24,188 KB
testcase_19 AC 143 ms
22,500 KB
testcase_20 AC 114 ms
22,084 KB
testcase_21 AC 119 ms
21,608 KB
testcase_22 AC 61 ms
19,140 KB
testcase_23 AC 86 ms
21,852 KB
testcase_24 AC 5 ms
16,824 KB
testcase_25 AC 5 ms
16,712 KB
testcase_26 AC 5 ms
16,328 KB
testcase_27 AC 6 ms
17,356 KB
testcase_28 AC 6 ms
17,604 KB
testcase_29 AC 5 ms
16,936 KB
testcase_30 AC 5 ms
16,640 KB
testcase_31 AC 5 ms
17,272 KB
testcase_32 AC 6 ms
17,532 KB
testcase_33 AC 5 ms
18,008 KB
testcase_34 AC 5 ms
17,288 KB
testcase_35 AC 5 ms
16,272 KB
testcase_36 AC 5 ms
16,240 KB
testcase_37 AC 6 ms
16,316 KB
testcase_38 AC 4 ms
17,848 KB
testcase_39 AC 5 ms
16,876 KB
testcase_40 AC 5 ms
16,732 KB
testcase_41 AC 4 ms
17,144 KB
testcase_42 AC 5 ms
16,324 KB
testcase_43 AC 4 ms
16,632 KB
権限があれば一括ダウンロードができます
コンパイルメッセージ
main.cpp:804:9: warning: #pragma once in main file
  804 | #pragma once
      |         ^~~~
main.cpp:857:9: warning: #pragma once in main file
  857 | #pragma once
      |         ^~~~
main.cpp:869:9: warning: #pragma once in main file
  869 | #pragma once
      |         ^~~~

ソースコード

diff #

#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
template<class T>bool chmax(T &a, const T &b) { if (a<b) { a=b; return true; } return false; }
template<class T>bool chmin(T &a, const T &b) { if (b<a) { a=b; return true; } return false; }
#define vi vector<int>
#define vl vector<ll>
#define vii vector<pair<int,int>>
#define vll vector<pair<ll,ll>>
#define vvi vector<vector<int>>
#define vvl vector<vector<ll>>
#define vvii vector<vector<pair<int,int>>>
#define vvll vector<vector<pair<ll,ll>>>
#define vst vector<string>
#define pii pair<int,int>
#define pll pair<ll,ll>
#define pb push_back
#define all(x) (x).begin(),(x).end()
#define mkunique(x) sort(all(x));(x).erase(unique(all(x)),(x).end())
#define fi first
#define se second
#define mp make_pair
#define si(x) int(x.size())
const int mod=998244353,MAX=1000005,INF=15<<26;

//modint+畳み込み+逆元テーブル

// from: https://gist.github.com/yosupo06/ddd51afb727600fd95d9d8ad6c3c80c9
// (based on AtCoder STL)

#include <algorithm>
#include <array>

#ifdef _MSC_VER
#include <intrin.h>
#endif

namespace atcoder {

namespace internal {

int ceil_pow2(int n) {
    int x = 0;
    while ((1U << x) < (unsigned int)(n)) x++;
    return x;
}

int bsf(unsigned int n) {
#ifdef _MSC_VER
    unsigned long index;
    _BitScanForward(&index, n);
    return index;
#else
    return __builtin_ctz(n);
#endif
}

}  // namespace internal

}  // namespace atcoder



#include <utility>

namespace atcoder {

namespace internal {

constexpr long long safe_mod(long long x, long long m) {
    x %= m;
    if (x < 0) x += m;
    return x;
}

struct barrett {
    unsigned int _m;
    unsigned long long im;
    
    barrett(unsigned int m) : _m(m), im((unsigned long long)(-1) / m + 1) {}
    
    unsigned int umod() const { return _m; }
    
    unsigned int mul(unsigned int a, unsigned int b) const {
        
        unsigned long long z = a;
        z *= b;
#ifdef _MSC_VER
        unsigned long long x;
        _umul128(z, im, &x);
#else
        unsigned long long x =
        (unsigned long long)(((unsigned __int128)(z)*im) >> 64);
#endif
        unsigned int v = (unsigned int)(z - x * _m);
        if (_m <= v) v += _m;
        return v;
    }
};

constexpr long long pow_mod_constexpr(long long x, long long n, int m) {
    if (m == 1) return 0;
    unsigned int _m = (unsigned int)(m);
    unsigned long long r = 1;
    unsigned long long y = safe_mod(x, m);
    while (n) {
        if (n & 1) r = (r * y) % _m;
        y = (y * y) % _m;
        n >>= 1;
    }
    return r;
}

constexpr bool is_prime_constexpr(int n) {
    if (n <= 1) return false;
    if (n == 2 || n == 7 || n == 61) return true;
    if (n % 2 == 0) return false;
    long long d = n - 1;
    while (d % 2 == 0) d /= 2;
    for (long long a : {2, 7, 61}) {
        long long t = d;
        long long y = pow_mod_constexpr(a, t, n);
        while (t != n - 1 && y != 1 && y != n - 1) {
            y = y * y % n;
            t <<= 1;
        }
        if (y != n - 1 && t % 2 == 0) {
            return false;
        }
    }
    return true;
}
template <int n> constexpr bool is_prime = is_prime_constexpr(n);

constexpr std::pair<long long, long long> inv_gcd(long long a, long long b) {
    a = safe_mod(a, b);
    if (a == 0) return {b, 0};
    
    long long s = b, t = a;
    long long m0 = 0, m1 = 1;
    
    while (t) {
        long long u = s / t;
        s -= t * u;
        m0 -= m1 * u;  // |m1 * u| <= |m1| * s <= b
        
        
        auto tmp = s;
        s = t;
        t = tmp;
        tmp = m0;
        m0 = m1;
        m1 = tmp;
    }
    if (m0 < 0) m0 += b / s;
    return {s, m0};
}

constexpr int primitive_root_constexpr(int m) {
    if (m == 2) return 1;
    if (m == 167772161) return 3;
    if (m == 469762049) return 3;
    if (m == 754974721) return 11;
    if (m == 998244353) return 3;
    int divs[20] = {};
    divs[0] = 2;
    int cnt = 1;
    int x = (m - 1) / 2;
    while (x % 2 == 0) x /= 2;
    for (int i = 3; (long long)(i)*i <= x; i += 2) {
        if (x % i == 0) {
            divs[cnt++] = i;
            while (x % i == 0) {
                x /= i;
            }
        }
    }
    if (x > 1) {
        divs[cnt++] = x;
    }
    for (int g = 2;; g++) {
        bool ok = true;
        for (int i = 0; i < cnt; i++) {
            if (pow_mod_constexpr(g, (m - 1) / divs[i], m) == 1) {
                ok = false;
                break;
            }
        }
        if (ok) return g;
    }
}
template <int m> constexpr int primitive_root = primitive_root_constexpr(m);

}  // namespace internal

}  // namespace atcoder


#include <cassert>
#include <numeric>
#include <type_traits>

namespace atcoder {

namespace internal {

#ifndef _MSC_VER
template <class T>
using is_signed_int128 =
typename std::conditional<std::is_same<T, __int128_t>::value ||
std::is_same<T, __int128>::value,
std::true_type,
std::false_type>::type;

template <class T>
using is_unsigned_int128 =
typename std::conditional<std::is_same<T, __uint128_t>::value ||
std::is_same<T, unsigned __int128>::value,
std::true_type,
std::false_type>::type;

template <class T>
using make_unsigned_int128 =
typename std::conditional<std::is_same<T, __int128_t>::value,
__uint128_t,
unsigned __int128>;

template <class T>
using is_integral = typename std::conditional<std::is_integral<T>::value ||
is_signed_int128<T>::value ||
is_unsigned_int128<T>::value,
std::true_type,
std::false_type>::type;

template <class T>
using is_signed_int = typename std::conditional<(is_integral<T>::value &&
                                                 std::is_signed<T>::value) ||
is_signed_int128<T>::value,
std::true_type,
std::false_type>::type;

template <class T>
using is_unsigned_int =
typename std::conditional<(is_integral<T>::value &&
                           std::is_unsigned<T>::value) ||
is_unsigned_int128<T>::value,
std::true_type,
std::false_type>::type;

template <class T>
using to_unsigned = typename std::conditional<
is_signed_int128<T>::value,
make_unsigned_int128<T>,
typename std::conditional<std::is_signed<T>::value,
std::make_unsigned<T>,
std::common_type<T>>::type>::type;

#else

template <class T> using is_integral = typename std::is_integral<T>;

template <class T>
using is_signed_int =
typename std::conditional<is_integral<T>::value && std::is_signed<T>::value,
std::true_type,
std::false_type>::type;

template <class T>
using is_unsigned_int =
typename std::conditional<is_integral<T>::value &&
std::is_unsigned<T>::value,
std::true_type,
std::false_type>::type;

template <class T>
using to_unsigned = typename std::conditional<is_signed_int<T>::value,
std::make_unsigned<T>,
std::common_type<T>>::type;

#endif

template <class T>
using is_signed_int_t = std::enable_if_t<is_signed_int<T>::value>;

template <class T>
using is_unsigned_int_t = std::enable_if_t<is_unsigned_int<T>::value>;

template <class T> using to_unsigned_t = typename to_unsigned<T>::type;

}  // namespace internal

}  // namespace atcoder

#include <cassert>
#include <numeric>
#include <type_traits>

#ifdef _MSC_VER
#include <intrin.h>
#endif

namespace atcoder {

namespace internal {

struct modint_base {};
struct static_modint_base : modint_base {};

template <class T> using is_modint = std::is_base_of<modint_base, T>;
template <class T> using is_modint_t = std::enable_if_t<is_modint<T>::value>;

}  // namespace internal

template <int m, std::enable_if_t<(1 <= m)>* = nullptr>
struct static_modint : internal::static_modint_base {
    using mint = static_modint;
    
public:
    static constexpr int mod() { return m; }
    static mint raw(int v) {
        mint x;
        x._v = v;
        return x;
    }
    
    static_modint() : _v(0) {}
    template <class T, internal::is_signed_int_t<T>* = nullptr>
    static_modint(T v) {
        long long x = (long long)(v % (long long)(umod()));
        if (x < 0) x += umod();
        _v = (unsigned int)(x);
    }
    template <class T, internal::is_unsigned_int_t<T>* = nullptr>
    static_modint(T v) {
        _v = (unsigned int)(v % umod());
    }
    static_modint(bool v) { _v = ((unsigned int)(v) % umod()); }
    
    unsigned int val() const { return _v; }
    
    mint& operator++() {
        _v++;
        if (_v == umod()) _v = 0;
        return *this;
    }
    mint& operator--() {
        if (_v == 0) _v = umod();
        _v--;
        return *this;
    }
    mint operator++(int) {
        mint result = *this;
        ++*this;
        return result;
    }
    mint operator--(int) {
        mint result = *this;
        --*this;
        return result;
    }
    
    mint& operator+=(const mint& rhs) {
        _v += rhs._v;
        if (_v >= umod()) _v -= umod();
        return *this;
    }
    mint& operator-=(const mint& rhs) {
        _v -= rhs._v;
        if (_v >= umod()) _v += umod();
        return *this;
    }
    mint& operator*=(const mint& rhs) {
        unsigned long long z = _v;
        z *= rhs._v;
        _v = (unsigned int)(z % umod());
        return *this;
    }
    mint& operator/=(const mint& rhs) { return *this = *this * rhs.inv(); }
    
    mint operator+() const { return *this; }
    mint operator-() const { return mint() - *this; }
    
    mint pow(long long n) const {
        assert(0 <= n);
        mint x = *this, r = 1;
        while (n) {
            if (n & 1) r *= x;
            x *= x;
            n >>= 1;
        }
        return r;
    }
    mint inv() const {
        if (prime) {
            assert(_v);
            return pow(umod() - 2);
        } else {
            auto eg = internal::inv_gcd(_v, m);
            assert(eg.first == 1);
            return eg.second;
        }
    }
    
    friend mint operator+(const mint& lhs, const mint& rhs) {
        return mint(lhs) += rhs;
    }
    friend mint operator-(const mint& lhs, const mint& rhs) {
        return mint(lhs) -= rhs;
    }
    friend mint operator*(const mint& lhs, const mint& rhs) {
        return mint(lhs) *= rhs;
    }
    friend mint operator/(const mint& lhs, const mint& rhs) {
        return mint(lhs) /= rhs;
    }
    friend bool operator==(const mint& lhs, const mint& rhs) {
        return lhs._v == rhs._v;
    }
    friend bool operator!=(const mint& lhs, const mint& rhs) {
        return lhs._v != rhs._v;
    }
    
private:
    unsigned int _v;
    static constexpr unsigned int umod() { return m; }
    static constexpr bool prime = internal::is_prime<m>;
};

template <int id> struct dynamic_modint : internal::modint_base {
    using mint = dynamic_modint;
    
public:
    static int mod() { return (int)(bt.umod()); }
    static void set_mod(int m) {
        assert(1 <= m);
        bt = internal::barrett(m);
    }
    static mint raw(int v) {
        mint x;
        x._v = v;
        return x;
    }
    
    dynamic_modint() : _v(0) {}
    template <class T, internal::is_signed_int_t<T>* = nullptr>
    dynamic_modint(T v) {
        long long x = (long long)(v % (long long)(mod()));
        if (x < 0) x += mod();
        _v = (unsigned int)(x);
    }
    template <class T, internal::is_unsigned_int_t<T>* = nullptr>
    dynamic_modint(T v) {
        _v = (unsigned int)(v % mod());
    }
    dynamic_modint(bool v) { _v = ((unsigned int)(v) % mod()); }
    
    unsigned int val() const { return _v; }
    
    mint& operator++() {
        _v++;
        if (_v == umod()) _v = 0;
        return *this;
    }
    mint& operator--() {
        if (_v == 0) _v = umod();
        _v--;
        return *this;
    }
    mint operator++(int) {
        mint result = *this;
        ++*this;
        return result;
    }
    mint operator--(int) {
        mint result = *this;
        --*this;
        return result;
    }
    
    mint& operator+=(const mint& rhs) {
        _v += rhs._v;
        if (_v >= umod()) _v -= umod();
        return *this;
    }
    mint& operator-=(const mint& rhs) {
        _v += mod() - rhs._v;
        if (_v >= umod()) _v -= umod();
        return *this;
    }
    mint& operator*=(const mint& rhs) {
        _v = bt.mul(_v, rhs._v);
        return *this;
    }
    mint& operator/=(const mint& rhs) { return *this = *this * rhs.inv(); }
    
    mint operator+() const { return *this; }
    mint operator-() const { return mint() - *this; }
    
    mint pow(long long n) const {
        assert(0 <= n);
        mint x = *this, r = 1;
        while (n) {
            if (n & 1) r *= x;
            x *= x;
            n >>= 1;
        }
        return r;
    }
    mint inv() const {
        auto eg = internal::inv_gcd(_v, mod());
        assert(eg.first == 1);
        return eg.second;
    }
    
    friend mint operator+(const mint& lhs, const mint& rhs) {
        return mint(lhs) += rhs;
    }
    friend mint operator-(const mint& lhs, const mint& rhs) {
        return mint(lhs) -= rhs;
    }
    friend mint operator*(const mint& lhs, const mint& rhs) {
        return mint(lhs) *= rhs;
    }
    friend mint operator/(const mint& lhs, const mint& rhs) {
        return mint(lhs) /= rhs;
    }
    friend bool operator==(const mint& lhs, const mint& rhs) {
        return lhs._v == rhs._v;
    }
    friend bool operator!=(const mint& lhs, const mint& rhs) {
        return lhs._v != rhs._v;
    }
    
private:
    unsigned int _v;
    static internal::barrett bt;
    static unsigned int umod() { return bt.umod(); }
};
template <int id> internal::barrett dynamic_modint<id>::bt = 998244353;

using modint998244353 = static_modint<998244353>;
using modint1000000007 = static_modint<1000000007>;
using modint = dynamic_modint<-1>;

namespace internal {

template <class T>
using is_static_modint = std::is_base_of<internal::static_modint_base, T>;

template <class T>
using is_static_modint_t = std::enable_if_t<is_static_modint<T>::value>;

template <class> struct is_dynamic_modint : public std::false_type {};
template <int id>
struct is_dynamic_modint<dynamic_modint<id>> : public std::true_type {};

template <class T>
using is_dynamic_modint_t = std::enable_if_t<is_dynamic_modint<T>::value>;

}  // namespace internal

}  // namespace atcoder

#include <cassert>
#include <type_traits>
#include <vector>

namespace atcoder {

namespace internal {

template <class mint, internal::is_static_modint_t<mint>* = nullptr>
void butterfly(std::vector<mint>& a) {
    static constexpr int g = internal::primitive_root<mint::mod()>;
    int n = int(a.size());
    int h = internal::ceil_pow2(n);
    
    static bool first = true;
    static mint sum_e[30];  // sum_e[i] = ies[0] * ... * ies[i - 1] * es[i]
    if (first) {
        first = false;
        mint es[30], ies[30];  // es[i]^(2^(2+i)) == 1
        int cnt2 = bsf(mint::mod() - 1);
        mint e = mint(g).pow((mint::mod() - 1) >> cnt2), ie = e.inv();
        for (int i = cnt2; i >= 2; i--) {
            es[i - 2] = e;
            ies[i - 2] = ie;
            e *= e;
            ie *= ie;
        }
        mint now = 1;
        for (int i = 0; i < cnt2 - 2; i++) {
            sum_e[i] = es[i] * now;
            now *= ies[i];
        }
    }
    for (int ph = 1; ph <= h; ph++) {
        int w = 1 << (ph - 1), p = 1 << (h - ph);
        mint now = 1;
        for (int s = 0; s < w; s++) {
            int offset = s << (h - ph + 1);
            for (int i = 0; i < p; i++) {
                auto l = a[i + offset];
                auto r = a[i + offset + p] * now;
                a[i + offset] = l + r;
                a[i + offset + p] = l - r;
            }
            now *= sum_e[bsf(~(unsigned int)(s))];
        }
    }
}

template <class mint, internal::is_static_modint_t<mint>* = nullptr>
void butterfly_inv(std::vector<mint>& a) {
    static constexpr int g = internal::primitive_root<mint::mod()>;
    int n = int(a.size());
    int h = internal::ceil_pow2(n);
    
    static bool first = true;
    static mint sum_ie[30];  // sum_ie[i] = es[0] * ... * es[i - 1] * ies[i]
    if (first) {
        first = false;
        mint es[30], ies[30];  // es[i]^(2^(2+i)) == 1
        int cnt2 = bsf(mint::mod() - 1);
        mint e = mint(g).pow((mint::mod() - 1) >> cnt2), ie = e.inv();
        for (int i = cnt2; i >= 2; i--) {
            es[i - 2] = e;
            ies[i - 2] = ie;
            e *= e;
            ie *= ie;
        }
        mint now = 1;
        for (int i = 0; i < cnt2 - 2; i++) {
            sum_ie[i] = ies[i] * now;
            now *= es[i];
        }
    }
    
    for (int ph = h; ph >= 1; ph--) {
        int w = 1 << (ph - 1), p = 1 << (h - ph);
        mint inow = 1;
        for (int s = 0; s < w; s++) {
            int offset = s << (h - ph + 1);
            for (int i = 0; i < p; i++) {
                auto l = a[i + offset];
                auto r = a[i + offset + p];
                a[i + offset] = l + r;
                a[i + offset + p] =
                (unsigned long long)(mint::mod() + l.val() - r.val()) *
                inow.val();
            }
            inow *= sum_ie[bsf(~(unsigned int)(s))];
        }
    }
}

}  // namespace internal

template <class mint, internal::is_static_modint_t<mint>* = nullptr>
std::vector<mint> convolution(std::vector<mint> a, std::vector<mint> b) {
    int n = int(a.size()), m = int(b.size());
    if (!n || !m) return {};
    if (std::min(n, m) <= 60) {
        if (n < m) {
            std::swap(n, m);
            std::swap(a, b);
        }
        std::vector<mint> ans(n + m - 1);
        for (int i = 0; i < n; i++) {
            for (int j = 0; j < m; j++) {
                ans[i + j] += a[i] * b[j];
            }
        }
        return ans;
    }
    int z = 1 << internal::ceil_pow2(n + m - 1);
    a.resize(z);
    internal::butterfly(a);
    b.resize(z);
    internal::butterfly(b);
    for (int i = 0; i < z; i++) {
        a[i] *= b[i];
    }
    internal::butterfly_inv(a);
    a.resize(n + m - 1);
    mint iz = mint(z).inv();
    for (int i = 0; i < n + m - 1; i++) a[i] *= iz;
    return a;
}

template <unsigned int mod = 998244353,
class T,
std::enable_if_t<internal::is_integral<T>::value>* = nullptr>
std::vector<T> convolution(const std::vector<T>& a, const std::vector<T>& b) {
    int n = int(a.size()), m = int(b.size());
    if (!n || !m) return {};
    
    using mint = static_modint<mod>;
    std::vector<mint> a2(n), b2(m);
    for (int i = 0; i < n; i++) {
        a2[i] = mint(a[i]);
    }
    for (int i = 0; i < m; i++) {
        b2[i] = mint(b[i]);
    }
    auto c2 = convolution(move(a2), move(b2));
    std::vector<T> c(n + m - 1);
    for (int i = 0; i < n + m - 1; i++) {
        c[i] = c2[i].val();
    }
    return c;
}

std::vector<long long> convolution_ll(const std::vector<long long>& a,
                                      const std::vector<long long>& b) {
    int n = int(a.size()), m = int(b.size());
    if (!n || !m) return {};
    
    static constexpr unsigned long long MOD1 = 754974721;  // 2^24
    static constexpr unsigned long long MOD2 = 167772161;  // 2^25
    static constexpr unsigned long long MOD3 = 469762049;  // 2^26
    static constexpr unsigned long long M2M3 = MOD2 * MOD3;
    static constexpr unsigned long long M1M3 = MOD1 * MOD3;
    static constexpr unsigned long long M1M2 = MOD1 * MOD2;
    static constexpr unsigned long long M1M2M3 = MOD1 * MOD2 * MOD3;
    
    static constexpr unsigned long long i1 =
    internal::inv_gcd(MOD2 * MOD3, MOD1).second;
    static constexpr unsigned long long i2 =
    internal::inv_gcd(MOD1 * MOD3, MOD2).second;
    static constexpr unsigned long long i3 =
    internal::inv_gcd(MOD1 * MOD2, MOD3).second;
    
    auto c1 = convolution<MOD1>(a, b);
    auto c2 = convolution<MOD2>(a, b);
    auto c3 = convolution<MOD3>(a, b);
    
    std::vector<long long> c(n + m - 1);
    for (int i = 0; i < n + m - 1; i++) {
        unsigned long long x = 0;
        x += (c1[i] * i1) % MOD1 * M2M3;
        x += (c2[i] * i2) % MOD2 * M1M3;
        x += (c3[i] * i3) % MOD3 * M1M2;
        long long diff =
        c1[i] - internal::safe_mod((long long)(x), (long long)(MOD1));
        if (diff < 0) diff += MOD1;
        static constexpr unsigned long long offset[5] = {
            0, 0, M1M2M3, 2 * M1M2M3, 3 * M1M2M3};
        x -= offset[diff % 5];
        c[i] = x;
    }
    
    return c;
}

}  // namespace atcoder

using mint=atcoder::modint998244353;

mint inv[MAX],fac[MAX],finv[MAX];

void make(){
    
    fac[0]=fac[1]=1;
    finv[0]=finv[1]=1;
    inv[1]=1;
    
    for(int i=2;i<MAX;i++){
        inv[i]=-inv[mod%i]*(mod/i);
        fac[i]=fac[i-1]*i;
        finv[i]=finv[i-1]*inv[i];
    }
}

mint comb(ll a,ll b){
    if(a<b) return 0;
    return fac[a]*finv[b]*finv[a-b];
}

mint perm(ll a,ll b){
    if(a<b) return 0;
    return fac[a]*finv[a-b];
}


//高速素因数分解

/**
 * Author: chilli, Ramchandra Apte, Noam527, Simon Lindholm
 * Date: 2019-04-24
 * License: CC0
 * Source: https://github.com/RamchandraApte/OmniTemplate/blob/master/modulo.hpp…
 * Description: Calculate $a\cdot b\bmod c$ (or $a^b \bmod c$) for $0 \le a, b \le c \le 7.2\cdot 10^{18}$.
 * Time: O(1) for \texttt{modmul}, O(\log b) for \texttt{modpow}
 * Status: stress-tested, proven correct
 * Details:
 * This runs ~2x faster than the naive (__int128_t)a * b % M.
 * A proof of correctness is in doc/modmul-proof.tex. An earlier version of the proof,
 * from when the code used a * b / (long double)M, is in doc/modmul-proof.md.
 * The proof assumes that long doubles are implemented as x87 80-bit floats; if they
 * are 64-bit, as on e.g. MSVC, the implementation is only valid for
 * $0 \le a, b \le c < 2^{52} \approx 4.5 \cdot 10^{15}$.
 */
#pragma once

typedef unsigned long long ull;
ull modmul(ull a, ull b, ull M) {
    ll ret = a * b - M * ull(1.L / M * a * b);
    return ret + M * (ret < 0) - M * (ret >= (ll)M);
}
ull modpow(ull b, ull e, ull mod) {
    ull ans = 1;
    for (; e; b = modmul(b, b, mod), e /= 2)
        if (e & 1) ans = modmul(ans, b, mod);
    return ans;
}

/**
 * Author: chilli, SJTU, pajenegod
 * Date: 2020-03-04
 * License: CC0
 * Source: own
 * Description: Pollard-rho randomized factorization algorithm. Returns prime
 * factors of a number, in arbitrary order (e.g. 2299 -> \{11, 19, 11\}).
 * Time: $O(n^{1/4})$, less for numbers with small factors.
 * Status: stress-tested
 *
 * Details: This implementation uses the improvement described here
 * (https://en.wikipedia.org/wiki/Pollard%27s_rho_algorithm#Variants…), where
 * one can accumulate gcd calls by some factor (40 chosen here through
 * exhaustive testing). This improves performance by approximately 6-10x
 * depending on the inputs and speed of gcd. Benchmark found here:
 * (https://ideone.com/nGGD9T)
 *
 * GCD can be improved by a factor of 1.75x using Binary GCD
 * (https://lemire.me/blog/2013/12/26/fastest-way-to-compute-the-greatest-common-divisor/…).
 * However, with the gcd accumulation the bottleneck moves from the gcd calls
 * to the modmul. As GCD only constitutes ~12% of runtime, speeding it up
 * doesn't matter so much.
 *
 * This code can probably be sped up by using a faster mod mul - potentially
 * montgomery reduction on 128 bit integers.
 * Alternatively, one can use a quadratic sieve for an asymptotic improvement,
 * which starts being faster in practice around 1e13.
 *
 * Brent's cycle finding algorithm was tested, but doesn't reduce modmul calls
 * significantly.
 *
 * Subtle implementation notes:
 * - we operate on residues in [1, n]; modmul can be proven to work for those
 * - prd starts off as 2 to handle the case n = 4; it's harmless for other n
 *   since we're guaranteed that n > 2. (Pollard rho has problems with prime
 *   powers in general, but all larger ones happen to work.)
 * - t starts off as 30 to make the first gcd check come earlier, as an
 *   optimization for small numbers.
 */
#pragma once

/**
 * Author: chilli, c1729, Simon Lindholm
 * Date: 2019-03-28
 * License: CC0
 * Source: Wikipedia, https://miller-rabin.appspot.com
 * Description: Deterministic Miller-Rabin primality test.
 * Guaranteed to work for numbers up to $7 \cdot 10^{18}$; for larger numbers, use Python and extend A randomly.
 * Time: 7 times the complexity of $a^b \mod c$.
 * Status: Stress-tested
 */
#pragma once

bool isPrime(ull n) {
    if (n < 2 || n % 6 % 4 != 1) return (n | 1) == 3;
    ull A[] = {2, 325, 9375, 28178, 450775, 9780504, 1795265022},
    s = __builtin_ctzll(n-1), d = n >> s;
    for (ull a : A) {   // ^ count trailing zeroes
        ull p = modpow(a%n, d, n), i = s;
        while (p != 1 && p != n - 1 && a % n && i--)
            p = modmul(p, p, n);
        if (p != n-1 && i != s) return 0;
    }
    return 1;
}

ull pollard(ull n) {
    auto f = [n](ull x) { return modmul(x, x, n) + 1; };
    ull x = 0, y = 0, t = 30, prd = 2, i = 1, q;
    while (t++ % 40 || __gcd(prd, n) == 1) {
        if (x == y) x = ++i, y = f(x);
        if ((q = modmul(prd, max(x,y) - min(x,y), n))) prd = q;
        x = f(x), y = f(f(y));
    }
    return __gcd(prd, n);
}
vector<ull> factor(ull n) {
    if (n == 1) return {};
    if (isPrime(n)) return {n};
    ull x = pollard(n);
    auto l = factor(x), r = factor(n / x);
    l.insert(l.end(), all(r));
    return l;
}

vector<int> prime;//i番目の素数
bool is_prime[MAX+1];

void sieve(int n){
    for(int i=0;i<=n;i++){
        is_prime[i]=true;
    }
    
    is_prime[0]=is_prime[1]=false;
    
    for(int i=2;i<=n;i++){
        if(is_prime[i]){
            prime.push_back(i);
            for(int j=2*i;j<=n;j+=i){
                is_prime[j] = false;
            }
        }
    }
}

ll cn[MAX];

int main(){
    
    std::ifstream in("text.txt");
    std::cin.rdbuf(in.rdbuf());
    cin.tie(0);
    ios::sync_with_stdio(false);
    
    ll N;cin>>N;
    sieve(N);
    map<ll,ll> MA;
    for(ll p:prime){
        for(ll x=p;x<=N;x+=p){
            ll now=x;
            while(now%p==0){
                cn[p]++;
                now/=p;
            }
        }
        MA[cn[p]]++;
    }
    mint ans=0;
    
    //for(auto [a,b]:MA) cout<<a<<" "<<b<<endl;
    
    for(ll s=1;s<=N;s++){
        mint seki=1;
        vl NG;
        for(auto [a,b]:MA){
            ll K=a/s+1;
            if(K>1) seki*=mint(K).pow(b);
            else{
                NG.pb(a);
            }
        }
        for(ll a:NG) MA.erase(a);
        seki--;
        ans+=seki;
    }
    cout<<ans.val()<<endl;
}


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