#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=300005;
const ll INF=15LL<<58;

//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;

vector<mint> inv,fac,finv;

void make(){
    
    inv.resize(MAX);
    fac.resize(MAX);
    finv.resize(MAX);
    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];
}

int main(){
    
    std::ifstream in("text.txt");
    std::cin.rdbuf(in.rdbuf());
    cin.tie(0);
    ios::sync_with_stdio(false);
    
    mint r2=mint(2).inv();
    
    vector<mint> ume={563039326,369342839,57018046,483714709,922199560,793414763,738864680,775765369,130713524,463301220,631942102,208411044,801787053,790378971,931170244,814860648,903705984,752337161,281321481,419940687,18410204,372095227,98042605,603270638,214867440,11989264,862970568,177912413,108362786,34328138,161080834,817859489,702572756,463989271,76809916,784524273,100932300,843748480,735048675,87303214,869622709,723596860,437610167,125280016,277816977,388071528,683210306,656230193,376766136,199614294,949331897,992958200,606341395,269873800,635188742,36252798,84842243,183292986,200682441,347639222,9067829,468412178,15992275,129870228,735573319,70759026,63786113,613182996,913526057,723392426,608084907,209628863,742224416,900500458,953614143,279864114,715974760,807754509,915815098,67487393,50919027,37024629,27909326,110182592,488957974,638990412,402600836,733222421,197816803,242773264,143718428,500864354,708272213,737062848,560265652,89291186,560447299,593638793,264283761,599977003,891182050,303029818,532671776,569693534,491282655,329752920,889900429,955090791,435024844,957968631,194717159,121775514,607532329,109420941,244337977,612310250,671938621,166354474,789157313,53508748,183960940,454821693,840861390,346634569,486149277,656880179,664770350,623899811,679276758,411158479,927895683,692209939,127057269,40232406,384317493,755107439,514531706,430314053,328152489,879216417,985543100,890299692,295325802,793619821,849040255,918562249,574739602,509718453,766982383,763410039,54515607,727762181,475856011,753275006,632045624,282200106,920200063,309605675,759478325,521988794,93957573,64275002,338311264,326417806,711189860,757065159,834593543,442400637,983059502,627679507,674298360,488677043,788489609,222374861,111262956,176323748,507037334,729889457,30719976,160127759,175578096,480398779,299964187,210413382,206782832,714713085,935375939,826061196,239998878,14674770,998021279,291752105,593080919,933319544,336541518,317678915,135626962,893039426,362653062,506526066,296542749,47162576,31549761,668242852,767454332,740353835,175786066,830773658,401182175,924179574,202989059,667133288,188471932,224665133,218945799,787614550,67633533,867732128,131802423,897888372,188791464,365117719,265622435,433099386,469997021,194343570,997962966,967383480,96085127,436178330,945973959,117920930,330995204,220986754,851040047,831128432,67973490,35389897,350873338,27247914,979547667,487363320,735281918,299062720,69308670,819960937,341488557,637972507,392637257,561590858,377034712,653389678,7031957,553311944,846582108,435129360,228397086,897913664,283119663,327997212,333250239,72808925,450486861,362352706,890259581,707999338,692299846,862428826,101030829,18549253,36314162,412595273,249007599,303244921,543073439,586977593,866886864,46171500,465412914,453238517,40302332,995827618,7747316,588267653,323313973,312168455,912347107,492093104,335501659,126764754,987110566,90940702,717460631,111499184,111551285,514385598,236998546,112499046,879745967,64922719,935502582,920751254,546003727,462626245,896105548,547814065,681423461,352903116,610937895,788198148,219130125,438984782,480177305,374292988,489148244,839711234,399551921,375492432,684193331,205941319,804700200,706809705,212070233,12432814,556384664,153425005,311864697,584105281,273063701,179113738,763018459,863142631,248120268,632890827,621536969,740524550,435136522,283728665,675466302,416795738,380039647,630304766,94984825,527991135,508785241,231687142,222766502,578280226,177047673,61150820,180459193,797142070,292906722,270186359,211980238,150052477,905873905,968795548,704835477,257561555,943634294,966570375,823717233,687369178,227345439,675531091,563138351,792413109,644241497,743604441,276075809,455785370,432449697,854411557,473329671,565648573,373629320,135677279,132899909,99932800,917439035,101025071,346730477,912228597,540999009,957144559,209218119,475386621,103309107,966870703,618835116,559738897,19225595,493550889,825094025,977941349,61247506,253381439,674356905,569210217,288184764,273039591,868213402,991425622,612324762,94952214,631878225,963506121,761568456,65390895,183084590,767778805,974912473,881048631,462119315,407338097,964209797,589767895,218277756,292806320,205122038,54072496,250854118,270320331,622755650,209162451,91618433,167156350,847092451,751530189,828026690,353927945,724042652,718402817,884256540,159227640,714641671,418216539,899676084,238087605,69610456,173505204,200188627,493548919,710019767,405145424,777107695,771124645,900576822,848886024,359326179,949879501,685384036,730897024,270174981,458894291,758593053,860925383,905048481,244521373,352520207,194107600,730296271,898632004,778839544,550102824,480497142,527480477,360915764,28061909,668039952,587582460,289440243,635160339,523345363,4430814,69152518,183233477,125635832,159157508,372037980,480369926,743502563,449671777,703779722,755473699,892190711,892560765,801980455,289655071,381431778,754345762,233269083,313955543,874007247,982133606,647317720,63420981,264478843,175041949,695920505,366345780,387360056,384813380,233879407,876226860,42013049,80669925,839514022,267435013,96422750,144701921,679138825,839257285,332173017,645755628,276314363,878196595,98168884,23897573,876637680,965675953,135255350,375716254,939696619,825560244,161744316,570079040,403492623,481942468,67072866,432848773,214234812,376068194,658864568,162722591,452733898,399609339,535157345,889204280,510266393,831152456,802300820,870558443,918877260,671693071,465204202,921212125,493512336,722756218,218158695,578685951,983075894,497561392,553662167,785510453,253040808,309725980,318735307,52007753,405340280,244105093,422698584,296916991,418535223,628902966,991149309,969978045,450002502,373036476,372747252,49274384,247077831,225595867,329377763,688645051,345998757,156202419,467065940,74173706,945957595,448042904,830798477,661817267,754604295,705165062,888921770,19504355,484078419,923971814,224989020,901730616,638273892,639610823,199015468,543861710,10939252,573077008,186596094,815141880,634260074,113933007,17065481,169572607,730488849,560861444,102190810,318239774,752756539,234646761,979303563,39965629,670009713,421206412,220847114,720789909,394372397,809450016,715034437,554271632,687332196,522948402,777618878,346894019,437147991,325216527,536145643,314834298,582923864,550310019,905024972,680211612,557423082,521894919,879812298,976209137,539501713,789684752,802683554,213687176,967162610,161511112,169447521,327259781,655146848,363745571,852395183,228258996,958739133,189019557,359510235,862556216,483005217,231539750,676945330,116949719,395417300,316885051,395192297,592670701,610508794,242442600,571038157,333308361,213030640,443499695,475837122,494219720,836491004,229809578,548468130,642758100,938572692,722994520,417385900,609929192,282778638,497379261,743352032,477559759,550492549,689545084,759576777,921992179,583551780,721249249,696148930,106920758,427085844,587301421,28477168,824924559,212858432,531733749,60407643,474386780,413874861,940755315,502823177,840332027,201445712,606494224,25964441,678626651,813862638,771677862,710275054,678521536,947129298,292233544,811695809,277003728,342608441,62388640,718173768,669348312,317792820,78320291,139540398,698213945,899444457,176196315,86834909,934246154,580070721,627489025,609080033,690840696,411587256,315123676,564148931,364024921,979536696,941109799,660442016,908090870,268961675,540456205,202115980,891755259,447185208,175127778,36748514,341301176,213900212,301069325,852795621,120249756,77323390,923331717,355277731,459696507,295501566,499716930,116693997,875236333,757136461,897545734,975306291,635663807,26420205,863210697,599848782,607198493,50073741,28389291,646699796,591982926,200383749,873365108,746655406,865801455,549808315,357905975,245947560,27396384,487664605,245550619,13313226,238319745,834269172,218863351,459678457,68923352,4708232,718081982,540766091,770689814,888762535,790754054,653620128,938206163,18889041,759629710,695426234,372622616,774538191,493617228,887287203,18479979,208839949,528857590,899918656,842909050,906311619,175948672,585985504,610262479,246767488,604219414,737479680,184096063,125172635,604631686,249178756,484935518,65404451,535657252,551024946,756401619,602617367,34361876,358139089,637279800,132392257,278815583,235897676,84283608,403410265,312097164,459364106,38250844,74484166,230874636,768391610,10481614,256977047,676486123,468566099,24901802,702241822,665637257,907909145,599961785,714809231,596778550,51847005,352400114,155791213,539434338,854626507,554792568,718058106,361814829,473326885,554219109,987084535,433203418,844491010,908597350,101389303,153064915,962834731,483680900,689498370,932627079,265521107,635210193,800977648,699773801,562523503,59332097,568696865,756609252,858461962,655470409,528876138,79321940,571331213,437058605,885899904,537886657,258896532,915230539,645548212,677896443,108351150,373239689,206969284,967157064,569627742,794133346,881877308,962636596,648974367,483353415,659788280,973349943,813099037,781014631,717047776,181094707,482367333,48224991,330445186,252117294,879222970,372926084,438607637,326276889,211208738,867184235,733289120,242573402,276484652,93970560,443315691,54080748,263633573,31446328,324650772,34744864,749883257,162179778,747119543,676733121,711879438,861665152,559814038,835883524,961962739,432921688,502408208,210050763,438118445,590237938,838606038,21240580,531841258,575228096,17624483,671417778,708411648,54789855,31561960,542735386,821098804,330241367,995481744,104429484,887837039,299511425,549252455,40606311,165975198,461224965,71239698,64258801,767039177,433940071,382301349,810819793,115595260,513395407,408553401,125050602,526518289,154068323,353970756,553977942,34204353,584234100,285861301,515054903,211456362,338097216,854978058,888319744,994168625,416199582,252533505,642069540,905487192,137840351,108982888,12676422,549794498,541385864,734358880,443800275,755480427,681850849,811819883,946593277,881222058,47487641,960004486,57512637,633585111,530771023};
    
    ll N;cin>>N;
    ll okn=0;
    mint ans=0;
    for(ll i=1000000;;i+=1000000){
        if((i+1)*(i+1)-1<=N){
            okn=i;
            ans=ume[i/1000000-1];
        }else{
            break;
        }
    }
    
    vl S(62,1),T(62,1);
    
    for(ll n=okn+1;;n++){
        ll L=n*n,R=min((n+1)*(n+1)-1,N);
        if(L>R) break;
        
        S[2]=n;
        
        mint sum=0;
        
        while(1){
            pll mi=mp(INF,INF);
            for(ll k=3;k<=60;k++){
                if(T[k]<=R){
                    chmin(mi,mp(T[k]-1,k));
                }
            }
            //cout<<n<<" "<<mi.fi<<" "<<mi.se<<" "<<sum.val()<<endl;
            if(mi.fi==INF){
                mint X=1;
                for(ll k=3;k<=60;k++) X*=(S[k]-1);
                X*=(L+R);
                X*=(R-L+1);
                X*=r2;
                X*=n;
                sum+=X;
                break;
            }else{
                if(L<=mi.fi){
                    mint X=1;
                    for(ll k=3;k<=60;k++) X*=(S[k]-1);
                    X*=(L+mi.fi);
                    X*=(mi.fi-L+1);
                    X*=r2;
                    X*=n;
                    sum+=X;
                }
                
                chmax(L,mi.fi+1);
                //L=mi.fi+1;
                {
                    ll k=mi.se;
                    S[k]++;
                    T[k]=1;
                    for(ll t=0;t<k;t++){
                        T[k]*=S[k];
                        if(T[k]>1000000000000000000LL){
                            T[k]=INF;
                            break;
                        }
                    }
                }
            }
        }
        
        ans+=sum;
    }
    
    cout<<ans.val()<<endl;
    
}