//#pragma GCC optimize("Ofast")
//#pragma GCC target("avx")
//#undef LOCAL




#include <algorithm>

#include <array>

#include <bitset>

#include <cassert>

#include <complex>

#include <cstdio>

#include <cstring>

#include <iostream>

#include <map>

#include <numeric>

#include <queue>

#include <set>

#include <string>

#include <unordered_map>

#include <unordered_set>

#include <vector>

using namespace std;

using uint = unsigned int;
using ll = long long;
using ull = unsigned long long;
constexpr ll TEN(int n) { return (n == 0) ? 1 : 10 * TEN(n - 1); }
template <class T> using V = vector<T>;
template <class T> using VV = V<V<T>>;

struct Scanner {
    FILE* fp = nullptr;
    char line[(1 << 15) + 1];
    size_t st = 0, ed = 0;
    void reread() {
        memmove(line, line + st, ed - st);
        ed -= st;
        st = 0;
        ed += fread(line + ed, 1, (1 << 15) - ed, fp);
        line[ed] = '\0';
    }
    bool succ() {
        while (true) {
            if (st == ed) {
                reread();
                if (st == ed) return false;
            }
            while (st != ed && isspace(line[st])) st++;
            if (st != ed) break;
        }
        if (ed - st <= 50) reread();
        return true;
    }
    template <class T, enable_if_t<is_same<T, string>::value, int> = 0>
    bool read_single(T& ref) {
        if (!succ()) return false;
        while (true) {
            size_t sz = 0;
            while (st + sz < ed && !isspace(line[st + sz])) sz++;
            ref.append(line + st, sz);
            st += sz;
            if (!sz || st != ed) break;
            reread();
        }
        return true;
    }
    template <class T, enable_if_t<is_integral<T>::value, int> = 0>
    bool read_single(T& ref) {
        if (!succ()) return false;
        bool neg = false;
        if (line[st] == '-') {
            neg = true;
            st++;
        }
        ref = T(0);
        while (isdigit(line[st])) {
            ref = 10 * ref + (line[st++] - '0');
        }
        if (neg) ref = -ref;
        return true;
    }
    template <class T> bool read_single(V<T>& ref) {
        for (auto& d : ref) {
            if (!read_single(d)) return false;
        }
        return true;
    }
    void read() {}
    template <class H, class... T> void read(H& h, T&... t) {
        bool f = read_single(h);
        assert(f);
        read(t...);
    }
    Scanner(FILE* _fp) : fp(_fp) {}
};

struct Printer {
  public:
    template <bool F = false> void write() {}
    template <bool F = false, class H, class... T>
    void write(const H& h, const T&... t) {
        if (F) write_single(' ');
        write_single(h);
        write<true>(t...);
    }
    template <class... T> void writeln(const T&... t) {
        write(t...);
        write_single('\n');
    }

    Printer(FILE* _fp) : fp(_fp) {}
    ~Printer() { flush(); }

  private:
    static constexpr size_t SIZE = 1 << 15;
    FILE* fp;
    char line[SIZE], small[50];
    size_t pos = 0;
    void flush() {
        fwrite(line, 1, pos, fp);
        pos = 0;
    }
    void write_single(const char& val) {
        if (pos == SIZE) flush();
        line[pos++] = val;
    }
    template <class T, enable_if_t<is_integral<T>::value, int> = 0>
    void write_single(T val) {
        if (pos > (1 << 15) - 50) flush();
        if (val == 0) {
            write_single('0');
            return;
        }
        if (val < 0) {
            write_single('-');
            val = -val; // todo min
        }
        size_t len = 0;
        while (val) {
            small[len++] = char('0' + (val % 10));
            val /= 10;
        }
        for (size_t i = 0; i < len; i++) {
            line[pos + i] = small[len - 1 - i];
        }
        pos += len;
    }
    void write_single(const string& s) {
        for (char c : s) write_single(c);
    }
    void write_single(const char* s) {
        size_t len = strlen(s);
        for (size_t i = 0; i < len; i++) write_single(s[i]);
    }
    template <class T> void write_single(const V<T>& val) {
        auto n = val.size();
        for (size_t i = 0; i < n; i++) {
            if (i) write_single(' ');
            write_single(val[i]);
        }
    }
};

Scanner sc = Scanner(stdin);
Printer pr = Printer(stdout);

ll gcd(ll a, ll b) {
    if (b == 0) return a;
    return gcd(b, a % b);
}

const int MX = TEN(6) + 100;
VV<ll> prs(MX);
void init() {
    V<ll> used(MX, false);
    for (ll i = 2; i < MX; i++) {
        if (used[i]) continue;
        for (ll j = i; j < MX; j += i) {
            prs[j].push_back(i);
            used[j] = true;
        }
    }
}

const ll MOD = 998244353;
int main() {
    init();
    ll n;
    sc.read(n);
/*    using P = pair<ll, ll>;
    const ll B = ll(sqrt(n) + 10);
    V<P> pots;
    for (ll p1 = -B; p1 <= B; p1++) {
        for (ll p2 = -B; p2 <= B; p2++) {
            if (p1 * p1 + p2 * p2 <= n) {
                pots.push_back({p1, p2});
            }
        }
    }
    VV<ll> mp(2 * B + 1, V<ll>(2 * B + 1));
    for (auto p: pots) {
        for (auto q: pots) {
            if (p.first * q.second - p.second * q.first == 1) {
                mp[B+p.first][B+p.second]++;
                mp[B+q.first][B+q.second]++;
            }
        }
    }
    ll sum = 0;
    for (ll p1 = -B; p1 <= B; p1++) {
        for (ll p2 = -B; p2 <= B; p2++) {
            ll u = mp[B+p1][B+p2];
            if (u) printf("%3lld ", u);
            else if (p1 == 0 && p2 == 0) printf("  + ");
            else printf("    ");
            sum += u * (abs(p1) + abs(p2));
        }
        cout << endl;
    }
    cout << sum << endl;
    ll sum2 = 8;
    for (ll p1 = 1; p1 <= B; p1++) {
        for (ll p2 = 1; p2 <= B; p2++) {
            if (p1 * p1 + p2 * p2 <= n) {
                if (gcd(p1, p2) == 1) {
                    sum2 += (p1 + p2) * 24;                    
                }
            }
        }
    }
    cout << sum2 << endl;*/

    ll ans = 8;
    for (ll p1 = 1; p1 * p1 <= n; p1++) {
        // p1 * p1 + p2 * p2 <= n
        // p2 * p2 <= n - p1 * p1
        ll up2 = ll(sqrt(n - p1 * p1) + 10);
        while (p1 * p1 + up2 * up2 > n) up2--;
/*        ll naive_cnt = 0;
        for (ll p2 = 1; p2 <= up2; p2++) {
            if (gcd(p1, p2) == 1) {
                naive_cnt++;
            }
        }*/
        ll cnt = 0;
        // gcd(p1, p2) == 1, 1 <= p2 <= up2
        int m = int(prs[p1].size());
        for (int f = 0; f < (1 << m); f++) {
            ll z = 1;
            int freq = 1;
            for (int i = 0; i < m; i++) {
                if (f & (1 << i)) {
                    z *= prs[p1][i];
                    freq *= -1;
                }
            }
            cnt += freq * (up2 / z) % MOD;
        }
//        assert(cnt == naive_cnt);
        ans += (48 * p1 * cnt) % MOD;
        ans = (ans + MOD) % MOD;
    }
    pr.writeln(ans);
    return 0;
}