#include <bits/stdc++.h>
#define fi first
#define se second
#define rep(i,n) for(int i = 0; i < (n); ++i)
#define rrep(i,n) for(int i = 1; i <= (n); ++i)
#define drep(i,n) for(int i = (n)-1; i >= 0; --i)
#define srep(i,s,t) for (int i = s; i < t; ++i)
#define rng(a) a.begin(),a.end()
#define rrng(a) a.rbegin(),a.rend()
#define maxs(x,y) (x = max(x,y))
#define mins(x,y) (x = min(x,y))
#define limit(x,l,r) max(l,min(x,r))
#define lims(x,l,r) (x = max(l,min(x,r)))
#define isin(x,l,r) ((l) <= (x) && (x) < (r))
#define pb push_back
#define eb emplace_back
#define sz(x) (int)(x).size()
#define pcnt __builtin_popcountll
#define uni(x) x.erase(unique(rng(x)),x.end())
#define snuke srand((unsigned)clock()+(unsigned)time(NULL));
#define show(x) cout<<#x<<" = "<<x<<endl;
#define PQ(T) priority_queue<T,v(T),greater<T> >
#define bn(x) ((1<<x)-1)
#define dup(x,y) (((x)+(y)-1)/(y))
#define newline puts("")
#define v(T) vector<T>
#define vv(T) v(v(T))
using namespace std;
typedef long long int ll;
typedef unsigned uint;
typedef unsigned long long ull;
typedef pair<int,int> P;
typedef tuple<int,int,int> T;
typedef vector<int> vi;
typedef vector<vi> vvi;
typedef vector<ll> vl;
typedef vector<P> vp;
typedef vector<T> vt;
inline int getInt() { int x; scanf("%d",&x); return x;}
template<typename T>inline istream& operator>>(istream&i,v(T)&v)
{rep(j,sz(v))i>>v[j];return i;}
template<typename T>string join(const v(T)&v)
{stringstream s;rep(i,sz(v))s<<' '<<v[i];return s.str().substr(1);}
template<typename T>inline ostream& operator<<(ostream&o,const v(T)&v)
{if(sz(v))o<<join(v);return o;}
template<typename T1,typename T2>inline istream& operator>>(istream&i,pair<T1,T2>&v)
{return i>>v.fi>>v.se;}
template<typename T1,typename T2>inline ostream& operator<<(ostream&o,const pair<T1,T2>&v)
{return o<<v.fi<<","<<v.se;}
template<typename T>inline ll suma(const v(T)& a) { ll res(0); for (auto&& x : a) res += x; return res;}
const double eps = 1e-10;
const ll LINF = 1001002003004005006ll;
const int INF = 1001001001;
#define dame { puts("-1"); return 0;}
#define yn {puts("Yes");}else{puts("No");}
const int MX = 1000005;

// linear sieve
vi ps, pf;
void sieve(int mx) {
  pf = vi(mx+1);
  rep(i,mx+1) pf[i] = i;
  for (int i = 2; i <= mx; ++i) {
    if (pf[i] == i) ps.pb(i);
    for (int j = 0; j < sz(ps) && ps[j] <= pf[i]; ++j) {
      int x = ps[j]*i;
      if (x > mx) break;
      pf[x] = ps[j];
    }
  }
}
inline bool isp(int x) { return pf[x] == x && x >= 2;}
vp factor(int x) { // asc
  if (x == 1) return {};
  vp res(1, P(pf[x], 0));
  while (x != 1) {
    if (res.back().fi == pf[x]) res.back().se++;
    else res.pb(P(pf[x],1));
    x /= pf[x];
  }
  return res;
}
//

vi meb;
void mebinit(int n) {
  sieve(n+1);
  meb = vi(n+1,1);
  meb[0] = 0;
  for (int p : ps) {
    for (int i = p; i <= n; i += p) meb[i] = -meb[i];
    ll p2 = (ll)p*p;
    for (ll i = p2; i <= n; i += p2) meb[i] = 0;
  }
}


// Mod int
const int mod = 998244353;
struct mint {
  ll x;
  mint():x(0){}
  mint(ll x):x((x%mod+mod)%mod){}
  // mint(ll x):x(x){}
  mint& fix() { x = (x%mod+mod)%mod; return *this;}
  mint operator-() const { return mint(0) - *this;}
  mint& operator+=(const mint& a){ if((x+=a.x)>=mod) x-=mod; return *this;}
  mint& operator-=(const mint& a){ if((x+=mod-a.x)>=mod) x-=mod; return *this;}
  mint& operator*=(const mint& a){ (x*=a.x)%=mod; return *this;}
  mint operator+(const mint& a)const{ return mint(*this) += a;}
  mint operator-(const mint& a)const{ return mint(*this) -= a;}
  mint operator*(const mint& a)const{ return mint(*this) *= a;}
  bool operator<(const mint& a)const{ return x < a.x;}
  bool operator==(const mint& a)const{ return x == a.x;}
};
istream& operator>>(istream&i,mint&a){i>>a.x;return i;}
ostream& operator<<(ostream&o,const mint&a){o<<a.x;return o;}
typedef vector<mint> vm;
//

mint f(ll n) {
  if (n == 0) return 0;
  mint res;
  ll j = 1;
  for (; j*j <= n; ++j);
  for (ll i = 1; i*i <= n; ++i) {
    while (i*i + j*j > n) --j;
    mint now = i*j;
    now += j*(j+1)/2;
    res += now*4*6;
  }
  return res;
}

int main() {
  ll n;
  cin>>n;
  mebinit(MX);
  mint ans = 0;
  rrep(i,MX) {
    if (meb[i] == 0) continue;
    mint now = f(n/i/i);
    now *= i;
    ans += now*meb[i];
  }
  ans += 8;
  cout<<ans<<endl;
  return 0;
}