#include <bits/stdc++.h> using namespace std; template<typename T1,typename T2> inline void chmin(T1 &a,T2 b){if(a>b) a=b;} template<typename T1,typename T2> inline void chmax(T1 &a,T2 b){if(a<b) a=b;} using Int = long long; const char newl = '\n'; template<typename T,T MOD = 1000000007> struct Mint{ static constexpr T mod = MOD; T v; Mint():v(0){} Mint(signed v):v(v){} Mint(long long t){v=t%MOD;if(v<0) v+=MOD;} Mint pow(long long k){ Mint res(1),tmp(v); while(k){ if(k&1) res*=tmp; tmp*=tmp; k>>=1; } return res; } static Mint add_identity(){return Mint(0);} static Mint mul_identity(){return Mint(1);} Mint inv(){return pow(MOD-2);} Mint& operator+=(Mint a){v+=a.v;if(v>=MOD)v-=MOD;return *this;} Mint& operator-=(Mint a){v+=MOD-a.v;if(v>=MOD)v-=MOD;return *this;} Mint& operator*=(Mint a){v=1LL*v*a.v%MOD;return *this;} Mint& operator/=(Mint a){return (*this)*=a.inv();} Mint operator+(Mint a) const{return Mint(v)+=a;} Mint operator-(Mint a) const{return Mint(v)-=a;} Mint operator*(Mint a) const{return Mint(v)*=a;} Mint operator/(Mint a) const{return Mint(v)/=a;} Mint operator-() const{return v?Mint(MOD-v):Mint(v);} bool operator==(const Mint a)const{return v==a.v;} bool operator!=(const Mint a)const{return v!=a.v;} bool operator <(const Mint a)const{return v <a.v;} static Mint comb(long long n,int k){ Mint num(1),dom(1); for(int i=0;i<k;i++){ num*=Mint(n-i); dom*=Mint(i+1); } return num/dom; } }; template<typename T,T MOD> constexpr T Mint<T, MOD>::mod; template<typename T,T MOD> ostream& operator<<(ostream &os,Mint<T, MOD> m){os<<m.v;return os;} //INSERT ABOVE HERE const int MAX = 1e6 + 10; vector<int> dp[MAX]; using ll = long long; ll naive(ll n){ ll ans=0; for(ll p1=-n;p1<=n;p1++){ for(ll p2=-n;p2<=n;p2++){ for(ll q1=-n;q1<=n;q1++){ for(ll q2=-n;q2<=n;q2++){ if(p1*p1+p2*p2>n) continue; if(q1*q1+q2*q2>n) continue; if(p1*q2-p2*q1!=1) continue; ans+=abs(p1)+abs(p2)+abs(q1)+abs(q2); } } } } return ans; } signed main(){ cin.tie(0); ios::sync_with_stdio(0); using ll = long long; ll n; cin>>n; // cout<<naive(n)<<endl; for(ll i=2;i<MAX;i++){ if(!dp[i].empty()) continue; for(ll j=i;j<MAX;j+=i) dp[j].emplace_back(i); } using M = Mint<int, 998244353>; M ans{0}; for(ll i=1;i*i<=n;i++){ ll j=sqrtl(n-i*i); while(i*i+(j+1)*(j+1)<=n) j++; while(i*i+j*j>n) j--; ll m=dp[i].size(); ll s=1<<m; ll cnt=0; for(ll b=0;b<s;b++){ ll prod=1; for(ll k=0;k<m;k++) if((b>>k)&1) prod*=dp[i][k]; if(__builtin_parity(b)) cnt-=j/prod; else cnt+=j/prod; } ans+=M(i*4)*M(6)*M(cnt); } ans*=M(2); ans+=M(8); cout<<ans<<newl; return 0; }