#include <bits/stdc++.h>
using namespace std;

constexpr int64_t MOD=998244353;

int64_t F(int64_t N) {
  int64_t ret=0;
  for (int64_t x=1;x*x<=N;++x) {
    int64_t ma=sqrt(N-x*x);
    ret=(ret+((ma+1)*x%MOD+ma*(ma+1)/2%MOD)%MOD)%MOD;
  }
  ret=ret*4%MOD;
  return ret;
}

int64_t f(int64_t N) {
  int64_t ret=0;
  int64_t sqrtn=(int)sqrt(N);
  while ((sqrtn+1)*(sqrtn+1)<=N) ++sqrtn;
  vector<int64_t> mu(sqrtn+1,1);
  vector<bool> prime(sqrtn+1,true);
  prime[0]=prime[1]=false;
  for (int i=2;i<=sqrtn;++i) {
    if (!prime[i]) continue;
    for (int j=2*i;j<=sqrtn;j+=i) {
      prime[j]=false;
    }
  }
  for (int64_t i=2;i<=sqrtn;++i) {
    if (!prime[i]) continue;
    for (int64_t j=i*i;j<=sqrtn;j+=i*i) mu[j]=0;
    for (int j=i;j<=sqrtn;j+=i) mu[j]=mu[j]*(MOD-1)%MOD;
  }
  for (int d=1;d<=sqrtn;++d) {
    ret+=d*mu[d]%MOD*F(N/d/d)%MOD;
    ret%=MOD;
  }
  return ret;
}

int64_t solve(int64_t N) {
  return (6*f(N)%MOD+MOD-16)%MOD;
}

int main() {
  int64_t N;
  scanf("%ld",&N);
  printf("%ld\n",solve(N));
}