#include #include #include using namespace std; typedef long long ll; ll mod = 998244353; vectoryk[1010101]; bool isco[1010101]; int main() { for (int i = 2; i <= 1000000; i++) { if (isco[i])continue; yk[i].push_back(i); for (int j = i + i; j <= 1000000; j += i)isco[j] = true, yk[j].push_back(i); } ll num; scanf("%lld", &num); ll ans = 0; for (ll a = 1;; a++) { if (a*a > num)break; ll beg = 0, end = 1000000; for (;;) { if (beg == end)break; ll med = (beg + end + 1) / 2; if (a*a + med*med > num)end = med - 1; else beg = med; } ll b = beg; ll s1 = 0, s2 = 0; int t = yk[a].size(); for (int p = 0; p < (1 << t); p++) { bool f = false; ll x = 1; for (int i = 0; i < t; i++)if (p&(1 << i))x *= yk[a][i], f = !f; ll z1 = b / x, z2 = z1*(z1 + 1) / 2 * x; if (!f)s1 = (s1 + z1) % mod, s2 = (s2 + z2) % mod; else s1 = (s1 + mod - z1) % mod, s2 = (s2 + mod - z2%mod) % mod; } //printf("%lld %lld %lld %lld %lld %d\n", a, b, s1, s2, s1*a + s2, t); ans = (ans + s1*a + s2) % mod; } printf("%lld\n", (ans * 24 + 8) % mod); }