#include #include #include using namespace std; std::vector> mul(const std::vector> &v1, const std::vector> &v2, long long mod = 1001001001001001001) { std::vector> ans; if (v1[0].size() != v2.size()) { std::cout << "matrix mul size error: (" << v1[0].size() << ", " << v2.size() << ")" << std::endl; std::exit(1); } ans.resize(v1.size(), std::vector (v2[0].size())); for (int i = 0; i < v1.size(); ++i) for (int j = 0; j < v2[0].size(); ++j) for (int k = 0; k < v1[0].size(); ++k) ans[i][j] = (ans[i][j] + v1[i][k] * v2[k][j]) % mod; return ans; } std::vector> pow(std::vector> v, long long k, long long mod = 1001001001001001001) { std::vector> ans; if (v.size() != v[0].size()) { std::cout << "matrix pow size error: (" << v.size() << ", " << v[0].size() << ")" << std::endl; std::exit(1); } ans.resize(v.size(), std::vector (v.size())); for (int i = 0; i < v.size(); ++i) ans[i][i] = 1; for (; k > 0; k >>= 1, v = mul(v, v, mod)) if (k & 1) ans = mul(v, ans, mod); return ans; } int main() { const int mod = 998244353; long long n; cin >> n; auto cal = [&](long long x, long long k) -> long long { vector> mat(2, vector (2)); mat[0][0] = x; mat[1][0] = mat[1][1] = 1; auto res = pow(mat, k + 1, mod); return res[1][0]; }; long long x = 1, v = n, ans = 0; while (x <= n) { long long nx = n / v + 1; ans = (ans + (cal(v, nx - 1) - cal(v, x - 1) + mod)) % mod; x = nx; v = n / x; } cout << ans << endl; }