#include #include #include #include #include #include #include #include #include static const int MOD = 998244353; using ll = long long; using u32 = unsigned; using u64 = unsigned long long; using namespace std; template constexpr T INF = ::numeric_limits::max() / 32 * 15 + 208; template struct modint { u32 val; public: static modint raw(int v) { modint x; x.val = v; return x; } modint() : val(0) {} template modint(T v) { ll x = (ll)(v%(ll)(M)); if (x < 0) x += M; val = u32(x); } modint(bool v) { val = ((unsigned int)(v) % M); } modint& operator++() { val++; if (val == M) val = 0; return *this; } modint& operator--() { if (val == 0) val = M; val--; return *this; } modint operator++(int) { modint result = *this; ++*this; return result; } modint operator--(int) { modint result = *this; --*this; return result; } modint& operator+=(const modint& b) { val += b.val; if (val >= M) val -= M; return *this; } modint& operator-=(const modint& b) { val -= b.val; if (val >= M) val += M; return *this; } modint& operator*=(const modint& b) { u64 z = val; z *= b.val; val = (u32)(z % M); return *this; } modint& operator/=(const modint& b) { return *this = *this * b.inv(); } modint operator+() const { return *this; } modint operator-() const { return modint() - *this; } modint pow(long long n) const { modint x = *this, r = 1; while (n) { if (n & 1) r *= x; x *= x; n >>= 1; } return r; } modint inv() const { return pow(M-2); } friend modint operator+(const modint& a, const modint& b) { return modint(a) += b; } friend modint operator-(const modint& a, const modint& b) { return modint(a) -= b; } friend modint operator*(const modint& a, const modint& b) { return modint(a) *= b; } friend modint operator/(const modint& a, const modint& b) { return modint(a) /= b; } friend bool operator==(const modint& a, const modint& b) { return a.val == b.val; } friend bool operator!=(const modint& a, const modint& b) { return a.val != b.val; } }; using mint = modint; class Factorial { vector facts, factinv; public: explicit Factorial(int n) : facts(n+1), factinv(n+1) { facts[0] = 1; for (int i = 1; i < n+1; ++i) facts[i] = facts[i-1] * mint(i); factinv[n] = facts[n].inv(); for (int i = n-1; i >= 0; --i) factinv[i] = factinv[i+1] * mint(i+1); } mint fact(int k) const { if(k >= 0) return facts[k]; else return factinv[-k]; } mint operator[](const int &k) const { if(k >= 0) return facts[k]; else return factinv[-k]; } mint C(int p, int q) const { if(q < 0 || p < q) return 0; return facts[p] * factinv[q] * factinv[p-q]; } mint P(int p, int q) const { if(q < 0 || p < q) return 0; return facts[p] * factinv[p-q]; } mint H(int p, int q) const { if(p < 0 || q < 0) return 0; return q == 0 ? 1 : C(p+q-1, q); } }; int main() { int n; cin >> n; Factorial f(n); mint ans = 0, val = mint(n).pow(n-2).inv()*f[n-2]; for (int i = 0; i <= n-2; ++i) { ans += f.C(n, n-2-i)*val*f[-i]; val *= n; } cout << ans.val << "\n"; return 0; }