/** * @FileName a.cpp * @Author kanpurin * @Created 2022.06.05 20:23:59 **/ #include "bits/stdc++.h" using namespace std; typedef long long ll; template< int MOD > struct mint { public: unsigned int x; mint() : x(0) {} mint(long long v) { long long w = (long long)(v % (long long)(MOD)); if (w < 0) w += MOD; x = (unsigned int)(w); } mint(std::string &s) { unsigned int z = 0; for (int i = 0; i < s.size(); i++) { z *= 10; z += s[i] - '0'; z %= MOD; } x = z; } mint operator+() const { return *this; } mint operator-() const { return mint() - *this; } mint& operator+=(const mint &a) { if ((x += a.x) >= MOD) x -= MOD; return *this; } mint& operator-=(const mint &a) { if ((x -= a.x) >= MOD) x += MOD; return *this; } mint& operator*=(const mint &a) { unsigned long long z = x; z *= a.x; x = (unsigned int)(z % MOD); return *this; } mint& operator/=(const mint &a) {return *this = *this * a.inv(); } friend mint operator+(const mint& lhs, const mint& rhs) { return mint(lhs) += rhs; } friend mint operator-(const mint& lhs, const mint& rhs) { return mint(lhs) -= rhs; } friend mint operator*(const mint& lhs, const mint& rhs) { return mint(lhs) *= rhs; } friend mint operator/(const mint& lhs, const mint& rhs) { return mint(lhs) /= rhs; } friend bool operator==(const mint& lhs, const mint& rhs) { return lhs.x == rhs.x; } friend bool operator!=(const mint& lhs, const mint& rhs) { return lhs.x != rhs.x; } friend std::ostream& operator<<(std::ostream &os, const mint &n) { return os << n.x; } friend std::istream &operator>>(std::istream &is, mint &n) { unsigned int x; is >> x; n = mint(x); return is; } mint inv() const { assert(x); return pow(MOD-2); } mint pow(long long n) const { assert(0 <= n); mint p = *this, r = 1; while (n) { if (n & 1) r *= p; p *= p; n >>= 1; } return r; } mint sqrt() const { if (this->x < 2) return *this; if (this->pow((MOD-1)>>1).x != 1) return mint(0); mint b = 1, one = 1; while (b.pow((MOD-1) >> 1) == 1) b += one; long long m = MOD-1, e = 0; while (m % 2 == 0) m >>= 1, e += 1; mint x = this->pow((m - 1) >> 1); mint y = (*this) * x * x; x *= (*this); mint z = b.pow(m); while (y.x != 1) { int j = 0; mint t = y; while (t != one) j += 1, t *= t; z = z.pow(1LL << (e-j-1)); x *= z; z *= z; y *= z; e = j; } return x; } }; constexpr int MOD = 998244353; vector> pow_sparse(vector> f, ll m) { assert(f.size() > 0 && f[0] != 0); vector> g(f.size()); vector fl; mint invf0 = f[0].inv(); vector inv(g.size(),1); g[0] = f[0].pow(m); for (int i = 2; i < g.size(); i++) inv[i] = MOD - (MOD / i) * inv[MOD%i] % MOD; for (int i = 0; i < f.size(); i++) { if (f[i] == 0) continue; fl.push_back(i); } for (int i = 1; i < g.size(); i++) { for (int j = 0; j < fl.size(); j++) { int p = fl[j]; if (1 <= p && p <= i) g[i] += f[p]*g[i-p]*p*m; if (1 <= p && p <= i-1) g[i] -= f[p]*g[i-p]*(i-p); } g[i] = g[i]*f[0]*inv[i]; } return g; } template struct Combination { private: int N; public: vector< T > FACT, IFACT; Combination(int n) : N(n) { FACT.resize(n + 1); IFACT.resize(n + 1); FACT[0] = 1; for (int i = 1; i <= n; i++) { FACT[i] = FACT[i - 1] * i; } IFACT[n] = T(1) / FACT[n]; for (int i = n-1; i >= 0; i--) { IFACT[i] = IFACT[i+1] * (i+1); } } T comb(int n, int r) { if (n < 0 || r < 0 || r > n) return 0; if (r > n / 2) r = n - r; return FACT[n] * IFACT[n - r] * IFACT[r]; } }; int main() { int n;cin >> n; vector> f(201); Combination> cb(2*n); f[0] = 1; f[8] = 1; f[9] = -1; f[97] = 1; f[98] = -1; f[200] = -1; f = pow_sparse(f,n); mint ans = 0; for (int i = 0; i <= n-1; i++) { ans += f[i]*cb.comb(2*n-i-2,n-1-i); } cout << ans << endl; return 0; }