#include #include using namespace std; using namespace atcoder; istream &operator>>(istream &is, modint &a) { long long v; is >> v; a = v; return is; } ostream &operator<<(ostream &os, const modint &a) { return os << a.val(); } istream &operator>>(istream &is, modint998244353 &a) { long long v; is >> v; a = v; return is; } ostream &operator<<(ostream &os, const modint998244353 &a) { return os << a.val(); } istream &operator>>(istream &is, modint1000000007 &a) { long long v; is >> v; a = v; return is; } ostream &operator<<(ostream &os, const modint1000000007 &a) { return os << a.val(); } typedef long long ll; typedef vector> Graph; typedef pair pii; typedef pair pll; #define FOR(i,l,r) for (int i = l;i < (int)(r); i++) #define rep(i,n) for (int i = 0;i < (int)(n); i++) #define all(x) x.begin(), x.end() #define rall(x) x.rbegin(), x.rend() #define my_sort(x) sort(x.begin(), x.end()) #define my_max(x) *max_element(all(x)) #define my_min(x) *min_element(all(x)) template inline bool chmax(T& a, T b) { if (a < b) { a = b; return 1; } return 0; } template inline bool chmin(T& a, T b) { if (a > b) { a = b; return 1; } return 0; } const int INF = (1<<30) - 1; const ll LINF = (1LL<<62) - 1; const int MOD = 998244353; const int MOD2 = 1e9+7; const double PI = acos(-1); vector di = {1,0,-1,0}; vector dj = {0,1,0,-1}; #ifdef LOCAL # include # define debug(...) debug_print::multi_print(#__VA_ARGS__, __VA_ARGS__) #else # define debug(...) (static_cast(0)) #endif using mint = modint998244353; int main(){ cin.tie(0); ios_base::sync_with_stdio(false); int N; cin >> N; if(N == 1){ cout << mint(3) / mint(5) << endl; return 0; } vector dp(5, vector(5)); vector p(5, vector(5)); rep(k, 5){ int deno = min(4, k + 1) - max(0, k - 1) + 1; for(int j = max(0, k - 1); j <= min(4, k + 1); j++){ p[j][k] = 1 / (mint)(deno * 5); dp[j][k] = ((1 <= j && j <= 3) + (1 <= k && k <= 3)) / (mint)(deno * 5); } } mint inv2 = mint(1) / mint(2); mint inv3 = mint(1) / mint(3); vector ndp(5, vector(5)); vector np(5, vector(5)); mint e, prob, coef; FOR(i, 1, N - 1){ rep(j, 5)rep(k, 5){ ndp[j][k] = 0; np[j][k] = 0; } rep(j, 5)rep(k, 5){ e = dp[j][k]; prob = p[j][k]; coef = (j == 0 || j == 4 ? inv2 : inv3); if(prob == 0) continue; for(int l = max(0, j - 1); l <= min(4, j + 1); l++){ if(1 <= l && l <= 3){ ndp[l][j] += (e + prob) * coef; } else{ ndp[l][j] += e * coef; } np[l][j] += prob * coef; } } swap(ndp, dp); swap(np, p); } mint ans = 0; rep(j, 5)rep(k, 5) ans += dp[j][k]; cout << ans << endl; }