#pragma GCC target("avx2") #pragma GCC optimize("O3") #pragma GCC optimize("unroll-loops") #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include using namespace std; using namespace atcoder; typedef long long ll; #define rep(i, n) for (int i = 0; i < (int)(n); i++) #define repr(i, n) for (int i = (int)(n) - 1; i >= 0; i--) #define repk(i, k, n) for (int i = k; i < (int)(n); i++) #define all(v) v.begin(), v.end() #define mod1 1000000007 #define mod2 998244353 #define mod3 100000007 #define vi vector #define vs vector #define vc vector #define vl vector #define vb vector #define vvi vector> #define vvc vector> #define vvl vector> #define vvb vector> #define vvvi vector>> #define vvvl vector>> #define pii pair #define pil pair #define pli pair #define pll pair #define vpii vector> #define vpll vector> #define vvpii vector>> #define vvpll vector>> // using mint = modint998244353; template void debug(T e) { cerr << e << endl; } template void debug(vector &v) { rep(i, v.size()) { cerr << v[i] << " "; } cerr << endl; } template void debug(vector> &v) { rep(i, v.size()) { rep(j, v[i].size()) { cerr << v[i][j] << " "; } cerr << endl; } } template void debug(vector> &v) { rep(i, v.size()) { cerr << v[i].first << " " << v[i].second << endl; } } template void debug(set &st) { for (auto itr = st.begin(); itr != st.end(); itr++) { cerr << *itr << " "; } cerr << endl; } template void debug(multiset &ms) { for (auto itr = ms.begin(); itr != ms.end(); itr++) { cerr << *itr << " "; } cerr << endl; } template void debug(map &mp) { for (auto itr = mp.begin(); itr != mp.end(); itr++) { cerr << itr->first << " " << itr->second << endl; } } void debug_out() { cerr << endl; } template void debug_out(Head H, Tail... T) { cerr << H << " "; debug_out(T...); } int main() { ll N; cin >> N; ll inv_2 = (mod2 + 1) / 2; ll inv_3 = (mod2 + 1) / 3; ll inv_5 = (mod2 * 3LL + 1) / 5; vector> dp(N, vector(5)); vector> dpr(N, vector(5)); dp[0][0] = 0; dp[0][1] = inv_5; dp[0][2] = inv_5; dp[0][3] = inv_5; dp[0][4] = 0; for (ll i = 0; i < 5; i++) { dpr[0][i] = inv_5; } for (ll i = 0; i < N - 1; i++) { for (ll j = 0; j < 5; j++) { for (ll k = 0; k < 5; k++) { if (abs(j - k) > 1) { continue; } if (j >= 1 && j <= 3) { if (k >= 1 && k <= 3) { dp[i + 1][k] += ((dp[i][j] + dpr[i][j]) * inv_3) % mod2; dp[i + 1][k] %= mod2; } else { dp[i + 1][k] += (dp[i][j] * inv_3) % mod2; dp[i + 1][k] %= mod2; } dpr[i + 1][k] += (dpr[i][j] * inv_3) % mod2; dpr[i + 1][k] %= mod2; } else { if (k >= 1 && k <= 3) { dp[i + 1][k] += ((dp[i][j] + dpr[i][j]) * inv_2) % mod2; dp[i + 1][k] %= mod2; } else { dp[i + 1][k] += (dp[i][j] * inv_2) % mod2; dp[i + 1][k] %= mod2; } dpr[i + 1][k] += (dpr[i][j] * inv_2) % mod2; dpr[i + 1][k] %= mod2; } dp[i + 1][k] %= mod2; } } } ll ans = 0; for (ll j = 0; j < 5; j++) { ans = (ans + dp[N - 1][j]) % mod2; } cout << ans << endl; }