#define ATCODER #define _USE_MATH_DEFINES #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include using namespace std; using ll = long long; using ld = long double; using pll = pair; using pdd = pair; //template using pq = priority_queue, greater>; #define FOR(i, a, b) for(ll i=(a); i<(b);i++) #define REP(i, n) for(ll i=0; i<(n);i++) #define ROF(i, a, b) for(ll i=(b-1); i>=(a);i--) #define PER(i, n) for(ll i=n-1; i>=0;i--) #define REPREP(i,j,a,b) for(ll i=0;i > #define VV2(type,n,m,val) vector< vector > val;val.resize(n);for(ll i;i #define VEC(type,n,val) vector val;val.resize(n) #define VL vector #define VVL vector< vector > #define VP vector< pair > #define SZ size() #define all(i) begin(i),end(i) #define SORT(i) sort(all(i)) #define BITI(i) (1<>i) & 1) != 0) #define ALLBIT(n) (ll(1)<v?v:n #define MP(a,b) make_pair(a,b) #define DET2(x1,y1,x2,y2) (x1)*(y2)-(x2)*(y1) #define DET3(x1,y1,z1,x2,y2,z2,x3,y3,z3) (x1)*(y2)*(z3)+(x2)*(y3)*(z1)+(x3)*(y1)*(z2)-(z1)*(y2)*(x3)-(z2)*(y3)*(x1)-(z3)*(y1)*(x2) #define INC(a) for(auto& v:a)v++; #define DEC(a) for(auto& v:a)v--; #define SQU(x) (x)*(x) #define L0 ll(0) #ifdef ATCODER #include using namespace atcoder; using mint = modint1000000007; using mint2 = modint998244353; #endif template vector read(size_t n) { vector ts(n); for (size_t i = 0; i < n; i++) cin >> ts[i]; return ts; } template void read_tuple_impl(TV&) {} template void read_tuple_impl(TV& ts) { get(ts).emplace_back(*(istream_iterator(cin))); read_tuple_impl(ts); } template decltype(auto) read_tuple(size_t n) { tuple...> ts; for (size_t i = 0; i < n; i++) read_tuple_impl(ts); return ts; } using val = ll; using func = pair; val opm(val a, val b) { return min(a, b); } val em() { return 1e18; } val opM(val a, val b) { return max(a, b); } val eM() { return 0; } //val mp(func f, val a) //{ // if (f.first < 0) // return a; // return f; //} //func comp(func f, func g) { // if (g.first < 0) // return f; // return g; //} // //func id() { // return MP(-1, -1); //} ll di[4] = { 1,0,-1,0 }; ll dj[4] = { 0,1,0,-1 }; ll si[4] = { 0,3,3,0 }; ll sj[4] = { 0,0,3,3 }; //ll di[4] = { -1,-1,1,1 }; //ll dj[4] = { -1,1,-1,1 }; ll di8[8] = { 0,-1,-1,-1,0,1,1,1 }; ll dj8[8] = { -1,-1,0,1,1,1,0,-1 }; void solve() { ll n; cin >> n; mint2 inv2 = mint2(2).inv(); mint2 inv3 = mint2(3).inv(); mint2 inv5 = mint2(5).inv(); //double inv2 = 1.0 / 2; //double inv3 = 1.0 / 3; //double inv5 = 1.0 / 5; //vector tdp(n, vector(n + 1, vector(5))); //tdp[0][0][0] = mint2(5).inv(); //tdp[0][1][1] = mint2(5).inv(); //tdp[0][1][2] = mint2(5).inv(); //tdp[0][1][3] = mint2(5).inv(); //tdp[0][0][4] = mint2(5).inv(); //REP(i, n - 1) { // REP(j, n) { // REP(k, 5) { // REP(k2, 5) { // if (abs(k - k2) > 1) // continue; // ll nj = k2 == 0 || k2 == 4 ? j : j + 1; // mint2 in = k == 0 || k == 4 ? inv2 : inv3; // tdp[i + 1][nj][k2] += tdp[i][j][k] * in; // } // } // } //} //mint2 tans = 0; //REP(i, n + 1) { // REP(j, 5) { // tans += tdp[n - 1][i][j] * i; // } //} //cout << tans.val(); //return; vector dp(n, vector(5)); auto dp2 = dp; dp[0][1] = inv5; dp[0][2] = inv5; dp[0][3] = inv5; REP(i, 5) dp2[0][i] = inv5; REP(i, n - 1) { REP(j, 5) { REP(k, 3) { ll j2 = j + k - 1; if (j2 < 0 || j2 >= 5) continue; auto mul = j == 0 || j == 4 ? inv2 : inv3; dp[i + 1][j2] += dp[i][j] * mul; dp2[i + 1][j2] += dp2[i][j] * mul; } } FOR(j, 1, 4) { dp[i + 1][j] += dp2[i + 1][j]; } } mint2 sum = 0, sum2 = 0;; REP(i, 5) { sum += dp[n - 1][i]; sum2 += dp2[n - 1][i]; } cout << sum.val(); return; } int main() { ll t = 1; //cin >> t; while (t--) { solve(); } return 0; }