#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 #include #include #include using namespace std; //#define int long long typedef long long ll; typedef unsigned long long ul; typedef unsigned int ui; //constexpr ll mod = 998244353; constexpr ll mod = 1000000007; const ll INF = mod * mod; typedef pairP; #define rep(i,n) for(int i=0;i=0;i--) #define Rep(i,sta,n) for(int i=sta;i=1;i--) #define Rep1(i,sta,n) for(int i=sta;i<=n;i++) #define all(v) (v).begin(),(v).end() typedef pair LP; template void chmin(T& a, T b) { a = min(a, b); } template void chmax(T& a, T b) { a = max(a, b); } template void cinarray(vector& v) { rep(i, v.size())cin >> v[i]; } template void coutarray(vector& v) { rep(i, v.size()) { if (i > 0)cout << " "; cout << v[i]; } cout << "\n"; } ll mod_pow(ll x, ll n, ll m = mod) { if (n < 0) { ll res = mod_pow(x, -n, m); return mod_pow(res, m - 2, m); } if (abs(x) >= m)x %= m; if (x < 0)x += m; //if (x == 0)return 0; ll res = 1; while (n) { if (n & 1)res = res * x % m; x = x * x % m; n >>= 1; } return res; } //mod should be <2^31 struct modint { int n; modint() :n(0) { ; } modint(ll m) { if (m < 0 || mod <= m) { m %= mod; if (m < 0)m += mod; } n = m; } operator int() { return n; } }; bool operator==(modint a, modint b) { return a.n == b.n; } bool operator<(modint a, modint b) { return a.n < b.n; } modint operator+=(modint& a, modint b) { a.n += b.n; if (a.n >= mod)a.n -= (int)mod; return a; } modint operator-=(modint& a, modint b) { a.n -= b.n; if (a.n < 0)a.n += (int)mod; return a; } modint operator*=(modint& a, modint b) { a.n = ((ll)a.n * b.n) % mod; return a; } modint operator+(modint a, modint b) { return a += b; } modint operator-(modint a, modint b) { return a -= b; } modint operator*(modint a, modint b) { return a *= b; } modint operator^(modint a, ll n) { if (n == 0)return modint(1); modint res = (a * a) ^ (n / 2); if (n % 2)res = res * a; return res; } ll inv(ll a, ll p) { return (a == 1 ? 1 : (1 - p * inv(p % a, a)) / a + p); } modint operator/(modint a, modint b) { return a * modint(inv(b, mod)); } modint operator/=(modint& a, modint b) { a = a / b; return a; } const int max_n = 1 << 21; modint fact[max_n], factinv[max_n]; void init_f() { fact[0] = modint(1); for (int i = 0; i < max_n - 1; i++) { fact[i + 1] = fact[i] * modint(i + 1); } factinv[max_n - 1] = modint(1) / fact[max_n - 1]; for (int i = max_n - 2; i >= 0; i--) { factinv[i] = factinv[i + 1] * modint(i + 1); } } modint comb(int a, int b) { if (a < 0 || b < 0 || a < b)return 0; return fact[a] * factinv[b] * factinv[a - b]; } modint combP(int a, int b) { if (a < 0 || b < 0 || a < b)return 0; return fact[a] * factinv[a - b]; } ll gcd(ll a, ll b) { a = abs(a); b = abs(b); if (a < b)swap(a, b); while (b) { ll r = a % b; a = b; b = r; } return a; } using ld = long double; //typedef long double ld; typedef pair LDP; const ld eps = 1e-10; const ld pi = acosl(-1.0); template void addv(vector& v, int loc, T val) { if (loc >= v.size())v.resize(loc + 1, 0); v[loc] += val; } /*const int mn = 2000005; bool isp[mn]; vector ps; void init() { fill(isp + 2, isp + mn, true); for (int i = 2; i < mn; i++) { if (!isp[i])continue; ps.push_back(i); for (int j = 2 * i; j < mn; j += i) { isp[j] = false; } } }*/ //[,val) template auto prev_itr(set& st, T val) { auto res = st.lower_bound(val); if (res == st.begin())return st.end(); res--; return res; } //[val,) template auto next_itr(set& st, T val) { auto res = st.lower_bound(val); return res; } using mP = pair; mP operator+(mP a, mP b) { return { a.first + b.first,a.second + b.second }; } mP operator+=(mP& a, mP b) { a = a + b; return a; } mP operator-(mP a, mP b) { return { a.first - b.first,a.second - b.second }; } mP operator-=(mP& a, mP b) { a = a - b; return a; } LP operator+(LP a, LP b) { return { a.first + b.first,a.second + b.second }; } LP operator+=(LP& a, LP b) { a = a + b; return a; } LP operator-(LP a, LP b) { return { a.first - b.first,a.second - b.second }; } LP operator-=(LP& a, LP b) { a = a - b; return a; } mt19937 mt(time(0)); const string drul = "DRUL"; string senw = "SENW"; //DRUL,or SENW int dx[4] = { 1,0,-1,0 }; int dy[4] = { 0,1,0,-1 }; //----------------------------------------- struct uf { private: vector par, ran; public: uf(int n) { par.resize(n, 0); ran.resize(n, 0); rep(i, n) { par[i] = i; } } int find(int x) { if (par[x] == x)return x; else return par[x] = find(par[x]); } void unite(int x, int y) { x = find(x), y = find(y); if (x == y)return; if (ran[x] < ran[y]) { par[x] = y; } else { par[y] = x; if (ran[x] == ran[y])ran[x]++; } } bool same(int x, int y) { return find(x) == find(y); } }; typedef vector> mat; typedef vector vec; mat mtmul(mat& A, mat& B) { mat C(A.size(), vec(B[0].size())); rep(i, (int)A.size()) { rep(k, (int)B.size()) { rep(j, (int)B[0].size()) { C[i][j] += A[i][k] * B[k][j]; } } } return C; } mat mtpow(mat A, ll n) { mat B(A.size(), vec(A.size())); rep(i, (int)A.size()) { B[i][i] = 1; } while (n > 0) { if (n & (ll)1)B = mtmul(B, A); A = mtmul(A, A); n >>= 1; } return B; } void solve() { vector> v; rep(i, 8)if (i > 0) { v.push_back({ i }); } v.push_back({ 1,4 }); const int ad = v.size() + 2; mat A(2*ad, vector(2*ad)); rep(i, v.size()) { rep1(j, 7) { if (v[i] == vector{5}&& j == 7)continue; int id[3][2]; rep(x, 3)rep(y, 2)id[x][y] = -1; rep(k, v[i].size()) { rep(l, 3) { if (v[i][k] & (1 << l)) { id[l][0] = k; } } } int tmp = v[i].size(); rep(x, 3) { if (j & (1 << x)) { id[x][1] = tmp; tmp++; } else { id[x][1] = -1; } } bool valid = true; rep(i, 2)rep(t, 2) { int c = 0; rep(x, 2)rep(y, 2) { int b = (id[i + x][y] >= 0); if ((x + y) % 2)b ^= 1; b ^= t; c += b; } if (c == 4)valid = false; } if (!valid)continue; if (id[1][0] < 0 && id[0][0] == id[2][0] && (j & 2)) { assert(false); } //if (id[1][0] >= 0 && (id[0][0] < 0 || id[2][0] < 0) && j == 5)assert(false); uf u(tmp); auto upd = [&](int a, int b) { if (a < 0 || b < 0)return; u.unite(a, b); }; rep(x, 3)rep(y, 2) { if (x + 1 < 3) { upd(id[x][y], id[x + 1][y]); } if (y + 1 < 2) { upd(id[x][y], id[x][y + 1]); } } vector ps; rep(x, 3)rep(y, 2) { if (id[x][y] >= 0) { id[x][y] = u.find(id[x][y]); ps.push_back(id[x][y]); } } sort(all(ps)); ps.erase(unique(all(ps)), ps.end()); vector nex; for (int p : ps) { int s = 0; rep(x, 3)if (id[x][1] == p) { s |= (1 << x); } nex.push_back(s); } sort(all(nex)); int z = -1; rep(x, v.size()) { if (v[x] == nex)z = x; } if (z >= 0) { A[z][i] += 1; A[z + ad][i + ad] += 1; for (int j = -1; j <= 2; j++) { int c = 0; rep(x, 2)rep(y, 2) { if (j + x >= 0 && j + x <= 2 && id[j+x][y] >= 0)c++; } if (0 < c && c < 4) { A[z + ad][i] += 1; } } } } } A[v.size()][v.size()] = 1; rep(i, v.size()) { if (v[i] != vector{5}) { A[i][v.size()] += 1; bool exi[3] = {}; for (int s : v[i])rep(j, 3)if (s & (1 << j))exi[j] = true; rep(j, 4) { bool e = false; if (j - 1 >= 0 && exi[j - 1])e = true; if (j < 3 && exi[j])e = true; if (e)A[i+ad][v.size()] += 1; } } } A[ad+v.size() + 1][ad+v.size() + 1] = 1; rep(i, v.size()) { if (v[i].size() == 1) { A[ad+v.size() + 1][ad+i] += 1; bool exi[3] = {}; for (int s : v[i])rep(j, 3)if (s & (1 << j))exi[j] = true; rep(j, 4) { bool e = false; if (j - 1 >= 0 && exi[j - 1])e = true; if (j < 3 && exi[j])e = true; if (e)A[ad + v.size() + 1][i] += 1; } } } ll n; cin >> n; A = mtpow(A, n + 1); cout << A[ad+v.size() + 1][v.size()] << "\n"; } signed main() { ios::sync_with_stdio(false); cin.tie(0); //cout << fixed << setprecision(10); //init_f(); //init(); //expr(); //while(true) //int t; cin >> t; rep(i, t) solve(); return 0; }