#include #include #include #include #include #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; using lint = long long; using pint = pair; using plint = pair; struct fast_ios { fast_ios(){ cin.tie(nullptr), ios::sync_with_stdio(false), cout << fixed << setprecision(20); }; } fast_ios_; #define ALL(x) (x).begin(), (x).end() #define FOR(i, begin, end) for(int i=(begin),i##_end_=(end);i=i##_begin_;i--) #define REP(i, n) FOR(i,0,n) #define IREP(i, n) IFOR(i,0,n) template void ndarray(vector& vec, const V& val, int len) { vec.assign(len, val); } template void ndarray(vector& vec, const V& val, int len, Args... args) { vec.resize(len), for_each(begin(vec), end(vec), [&](T& v) { ndarray(v, val, args...); }); } template bool chmax(T &m, const T q) { if (m < q) {m = q; return true;} else return false; } template bool chmin(T &m, const T q) { if (m > q) {m = q; return true;} else return false; } int floor_lg(long long x) { return x <= 0 ? -1 : 63 - __builtin_clzll(x); } template pair operator+(const pair &l, const pair &r) { return make_pair(l.first + r.first, l.second + r.second); } template pair operator-(const pair &l, const pair &r) { return make_pair(l.first - r.first, l.second - r.second); } template vector sort_unique(vector vec) { sort(vec.begin(), vec.end()), vec.erase(unique(vec.begin(), vec.end()), vec.end()); return vec; } template int arglb(const std::vector &v, const T &x) { return std::distance(v.begin(), std::lower_bound(v.begin(), v.end(), x)); } template int argub(const std::vector &v, const T &x) { return std::distance(v.begin(), std::lower_bound(v.begin(), v.end(), x)); } template istream &operator>>(istream &is, vector &vec) { for (auto &v : vec) is >> v; return is; } template ostream &operator<<(ostream &os, const vector &vec) { os << '['; for (auto v : vec) os << v << ','; os << ']'; return os; } template ostream &operator<<(ostream &os, const array &arr) { os << '['; for (auto v : arr) os << v << ','; os << ']'; return os; } #if __cplusplus >= 201703L template istream &operator>>(istream &is, tuple &tpl) { std::apply([&is](auto &&... args) { ((is >> args), ...);}, tpl); return is; } template ostream &operator<<(ostream &os, const tuple &tpl) { std::apply([&os](auto &&... args) { ((os << args << ','), ...);}, tpl); return os; } #endif template ostream &operator<<(ostream &os, const deque &vec) { os << "deq["; for (auto v : vec) os << v << ','; os << ']'; return os; } template ostream &operator<<(ostream &os, const set &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; } template ostream &operator<<(ostream &os, const unordered_set &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; } template ostream &operator<<(ostream &os, const multiset &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; } template ostream &operator<<(ostream &os, const unordered_multiset &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; } template ostream &operator<<(ostream &os, const pair &pa) { os << '(' << pa.first << ',' << pa.second << ')'; return os; } template ostream &operator<<(ostream &os, const map &mp) { os << '{'; for (auto v : mp) os << v.first << "=>" << v.second << ','; os << '}'; return os; } template ostream &operator<<(ostream &os, const unordered_map &mp) { os << '{'; for (auto v : mp) os << v.first << "=>" << v.second << ','; os << '}'; return os; } #ifdef HITONANODE_LOCAL const string COLOR_RESET = "\033[0m", BRIGHT_GREEN = "\033[1;32m", BRIGHT_RED = "\033[1;31m", BRIGHT_CYAN = "\033[1;36m", NORMAL_CROSSED = "\033[0;9;37m", RED_BACKGROUND = "\033[1;41m", NORMAL_FAINT = "\033[0;2m"; #define dbg(x) cerr << BRIGHT_CYAN << #x << COLOR_RESET << " = " << (x) << NORMAL_FAINT << " (L" << __LINE__ << ") " << __FILE__ << COLOR_RESET << endl #else #define dbg(x) (x) #endif template struct ModInt { #if __cplusplus >= 201402L #define MDCONST constexpr #else #define MDCONST #endif using lint = long long; MDCONST static int get_mod() { return mod; } static int get_primitive_root() { static int primitive_root = 0; if (!primitive_root) { primitive_root = [&]() { std::set fac; int v = mod - 1; for (lint i = 2; i * i <= v; i++) while (v % i == 0) fac.insert(i), v /= i; if (v > 1) fac.insert(v); for (int g = 1; g < mod; g++) { bool ok = true; for (auto i : fac) if (ModInt(g).pow((mod - 1) / i) == 1) { ok = false; break; } if (ok) return g; } return -1; }(); } return primitive_root; } int val; MDCONST ModInt() : val(0) {} MDCONST ModInt &_setval(lint v) { return val = (v >= mod ? v - mod : v), *this; } MDCONST ModInt(lint v) { _setval(v % mod + mod); } MDCONST explicit operator bool() const { return val != 0; } MDCONST ModInt operator+(const ModInt &x) const { return ModInt()._setval((lint)val + x.val); } MDCONST ModInt operator-(const ModInt &x) const { return ModInt()._setval((lint)val - x.val + mod); } MDCONST ModInt operator*(const ModInt &x) const { return ModInt()._setval((lint)val * x.val % mod); } MDCONST ModInt operator/(const ModInt &x) const { return ModInt()._setval((lint)val * x.inv() % mod); } MDCONST ModInt operator-() const { return ModInt()._setval(mod - val); } MDCONST ModInt &operator+=(const ModInt &x) { return *this = *this + x; } MDCONST ModInt &operator-=(const ModInt &x) { return *this = *this - x; } MDCONST ModInt &operator*=(const ModInt &x) { return *this = *this * x; } MDCONST ModInt &operator/=(const ModInt &x) { return *this = *this / x; } friend MDCONST ModInt operator+(lint a, const ModInt &x) { return ModInt()._setval(a % mod + x.val); } friend MDCONST ModInt operator-(lint a, const ModInt &x) { return ModInt()._setval(a % mod - x.val + mod); } friend MDCONST ModInt operator*(lint a, const ModInt &x) { return ModInt()._setval(a % mod * x.val % mod); } friend MDCONST ModInt operator/(lint a, const ModInt &x) { return ModInt()._setval(a % mod * x.inv() % mod); } MDCONST bool operator==(const ModInt &x) const { return val == x.val; } MDCONST bool operator!=(const ModInt &x) const { return val != x.val; } MDCONST bool operator<(const ModInt &x) const { return val < x.val; } // To use std::map friend std::istream &operator>>(std::istream &is, ModInt &x) { lint t; return is >> t, x = ModInt(t), is; } MDCONST friend std::ostream &operator<<(std::ostream &os, const ModInt &x) { return os << x.val; } MDCONST ModInt pow(lint n) const { lint ans = 1, tmp = this->val; while (n) { if (n & 1) ans = ans * tmp % mod; tmp = tmp * tmp % mod, n /= 2; } return ans; } static std::vector facs, invs; MDCONST static void _precalculation(int N) { int l0 = facs.size(); if (N <= l0) return; facs.resize(N), invs.resize(N); for (int i = l0; i < N; i++) facs[i] = facs[i - 1] * i % mod; long long facinv = ModInt(facs.back()).pow(mod - 2).val; for (int i = N - 1; i >= l0; i--) { invs[i] = facinv * facs[i - 1] % mod; facinv = facinv * i % mod; } } MDCONST lint inv() const { if (this->val < std::min(mod >> 1, 1 << 21)) { while (this->val >= int(facs.size())) _precalculation(facs.size() * 2); return invs[this->val]; } else { return this->pow(mod - 2).val; } } MDCONST ModInt fac() const { while (this->val >= int(facs.size())) _precalculation(facs.size() * 2); return facs[this->val]; } MDCONST ModInt doublefac() const { lint k = (this->val + 1) / 2; return (this->val & 1) ? ModInt(k * 2).fac() / (ModInt(2).pow(k) * ModInt(k).fac()) : ModInt(k).fac() * ModInt(2).pow(k); } MDCONST ModInt nCr(const ModInt &r) const { return (this->val < r.val) ? 0 : this->fac() / ((*this - r).fac() * r.fac()); } ModInt sqrt() const { if (val == 0) return 0; if (mod == 2) return val; if (pow((mod - 1) / 2) != 1) return 0; ModInt b = 1; while (b.pow((mod - 1) / 2) == 1) b += 1; int e = 0, m = mod - 1; while (m % 2 == 0) m >>= 1, e++; ModInt x = pow((m - 1) / 2), y = (*this) * x * x; x *= (*this); ModInt z = b.pow(m); while (y != 1) { int j = 0; ModInt t = y; while (t != 1) j++, t *= t; z = z.pow(1LL << (e - j - 1)); x *= z, z *= z, y *= z; e = j; } return ModInt(std::min(x.val, mod - x.val)); } }; template std::vector ModInt::facs = {1}; template std::vector ModInt::invs = {0}; using mint = ModInt<1000000007>; // Berlekamp–Massey algorithm // https://en.wikipedia.org/wiki/Berlekamp%E2%80%93Massey_algorithm // Complexity: O(N^2) // input: S = sequence from field K // return: L = degree of minimal polynomial, // C_reversed = monic min. polynomial (size = L + 1, reversed order, C_reversed[0] = 1)) // Formula: convolve(S, C_reversed)[i] = 0 for i >= L // Example: // - [1, 2, 4, 8, 16] -> (1, [1, -2]) // - [1, 1, 2, 3, 5, 8] -> (2, [1, -1, -1]) // - [0, 0, 0, 0, 1] -> (5, [1, 0, 0, 0, 0, 998244352]) (mod 998244353) // - [] -> (0, [1]) // - [0, 0, 0] -> (0, [1]) // - [-2] -> (1, [1, 2]) template std::pair> find_linear_recurrence(const std::vector &S) { int N = S.size(); using poly = std::vector; poly C_reversed{1}, B{1}; int L = 0, m = 1; Tfield b = 1; // adjust: C(x) <- C(x) - (d / b) x^m B(x) auto adjust = [](poly C, const poly &B, Tfield d, Tfield b, int m) -> poly { C.resize(std::max(C.size(), B.size() + m)); Tfield a = d / b; for (unsigned i = 0; i < B.size(); i++) C[i + m] -= a * B[i]; return C; }; for (int n = 0; n < N; n++) { Tfield d = S[n]; for (int i = 1; i <= L; i++) d += C_reversed[i] * S[n - i]; if (d == 0) m++; else if (2 * L <= n) { poly T = C_reversed; C_reversed = adjust(C_reversed, B, d, b, m); L = n + 1 - L; B = T; b = d; m = 1; } else C_reversed = adjust(C_reversed, B, d, b, m++); } return std::make_pair(L, C_reversed); } // Calculate ^N \bmod f(x)$ // Known as `Kitamasa method` // Input: f_reversed: monic, reversed (f_reversed[0] = 1) // Complexity: (K^2 \log N)$ ($: deg. of $) // Example: (4, [1, -1, -1]) -> [2, 3] // ( x^4 = (x^2 + x + 2)(x^2 - x - 1) + 3x + 2 ) // Reference: http://misawa.github.io/others/fast_kitamasa_method.html // http://sugarknri.hatenablog.com/entry/2017/11/18/233936 template std::vector monomial_mod_polynomial(long long N, const std::vector &f_reversed) { assert(!f_reversed.empty() and f_reversed[0] == 1); int K = f_reversed.size() - 1; if (!K) return {}; int D = 64 - __builtin_clzll(N); std::vector ret(K, 0); ret[0] = 1; auto self_conv = [](std::vector x) -> std::vector { int d = x.size(); std::vector ret(d * 2 - 1); for (int i = 0; i < d; i++) { ret[i * 2] += x[i] * x[i]; for (int j = 0; j < i; j++) ret[i + j] += x[i] * x[j] * 2; } return ret; }; for (int d = D; d--;) { ret = self_conv(ret); for (int i = 2 * K - 2; i >= K; i--) { for (int j = 1; j <= K; j++) ret[i - j] -= ret[i] * f_reversed[j]; } ret.resize(K); if ((N >> d) & 1) { std::vector c(K); c[0] = -ret[K - 1] * f_reversed[K]; for (int i = 1; i < K; i++) { c[i] = ret[i - 1] - ret[K - 1] * f_reversed[K - i]; } ret = c; } } return ret; } // Guess k-th element of the sequence, assuming linear recurrence // initial_elements: 0-ORIGIN // Verify: abc198f https://atcoder.jp/contests/abc198/submissions/21837815 template Tfield guess_kth_term(const std::vector &initial_elements, long long k) { assert(k >= 0); if (k < static_cast(initial_elements.size())) return initial_elements[k]; const auto f = find_linear_recurrence(initial_elements).second; const auto g = monomial_mod_polynomial(k, f); Tfield ret = 0; for (unsigned i = 0; i < g.size(); i++) ret += g[i] * initial_elements[i]; return ret; } int main() { int N; cin >> N; constexpr int B = 2000, C = B / 2; using BS = bitset; vector mp(B); mp[C][C] = 1; vector seq{1}; REP(T, C / 4) { vector nxt(B); REP(x, mp.size()) { if (x >= 3) nxt[x - 3] |= mp[x] | (mp[x] << 2) | (mp[x] >> 2); if (x + 3 < nxt.size()) nxt[x + 3] |= mp[x] | (mp[x] << 2) | (mp[x] >> 2); nxt[x] |= (mp[x] << 3) | (mp[x] >> 3); if (x >= 2) nxt[x - 2] |= (mp[x] << 3) | (mp[x] >> 3); if (x + 2 < nxt.size()) nxt[x + 2] |= (mp[x] << 3) | (mp[x] >> 3); } mp = nxt; mint n = 0; for (auto b : mp) n += b.count(); seq.push_back(n); } dbg(seq); cout << guess_kth_term(seq, N) << '\n'; }