#define PROBLEM "http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=3119" #include <iostream> #include <vector> #include "Mylib/Convolution/fast_mobius_transform_superset.cpp" #include "Mylib/Convolution/fast_zeta_transform_superset.cpp" #include "Mylib/IO/input_vector.cpp" #include "Mylib/Number/Mint/mint.cpp" namespace hl = haar_lib; using mint = hl::modint<1000000007>; int main() { int n; std::cin >> n; auto a = hl::input_vector<int>(n); std::vector<int> dp(1 << 20); for (auto x : a) dp[x] += 1; dp = hl::fast_zeta_transform_superset(dp); std::vector<mint> f(1 << 20); for (int i = 0; i < 1 << 20; ++i) f[i] = mint::pow(2, dp[i]) - 1; auto ans = hl::fast_mobius_transform_superset(f); std::cout << ans[0] << std::endl; return 0; }
#line 1 "test/aoj/3119/main.test.cpp" #define PROBLEM "http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=3119" #include <iostream> #include <vector> #line 2 "Mylib/Convolution/fast_mobius_transform_superset.cpp" #include <cassert> #include <functional> #line 5 "Mylib/Convolution/fast_mobius_transform_superset.cpp" namespace haar_lib { template <typename T, typename Func = std::minus<T>> std::vector<T> fast_mobius_transform_superset(std::vector<T> f, const Func &op = std::minus<T>()) { const int N = f.size(); assert((N & (N - 1)) == 0 && "N must be a power of 2"); for (int i = 1; i < N; i <<= 1) { for (int j = 0; j < N; ++j) { if (not(j & i)) f[j] = op(f[j], f[j ^ i]); } } return f; } } // namespace haar_lib #line 5 "Mylib/Convolution/fast_zeta_transform_superset.cpp" namespace haar_lib { template <typename T, typename Func = std::plus<T>> std::vector<T> fast_zeta_transform_superset(std::vector<T> f, const Func &op = std::plus<T>()) { const int N = f.size(); assert((N & (N - 1)) == 0 && "N must be a power of 2"); for (int i = 1; i < N; i <<= 1) { for (int j = 0; j < N; ++j) { if (not(j & i)) f[j] = op(f[j], f[j ^ i]); } } return f; } } // namespace haar_lib #line 4 "Mylib/IO/input_vector.cpp" namespace haar_lib { template <typename T> std::vector<T> input_vector(int N) { std::vector<T> ret(N); for (int i = 0; i < N; ++i) std::cin >> ret[i]; return ret; } template <typename T> std::vector<std::vector<T>> input_vector(int N, int M) { std::vector<std::vector<T>> ret(N); for (int i = 0; i < N; ++i) ret[i] = input_vector<T>(M); return ret; } } // namespace haar_lib #line 3 "Mylib/Number/Mint/mint.cpp" #include <utility> namespace haar_lib { template <int32_t M> class modint { uint32_t val_; public: constexpr static auto mod() { return M; } constexpr modint() : val_(0) {} constexpr modint(int64_t n) { if (n >= M) val_ = n % M; else if (n < 0) val_ = n % M + M; else val_ = n; } constexpr auto &operator=(const modint &a) { val_ = a.val_; return *this; } constexpr auto &operator+=(const modint &a) { if (val_ + a.val_ >= M) val_ = (uint64_t) val_ + a.val_ - M; else val_ += a.val_; return *this; } constexpr auto &operator-=(const modint &a) { if (val_ < a.val_) val_ += M; val_ -= a.val_; return *this; } constexpr auto &operator*=(const modint &a) { val_ = (uint64_t) val_ * a.val_ % M; return *this; } constexpr auto &operator/=(const modint &a) { val_ = (uint64_t) val_ * a.inv().val_ % M; return *this; } constexpr auto operator+(const modint &a) const { return modint(*this) += a; } constexpr auto operator-(const modint &a) const { return modint(*this) -= a; } constexpr auto operator*(const modint &a) const { return modint(*this) *= a; } constexpr auto operator/(const modint &a) const { return modint(*this) /= a; } constexpr bool operator==(const modint &a) const { return val_ == a.val_; } constexpr bool operator!=(const modint &a) const { return val_ != a.val_; } constexpr auto &operator++() { *this += 1; return *this; } constexpr auto &operator--() { *this -= 1; return *this; } constexpr auto operator++(int) { auto t = *this; *this += 1; return t; } constexpr auto operator--(int) { auto t = *this; *this -= 1; return t; } constexpr static modint pow(int64_t n, int64_t p) { if (p < 0) return pow(n, -p).inv(); int64_t ret = 1, e = n % M; for (; p; (e *= e) %= M, p >>= 1) if (p & 1) (ret *= e) %= M; return ret; } constexpr static modint inv(int64_t a) { int64_t b = M, u = 1, v = 0; while (b) { int64_t t = a / b; a -= t * b; std::swap(a, b); u -= t * v; std::swap(u, v); } u %= M; if (u < 0) u += M; return u; } constexpr static auto frac(int64_t a, int64_t b) { return modint(a) / modint(b); } constexpr auto pow(int64_t p) const { return pow(val_, p); } constexpr auto inv() const { return inv(val_); } friend constexpr auto operator-(const modint &a) { return modint(M - a.val_); } friend constexpr auto operator+(int64_t a, const modint &b) { return modint(a) + b; } friend constexpr auto operator-(int64_t a, const modint &b) { return modint(a) - b; } friend constexpr auto operator*(int64_t a, const modint &b) { return modint(a) * b; } friend constexpr auto operator/(int64_t a, const modint &b) { return modint(a) / b; } friend std::istream &operator>>(std::istream &s, modint &a) { s >> a.val_; return s; } friend std::ostream &operator<<(std::ostream &s, const modint &a) { s << a.val_; return s; } template <int N> static auto div() { static auto value = inv(N); return value; } explicit operator int32_t() const noexcept { return val_; } explicit operator int64_t() const noexcept { return val_; } }; } // namespace haar_lib #line 9 "test/aoj/3119/main.test.cpp" namespace hl = haar_lib; using mint = hl::modint<1000000007>; int main() { int n; std::cin >> n; auto a = hl::input_vector<int>(n); std::vector<int> dp(1 << 20); for (auto x : a) dp[x] += 1; dp = hl::fast_zeta_transform_superset(dp); std::vector<mint> f(1 << 20); for (int i = 0; i < 1 << 20; ++i) f[i] = mint::pow(2, dp[i]) - 1; auto ans = hl::fast_mobius_transform_superset(f); std::cout << ans[0] << std::endl; return 0; }