#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 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 < 1 << 20) { 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>; void bad() { puts("0"); exit(0); } int main() { int N; cin >> N; vector B(N); cin >> B; int mask = 0; int cnt = 0; mint tmp = 1; vector pow2(N + 31, 1); REP(i, pow2.size() - 1) pow2[i + 1] = pow2[i] * 2; constexpr int D = 30; vector>> dp(D + 1, vector(D + 1, vector(N + 1))); REP(d, D + 1) dp[d][d][0] = 1; REP(i, N) { REP(d, D + 1) FOR(e, d, D + 1) FOR(f, e, D + 1) { if (e == f) dp[d][f].at(i + 1) += dp[d][e][i] * mint(pow2.at(e) - mint(1)); else dp[d][f][i + 1] += dp[d][e][i] * mint(pow2[e]) * mint(D - e).nCr(f - e); } } dbg(dp[0][15][7]); for (int b : B) { cnt++; if (b < 0) continue; else { dbg(cnt); if ((mask & ~b)) bad(); int pc = __builtin_popcount(mask); int pcb = __builtin_popcount(b); dbg((pint(pc, pcb))); tmp *= dp[pc][pcb][cnt] / mint(D - pc).nCr(D - pcb); cnt = 0; mask = b; } } cout << tmp << '\n'; }