#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 ll = long long; constexpr int INF = 1001001001; // constexpr int mod = 1000000007; constexpr int mod = 998244353; template inline bool chmax(T& x, T y){ if(x < y){ x = y; return true; } return false; } template inline bool chmin(T& x, T y){ if(x > y){ x = y; return true; } return false; } struct ExtendedSieve{ vector table; const int n; ExtendedSieve(int n) : n(n) { table.assign(n + 1, 0); table[0] = table[1] = 1; for(int i = 2; i <= n; ++i){ if(table[i] > 0) continue; table[i] = i; for(int j = i + i; j <= n; j += i){ if(table[j] == 0) table[j] = i; } } } int operator[](const int& k){ return table[k]; } bool is_prime(int x){ if(x < 2) return false; return x == table[x]; } map prime_factorization(int x){ map res; while(x > 1){ ++res[table[x]]; x /= table[x]; } return res; } }; int main(){ ios::sync_with_stdio(false); cin.tie(nullptr); int N; cin >> N; vector M(N); for(int i = 0; i < N; ++i) cin >> M[i]; vector grundy(20, -1); auto func = [&](auto&& self, int i) -> int { if(grundy[i] != -1) return grundy[i]; if(i == 0) return grundy[i] = 0; int res = 0; vector g(3); g[self(self, i - 1)] = true; if(i - 2 >= 0) g[self(self, i - 2)] = true; for(int i = 0; i < 3; ++i){ if(!g[i]){ res = i; break; } } return grundy[i] = res; }; ExtendedSieve sieve(10000); int xorsum = 0; for(int i = 0; i < N; ++i){ auto primes = sieve.prime_factorization(M[i]); for(auto& [prime, cnt] : primes){ xorsum ^= func(func, cnt); } } cout << (xorsum ? "Alice" : "Bob") << endl; return 0; }