#include using namespace std; #ifdef LOCAL_ void debug_out() { cerr << "\033[0m" << endl; } template void debug_out(Head H, Tail... T) { cerr << ' ' << H << ','; debug_out(T...); } #define debug(...) cerr << "\033[1;36m" << __func__ << ":L" << __LINE__ << " " << #__VA_ARGS__ << ":", debug_out(__VA_ARGS__) #define dump(x) cerr << __func__ << ":L" << __LINE__ << " " << #x << " = " << (x) << endl #else #define debug(...) (void(0)) #define dump(x) (void(0)) #endif #define rep(i, n) for (int i = 0; i < (int)(n); i++) #define irep(i, n) for (int i = (int)(n)-1; i >= 0; --i) using ll = long long; using pii = pair; using pil = pair; using pli = pair; using pll = pair; constexpr int INF = 1000'000'000; constexpr long long HINF = 4000'000'000000'000'000; constexpr long long MOD = 1000000007; // = 998244353; constexpr double EPS = 1e-4; constexpr double PI = 3.14159265358979; #pragma region Macros template ostream &operator<<(ostream &os, const pair &p) { os << '(' << p.first << ',' << p.second << ')'; return os; } template ostream &operator<<(ostream &os, const vector &v) { os << '['; for (auto &e : v) { os << e << ','; } os << ']'; return os; } template ostream &operator<<(ostream &os, const set &st) { os << '{'; for (auto itr = st.begin(); itr != st.end(); itr++) { os << *itr << ','; } os << '}'; return os; } template ostream &operator<<(ostream &os, const map &mp) { os << '{'; for (auto itr = mp.begin(); itr != mp.end(); itr++) { os << itr->first << ": " << itr->second << ','; } os << '}'; return os; } void yn(bool cond, string Yes = "Yes", string No = "No") { cout << (cond ? Yes : No) << '\n'; } template bool chmax(T &x, const T &y) { return (x < y) ? (x = y, true) : false; } template bool chmin(T &x, const T &y) { return (x > y) ? (x = y, true) : false; } #pragma endregion // OsaK // n以下の整数の素因数分解を高速に行う. // 制約: n >= 1 struct OsaK { int n; vector smallest_prime_factor; OsaK(int n) : n(n) { smallest_prime_factor.assign(n + 1, -1); } // build // spf配列を用意する. // 計算量: O(nloglogn) void build() { long long i = 2; for (; i * i <= n; ++i) { if (smallest_prime_factor[i] < 0) { smallest_prime_factor[i] = i; for (long long p = i * i; p <= n; p += i) { if (smallest_prime_factor[p] < 0) smallest_prime_factor[p] = i; } } } for (int j = i; j <= n; ++j) { if (smallest_prime_factor[j] < 0) smallest_prime_factor[j] = j; } } // factorize // 整数mを素因数分解する // 制約: 1 <= m <= n // 計算量: O(logm) template vector> factorize(T m) { vector> ans; while (m > 1) { int p = smallest_prime_factor[m], e = 1; m /= p; while (p == smallest_prime_factor[m]) { ++e; m /= p; } ans.emplace_back(p, e); } return ans; } // count_factor // 整数mの約数の数を数える. // 制約: 1 <= m <= n // 計算量: O(logm) template long long count_factor(T m) { auto ret = factorize(m); long long ans = 1; for (const auto &p : ret) { ans *= (p.second + 1); } return ans; } }; const int MAXN = 10006; vector grundy(MAXN, 0); void solve() { OsaK osk(MAXN); osk.build(); grundy[1] = 0; for (int i = 2; i < MAXN; i++) { set s; auto f = osk.factorize(i); for (const auto &p : f) { if (p.second == 1) { s.insert(grundy[i / p.first]); } else { s.insert(grundy[i / p.first]); s.insert(grundy[i / p.first / p.first]); } } int g = 0; while (s.count(g)) g++; grundy[i] = g; } } int main() { cin.tie(nullptr); ios::sync_with_stdio(false); cout << fixed << setprecision(20); solve(); int n; cin >> n; vector M(n); rep(i, n) cin >> M[i]; int ans = 0; for (int m : M) ans ^= grundy[m]; yn(ans, "Alice", "Bob"); return 0; }