#include #include #include #include #include #include #define repeat(i,n) for (int i = 0; (i) < (n); ++(i)) using namespace std; vector sieve_of_eratosthenes(int n) { // enumerate primes in [2,n] with O(n log log n) vector is_prime(n+1, true); is_prime[0] = is_prime[1] = false; for (int i = 2; i*i <= n; ++ i) if (is_prime[i]) for (int k = i+i; k <= n; k += i) is_prime[k] = false; vector primes; for (int i = 2; i <= n; ++i) if (is_prime[i]) primes.push_back(i); return primes; } map factors(int n, vector const & primes) { map result; for (int p : primes) { if (n < p *(int) p) break; while (n % p == 0) { result[p] += 1; n /= p; } } if (n != 1) result[n] += 1; return result; } template int mex(C const & xs) { int y = 0; for (int x : xs) { // xs must be sorted (duplication is permitted) if (y < x) break; if (y == x) ++ y; } return y; } int grandy(int n, vector const & primes, map & memo) { if (n <= 1) return 0; if (memo.count(n)) return memo[n]; set g; for (auto it : factors(n, primes)) { int p, cnt; tie(p, cnt) = it; int m = n; repeat (i,cnt) { m /= p; g.insert(grandy(m, primes, memo)); } } return memo[n] = mex(g); } int main() { int n; cin >> n; vector primes = sieve_of_eratosthenes(sqrt(n) + 3); map memo; cout << (grandy(n, primes, memo) ? "Alice" : "Bob") << endl; return 0; }