#ifdef __LOCAL #define _GLIBCXX_DEBUG #endif #include #include using namespace std; using namespace atcoder; typedef unsigned long long ull; typedef long long ll; const double PI = 3.14159265358979323846; #define rep(i, n) for (ll i = 0; i < (ll)(n); i++) // aよりもbが大きいならばaをbで更新する // (更新されたならばtrueを返す) template bool chmax(T& a, const T& b) { if (a < b) { a = b; // aをbで更新 return true; } return false; } // aよりもbが小さいならばaをbで更新する // (更新されたならばtrueを返す) template bool chmin(T& a, const T& b) { if (a > b) { a = b; // aをbで更新 return true; } return false; } // a^p // 2^3 = 2 * 2^2 // 2^2 = 2 * (2^1) // 2^1 = 2 ll powpow(ll a, ll p) { if (p == 0) return 1; if (p % 2 == 0) { ll half = powpow(a, p / 2); return half * half; } else { return a * powpow(a, p - 1); } } class combination { private: ll N; vector> C; public: explicit combination(ll _n) : N(_n) { C.resize(N + 1); rep(i, N + 1) C[i].resize(N + 1); C[0][0] = 1; rep(i, N) rep(j, i + 1) { C[i + 1][j + 1] += C[i][j]; C[i + 1][j] += C[i][j]; } } ll operator()(ll n, ll k) { if (n < k) return 0; if (n < 0 || k < 0) return 0; return C[n][k]; } }; // ref. https://drken1215.hatenablog.com/entry/2018/06/08/210000 class modcombination { private: ll mod; vector fac, finv, inv; public: modcombination(ll n, ll _mod) : mod(_mod) { fac.resize(n + 1); finv.resize(n + 1); inv.resize(n + 1); fac[0] = fac[1] = 1; finv[0] = finv[1] = 1; inv[1] = 1; for (ll i = 2; i <= n; i++) { fac[i] = fac[i - 1] * i % mod; inv[i] = mod - inv[mod % i] * (mod / i) % mod; finv[i] = finv[i - 1] * inv[i] % mod; } } ll operator()(ll n, ll k) { if (n < k) return 0; if (n < 0 || k < 0) return 0; return fac[n] * (finv[k] * finv[n - k] % mod) % mod; } }; // cf. https://qiita.com/drken/items/a14e9af0ca2d857dad23 vector enum_divisors(ll n) { vector res; // sqrt(n)まで試し割り for (ll i = 1; i * i <= n; i++) { if (n % i == 0) { res.push_back(i); // 重複しないならばiの相方であるn/iも約数 // e.g. n=25のときのi=5は重複 if (n / i != i) res.push_back(n / i); } } sort(res.begin(), res.end()); return res; } // cf. https://qiita.com/drken/items/a14e9af0ca2d857dad23 map prime_factors(ll n) { map res; // sqrt(n)まで試し割り for (ll a = 2; a * a <= n; a++) { if (n % a != 0) continue; // nで割れる限り割る while (n % a == 0) { res[a]++; n /= a; } } if (n != 1) res[n]++; return res; } // p/q struct fraction { ll p, q; fraction(ll _p = 0, ll _q = 1) : p(_p), q(_q) { if (q == 0) { p = 1; return; } if (q < 0) { p = -p; q = -q; } ll g = gcd(p, q); p /= g; q /= g; } bool operator<(const fraction& other) const { return p * other.q < q * other.p; } bool operator<=(const fraction& other) const { return p * other.q <= q * other.p; } bool operator==(const fraction& other) const { return p == other.p && q == other.q; } }; // res[i][c] := i 文字目以降で最初に文字 c が登場する index (存在しないときは n) vector> calcNext(const string& S) { ll n = (ll)S.size(); vector> res(n + 1, vector(26, n)); for (ll i = n - 1; i >= 0; --i) { for (ll j = 0; j < 26; ++j) res[i][j] = res[i + 1][j]; res[i][S[i] - 'a'] = i; } return res; } // ref. https://algo-logic.info/bridge-lowlink/ struct LowLink { vector> G; vector ord, low; vector visited; vector> bridges; explicit LowLink(const vector>& _G) : G(_G) { visited.resize(G.size(), false); ord.resize(G.size(), 0); low.resize(G.size(), 0); ll k = 0; rep(i, (ll)G.size()) { if (visited[i]) continue; k = dfs(i, k); } } ll dfs(ll node, ll k, ll parent = -1) { visited[node] = true; ord[node] = k; low[node] = k; k++; for (auto g : G[node]) { if (!visited[g]) { k = dfs(g, k, node); low[node] = min(low[node], low[g]); if (ord[node] < low[g]) { bridges.emplace_back(node, g); } } else if (g != parent) { low[node] = min(low[node], ord[g]); } } return k; } }; // 3x3(アフィン変換) struct matrix { vector> a; matrix(const vector>& _a = {{1, 0, 0}, {0, 1, 0}, {0, 0, 1}}) : a(_a) {} matrix operator*(const matrix& x) { matrix res({{0, 0, 0}, {0, 0, 0}, {0, 0, 0}}); rep(i, 3) rep(j, 3) rep(k, 3) { // cout << i << "," << j << " <- " << a[i][k] << "*" << x.a[k][j] << endl; res.a[i][j] += a[i][k] * x.a[k][j]; } return res; } vector operator*(const vector& x) { matrix other({{x[0], 0, 0}, {x[1], 0, 0}, {1, 0, 0}}); auto res = *this * other; return vector({res.a[0][0], res.a[1][0], res.a[2][0]}); } }; int main() { cin.tie(nullptr); ios_base::sync_with_stdio(false); cout << fixed << setprecision(15); ll N; cin >> N; vector is_prime(N + 1, true); is_prime[0] = false; is_prime[1] = false; for (ll i = 2; i <= N; i++) { if (!is_prime[i]) continue; for (ll j = 2 * i; j <= N; j += i) { is_prime[j] = false; } } map visited; auto rec = [&](auto f, ll x) -> ll { if (is_prime[x]) { return 1; } if (visited.find(x) != visited.end()) { return visited[x]; } for (auto [p, e] : prime_factors(x)) { ll k = x; while (k % p == 0) { k /= p; ll v = f(f, k); if (v == 0) { visited[x] = 1; return 1; } } } visited[x] = 0; return 0; }; if (rec(rec, N)) { cout << "Alice" << endl; } else { cout << "Bob" << endl; } // for (auto [i, g] : visited) { // cout << i << " " << g << endl; // } // vector grundy(N + 1); // grundy[0] = 0; // grundy[1] = 0; // for (ll i = 2; i <= N; i++) { // vector mex(N + 1); // auto pe = prime_factors(i); // for (auto [p, e] : pe) { // ll k = i; // while (k % p == 0) { // k /= p; // mex[grundy[k]] = 1; // } // } // for (ll j = 0; i <= N; j++) { // if (mex[j] == 0) { // grundy[i] = j; // break; // } // } // } // cout << grundy[N] << endl; // for (ll i = 1; i <= N; i++) { // if (grundy[i] == 0) { // cout << i << " " << grundy[i] << " lose " << endl; // for (auto [p, e] : prime_factors(i)) { // cout << " " << p << " ^ " << e << endl; // } // } else { // cout << i << " " << grundy[i] << " win " << endl; // for (auto [p, e] : prime_factors(i)) { // cout << " " << p << " ^ " << e << endl; // } // } // } return 0; }