#include "math.h" #include #include #include #include #include #include #include #include #include #define ifor(i, a, b) for (int i = (a); i < (b); i++) #define rfor(i, a, b) for (int i = (b)-1; i >= (a); i--) #define rep(i, n) for (int i = 0; i < (n); i++) #define rrep(i, n) for (int i = (n)-1; i >= 0; i--) using namespace std; typedef long double ld; typedef long long int lli; typedef complex P; const double eps = 1e-11; int vex[4] = {1, 0, -1, 0}; int vey[4] = {0, 1, 0, -1}; typedef vector Vec; typedef vector vec; typedef vector MAT; typedef vector mat; lli MOD = 1000000007; //Ax=bをとくAは正方行列 //rankA<=min(m,n)ならば配列0のvecが帰る /*c++11から使える for (auto itr = data.begin(); itr != data.end(); ++itr) { ans = ans * (itr->second + 1) % MOD; }*/ map prime_factor(lli m) { map data; int a = 2; while (m >= a * a) { if (m % a == 0) { data[a]++; m /= a; } else { a++; } } data[m]++; return data; } Vec gauss_jordan(const MAT& A, const Vec& b) { int n = A.size(); MAT B(n, Vec(n + 1)); rep(i, n) rep(j, n) B[i][j] = A[i][j]; rep(i, n) B[i][n] = b[i]; rep(i, n) { int pivot = i; for (int j = i; j < n; j++) { if (abs(B[j][i]) > abs(B[pivot][i])) pivot = j; } swap(B[i], B[pivot]); if (abs(B[i][i]) < eps) return Vec(); //B_i_i成分が0であるつまり階数が for (int j = i + 1; j <= n; j++) B[i][j] /= B[i][i]; rep(j, n) { if (i != j) for (int k = i + 1; k <= n; k++) { B[j][k] -= B[j][i] * B[i][k]; } } } Vec x(n); for (int i = 0; i < n; i++) { x[i] = B[i][n]; } return x; } double det(const MAT& A) { int n = A.size(); MAT B(n, Vec(n)); rep(i, n) rep(j, n) B[i][j] = A[i][j]; double ans = 1; rep(i, n) { int pivot = i; for (int j = i; j < n; j++) { if (abs(B[j][i]) > abs(B[pivot][i])) pivot = j; } if (i != pivot) ans *= -1; swap(B[i], B[pivot]); if (abs(B[i][i]) < eps) return 0; ans *= B[i][i]; for (int j = i + 1; j < n; j++) B[i][j] /= B[i][i]; rep(j, n) { if (i != j) for (int k = i + 1; k < n; k++) { B[j][k] -= B[j][i] * B[i][k]; } } } return ans; } int rank(const MAT& A) { int n = A.size(); MAT B(n, Vec(n)); rep(i, n) rep(j, n) B[i][j] = A[i][j]; rep(i, n) { int pivot = i; for (int j = i; j < n; j++) { if (abs(B[j][i]) > abs(B[pivot][i])) pivot = j; } swap(B[i], B[pivot]); if (abs(B[i][i]) < eps) return i; for (int j = i + 1; j < n; j++) B[i][j] /= B[i][i]; rep(j, n) { if (i != j) for (int k = i + 1; k < n; k++) { B[j][k] -= B[j][i] * B[i][k]; } } } return n; } lli euler(lli m) { vector p; lli M = m; for (int i = 2; i <= m; i++) { if (m % i == 0) { p.push_back(i); while (m % i == 0) m /= i; } if (M < i * i && p.size() == 0) { p.push_back(M); break; } } lli ans = M; rep(i, p.size()) { //cout << p[i]< 0) { if (p & 1) ans = (ans * a) % mod; a = (a * a) % mod; p >>= 1; } return ans % mod; } lli inv(lli a, lli mod) { return powm(a, euler(mod) - 1, mod); } lli inv(lli a) { return powm(a, MOD - 2, MOD); } lli gcd(lli A, lli B) { if (A % B == 0) return B; else return gcd(B, A % B); } mat mul_mat_mod(mat A, mat B, lli m) { int n = A.size(); mat C(n, vec(n)); rep(i, n) rep(j, n) rep(k, n) { C[i][j] += A[i][k] * B[k][j] % m; C[i][j] %= m; } return C; } mat pow_mat(mat A, lli p, lli mod) { int n = A.size(); mat B = mat(n, vec(n)); while (p > 0) { if (p & 1) { B = mul_mat_mod(A, B, mod); } A = mul_mat_mod(A, A, mod); p >>= 1; } return B; } lli comb(lli a, lli b) { lli ans = 1; rep(i, b) { ans = ans % MOD * (a - i) % MOD * inv(b - i) % MOD; } return ans; } int near(double a) { int b = (int)a; if (a - b > 0.5) b++; return b; } int main() { int N, M; int ans = 0; cin >> N; rep(i, N) { cin >> M; map data = prime_factor(M); for (auto itr = data.begin(); itr != data.end(); ++itr) { ans ^= (itr->second) % 3; } } if (ans) cout << "Alice" << endl; else cout << "Bob" << endl; }