#include <bits/stdc++.h>
#pragma GCC optimize("Ofast")
const long double EPSILON = 0.000000001;
const long long int mod = 1e9 + 7;
const long long int AM = 2e5 + 5;
const long double pi = 3.14159265358979323846;
long long int max(long long int a, long long int b) {
  if (a > b)
    return a;
  else
    return b;
}
using namespace std;
long long int fact(long long int n) {
  long long int ans = 1;
  for (long long int i = 1; i <= n; i++) ans *= i;
  return ans;
}
long long int powm(long long int a, long long int b, long long int n) {
  long long int x = 1, y = a;
  while (b > 0) {
    if (b % 2 == 1) {
      x = (x * y) % n;
    }
    y = (y * y) % n;
    b /= 2;
  }
  return x % n;
}
long long int pow(long long int x, long long int y) {
  long long int res = 1;
  while (y > 0) {
    if (y & 1) res = ((res) * (x));
    y = y >> 1;
    x = ((x) * (x));
  }
  return res;
}
long long int min(long long int a, long long int b) {
  if (a > b)
    return b;
  else
    return a;
}
bool cmp(long double x, long double y) {
  if (abs(x - y) <= EPSILON) return 1;
  return 0;
}
bool checkprime(long long int n) {
  for (long long int i = 2; i * i <= n; i++)
    if (n % i == 0) return false;
  return true;
}
long long int gcd(long long int a, long long int b) {
  return b ? gcd(b, a % b) : a;
}
long long int lcm(long long int a, long long int b) {
  return (a * b) / gcd(a, b);
}
long long int modInverse(long long int a, long long int m) {
  long long int g = gcd(a, m);
  return powm(a, m - 2, m);
}
bool prime[10000001];
void SieveOfEratosthenes(int n = 10000000) {
  memset(prime, true, sizeof(prime));
  for (int p = 2; p * p <= n; p++) {
    if (prime[p] == true) {
      for (int i = p * p; i <= n; i += p) prime[i] = false;
    }
  }
}
int main() {
  int n;
  cin >> n;
  vector<long long int> v(n);
  cin >> v[0];
  long long int maxi = v[0];
  long long int gcds = v[0];
  for (int i = 1; i < n; i++) {
    cin >> v[i];
    maxi = max(maxi, v[i]);
    gcds = gcd(gcds, v[i]);
  }
  if (((maxi / gcds - n)) % 2 != 0)
    cout << "Alice"
         << "\n";
  else
    cout << "Bob"
         << "\n";
  return 0;
}

### Prompt

Develop a solution in cpp to the problem described below:

It is so boring in the summer holiday, isn't it? So Alice and Bob have invented a new game to play. The rules are as follows. First, they get a set of n distinct integers. And then they take turns to make the following moves. During each move, either Alice or Bob (the player whose turn is the current) can choose two distinct integers x and y from the set, such that the set doesn't contain their absolute difference |x - y|. Then this player adds integer |x - y| to the set (so, the size of the set increases by one).

If the current player has no valid move, he (or she) loses the game. The question is who will finally win the game if both players play optimally. Remember that Alice always moves first.

Input

The first line contains an integer n (2 ≤ n ≤ 100) — the initial number of elements in the set. The second line contains n distinct space-separated integers a1, a2, ..., an (1 ≤ ai ≤ 109) — the elements of the set.

Output

Print a single line with the winner's name. If Alice wins print "Alice", otherwise print "Bob" (without quotes).

Examples

Input

2
2 3


Output

Alice


Input

2
5 3


Output

Alice


Input

3
5 6 7


Output

Bob

Note

Consider the first test sample. Alice moves first, and the only move she can do is to choose 2 and 3, then to add 1 to the set. Next Bob moves, there is no valid move anymore, so the winner is Alice.

### Response

```cpp
#include <bits/stdc++.h>
#pragma GCC optimize("Ofast")
const long double EPSILON = 0.000000001;
const long long int mod = 1e9 + 7;
const long long int AM = 2e5 + 5;
const long double pi = 3.14159265358979323846;
long long int max(long long int a, long long int b) {
  if (a > b)
    return a;
  else
    return b;
}
using namespace std;
long long int fact(long long int n) {
  long long int ans = 1;
  for (long long int i = 1; i <= n; i++) ans *= i;
  return ans;
}
long long int powm(long long int a, long long int b, long long int n) {
  long long int x = 1, y = a;
  while (b > 0) {
    if (b % 2 == 1) {
      x = (x * y) % n;
    }
    y = (y * y) % n;
    b /= 2;
  }
  return x % n;
}
long long int pow(long long int x, long long int y) {
  long long int res = 1;
  while (y > 0) {
    if (y & 1) res = ((res) * (x));
    y = y >> 1;
    x = ((x) * (x));
  }
  return res;
}
long long int min(long long int a, long long int b) {
  if (a > b)
    return b;
  else
    return a;
}
bool cmp(long double x, long double y) {
  if (abs(x - y) <= EPSILON) return 1;
  return 0;
}
bool checkprime(long long int n) {
  for (long long int i = 2; i * i <= n; i++)
    if (n % i == 0) return false;
  return true;
}
long long int gcd(long long int a, long long int b) {
  return b ? gcd(b, a % b) : a;
}
long long int lcm(long long int a, long long int b) {
  return (a * b) / gcd(a, b);
}
long long int modInverse(long long int a, long long int m) {
  long long int g = gcd(a, m);
  return powm(a, m - 2, m);
}
bool prime[10000001];
void SieveOfEratosthenes(int n = 10000000) {
  memset(prime, true, sizeof(prime));
  for (int p = 2; p * p <= n; p++) {
    if (prime[p] == true) {
      for (int i = p * p; i <= n; i += p) prime[i] = false;
    }
  }
}
int main() {
  int n;
  cin >> n;
  vector<long long int> v(n);
  cin >> v[0];
  long long int maxi = v[0];
  long long int gcds = v[0];
  for (int i = 1; i < n; i++) {
    cin >> v[i];
    maxi = max(maxi, v[i]);
    gcds = gcd(gcds, v[i]);
  }
  if (((maxi / gcds - n)) % 2 != 0)
    cout << "Alice"
         << "\n";
  else
    cout << "Bob"
         << "\n";
  return 0;
}

```