CF 346A(Alice and Bob-Python,sort)

A. Alice and Bob

time limit per test

memory limit per test

input

output

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|

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

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

Output

Alice", otherwise print "Bob" (without quotes).

Sample test(s)

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.

因为最后凑出来的一定是d,2d,...,nd

def gcd(a,b):
    if (b==0):
        return a
    else:
        return gcd(b,a%b)

n=input()
a=map(int,raw_input().split())
a.sort() 
g=reduce(gcd,a)
print (['Bob','Alice'][(max(a)/g-n)&1])