346A Alice and Bob:数论&想法题

Codeforces Round #201 （Div. 1） / 346A Alice and Bob:数论&想法题2014-07-14 synapse7 A. Alice and Bob

http://codeforces.com/problemset/problem/346/A

time limit per test

2 seconds

memory limit per test

256 megabytes

input

standard input

output

standard output

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,...,a_n （1≤a_i≤10⁹） — the elements of the set.

Output