<s>[INST] In this problem, we will consider the following game, where two players take turns to remove one stone from one of several stone heaps.  The game starts with the following configuration:  $(x, y, z)$, where $x$, $y$ and $z$ are positive integers.  We are also given $s$, which is the sum of $x$, $y$, and $z$.  The game continues until one player has removed all the stones.  That player is the loser.  We want to determine if it is possible for the first player to win for a given starting configuration.
The rules of the game are as follows:
- The players alternate turns.  The first player can remove one stone from any of the heaps of his choice to reduce its size to a non-negative integer.  The second player can then also remove a stone from any heap and so on.
- A player can only remove one stone per turn and only from one heap.
- The game ends when the sum of the stones left in all heaps is 0.
- The player who removes the last stone loses.
We would like to determine, given the sizes $x$, $y$, and $z$ of the stone heaps and their sum $s$, whether the first player can win or not.
Given that $s$ is even, is it possible for the first player to win?[/INST]