PROBLEM STATEMENT

Consider the following solitaire game:
We have a deck of identical cards. Initially, these cards are split into several heaps, with 
heaps[i] cards on the i-th heap.
Each step of the game looks as follows: Pick one card from each of the heaps and make a new heap 
out of these cards.
 


When describing a position in the game, only the heap sizes matter, their order does not.
Clearly, sooner or later a position will repeat and the game will become periodic from that point 
on.



Write a method that takes a vector <int> heaps and returns the length of the shortest period of 
the game.

In other words, find the smallest number of steps S such that for some X the positions after X and 
X+S steps are equal.


DEFINITION
Class:SolitaireSimulation
Method:periodLength
Parameters:vector <int>
Returns:int
Method signature:int periodLength(vector <int> heaps)


NOTES
-After some finite number of moves the game must always become periodic.


CONSTRAINTS
-heaps will contain between 1 and 50 elements, inclusive.
-Each element in heaps will be between 1 and 50, inclusive.
-The sum of all elements in heaps will be between 1 and 50, inclusive.


EXAMPLES

0)
{3,1,3}

Returns: 4


In the first step of this game we take one card from each of the heaps, leaving two heaps with two 
cards each. Then we form a new heap consisting of the three cards we took. Thus the new heap sizes 
are 2, 2, and 3.


In the next step, the sizes of these heaps decrease to 1, 1, 2, and a new heap of size 3 appears.


After the third step the heap sizes will be 1, 2, and 4.


After the fourth step the heap sizes will be 1, 3, and 3. This is exactly the starting position.


1)
{1,4}

Returns: 3

In this case, the positions after the next few steps will look as follows:

2,3
1,2,2
1,1,3
2,3
1,2,2
...

The shortest period has length 3. Note that the starting position 1,4 is never repeated again.

2)
{1}

Returns: 1

After each step we have the same heap with one card.

3)
{4,3,2,1}

Returns: 1



4)
{3,3,3,3}

Returns: 5



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