Algorithm Traces.  The input is the M preferences (with row i giving the preference
order for m_i) and the W preferences (with row i giving the preference order for w_i).

The output is the matching computed with respect to M - so the i-th entry is the W that m_i is matched to.  

The trace is the list proposals with the result given.  The pair in brackets [i, j] indicates that at the time of 
the proposal w_i is matched with m_j.   (A -1 is used to indicate w_i is unmatched.)   The trace is from one partcular 
implementation of the Gale-Shapley algorithm - you may get different proposals,  but you should get the same overall result.
The specific implementation uses a Stack for ordering the unmatched W's.

==================================== 




Input:
[2, 0, 1]
[2, 0, 1]
[2, 1, 0]


[2, 0, 1]
[0, 2, 1]
[2, 0, 1]

Output:
[0, 1, 2]

Trace
2 proposes to 2 [2,-1]  Accepted
1 proposes to 2 [2,2]  Rejected
1 proposes to 0 [0,-1]  Accepted
0 proposes to 2 [2,2]  Rejected
0 proposes to 0 [0,1]  Accepted
1 proposes to 1 [1,-1]  Accepted

==========================================

Input:
[3, 1, 0, 2]
[3, 0, 1, 2]
[3, 1, 2, 0]
[0, 3, 2, 1]


[3, 0, 2, 1]
[3, 1, 2, 0]
[0, 1, 3, 2]
[3, 0, 2, 1]

Output:
[3, 1, 2, 0]

Trace:
3 proposes to 0 [0,-1]  Accepted
2 proposes to 3 [3,-1]  Accepted
1 proposes to 3 [3,2]  Rejected
1 proposes to 0 [0,3]  Rejected
1 proposes to 1 [1,-1]  Accepted
0 proposes to 3 [3,2]  Accepted
2 proposes to 1 [1,1]  Rejected
2 proposes to 2 [2,-1]  Accepted

=============================================

Input:
[1, 3, 0, 2]
[3, 0, 2, 1]
[2, 3, 1, 0]
[2, 0, 3, 1]


[1, 2, 0, 3]
[0, 3, 2, 1]
[1, 2, 3, 0]
[0, 1, 2, 3]

Output:
[1, 3, 2, 0]

Trace:
3 proposes to 2 [2,-1]  Accepted
2 proposes to 2 [2,3]  Accepted
3 proposes to 0 [0,-1]  Accepted
1 proposes to 3 [3,-1]  Accepted
0 proposes to 1 [1,-1]  Accepted

=============================================

Input:
[4, 2, 0, 1, 3]
[0, 1, 4, 2, 3]
[4, 0, 1, 3, 2]
[1, 4, 3, 0, 2]
[0, 1, 3, 4, 2]


[2, 3, 4, 0, 1]
[2, 4, 0, 3, 1]
[1, 4, 2, 3, 0]
[3, 0, 1, 4, 2]
[0, 3, 1, 2, 4]

Output:
[4, 2, 0, 3, 1]

Trace

4 proposes to 0 [0,-1]  Accepted
3 proposes to 1 [1,-1]  Accepted
2 proposes to 4 [4,-1]  Accepted
1 proposes to 0 [0,4]  Rejected
1 proposes to 1 [1,3]  Rejected
1 proposes to 4 [4,2]  Accepted
2 proposes to 0 [0,4]  Accepted
4 proposes to 1 [1,3]  Accepted
3 proposes to 4 [4,1]  Accepted
1 proposes to 2 [2,-1]  Accepted
0 proposes to 4 [4,3]  Accepted
3 proposes to 3 [3,-1]  Accepted