Factorization of permutations
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We consider the problem of factoring a permutation as product of special types of 
permutations.

Here are some smaple questions.

1) How to factor a permutation in S_n as the product of the long cycle (1,2,...,n)
   and the transposition (1,2).

2) Fix m in {2,..., n}.
   How to factor a permutation in S_n as the product of transpositions (i,j) with
           |i-j| < m.

3) How to factor a permutation in S_n as the product of transpositions:
       (1,2), (2,3), ..., (n-1,n), (n,1).

4) How to factor a permutation in S_N with N = 2^n using the transposition corresponding
   to controlled qubits.