Some information about task TWOFIVE

There are over 700 million valid words. Therfore, in computing the
number that corresponds to a word, we must avoid explicitly counting
every lexicographically preceding word.  The key observation is that
the number of valid words consistent within an assignment of the first
k letters of the alphabet (i.e. A .. letter[k]) to a set of locations
depends on the locations occupied by these letters, but not on which
letter is assigned to each location.  For example, the number of valid
words consistent with the letters A..G in either of the configurations
below is the same:

Configuration 1:	A B E F
			C G
			D
Configuration 2:
			A D F G
			B E
			C
This is enough to permit a dynammic programming approach to succeed in
the permitted time.  Indeed, we have an "untuned" 8 millisecond solution.

20 test cases were given as 10 pairs. The first of each pair gives a
word, from which we are to compute the number, while the second asks
for the inverse computation.  As a consequence, brute forse does work
for small numbers and their inverses.

The data consisted of:

3 and its inverse, "ABCDEFGHIJKLMNOPQRSVTUWXY";
20 and its inverse;
1 000 000 and its inverse;
the maximum number (701149020) and its inverse;
and seven other essentially random nine digit values.

Case  T          N  
----  -  ---------
  1   W         20
  2   N         20
  3   W          3
  4   N          3
  5   W  701149020  Last word in the lexicon
  6   N  701149020
  7   W    1000000
  8   N    1000000
  9   W  350574511
 10   N  350574511
 11   W  106407948
 12   N  106407948
 13   W  100000000
 14   N  100000000
 15   W  299925684
 16   N  299925684
 17   W  699509817
 18   N  699509817
 19   W  660689109
 20   N  660689109

where
  T = kind of case (W or N)
  N = ordinal number