Pre-Post-erous!

Time Limit: 2 Seconds
Memory Limit: 65536 KB

We are all familiar with pre-order, in-order and post-order traversals of binary
trees. A common problem in data structure classes is to find the pre-order traversal
of a binary tree when given the in-order and post-order traversals. Alternatively,
you can find the post-order traversal when given the in-order and pre-order.
However, in general you cannot determine the in-order traversal of a tree when
given its pre-order and post-order traversals. Consider the four binary trees
below:

All of these trees have the same pre-order and post-order traversals. This
phenomenon is not restricted to binary trees, but holds for general m-ary trees
as well.

**Input**

Input will consist of multiple problem instances. Each instance will consist
of a line of the form

m s1 s2

indicating that the trees are m-ary trees, s1 is the pre-order traversal and
s2 is the post-order traversal. All traversal strings will consist of lowercase
alphabetic characters. For all input instances, 1 <= m <= 20 and the length
of s1 and s2 will be between 1 and 26 inclusive. If the length of s1 is k (which
is the same as the length of s2, of course), the first k letters of the alphabet
will be used in the strings. An input line of 0 will terminate the input.

**Output**

For each problem instance, you should output one line containing the number
of possible trees which would result in the pre-order and post-order traversals
for the instance. All output values will be within the range of a 32-bit signed
integer. For each problem instance, you are guaranteed that there is at least
one tree with the given pre-order and post-order traversals.

**Sample Input**

2 abc cba

2 abc bca

10 abc bca

13 abejkcfghid jkebfghicda

0

**Sample Output**

4

1

45

207352860

Source:

**East Central North America 2002**
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