Scansion

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Points: 10
Time limit: 1.0s
Memory limit: 16M

Problem type

Capba is doing a poetry analysis. He has scanned the lines of a poem and determined which syllables are stressed and which are unstressed. There are nineteen different "feet", that is, patterns of stressed and unstressed syllables. 0 represents an unstressed syllable and 1 represents a stressed syllable:

00   pyrrhic
01   iamb
10   trochee
11   spondee
000  tribrach
001  anapest
010  amphibrach
011  bacchius
100  dactyl
101  amphimacer
110  antibacchius
111  molossos
0001 fourth paeon
0010 third paeon
0011 ionic a minore
0100 second paeon
0110 antispast
1000 first paeon
1001 choriamb

A line with the pattern 001001, for example could be

  • two anapests;
  • a pyrrhic, a trochee, and an iamb;
  • a pyrrhic and a choriamb; or
  • a third paeon and an iamb.

Capba is having some trouble determining which.
He decides to guess the breakdown of the line into feet, and, through extensive shovelling, justify his assertion whether or not it be right (this leads to excellent results if done properly.) He would like to know how many different ways each line can be broken down into the feet as listed above.

Input Specification

Line 1: A sequence of ones or zeroes, up to 10\,000 characters long, corresponding to a pattern of stressed and unstressed syllables. 0 represents an unstressed syllable, 1 represents a stressed syllable.

Output Specification

An integer, on a single line – the number of ways that the given line can be broken down into feet, modulo 10\,007.

Sample Input

001001

Sample Output

4

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