Linus Sequence

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Problem

<img src=http://i.imgur.com/BfCoj.gif>

Define A as a sequence of 1 and 2 where:
A(1) = 1 and
A(n) minimizes the length of the longest possible doubled suffix of A(1..n).

For example, the next element of the sequence 1,2,1,1,2,2,1,2 would be a 1, which creates the longest doubled suffix of "(2,1),(2,1)", whereas putting a 2 instead would create a longer doubled suffix of "(1,2,2),(1,2,2)".

Output the first 1,000 elements of A.

- leonid

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now post-mortem time, all source codes will be revealed

Sample input:_

*NOTHING*

Sample output:

1211221211212211211122121122111211221211212211211122121122122211212211222122112122121122122211212211222122111211221211212211211122121122111211221211212211211122122211212211222122112122121122122211212211222122112122111211221211212211211122121122111211221211212211211122122211212211222122112122121122122211212211222122121122122211212211211122121122111211221211212211211122121122111211222122112122121122122211212211222122112122121122122211211122121122111211221211212211211122121122111211221211222122112122121122122211212211222122112122121122122211211122121122111211221211212211211122121122111211212211211122121122122211212211222122112122121122122211212211222122111211221211212211211122121122111211221211212211211122122211212211222122112122121122122211212211222122112122111211221211212211211122121122111211221211212211211122122211212211222122112122121122122211212211222122121122122211212211211122121122111211221211212211211122121122111211222122112122121122122211212211222122112122121122122211211122121122

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