perl -le'$==1,(1x$_)=~/^(1|11)*(?{$=++})^/,print$=for 0..20'
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perl -le'$==1,(1x$_)=~/^(1|11(??{}))*(?{$=++})^/,print$=for 0..20'
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perl -le'$==0,(1x$_)=~/^(1|11(??{}))*$(?{$=++})^/,print$=for 0..20'
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1 (1)(1)(1)(1)(1)(1)
2 (1)(1)(1)(1)(1 1)
3 (1)(1)(1)(1 1)(1)
4 (1)(1)(1 1)(1)(1)
5 (1)(1)(1 1)(1 1)
6 (1)(1 1)(1)(1)(1)
7 (1)(1 1)(1)(1 1)
8 (1)(1 1)(1 1)(1)
9 (1 1)(1)(1)(1)(1)
10 (1 1)(1)(1)(1 1)
11 (1 1)(1)(1 1)(1)
12 (1 1)(1 1)(1)(1)
13 (1 1)(1 1)(1 1)
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1 (1)(1)(1)(1)
2 (1)(1)(1) 1
3 (1)(1)(1 1)
4 (1)(1) 1 1
5 (1)(1 1)(1)
6 (1)(1 1) 1
7 (1) 1 1 1
8 (1 1)(1)(1)
9 (1 1)(1) 1
10 (1 1)(1 1)
11 (1 1) 1 1
12 1 1 1 1