edit this statistic or download as text // json
Identifier
  • St000012: Dyck paths ⟶ ℤ (values match St001295Gives the vector space dimension of the homomorphism space between J^2 and J^2.)
Values
=>
Cc0005;cc-rep
[1,0]=>0 [1,0,1,0]=>0 [1,1,0,0]=>1 [1,0,1,0,1,0]=>0 [1,0,1,1,0,0]=>1 [1,1,0,0,1,0]=>1 [1,1,0,1,0,0]=>2 [1,1,1,0,0,0]=>3 [1,0,1,0,1,0,1,0]=>0 [1,0,1,0,1,1,0,0]=>1 [1,0,1,1,0,0,1,0]=>1 [1,0,1,1,0,1,0,0]=>2 [1,0,1,1,1,0,0,0]=>3 [1,1,0,0,1,0,1,0]=>1 [1,1,0,0,1,1,0,0]=>2 [1,1,0,1,0,0,1,0]=>2 [1,1,0,1,0,1,0,0]=>3 [1,1,0,1,1,0,0,0]=>4 [1,1,1,0,0,0,1,0]=>3 [1,1,1,0,0,1,0,0]=>4 [1,1,1,0,1,0,0,0]=>5 [1,1,1,1,0,0,0,0]=>6 [1,0,1,0,1,0,1,0,1,0]=>0 [1,0,1,0,1,0,1,1,0,0]=>1 [1,0,1,0,1,1,0,0,1,0]=>1 [1,0,1,0,1,1,0,1,0,0]=>2 [1,0,1,0,1,1,1,0,0,0]=>3 [1,0,1,1,0,0,1,0,1,0]=>1 [1,0,1,1,0,0,1,1,0,0]=>2 [1,0,1,1,0,1,0,0,1,0]=>2 [1,0,1,1,0,1,0,1,0,0]=>3 [1,0,1,1,0,1,1,0,0,0]=>4 [1,0,1,1,1,0,0,0,1,0]=>3 [1,0,1,1,1,0,0,1,0,0]=>4 [1,0,1,1,1,0,1,0,0,0]=>5 [1,0,1,1,1,1,0,0,0,0]=>6 [1,1,0,0,1,0,1,0,1,0]=>1 [1,1,0,0,1,0,1,1,0,0]=>2 [1,1,0,0,1,1,0,0,1,0]=>2 [1,1,0,0,1,1,0,1,0,0]=>3 [1,1,0,0,1,1,1,0,0,0]=>4 [1,1,0,1,0,0,1,0,1,0]=>2 [1,1,0,1,0,0,1,1,0,0]=>3 [1,1,0,1,0,1,0,0,1,0]=>3 [1,1,0,1,0,1,0,1,0,0]=>4 [1,1,0,1,0,1,1,0,0,0]=>5 [1,1,0,1,1,0,0,0,1,0]=>4 [1,1,0,1,1,0,0,1,0,0]=>5 [1,1,0,1,1,0,1,0,0,0]=>6 [1,1,0,1,1,1,0,0,0,0]=>7 [1,1,1,0,0,0,1,0,1,0]=>3 [1,1,1,0,0,0,1,1,0,0]=>4 [1,1,1,0,0,1,0,0,1,0]=>4 [1,1,1,0,0,1,0,1,0,0]=>5 [1,1,1,0,0,1,1,0,0,0]=>6 [1,1,1,0,1,0,0,0,1,0]=>5 [1,1,1,0,1,0,0,1,0,0]=>6 [1,1,1,0,1,0,1,0,0,0]=>7 [1,1,1,0,1,1,0,0,0,0]=>8 [1,1,1,1,0,0,0,0,1,0]=>6 [1,1,1,1,0,0,0,1,0,0]=>7 [1,1,1,1,0,0,1,0,0,0]=>8 [1,1,1,1,0,1,0,0,0,0]=>9 [1,1,1,1,1,0,0,0,0,0]=>10 [1,0,1,0,1,0,1,0,1,0,1,0]=>0 [1,0,1,0,1,0,1,0,1,1,0,0]=>1 [1,0,1,0,1,0,1,1,0,0,1,0]=>1 [1,0,1,0,1,0,1,1,0,1,0,0]=>2 [1,0,1,0,1,0,1,1,1,0,0,0]=>3 [1,0,1,0,1,1,0,0,1,0,1,0]=>1 [1,0,1,0,1,1,0,0,1,1,0,0]=>2 [1,0,1,0,1,1,0,1,0,0,1,0]=>2 [1,0,1,0,1,1,0,1,0,1,0,0]=>3 [1,0,1,0,1,1,0,1,1,0,0,0]=>4 [1,0,1,0,1,1,1,0,0,0,1,0]=>3 [1,0,1,0,1,1,1,0,0,1,0,0]=>4 [1,0,1,0,1,1,1,0,1,0,0,0]=>5 [1,0,1,0,1,1,1,1,0,0,0,0]=>6 [1,0,1,1,0,0,1,0,1,0,1,0]=>1 [1,0,1,1,0,0,1,0,1,1,0,0]=>2 [1,0,1,1,0,0,1,1,0,0,1,0]=>2 [1,0,1,1,0,0,1,1,0,1,0,0]=>3 [1,0,1,1,0,0,1,1,1,0,0,0]=>4 [1,0,1,1,0,1,0,0,1,0,1,0]=>2 [1,0,1,1,0,1,0,0,1,1,0,0]=>3 [1,0,1,1,0,1,0,1,0,0,1,0]=>3 [1,0,1,1,0,1,0,1,0,1,0,0]=>4 [1,0,1,1,0,1,0,1,1,0,0,0]=>5 [1,0,1,1,0,1,1,0,0,0,1,0]=>4 [1,0,1,1,0,1,1,0,0,1,0,0]=>5 [1,0,1,1,0,1,1,0,1,0,0,0]=>6 [1,0,1,1,0,1,1,1,0,0,0,0]=>7 [1,0,1,1,1,0,0,0,1,0,1,0]=>3 [1,0,1,1,1,0,0,0,1,1,0,0]=>4 [1,0,1,1,1,0,0,1,0,0,1,0]=>4 [1,0,1,1,1,0,0,1,0,1,0,0]=>5 [1,0,1,1,1,0,0,1,1,0,0,0]=>6 [1,0,1,1,1,0,1,0,0,0,1,0]=>5 [1,0,1,1,1,0,1,0,0,1,0,0]=>6 [1,0,1,1,1,0,1,0,1,0,0,0]=>7 [1,0,1,1,1,0,1,1,0,0,0,0]=>8 [1,0,1,1,1,1,0,0,0,0,1,0]=>6 [1,0,1,1,1,1,0,0,0,1,0,0]=>7 [1,0,1,1,1,1,0,0,1,0,0,0]=>8 [1,0,1,1,1,1,0,1,0,0,0,0]=>9 [1,0,1,1,1,1,1,0,0,0,0,0]=>10 [1,1,0,0,1,0,1,0,1,0,1,0]=>1 [1,1,0,0,1,0,1,0,1,1,0,0]=>2 [1,1,0,0,1,0,1,1,0,0,1,0]=>2 [1,1,0,0,1,0,1,1,0,1,0,0]=>3 [1,1,0,0,1,0,1,1,1,0,0,0]=>4 [1,1,0,0,1,1,0,0,1,0,1,0]=>2 [1,1,0,0,1,1,0,0,1,1,0,0]=>3 [1,1,0,0,1,1,0,1,0,0,1,0]=>3 [1,1,0,0,1,1,0,1,0,1,0,0]=>4 [1,1,0,0,1,1,0,1,1,0,0,0]=>5 [1,1,0,0,1,1,1,0,0,0,1,0]=>4 [1,1,0,0,1,1,1,0,0,1,0,0]=>5 [1,1,0,0,1,1,1,0,1,0,0,0]=>6 [1,1,0,0,1,1,1,1,0,0,0,0]=>7 [1,1,0,1,0,0,1,0,1,0,1,0]=>2 [1,1,0,1,0,0,1,0,1,1,0,0]=>3 [1,1,0,1,0,0,1,1,0,0,1,0]=>3 [1,1,0,1,0,0,1,1,0,1,0,0]=>4 [1,1,0,1,0,0,1,1,1,0,0,0]=>5 [1,1,0,1,0,1,0,0,1,0,1,0]=>3 [1,1,0,1,0,1,0,0,1,1,0,0]=>4 [1,1,0,1,0,1,0,1,0,0,1,0]=>4 [1,1,0,1,0,1,0,1,0,1,0,0]=>5 [1,1,0,1,0,1,0,1,1,0,0,0]=>6 [1,1,0,1,0,1,1,0,0,0,1,0]=>5 [1,1,0,1,0,1,1,0,0,1,0,0]=>6 [1,1,0,1,0,1,1,0,1,0,0,0]=>7 [1,1,0,1,0,1,1,1,0,0,0,0]=>8 [1,1,0,1,1,0,0,0,1,0,1,0]=>4 [1,1,0,1,1,0,0,0,1,1,0,0]=>5 [1,1,0,1,1,0,0,1,0,0,1,0]=>5 [1,1,0,1,1,0,0,1,0,1,0,0]=>6 [1,1,0,1,1,0,0,1,1,0,0,0]=>7 [1,1,0,1,1,0,1,0,0,0,1,0]=>6 [1,1,0,1,1,0,1,0,0,1,0,0]=>7 [1,1,0,1,1,0,1,0,1,0,0,0]=>8 [1,1,0,1,1,0,1,1,0,0,0,0]=>9 [1,1,0,1,1,1,0,0,0,0,1,0]=>7 [1,1,0,1,1,1,0,0,0,1,0,0]=>8 [1,1,0,1,1,1,0,0,1,0,0,0]=>9 [1,1,0,1,1,1,0,1,0,0,0,0]=>10 [1,1,0,1,1,1,1,0,0,0,0,0]=>11 [1,1,1,0,0,0,1,0,1,0,1,0]=>3 [1,1,1,0,0,0,1,0,1,1,0,0]=>4 [1,1,1,0,0,0,1,1,0,0,1,0]=>4 [1,1,1,0,0,0,1,1,0,1,0,0]=>5 [1,1,1,0,0,0,1,1,1,0,0,0]=>6 [1,1,1,0,0,1,0,0,1,0,1,0]=>4 [1,1,1,0,0,1,0,0,1,1,0,0]=>5 [1,1,1,0,0,1,0,1,0,0,1,0]=>5 [1,1,1,0,0,1,0,1,0,1,0,0]=>6 [1,1,1,0,0,1,0,1,1,0,0,0]=>7 [1,1,1,0,0,1,1,0,0,0,1,0]=>6 [1,1,1,0,0,1,1,0,0,1,0,0]=>7 [1,1,1,0,0,1,1,0,1,0,0,0]=>8 [1,1,1,0,0,1,1,1,0,0,0,0]=>9 [1,1,1,0,1,0,0,0,1,0,1,0]=>5 [1,1,1,0,1,0,0,0,1,1,0,0]=>6 [1,1,1,0,1,0,0,1,0,0,1,0]=>6 [1,1,1,0,1,0,0,1,0,1,0,0]=>7 [1,1,1,0,1,0,0,1,1,0,0,0]=>8 [1,1,1,0,1,0,1,0,0,0,1,0]=>7 [1,1,1,0,1,0,1,0,0,1,0,0]=>8 [1,1,1,0,1,0,1,0,1,0,0,0]=>9 [1,1,1,0,1,0,1,1,0,0,0,0]=>10 [1,1,1,0,1,1,0,0,0,0,1,0]=>8 [1,1,1,0,1,1,0,0,0,1,0,0]=>9 [1,1,1,0,1,1,0,0,1,0,0,0]=>10 [1,1,1,0,1,1,0,1,0,0,0,0]=>11 [1,1,1,0,1,1,1,0,0,0,0,0]=>12 [1,1,1,1,0,0,0,0,1,0,1,0]=>6 [1,1,1,1,0,0,0,0,1,1,0,0]=>7 [1,1,1,1,0,0,0,1,0,0,1,0]=>7 [1,1,1,1,0,0,0,1,0,1,0,0]=>8 [1,1,1,1,0,0,0,1,1,0,0,0]=>9 [1,1,1,1,0,0,1,0,0,0,1,0]=>8 [1,1,1,1,0,0,1,0,0,1,0,0]=>9 [1,1,1,1,0,0,1,0,1,0,0,0]=>10 [1,1,1,1,0,0,1,1,0,0,0,0]=>11 [1,1,1,1,0,1,0,0,0,0,1,0]=>9 [1,1,1,1,0,1,0,0,0,1,0,0]=>10 [1,1,1,1,0,1,0,0,1,0,0,0]=>11 [1,1,1,1,0,1,0,1,0,0,0,0]=>12 [1,1,1,1,0,1,1,0,0,0,0,0]=>13 [1,1,1,1,1,0,0,0,0,0,1,0]=>10 [1,1,1,1,1,0,0,0,0,1,0,0]=>11 [1,1,1,1,1,0,0,0,1,0,0,0]=>12 [1,1,1,1,1,0,0,1,0,0,0,0]=>13 [1,1,1,1,1,0,1,0,0,0,0,0]=>14 [1,1,1,1,1,1,0,0,0,0,0,0]=>15 [1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0 [1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>1 [1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>1 [1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>2 [1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>3 [1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>1 [1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>2 [1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>2 [1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>3 [1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>4 [1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>3 [1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>4 [1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>5 [1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>6 [1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>1 [1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>2 [1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>2 [1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>3 [1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>4 [1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>2 [1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>3 [1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>3 [1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>4 [1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>5 [1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>4 [1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>5 [1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>6 [1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>7 [1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>3 [1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>4 [1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>4 [1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>5 [1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>6 [1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>5 [1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>6 [1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>7 [1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>8 [1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>6 [1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>7 [1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>8 [1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>9 [1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>10 [1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>1 [1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>2 [1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>2 [1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>3 [1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>4 [1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>2 [1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>3 [1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>3 [1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>4 [1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>5 [1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>4 [1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>5 [1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>6 [1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>7 [1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>2 [1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>3 [1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>3 [1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>4 [1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>5 [1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>3 [1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>4 [1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>4 [1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>5 [1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>6 [1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>5 [1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>6 [1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>7 [1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>8 [1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>4 [1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>5 [1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>5 [1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>6 [1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>7 [1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>6 [1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>7 [1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>8 [1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>9 [1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>7 [1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>8 [1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>9 [1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>10 [1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>11 [1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>3 [1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>4 [1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>4 [1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>5 [1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>6 [1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>4 [1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>5 [1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>5 [1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>6 [1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>7 [1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>6 [1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>7 [1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>8 [1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>9 [1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>5 [1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>6 [1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>6 [1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>7 [1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>8 [1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>7 [1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>8 [1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>9 [1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>10 [1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>8 [1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>9 [1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>10 [1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>11 [1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>12 [1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>6 [1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>7 [1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>7 [1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>8 [1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>9 [1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>8 [1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>9 [1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>10 [1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>11 [1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>9 [1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>10 [1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>11 [1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>12 [1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>13 [1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>10 [1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>11 [1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>12 [1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>13 [1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>14 [1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>15 [1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>1 [1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>2 [1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>2 [1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>3 [1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>4 [1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>2 [1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>3 [1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>3 [1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>4 [1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>5 [1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>4 [1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>5 [1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>6 [1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>7 [1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>2 [1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>3 [1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>3 [1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>4 [1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>5 [1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>3 [1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>4 [1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>4 [1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>5 [1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>6 [1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>5 [1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>6 [1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>7 [1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>8 [1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>4 [1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>5 [1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>5 [1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>6 [1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>7 [1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>6 [1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>7 [1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>8 [1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>9 [1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>7 [1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>8 [1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>9 [1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>10 [1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>11 [1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>2 [1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>3 [1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>3 [1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>4 [1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>5 [1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>3 [1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>4 [1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>4 [1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>5 [1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>6 [1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>5 [1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>6 [1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>7 [1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>8 [1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>3 [1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>4 [1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>4 [1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>5 [1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>6 [1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>4 [1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>5 [1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>5 [1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>6 [1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>7 [1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>6 [1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>7 [1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>8 [1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>9 [1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>5 [1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>6 [1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>6 [1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>7 [1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>8 [1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>7 [1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>8 [1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>9 [1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>10 [1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>8 [1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>9 [1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>10 [1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>11 [1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>12 [1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>4 [1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>5 [1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>5 [1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>6 [1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>7 [1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>5 [1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>6 [1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>6 [1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>7 [1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>8 [1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>7 [1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>8 [1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>9 [1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>10 [1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>6 [1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>7 [1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>7 [1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>8 [1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>9 [1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>8 [1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>9 [1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>10 [1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>11 [1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>9 [1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>10 [1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>11 [1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>12 [1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>13 [1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>7 [1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>8 [1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>8 [1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>9 [1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>10 [1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>9 [1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>10 [1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>11 [1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>12 [1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>10 [1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>11 [1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>12 [1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>13 [1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>14 [1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>11 [1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>12 [1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>13 [1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>14 [1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>15 [1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>16 [1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>3 [1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>4 [1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>4 [1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>5 [1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>6 [1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>4 [1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>5 [1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>5 [1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>6 [1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>7 [1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>6 [1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>7 [1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>8 [1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>9 [1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>4 [1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>5 [1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>5 [1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>6 [1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>7 [1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>5 [1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>6 [1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>6 [1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>7 [1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>8 [1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>7 [1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>8 [1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>9 [1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>10 [1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>6 [1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>7 [1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>7 [1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>8 [1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>9 [1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>8 [1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>9 [1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>10 [1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>11 [1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>9 [1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>10 [1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>11 [1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>12 [1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>13 [1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>5 [1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>6 [1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>6 [1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>7 [1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>8 [1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>6 [1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>7 [1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>7 [1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>8 [1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>9 [1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>8 [1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>9 [1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>10 [1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>11 [1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>7 [1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>8 [1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>8 [1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>9 [1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>10 [1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>9 [1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>10 [1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>11 [1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>12 [1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>10 [1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>11 [1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>12 [1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>13 [1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>14 [1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>8 [1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>9 [1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>9 [1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>10 [1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>11 [1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>10 [1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>11 [1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>12 [1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>13 [1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>11 [1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>12 [1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>13 [1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>14 [1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>15 [1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>12 [1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>13 [1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>14 [1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>15 [1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>16 [1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>17 [1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>6 [1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>7 [1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>7 [1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>8 [1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>9 [1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>7 [1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>8 [1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>8 [1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>9 [1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>10 [1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>9 [1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>10 [1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>11 [1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>12 [1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>8 [1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>9 [1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>9 [1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>10 [1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>11 [1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>10 [1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>11 [1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>12 [1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>13 [1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>11 [1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>12 [1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>13 [1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>14 [1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>15 [1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>9 [1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>10 [1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>10 [1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>11 [1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>12 [1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>11 [1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>12 [1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>13 [1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>14 [1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>12 [1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>13 [1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>14 [1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>15 [1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>16 [1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>13 [1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>14 [1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>15 [1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>16 [1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>17 [1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>18 [1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>10 [1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>11 [1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>11 [1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>12 [1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>13 [1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>12 [1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>13 [1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>14 [1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>15 [1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>13 [1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>14 [1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>15 [1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>16 [1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>17 [1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>14 [1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>15 [1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>16 [1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>17 [1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>18 [1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>19 [1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>15 [1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>16 [1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>17 [1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>18 [1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>19 [1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>20 [1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>21 [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0 [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>1 [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>1 [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>2 [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>3 [1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>1 [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>2 [1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>2 [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>3 [1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>4 [1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>3 [1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>4 [1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>5 [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>6 [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>1 [1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>2 [1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>2 [1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>3 [1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>4 [1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>2 [1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>3 [1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>3 [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>4 [1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>5 [1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>4 [1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>5 [1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>6 [1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>7 [1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>3 [1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>4 [1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>4 [1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>5 [1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>6 [1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>5 [1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>6 [1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>7 [1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>8 [1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>6 [1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>7 [1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>8 [1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>9 [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>10 [1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>1 [1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>2 [1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>2 [1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>3 [1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>4 [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>2 [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>3 [1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>3 [1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>4 [1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>5 [1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>4 [1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>5 [1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>6 [1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>7 [1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>2 [1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>3 [1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>3 [1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>4 [1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>5 [1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>3 [1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>4 [1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>4 [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>5 [1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>6 [1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>5 [1,0,1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>6 [1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>7 [1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>8 [1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>4 [1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>5 [1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>5 [1,0,1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>6 [1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>7 [1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>6 [1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>7 [1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>8 [1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>9 [1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>7 [1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>8 [1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>9 [1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>10 [1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>11 [1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>3 [1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>4 [1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>4 [1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>5 [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>6 [1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>4 [1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>5 [1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>5 [1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>6 [1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>7 [1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>6 [1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>7 [1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>8 [1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>9 [1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>5 [1,0,1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>6 [1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>6 [1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>7 [1,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>8 [1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>7 [1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>8 [1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>9 [1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>10 [1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>8 [1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>9 [1,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>10 [1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>11 [1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>12 [1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>6 [1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>7 [1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>7 [1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>8 [1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>9 [1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>8 [1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>9 [1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>10 [1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>11 [1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>9 [1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>10 [1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>11 [1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>12 [1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>13 [1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>10 [1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>11 [1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>12 [1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>13 [1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>14 [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>15 [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>1 [1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>2 [1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>2 [1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>3 [1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>4 [1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>2 [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>3 [1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>3 [1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>4 [1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>5 [1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>4 [1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>5 [1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>6 [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>7 [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>2 [1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>3 [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>3 [1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>4 [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>5 [1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>3 [1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>4 [1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>4 [1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>5 [1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>6 [1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>5 [1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>6 [1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>7 [1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>8 [1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>4 [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>5 [1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>5 [1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>6 [1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>7 [1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>6 [1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>7 [1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>8 [1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>9 [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>7 [1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>8 [1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>9 [1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>10 [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>11 [1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>2 [1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>3 [1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>3 [1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>4 [1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>5 [1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>3 [1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>4 [1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>4 [1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>5 [1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>6 [1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>5 [1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>6 [1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>7 [1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>8 [1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>3 [1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>4 [1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>4 [1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>5 [1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>6 [1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>4 [1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>5 [1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>5 [1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>6 [1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>7 [1,0,1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>6 [1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>7 [1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>8 [1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>9 [1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>5 [1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>6 [1,0,1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>6 [1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>7 [1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>8 [1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>7 [1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>8 [1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>9 [1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>10 [1,0,1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>8 [1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>9 [1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>10 [1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>11 [1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>12 [1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>4 [1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>5 [1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>5 [1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>6 [1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>7 [1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>5 [1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>6 [1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>6 [1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>7 [1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>8 [1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>7 [1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>8 [1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>9 [1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>10 [1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>6 [1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>7 [1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>7 [1,0,1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>8 [1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>9 [1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>8 [1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>9 [1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>10 [1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>11 [1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>9 [1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>10 [1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>11 [1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>12 [1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>13 [1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>7 [1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>8 [1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>8 [1,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>9 [1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>10 [1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>9 [1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>10 [1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>11 [1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>12 [1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>10 [1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>11 [1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>12 [1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>13 [1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>14 [1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>11 [1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>12 [1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>13 [1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>14 [1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>15 [1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>16 [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>3 [1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>4 [1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>4 [1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>5 [1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>6 [1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>4 [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>5 [1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>5 [1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>6 [1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>7 [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>6 [1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>7 [1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>8 [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>9 [1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>4 [1,0,1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>5 [1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>5 [1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>6 [1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>7 [1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>5 [1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>6 [1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>6 [1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>7 [1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>8 [1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>7 [1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>8 [1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>9 [1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>10 [1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>6 [1,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>7 [1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>7 [1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>8 [1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>9 [1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>8 [1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>9 [1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>10 [1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>11 [1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>9 [1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>10 [1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>11 [1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>12 [1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>13 [1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>5 [1,0,1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>6 [1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>6 [1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>7 [1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>8 [1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>6 [1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>7 [1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>7 [1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>8 [1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>9 [1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>8 [1,0,1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>9 [1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>10 [1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>11 [1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>7 [1,0,1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>8 [1,0,1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>8 [1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>9 [1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>10 [1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>9 [1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>10 [1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>11 [1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>12 [1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>10 [1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>11 [1,0,1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>12 [1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>13 [1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>14 [1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>8 [1,0,1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>9 [1,0,1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>9 [1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>10 [1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>11 [1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>10 [1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>11 [1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>12 [1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>13 [1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>11 [1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>12 [1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>13 [1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>14 [1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>15 [1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>12 [1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>13 [1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>14 [1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>15 [1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>16 [1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>17 [1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>6 [1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>7 [1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>7 [1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>8 [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>9 [1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>7 [1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>8 [1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>8 [1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>9 [1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>10 [1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>9 [1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>10 [1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>11 [1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>12 [1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>8 [1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>9 [1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>9 [1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>10 [1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>11 [1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>10 [1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>11 [1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>12 [1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>13 [1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>11 [1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>12 [1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>13 [1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>14 [1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>15 [1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>9 [1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>10 [1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>10 [1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>11 [1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>12 [1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>11 [1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>12 [1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>13 [1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>14 [1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>12 [1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>13 [1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>14 [1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>15 [1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>16 [1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>13 [1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>14 [1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>15 [1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>16 [1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>17 [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>18 [1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>10 [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>11 [1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>11 [1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>12 [1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>13 [1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>12 [1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>13 [1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>14 [1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>15 [1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>13 [1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>14 [1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>15 [1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>16 [1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>17 [1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>14 [1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>15 [1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>16 [1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>17 [1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>18 [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>19 [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>15 [1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>16 [1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>17 [1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>18 [1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>19 [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>20 [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>21 [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>1 [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>2 [1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0]=>2 [1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0]=>3 [1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0]=>4 [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0]=>2 [1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0]=>3 [1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0]=>3 [1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0]=>4 [1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0]=>5 [1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0]=>4 [1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0]=>5 [1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0]=>6 [1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0]=>7 [1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0]=>2 [1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0]=>3 [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0]=>3 [1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0]=>4 [1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0]=>5 [1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0]=>3 [1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0]=>4 [1,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0]=>4 [1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0]=>5 [1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0]=>6 [1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0]=>5 [1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0]=>6 [1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0]=>7 [1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0]=>8 [1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0]=>4 [1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0]=>5 [1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0]=>5 [1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0]=>6 [1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0]=>7 [1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0]=>6 [1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0]=>7 [1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0]=>8 [1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0]=>9 [1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0]=>7 [1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0]=>8 [1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0]=>9 [1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0]=>10 [1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]=>11 [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>2 [1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0]=>3 [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0]=>3 [1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0]=>4 [1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0]=>5 [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0]=>3 [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>4 [1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0]=>4 [1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0]=>5 [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0]=>6 [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0]=>5 [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>6 [1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0]=>7 [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>8 [1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0]=>3 [1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0]=>4 [1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0]=>4 [1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0]=>5 [1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0]=>6 [1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0]=>4 [1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0]=>5 [1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0]=>5 [1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0]=>6 [1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0]=>7 [1,1,0,0,1,1,0,1,0,1,1,0,0,0,1,0]=>6 [1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0]=>7 [1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0]=>8 [1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0]=>9 [1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0]=>5 [1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0]=>6 [1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0]=>6 [1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0]=>7 [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0]=>8 [1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0]=>7 [1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0]=>8 [1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0]=>9 [1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0]=>10 [1,1,0,0,1,1,0,1,1,1,0,0,0,0,1,0]=>8 [1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0]=>9 [1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0]=>10 [1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0]=>11 [1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0]=>12 [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0]=>4 [1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0]=>5 [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0]=>5 [1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0]=>6 [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>7 [1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0]=>5 [1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>6 [1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0]=>6 [1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0]=>7 [1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0]=>8 [1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0]=>7 [1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]=>8 [1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0]=>9 [1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0]=>10 [1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0]=>6 [1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0]=>7 [1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0]=>7 [1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0]=>8 [1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0]=>9 [1,1,0,0,1,1,1,0,1,0,1,0,0,0,1,0]=>8 [1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0]=>9 [1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0]=>10 [1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0]=>11 [1,1,0,0,1,1,1,0,1,1,0,0,0,0,1,0]=>9 [1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0]=>10 [1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0]=>11 [1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0]=>12 [1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0]=>13 [1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0]=>7 [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>8 [1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0]=>8 [1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0]=>9 [1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0]=>10 [1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0]=>9 [1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]=>10 [1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0]=>11 [1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0]=>12 [1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0]=>10 [1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0]=>11 [1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0]=>12 [1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0]=>13 [1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0]=>14 [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>11 [1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0]=>12 [1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0]=>13 [1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0]=>14 [1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0]=>15 [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>16 [1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>2 [1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0]=>3 [1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0]=>3 [1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0]=>4 [1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0]=>5 [1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0]=>3 [1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0]=>4 [1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0]=>4 [1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0]=>5 [1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0]=>6 [1,1,0,1,0,0,1,0,1,1,1,0,0,0,1,0]=>5 [1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0]=>6 [1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0]=>7 [1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0]=>8
search for individual values
searching the database for the individual values of this statistic
/ search for generating function
searching the database for statistics with the same generating function
click to show known generating functions       
Description
The area of a Dyck path.
This is the number of complete squares in the integer lattice which are below the path and above the x-axis. The 'half-squares' directly above the axis do not contribute to this statistic.
1. Dyck paths are bijection with area sequences $(a_1,\ldots,a_n)$ such that $a_1 = 0, a_{k+1} \leq a_k + 1$.
2. The generating function $\mathbf{D}_n(q) = \sum_{D \in \mathfrak{D}_n} q^{\operatorname{area}(D)}$ satisfy the recurrence $$\mathbf{D}_{n+1}(q) = \sum q^k \mathbf{D}_k(q) \mathbf{D}_{n-k}(q).$$
3. The area is equidistributed with St000005The bounce statistic of a Dyck path. and St000006The dinv of a Dyck path.. Pairs of these statistics play an important role in the theory of $q,t$-Catalan numbers.
References
[1] Haglund, J. The $q$,$t$-Catalan numbers and the space of diagonal harmonics MathSciNet:2371044
Code
def statistic(x):
    return x.area()
Created
Sep 27, 2011 at 19:29 by Chris Berg
Updated
Jun 17, 2019 at 17:03 by Christian Stump