Identifier
Values
[[1,2]] => [2] => 100 => 1
[[2,2]] => [2] => 100 => 1
[[1],[2]] => [1,1] => 110 => 1
[[1,3]] => [2] => 100 => 1
[[2,3]] => [2] => 100 => 1
[[3,3]] => [2] => 100 => 1
[[1],[3]] => [1,1] => 110 => 1
[[2],[3]] => [1,1] => 110 => 1
[[1,1,2]] => [3] => 1000 => 1
[[1,2,2]] => [3] => 1000 => 1
[[2,2,2]] => [3] => 1000 => 1
[[1,1],[2]] => [2,1] => 1010 => 0
[[1,2],[2]] => [2,1] => 1010 => 0
[[1,4]] => [2] => 100 => 1
[[2,4]] => [2] => 100 => 1
[[3,4]] => [2] => 100 => 1
[[4,4]] => [2] => 100 => 1
[[1],[4]] => [1,1] => 110 => 1
[[2],[4]] => [1,1] => 110 => 1
[[3],[4]] => [1,1] => 110 => 1
[[1,1,3]] => [3] => 1000 => 1
[[1,2,3]] => [3] => 1000 => 1
[[1,3,3]] => [3] => 1000 => 1
[[2,2,3]] => [3] => 1000 => 1
[[2,3,3]] => [3] => 1000 => 1
[[3,3,3]] => [3] => 1000 => 1
[[1,1],[3]] => [2,1] => 1010 => 0
[[1,2],[3]] => [2,1] => 1010 => 0
[[1,3],[2]] => [2,1] => 1010 => 0
[[1,3],[3]] => [2,1] => 1010 => 0
[[2,2],[3]] => [2,1] => 1010 => 0
[[2,3],[3]] => [2,1] => 1010 => 0
[[1],[2],[3]] => [1,1,1] => 1110 => 2
[[1,1],[2,2]] => [2,2] => 1100 => 1
[[1,5]] => [2] => 100 => 1
[[2,5]] => [2] => 100 => 1
[[3,5]] => [2] => 100 => 1
[[4,5]] => [2] => 100 => 1
[[5,5]] => [2] => 100 => 1
[[1],[5]] => [1,1] => 110 => 1
[[2],[5]] => [1,1] => 110 => 1
[[3],[5]] => [1,1] => 110 => 1
[[4],[5]] => [1,1] => 110 => 1
[[1,1,4]] => [3] => 1000 => 1
[[1,2,4]] => [3] => 1000 => 1
[[1,3,4]] => [3] => 1000 => 1
[[1,4,4]] => [3] => 1000 => 1
[[2,2,4]] => [3] => 1000 => 1
[[2,3,4]] => [3] => 1000 => 1
[[2,4,4]] => [3] => 1000 => 1
[[3,3,4]] => [3] => 1000 => 1
[[3,4,4]] => [3] => 1000 => 1
[[4,4,4]] => [3] => 1000 => 1
[[1,1],[4]] => [2,1] => 1010 => 0
[[1,2],[4]] => [2,1] => 1010 => 0
[[1,4],[2]] => [2,1] => 1010 => 0
[[1,3],[4]] => [2,1] => 1010 => 0
[[1,4],[3]] => [2,1] => 1010 => 0
[[1,4],[4]] => [2,1] => 1010 => 0
[[2,2],[4]] => [2,1] => 1010 => 0
[[2,3],[4]] => [2,1] => 1010 => 0
[[2,4],[3]] => [2,1] => 1010 => 0
[[2,4],[4]] => [2,1] => 1010 => 0
[[3,3],[4]] => [2,1] => 1010 => 0
[[3,4],[4]] => [2,1] => 1010 => 0
[[1],[2],[4]] => [1,1,1] => 1110 => 2
[[1],[3],[4]] => [1,1,1] => 1110 => 2
[[2],[3],[4]] => [1,1,1] => 1110 => 2
[[1,1],[2,3]] => [2,2] => 1100 => 1
[[1,1],[3,3]] => [2,2] => 1100 => 1
[[1,2],[2,3]] => [2,2] => 1100 => 1
[[1,2],[3,3]] => [2,2] => 1100 => 1
[[2,2],[3,3]] => [2,2] => 1100 => 1
[[1,6]] => [2] => 100 => 1
[[2,6]] => [2] => 100 => 1
[[3,6]] => [2] => 100 => 1
[[4,6]] => [2] => 100 => 1
[[5,6]] => [2] => 100 => 1
[[6,6]] => [2] => 100 => 1
[[1],[6]] => [1,1] => 110 => 1
[[2],[6]] => [1,1] => 110 => 1
[[3],[6]] => [1,1] => 110 => 1
[[4],[6]] => [1,1] => 110 => 1
[[5],[6]] => [1,1] => 110 => 1
[[1,1,5]] => [3] => 1000 => 1
[[1,2,5]] => [3] => 1000 => 1
[[1,3,5]] => [3] => 1000 => 1
[[1,4,5]] => [3] => 1000 => 1
[[1,5,5]] => [3] => 1000 => 1
[[2,2,5]] => [3] => 1000 => 1
[[2,3,5]] => [3] => 1000 => 1
[[2,4,5]] => [3] => 1000 => 1
[[2,5,5]] => [3] => 1000 => 1
[[3,3,5]] => [3] => 1000 => 1
[[3,4,5]] => [3] => 1000 => 1
[[3,5,5]] => [3] => 1000 => 1
[[4,4,5]] => [3] => 1000 => 1
[[4,5,5]] => [3] => 1000 => 1
[[5,5,5]] => [3] => 1000 => 1
[[1,1],[5]] => [2,1] => 1010 => 0
[[1,2],[5]] => [2,1] => 1010 => 0
>>> Load all 406 entries. <<<
[[1,5],[2]] => [2,1] => 1010 => 0
[[1,3],[5]] => [2,1] => 1010 => 0
[[1,5],[3]] => [2,1] => 1010 => 0
[[1,4],[5]] => [2,1] => 1010 => 0
[[1,5],[4]] => [2,1] => 1010 => 0
[[1,5],[5]] => [2,1] => 1010 => 0
[[2,2],[5]] => [2,1] => 1010 => 0
[[2,3],[5]] => [2,1] => 1010 => 0
[[2,5],[3]] => [2,1] => 1010 => 0
[[2,4],[5]] => [2,1] => 1010 => 0
[[2,5],[4]] => [2,1] => 1010 => 0
[[2,5],[5]] => [2,1] => 1010 => 0
[[3,3],[5]] => [2,1] => 1010 => 0
[[3,4],[5]] => [2,1] => 1010 => 0
[[3,5],[4]] => [2,1] => 1010 => 0
[[3,5],[5]] => [2,1] => 1010 => 0
[[4,4],[5]] => [2,1] => 1010 => 0
[[4,5],[5]] => [2,1] => 1010 => 0
[[1],[2],[5]] => [1,1,1] => 1110 => 2
[[1],[3],[5]] => [1,1,1] => 1110 => 2
[[1],[4],[5]] => [1,1,1] => 1110 => 2
[[2],[3],[5]] => [1,1,1] => 1110 => 2
[[2],[4],[5]] => [1,1,1] => 1110 => 2
[[3],[4],[5]] => [1,1,1] => 1110 => 2
[[1,1],[2,4]] => [2,2] => 1100 => 1
[[1,1],[3,4]] => [2,2] => 1100 => 1
[[1,1],[4,4]] => [2,2] => 1100 => 1
[[1,2],[2,4]] => [2,2] => 1100 => 1
[[1,2],[3,4]] => [2,2] => 1100 => 1
[[1,3],[2,4]] => [2,2] => 1100 => 1
[[1,2],[4,4]] => [2,2] => 1100 => 1
[[1,3],[3,4]] => [2,2] => 1100 => 1
[[1,3],[4,4]] => [2,2] => 1100 => 1
[[2,2],[3,4]] => [2,2] => 1100 => 1
[[2,2],[4,4]] => [2,2] => 1100 => 1
[[2,3],[3,4]] => [2,2] => 1100 => 1
[[2,3],[4,4]] => [2,2] => 1100 => 1
[[3,3],[4,4]] => [2,2] => 1100 => 1
[[1,7]] => [2] => 100 => 1
[[2,7]] => [2] => 100 => 1
[[3,7]] => [2] => 100 => 1
[[4,7]] => [2] => 100 => 1
[[5,7]] => [2] => 100 => 1
[[6,7]] => [2] => 100 => 1
[[7,7]] => [2] => 100 => 1
[[1],[7]] => [1,1] => 110 => 1
[[2],[7]] => [1,1] => 110 => 1
[[3],[7]] => [1,1] => 110 => 1
[[4],[7]] => [1,1] => 110 => 1
[[5],[7]] => [1,1] => 110 => 1
[[6],[7]] => [1,1] => 110 => 1
[[1,1,6]] => [3] => 1000 => 1
[[1,2,6]] => [3] => 1000 => 1
[[1,3,6]] => [3] => 1000 => 1
[[1,4,6]] => [3] => 1000 => 1
[[1,5,6]] => [3] => 1000 => 1
[[1,6,6]] => [3] => 1000 => 1
[[2,2,6]] => [3] => 1000 => 1
[[2,3,6]] => [3] => 1000 => 1
[[2,4,6]] => [3] => 1000 => 1
[[2,5,6]] => [3] => 1000 => 1
[[2,6,6]] => [3] => 1000 => 1
[[3,3,6]] => [3] => 1000 => 1
[[3,4,6]] => [3] => 1000 => 1
[[3,5,6]] => [3] => 1000 => 1
[[3,6,6]] => [3] => 1000 => 1
[[4,4,6]] => [3] => 1000 => 1
[[4,5,6]] => [3] => 1000 => 1
[[4,6,6]] => [3] => 1000 => 1
[[5,5,6]] => [3] => 1000 => 1
[[5,6,6]] => [3] => 1000 => 1
[[6,6,6]] => [3] => 1000 => 1
[[1,1],[6]] => [2,1] => 1010 => 0
[[1,2],[6]] => [2,1] => 1010 => 0
[[1,6],[2]] => [2,1] => 1010 => 0
[[1,3],[6]] => [2,1] => 1010 => 0
[[1,6],[3]] => [2,1] => 1010 => 0
[[1,4],[6]] => [2,1] => 1010 => 0
[[1,6],[4]] => [2,1] => 1010 => 0
[[1,5],[6]] => [2,1] => 1010 => 0
[[1,6],[5]] => [2,1] => 1010 => 0
[[1,6],[6]] => [2,1] => 1010 => 0
[[2,2],[6]] => [2,1] => 1010 => 0
[[2,3],[6]] => [2,1] => 1010 => 0
[[2,6],[3]] => [2,1] => 1010 => 0
[[2,4],[6]] => [2,1] => 1010 => 0
[[2,6],[4]] => [2,1] => 1010 => 0
[[2,5],[6]] => [2,1] => 1010 => 0
[[2,6],[5]] => [2,1] => 1010 => 0
[[2,6],[6]] => [2,1] => 1010 => 0
[[3,3],[6]] => [2,1] => 1010 => 0
[[3,4],[6]] => [2,1] => 1010 => 0
[[3,6],[4]] => [2,1] => 1010 => 0
[[3,5],[6]] => [2,1] => 1010 => 0
[[3,6],[5]] => [2,1] => 1010 => 0
[[3,6],[6]] => [2,1] => 1010 => 0
[[4,4],[6]] => [2,1] => 1010 => 0
[[4,5],[6]] => [2,1] => 1010 => 0
[[4,6],[5]] => [2,1] => 1010 => 0
[[4,6],[6]] => [2,1] => 1010 => 0
[[5,5],[6]] => [2,1] => 1010 => 0
[[5,6],[6]] => [2,1] => 1010 => 0
[[1],[2],[6]] => [1,1,1] => 1110 => 2
[[1],[3],[6]] => [1,1,1] => 1110 => 2
[[1],[4],[6]] => [1,1,1] => 1110 => 2
[[1],[5],[6]] => [1,1,1] => 1110 => 2
[[2],[3],[6]] => [1,1,1] => 1110 => 2
[[2],[4],[6]] => [1,1,1] => 1110 => 2
[[2],[5],[6]] => [1,1,1] => 1110 => 2
[[3],[4],[6]] => [1,1,1] => 1110 => 2
[[3],[5],[6]] => [1,1,1] => 1110 => 2
[[4],[5],[6]] => [1,1,1] => 1110 => 2
[[1,1],[2,5]] => [2,2] => 1100 => 1
[[1,1],[3,5]] => [2,2] => 1100 => 1
[[1,1],[4,5]] => [2,2] => 1100 => 1
[[1,1],[5,5]] => [2,2] => 1100 => 1
[[1,2],[2,5]] => [2,2] => 1100 => 1
[[1,2],[3,5]] => [2,2] => 1100 => 1
[[1,3],[2,5]] => [2,2] => 1100 => 1
[[1,2],[4,5]] => [2,2] => 1100 => 1
[[1,4],[2,5]] => [2,2] => 1100 => 1
[[1,2],[5,5]] => [2,2] => 1100 => 1
[[1,3],[3,5]] => [2,2] => 1100 => 1
[[1,3],[4,5]] => [2,2] => 1100 => 1
[[1,4],[3,5]] => [2,2] => 1100 => 1
[[1,3],[5,5]] => [2,2] => 1100 => 1
[[1,4],[4,5]] => [2,2] => 1100 => 1
[[1,4],[5,5]] => [2,2] => 1100 => 1
[[2,2],[3,5]] => [2,2] => 1100 => 1
[[2,2],[4,5]] => [2,2] => 1100 => 1
[[2,2],[5,5]] => [2,2] => 1100 => 1
[[2,3],[3,5]] => [2,2] => 1100 => 1
[[2,3],[4,5]] => [2,2] => 1100 => 1
[[2,4],[3,5]] => [2,2] => 1100 => 1
[[2,3],[5,5]] => [2,2] => 1100 => 1
[[2,4],[4,5]] => [2,2] => 1100 => 1
[[2,4],[5,5]] => [2,2] => 1100 => 1
[[3,3],[4,5]] => [2,2] => 1100 => 1
[[3,3],[5,5]] => [2,2] => 1100 => 1
[[3,4],[4,5]] => [2,2] => 1100 => 1
[[3,4],[5,5]] => [2,2] => 1100 => 1
[[4,4],[5,5]] => [2,2] => 1100 => 1
[[1,8]] => [2] => 100 => 1
[[2,8]] => [2] => 100 => 1
[[3,8]] => [2] => 100 => 1
[[4,8]] => [2] => 100 => 1
[[5,8]] => [2] => 100 => 1
[[6,8]] => [2] => 100 => 1
[[7,8]] => [2] => 100 => 1
[[8,8]] => [2] => 100 => 1
[[1],[8]] => [1,1] => 110 => 1
[[2],[8]] => [1,1] => 110 => 1
[[3],[8]] => [1,1] => 110 => 1
[[4],[8]] => [1,1] => 110 => 1
[[5],[8]] => [1,1] => 110 => 1
[[6],[8]] => [1,1] => 110 => 1
[[7],[8]] => [1,1] => 110 => 1
[[1,1,7]] => [3] => 1000 => 1
[[1,2,7]] => [3] => 1000 => 1
[[1,3,7]] => [3] => 1000 => 1
[[1,4,7]] => [3] => 1000 => 1
[[1,5,7]] => [3] => 1000 => 1
[[1,6,7]] => [3] => 1000 => 1
[[1,7,7]] => [3] => 1000 => 1
[[2,2,7]] => [3] => 1000 => 1
[[2,3,7]] => [3] => 1000 => 1
[[2,4,7]] => [3] => 1000 => 1
[[2,5,7]] => [3] => 1000 => 1
[[2,6,7]] => [3] => 1000 => 1
[[2,7,7]] => [3] => 1000 => 1
[[3,3,7]] => [3] => 1000 => 1
[[3,4,7]] => [3] => 1000 => 1
[[3,5,7]] => [3] => 1000 => 1
[[3,6,7]] => [3] => 1000 => 1
[[3,7,7]] => [3] => 1000 => 1
[[4,4,7]] => [3] => 1000 => 1
[[4,5,7]] => [3] => 1000 => 1
[[4,6,7]] => [3] => 1000 => 1
[[4,7,7]] => [3] => 1000 => 1
[[5,5,7]] => [3] => 1000 => 1
[[5,6,7]] => [3] => 1000 => 1
[[5,7,7]] => [3] => 1000 => 1
[[6,6,7]] => [3] => 1000 => 1
[[6,7,7]] => [3] => 1000 => 1
[[7,7,7]] => [3] => 1000 => 1
[[1,1],[7]] => [2,1] => 1010 => 0
[[1,2],[7]] => [2,1] => 1010 => 0
[[1,7],[2]] => [2,1] => 1010 => 0
[[1,3],[7]] => [2,1] => 1010 => 0
[[1,7],[3]] => [2,1] => 1010 => 0
[[1,4],[7]] => [2,1] => 1010 => 0
[[1,7],[4]] => [2,1] => 1010 => 0
[[1,5],[7]] => [2,1] => 1010 => 0
[[1,7],[5]] => [2,1] => 1010 => 0
[[1,6],[7]] => [2,1] => 1010 => 0
[[1,7],[6]] => [2,1] => 1010 => 0
[[1,7],[7]] => [2,1] => 1010 => 0
[[2,2],[7]] => [2,1] => 1010 => 0
[[2,3],[7]] => [2,1] => 1010 => 0
[[2,7],[3]] => [2,1] => 1010 => 0
[[2,4],[7]] => [2,1] => 1010 => 0
[[2,7],[4]] => [2,1] => 1010 => 0
[[2,5],[7]] => [2,1] => 1010 => 0
[[2,7],[5]] => [2,1] => 1010 => 0
[[2,6],[7]] => [2,1] => 1010 => 0
[[2,7],[6]] => [2,1] => 1010 => 0
[[2,7],[7]] => [2,1] => 1010 => 0
[[3,3],[7]] => [2,1] => 1010 => 0
[[3,4],[7]] => [2,1] => 1010 => 0
[[3,7],[4]] => [2,1] => 1010 => 0
[[3,5],[7]] => [2,1] => 1010 => 0
[[3,7],[5]] => [2,1] => 1010 => 0
[[3,6],[7]] => [2,1] => 1010 => 0
[[3,7],[6]] => [2,1] => 1010 => 0
[[3,7],[7]] => [2,1] => 1010 => 0
[[4,4],[7]] => [2,1] => 1010 => 0
[[4,5],[7]] => [2,1] => 1010 => 0
[[4,7],[5]] => [2,1] => 1010 => 0
[[4,6],[7]] => [2,1] => 1010 => 0
[[4,7],[6]] => [2,1] => 1010 => 0
[[4,7],[7]] => [2,1] => 1010 => 0
[[5,5],[7]] => [2,1] => 1010 => 0
[[5,6],[7]] => [2,1] => 1010 => 0
[[5,7],[6]] => [2,1] => 1010 => 0
[[5,7],[7]] => [2,1] => 1010 => 0
[[6,6],[7]] => [2,1] => 1010 => 0
[[6,7],[7]] => [2,1] => 1010 => 0
[[1],[2],[7]] => [1,1,1] => 1110 => 2
[[1],[3],[7]] => [1,1,1] => 1110 => 2
[[1],[4],[7]] => [1,1,1] => 1110 => 2
[[1],[5],[7]] => [1,1,1] => 1110 => 2
[[1],[6],[7]] => [1,1,1] => 1110 => 2
[[2],[3],[7]] => [1,1,1] => 1110 => 2
[[2],[4],[7]] => [1,1,1] => 1110 => 2
[[2],[5],[7]] => [1,1,1] => 1110 => 2
[[2],[6],[7]] => [1,1,1] => 1110 => 2
[[3],[4],[7]] => [1,1,1] => 1110 => 2
[[3],[5],[7]] => [1,1,1] => 1110 => 2
[[3],[6],[7]] => [1,1,1] => 1110 => 2
[[4],[5],[7]] => [1,1,1] => 1110 => 2
[[4],[6],[7]] => [1,1,1] => 1110 => 2
[[5],[6],[7]] => [1,1,1] => 1110 => 2
[[1,1],[2,6]] => [2,2] => 1100 => 1
[[1,1],[3,6]] => [2,2] => 1100 => 1
[[1,1],[4,6]] => [2,2] => 1100 => 1
[[1,1],[5,6]] => [2,2] => 1100 => 1
[[1,1],[6,6]] => [2,2] => 1100 => 1
[[1,2],[2,6]] => [2,2] => 1100 => 1
[[1,2],[3,6]] => [2,2] => 1100 => 1
[[1,3],[2,6]] => [2,2] => 1100 => 1
[[1,2],[4,6]] => [2,2] => 1100 => 1
[[1,4],[2,6]] => [2,2] => 1100 => 1
[[1,2],[5,6]] => [2,2] => 1100 => 1
[[1,5],[2,6]] => [2,2] => 1100 => 1
[[1,2],[6,6]] => [2,2] => 1100 => 1
[[1,3],[3,6]] => [2,2] => 1100 => 1
[[1,3],[4,6]] => [2,2] => 1100 => 1
[[1,4],[3,6]] => [2,2] => 1100 => 1
[[1,3],[5,6]] => [2,2] => 1100 => 1
[[1,5],[3,6]] => [2,2] => 1100 => 1
[[1,3],[6,6]] => [2,2] => 1100 => 1
[[1,4],[4,6]] => [2,2] => 1100 => 1
[[1,4],[5,6]] => [2,2] => 1100 => 1
[[1,5],[4,6]] => [2,2] => 1100 => 1
[[1,4],[6,6]] => [2,2] => 1100 => 1
[[1,5],[5,6]] => [2,2] => 1100 => 1
[[1,5],[6,6]] => [2,2] => 1100 => 1
[[2,2],[3,6]] => [2,2] => 1100 => 1
[[2,2],[4,6]] => [2,2] => 1100 => 1
[[2,2],[5,6]] => [2,2] => 1100 => 1
[[2,2],[6,6]] => [2,2] => 1100 => 1
[[2,3],[3,6]] => [2,2] => 1100 => 1
[[2,3],[4,6]] => [2,2] => 1100 => 1
[[2,4],[3,6]] => [2,2] => 1100 => 1
[[2,3],[5,6]] => [2,2] => 1100 => 1
[[2,5],[3,6]] => [2,2] => 1100 => 1
[[2,3],[6,6]] => [2,2] => 1100 => 1
[[2,4],[4,6]] => [2,2] => 1100 => 1
[[2,4],[5,6]] => [2,2] => 1100 => 1
[[2,5],[4,6]] => [2,2] => 1100 => 1
[[2,4],[6,6]] => [2,2] => 1100 => 1
[[2,5],[5,6]] => [2,2] => 1100 => 1
[[2,5],[6,6]] => [2,2] => 1100 => 1
[[3,3],[4,6]] => [2,2] => 1100 => 1
[[3,3],[5,6]] => [2,2] => 1100 => 1
[[3,3],[6,6]] => [2,2] => 1100 => 1
[[3,4],[4,6]] => [2,2] => 1100 => 1
[[3,4],[5,6]] => [2,2] => 1100 => 1
[[3,5],[4,6]] => [2,2] => 1100 => 1
[[3,4],[6,6]] => [2,2] => 1100 => 1
[[3,5],[5,6]] => [2,2] => 1100 => 1
[[3,5],[6,6]] => [2,2] => 1100 => 1
[[4,4],[5,6]] => [2,2] => 1100 => 1
[[4,4],[6,6]] => [2,2] => 1100 => 1
[[4,5],[5,6]] => [2,2] => 1100 => 1
[[4,5],[6,6]] => [2,2] => 1100 => 1
[[5,5],[6,6]] => [2,2] => 1100 => 1
[[1]] => [1] => 10 => 1
[[2]] => [1] => 10 => 1
[[1,1]] => [2] => 100 => 1
[[3]] => [1] => 10 => 1
[[1,1,1]] => [3] => 1000 => 1
[[4]] => [1] => 10 => 1
[[5]] => [1] => 10 => 1
[[6]] => [1] => 10 => 1
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
Description
The number of indecomposable projective-injective modules in the algebra corresponding to a subset.
Let $A_n=K[x]/(x^n)$.
We associate to a nonempty subset S of an (n-1)-set the module $M_S$, which is the direct sum of $A_n$-modules with indecomposable non-projective direct summands of dimension $i$ when $i$ is in $S$ (note that such modules have vector space dimension at most n-1). Then the corresponding algebra associated to S is the stable endomorphism ring of $M_S$. We decode the subset as a binary word so that for example the subset $S=\{1,3 \} $ of $\{1,2,3 \}$ is decoded as 101.
Map
shape
Description
Return the shape of a tableau.
Map
to binary word
Description
Return the partition as binary word, by traversing its shape from the first row to the last row, down steps as 1 and left steps as 0.