CF109C Lucky Tree

Petya loves lucky numbers. We all know that lucky numbers are the positive integers whose decimal representations contain only the lucky digits 4 and 7. For example, numbers 47, 744, 4 are lucky and 5, 17, 467 are not. One day Petya encountered a tree with $ n $ vertexes. Besides, the tree was weighted, i. e. each edge of the tree has weight (a positive integer). An edge is lucky if its weight is a lucky number. Note that a tree with $ n $ vertexes is an undirected connected graph that has exactly $ n-1 $ edges. Petya wondered how many vertex triples $ (i,j,k) $ exists that on the way from $ i $ to $ j $ , as well as on the way from $ i $ to $ k $ there must be at least one lucky edge (all three vertexes are pairwise distinct). The order of numbers in the triple matters, that is, the triple $ (1,2,3) $ is not equal to the triple $ (2,1,3) $ and is not equal to the triple $ (1,3,2) $ . Find how many such triples of vertexes exist.

N/A

N/A

The $ 16 $ triples of vertexes from the first sample are: $ (1,2,4),(1,4,2),(2,1,3),(2,1,4),(2,3,1),(2,3,4),(2,4,1),(2,4,3),(3,2,4),(3,4,2),(4,1,2),(4,1,3),(4,2,1),(4,2,3),(4,3,1),(4,3,2) $ . In the second sample all the triples should be counted: $ 4·3·2=24 $ .