A8197. 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.

The first line contains the single integer $n$ ( $1<=n<=10^{5}$ ) — the number of tree vertexes. Next $n-1$ lines contain three integers each: $u_{i}$ $v_{i}$ $w_{i}$ ( $1<=u_{i},v_{i}<=n,1<=w_{i}<=10^{9}$ ) — the pair of vertexes connected by the edge and the edge's weight.

On the single line print the single number — the answer.

Please do not use the %lld specificator to read or write 64-bit numbers in С++. It is recommended to use the cin, cout streams or the %I64d specificator.

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: $4·3·2=24$ .