A8454 | Lucky Pair

Petya loves lucky numbers very much. Everybody knows that lucky numbers are positive integers whose decimal record contains only the lucky digits 4 and 7. For example, numbers 47, 744, 4 are lucky and 5, 17, 467 are not.

Petya has an array $a$ of $n$ integers. The numbers in the array are numbered starting from $1$ . Unfortunately, Petya has been misbehaving and so, his parents don't allow him play with arrays that have many lucky numbers. It is guaranteed that no more than $1000$ elements in the array $a$ are lucky numbers.

Petya needs to find the number of pairs of non-intersecting segments $[l_{1};r_{1}]$ and $[l_{2};r_{2}]$ ( $1<=l_{1}<=r_{1}<l_{2}<=r_{2}<=n$ , all four numbers are integers) such that there's no such lucky number that occurs simultaneously in the subarray $a[l_{1}..r_{1}]$ and in the subarray $a[l_{2}..r_{2}]$ . Help Petya count the number of such pairs.

The first line contains an integer $n$ $(2<=n<=10^{5})$ — the size of the array $a$ . The second line contains $n$ space-separated integers $a_{i}$ ( $1<=a_{i}<=10^{9}$ ) — array $a$ . It is guaranteed that no more than $1000$ elements in the array $a$ are lucky numbers.

On the single line print the only number — the answer to the problem.

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