Jonathan is writing a problem for the GlobeX Canada Cup. However, he lost his ideas for the first problems of the junior division. So, Jonathan is making a problem about the numbers he loves the most: prime numbers. A good number is defined as an integer such that it is prime, and the sum of its digits is also prime. A number is prime if it only has two divisors, and itself ().
Given a list of integers, find out how many of them are good numbers.
The first line will contain the integer , the number of integers to test.
The next lines will each contain an integer, , the integer to test.
On the first line, output one integer, the number of good numbers in the list.
Subtask 1 [30%]
Subtask 2 [70%]
No further constraints.
3 3 23 51