Jonathan is writing a problem for the GlobeX Canada Cup. However, he lost his ideas for the first ~3~ 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 ~p~ is prime if it only has two divisors, ~1~ and itself (~p~).
Given a list of ~N~ integers, find out how many of them are good numbers.
The first line will contain the integer ~N~ ~(1 \le N \le 5\,000)~, the number of integers to test.
The next ~N~ lines will each contain an integer, ~x~ ~(1 \le x \le 10^5)~, the integer to test.
On the first line, output one integer, the number of good numbers in the list.
Subtask 1 [30%]
~x \le 100~
Subtask 2 [70%]
No additional constraints.
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