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Points:
5 (partial)

Time limit:
1.0s

Memory limit:
64M

Authors:

Problem type

Allowed languages

Ada, Assembly, Awk, Brain****, C, C#, C++, COBOL, ~~CommonLisp~~, D, Dart, F#, Forth, Fortran, Go, ~~Groovy~~, Haskell, Intercal, Java, JS, Kotlin, Lisp, Lua, ~~Nim~~, ~~ObjC~~, OCaml, ~~Octave~~, Pascal, Perl, PHP, Pike, Prolog, Python, Racket, Ruby, Rust, Scala, Scheme, Sed, Swift, TCL, Text, Turing, VB, Zig

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.

#### Input Specification

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.

#### Output Specification

On the first line, output one integer, the number of good numbers in the list.

#### Constraints

##### Subtask 1 [30%]

##### Subtask 2 [70%]

No further constraints.

#### Sample Input

```
3
3
23
51
```

#### Sample Output

`2`

## Comments