Average of Prime Numbers

Given a list of n integers, compute the average of all the prime numbers present in the list. A prime number is defined as a natural number greater than 1 that has no positive divisors other than 1 and itself. If there are no prime numbers in the list, the output should be 0.0.

You can use the following mathematical formula for the arithmetic mean of primes:

\(\text{Average} = \frac{\sum_{p \in P} p}{|P|}\), where \(P\) is the set of prime numbers.

The input is read from standard input and the output is written to standard output.

inputFormat

The first line contains an integer n denoting the number of elements in the list. The second line contains n space-separated integers.

For example:

8
2 3 4 5 6 7 8 9

outputFormat

Output a single floating-point number which is the average of all prime numbers in the list. If there are no prime numbers, output 0.0.

For instance, for the sample input above, the output should be:

4.25

## sample

8
2 3 4 5 6 7 8 9

4.25