Prime Sum Pair

You are given an integer array. Your task is to determine whether there exist two distinct indices i and j (with i < j) such that the sum of the two corresponding elements is a prime number.

More formally, given an array a[0...n-1], you need to check if there exist indices i and j satisfying:

\(0 \leq i < j \leq n-1\)

such that the number \(S = a[i] + a[j]\) is prime. A number \(p\) is prime if \(p > 1\) and it has no divisors other than 1 and itself.

If at least one such pair exists, print True; otherwise, print False.

inputFormat

The first line of input contains an integer n, representing the number of elements in the array.

The second line contains n space-separated integers denoting the elements of the array.

If n is 0, the array is empty.

outputFormat

Print True if there exists at least one pair \( (i, j) \) with i < j such that the sum of a[i] + a[j] is a prime number. Otherwise, print False.

The output should be printed in a single line.

## sample

4
4 6 8 10

False

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