Three Prime Sum Challenge

You are given a positive integer n. Your task is to determine whether n can be expressed as the sum of three distinct prime numbers. In mathematical terms, you need to check if there exist three distinct prime numbers p₁, p₂, and p₃ such that:

\(p_{1} + p_{2} + p_{3} = n\)

If such primes exist, output YES; otherwise, output NO.

Note: The smallest sum of three primes (2, 3, and 5) is 10, so any n < 6 automatically returns NO.

inputFormat

The input consists of a single integer n provided via standard input (stdin).

outputFormat

Output a single line with either YES or NO via standard output (stdout) depending on whether n can be expressed as the sum of three distinct prime numbers.

23

YES