Factorial Divisibility Check

Given a non-negative integer \(n\), determine whether \(n!\) is divisible by \(n+1\) (i.e. whether \(n+1\) divides \(n!\)). In other words, check if \(n! \mod (n+1)=0\). Output YES if the condition holds, and NO otherwise.

Recall that \(n!\) (n factorial) is defined as the product of all positive integers less than or equal to \(n\), with the convention \(0! = 1\). For example, \(3! = 1 \times 2 \times 3 = 6\).

inputFormat

The input consists of a single non-negative integer \(n\) (where \(n \ge 0\)).

outputFormat

Output a single line containing YES if \(n!\) is divisible by \(n+1\) and NO otherwise.

sample

0

YES