Can You Rearrange to Prime?

Given a positive integer \(N\), determine whether it is possible to rearrange its digits to form a prime number. The rearranged number must be a prime and should not have any leading zeroes.

For instance, for \(N = 13\), rearranging the digits can yield \(31\), which is a prime number, hence the answer is True. However, for \(N = 15\), no permutation of its digits results in a prime number, so the answer is False.

Note: The check must consider all permutations of the digits without allowing a permutation that starts with a zero.

inputFormat

The input consists of a single line containing a positive integer \(N\). This will be provided via standard input (stdin).

outputFormat

Output a single line: True if some permutation of the digits of \(N\) forms a prime number (with no leading zeros), and False otherwise. The output should be written to standard output (stdout).

13

True