Palindrome Permutation

Given a string s, determine whether any permutation of the alphanumeric characters in s can form a palindrome. In this problem, spaces and all non-alphanumeric characters should be ignored, and uppercase and lowercase letters are considered equivalent.

A string can be rearranged into a palindrome if and only if at most one character has an odd frequency. More formally, if we let \(f(c)\) denote the frequency of character \(c\) (after converting the string to lowercase and filtering out non-alphanumeric characters), then there exists a permutation of the characters that forms a palindrome if and only if:

\[ \text{odd_count} = \sum_{c} \bigl[ f(c) \bmod 2 \neq 0 \bigr] \leq 1. \]

Your task is to implement a program that reads a single line from standard input and prints True if a palindrome permutation exists, and False otherwise.

inputFormat

The input consists of a single line containing the string s. The string may include spaces, punctuation, and mixed case letters.

outputFormat

Output a single line containing either True if any permutation of the string can form a palindrome, or False otherwise.

## sample

aabb

True