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Given a string, determine if any of its permutations is a palindrome. A string is said to be a palindrome if the string read from left to right is equal to the string read from right to left. Assume lowercase string.

Examples:
`Input: "abcd"`
`Output: false`
`Explanation: No permutation of "abcd" reads the same as its reverse string.`

`Input: "abcdbca"`
`Output: true`
`Explanation: The permutation "abcdcba" reads the same as its reverse string.`