A string A contains k lowercase letters and can form multiple subsequences (not necessarily contiguous). If each lowercase letter appears with the same frequency in a subsequence as in the original string, then this subsequence is considered a perfect subsequence. Given a string A, determine the number of its perfect subsequences.

For example, in the string "abca", the subsequences "a", "b", "c", "a", "ab", "bc", "ca", "aa", etc., are all valid.

Question

A string A contains k lowercase letters and can form multiple subsequences (not necessarily contiguous). If each lowercase letter appears with the same frequency in a subsequence as in the original string, then this subsequence is considered a perfect subsequence. Given a string A, determine the number of its perfect subsequences.​

For example, in the string "abca", the subsequences "a", "b", "c", "a", "ab", "bc", "ca", "aa", etc., are all valid.

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