given question is :-

Given a string of length N, find whether there exits an even length
palindrome substring.

question is unclear, you want a palindrome whose substring of even length 
is present in the given string of length N, right ? where the palindrome is 
itself formed from the given string.
so for

str = abcdtrwdcba
answers can be many, there is no restriction that palindrome itself has to 
be of even length, so if palindrome from above string is *abcdrdcba, *then 
substrings of even length present in str are *abcd, dcba.*
*
*
str = abcdtrwdcba
answers can be many, there is no restriction that palindrome itself has to 
be of even length, so if palindrome from above string is *abcdtdcba, *then 
substrings of even length present in str are *abcd, bcdt, dcba.*
*
*

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