A palindrome is a string that reads the same forwards and backwards.
For example, "abba" and "racecar" are palindromes.
An odd palindrome is a palindrome with an odd length.
For example, "racecar" is an odd palindrome but "abba" is not.
The middle letter of an odd palindrome is called its center.
Limak has a String **s** consisting of N lowercase English letters.
For each valid i, let X[i] be the number of palidromic subsequences of **s** such that their center is **s**[i].
In other words:
For a fixed i, there are exactly 2^(N-1) ways to erase some characters of **s** other than the character **s**[i].
X[i] is the number of ways of erasing for which the string that remains to the left of **s**[i] is the reverse of the string that remains to the right of **s**[i].
For each i, compute the value Y[i] = ((i+1) * X[i]) modulo 1,000,000,007.
Then, compute and return the bitwise XOR of all the values Y[i]. |