C. Palindrome Partitiontime limit per test1 secondmemory limit per test256 megabytesinputstandard inputoutputstandard outputA substring is a continuous and non-empty segment of letters from a given string, without any reorders.An even palindrome is a string that reads the same backward as forward and has an even length. For example, strings "zz", "abba", "abccba" are even palindromes, but strings "codeforces", "reality", "aba", "c" are not.A beautiful string is an even palindrome or a string that can be partitioned into some smaller even palindromes.You are given a string s, consisting of n lowercase Latin letters. Count the number of beautiful substrings of s.InputEach test contains multiple test cases. The first line contains the number of test cases t (1 \le t \le 10^4). The description of the test cases follows.The first line of each test case contains a single integer n (1 \le n \le 5\cdot 10^5).The second line of each test case contains a string s. String s consists of only lowercase Latin letters and has a length of n.It is guaranteed that the sum of n over all test cases does not exceed 5\cdot 10^5.OutputFor each test case print the number of beautiful substrings.ExampleInput
66abaaba1a2aa6abcdef12accabccbacca6abbaaaOutput
3
0
1
0
14
6
NoteIn the first test case, the beautiful substrings are "abaaba", "baab", "aa".In the last test case, the beautiful substrings are "aa" (counted twice), "abba", "bb", "bbaa", "abbaaa".
66abaaba1a2aa6abcdef12accabccbacca6abbaaa
3 0 1 0 14 6 
['binary search', 'brute force', 'data structures', 'dp', 'hashing', 'strings', '*2600']