Codeforces Round 873 (Div. 1) |
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binary search

brute force

data structures

dp

hashing

strings

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C. Palindrome Partition

time limit per test

1 secondmemory limit per test

256 megabytesinput

standard inputoutput

standard 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 $$$s$$$.

Input

Each 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 $$$5\cdot 10^5$$$.

Output

For each test case print the number of beautiful substrings.

Example

Input

66abaaba1a2aa6abcdef12accabccbacca6abbaaa

Output

3 0 1 0 14 6

Note

In 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".

Codeforces (c) Copyright 2010-2023 Mike Mirzayanov

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