You are given a string \(S = S_0S_1 \cdots S_{n-1}\) of length n.
Find the sum of length of LCP(Longest Common Prefix) over all the \( \frac{n^2(n+1)^2}{4} \) ordered pairs of its substrings.
Formally, say the substring of S starting at index i and ending at index j is represented by \(S_{ij}\), and let \(L(A,B)\) represent the length of LCP of strings A and B.
Then compute the value of :

\( \displaystyle \large \sum_{i=0}^{n-1} \sum_{j=i}^{n-1} \sum_{k=0}^{n-1} \sum_{l=k}^{n-1} L(S_{ij},S_{kl}) \)

As this value may be very large, print it modulo 10^9 + 7

Input
The first line contains T, the number of test cases. It is followed by \(2T\) lines, describing the strings in the testcases . Each string is described by two lines.
The first line contains n, length of the string S.
Second line contains the string S consisting of lowercase english alphabets only.

Output
Print T lines containing the sum of lengths of lcp over all ordered pairs of substrings of S modulo 10^9+7 for the T testcases, each on a new line.

Constraints

\(T \le 5 \)
S consists of lowercase english alphabets only.
(25 points) : \(n \le 10^3 \)
(75 points) : \(n \le 10^5 \)