Problem:
Score : 500 points

Problem Statement

Given is a string S of length N.

Find the maximum length of a non-empty string that occurs twice or more in S as contiguous substrings without overlapping.

More formally, find the maximum positive integer len such that there exist integers l_1 and l_2 ( 1 \leq l_1, l_2 \leq N - len + 1 ) that satisfy the following:

l_1 + len \leq l_2

S[l_1+i] = S[l_2+i] (i = 0, 1, ..., len - 1)

If there is no such integer len, print 0.

Constraints

2 \leq N \leq 5 \times 10^3

|S| = N

S consists of lowercase English letters.

Input

Input is given from Standard Input in the following format:

N
S

Output

Print the maximum length of a non-empty string that occurs twice or more in S as contiguous substrings without overlapping. If there is no such non-empty string, print 0 instead.

Sample Input 1

5
ababa

Sample Output 1

2

The strings satisfying the conditions are: a, b, ab, and ba. The maximum length among them is 2, which is the answer.
Note that aba occurs twice in S as contiguous substrings, but there is no pair of integers l_1 and l_2 mentioned in the statement such that l_1 + len \leq l_2.

Sample Input 2

2
xy

Sample Output 2

0

No non-empty string satisfies the conditions.

Sample Input 3

13
strangeorange

Sample Output 3

5

Solution in OCaml (4.02.3) (judge verdict: Time Limit Exceeded)

let () =
    let main () =
        let n = int_of_string (read_line ()) in
        let s = read_line () in
        let rec loop_i i acc =
            let rec loop_j j acc =
                let rec loop_k k =
                    if j + k = n then k else
                        if i + k = j then k else
                        if s.[i + k] <> s.[j + k] then k else
                            loop_k (k + 1)
                in
                if j = n then acc else loop_j (j + 1) (max acc (loop_k 0))
            in
            if i = n - 1 then acc else loop_i (i + 1) (loop_j (i + 1) acc)
        in
        let r = loop_i 0 0 in
        Printf.printf "%d\n" r
    in
    main ()