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: Wrong Answer)

let () =
    let main () =
        let n = int_of_string (read_line ()) in
        let s = read_line () in
        let compare_sa rank k i j =
            let c = compare rank.(i) rank.(j) in
            if c <> 0 then c else
                let ri = if i + k <= n then rank.(i + k) else (-1) in
                let rj = if j + k <= n then rank.(j + k) else (-1) in
                compare ri rj
        in
        let construct_sa s n =
            let sa   = Array.init (n + 1) (fun i -> i) in
            let rec loop_k rank k =
                if k > n then sa else (
                    Array.sort (compare_sa rank k) sa;
                    let tmp = Array.make (n + 1) 0 in
                    tmp.(sa.(0)) <- 0;
                    for i = 1 to n do
                        tmp.(sa.(i)) <- tmp.(sa.(i - 1)) + if compare_sa rank k sa.(i - 1) sa.(i) < 0 then 1 else 0
                    done;
                    loop_k tmp (k * 2)
                )
            in
            let rank = Array.init (n + 1) (fun i -> if i < n then int_of_char s.[i] else (-1)) in
            loop_k rank 1;
        in
        let sa = construct_sa s n in

        let construct_lcp s n sa =
            let rank = Array.make (n + 1) 0 in
            for i = 0 to n do rank.(sa.(i)) <- i done;
            let lcp = Array.make (n + 1) 0 in
            let rec loop_i i h =
                if i = n then lcp else (
                    let j = sa.(rank.(i) - 1) in
                    let h = if h > 0 then h - 1 else h in
                    let rec loop_h h =
                        if j + h >= n || i + h >= n then h else (
                            if s.[j + h] <> s.[i + h] then h else
                                if (i < j && i + h >= j) || (j < i && j + h >= i) then h else
                                loop_h (h + 1)
                        )
                    in
                    let h = loop_h h in
                    lcp.(rank.(i) - 1) <- h;
                    loop_i (i + 1) h
                )
            in
            loop_i 0 0
        in
        let lcp = construct_lcp s n sa in
        let r = Array.fold_left max 0 lcp in
        Printf.printf "%d\n" r
    in
    main ()