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 rec upper_bound l r p =
  if r <= 1 + l
  then l
  else let m = (l + r) / 2 in
       if p m 
       then upper_bound m r p
       else upper_bound l m p

let () = Scanf.scanf "%d\n%s" @@ fun n s ->
  let dp = Array.make_matrix (n + 1) (n + 1) 0 in
  let f k =
    for i = 0 to k - 1 do
      for j = 0 to n - k - 1 do
        dp.(i + 1).(j + 1) <-
          if s.[i] = s.[k + j]
          then 1 + dp.(i).(j)
          else max dp.(i + 1).(j) dp.(i).(j + 1)
      done
    done;
    dp.(k).(n - k) in
  Printf.printf "%d\n" @@
  f @@
  upper_bound 0 (n - 1) @@
  fun i -> f i <= f (i + 1)