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 Ruby (2.3.3) (judge verdict: Time Limit Exceeded)

def who_says_a_pun(n, s)
  dp = Array.new(n + 1) { Array.new(n + 1, 0) }
  (n - 1).downto(0) do |i|
    (n - 1).downto(0) do |j|
      if s[i] != s[j]
        dp[i][j] = 0
      else
        dp[i][j] = dp[i + 1][j + 1] + 1
      end
    end
  end

  ans = 0
  0.upto(n - 1) do |i|
    (i + 1).upto(n -1) do |j|
      now = [dp[i][j], j - i].min
      ans = [now, ans].max
    end
  end
  ans
end

n = gets.to_i
s = gets.chomp
puts who_says_a_pun(n, s)