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)

class String
  def z_algorithm
    n = size
    c = 0
    z = [0] * n
    ( 1 ... n ).each do |i|
      l = i - c
      if l < z[c] - z[l]
        z[i] = z[l] 
      else
        j = [0, z[c] - l].max
        j += 1 while i + j < n && self[j] == self[i+j]
        z[i] = j
        c = i
      end
    end
    #z[0] = n
    z
  end
end

class Array
  def z_algorithm
    n = size
    c = 0
    z = [0] * n
    ( 1 ... n ).each do |i|
      l = i - c
      if l < z[c] - z[l]
        z[i] = z[l]
      else
        j = [0, z[c] - l].max
        j += 1 while i + j < n && self[j] == self[i+j]
        z[i] = j
        c = i
      end
    end
    #z[0] = n
    z
  end
end

n = gets.to_s.to_i
s = gets.to_s.chomp

ans = 0
(n-1).times do |i|
  lcp = s[i, n-i].z_algorithm
  lcp.size.times do |j|
    l = [lcp[j], j].min
    ans = l if ans < l
  end
end

puts ans