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)

n = gets.to_i
s = gets.chomp
(1..(n / 2)).to_a.reverse_each do |j|
  map = Hash.new{[]}
  (0...n).each do |i|
    next if i + j > n
    key = s.slice(i, j)
    map[key] = map[key].push([i, j])
  end
  map.each do |_, v|
    next if v.count <= 1
    prev = v.first
    v.each do |k|
      prev_sum = prev[0] + prev[1]
      cur_sum = k[0] + k[1]
      if cur_sum - prev_sum >= j
        puts j
        exit 0
      end
      prev = k
    end
  end
end
puts 0