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 Z_Algorithm_ex(s, lim)
  ret = Array.new(s.size, 0)
  wk = 0
  i, j = [1, 0]
  i = lim if lim > 0
  while i < s.size do
    break if s.size - i < lim
    while i+j < s.size && s[j] == s[i+j] do j += 1 end
    ret[i] = j
    wk = calc(wk, i, j)
    (i += 1; next) if j == 0
    k = 1
    while i+k < s.size && k + ret[k] < j do
      ret[j+k] = ret[k]
      wk = calc(wk, j+k, ret[k])
      k += 1
    end
    i += k
    j -= k
  end
  wk
end

def calc(wk, i, j)
  tmp = i > j ? j : i
  wk < tmp ? tmp : wk
end

N = gets.to_i
S = gets.chomp.chars

ans = 0
(0..(N-2)).each{|i|
  break if i + ans > N
  wk = Z_Algorithm_ex(S[i...N], ans)
  ans = wk if ans < wk
}

puts ans