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 PyPy3 (2.4.0) (judge verdict: Wrong Answer)

N = int(input())
S = list(input())
ba = ord("a")
for i in range(N):
  S[i] = ord(S[i]) - ba + 1
B = 27
mod = 10 ** 11 + 7
def contain(a, b):
  al = len(a)
  bl = len(b)
  #print(al, a)
  if al > bl: return False
  t = pow(B, al)
  ah = 0; bh = 0
  for i in range(al):
    ah = ah * B + a[i]
    bh = bh * B + b[i]
  for i in range(bl - al + 1):
    if ah == bh: return True
    if i + al < bl:
      #print(i, i + al)
      bh = bh * B + b[i + al] - b[i] * t
  return False
res = 0
for i in range(N):
  r = min(i + N // 2, N + 1)
  l = i + res + 1
  m = (l + r) // 2
  if l > r: continue
  while r - l > 3:
    m = (l + r) // 2
    if contain(S[i: m], S[m: ]):
      l = m
      res = max(res, m - i)
    else:
      r = m
  if m <= N:
    if contain(S[i: m + 1], S[m + 1: ]):
      res = max(res, m + 1 - i)
  if m + 1 <= N:
    if contain(S[i: m + 2], S[m + 2: ]):
      res = max(res, m + 2 - i)
  if m + 2 <= N:
    if contain(S[i: m + 3], S[m + 3: ]):
      res = max(res, m + 3 - i)
print(res)