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: Accepted)

def Z_algo(S):
    n = len(S)
    LCP = [0]*n
    i = 1
    j = 0
    c = 0#最も末尾側までLCPを求めたインデックス
    for i in range(1, n):
        #i番目からのLCPが以前計算したcからのLCPに含まれている場合
        if i+LCP[i-c] < c+LCP[c]:
            LCP[i] = LCP[i-c]
        else:
            j = max(0, c+LCP[c]-i)
            while i+j < n and S[j] == S[i+j]: j+=1
            LCP[i] = j
            c = i
    LCP[0] = n
    return LCP
  
ans = 0
N = int(input())
S = input()
for i in range(N):
    LCP = Z_algo(S[i:])
    for j, l in enumerate(LCP):
        tmp = min(l, j)
        ans = max(ans, tmp)
print(ans)