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 = input()


def check(l):
    if l == 0:
        return True
    for i in range(n-l*2 + 1):
        cnt = 0
        k = 0
        for j in range(i+l, n):
            if s[i+k] == s[j]:
                k += 1
                cnt += 1
            else:
                if j > n-l:
                    break

                j -= k
                k = 0
                cnt = 0

            if cnt == l:
                # print(l, i, j, cnt,)
                return True

    return False


lb = 0
ub = n // 2 + 1
while ub - lb > 1:
    mid = (ub + lb) // 2
    if check(mid):
        lb = mid
    else:
        ub = mid

print(lb)