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 Julia (0.5.0) (judge verdict: Accepted)

function f(s)
	N=length(s)
	ret=zeros(Int,N)
	ret[1]=N
	i=1
	j=0
	while i<N
		while i+j<N&&s[j+1]==s[i+j+1]
			j+=1
		end
		ret[i+1]=j
		if j==0
			i+=1
			continue
		end
		k=1
		while i+k<N&&k+ret[k+1]<j
			ret[i+k+1]=ret[k+1]
			k+=1
		end
		i+=k
		j-=k
	end
	ret
end
function main()
	N=parse(Int,readline())
	s=chomp(readline())
	ans=0
	for i=1:N
		A=f(s[i:end])
		for j=0:N-i
			ans=max(ans,min(j,A[j+1]))
		end
	end
	println(ans)
end
main()