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: Time Limit Exceeded)

parseInt(x) = parse(Int, x)
parseMap(x::Array{SubString{String},1}) = map(parseInt, x)
mod(i,p)=i%p>0?i%p:i%p+p

function main()
	p = 10^9+7
	n = readline() |> parseInt
	t = readline() |> chomp
	s = zeros(Int,n)
	for i in 1:n
		s[i]=Int(t[i])
	end
	b = 101
	c = zeros(Int,n>>1+1)
	c[1] = 1
	for i in 1:n>>1
		c[i+1] = c[i]*b%p
	end
	m = 0
	for i in 1:n>>1
		for j in 1:n-2*i
			l = 0
			for k in 1:i
				l = mod(l+s[j+k-1]*c[i-k+1],p)
			end
			r = 0
			for k in 1:i
				r = mod(r+s[i+j+k-1]*c[i-k+1],p)
			end
			if l==r
				m = max(m,i)
			end
			for k in j+2*i:n
				r = mod(mod(mod(r-s[k-i]*c[i],p)*b,p)+s[k],p)
				if l==r
					m = max(m,i)
				end
			end
		end
	end
	println(m)
end

main()