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)

N=parse(Int,readline())
S=readline()
S="?"*S
#dp=[[0 for j in range(N+1)]for i in range(N+1)]
dp=zeros(Int,N+1,N+1)
res=0
for l in 2:N
    for r in (l+res):(N+1)
        global res
        if S[l]==S[r]
            
            dp[l,r]=min(dp[l-1,r-1]+1,r-l)
            res=max(res,dp[l,r])
        else
            #println(l,r)
            #println(dp)
            dp[l,r]=0
        end
    end
end

print(res)