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 Kotlin (1.0.0) (judge verdict: Time Limit Exceeded)

//絶対時間足りないけど多分動くやつ
fun main(args: Array<String>){
  val N = readLine()!!.toInt()
  val S = readLine()!!

  var i = 0
  var result = 0
  var j: Int
  var k: Int
  while( i + result*2+1 < N ){
    j = 1
    while( i+j < N ){
      if( S[i] == S[i+j] ){
        k = 1
        while( i+j+k < N && S[i+k] == S[i+j+k] && i+k < i+j )
          k++
        if( result < k )
          result = k
      }
      j++
    }
    i++
  }

  println(result)
}