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 Scala (2.11.7) (judge verdict: Time Limit Exceeded)

import scala.collection.mutable
import scala.io.StdIn
import java.util._
import util.control.Breaks._

object Main extends App {
  StdIn.readLine()
  val l = StdIn.readLine()
  var max = 0
  for (c <- 0 until l.size){
    for(i <- 1 until l.size-c){
      if (l(c+i) == l(c)){
        breakable {
         // println(c,i)
          if (Math.min(i, l.size-c-i) > max) {
            for (j <- 0 until Math.min(i, l.size - c - i)) {
              //println(l(c + i + j), l(c + j))
              if (l(c + i + j) == l(c + j)) {
                if (j + 1 > max) max = j + 1
              } else break
            }
          }
        }
      }
    }
  }
  println(max)
}