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: Wrong Answer)

import collection.mutable.PriorityQueue

object Main {
  def main(args:Array[String]) = {
    val sc = new java.util.Scanner(System.in)
    val n = sc.nextInt
    val s = sc.next
    var rw = new Array[Int](0) :+ 0
    var sum = 0
    val a = 'a'.toInt
    s.foreach { v =>
      sum += (v.toInt - a)
      rw = rw :+ sum
    }
    //println(rw.deep)
    for(len <- (s.length-1)/2 to (1, -1)) {
      for(i <- 0 to s.length-len) {
        for(j <- i+len to s.length-len) {
          if (rw(i+len)-rw(i) == rw(j+len)-rw(j)) {
            //println(s.substring(i, i+len))
            //println(s.substring(j, j+len))
            if (s.substring(i, i+len) == s.substring(j, j+len)) {
              println(len)
              System.exit(0)
            }
          }
        }
      }
    }
    println(0)
  }
}