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)

//object ABC141EJvm {
object Main {

  def main(args: Array[String]): Unit = println(solve(parse()))

  def solve(input: (Int, String)): Int = {
    val (n, s) = input
    val maxSubStringLength = s.length / 2 - (if (s.length % 2 == 0) 1 else 0)
    val r = (1 to maxSubStringLength).reverse.find { i =>
      (0 until i).exists { j =>
        val slicedString = s.slice(j, j + i)
        (s.take(j) ++ s.drop(j + i)).contains(slicedString)
      }
    }.toList
    if (r.isEmpty) 0 else r.max
  }

  def parse(): (Int, String) = {
    val input: List[String] = io.Source.stdin.getLines().toList
    val n :: s :: Nil = input
    (n.toInt, s)
  }
}