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 Java8 (OpenJDK 1.8.0) (judge verdict: Wrong Answer)

import java.util.Scanner;

public class Main {
    public static void debug(String str) {
        System.out.println(str);
    }

    public static void main(String[] args) {

        int N;
        String S;

        try (Scanner sc = new Scanner(System.in)) {
            N = sc.nextInt();
            S = sc.next();

        }
        //len(暫定値)
        int NStart = 0;
        int NEnd = N;
        int window =0;
        int result = 0;
        while (true) {

            window = (NEnd + NStart) / 2;

            //探索
            boolean check = chackSub(S, window);
            if (check) {
                result = window;
                NStart = window;
            } else {
                NEnd = window;
            }
            if(NEnd - NStart  <=1){
                break;
            }
        }

        System.out.println(result);
    }

    private static boolean chackSub(String S, int window) {
        int i = 0;
        while (true) {
            int start = i;
            int end = start + window;

            if (end + window > S.length()) {
                break;
            }
            String sub1 = S.substring(start, end);
            String sub2 = S.substring(end+1);

            if (sub2.contains(sub1)) {
                return true;
            }
            i++;
        }
        return false;
    }
}