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 C (GCC 5.4.1) (judge verdict: Wrong Answer)

#include <stdio.h>

#define N_MAX  5001

char s[N_MAX];
unsigned int ans[N_MAX][N_MAX];


int main(void)
{
    unsigned int n;
    unsigned int i, j, k;
    unsigned int len = 0;

    scanf("%d", &n);
    scanf("%s", s);

    for (i = 0; i < n; i++) {
        j = i + 1;
        while (j < n) {
            k = 0;
            while ((s[i + k] == s[j + k]) && (j + k < n) && (i + k < j)) {
                k++;
            }
            ans[i][j] = k;
            if (len <= ans[i][j]) {
                len = ans[i][j];
            }
            if (k == 0) {
                j++;
            } else {
                j += k;
            }
        }
    }

    printf("%d", len);

    return 0;
}