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 Rust (1.15.1) (judge verdict: Wrong Answer)

use std::io::{self, BufRead, Write};

fn solve<R, W>(reader: R, mut writer: W)
where
    R: BufRead,
    W: Write,
{
    let mut lines = reader.lines();
    let _ = lines.next().unwrap().unwrap();
    let a_line = lines.next().unwrap().unwrap();
    let s: Vec<char> = a_line.trim().chars().collect();
    let n = s.len();

    let mut m = vec![vec![0; n]; n];

    let mut ans = 0;
    for i in 0..n {
        for j in i + 1..n {
            if s[i] == s[j] {
                m[i][j] = if i >= 1 && j >= 1 {
                    m[i - 1][j - 1] + 1
                } else {
                    0
                };
                if ans < m[i][j] {
                    ans = m[i][j];
                }
            }
        }
    }

    writeln!(&mut writer, "{}", ans).unwrap();
}

fn main() {
    let stdio = io::stdin();
    let input = stdio.lock();

    let output = io::stdout();

    solve(input, output);
}

#[cfg(test)]
mod tests {
    use super::*;

    const TESTS: &'static [(&'static [u8], &'static [u8])] = &[
        (
            br"5
ababa", br"2
",
        ),
        (
            br"2
xy", br"0
",
        ),
        (
            br"13
strangeorange", br"5
",
        ),
    ];

    #[test]
    fn test_e() {
        for &(input, expected) in TESTS {
            let mut output = Vec::new();
            solve(input, &mut output);
            let expected_str = String::from_utf8(expected.to_vec()).unwrap();
            let output_str = String::from_utf8(output).unwrap();
            assert_eq!(expected_str, output_str);
        }
    }
}