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: Accepted)

use std::str::FromStr;
use std::fmt::Debug;
use std::cmp;

#[allow(dead_code)]
fn read_as_vec<T>() -> Vec<T>
where T: FromStr, <T as FromStr>::Err : Debug{
    let mut s = String::new();
    std::io::stdin().read_line(&mut s).unwrap();
    s.trim().split_whitespace().map(|c| T::from_str(c).unwrap()).collect()

}

#[allow(dead_code)]
fn read_as_string() -> String{
    let mut s = String::new();
    std::io::stdin().read_line(&mut s).unwrap();
    s.trim().to_string()
}

fn main(){

    let n: usize = read_as_vec()[0];
    let s: Vec<char> = read_as_string().chars().collect::<Vec<char>>();

    let mut ans: u64 = 0;
    for i in 0..n{
        let tmp_s: Vec<char>;
        if i > 0{
            tmp_s = s.clone().into_iter().skip(i).collect::<Vec<char>>();
        }else{
            tmp_s = s.clone();
        }
        // println!("\ni = {}", i);
        let res: Vec<u64> = z_algorithm(&tmp_s);
        // println!("res = {:?}", res);
        let mut tmp_ans = 0;
        for j in 1..tmp_s.len(){
            if res[j] <= j as u64 {
                tmp_ans = cmp::max(tmp_ans, res[j]);
            }
        }
        //println!("tmp_ans = {}", tmp_ans);
        ans = cmp::max(ans, tmp_ans);
    }

    println!("{}", ans);

}

fn z_algorithm(v: &Vec<char>) -> Vec<u64>{
    let mut z: Vec<u64> = vec![0;v.len()];
    z[0] = z.len() as u64;
    let (mut i, mut j): (usize, usize) = (1, 0);
    while i < v.len(){
        while i + j < v.len() && v[j] == v[i+j]{
            j += 1;
        }
         z[i] = j as u64;
         if j == 0{
            i += 1;
            continue;
        }

        let mut k: usize = 1;
        while i+k < v.len() && (k + z[k] as usize) < j{
            z[i+k] = z[k];
            k += 1;
        }
        i += k;
        j -= k;
    }
    z
}