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++14 (GCC 5.4.1) (judge verdict: Time Limit Exceeded)

#include <bits/stdc++.h>

using namespace std;

typedef long long ll;

const ll P = 43;
const ll MOD = 1e9+7;

int main(){

    int n;
    string s;
    cin >> n >> s;
    vector<ll> pw(n+1);
    pw[0] = 1;
    for(int i = 1; i <= n; i++)
        pw[i] = (pw[i-1]*P)%MOD;
    map<int, int> mp;
    int ans = 0;
    for(int i = 0; i < n; i++){
        ll hash = 0;
        for(int j = i, len = 1; j < n; j++, len++){
            hash = ( hash + (s[j]-'a'+1)*pw[len-1] )%MOD;
            if(mp.find(hash) != mp.end()){
                if(mp[hash]+len <= j)
                    ans = max(ans, len);
            }else{
                mp[hash] = j;
            }
        }
    }

    cout << ans << endl;
    return 0;
}