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: Accepted)

//PDF解説に倣ってZ-algorithm
#include<bits/stdc++.h>
using namespace std;

int main(){
  int n;
  string s;
  cin>> n >> s;
  
  int ans=0;
  for (int i=0; i<n; i++){
    vector<int> v(n);
    v[i]=n-i;
    int j=i+1,k=0;
    while (j<n){
      while (j+k<n && s[i+k]==s[j+k]) k++;
      v[j]=k;
      if (k==0){
        j++;
        continue;
      }
      int l=1;
      while (l+v[i+l]<k){
        v[j+l]=v[i+l];
        l++;
      }
      j+=l; k-=l;
    }
    for (int j=i+1; j<n-ans; j++){
      if (v[j]<=j-i) ans=max(ans,v[j]);
    }
  }
      
  cout<< ans <<endl;
}