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 JavaScript (node.js v5.12) (judge verdict: Time Limit Exceeded)

const main = (input) => {
  var N = input[0]-0;
  var str = input[1];
  var ans = 0;
  var min = 0;
  var max = ~~(N/2);
  start:while(min<=max){
    var ave = ~~((min+max)/2);
    for(var i=0;i<N-ave;i++){
      var base = str.substring(i,i+ave);
      if(str.lastIndexOf(base) >= i+ave){
        min = ave+1;
        ans = ave;
        continue start;
      }
    }
    max = ave-1;
  }
  console.log(ans);
}
main(require('fs').readFileSync('/dev/stdin', 'UTF-8').trim().split("\n"));