Contest Duration: - (local time) (100 minutes) Back to Home
E - Who Says a Pun? /

Time Limit: 2 sec / Memory Limit: 1024 MB

### 問題文

より厳密には、

• l_1 + len \leq l_2

• S[l_1+i] = S[l_2+i] (i = 0, 1, ..., len - 1)

を満たす整数 l_1 , l_2 ( 1 \leq l_1, l_2 \leq N - len + 1 ) が存在するような正整数 len の最大値を求めてください。そのような len が存在しないときは、0 を出力してください。

### 制約

• 2 ≤ N ≤ 5 \times 10^3
• |S| = N
• S は英小文字から成る

### 入力

N
S


### 入力例 1

5
ababa


### 出力例 1

2


### 入力例 2

2
xy


### 出力例 2

0


### 入力例 3

13
strangeorange


### 出力例 3

5


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