#include <bits/stdc++.h>
using namespace std;

typedef unsigned long long hash_t;

const int maxn = 5e3 + 10;

char s[maxn];
int lcp[maxn][maxn];

int main() {
  int n; cin >> n;
  scanf("%s", s + 1);
  for (int i = n; i >= 1; i--)
    for (int j = n; j >= 1; j--) 
      lcp[i][j] = s[i] == s[j] ? lcp[i + 1][j + 1] + 1 : 0;
  int ans = 0;
  for (int i = 1; i <= n; i++)
    for (int j = i; j <= n; j++)
      ans = max(ans, min(lcp[i][j], j - i));
  cout << ans << endl;
}

### Prompt

Generate a cpp solution to the following problem:

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.

Examples

Input

5
ababa


Output

2


Input

2
xy


Output

0


Input

13
strangeorange


Output

5

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;

typedef unsigned long long hash_t;

const int maxn = 5e3 + 10;

char s[maxn];
int lcp[maxn][maxn];

int main() {
  int n; cin >> n;
  scanf("%s", s + 1);
  for (int i = n; i >= 1; i--)
    for (int j = n; j >= 1; j--) 
      lcp[i][j] = s[i] == s[j] ? lcp[i + 1][j + 1] + 1 : 0;
  int ans = 0;
  for (int i = 1; i <= n; i++)
    for (int j = i; j <= n; j++)
      ans = max(ans, min(lcp[i][j], j - i));
  cout << ans << endl;
}

```