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
#include <iostream>
#define REP(i, a, b) for (auto i = (a); i < (b); ++i)

using namespace std;

signed main() {
   int n; cin >> n;
   string s; cin >> s;
   int lcs[n + 1][n + 1];
   REP(i, 0, n + 1) REP(j, 0, n + 1) lcs[i][j] = 0;
   REP(i, 1, n + 1)
       REP(j, i + 1, n + 1)
           if (s[i - 1] == s[j - 1] && lcs[i - 1][j - 1] < j - i)
               lcs[i][j] = lcs[i - 1][j - 1] + 1;
   int ans = 0;
   REP(i, 0, n + 1) REP(j, 0, n + 1) ans = max(ans, lcs[i][j]);
   cout << ans;
}