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
# -*- coding: utf-8 -*-
# if x < y:
#     z = x
# elif True:
#     z = y
# else:
#     z = 100
import sys,os,math
from collections import Counter, defaultdict
import bisect
from sys import stdin, stdout
from itertools import repeat


# n, k = map(int, raw_input().split())
# da = map(int, raw_input().split())
# db = map(int, raw_input().split())

def main():
    n = map(int, raw_input().split())[0]
    s = raw_input().strip()
    d = [[0 for i in range(n+5)] for i in range(n+5)]
    mx = 0
    for i in range(1, n+1):
        for j in range(i, n+1):
            if s[i-1] == s[j-1]:
                d[i][j] = min(d[i-1][j-1]+1, abs(j-i))
                # print d[i][j], i, j
                mx = max(mx, d[i][j])
            else:
                d[i][j] = 0
    print mx

main()
