Problem:
Score : 300 points

Problem Statement

You are given an integer sequence of length N, a_1,a_2,...,a_N.

For each 1≤i≤N, you have three choices: add 1 to a_i, subtract 1 from a_i or do nothing.

After these operations, you select an integer X and count the number of i such that a_i=X.

Maximize this count by making optimal choices.

Constraints

1≤N≤10^5

0≤a_i<10^5 (1≤i≤N)

a_i is an integer.

Input

The input is given from Standard Input in the following format:

N
a_1 a_2 .. a_N

Output

Print the maximum possible number of i such that a_i=X.

Sample Input 1

7
3 1 4 1 5 9 2

Sample Output 1

4

For example, turn the sequence into 2,2,3,2,6,9,2 and select X=2 to obtain 4, the maximum possible count.

Sample Input 2

10
0 1 2 3 4 5 6 7 8 9

Sample Output 2

3

Sample Input 3

1
99999

Sample Output 3

1

Solution in Haskell (GHC 7.10.3) (judge verdict: Wrong Answer)

import qualified Data.IntMap.Lazy as M
 
main = do
  getLine
  as <- map read . words <$> getLine
  print $ solve as
 
solve as = f M.empty as
 
f m [] = M.size $ M.filter (== x) m
  where x = M.foldr max 0 m
f m (a:as) = f m' as
  where
    m' = M.insertWith (+) (a+1) 1 . M.insertWith (+) (a-1) 1 . M.insertWith (+) a 1 $ m