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: Accepted)

import Data.List
import Data.Bool

main = print . solve . map (\xs -> (head xs, length xs)) . group . sort . map read . drop 1 . words =<< getContents

solve :: [(Int,Int)] -> Int
solve xls = maximum $ zipWith3 (\(a,al) (b,bl) (c,cl) -> bl + (bool 0 al $ abs(a-b) == 1) + (bool 0 cl $ abs(c-b) == 1)) xls' (drop 1 xls') (drop 2 xls')
    where
        xls' = [(0,0)] ++ xls ++ [(0,0)]