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 Data.Array.Unboxed
import Data.List

main = do
  n <- readLn
  as <- map read . words <$> getLine
  print (together n as)

together :: Int -> [Int] -> Int
together 1 _ = 1
together n as = nsum 2 das + 2
  where
    sas = sort as
    das = buildA $ zipWith (-) (tail sas) sas


type Index = Int

-- 1-indexed
buildA :: IArray a e => [e] -> a Index e
buildA xs = listArray (1, length xs) xs

nsum :: Int -> Array Index Int -> Int
nsum x arr = go 1 1 (arr ! 1)
  where
    (_, l) = bounds arr
    go i j acc
      | i == l && j == l = (if acc == x then 1 else 0)
      | i == j = max (if acc == x then 1 else 0) (go i (j + 1) (acc + arr ! (j + 1)))
      | j == l = max (if acc == x then (j-i) else 0) (go (i + 1) j (acc - arr ! i))
      | acc == x = max (j-i) (go i (j + 1) (acc + arr ! (j + 1)))
      | acc < x = go i (j + 1) (acc + arr ! (j + 1))
      | acc > x = go (i + 1) j (acc - arr ! i)
      | otherwise = error "nsum: Pattern match failed."