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 Fortran (gfortran v4.8.4) (judge verdict: Wrong Answer)

program name
    use,intrinsic :: iso_fortran_env
    implicit none
    integer(int32):: n,i, ans
    integer(int32), allocatable:: a(:), numc(:)

    read*, n
    allocate(a(n))
    read*, a(:)
    allocate(numc(0:maxval(a)), source=0)
    do i=1,n
        numc(a(i)) = numc(a(i)) + 1
    end do
    ans=0

    do i=1,ubound(numc,1)-1
        ans=max(ans,sum(numc(i-1:i+1)))
    end do

    print*, ans
end program name