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 Lua (5.3.2) (judge verdict: Accepted)

n=io.read("*n")
a={}
for i=1,n do
    x=io.read("*n")
    if not a[x] then
        a[x]=1
    else
        a[x]=a[x]+1
    end
end

max=0
for integer,_ in pairs(a) do
    counter=a[integer]
    if a[integer-1] then
        counter=counter+a[integer-1]
    end
    if a[integer+1] then
        counter=counter+a[integer+1]
    end
    max=math.max(counter,max)
end
print(max)