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 LuaJIT (2.0.4) (judge verdict: Accepted)

local ior = io.input()
local t = {}
for i = 1, 100000 do t[i] = 0 end
local n = ior:read("*n")
for i = 1, n do
  local a = ior:read("*n")
  if 1 < a then t[a - 1] = t[a - 1] + 1 end
  if 0 < a then t[a] = t[a] + 1 end
  t[a + 1] = t[a + 1] + 1
end
local ret = 0
for i = 1, 100000 do
  ret = math.max(ret, t[i])
end
print(ret)