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 Python (3.4.3) (judge verdict: Accepted)

import collections
N=int(input())
A=sorted(list(map(int,input().split())))
p=collections.Counter(A)
B=list(set(A))
ans=0
l=len(B)
if l==1:
  ans = p[B[0]]
elif l==2:
  if B[1]-B[0] <= 2:
    ans = p[B[0]]+p[B[1]]
  else:
    ans = max(p[B[0]],p[B[1]])
else:  
  for i in range(l-2):
    sum_a = p[B[i]]+p[B[i+1]]+p[B[i+2]]
    if sum_a > ans:
      ans = sum_a
print(ans)