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: Time Limit Exceeded)

import collections
N = int(input())
a = list(map(int, input().split()))
cand = collections.Counter(a)
cand_list = cand.most_common(len(set(a)))
ans = 0
for i in range(len(set(a))):
  num = cand_list[i][0]
  count = cand[num]
  if num + 1 in a:
    count += cand[num + 1]
  if num - 1 in a:
    count += cand[num - 1]
  if ans < count:
    ans = count

print(ans)