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: Wrong Answer)

import collections

N = int(input())
a = list(map(int, input().split()))

c = collections.Counter(a)

cm = c.most_common()
key = []
count = 0
for tup in cm:
    if tup[1] >= count:
        key.append(tup[0])
        count = tup[1]
    else:
        break

ans = 0
for i in key:
    maxx = max(c[i - 2] + c[i - 1] + c[i], c[i - 1] + c[i] + c[i + 1], c[i] + c[i + 1] + c[i + 2])
    if maxx > ans:
        ans = maxx

print(ans)