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)

from collections import Counter

N, *a = map(int, open(0).read().split())
c = sorted(Counter(a).most_common())
ans = len(c)
for i in range(len(c) - 2):
    x = c[i]
    y = c[i + 1]
    z = c[i + 2]
    
    cnt = y[1]
    cnt += x[1] if x[0] + 1 == y[0] else 0
    cnt += z[1] if z[0] - 1 == y[0] else 0
    ans = max(ans, cnt)
    
print(ans)