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 sys
readline = sys.stdin.readline
from collections import Counter

def main():
    N = int(readline())
    A = list(map(int, readline().rstrip().split()))
    c = Counter(A)
    mi = min(A)+1
    m = c[mi-1] + c[mi] + c[mi+1]
    ans = m
    for i in range(mi+1, max(A)):
        m -= c[i-2]
        m += c[i+1]
        ans = max(ans, m)
    
    print(ans)


if __name__ == '__main__':
    main()