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)

def c_together(N, A):
    from collections import defaultdict
    count = defaultdict(int)
    for i in A:
        count[i] += 1
    ans = 0
    for i in range(max(A) + 1):
        # ある整数iにするには、i-1に+1する、何もしない、i+1に-1する3パターン
        tmp = count[i - 1] + count[i] + count[i + 1]
        ans = max(ans, tmp)
    return ans

N = int(input())
A = [int(i) for i in input().split()]
print(c_together(N, A))