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 PyPy3 (2.4.0) (judge verdict: Wrong Answer)

from collections import Counter

N = int(input())
A = list(map(int, input().split()))
A.sort()
A_c = Counter(A)
ans = 1

for i in range(1, N - 1):

    if A[i] * 3 - 3 <= sum(A[i - 1:i + 2]) <= A[i] * 3 + 3:
        ans = max(ans, sum([A_c[j] for j in set(A[i - 1:i + 2])]))

print(2 if len(A) == 2 and A[0] + 1 == A[1] else ans)