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: Runtime Error)

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

a_hash = {}
for i in range(N):
    if a[i] in a_hash:
        a_hash[a[i]] += 1
    else:
        a_hash[a[i]] = 1

a_sort = sorted(a_hash.items(), key = lambda x: x[0])
a_sort = list(a_sort)
ans_list = [0] * N

if len(a) == 1:
    print(1)
    exit()

for i in range(len(a_sort)):
    if i == 0:
        if a_sort[0][0] == a_sort[1][0] - 1:
            ans_list[0] += a_sort[0][1] + a_sort[1][1]
    elif i == len(a_sort) -1:
        if a_sort[i][0] == a_sort[i-1][0] + 1:
            ans_list[i] += a_sort[i][1] + a_sort[i-1][1]
        else:
            ans_list[i] = a_sort[i][1]
    else:
        if a_sort[i][0] == a_sort[i-1][0] + 1:
            ans_list[i] += a_sort[i][1] + a_sort[i-1][1]
        if a_sort[i][0] == a_sort[i+1][0] - 1:
            ans_list[i] += a_sort[i+1][1]


print(max(ans_list))