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)

# encoding:utf-8
import copy
import numpy as np
import random
import bisect #bisect_left　これで二部探索の大小検索が行える
import math

N = int(input())
a = [int(i) for i in input().split()]

a.sort()

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

counts_list = []
tmp = 0
for num in range(max(a)+1):
    try:
        tmp += counts[num]
        # counts_list.append(tmp)
    except:
        pass

    counts_list.append(tmp)
# print(counts_list)
ans = -1
for i in range(len(counts_list)-3):
    ans = max(ans,counts_list[i+3]-counts_list[i])
    # print(ans)

print(ans)