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)

from collections import Counter as C
n=int(input())
B=list(map(int,input().split()))
if n==1:
  print(1)
  exit()
if n==2:
  print(2 if abs(B[1]-B[0])<=2 else 1)
  exit()
A=C(B+[i for i in range(1,max(B)+1)]).most_common()
print(A)
m=0
for i in range(1,len(A)-1):
  m=max(m,A[i-1][1]+A[i][1]+A[i+1][1]-3)
  print(A[i-1][1]+A[i][1]+A[i+1][1]-3)
print(m)