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)

n = int(input())
a = list(map(int,input().split()))
dict = {}
ans = 0

for i in range(n):
  if a[i] not in dict:
    dict[a[i]] = 1
  else:
    dict[a[i]] += 1

l = sorted(dict.items())
l += [(-1,0),(-2,0)]

for j in range(len(l)-2):
  if l[j][0]+1 == l[j+1][0] and l[j][0]+2 == l[j+2][0]:
     ans = max(ans,l[j][1]+l[j+1][1]+l[j+2][1])
  elif l[j][0]+1 == l[j+1][0] and l[j][0]+2 != l[j+2][0]:
     ans = max(ans,l[j][1]+l[j+1][1])
  elif l[j][0]+1 != l[j+1][0] and l[j][0]+2 != l[j+2][0]:
     ans = max(ans,l[j][1])
   
  
print(ans)