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()))

a=sorted(a)
a.append(a[-1]+1)
arr=[]
tmp=a[0]
cnt=0
for i in range(N+1):
    if a[i]==tmp:
        cnt+=1
    elif a[i]==tmp+1:
        arr.append(cnt)
        tmp=a[i]
        cnt=1
    else:
        arr.append(cnt)
        step=a[i]-tmp
        for _ in range(step-1):
            arr.append(0)
        tmp=a[i]
        cnt=1
num=0
if len(arr)>=3:
    for i in range(len(arr)-2):
        num=max(num,sum(arr[i:i+3]))
else:
    num=sum(arr)
print(num)