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: Time Limit Exceeded)

def f(mc):
    if mc-1 in a and mc+1 in a:
        ans = a.count(mc-1) + a.count(mc) + a.count(mc+1)
    elif (mc-1 not in a) and (mc+1 in a):
        ans = a.count(mc) + a.count(mc+1) + a.count(mc+2)
    elif (mc-1 in a) and (mc+1 not in a):
        ans = a.count(mc) + a.count(mc-1) + a.count(mc-2)
    else:
        ans = a.count(mc)
    return ans

from collections import Counter

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

c = Counter(a)

# mc = c.most_common()[0][0]
# if mc == 0:
#     mc = c.most_common()[1][0]

# if 10**5 - 1 > mc > 1:
#     ans = c.most_common()[0][1] + a.count(mc-1) + a.count(mc+1)
# elif mc == 1:
#     ans = a.count(1) + a.count(2) + a.count(3)

# if mc-1 in a and mc+1 in a:
#     ans = a.count(mc-1) + a.count(mc) + a.count(mc+1)
# elif (mc-1 not in a) and (mc+1 in a):
#     ans = a.count(mc) + a.count(mc+1) + a.count(mc+2)
# elif (mc-1 in a) and (mc+1 not in a):
#     ans = a.count(mc) + a.count(mc-1) + a.count(mc-2)
# else:
#     ans = a.count(mc)

ans = []
mc = c.most_common()

for i in range(len(mc)):
    ans.append(f(mc[i][0]))

print(max(ans))