Together

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.

Examples

Input

7 3 1 4 1 5 9 2

Output

4

Input

10 0 1 2 3 4 5 6 7 8 9

Output

3

Input

1 99999

Output

1

inputFormat

Input

The input is given from Standard Input in the following format:

N a_1 a_2 .. a_N

outputFormat

Output

Print the maximum possible number of i such that a_i=X.

Examples

Input

7 3 1 4 1 5 9 2

Output

4

Input

10 0 1 2 3 4 5 6 7 8 9

Output

3

Input

1 99999

Output

1

样例

7
3 1 4 1 5 9 2

4