F. Kozak Vus and the Candies

Input

The first line contains two integers $n$ and $g$ (1 \leq n \leq 10^5;~0 \leq g \leq 6) — the number of candies and the block number, respectively.

The second line contains $n$ integers a_1, a_2, \dotsc, a_n (1 \leq a_i \leq 10^9) — the positions where the candies are located. It is guaranteed that all a_i are distinct.

Interaction

You need to implement the following function:

integer solve(integer n, integer g, array of integers m)

• $n$ — the number of candies;

• $g$ — block number;

• $m$ — array of candy positions;

• The function should return a single integer — the maximum number of candies Vus can collect.

Output

Output a single integer — the maximum number of candies Vus can collect.

Examples

Note

In the first example, Vus can choose x = 2 and collect candies at positions $1$, $3$, and $7$.

In the second example, Vus can choose x = 3 and collect candies at positions $1$, $4$, $7$, $10$, and $13$.

Scoring

1. (4 points) n \leq 2, a_i \leq 10;

2. (5 points) n \leq 3, a_i \leq 10^2;

3. (12 points) n \leq 10, a_i \leq 10^2;

4. (20 points) n \leq 10^3, a_i \leq 10^4;

5. (25 points) n \leq 10^4, a_i \leq 10^6;

6. (34 points) no additional constraints.