Choosing Teams

Source: Codeforces

Version: Phuoc Hung OJ Extended

Problem Statement

There are $n$ students. Student $i$ has already participated in the world championship $y_i$ times, and no student may participate more than $5$ times.

Each new team must contain exactly $3$ distinct students, and no student may belong to two teams. Every chosen team must be able to participate with the same members at least $k$ more times.

Thus student $i$ is eligible exactly when

Compute the maximum number of teams that can be formed.

Input

• The first line contains integers $n$ and $k$.
• The second line contains $n$ integers $y_0,y_1,\ldots,y_{n-1}$.

Output

Print one integer: the maximum number of teams.

Subtasks

Subtask 1 (100 points): $1\le n\le2000$; $1\le k\le5$; $0\le y_i\le5$.

Examples

Input

5 2
0 4 5 1 0

Output

1

Explanation

The condition is $y_i+2\le5$, or $y_i\le3$. Exactly three students are eligible, so exactly one team can be formed.