Maximum Valid Groups Formation

You are given n players with their respective skill levels. Your task is to form as many groups as possible under the following conditions:

• Each group must contain exactly k players.
• For each group, if you denote the players' skill levels in that group as s1, s2, \dots, sk sorted in non-decreasing order, then it must hold that \[ s_k - s_1 \le d, \] where d is the maximum allowed difference in skill levels.
• Each player can be a member of at most one group.

Your goal is to compute the maximum number of valid groups that can be formed.

inputFormat

The first line of input contains three integers n, k, and d separated by spaces, where:

• n is the number of players.
• k is the exact number of players that should form a group.
• d is the maximum allowed difference in skill levels between the highest and the lowest in a group.

The second line contains n space separated integers, representing the skill levels of the players.

outputFormat

Output a single integer which is the maximum number of valid groups that can be formed.

8 3 2
4 8 5 6 7 9 5 3

2