Pair Cards

Takahashi is playing with N cards.

The i-th card has an integer X_i on it.

Takahashi is trying to create as many pairs of cards as possible satisfying one of the following conditions:

• The integers on the two cards are the same.
• The sum of the integers on the two cards is a multiple of M.

Find the maximum number of pairs that can be created.

Note that a card cannot be used in more than one pair.

Constraints

• 2≦N≦10^5
• 1≦M≦10^5
• 1≦X_i≦10^5

Input

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

N M X_1 X_2 ... X_N

Output

Print the maximum number of pairs that can be created.

Examples

Input

7 5 3 1 4 1 5 9 2

Output

3

Input

15 10 1 5 6 10 11 11 11 20 21 25 25 26 99 99 99

Output

6

inputFormat

Input

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

N M X_1 X_2 ... X_N

outputFormat

Output

Print the maximum number of pairs that can be created.

Examples

Input

7 5 3 1 4 1 5 9 2

Output

3

Input

15 10 1 5 6 10 11 11 11 20 21 25 25 26 99 99 99

Output

6

样例

7 5
3 1 4 1 5 9 2

3