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B. Preparation for International Women's Day

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputInternational Women's Day is coming soon! Polycarp is preparing for the holiday.

There are $$$n$$$ candy boxes in the shop for sale. The $$$i$$$-th box contains $$$d_i$$$ candies.

Polycarp wants to prepare the maximum number of gifts for $$$k$$$ girls. Each gift will consist of exactly two boxes. The girls should be able to share each gift equally, so the total amount of candies in a gift (in a pair of boxes) should be divisible by $$$k$$$. In other words, two boxes $$$i$$$ and $$$j$$$ ($$$i \ne j$$$) can be combined as a gift if $$$d_i + d_j$$$ is divisible by $$$k$$$.

How many boxes will Polycarp be able to give? Of course, each box can be a part of no more than one gift. Polycarp cannot use boxes "partially" or redistribute candies between them.

Input

The first line of the input contains two integers $$$n$$$ and $$$k$$$ ($$$1 \le n \le 2 \cdot 10^5, 1 \le k \le 100$$$) — the number the boxes and the number the girls.

The second line of the input contains $$$n$$$ integers $$$d_1, d_2, \dots, d_n$$$ ($$$1 \le d_i \le 10^9$$$), where $$$d_i$$$ is the number of candies in the $$$i$$$-th box.

Output

Print one integer — the maximum number of the boxes Polycarp can give as gifts.

Examples

Input

7 2 1 2 2 3 2 4 10

Output

6

Input

8 2 1 2 2 3 2 4 6 10

Output

8

Input

7 3 1 2 2 3 2 4 5

Output

4

Note

In the first example Polycarp can give the following pairs of boxes (pairs are presented by indices of corresponding boxes):

- $$$(2, 3)$$$;
- $$$(5, 6)$$$;
- $$$(1, 4)$$$.

So the answer is $$$6$$$.

In the second example Polycarp can give the following pairs of boxes (pairs are presented by indices of corresponding boxes):

- $$$(6, 8)$$$;
- $$$(2, 3)$$$;
- $$$(1, 4)$$$;
- $$$(5, 7)$$$.

So the answer is $$$8$$$.

In the third example Polycarp can give the following pairs of boxes (pairs are presented by indices of corresponding boxes):

- $$$(1, 2)$$$;
- $$$(6, 7)$$$.

So the answer is $$$4$$$.

Codeforces (c) Copyright 2010-2021 Mike Mirzayanov

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