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
#include<cstdio>
#include<map>
#include<algorithm>
std::map<int,int>g;
int i,j,n,m,s[100001],f[100001];
int cal(int i,int j)
{
	if(f[i]==f[j])return f[i];
	if(f[i]>f[j])std::swap(i,j);
	return f[i]+std::min(f[j]-f[i]>>1,s[j]);
}
int main()
{
	scanf("%d%d",&n,&m);
	for(i=1;i<=n;++i)
	{
		scanf("%d",&j),++f[j%m];
		if(!(++g[j]&1))++s[j%m];
	}
	for(j=0,i=1;i+i<m;++i)
		j+=cal(i,m-i);
	if(m%2==0)j+=f[m/2]>>1;
	printf("%d",j+*f/2);
}