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<bits/stdc++.h>
using namespace std;
#define ran 111111
int e[ran];
int m;
int chk(int x){
	int res = 0;
	for(int i=x; i<ran; i+=m)
		res += e[i];
//	printf("%d\n",res);
	return res/2;
}
int chk2(int x){
	int A = 0, B = 0, C = 0, D = 0;
	for(int i=x; i<ran; i+=m){
		A += e[i]/2;
		C += e[i];
	}
	for(int i=m-x; i<ran; i+=m){
		B += e[i]/2;
		D += e[i];
	}
	int tmp1 = min(D-B*2,C);
	int tmp2 = min(C-A*2,D);
//	printf("%d %d %d %d\n",A,B,C,D);
	return max(tmp1+B+min((C-tmp1)/2,A), tmp2+A+min((D-tmp2)/2,B));
}
int main(){
	int x,y;
	for(scanf("%d%d",&x,&m); x--;){
		scanf("%d",&y);
		e[y] ++;
	}
	int res = chk(0);
	if(m % 2 == 0)res += chk(m/2);
	for(int i=1; i+i<m; i++)
		res += chk2(i);
	printf("%d\n",res);
	return 0;
}
