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>
#define REP(i,a,b) for(int i=(a);i<(b);i++)
#define RREP(i,a,b) for(int i=(a);i>=(b);i--)
#define pq priority_queue
#define P pair<int,int>
#define P2 pair<int,P>
#define P3 pair<int,P2>
typedef long long ll; typedef long double ld;
using namespace std;
const int INF=1e9, MOD=1e9+7, around[]={0,1,1,-1,-1,0,-1,1,0,0};
const ll LINF=1e18;
const ld PI=abs(acos(-1));
int n,m,a[100010],li[100010],li2[100010];

int main(){
	cin >> n >> m;
	REP(i,0,n) cin >> a[i],li[a[i]%m]++;
	sort(a,a+n);
	REP(i,0,n-1) if(a[i]==a[i+1]) i++,li2[a[i]%m]++;
	int pos=li[0]/2;
	REP(i,1,m/2+1){
		if(i==m-i){pos+=li[i]/2; continue;}
		int mi=min(li[i],li[m-i]);
		pos+=mi; li[i]-=mi; li[m-i]-=mi;
		pos+=min(li2[i],li[i]/2);
		pos+=min(li2[m-i],li[m-i]/2);
	}
	cout << pos << endl;
	return 0;
}
