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 rep(i,n) for(int i=0;i<n;i++)
typedef pair<int,int> P;
int n,m,x,ans;
map<int,int>mp;
int cnt[100010][2];//[mod M] 1:pair
int main(){
	cin>>n>>m;
	rep(i,n){
		cin>>x;
		mp[x]++;
	}
	for(P p:mp){
		cnt[p.first%m][0]+=p.second%2;
		cnt[p.first%m][1]+=p.second-(p.second%2);
	}
	for(int i=0;i<=m/2;i++){
		if(i+i==m||i==0){
			ans+=(cnt[i][0]+cnt[i][1])/2;
		}
		else{
			if(cnt[i][0]+cnt[i][1]>=cnt[m-i][0]+cnt[m-i][1]){
				ans+=cnt[m-i][0]+cnt[m-i][1];
				ans+=min(cnt[i][1]/2,((cnt[i][0]+cnt[i][1])-(cnt[m-i][0]+cnt[m-i][1]))/2);
			}
			else{
				ans+=cnt[i][0]+cnt[i][1];
				ans+=min(cnt[m-i][1]/2,((cnt[m-i][0]+cnt[m-i][1])-(cnt[i][0]+cnt[i][1]))/2);
			}
		}
		
	}
	cout<<ans<<endl;
}
			
