#include <bits/stdc++.h>
using namespace std;
int n, m;
map<int,int>mpm,mpt , mp; 
int ans;
int main(){
	cin>>n>>m;
	for(int i = 0; i < n ;i++){
		int x;cin>>x;
		mpm[x%m]++;
		mpt[x]++;
	}
	for(int i= 0; i < m ; i++){
		int ts = (m-i)%m;
		if(ts == i){
			ans+=mpm[i]/2;
			mp[i] =mpm[i]%2;
		}else if(ts > i){
			int tt = min(mpm[i] , mpm[ts]);
			ans+=tt;
			mp[i] = mpm[i] - tt;
			mp[ts] = mpm[ts]-tt;
		}else break;
	}
	for(int i = 1 ;i <= 100000 ; i++){
		int z  =min(mpt[i] ,mp[i%m])/2;
		ans+=z;
		mp[i%m]-=(2*z);
	}
	cout<<ans;
	return 0;
}


### Prompt

Please formulate a CPP solution to the following problem:

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

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
int n, m;
map<int,int>mpm,mpt , mp; 
int ans;
int main(){
	cin>>n>>m;
	for(int i = 0; i < n ;i++){
		int x;cin>>x;
		mpm[x%m]++;
		mpt[x]++;
	}
	for(int i= 0; i < m ; i++){
		int ts = (m-i)%m;
		if(ts == i){
			ans+=mpm[i]/2;
			mp[i] =mpm[i]%2;
		}else if(ts > i){
			int tt = min(mpm[i] , mpm[ts]);
			ans+=tt;
			mp[i] = mpm[i] - tt;
			mp[ts] = mpm[ts]-tt;
		}else break;
	}
	for(int i = 1 ;i <= 100000 ; i++){
		int z  =min(mpt[i] ,mp[i%m])/2;
		ans+=z;
		mp[i%m]-=(2*z);
	}
	cout<<ans;
	return 0;
}


```