#include<bits/stdc++.h>
using namespace std;
int main(){
  int n,m;cin>>n>>m;
  int x[n];
  vector<int>v[m];
  for(int i=0;i<n;i++){
    cin>>x[i];
    v[x[i]%m].push_back(x[i]);
  }
  for(int i=0;i<m;i++)sort(v[i].begin(),v[i].end());
  int ans=0;
  for(int i=0;i<=m/2;i++){
    if(i*2==m||i==0){
      ans+=v[i].size()/2;
    }
    else{
    int t=m-i;
    int is=v[i].size();
    int ts=v[t].size();
    if(is==ts){
      ans+=is;
    }
    else if(is>ts){
      for(int j=0;j<v[i].size()-1;){
        if(v[i][j]==v[i][j+1]){
          ans++;
          is-=2;
          j+=2;
        }
        else j++;
        if(is<=ts)break;
      }
      ans+=min(ts,is);
      
    }
    else if(is<ts){
      for(int j=0;j<v[t].size()-1;){
        if(v[t][j]==v[t][j+1]){
          ans++;
          ts-=2;
          j+=2;
        }
        else j++;
        if(ts<=is)break;
      }
      ans+=min(is,ts);
      
    }
    //cout<<ans<<endl;
    }
  }
  cout<<ans<<endl;
}
      
        
  
### Prompt

Generate 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 main(){
  int n,m;cin>>n>>m;
  int x[n];
  vector<int>v[m];
  for(int i=0;i<n;i++){
    cin>>x[i];
    v[x[i]%m].push_back(x[i]);
  }
  for(int i=0;i<m;i++)sort(v[i].begin(),v[i].end());
  int ans=0;
  for(int i=0;i<=m/2;i++){
    if(i*2==m||i==0){
      ans+=v[i].size()/2;
    }
    else{
    int t=m-i;
    int is=v[i].size();
    int ts=v[t].size();
    if(is==ts){
      ans+=is;
    }
    else if(is>ts){
      for(int j=0;j<v[i].size()-1;){
        if(v[i][j]==v[i][j+1]){
          ans++;
          is-=2;
          j+=2;
        }
        else j++;
        if(is<=ts)break;
      }
      ans+=min(ts,is);
      
    }
    else if(is<ts){
      for(int j=0;j<v[t].size()-1;){
        if(v[t][j]==v[t][j+1]){
          ans++;
          ts-=2;
          j+=2;
        }
        else j++;
        if(ts<=is)break;
      }
      ans+=min(is,ts);
      
    }
    //cout<<ans<<endl;
    }
  }
  cout<<ans<<endl;
}
      
        
  
```