#include <bits/stdc++.h>
using namespace std;
#define MOD 1000000007
//#define MOD 998244353
#define INF 1145141919810893364
typedef pair<int,int> PP;
typedef long long ll;
#define int ll
#define setdouble setprecision
#define REP(i,n) for(int i=0;i<(n);++i)
#define OREP(i,n) for(int i=1;i<=(n);++i)
#define RREP(i,n) for(int i=(n)-1;i>=0;--i)
#define GOODBYE cout << -1 << endl;return 0
#define MM <<" "<<
#define Endl endl


signed main(void){
    int N,M;
    int X[114514];
    int maxX=0;
    int F[114514]={},G[114514]={},H[114514]={};
    cin >> N >> M;
    REP(i,N){
        cin >> X[i];
        H[X[i]]++;
        maxX=max(maxX,X[i]);
    }
    REP(i,maxX+1){
        G[i%M]+=H[i]/2;
        F[i%M]+=H[i];
    }
    int Ans=0;
    Ans+=F[0]/2;
    if(M%2==0){
        Ans+=F[M/2]/2;
    }
    
    //REP(i,M){cout << G[i] << " ";}cout << endl;
    
    for(int i=1;i<(M+1)/2;i++){
        if(F[i]>F[M-i]){
            Ans+=F[M-i];
            Ans+=min(((F[i]-F[M-i])/2),G[i]);
        }else{
            Ans+=F[i];
            Ans+=min(((F[M-i]-F[i])/2),G[M-i]);
        }
    }
    cout << Ans << endl;
    
    return 0;
}


### Prompt

Your challenge is to write 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;
#define MOD 1000000007
//#define MOD 998244353
#define INF 1145141919810893364
typedef pair<int,int> PP;
typedef long long ll;
#define int ll
#define setdouble setprecision
#define REP(i,n) for(int i=0;i<(n);++i)
#define OREP(i,n) for(int i=1;i<=(n);++i)
#define RREP(i,n) for(int i=(n)-1;i>=0;--i)
#define GOODBYE cout << -1 << endl;return 0
#define MM <<" "<<
#define Endl endl


signed main(void){
    int N,M;
    int X[114514];
    int maxX=0;
    int F[114514]={},G[114514]={},H[114514]={};
    cin >> N >> M;
    REP(i,N){
        cin >> X[i];
        H[X[i]]++;
        maxX=max(maxX,X[i]);
    }
    REP(i,maxX+1){
        G[i%M]+=H[i]/2;
        F[i%M]+=H[i];
    }
    int Ans=0;
    Ans+=F[0]/2;
    if(M%2==0){
        Ans+=F[M/2]/2;
    }
    
    //REP(i,M){cout << G[i] << " ";}cout << endl;
    
    for(int i=1;i<(M+1)/2;i++){
        if(F[i]>F[M-i]){
            Ans+=F[M-i];
            Ans+=min(((F[i]-F[M-i])/2),G[i]);
        }else{
            Ans+=F[i];
            Ans+=min(((F[M-i]-F[i])/2),G[M-i]);
        }
    }
    cout << Ans << endl;
    
    return 0;
}


```