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;
typedef long long ll;
#define rep(i,a) for(int i=0;i<(a);i++)
const ll MOD=1000000007;

int cnt[101010],cnt2[101010];
map<int,int> mp;

int main(){
  int N,M; cin>>N>>M;
  rep(i,N){
    int X; cin>>X;
    int Y=X%M;
    if(mp[X]>=1&&Y!=0){
      cnt[Y]--;
      cnt2[Y]+=2;
      mp[X]--;
    }else{
      cnt[Y]++;
      mp[X]++;
    }
  }

  int ans=cnt[0]/2+(M%2==0?(cnt[M/2]+cnt2[M/2])/2:0);
  for(int i=1;i<=(M-1)/2;i++){
    int sum=cnt[i]+cnt2[i], sum2=cnt[M-i]+cnt2[M-i];
    if(sum<sum2){
      swap(sum,sum2);
      swap(cnt[i],cnt[M-i]);
      swap(cnt2[i],cnt2[M-i]);
    }
    cnt2[i]-=max(sum2-cnt[i],0);
    ans+=sum2+max(0,cnt2[i]/2);
  }
  cout<<ans<<endl;
  return 0;
}
