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>
#define REP(i,n) for(int i=0;i<(int)(n);i++)
#define ALL(x) (x).begin(),(x).end()
#define LL long long

using namespace std;

int main(){

    int N,M;cin>>N>>M;
    int X[N];REP(i,N)cin>>X[i];
    sort(X,X+N);

    int cnt[M];
    fill_n(cnt,M,0);
    int pr[M];
    fill_n(pr,M,0);

    REP(i,N)cnt[X[i]%M]++;
    REP(i,N)if(X[i]==X[i+1])pr[X[i++]%M]++;

    int ans=cnt[0]/2;
    for (int i=1;i<M;i++){
        int num = min(cnt[i],cnt[M-i]);
        if(i==M-i)num/=2;
        ans +=num;
        cnt[i]-=num;
        cnt[M-i]-=num;
    }
    for(int i=1;i<M;i++)ans += min(pr[i],cnt[i]/2);
    cout<<ans<<endl;


    return 0;
}