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
import java.util.*;

class Main {
    static final int A=100001;
    public static void main(String[] args) {
        Scanner scan = new Scanner(System.in);
        int n=scan.nextInt();
        int m=scan.nextInt();
        int[]f=new int[A];
        for(int i=0;i<n;++i){
            f[Integer.parseInt(scan.next())]++;
        }
        int[]g=new int[m];
        int[]e=new int[m];
        for(int i=0;i<A;++i)g[i%m]+=f[i];
        for(int i=0;i<A;++i)e[i%m]+=f[i]/2;
        int t=g[0]/2;
        if(m%2==0)t+=g[m/2]/2;
        for(int i=1;2*i<m;++i){
            int u=Math.min(g[i],g[m-i]);
            t+=u+Math.min(e[i],(g[i]-u)/2)+Math.min(e[m-i],(g[m-i]-u)/2);
        }
        System.out.println(t);
    }
}
