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.Arrays;
import java.util.Scanner;

public class Main {
	public static void main(String[] args) {
		new Main().run();
	}

	public void run() {
		Scanner sc = new Scanner(System.in);
		int n = sc.nextInt();
		int m = sc.nextInt();
		int[] lis = new int[(int) 1e5 + 1];
		for (int i = 0; i < n; ++i) {
			int x = sc.nextInt();
			++lis[x];
		}
		int[] c2 = new int[m];
		int[] c1 = new int[m];
		for (int i = 0; i < lis.length; ++i) {
			c2[i % m] += lis[i] / 2 * 2;
			c1[i % m] += lis[i] % 2;
		}
		for (int i = 0; i <= m / 2; ++i) {
			int j = (m - i) % m;
			if (i == j) {
				c2[i] += c1[i] / 2 * 2;
				c1[i] %= 2;
				continue;
			}
			int tmp = Math.min(c1[i], c1[j]);
			c1[i] -= tmp;
			c1[j] -= tmp;
			if (c1[i] > c1[j]) {
				tmp = c1[i];
				c1[i] = c1[j];
				c1[j] = tmp;
				tmp = c2[i];
				c2[i] = c2[j];
				c2[j] = tmp;
			}
			tmp = Math.min(c2[i], c1[j] / 2 * 2);
			c1[j] -= tmp;
			c2[i] -= tmp;
		}
		int ans = 0;
		for (int v : c1) {
			ans += v;
		}
		if ((n - ans) % 2 == 1) {
			throw new AssertionError();
		}
		System.out.println((n - ans) / 2);
	}

	void tr(Object... objects) {
		System.out.println(Arrays.deepToString(objects));
	}
}
