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;
int main() {
	int N, M;
	cin >> N >> M;
	map<int,int> cnt;
	for (int i = 0; i < N; ++ i) {
		int x;
		cin >> x;
		++cnt[x];
	}
	map<int,int> a;
	map<int,int> b;
	for (auto p : cnt) {
		a[p.first % M] += p.second;
		b[p.first % M] += p.second / 2;
	}
	int r = 0;
	for (int i = 0; i <= M-i; ++ i) {
		if (i == 0 || i == M-i) {
			r += a[i] / 2;
		} else {
			int p = min(a[i], a[M-i]);
			r += p;
			a[i] -= p;
			a[M-i] -= p;
			r += min(a[i]/2, b[i]);
			r += min(a[M-i]/2, b[M-i]);
		}
	}
	cout << r << endl;
}
