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;
#define rep(i,a,b) for(int i=a;i<b;i++)



int N, M;
int X[101010];
//-----------------------------------------------------------------
int cnt1[101010]; // cnt1[i] : ?? mod M == iの個数
int cnt2[101010]; // cnt2[i] : ?? mod M == iで同じ数のペアが作れる個数
int main() {
	cin >> N >> M;
	rep(i, 0, N) scanf("%d", &X[i]);

	map<int, int> m;
	rep(i, 0, N) m[X[i]]++;

	for (auto p : m) {
		cnt1[p.first % M] += p.second;
		cnt2[p.first % M] += p.second / 2;
	}

	int ans = 0;
	rep(i, 0, M / 2 + 1) {
		int j = M - i;

		if (i == 0 || i == j) {
			ans += cnt1[i] / 2;
		}
		else {
			

			if (cnt1[i] < cnt1[j])
			{
				ans += cnt1[i];
				int d = cnt1[j] - cnt1[i];
				d = d / 2;
				ans += min(d, cnt2[j]);
			}
			else {
				ans += cnt1[j];
				int d = cnt1[i] - cnt1[j];
				d = d / 2;
				ans += min(d, cnt2[i]);
			}
		}
	}

	cout << ans << endl;
}