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 <iostream>
#include <vector>
#include <algorithm>
#include <map>
using namespace std;

int main(){
	int n,m,x[100000],ans = 0,p[100000] = {},cnt[100000] = {};
	map<int,int> mp;
	cin >> n >> m;
	for(int i = 0;i < n;i++) {
		cin >> x[i];
		mp[x[i]]++;
		cnt[x[i] % m]++;
	}
	for(auto it = mp.begin();it != mp.end();it++){
		p[it->first % m] += it->second / 2;
	}
	ans += cnt[0] / 2;
	for(int i = 1;i < (m + 1) / 2;i++){
		int pa = min(cnt[i],cnt[m - i]);
		cnt[i] -= pa;
		cnt[m - i] -= pa;
		ans += pa + min(cnt[i] / 2,p[i]) + min(cnt[m - i] / 2,p[m - i]);
	}
	if(m % 2 == 0) ans += cnt[m / 2] / 2;
	cout << ans << endl;
	return 0;
}