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;
typedef long long ll;
typedef long double ld;
typedef pair<ll,ll> P;
typedef pair<int,int> Pi;
#define rep(i,n) for(ll i=0;i<n;i++)
#define FOR(i,a,b) for(ll i=a;i<b;i++)
#define fi first
#define se second

template<typename T> inline bool chmax(T &a, T b){if(a<b){a=b;return true;}return false;}
template<typename T> inline bool chmin(T &a, T b){if(a>b){a=b;return true;}return false;}
template<typename T> ostream& operator<<(ostream& s,const complex<T>& d) {return s<<"("<<d.real()<<", "<<d.imag()<< ")";}
template<typename T1, typename T2> ostream& operator<<(ostream& s,const pair<T1,T2>& d) {return s<<"("<<d.first<<", "<<d.second<<")";}
template<typename T> ostream& operator<<(ostream& s, const vector<T>& d){int len=d.size();rep(i,len){s<<d[i];if(i<len-1) s<<" ";}return s;}
template<typename T> ostream& operator<<(ostream& s,const vector<vector<T>>& d){int len=d.size();rep(i,len){s<<d[i]<<endl;}return s;}
template<typename T> ostream& operator<<(ostream& s,const set<T>& v){s<<"{ ";for(auto itr=v.begin();itr!=v.end();++itr) {if (itr!=v.begin()) {s<< ", ";}s<<(*itr);}s<<" }";return s;}
template<typename T1, typename T2> ostream& operator<<(ostream& s,const map<T1,T2>& m){s<<"{"<<endl;for(auto itr=m.begin();itr!=m.end();++itr){s<<" "<<(*itr).first<<" : "<<(*itr).second<<endl;}s<<"}"<<endl;return s;}

const ll mod=1e9+7;
const ll inf=1e17;
const int INF=1e9;
const double PI=acos(-1);
const double EPS=1e-10;

int main(){
	cin.tie(0);ios::sync_with_stdio(false);
	int n,m;
	cin>>n>>m;
	vector<int> a(n);
	map<int,int> mp1,mp2;
	rep(i,n){
		cin>>a[i];
		mp1[a[i]]++;
		mp2[a[i]%m]++;
	}
	vector<vector<int>> cnt(m);
	for(auto itr:mp1){
		cnt[itr.fi%m].push_back(itr.se);
	}
	rep(i,m){
		sort(begin(cnt[i]),end(cnt[i]),greater<int>());
	}
	int ans=0;
	for(auto &itr:mp2){
		int r=itr.fi,now=itr.se;
		int tar=mp2[(m-r)%m];
		if(r!=(m-r)%m){
			if(tar>=now){
				itr.se-=now;
				ans+=now;
				mp2[(m-r)%m]-=now;
			}
		}else{
			ans+=mp2[r]/2;
		}
	}
	rep(i,m){
		if(i==(m-i)%m) continue;
		int ret=mp2[i];
		int now=0;
		for(auto x:cnt[i]){
			if(x>=ret){
				ans+=ret/2;
				break;
			}else{
				ans+=x/2;
				ret-=x/2*2;
			}
		}
	}
	cout<<ans<<endl;
}
