#include<bits/stdc++.h>
#define rep(i,n) for(int i=0;i<(int)n;i++)
#define all(c) (c).begin(),(c).end()
#define pb push_back
#define dbg(...) do{cerr<<__LINE__<<": ";dbgprint(#__VA_ARGS__, __VA_ARGS__);}while(0);

using namespace std;

namespace std{template<class S,class T>struct hash<pair<S,T>>{size_t operator()(const pair<S,T>&p)const{return ((size_t)1e9+7)*hash<S>()(p.first)+hash<T>()(p.second);}};template<class T>struct hash<vector<T>>{size_t operator()(const vector<T> &v)const{size_t h=0;for(auto i : v)h=h*((size_t)1e9+7)+hash<T>()(i)+1;return h;}};}
template<class T>ostream& operator<<(ostream &os, const vector<T> &v){os<<"[ ";rep(i,v.size())os<<v[i]<<(i==v.size()-1?" ]":", ");return os;}template<class T>ostream& operator<<(ostream &os,const set<T> &v){os<<"{ "; for(const auto &i:v)os<<i<<", ";return os<<"}";}
template<class T,class U>ostream& operator<<(ostream &os,const map<T,U> &v){os<<"{";for(const auto &i:v)os<<" "<<i.first<<": "<<i.second<<",";return os<<"}";}template<class T,class U>ostream& operator<<(ostream &os,const pair<T,U> &p){return os<<"("<<p.first<<", "<<p.second<<")";}
void dbgprint(const string &fmt){cerr<<endl;}template<class H,class... T>void dbgprint(const string &fmt,const H &h,const T&... r){cerr<<fmt.substr(0,fmt.find(","))<<"= "<<h<<" ";dbgprint(fmt.substr(fmt.find(",")+1),r...);}
typedef long long ll;typedef vector<int> vi;typedef pair<int,int> pi;const int inf = (int)1e9;const double INF = 1e12, EPS = 1e-9;

int main(){
	cin.tie(0); cin.sync_with_stdio(0);
	
	int n, m; cin >> n >> m;
	vector<vi> cards(m);
	vi mxpair(m);
	
	rep(i, n){
		int x; cin >> x;
		cards[x % m].pb(x);
	}
	rep(i, m){
		sort(all(cards[i]));
		rep(j, cards[i].size()){
			int k = j;
			for(; k < cards[i].size() && cards[i][j] == cards[i][k]; k++);
			mxpair[i] += (k - j) / 2;
			j = k - 1;
		}
	}
	
	int ans = cards[0].size() / 2;
	for(int i = 1; i * 2 < m; i++){
		int mx = 0;
		for(int j = 0, J = min(cards[i].size(), cards[m - i].size()); j <= J; j++){
			
			int tmp = j;
			tmp += min(mxpair[i], ((int)cards[i].size() - j) / 2);
			tmp += min(mxpair[m - i], ((int)cards[m - i].size() - j) / 2);
			mx = max(mx, tmp);
		}
		ans += mx;
	}
	if(m % 2 == 0) ans += cards[m / 2].size() / 2;
	
	cout << ans << endl;
	
	return 0;
}
### Prompt

Please create a solution in CPP to the following problem:

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

### Response

```cpp
#include<bits/stdc++.h>
#define rep(i,n) for(int i=0;i<(int)n;i++)
#define all(c) (c).begin(),(c).end()
#define pb push_back
#define dbg(...) do{cerr<<__LINE__<<": ";dbgprint(#__VA_ARGS__, __VA_ARGS__);}while(0);

using namespace std;

namespace std{template<class S,class T>struct hash<pair<S,T>>{size_t operator()(const pair<S,T>&p)const{return ((size_t)1e9+7)*hash<S>()(p.first)+hash<T>()(p.second);}};template<class T>struct hash<vector<T>>{size_t operator()(const vector<T> &v)const{size_t h=0;for(auto i : v)h=h*((size_t)1e9+7)+hash<T>()(i)+1;return h;}};}
template<class T>ostream& operator<<(ostream &os, const vector<T> &v){os<<"[ ";rep(i,v.size())os<<v[i]<<(i==v.size()-1?" ]":", ");return os;}template<class T>ostream& operator<<(ostream &os,const set<T> &v){os<<"{ "; for(const auto &i:v)os<<i<<", ";return os<<"}";}
template<class T,class U>ostream& operator<<(ostream &os,const map<T,U> &v){os<<"{";for(const auto &i:v)os<<" "<<i.first<<": "<<i.second<<",";return os<<"}";}template<class T,class U>ostream& operator<<(ostream &os,const pair<T,U> &p){return os<<"("<<p.first<<", "<<p.second<<")";}
void dbgprint(const string &fmt){cerr<<endl;}template<class H,class... T>void dbgprint(const string &fmt,const H &h,const T&... r){cerr<<fmt.substr(0,fmt.find(","))<<"= "<<h<<" ";dbgprint(fmt.substr(fmt.find(",")+1),r...);}
typedef long long ll;typedef vector<int> vi;typedef pair<int,int> pi;const int inf = (int)1e9;const double INF = 1e12, EPS = 1e-9;

int main(){
	cin.tie(0); cin.sync_with_stdio(0);
	
	int n, m; cin >> n >> m;
	vector<vi> cards(m);
	vi mxpair(m);
	
	rep(i, n){
		int x; cin >> x;
		cards[x % m].pb(x);
	}
	rep(i, m){
		sort(all(cards[i]));
		rep(j, cards[i].size()){
			int k = j;
			for(; k < cards[i].size() && cards[i][j] == cards[i][k]; k++);
			mxpair[i] += (k - j) / 2;
			j = k - 1;
		}
	}
	
	int ans = cards[0].size() / 2;
	for(int i = 1; i * 2 < m; i++){
		int mx = 0;
		for(int j = 0, J = min(cards[i].size(), cards[m - i].size()); j <= J; j++){
			
			int tmp = j;
			tmp += min(mxpair[i], ((int)cards[i].size() - j) / 2);
			tmp += min(mxpair[m - i], ((int)cards[m - i].size() - j) / 2);
			mx = max(mx, tmp);
		}
		ans += mx;
	}
	if(m % 2 == 0) ans += cards[m / 2].size() / 2;
	
	cout << ans << endl;
	
	return 0;
}
```