#include <iostream>
#include <fstream>
#include <cmath>  
#include <cstdlib>
#include <ctime>
#include <algorithm>
#include <numeric>
#include <functional>
#include <string> 
#include <vector>
#include <bitset>
#include <map>
#include <set>
#include <stack>
#include <queue>
#include <deque>
#include <random>


using namespace std;
using ll = long long;
using ull = unsigned long long;

#define REP(i,n) for(long long i = 0; i < (n); i++)
#define FOR(i, m, n) for(long long i = (m);i < (n); ++i)
#define ALL(obj) (obj).begin(),(obj).end()

template<class T> using V = vector<T>;
template<class T, class U> using P = pair<T, U>;

const ll MOD = (ll)1e9 + 7;
const ll MOD2 = 998244353;
const ll LLINF = (ll)1e18;
const ll INTINF = (ll)1e9;
const long double PI = 3.1415926535897932384626433;

template <class T> void corner(bool flg, T hoge) { if (flg) { cout << hoge << endl; exit(0); } }
template <class T, class U>ostream &operator<<(ostream &o, const map<T, U>&obj) { o << "{"; for (auto &x : obj) o << " {" << x.first << " : " << x.second << "}" << ","; o << " }"; return o; }
template <class T>ostream &operator<<(ostream &o, const set<T>&obj) { o << "{"; for (auto itr = obj.begin(); itr != obj.end(); ++itr) o << (itr != obj.begin() ? ", " : "") << *itr; o << "}"; return o; }
template <class T>ostream &operator<<(ostream &o, const vector<T>&obj) { o << "{"; for (int i = 0; i < (int)obj.size(); ++i)o << (i > 0 ? ", " : "") << obj[i]; o << "}"; return o; }
template <class T, class U>ostream &operator<<(ostream &o, const pair<T, U>&obj) { o << "{" << obj.first << ", " << obj.second << "}"; return o; }
template <template <class tmp>  class T, class U> ostream &operator<<(ostream &o, const T<U> &obj) { o << "{"; for (auto itr = obj.begin(); itr != obj.end(); ++itr)o << (itr != obj.begin() ? ", " : "") << *itr; o << "}"; return o; }
void print(void) { cout << endl; }
template <class Head> void print(Head&& head) { cout << head; print(); }
template <class Head, class... Tail> void print(Head&& head, Tail&&... tail) { cout << head << " "; print(forward<Tail>(tail)...); }
template <class T> void chmax(T& a, const T b) { a = max<T>(a, b); }
template <class T> void chmin(T& a, const T b) { a = min<T>(a, b); }
void YN(bool flg) { cout << ((flg) ? "YES" : "NO") << endl; }
void Yn(bool flg) { cout << ((flg) ? "Yes" : "No") << endl; }
void yn(bool flg) { cout << ((flg) ? "yes" : "no") << endl; }

int main() {
	int N, M; cin >> N >> M;
	V<int> cnt(M,0),cnt2(100001,0),cnt3(M,0);
	for(int i = 0; i < N; ++i) {
		int X; cin >> X;
		cnt[X%M]++;
		cnt2[X]++;
	}
	for (int i = 1; i < 100001; ++i) cnt3[i%M] += cnt2[i] / 2;

	int ans = cnt[0]/2;
	cnt[0] %= 2;
	for(int i = M-1; 0 < i; --i){
		if (M - i > i) break;
		if(M-i>0){
			if(M-i==i){
				ans += cnt[M - i] / 2;
				cnt[M - i] %= 2;
				continue;
			}
			int a = cnt[i];
			int b = cnt[M - i];
			cnt[i] -= min(a, b);
			cnt[M-i] -= min(a, b);
			ans += min(a, b);
			ans += min(cnt[i]/2,cnt3[i]);
			ans += min(cnt[M-i]/2,cnt3[M-i]);
		}
	}
	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 <iostream>
#include <fstream>
#include <cmath>  
#include <cstdlib>
#include <ctime>
#include <algorithm>
#include <numeric>
#include <functional>
#include <string> 
#include <vector>
#include <bitset>
#include <map>
#include <set>
#include <stack>
#include <queue>
#include <deque>
#include <random>


using namespace std;
using ll = long long;
using ull = unsigned long long;

#define REP(i,n) for(long long i = 0; i < (n); i++)
#define FOR(i, m, n) for(long long i = (m);i < (n); ++i)
#define ALL(obj) (obj).begin(),(obj).end()

template<class T> using V = vector<T>;
template<class T, class U> using P = pair<T, U>;

const ll MOD = (ll)1e9 + 7;
const ll MOD2 = 998244353;
const ll LLINF = (ll)1e18;
const ll INTINF = (ll)1e9;
const long double PI = 3.1415926535897932384626433;

template <class T> void corner(bool flg, T hoge) { if (flg) { cout << hoge << endl; exit(0); } }
template <class T, class U>ostream &operator<<(ostream &o, const map<T, U>&obj) { o << "{"; for (auto &x : obj) o << " {" << x.first << " : " << x.second << "}" << ","; o << " }"; return o; }
template <class T>ostream &operator<<(ostream &o, const set<T>&obj) { o << "{"; for (auto itr = obj.begin(); itr != obj.end(); ++itr) o << (itr != obj.begin() ? ", " : "") << *itr; o << "}"; return o; }
template <class T>ostream &operator<<(ostream &o, const vector<T>&obj) { o << "{"; for (int i = 0; i < (int)obj.size(); ++i)o << (i > 0 ? ", " : "") << obj[i]; o << "}"; return o; }
template <class T, class U>ostream &operator<<(ostream &o, const pair<T, U>&obj) { o << "{" << obj.first << ", " << obj.second << "}"; return o; }
template <template <class tmp>  class T, class U> ostream &operator<<(ostream &o, const T<U> &obj) { o << "{"; for (auto itr = obj.begin(); itr != obj.end(); ++itr)o << (itr != obj.begin() ? ", " : "") << *itr; o << "}"; return o; }
void print(void) { cout << endl; }
template <class Head> void print(Head&& head) { cout << head; print(); }
template <class Head, class... Tail> void print(Head&& head, Tail&&... tail) { cout << head << " "; print(forward<Tail>(tail)...); }
template <class T> void chmax(T& a, const T b) { a = max<T>(a, b); }
template <class T> void chmin(T& a, const T b) { a = min<T>(a, b); }
void YN(bool flg) { cout << ((flg) ? "YES" : "NO") << endl; }
void Yn(bool flg) { cout << ((flg) ? "Yes" : "No") << endl; }
void yn(bool flg) { cout << ((flg) ? "yes" : "no") << endl; }

int main() {
	int N, M; cin >> N >> M;
	V<int> cnt(M,0),cnt2(100001,0),cnt3(M,0);
	for(int i = 0; i < N; ++i) {
		int X; cin >> X;
		cnt[X%M]++;
		cnt2[X]++;
	}
	for (int i = 1; i < 100001; ++i) cnt3[i%M] += cnt2[i] / 2;

	int ans = cnt[0]/2;
	cnt[0] %= 2;
	for(int i = M-1; 0 < i; --i){
		if (M - i > i) break;
		if(M-i>0){
			if(M-i==i){
				ans += cnt[M - i] / 2;
				cnt[M - i] %= 2;
				continue;
			}
			int a = cnt[i];
			int b = cnt[M - i];
			cnt[i] -= min(a, b);
			cnt[M-i] -= min(a, b);
			ans += min(a, b);
			ans += min(cnt[i]/2,cnt3[i]);
			ans += min(cnt[M-i]/2,cnt3[M-i]);
		}
	}
	cout << ans << endl;
	return 0;
}


```