#include "bits/stdc++.h"
using namespace std;
#define int long long
#define rep(i,n) for(int i=0;i<n;i++)
const int mod = 1000000007;
const int inf = 1ll << 61;
typedef pair<int, int> P;
int x[100006];
int cnt[100006];
int modcnt[100006];
vector<int>modlst[100006];
int par[100006], notpar[100006];
signed main() {
	int n, m; cin >> n >> m;
	rep(i, n) {
		cin >> x[i]; cnt[x[i]]++; modcnt[x[i] % m]++;
		modlst[x[i] % m].push_back(x[i]);
	}
	rep(i, m) {
		sort(modlst[i].begin(), modlst[i].end());
		modlst[i].push_back(inf);
	}
	rep(i, m) {
		int now = modlst[i][0],c=0;
		rep(j, modlst[i].size()) {
			if (modlst[i][j] == now)c++;
			else {
				par[i] += c/2;
				notpar[i] += c%2;
				c = 1;
				now = modlst[i][j];
			}
		}
	}
	
//	rep(i, m)cout << par[i] << ' ' << notpar[i] << endl;

	int ans = 0;
	rep(i, m/2+1) {
		if (!i||i*2==m) {
			int x = modcnt[i] / 2;
			ans += x;
		}
		else {
			int x = min(modcnt[i], modcnt[(m - i) % m]);
			if (modcnt[i] > modcnt[(m - i) % m]) {
				x += min(par[i], par[i]-(modcnt[(m - i) % m] - notpar[i]+1)/2);
			}
			else {
				x += min(par[(m-i)%m], par[(m-i)%m] - (modcnt[i] - notpar[(m-i)%m] + 1) / 2);
			}
			ans += x;
		}
//		cout<<ans<<endl;
	}
	cout << ans << endl;
}
### Prompt

Your task is to create a cpp solution 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"
using namespace std;
#define int long long
#define rep(i,n) for(int i=0;i<n;i++)
const int mod = 1000000007;
const int inf = 1ll << 61;
typedef pair<int, int> P;
int x[100006];
int cnt[100006];
int modcnt[100006];
vector<int>modlst[100006];
int par[100006], notpar[100006];
signed main() {
	int n, m; cin >> n >> m;
	rep(i, n) {
		cin >> x[i]; cnt[x[i]]++; modcnt[x[i] % m]++;
		modlst[x[i] % m].push_back(x[i]);
	}
	rep(i, m) {
		sort(modlst[i].begin(), modlst[i].end());
		modlst[i].push_back(inf);
	}
	rep(i, m) {
		int now = modlst[i][0],c=0;
		rep(j, modlst[i].size()) {
			if (modlst[i][j] == now)c++;
			else {
				par[i] += c/2;
				notpar[i] += c%2;
				c = 1;
				now = modlst[i][j];
			}
		}
	}
	
//	rep(i, m)cout << par[i] << ' ' << notpar[i] << endl;

	int ans = 0;
	rep(i, m/2+1) {
		if (!i||i*2==m) {
			int x = modcnt[i] / 2;
			ans += x;
		}
		else {
			int x = min(modcnt[i], modcnt[(m - i) % m]);
			if (modcnt[i] > modcnt[(m - i) % m]) {
				x += min(par[i], par[i]-(modcnt[(m - i) % m] - notpar[i]+1)/2);
			}
			else {
				x += min(par[(m-i)%m], par[(m-i)%m] - (modcnt[i] - notpar[(m-i)%m] + 1) / 2);
			}
			ans += x;
		}
//		cout<<ans<<endl;
	}
	cout << ans << endl;
}
```